---
title: "`sitmo`'s BigCrush Results"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{`sitmo`'s BigCrush Results}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

# Introduction

[TestU01](http://www.iro.umontreal.ca/~simardr/testu01/tu01.html) is a software library produced by Pierre L'Ecuyer and Richard Simard written in C that provides a collection of utilities for the empirical statistical testing of uniform random number generators (RNGs). The suite is able to provide information on the quality of the randomness a psuedo-random number generator can produce. It is able to do so under four different branches:

* Implementing (pre-programmed) RNGs;
* implementing specific statistical tests;
* implementing batteries of statistical tests; and
* Applying tests to entire families of RNGs.

[TestU01](http://www.iro.umontreal.ca/~simardr/testu01/tu01.html) offers several batteries of tests including "Small Crush" (which consists of 10 tests), "Crush" (96 tests), and "Big Crush" (106 tests). With the later test being more extensive than the previous ones. For more information about the tests available, please consult the [TestU01 userguide](http://www.iro.umontreal.ca/~simardr/testu01/guideshorttestu01.pdf). The results of the "Big Crush" test are presented next.

# Results of the Test

Running the Big Crush test from the TestU01 suite has yielded a complete pass rate (e.g "All tests were passed") with the specifics of each of the 103 tests being detailed below.

```bash
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 
 
***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Sitmos-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE
 
   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
-----------------------------------------------
Test Results for Delta =   1.0000
 
Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59
 
 
-----------------------------------------------
CPU time used                    :  00:01:04.53
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE
 
   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1
 
-----------------------------------------------
Test Results for Delta =   1.0000
 
Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42
 
 
-----------------------------------------------
CPU time used                    :  00:01:08.78
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:03:49.93
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:03:44.17
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:43.85
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:38.33
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:45.35
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:41.50
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:45.18
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:41.13
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:43.98
 
Generator state:
 
 
 
 
***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE
 
       Collision test
 
       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47
 
 
-----------------------------------------------
Results of CollisionOver test:
 
POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:39.21
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1
 
 
      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71
 
 
-----------------------------------------------
CPU time used                    :  00:03:58.55
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1
 
 
      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44
 
 
-----------------------------------------------
CPU time used                    :  00:01:44.53
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1
 
 
      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23
 
 
-----------------------------------------------
CPU time used                    :  00:02:48.51
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1
 
 
      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71
 
 
-----------------------------------------------
CPU time used                    :  00:01:59.94
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1
 
 
      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27
 
 
-----------------------------------------------
CPU time used                    :  00:02:05.76
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1
 
 
      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47
 
 
-----------------------------------------------
CPU time used                    :  00:03:19.07
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1
 
 
      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61
 
 
-----------------------------------------------
CPU time used                    :  00:03:19.19
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1
 
 
      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29
 
 
-----------------------------------------------
CPU time used                    :  00:04:00.28
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1
 
 
      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182
 
 
----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33
 
 
-----------------------------------------------
CPU time used                    :  00:04:19.81
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE
 
 
---------------------------------------
Test based on the 2 nearest points (NP):
 
Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93
 
 
A2 test based on the spacings between the
   successive jump times of process Y_n(t):
 
A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69
 
Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15
 
Test on the jump times of Y
   (superposition of Yn):
 
Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     970
p-value of test                       :    0.01
 
Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24
 
Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18
 
-----------------------------------------------
CPU time used                    :  00:02:35.76
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE
 
 
---------------------------------------
Test based on the 2 nearest points (NP):
 
Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22
 
 
A2 test based on the spacings between the
   successive jump times of process Y_n(t):
 
A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67
 
Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51
 
Test on the jump times of Y
   (superposition of Yn):
 
Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82
 
Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23
 
Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48
 
-----------------------------------------------
CPU time used                    :  00:01:45.47
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE
 
 
---------------------------------------
Test based on the 2 nearest points (NP):
 
Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73
 
 
A2 test based on the spacings between the
   successive jump times of process Y_n(t):
 
A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94
 
Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18
 
Test on the jump times of Y
   (superposition of Yn):
 
Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     260
p-value of test                       :    0.99
 
Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55
 
Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63
 
-----------------------------------------------
CPU time used                    :  00:02:55.40
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE
 
 
---------------------------------------
Test based on the 2 nearest points (NP):
 
Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25
 
 
A2 test based on the spacings between the
   successive jump times of process Y_n(t):
 
A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70
 
Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23
 
Test on the jump times of Y
   (superposition of Yn):
 
Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51
 
Stat. AD (mNP2)                       :    3.70
p-value of test                       :    0.01
 
Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42
 
-----------------------------------------------
CPU time used                    :  00:03:22.78
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8
 
 
-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55
 
-----------------------------------------------
CPU time used                    :  00:00:59.10
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8
 
 
-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84
 
-----------------------------------------------
CPU time used                    :  00:01:09.35
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32
 
 
-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.52
p-value of test                       :    0.95
 
-----------------------------------------------
CPU time used                    :  00:01:02.60
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32
 
 
-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71
 
-----------------------------------------------
CPU time used                    :  00:01:13.81
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8
 
 
-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.18
p-value of test                       :    0.83
 
-----------------------------------------------
CPU time used                    :  00:01:16.02
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8
 
 
-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.86
p-value of test                       :    0.71
 
-----------------------------------------------
CPU time used                    :  00:01:28.55
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8
 
 
-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60
 
-----------------------------------------------
CPU time used                    :  00:01:28.60
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8
 
 
-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.93
p-value of test                       :    0.30
 
-----------------------------------------------
CPU time used                    :  00:01:28.68
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625
 
 
-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.26
p-value of test                       :    0.79
 
-----------------------------------------------
CPU time used                    :  00:01:32.96
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125
 
 
-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.76
p-value of test                       :    0.89
 
-----------------------------------------------
CPU time used                    :  00:02:06.14
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125
 
 
-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.41
p-value of test                       :    0.20
 
-----------------------------------------------
CPU time used                    :  00:02:13.51
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562
 
 
-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.64
p-value of test                       :    0.15
 
-----------------------------------------------
CPU time used                    :  00:02:08.09
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.05
 
Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77
 
Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07
 
Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.54
p-value of test                       :    0.83
 
-----------------------------------------------
CPU time used                    :  00:01:23.93
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35
 
Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59
 
Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75
 
Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.53
p-value of test                       :    0.53
 
-----------------------------------------------
CPU time used                    :  00:03:11.42
 
Generator state:
 
 
 
 
***********************************************************
Test sknuth_Permutation calling smultin_Multinomial
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE
 
       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE
 
   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1
 
-----------------------------------------------
Test Results for Delta =   1.0000
 
Number of degrees of freedom          :    5
Value of the statistic                :    8.17
p-value of test                       :    0.15
 
 
-----------------------------------------------
CPU time used                    :  00:00:46.93
 
Generator state:
 
 
 
 
***********************************************************
Test sknuth_Permutation calling smultin_Multinomial
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE
 
       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE
 
   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1
 
-----------------------------------------------
Test Results for Delta =   1.0000
 
Number of degrees of freedom          :  119
Value of the statistic                :  108.58
p-value of test                       :    0.74
 
 
-----------------------------------------------
CPU time used                    :  00:01:35.02
 
Generator state:
 
 
 
 
***********************************************************
Test sknuth_Permutation calling smultin_Multinomial
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE
 
       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE
 
   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1
 
-----------------------------------------------
Test Results for Delta =   1.0000
 
Number of degrees of freedom          : 5039
Value of the statistic                : 4810.30
p-value of test                       :    0.99
 
 
-----------------------------------------------
CPU time used                    :  00:01:24.63
 
Generator state:
 
 
 
 
***********************************************************
Test sknuth_Permutation calling smultin_Multinomial
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE
 
       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE
 
   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1
 
-----------------------------------------------
Test Results for Delta =   1.0000
 
Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80
 
 
-----------------------------------------------
CPU time used                    :  00:03:06.50
 
Generator state:
 
 
 
 
***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE
 
       Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
-----------------------------------------------
Test Results for Collisions
 
For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48
 
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :    1743165869892
  j =  1                              :        399908218
  j =  2                              :            45888
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:04:54.47
 
Generator state:
 
 
 
 
***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE
 
       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE
 
       Collision test,    Mu =      2293.9736,    Sigma =    47.8841
 
-----------------------------------------------
Test Results for Collisions
 
For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35
 
 
-----------------------------
Total number of cells containing j balls
 
  j =  0                              :    1743165869960
  j =  1                              :        399908084
  j =  2                              :            45952
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0
 
-----------------------------------------------
CPU time used                    :  00:05:01.14
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8
 
      Number of categories = 100000
      Expected number per category  = 100.00
 
 
-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:
 
Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35
 
Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88
 
Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64
 
Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77
 
 
-----------------------------------------------
Test results for Anderson-Darling:
 
Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49
 
Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77
 
Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84
 
 
-----------------------------------------------
CPU time used                    :  00:01:45.23
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16
 
      Number of categories = 100000
      Expected number per category  = 100.00
 
 
-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:
 
Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32
 
Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17
 
Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25
 
Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40
 
 
-----------------------------------------------
Test results for Anderson-Darling:
 
Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11
 
Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98
 
Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15
 
 
-----------------------------------------------
CPU time used                    :  00:01:43.48
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24
 
      Number of categories = 100000
      Expected number per category  = 100.00
 
 
-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:
 
Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38
 
Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54
 
Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69
 
Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64
 
 
-----------------------------------------------
Test results for Anderson-Darling:
 
Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91
 
Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23
 
Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39
 
 
-----------------------------------------------
CPU time used                    :  00:01:27.73
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32
 
      Number of categories = 100000
      Expected number per category  = 100.00
 
 
-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:
 
Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51
 
Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63
 
Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75
 
Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64
 
 
-----------------------------------------------
Test results for Anderson-Darling:
 
Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61
 
Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33
 
Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48
 
 
-----------------------------------------------
CPU time used                    :  00:01:43.31
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06
 
Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80
 
Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10
 
-----------------------------------------------
CPU time used                    :  00:01:54.64
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08
 
Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90
 
Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07
 
-----------------------------------------------
CPU time used                    :  00:01:29.65
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10
 
Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98
 
Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14
 
-----------------------------------------------
CPU time used                    :  00:02:04.43
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22
 
Kolmogorov-Smirnov- statistic = D-    : 7.01e-5
p-value of test                       :    0.82
 
Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74
 
-----------------------------------------------
CPU time used                    :  00:00:15.09
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47
 
Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50
 
Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76
 
-----------------------------------------------
CPU time used                    :  00:00:15.52
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1
 
 
-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96
 
-----------------------------------------------
CPU time used                    :  00:00:23.87
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2
 
 
-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14
 
-----------------------------------------------
CPU time used                    :  00:00:23.96
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15
 
   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits
 
 
 
-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62
 
-----------------------------------------------
CPU time used                    :  00:01:09.11
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15
 
   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits
 
 
 
-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78
 
-----------------------------------------------
CPU time used                    :  00:01:12.02
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.51
p-value of test                       :    0.88
 
-----------------------------------------------
CPU time used                    :  00:00:53.06
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.46
p-value of test                       :    0.20
 
-----------------------------------------------
CPU time used                    :  00:01:05.73
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25
 
 
-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.46
p-value of test                       :    0.50
 
-----------------------------------------------
CPU time used                    :  00:01:05.79
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.57
p-value of test                       :    0.68
 
-----------------------------------------------
CPU time used                    :  00:00:53.05
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.95
p-value of test                       :    0.04
 
-----------------------------------------------
CPU time used                    :  00:01:05.79
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625
 
 
-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.95
p-value of test                       :    0.9939
 
-----------------------------------------------
CPU time used                    :  00:01:05.73
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10
 
 
-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.00
p-value of test                       :    0.82
 
-----------------------------------------------
CPU time used                    :  00:01:58.36
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19
 
Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56
 
Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50
 
Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.66
p-value of test                       :    0.79
 
-----------------------------------------------
CPU time used                    :  00:01:16.26
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42
 
Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62
 
Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75
 
Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.46
p-value of test                       :    0.72
 
-----------------------------------------------
CPU time used                    :  00:01:16.23
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000
 
 
-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87
 
-----------------------------------------------
CPU time used                    :  00:03:44.79
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000
 
 
-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77
 
-----------------------------------------------
CPU time used                    :  00:03:44.77
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000
 
 
-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05
 
-----------------------------------------------
CPU time used                    :  00:03:28.23
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000
 
 
-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96
 
-----------------------------------------------
CPU time used                    :  00:02:51.20
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97
 
Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02
 
Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05
 
Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.06
p-value of test                       :    0.02
 
-----------------------------------------------
CPU time used                    :  00:00:37.67
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30
 
 
-----------------------------------------------
Test results for GCD values:
 
Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08
 
Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97
 
Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15
 
Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17122.72
p-value of test                       :    0.95
 
 
 
-----------------------------------------------
CPU time used                    :  00:01:54.05
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50
 
 
 
-----------------------------------------------
Test on the values of the Statistic H
 
Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.27
p-value of test                       :    0.74
 
 
-----------------------------------------------
Test on the values of the Statistic M
 
Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.79
p-value of test                       :    0.48
 
 
-----------------------------------------------
Test on the values of the Statistic J
 
Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.88
p-value of test                       :    0.09
 
 
-----------------------------------------------
Test on the values of the Statistic R
 
Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.02
p-value of test                       :    0.40
 
 
-----------------------------------------------
Test on the values of the Statistic C
 
Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.18
p-value of test                       :    0.11
 
 
-----------------------------------------------
CPU time used                    :  00:00:47.70
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50
 
 
 
-----------------------------------------------
Test on the values of the Statistic H
 
Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.87
p-value of test                       :    0.86
 
 
-----------------------------------------------
Test on the values of the Statistic M
 
Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.33
p-value of test                       :    0.89
 
 
-----------------------------------------------
Test on the values of the Statistic J
 
Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.08
p-value of test                       :    0.03
 
 
-----------------------------------------------
Test on the values of the Statistic R
 
Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.29
p-value of test                       :    0.74
 
 
-----------------------------------------------
Test on the values of the Statistic C
 
Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.45
p-value of test                       :    0.83
 
 
-----------------------------------------------
CPU time used                    :  00:00:48.73
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
-----------------------------------------------
Test on the values of the Statistic H
 
Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.55
p-value of test                       :    0.04
 
 
-----------------------------------------------
Test on the values of the Statistic M
 
Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.36
p-value of test                       :    0.96
 
 
-----------------------------------------------
Test on the values of the Statistic J
 
Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.13
p-value of test                       :    0.98
 
 
-----------------------------------------------
Test on the values of the Statistic R
 
Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.76
p-value of test                       :    0.84
 
 
-----------------------------------------------
Test on the values of the Statistic C
 
Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.45
p-value of test                       :    0.15
 
 
-----------------------------------------------
CPU time used                    :  00:01:06.36
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000
 
 
 
-----------------------------------------------
Test on the values of the Statistic H
 
Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.52
p-value of test                       :    0.85
 
 
-----------------------------------------------
Test on the values of the Statistic M
 
Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.85
p-value of test                       :    0.63
 
 
-----------------------------------------------
Test on the values of the Statistic J
 
Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.00
p-value of test                       :    0.38
 
 
-----------------------------------------------
Test on the values of the Statistic R
 
Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.25
p-value of test                       :    0.74
 
 
-----------------------------------------------
Test on the values of the Statistic C
 
Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.45
p-value of test                       :    0.66
 
 
-----------------------------------------------
CPU time used                    :  00:01:08.10
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
-----------------------------------------------
Test on the values of the Statistic H
 
Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.65
p-value of test                       :    0.32
 
 
-----------------------------------------------
Test on the values of the Statistic M
 
Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.98
p-value of test                       :    0.43
 
 
-----------------------------------------------
Test on the values of the Statistic J
 
Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.07
p-value of test                       :    0.55
 
 
-----------------------------------------------
Test on the values of the Statistic R
 
Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.70
p-value of test                       :    0.60
 
 
-----------------------------------------------
Test on the values of the Statistic C
 
Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.48
p-value of test                       :    0.44
 
 
-----------------------------------------------
CPU time used                    :  00:00:57.94
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000
 
 
 
-----------------------------------------------
Test on the values of the Statistic H
 
Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.10
p-value of test                       :    0.69
 
 
-----------------------------------------------
Test on the values of the Statistic M
 
Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.10
p-value of test                       :    0.70
 
 
-----------------------------------------------
Test on the values of the Statistic J
 
Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.41
p-value of test                       :    0.86
 
 
-----------------------------------------------
Test on the values of the Statistic R
 
Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.68
p-value of test                       :    0.77
 
 
-----------------------------------------------
Test on the values of the Statistic C
 
Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.54
p-value of test                       :    0.83
 
 
-----------------------------------------------
CPU time used                    :  00:00:58.79
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1
 
 
 
-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.60
p-value of test                       :    0.40
 
 
-----------------------------------------------
Normal statistic for number of jumps  :    2.51
p-value of test                       :  6.1e-3
 
 
 
-----------------------------------------------
CPU time used                    :  00:02:43.68
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1
 
 
 
-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.18
p-value of test                       :    0.77
 
 
-----------------------------------------------
Normal statistic for number of jumps  :   -1.55
p-value of test                       :    0.94
 
 
 
-----------------------------------------------
CPU time used                    :  00:02:43.05
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31
 
Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65
 
Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70
 
Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63
 
Sample variance                       :    1.17
p-value of test                       :    0.31
 
-----------------------------------------------
CPU time used                    :  00:00:54.70
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40
 
Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98
 
Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53
 
Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88
 
Sample variance                       :    0.89
p-value of test                       :    0.53
 
-----------------------------------------------
CPU time used                    :  00:00:55.27
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02
 
Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46
 
Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06
 
-----------------------------------------------
CPU time used                    :  00:00:39.04
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11
 
Kolmogorov-Smirnov- statistic = D-    : 4.76e-3
p-value of test                       :    0.83
 
Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16
 
-----------------------------------------------
CPU time used                    :  00:00:39.54
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020
 
 
-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.12
p-value of test                       :    0.33
 
-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14
 
 
 
-----------------------------------------------
CPU time used                    :  00:01:47.05
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020
 
 
-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78
 
-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14
 
 
 
-----------------------------------------------
CPU time used                    :  00:01:50.10
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13
 
Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68
 
Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45
 
Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.59
p-value of test                       :    0.79
 
-----------------------------------------------
CPU time used                    :  00:02:51.45
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25
 
Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51
 
Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74
 
Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.89
p-value of test                       :    0.57
 
-----------------------------------------------
CPU time used                    :  00:02:56.45
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57
 
Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43
 
Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34
 
Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10157.86
p-value of test                       :    0.13
 
-----------------------------------------------
CPU time used                    :  00:00:57.75
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48
 
Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04
 
Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18
 
Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.19
p-value of test                       :    0.20
 
-----------------------------------------------
CPU time used                    :  00:01:01.20
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30
 
 
 
-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09
 
-----------------------------------------------
CPU time used                    :  00:01:13.01
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300
 
 
 
-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36
 
-----------------------------------------------
CPU time used                    :  00:01:09.29
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200
 
 
 
-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55
 
-----------------------------------------------
CPU time used                    :  00:04:34.86
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0
 
 
 
Counters with expected numbers >= 10
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28
 
Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65
 
Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53
 
Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.28
p-value of test                       :    0.65
 
-----------------------------------------------
CPU time used                    :  00:01:53.80
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0
 
 
 
Counters with expected numbers >= 10
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24
 
Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74
 
Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59
 
Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.01
p-value of test                       :    0.77
 
-----------------------------------------------
CPU time used                    :  00:01:59.57
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0
 
 
 
Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.44
p-value of test                       :    0.23
 
-----------------------------------------------
CPU time used                    :  00:01:25.02
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0
 
 
 
Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.28
p-value of test                       :    0.37
 
-----------------------------------------------
CPU time used                    :  00:01:29.27
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0
 
 
 
Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.57
p-value of test                       :    0.55
 
-----------------------------------------------
CPU time used                    :  00:01:33.79
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0
 
 
 
Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.39
p-value of test                       :    0.58
 
-----------------------------------------------
CPU time used                    :  00:01:38.25
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3
 
 
-----------------------------------------------
Total number of 1 runs:  2000000000
 
Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.56
p-value of test                       :    0.20
 
 
-----------------------------------------------
Total number of bits:  7999957470
 
Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63
 
 
 
-----------------------------------------------
CPU time used                    :  00:01:16.00
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3
 
 
-----------------------------------------------
Total number of 1 runs:  2000000000
 
Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.11
p-value of test                       :    0.14
 
 
-----------------------------------------------
Total number of bits:  7999956321
 
Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64
 
 
 
-----------------------------------------------
CPU time used                    :  00:01:18.57
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18
 
Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76
 
Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74
 
Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69
 
Sample variance                       :    0.71
p-value of test                       :    0.70
 
-----------------------------------------------
CPU time used                    :  00:02:49.27
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66
 
Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51
 
Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94
 
Tests on the sum of all N observations
Standardized normal statistic         :   0.069
p-value of test                       :    0.47
 
Sample variance                       :    0.68
p-value of test                       :    0.73
 
-----------------------------------------------
CPU time used                    :  00:02:30.81
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78
 
Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14
 
Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35
 
Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33
 
Sample variance                       :    1.52
p-value of test                       :    0.13
 
-----------------------------------------------
CPU time used                    :  00:02:51.88
 
Generator state:
 
 
 
 
***********************************************************
HOST = Thijss-iMac.local, Darwin
 
sitmo
 
 
sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3
 
 
-----------------------------------------------
 
Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84
 
Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48
 
Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65
 
Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22
 
Sample variance                       :    1.85
p-value of test                       :    0.05
 
-----------------------------------------------
CPU time used                    :  00:02:32.94
 
Generator state:
 
 
 
 
 
========= Summary results of BigCrush =========
 
 Version:          TestU01 1.2.3
 Generator:        sitmo
 Number of statistics:  160
 Total CPU time:   03:44:06.82
 
 All tests were passed
```
