--- 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 ```