RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-05_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.71 13.8808 0.324480 2 to 25 16.09 18.6048 0.648320 3 to 26 15.76 19.8491 0.717979 4 to 27 15.95 16.2455 0.493499 5 to 28 15.58 26.2251 0.929544 6 to 29 15.77 8.9829 0.059203 7 to 30 15.74 11.5387 0.172769 8 to 31 16.12 12.9965 0.263581 9 to 32 15.77 27.1487 0.944077 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.986040 Tough bday spacings test for dh-ranFile-2015-12-05_01:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 11 37 77 99 106 81 42 24 14 5 4 (O-E)^2/E 0.4 0.0 0.2 0.0 0.7 0.1 2.0 1.1 0.1 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.919, p= 0.103 RESULTS OF GCD FOR dh-ranFile-2015-12-05_01:31 Euclid's algorithm: p-value, steps to gcd: 0.979634 p-value, dist. of gcd's: 0.215300 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-05_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.714 0.759 0.405 0.256 0.307 0.770 0.821 0.389 Bits 8 to 15---> 0.503 0.536 0.849 0.986 0.276 0.441 0.425 0.440 Bits 16 to 23---> 0.087 0.877 0.987 0.777 0.230 0.860 0.912 0.115 Bits 24 to 31---> 0.044 0.571 0.642 0.947 0.316 0.663 0.704 0.932 KS test for the above 32 p values: 0.785 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-05_01:31, p-values for 5 runs: 0.5389, 0.1532, 0.9836, 0.8867, 0.9339 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-05_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 190 211.4 2.170 2.170 r= 29 5257 5134.0 2.946 5.116 r= 30 23056 23103.0 0.096 5.212 r= 31 11497 11551.5 0.257 5.469 chi-square = 5.469 with df = 3; p-value = 0.860 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-05_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5208 5134.0 1.066 1.067 r= 31 23227 23103.0 0.665 1.732 r= 32 11354 11551.5 3.378 5.110 chi-square = 5.110 with df = 3; p-value = 0.836 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-05_01:31 b-rank test for bits 1 to 8, p=0.37391 b-rank test for bits 2 to 9, p=0.80628 b-rank test for bits 3 to 10, p=0.45792 b-rank test for bits 4 to 11, p=0.23691 b-rank test for bits 5 to 12, p=0.52713 b-rank test for bits 6 to 13, p=0.21612 b-rank test for bits 7 to 14, p=0.76706 b-rank test for bits 8 to 15, p=0.88328 b-rank test for bits 9 to 16, p=0.99421 b-rank test for bits 10 to 17, p=0.87152 b-rank test for bits 11 to 18, p=0.73485 b-rank test for bits 12 to 19, p=0.10728 b-rank test for bits 13 to 20, p=0.89314 b-rank test for bits 14 to 21, p=0.93868 b-rank test for bits 15 to 22, p=0.33236 b-rank test for bits 16 to 23, p=0.28714 b-rank test for bits 17 to 24, p=0.20967 b-rank test for bits 18 to 25, p=0.52432 b-rank test for bits 19 to 26, p=0.57144 b-rank test for bits 20 to 27, p=0.42881 b-rank test for bits 21 to 28, p=0.14365 b-rank test for bits 22 to 29, p=0.62119 b-rank test for bits 23 to 30, p=0.57231 b-rank test for bits 24 to 31, p=0.54500 b-rank test for bits 25 to 32, p=0.05515 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.951339 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-05_01:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141806 -0.24 0.404613 2 141388 -1.22 0.111600 3 141560 -0.82 0.207195 4 141437 -1.10 0.134889 5 142410 1.17 0.878957 6 142117 0.49 0.686236 7 141305 -1.41 0.078977 8 142170 0.61 0.728752 9 142087 0.42 0.660972 10 142448 1.26 0.895908 11 142880 2.27 0.988333 12 141950 0.10 0.537852 13 142428 1.21 0.887214 14 141923 0.03 0.512740 15 141327 -1.36 0.086823 16 141972 0.15 0.558207 17 142141 0.54 0.705844 18 141511 -0.93 0.176010 19 141358 -1.29 0.098846 20 142011 0.24 0.593884 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-05_01:31 Bits used No. missing words z-score p-value 23 to 32 141515 -1.3598 0.086953 22 to 31 141930 0.0713 0.528411 21 to 30 141943 0.1161 0.546215 20 to 29 141881 -0.0977 0.461089 19 to 28 141679 -0.7942 0.213528 18 to 27 142201 1.0058 0.842734 17 to 26 142241 1.1437 0.873624 16 to 25 141723 -0.6425 0.260269 15 to 24 141934 0.0851 0.533897 14 to 23 141802 -0.3701 0.355653 13 to 22 141819 -0.3115 0.377717 12 to 21 141493 -1.4356 0.075555 11 to 20 142219 1.0678 0.857201 10 to 19 141890 -0.0667 0.473428 9 to 18 141800 -0.3770 0.353087 8 to 17 141888 -0.0736 0.470684 7 to 16 142128 0.7540 0.774586 6 to 15 142127 0.7506 0.773549 5 to 14 142573 2.2885 0.988946 4 to 13 142019 0.3782 0.647349 3 to 12 141669 -0.8287 0.203630 2 to 11 142042 0.4575 0.676338 1 to 10 142065 0.5368 0.704295 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-05_01:31 Bits used No. missing words z-score p-value 28 to 32 142047 0.4667 0.679635 27 to 31 142419 1.7277 0.957979 26 to 30 142275 1.2396 0.892431 25 to 29 141761 -0.5028 0.307548 24 to 28 141788 -0.4113 0.340431 23 to 27 142356 1.5141 0.935004 22 to 26 141499 -1.3909 0.082120 21 to 25 141635 -0.9299 0.176203 20 to 24 141856 -0.1808 0.428270 19 to 23 141753 -0.5299 0.298080 18 to 22 141854 -0.1876 0.425611 17 to 21 142350 1.4938 0.932386 16 to 20 141845 -0.2181 0.413688 15 to 19 141606 -1.0282 0.151919 14 to 18 141833 -0.2587 0.397916 13 to 17 141923 0.0463 0.518480 12 to 16 141853 -0.1909 0.424283 11 to 15 141762 -0.4994 0.308741 10 to 14 141837 -0.2452 0.403156 9 to 13 141745 -0.5571 0.288746 8 to 12 141975 0.2226 0.588081 7 to 11 141963 0.1819 0.572182 6 to 10 141526 -1.2994 0.096899 5 to 9 141272 -2.1604 0.015369 4 to 8 141912 0.0091 0.503611 3 to 7 142163 0.8599 0.805077 2 to 6 141835 -0.2520 0.400534 1 to 5 142251 1.1582 0.876610 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-05_01:31 Bits used No. missing words z-score p-value 31 to 32 142164 0.7512 0.773746 30 to 31 142325 1.2262 0.889932 29 to 30 141706 -0.5998 0.274322 28 to 29 141832 -0.2281 0.409780 27 to 28 141822 -0.2576 0.398354 26 to 27 141845 -0.1898 0.424747 25 to 26 141705 -0.6027 0.273340 24 to 25 141891 -0.0541 0.478439 23 to 24 141519 -1.1514 0.124781 22 to 23 141815 -0.2783 0.390407 21 to 22 141903 -0.0187 0.492551 20 to 21 142245 0.9902 0.838956 19 to 20 142197 0.8486 0.801944 18 to 19 142258 1.0285 0.848149 17 to 18 141591 -0.9390 0.173859 16 to 17 142117 0.6126 0.729928 15 to 16 142033 0.3648 0.642373 14 to 15 141257 -1.9243 0.027160 13 to 14 141950 0.1200 0.547747 12 to 13 141819 -0.2665 0.394942 11 to 12 141843 -0.1957 0.422437 10 to 11 142524 1.8132 0.965098 9 to 10 141771 -0.4081 0.341617 8 to 9 142038 0.3796 0.647863 7 to 8 142296 1.1406 0.872986 6 to 7 141826 -0.2458 0.402914 5 to 6 141701 -0.6145 0.269428 4 to 5 142007 0.2881 0.613370 3 to 4 142195 0.8427 0.800298 2 to 3 141730 -0.5290 0.298404 1 to 2 141012 -2.6470 0.004061 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-05_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2528.56 0.404 0.656880 Test results for specific bytes for dh-ranFile-2015-12-05_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2451.44 -0.687 0.246123 2 to 9 2585.07 1.203 0.885531 3 to 10 2445.22 -0.775 0.219265 4 to 11 2513.69 0.194 0.576764 5 to 12 2528.77 0.407 0.657952 6 to 13 2513.08 0.185 0.573364 7 to 14 2434.31 -0.929 0.176442 8 to 15 2549.18 0.696 0.756637 9 to 16 2487.27 -0.180 0.428590 10 to 17 2559.09 0.836 0.798320 11 to 18 2547.37 0.670 0.748527 12 to 19 2563.90 0.904 0.816935 13 to 20 2476.83 -0.328 0.371553 14 to 21 2420.86 -1.119 0.131536 15 to 22 2439.05 -0.862 0.194362 16 to 23 2457.58 -0.600 0.274304 17 to 24 2359.01 -1.994 0.023078 18 to 25 2506.78 0.096 0.538199 19 to 26 2504.61 0.065 0.526003 20 to 27 2502.51 0.035 0.514158 21 to 28 2503.69 0.052 0.520832 22 to 29 2625.03 1.768 0.961482 23 to 30 2471.57 -0.402 0.343810 24 to 31 2415.46 -1.196 0.115941 25 to 32 2506.52 0.092 0.536749 CDPARK for dh-ranFile-2015-12-05_01:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3525 0.0913 0.536383 3519 -0.1826 0.427537 3537 0.6393 0.738676 3505 -0.8219 0.205562 3544 0.9589 0.831196 3552 1.3242 0.907282 3491 -1.4612 0.071982 3532 0.4110 0.659449 3515 -0.3653 0.357445 3547 1.0959 0.863437 Square side=100, avg. no. parked=3526.70 sample std.=18.52 p-value of the KSTEST for those 10 p-values: 0.876053 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-05_01:31 0.1896,0.6123,0.0140,0.1404,0.0913,0.3597,0.4551,0.4848,0.2857,0.5779, The KS test for those 10 p-values: 0.082270 The 3DSPHERES test for dh-ranFile-2015-12-05_01:31 sample no r^3 equiv. uni. 1 90.895 0.951676 2 55.681 0.843711 3 43.499 0.765420 4 26.163 0.581925 5 37.394 0.712482 6 99.299 0.963482 7 11.345 0.314893 8 3.610 0.113370 9 2.744 0.087417 10 13.795 0.368606 11 7.342 0.217084 12 20.565 0.496155 13 55.497 0.842745 14 25.467 0.572122 15 30.096 0.633300 16 13.946 0.371787 17 40.379 0.739710 18 0.345 0.011444 19 8.370 0.243467 20 71.053 0.906373 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.937195 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-05_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 0.6 0.5 0.9 -0.4 -0.0 -0.1 0.2 -0.6 0.4 0.7 0.0 -0.8 0.6 1.5 -1.3 0.1 0.6 -0.0 0.1 -2.3 1.1 0.7 -0.0 0.6 -1.3 -2.0 -0.9 1.1 0.8 1.1 0.1 0.1 1.0 0.4 -1.6 0.2 -0.4 -0.1 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:31.963239 z-score=-1.095100, p-value=0.130807 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-05_01:31 Test no p-value 1 0.174489 2 0.614252 3 0.817189 4 0.130286 5 0.160621 6 0.620166 7 0.215265 8 0.002417 9 0.005885 10 0.775984 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.048469 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-05_01:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66691 0.01 66872 0.63 3 25000.00 24953 0.09 24813 1.40 4 6666.67 6696 0.13 6644 0.08 5 1388.89 1389 0.00 1383 0.02 6 238.10 233 0.11 256 1.35 7 34.72 35 0.00 26 2.19 8 4.96 2 1.77 5 0.00 p=0.09011 p=0.53885 Number of rngs required: 687578, p-value: 0.170 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-05_01:31 No. of wins: Observed Expected 98471 98585.9 z-score=-0.514, pvalue=0.30373 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66819 66666.7 0.348 0.348 2 37337 37654.3 2.674 3.022 3 27113 26954.7 0.929 3.951 4 19213 19313.5 0.523 4.474 5 13969 13851.4 0.998 5.472 6 10023 9943.5 0.635 6.107 7 7160 7145.0 0.031 6.138 8 5180 5139.1 0.326 6.464 9 3676 3699.9 0.154 6.618 10 2697 2666.3 0.354 6.972 11 1878 1923.3 1.068 8.040 12 1365 1388.7 0.406 8.446 13 969 1003.7 1.201 9.647 14 741 726.1 0.304 9.951 15 494 525.8 1.927 11.878 16 390 381.2 0.205 12.084 17 247 276.5 3.155 15.239 18 232 200.8 4.838 20.077 19 122 146.0 3.940 24.017 20 107 106.2 0.006 24.023 21 268 287.1 1.272 25.296 Chisq= 25.30 for 20 degrees of freedom, p= 0.80965 SUMMARY of craptest p-value for no. of wins: 0.303726 p-value for throws/game: 0.809646 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-05_01:31 No. of wins: Observed Expected 98468 98585.9 z-score=-0.527, pvalue=0.29905 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66779 66666.7 0.189 0.189 2 37583 37654.3 0.135 0.324 3 26855 26954.7 0.369 0.693 4 19258 19313.5 0.159 0.853 5 13858 13851.4 0.003 0.856 6 10085 9943.5 2.012 2.868 7 7108 7145.0 0.192 3.060 8 5150 5139.1 0.023 3.083 9 3784 3699.9 1.913 4.996 10 2687 2666.3 0.161 5.157 11 1899 1923.3 0.308 5.465 12 1320 1388.7 3.403 8.868 13 1011 1003.7 0.053 8.920 14 702 726.1 0.803 9.723 15 567 525.8 3.222 12.945 16 360 381.2 1.174 14.119 17 282 276.5 0.108 14.227 18 209 200.8 0.332 14.559 19 152 146.0 0.248 14.807 20 86 106.2 3.847 18.655 21 265 287.1 1.703 20.358 Chisq= 20.36 for 20 degrees of freedom, p= 0.56425 SUMMARY of craptest p-value for no. of wins: 0.299051 p-value for throws/game: 0.564246 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0024,0.0041,0.0059,0.0114,0.0140,0.0154,0.0231,0.0272,0.0437,0.0485, 0.0551,0.0592,0.0720,0.0756,0.0790,0.0821,0.0823,0.0868,0.0868,0.0870, 0.0874,0.0901,0.0913,0.0969,0.0988,0.1035,0.1073,0.1116,0.1134,0.1153, 0.1159,0.1248,0.1303,0.1308,0.1315,0.1349,0.1404,0.1436,0.1519,0.1532, 0.1606,0.1697,0.1728,0.1739,0.1745,0.1760,0.1762,0.1764,0.1896,0.1944, 0.2036,0.2056,0.2072,0.2097,0.2135,0.2153,0.2153,0.2161,0.2171,0.2193, 0.2303,0.2369,0.2435,0.2461,0.2563,0.2603,0.2636,0.2694,0.2733,0.2743, 0.2743,0.2759,0.2857,0.2871,0.2887,0.2981,0.2984,0.2991,0.3037,0.3065, 0.3075,0.3087,0.3149,0.3160,0.3245,0.3324,0.3404,0.3416,0.3438,0.3531, 0.3557,0.3574,0.3597,0.3686,0.3716,0.3718,0.3739,0.3777,0.3890,0.3904, 0.3949,0.3979,0.3984,0.4005,0.4029,0.4032,0.4046,0.4052,0.4098,0.4137, 0.4224,0.4243,0.4247,0.4247,0.4256,0.4275,0.4283,0.4286,0.4288,0.4398, 0.4407,0.4551,0.4579,0.4611,0.4707,0.4734,0.4784,0.4848,0.4926,0.4935, 0.4962,0.5034,0.5036,0.5127,0.5142,0.5185,0.5208,0.5243,0.5260,0.5271, 0.5284,0.5339,0.5361,0.5364,0.5367,0.5379,0.5382,0.5389,0.5389,0.5450, 0.5462,0.5477,0.5582,0.5642,0.5709,0.5714,0.5721,0.5722,0.5723,0.5734, 0.5768,0.5779,0.5819,0.5881,0.5939,0.6123,0.6134,0.6143,0.6202,0.6212, 0.6333,0.6420,0.6424,0.6473,0.6479,0.6483,0.6569,0.6580,0.6594,0.6610, 0.6633,0.6763,0.6796,0.6862,0.7041,0.7043,0.7058,0.7125,0.7139,0.7180, 0.7288,0.7299,0.7349,0.7387,0.7397,0.7485,0.7566,0.7592,0.7654,0.7671, 0.7702,0.7735,0.7737,0.7746,0.7760,0.7769,0.7845,0.7983,0.8003,0.8019, 0.8051,0.8063,0.8096,0.8169,0.8172,0.8214,0.8312,0.8361,0.8390,0.8427, 0.8427,0.8437,0.8481,0.8493,0.8572,0.8595,0.8603,0.8634,0.8715,0.8730, 0.8736,0.8761,0.8766,0.8770,0.8790,0.8833,0.8855,0.8867,0.8872,0.8899, 0.8924,0.8931,0.8959,0.9064,0.9073,0.9121,0.9295,0.9319,0.9324,0.9339, 0.9350,0.9372,0.9387,0.9441,0.9466,0.9513,0.9517,0.9580,0.9615,0.9635, 0.9651,0.9796,0.9836,0.9860,0.9863,0.9868,0.9883,0.9889,0.9942, Overall p-value after applying KStest on 269 p-values = 0.890015 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.