RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-26_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 34.0216 0.991658 2 to 25 15.38 23.6082 0.869523 3 to 26 15.51 26.0443 0.926343 4 to 27 15.56 25.8563 0.922881 5 to 28 15.55 31.9079 0.984551 6 to 29 15.80 12.0803 0.204748 7 to 30 15.89 15.4908 0.439829 8 to 31 15.54 22.3798 0.829450 9 to 32 15.42 35.2617 0.994253 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.000215 Tough bday spacings test for dh-ranFile-2016-10-26_02:31: 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 6 31 82 98 106 76 47 31 8 12 3 (O-E)^2/E 1.1 0.9 1.0 0.0 0.7 0.1 0.5 0.1 3.2 4.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.161, p= 0.726 RESULTS OF GCD FOR dh-ranFile-2016-10-26_02:31 Euclid's algorithm: p-value, steps to gcd: 0.088535 p-value, dist. of gcd's: 0.629817 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-26_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.057 0.592 0.646 0.899 0.811 0.213 0.780 0.647 Bits 8 to 15---> 0.893 0.499 0.585 0.393 0.228 0.467 0.126 0.368 Bits 16 to 23---> 0.625 0.150 0.666 0.423 0.691 0.988 0.701 0.461 Bits 24 to 31---> 0.390 0.380 0.362 0.371 0.077 0.603 0.082 0.177 KS test for the above 32 p values: 0.345 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-26_02:31, p-values for 5 runs: 0.2331, 0.8582, 0.7108, 0.8497, 0.7898 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-26_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5219 5134.0 1.407 1.408 r= 30 23018 23103.0 0.313 1.721 r= 31 11552 11551.5 0.000 1.721 chi-square = 1.721 with df = 3; p-value = 0.368 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-26_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 240 211.4 3.864 3.864 r= 30 5072 5134.0 0.749 4.613 r= 31 23057 23103.0 0.092 4.705 r= 32 11631 11551.5 0.547 5.252 chi-square = 5.252 with df = 3; p-value = 0.846 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-26_02:31 b-rank test for bits 1 to 8, p=0.33188 b-rank test for bits 2 to 9, p=0.45174 b-rank test for bits 3 to 10, p=0.59304 b-rank test for bits 4 to 11, p=0.42905 b-rank test for bits 5 to 12, p=0.37728 b-rank test for bits 6 to 13, p=0.07704 b-rank test for bits 7 to 14, p=0.67561 b-rank test for bits 8 to 15, p=0.03293 b-rank test for bits 9 to 16, p=0.34436 b-rank test for bits 10 to 17, p=0.83294 b-rank test for bits 11 to 18, p=0.91996 b-rank test for bits 12 to 19, p=0.36865 b-rank test for bits 13 to 20, p=0.86084 b-rank test for bits 14 to 21, p=0.16426 b-rank test for bits 15 to 22, p=0.64483 b-rank test for bits 16 to 23, p=0.79964 b-rank test for bits 17 to 24, p=0.38585 b-rank test for bits 18 to 25, p=0.60555 b-rank test for bits 19 to 26, p=0.68657 b-rank test for bits 20 to 27, p=0.05473 b-rank test for bits 21 to 28, p=0.79063 b-rank test for bits 22 to 29, p=0.85664 b-rank test for bits 23 to 30, p=0.71309 b-rank test for bits 24 to 31, p=0.94368 b-rank test for bits 25 to 32, p=0.08389 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 = 0.880362 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-26_02:31 (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 141848 -0.14 0.443029 2 142427 1.21 0.886766 3 142134 0.52 0.700184 4 141187 -1.69 0.045736 5 142139 0.54 0.704232 6 141485 -0.99 0.160739 7 141979 0.16 0.564654 8 142122 0.50 0.690368 9 142143 0.55 0.707453 10 141588 -0.75 0.226395 11 142263 0.83 0.795692 12 142543 1.48 0.930635 13 142297 0.91 0.817471 14 142251 0.80 0.787650 15 141939 0.07 0.527634 16 141663 -0.58 0.282464 17 141916 0.02 0.506217 18 141868 -0.10 0.461536 19 141587 -0.75 0.225693 20 142572 1.55 0.939224 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-26_02:31 Bits used No. missing words z-score p-value 23 to 32 141411 -1.7184 0.042864 22 to 31 141639 -0.9322 0.175624 21 to 30 142010 0.3471 0.635756 20 to 29 142563 2.2540 0.987903 19 to 28 142053 0.4954 0.689846 18 to 27 141933 0.0816 0.532526 17 to 26 141987 0.2678 0.605584 16 to 25 141809 -0.3460 0.364684 15 to 24 141716 -0.6667 0.252496 14 to 23 141766 -0.4942 0.310568 13 to 22 142134 0.7747 0.780749 12 to 21 141404 -1.7425 0.040709 11 to 20 141509 -1.3804 0.083724 10 to 19 141843 -0.2287 0.409542 9 to 18 141855 -0.1873 0.425695 8 to 17 141889 -0.0701 0.472056 7 to 16 141661 -0.8563 0.195913 6 to 15 142199 0.9989 0.841069 5 to 14 141766 -0.4942 0.310568 4 to 13 141908 -0.0046 0.498170 3 to 12 141911 0.0058 0.502297 2 to 11 141805 -0.3598 0.359514 1 to 10 142202 1.0092 0.843562 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-26_02:31 Bits used No. missing words z-score p-value 28 to 32 142055 0.4938 0.689275 27 to 31 142265 1.2057 0.886026 26 to 30 142068 0.5379 0.704665 25 to 29 141802 -0.3638 0.357992 24 to 28 142112 0.6870 0.753964 23 to 27 141529 -1.2893 0.098655 22 to 26 141919 0.0328 0.513075 21 to 25 141881 -0.0960 0.461747 20 to 24 141347 -1.9062 0.028312 19 to 23 141690 -0.7435 0.228592 18 to 22 141650 -0.8791 0.189678 17 to 21 142368 1.5548 0.940005 16 to 20 141998 0.3006 0.618131 15 to 19 141735 -0.5909 0.277277 14 to 18 141697 -0.7198 0.235836 13 to 17 141838 -0.2418 0.404469 12 to 16 141952 0.1446 0.557504 11 to 15 141646 -0.8926 0.186024 10 to 14 142006 0.3277 0.628429 9 to 13 141584 -1.1028 0.135054 8 to 12 142113 0.6904 0.755031 7 to 11 142285 1.2735 0.898572 6 to 10 142328 1.4192 0.922083 5 to 9 142798 3.0124 0.998704 4 to 8 141907 -0.0079 0.496849 3 to 7 142130 0.7480 0.772780 2 to 6 141839 -0.2384 0.405783 1 to 5 142254 1.1684 0.878672 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-26_02:31 Bits used No. missing words z-score p-value 31 to 32 142209 0.8840 0.811647 30 to 31 141615 -0.8682 0.192634 29 to 30 141915 0.0167 0.506672 28 to 29 141892 -0.0511 0.479615 27 to 28 141704 -0.6057 0.272359 26 to 27 141683 -0.6676 0.252182 25 to 26 141569 -1.0039 0.157708 24 to 25 142463 1.6332 0.948791 23 to 24 142181 0.8014 0.788546 22 to 23 141835 -0.2193 0.413223 21 to 22 141971 0.1819 0.572176 20 to 21 142450 1.5949 0.944632 19 to 20 140993 -2.7030 0.003435 18 to 19 141997 0.2586 0.602033 17 to 18 141666 -0.7178 0.236444 16 to 17 142183 0.8073 0.790249 15 to 16 141678 -0.6824 0.247496 14 to 15 142331 1.2439 0.893225 13 to 14 142311 1.1849 0.881965 12 to 13 142030 0.3560 0.639064 11 to 12 141723 -0.5496 0.291281 10 to 11 142017 0.3176 0.624610 9 to 10 142204 0.8692 0.807640 8 to 9 142145 0.6952 0.756532 7 to 8 141688 -0.6529 0.256913 6 to 7 141990 0.2380 0.594046 5 to 6 141492 -1.2311 0.109150 4 to 5 142286 1.1111 0.866742 3 to 4 141812 -0.2871 0.387014 2 to 3 142166 0.7571 0.775517 1 to 2 141758 -0.4464 0.327654 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-26_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2417.97 -1.160 0.123020 Test results for specific bytes for dh-ranFile-2016-10-26_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2411.03 -1.258 0.104163 2 to 9 2527.38 0.387 0.650698 3 to 10 2577.10 1.090 0.862237 4 to 11 2576.36 1.080 0.859897 5 to 12 2557.00 0.806 0.789912 6 to 13 2449.95 -0.708 0.239513 7 to 14 2510.37 0.147 0.558316 8 to 15 2404.75 -1.347 0.088994 9 to 16 2545.53 0.644 0.740162 10 to 17 2480.62 -0.274 0.392037 11 to 18 2417.37 -1.169 0.121281 12 to 19 2493.06 -0.098 0.460889 13 to 20 2348.89 -2.137 0.016300 14 to 21 2576.68 1.084 0.860907 15 to 22 2603.46 1.463 0.928289 16 to 23 2524.38 0.345 0.634869 17 to 24 2431.71 -0.966 0.167063 18 to 25 2423.26 -1.085 0.138896 19 to 26 2702.80 2.868 0.997935 20 to 27 2565.97 0.933 0.824583 21 to 28 2434.74 -0.923 0.178039 22 to 29 2384.20 -1.638 0.050750 23 to 30 2402.01 -1.386 0.082916 24 to 31 2546.10 0.652 0.742771 25 to 32 2558.35 0.825 0.795362 CDPARK for dh-ranFile-2016-10-26_02:31: 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 3529 0.2740 0.607947 3476 -2.1461 0.015932 3526 0.1370 0.554479 3526 0.1370 0.554479 3517 -0.2740 0.392053 3541 0.8219 0.794438 3502 -0.9589 0.168804 3518 -0.2283 0.409702 3521 -0.0913 0.463617 3531 0.3653 0.642555 Square side=100, avg. no. parked=3518.70 sample std.=17.24 p-value of the KSTEST for those 10 p-values: 0.500320 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-26_02:31 0.5158,0.7837,0.4831,0.9392,0.8827,0.4854,0.3625,0.5824,0.9431,0.5940, The KS test for those 10 p-values: 0.106194 The 3DSPHERES test for dh-ranFile-2016-10-26_02:31 sample no r^3 equiv. uni. 1 10.621 0.298148 2 45.286 0.778984 3 145.661 0.992214 4 8.867 0.255896 5 15.451 0.402518 6 0.222 0.007385 7 18.038 0.451882 8 9.688 0.275981 9 76.317 0.921441 10 194.854 0.998489 11 8.012 0.234390 12 0.893 0.029340 13 25.519 0.572857 14 23.195 0.538447 15 42.098 0.754207 16 83.025 0.937182 17 40.179 0.737971 18 12.861 0.348638 19 14.545 0.384195 20 39.716 0.733895 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.485347 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-26_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.9 -0.1 -1.4 -1.1 0.5 -0.3 -0.1 0.6 -0.5 0.6 0.9 -0.5 1.3 -0.5 -0.7 0.6 -1.3 -0.8 -1.3 1.6 -0.0 1.5 -0.9 0.3 0.2 0.3 -0.1 -0.1 0.4 -0.1 -0.1 0.2 0.3 0.1 -0.5 0.3 0.8 2.5 -0.7 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:30.592171 z-score=-1.244696, p-value=0.095965 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-26_02:31 Test no p-value 1 0.414961 2 0.149566 3 0.010199 4 0.065307 5 0.061744 6 0.447322 7 0.276007 8 0.066979 9 0.549689 10 0.210228 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003086 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-26_02:31: (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 66571 0.14 66833 0.41 3 25000.00 25034 0.05 24778 1.97 4 6666.67 6730 0.60 6690 0.08 5 1388.89 1366 0.38 1423 0.84 6 238.10 261 2.20 233 0.11 7 34.72 33 0.09 39 0.53 8 4.96 4 0.19 3 0.77 p=0.27432 p=0.41939 Number of rngs required: 688312, p-value: 0.458 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-26_02:31 No. of wins: Observed Expected 98506 98585.9 z-score=-0.357, pvalue=0.36048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66521 66666.7 0.318 0.318 2 37836 37654.3 0.877 1.195 3 27002 26954.7 0.083 1.278 4 19421 19313.5 0.599 1.877 5 13845 13851.4 0.003 1.880 6 9959 9943.5 0.024 1.904 7 7047 7145.0 1.345 3.248 8 5140 5139.1 0.000 3.249 9 3627 3699.9 1.435 4.684 10 2659 2666.3 0.020 4.704 11 1905 1923.3 0.175 4.878 12 1346 1388.7 1.315 6.194 13 1015 1003.7 0.127 6.320 14 749 726.1 0.720 7.040 15 525 525.8 0.001 7.041 16 375 381.2 0.099 7.141 17 265 276.5 0.482 7.622 18 197 200.8 0.073 7.695 19 139 146.0 0.334 8.029 20 117 106.2 1.095 9.124 21 310 287.1 1.824 10.949 Chisq= 10.95 for 20 degrees of freedom, p= 0.05246 SUMMARY of craptest p-value for no. of wins: 0.360481 p-value for throws/game: 0.052458 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-26_02:31 No. of wins: Observed Expected 98426 98585.9 z-score=-0.715, pvalue=0.23731 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66353 66666.7 1.476 1.476 2 37837 37654.3 0.886 2.362 3 27324 26954.7 5.059 7.421 4 19186 19313.5 0.841 8.262 5 13769 13851.4 0.490 8.752 6 10028 9943.5 0.717 9.470 7 7089 7145.0 0.439 9.909 8 4964 5139.1 5.964 15.873 9 3698 3699.9 0.001 15.874 10 2661 2666.3 0.011 15.885 11 1994 1923.3 2.597 18.482 12 1441 1388.7 1.967 20.448 13 1000 1003.7 0.014 20.462 14 703 726.1 0.737 21.199 15 564 525.8 2.770 23.969 16 406 381.2 1.620 25.589 17 255 276.5 1.678 27.267 18 188 200.8 0.820 28.087 19 154 146.0 0.440 28.527 20 103 106.2 0.097 28.624 21 283 287.1 0.059 28.683 Chisq= 28.68 for 20 degrees of freedom, p= 0.90581 SUMMARY of craptest p-value for no. of wins: 0.237310 p-value for throws/game: 0.905808 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0031,0.0034,0.0074,0.0102,0.0159,0.0163,0.0283,0.0293,0.0329, 0.0407,0.0429,0.0457,0.0508,0.0525,0.0547,0.0574,0.0617,0.0653,0.0670, 0.0770,0.0771,0.0820,0.0829,0.0837,0.0839,0.0885,0.0890,0.0960,0.0987, 0.1042,0.1062,0.1091,0.1213,0.1230,0.1260,0.1351,0.1389,0.1496,0.1503, 0.1577,0.1607,0.1643,0.1671,0.1688,0.1756,0.1775,0.1780,0.1860,0.1897, 0.1926,0.1959,0.2047,0.2102,0.2129,0.2257,0.2264,0.2278,0.2286,0.2331, 0.2344,0.2358,0.2364,0.2373,0.2395,0.2475,0.2522,0.2525,0.2559,0.2569, 0.2724,0.2743,0.2760,0.2760,0.2773,0.2825,0.2913,0.2981,0.3106,0.3106, 0.3277,0.3319,0.3444,0.3446,0.3486,0.3580,0.3595,0.3605,0.3618,0.3625, 0.3647,0.3677,0.3684,0.3686,0.3714,0.3773,0.3803,0.3842,0.3858,0.3870, 0.3900,0.3920,0.3921,0.3934,0.4025,0.4045,0.4058,0.4095,0.4097,0.4132, 0.4150,0.4194,0.4226,0.4257,0.4291,0.4398,0.4430,0.4473,0.4517,0.4519, 0.4583,0.4607,0.4609,0.4615,0.4617,0.4636,0.4665,0.4721,0.4796,0.4831, 0.4853,0.4854,0.4968,0.4982,0.4989,0.5003,0.5023,0.5062,0.5067,0.5131, 0.5158,0.5276,0.5325,0.5384,0.5497,0.5545,0.5545,0.5575,0.5583,0.5647, 0.5722,0.5729,0.5824,0.5845,0.5919,0.5930,0.5940,0.5940,0.6020,0.6031, 0.6056,0.6056,0.6079,0.6181,0.6246,0.6246,0.6284,0.6298,0.6349,0.6358, 0.6391,0.6426,0.6448,0.6456,0.6473,0.6507,0.6665,0.6756,0.6866,0.6893, 0.6898,0.6904,0.6906,0.7002,0.7013,0.7042,0.7047,0.7075,0.7108,0.7131, 0.7256,0.7339,0.7380,0.7402,0.7428,0.7540,0.7542,0.7550,0.7565,0.7728, 0.7755,0.7790,0.7803,0.7807,0.7837,0.7877,0.7885,0.7898,0.7899,0.7902, 0.7906,0.7944,0.7954,0.7957,0.7996,0.8076,0.8111,0.8116,0.8175,0.8246, 0.8295,0.8329,0.8411,0.8436,0.8457,0.8497,0.8566,0.8582,0.8599,0.8608, 0.8609,0.8622,0.8667,0.8695,0.8787,0.8804,0.8820,0.8827,0.8860,0.8868, 0.8925,0.8932,0.8986,0.8991,0.9058,0.9200,0.9214,0.9221,0.9229,0.9263, 0.9283,0.9306,0.9372,0.9392,0.9392,0.9400,0.9431,0.9437,0.9446,0.9488, 0.9846,0.9878,0.9879,0.9917,0.9922,0.9943,0.9979,0.9985,0.9987, Overall p-value after applying KStest on 269 p-values = 0.893964 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.