RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-26_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 15.79 16.4943 0.510895 2 to 25 15.61 18.1386 0.619854 3 to 26 15.79 7.5509 0.024768 4 to 27 16.09 24.5651 0.895123 5 to 28 15.82 14.4742 0.366701 6 to 29 15.81 17.4548 0.576012 7 to 30 15.78 15.5179 0.441770 8 to 31 15.65 27.2934 0.946098 9 to 32 15.84 14.5466 0.371898 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.802918 Tough bday spacings test for dh-ranFile-2015-11-26_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 10 29 87 90 109 70 50 24 14 10 7 (O-E)^2/E 0.1 1.6 2.6 0.6 1.3 0.8 0.1 1.1 0.1 1.7 2.1 Birthday Spacings: Sum(O-E)^2/E= 12.112, p= 0.722 RESULTS OF GCD FOR dh-ranFile-2015-11-26_02:31 Euclid's algorithm: p-value, steps to gcd: 0.916556 p-value, dist. of gcd's: 0.064277 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-26_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.234 0.716 0.375 0.071 0.923 0.120 0.589 0.235 Bits 8 to 15---> 0.330 0.085 0.699 0.613 0.567 0.029 0.725 0.291 Bits 16 to 23---> 0.969 0.698 0.237 0.439 0.498 0.301 0.073 0.454 Bits 24 to 31---> 0.951 0.919 0.025 0.002 0.113 0.078 0.304 0.287 KS test for the above 32 p values: 0.928 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-26_02:31, p-values for 5 runs: 0.7015, 0.0877, 0.5516, 0.6625, 0.4659 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-26_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5104 5134.0 0.175 0.610 r= 30 23121 23103.0 0.014 0.624 r= 31 11554 11551.5 0.001 0.624 chi-square = 0.624 with df = 3; p-value = 0.109 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-26_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 241 211.4 4.139 4.139 r= 30 5124 5134.0 0.020 4.159 r= 31 23068 23103.0 0.053 4.212 r= 32 11567 11551.5 0.021 4.233 chi-square = 4.233 with df = 3; p-value = 0.763 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-26_02:31 b-rank test for bits 1 to 8, p=0.86054 b-rank test for bits 2 to 9, p=0.29997 b-rank test for bits 3 to 10, p=0.73773 b-rank test for bits 4 to 11, p=0.87462 b-rank test for bits 5 to 12, p=0.39737 b-rank test for bits 6 to 13, p=0.53557 b-rank test for bits 7 to 14, p=0.95757 b-rank test for bits 8 to 15, p=0.88772 b-rank test for bits 9 to 16, p=0.85939 b-rank test for bits 10 to 17, p=0.62787 b-rank test for bits 11 to 18, p=0.47029 b-rank test for bits 12 to 19, p=0.89839 b-rank test for bits 13 to 20, p=0.93490 b-rank test for bits 14 to 21, p=0.31159 b-rank test for bits 15 to 22, p=0.53118 b-rank test for bits 16 to 23, p=0.65716 b-rank test for bits 17 to 24, p=0.66153 b-rank test for bits 18 to 25, p=0.74166 b-rank test for bits 19 to 26, p=0.29425 b-rank test for bits 20 to 27, p=0.57338 b-rank test for bits 21 to 28, p=0.21760 b-rank test for bits 22 to 29, p=0.67275 b-rank test for bits 23 to 30, p=0.66517 b-rank test for bits 24 to 31, p=0.42745 b-rank test for bits 25 to 32, p=0.08535 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 = 0.087506 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-26_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 140914 -2.33 0.010022 2 142363 1.06 0.855422 3 141806 -0.24 0.404613 4 142467 1.30 0.903707 5 141377 -1.24 0.106794 6 141603 -0.72 0.237081 7 141629 -0.65 0.256241 8 142356 1.04 0.851670 9 141444 -1.09 0.138470 10 141259 -1.52 0.064323 11 141817 -0.22 0.414601 12 141783 -0.30 0.383935 13 141641 -0.63 0.265350 14 142015 0.25 0.597504 15 141629 -0.65 0.256241 16 141611 -0.70 0.242891 17 142248 0.79 0.785611 18 141458 -1.05 0.145825 19 141865 -0.10 0.458753 20 140832 -2.52 0.005916 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-26_02:31 Bits used No. missing words z-score p-value 23 to 32 142436 1.8161 0.965323 22 to 31 142456 1.8851 0.970290 21 to 30 141833 -0.2632 0.396196 20 to 29 141908 -0.0046 0.498170 19 to 28 142525 2.1230 0.983123 18 to 27 142061 0.5230 0.699513 17 to 26 142312 1.3885 0.917510 16 to 25 141624 -0.9839 0.162583 15 to 24 141811 -0.3391 0.367279 14 to 23 141738 -0.5908 0.277330 13 to 22 142280 1.2782 0.899406 12 to 21 142328 1.4437 0.925587 11 to 20 141811 -0.3391 0.367279 10 to 19 141869 -0.1391 0.444698 9 to 18 142099 0.6540 0.743455 8 to 17 142269 1.2402 0.892557 7 to 16 141777 -0.4563 0.324083 6 to 15 141338 -1.9701 0.024413 5 to 14 141651 -0.8908 0.186520 4 to 13 141212 -2.4046 0.008095 3 to 12 142312 1.3885 0.917510 2 to 11 141689 -0.7598 0.223699 1 to 10 141948 0.1333 0.553040 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-26_02:31 Bits used No. missing words z-score p-value 28 to 32 141977 0.2294 0.590717 27 to 31 141861 -0.1638 0.434932 26 to 30 141860 -0.1672 0.433598 25 to 29 142039 0.4396 0.669872 24 to 28 141435 -1.6079 0.053929 23 to 27 142265 1.2057 0.886026 22 to 26 142277 1.2463 0.893680 21 to 25 141736 -0.5876 0.278414 20 to 24 141671 -0.8079 0.209575 19 to 23 141896 -0.0452 0.481979 18 to 22 141947 0.1277 0.550805 17 to 21 141916 0.0226 0.509019 16 to 20 141745 -0.5571 0.288746 15 to 19 142256 1.1752 0.880033 14 to 18 142113 0.6904 0.755031 13 to 17 141885 -0.0825 0.467135 12 to 16 141974 0.2192 0.586761 11 to 15 141764 -0.4926 0.311132 10 to 14 142081 0.5819 0.719694 9 to 13 142048 0.4701 0.680847 8 to 12 141731 -0.6045 0.272753 7 to 11 141583 -1.1062 0.134319 6 to 10 141834 -0.2554 0.399224 5 to 9 141805 -0.3537 0.361797 4 to 8 141694 -0.7299 0.232716 3 to 7 141495 -1.4045 0.080084 2 to 6 141195 -2.4215 0.007729 1 to 5 142045 0.4599 0.677205 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-26_02:31 Bits used No. missing words z-score p-value 31 to 32 141663 -0.7266 0.233724 30 to 31 142143 0.6893 0.754680 29 to 30 141639 -0.7974 0.212600 28 to 29 141984 0.2203 0.587168 27 to 28 142393 1.4268 0.923175 26 to 27 141932 0.0669 0.526659 25 to 26 141803 -0.3137 0.376891 24 to 25 141666 -0.7178 0.236444 23 to 24 141737 -0.5083 0.305605 22 to 23 142432 1.5418 0.938439 21 to 22 141516 -1.1603 0.122970 20 to 21 142111 0.5949 0.724044 19 to 20 141421 -1.4405 0.074863 18 to 19 142037 0.3766 0.646767 17 to 18 142098 0.5565 0.711082 16 to 17 141921 0.0344 0.513731 15 to 16 141944 0.1023 0.540729 14 to 15 141809 -0.2960 0.383631 13 to 14 141470 -1.2960 0.097495 12 to 13 141974 0.1908 0.575646 11 to 12 142284 1.1052 0.865468 10 to 11 141728 -0.5349 0.296361 9 to 10 141682 -0.6706 0.251241 8 to 9 142216 0.9046 0.817170 7 to 8 141275 -1.8712 0.030660 6 to 7 141506 -1.1898 0.117070 5 to 6 142245 0.9902 0.838956 4 to 5 142439 1.5624 0.940909 3 to 4 141499 -1.2104 0.113060 2 to 3 142178 0.7925 0.785976 1 to 2 141656 -0.7473 0.227445 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-26_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2628.23 1.813 0.965118 Test results for specific bytes for dh-ranFile-2015-11-26_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2494.78 -0.074 0.470577 2 to 9 2447.67 -0.740 0.229650 3 to 10 2631.20 1.856 0.968238 4 to 11 2430.47 -0.983 0.162736 5 to 12 2542.73 0.604 0.727180 6 to 13 2601.79 1.440 0.924999 7 to 14 2450.15 -0.705 0.240421 8 to 15 2551.29 0.725 0.765873 9 to 16 2497.53 -0.035 0.486043 10 to 17 2436.14 -0.903 0.183225 11 to 18 2497.14 -0.040 0.483890 12 to 19 2495.69 -0.061 0.475695 13 to 20 2558.33 0.825 0.795286 14 to 21 2520.93 0.296 0.616368 15 to 22 2534.96 0.494 0.689512 16 to 23 2443.68 -0.797 0.212871 17 to 24 2532.22 0.456 0.675658 18 to 25 2653.98 2.178 0.985280 19 to 26 2520.24 0.286 0.612638 20 to 27 2358.84 -1.996 0.022953 21 to 28 2571.42 1.010 0.843776 22 to 29 2464.27 -0.505 0.306684 23 to 30 2462.00 -0.537 0.295492 24 to 31 2526.55 0.375 0.646355 25 to 32 2446.22 -0.761 0.223443 CDPARK for dh-ranFile-2015-11-26_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 3534 0.5023 0.692266 3529 0.2740 0.607947 3515 -0.3653 0.357445 3521 -0.0913 0.463617 3532 0.4110 0.659449 3531 0.3653 0.642555 3517 -0.2740 0.392053 3532 0.4110 0.659449 3515 -0.3653 0.357445 3496 -1.2329 0.108811 Square side=100, avg. no. parked=3522.20 sample std.=11.29 p-value of the KSTEST for those 10 p-values: 0.329789 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-26_02:31 0.0730,0.2037,0.8666,0.3994,0.0594,0.5185,0.2650,0.9498,0.2815,0.4624, The KS test for those 10 p-values: 0.491577 The 3DSPHERES test for dh-ranFile-2015-11-26_02:31 sample no r^3 equiv. uni. 1 5.462 0.166458 2 209.598 0.999076 3 126.787 0.985393 4 40.536 0.741073 5 5.526 0.168239 6 11.406 0.316268 7 8.446 0.245379 8 56.096 0.845855 9 27.218 0.596371 10 1.101 0.036027 11 6.879 0.204898 12 66.426 0.890761 13 36.004 0.698841 14 38.661 0.724369 15 45.197 0.778328 16 2.644 0.084358 17 1.090 0.035684 18 23.697 0.546106 19 31.892 0.654608 20 32.445 0.660917 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.551521 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-26_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 1.1 -0.1 -0.5 -1.9 -1.8 -1.2 -1.3 -0.2 1.2 0.5 -0.6 -1.2 2.5 -1.5 0.2 1.1 1.1 -0.7 -0.5 -1.0 0.7 0.5 0.9 0.4 -0.6 -0.3 -0.4 -1.3 1.5 -2.0 -1.1 1.5 0.2 0.6 0.7 1.5 -0.4 -0.7 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:50.252775 z-score=0.900452, p-value=0.820987 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-26_02:31 Test no p-value 1 0.588550 2 0.069555 3 0.410263 4 0.868090 5 0.001816 6 0.076835 7 0.763392 8 0.652671 9 0.195757 10 0.011099 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.059460 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-26_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 66922 0.98 66905 0.85 3 25000.00 24754 2.42 24880 0.58 4 6666.67 6665 0.00 6576 1.23 5 1388.89 1393 0.01 1348 1.20 6 238.10 219 1.53 245 0.20 7 34.72 42 1.53 40 0.80 8 4.96 4 0.19 5 0.00 p=0.64605 p=0.43922 Number of rngs required: 687584, p-value: 0.172 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-26_02:31 No. of wins: Observed Expected 98406 98585.9 z-score=-0.804, pvalue=0.21057 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66516 66666.7 0.341 0.341 2 37879 37654.3 1.341 1.681 3 26985 26954.7 0.034 1.715 4 19194 19313.5 0.739 2.454 5 13713 13851.4 1.383 3.837 6 9952 9943.5 0.007 3.845 7 7291 7145.0 2.982 6.827 8 5158 5139.1 0.070 6.897 9 3707 3699.9 0.014 6.910 10 2616 2666.3 0.949 7.859 11 1942 1923.3 0.181 8.040 12 1442 1388.7 2.043 10.083 13 1003 1003.7 0.001 10.083 14 738 726.1 0.194 10.277 15 511 525.8 0.419 10.696 16 379 381.2 0.012 10.708 17 250 276.5 2.547 13.255 18 213 200.8 0.737 13.992 19 139 146.0 0.334 14.326 20 94 106.2 1.405 15.731 21 278 287.1 0.289 16.021 Chisq= 16.02 for 20 degrees of freedom, p= 0.28465 SUMMARY of craptest p-value for no. of wins: 0.210574 p-value for throws/game: 0.284652 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-26_02:31 No. of wins: Observed Expected 98802 98585.9 z-score= 0.967, pvalue=0.83316 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66606 66666.7 0.055 0.055 2 37758 37654.3 0.285 0.341 3 26946 26954.7 0.003 0.344 4 19233 19313.5 0.335 0.679 5 13957 13851.4 0.805 1.483 6 9858 9943.5 0.736 2.219 7 7191 7145.0 0.296 2.515 8 5199 5139.1 0.699 3.214 9 3697 3699.9 0.002 3.216 10 2674 2666.3 0.022 3.239 11 1932 1923.3 0.039 3.278 12 1386 1388.7 0.005 3.283 13 978 1003.7 0.659 3.942 14 732 726.1 0.047 3.989 15 523 525.8 0.015 4.004 16 353 381.2 2.079 6.084 17 278 276.5 0.008 6.091 18 168 200.8 5.367 11.458 19 141 146.0 0.170 11.628 20 106 106.2 0.000 11.629 21 284 287.1 0.034 11.662 Chisq= 11.66 for 20 degrees of freedom, p= 0.07279 SUMMARY of craptest p-value for no. of wins: 0.833156 p-value for throws/game: 0.072794 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0018,0.0059,0.0077,0.0081,0.0100,0.0111,0.0230,0.0244,0.0247, 0.0248,0.0288,0.0307,0.0357,0.0360,0.0539,0.0594,0.0595,0.0643,0.0643, 0.0696,0.0708,0.0726,0.0728,0.0730,0.0749,0.0768,0.0778,0.0801,0.0844, 0.0847,0.0853,0.0875,0.0877,0.0975,0.1068,0.1088,0.1091,0.1131,0.1131, 0.1171,0.1199,0.1230,0.1343,0.1385,0.1458,0.1626,0.1627,0.1665,0.1682, 0.1715,0.1832,0.1865,0.1958,0.2037,0.2049,0.2096,0.2106,0.2126,0.2129, 0.2176,0.2234,0.2237,0.2274,0.2297,0.2327,0.2336,0.2337,0.2351,0.2364, 0.2371,0.2374,0.2404,0.2429,0.2454,0.2512,0.2562,0.2562,0.2650,0.2653, 0.2728,0.2773,0.2784,0.2815,0.2847,0.2874,0.2887,0.2910,0.2942,0.2955, 0.2964,0.3000,0.3015,0.3042,0.3056,0.3067,0.3111,0.3116,0.3163,0.3241, 0.3298,0.3298,0.3574,0.3574,0.3618,0.3667,0.3673,0.3673,0.3719,0.3746, 0.3769,0.3836,0.3839,0.3921,0.3962,0.3974,0.3992,0.3994,0.4046,0.4103, 0.4146,0.4275,0.4336,0.4349,0.4389,0.4392,0.4418,0.4447,0.4541,0.4588, 0.4624,0.4636,0.4659,0.4671,0.4703,0.4706,0.4757,0.4820,0.4839,0.4860, 0.4916,0.4981,0.4982,0.5090,0.5109,0.5137,0.5185,0.5267,0.5312,0.5356, 0.5407,0.5461,0.5508,0.5515,0.5516,0.5530,0.5667,0.5734,0.5756,0.5760, 0.5868,0.5872,0.5885,0.5887,0.5907,0.5964,0.5975,0.6079,0.6126,0.6133, 0.6164,0.6199,0.6279,0.6426,0.6460,0.6464,0.6468,0.6527,0.6546,0.6572, 0.6594,0.6594,0.6609,0.6615,0.6625,0.6652,0.6699,0.6728,0.6757,0.6772, 0.6808,0.6895,0.6923,0.6977,0.6988,0.6988,0.6995,0.7015,0.7111,0.7165, 0.7197,0.7223,0.7240,0.7244,0.7247,0.7272,0.7377,0.7411,0.7417,0.7435, 0.7547,0.7550,0.7626,0.7634,0.7659,0.7783,0.7856,0.7860,0.7953,0.8029, 0.8172,0.8210,0.8332,0.8390,0.8438,0.8459,0.8517,0.8554,0.8594,0.8605, 0.8655,0.8666,0.8681,0.8746,0.8800,0.8860,0.8877,0.8908,0.8926,0.8937, 0.8951,0.8984,0.8994,0.9037,0.9166,0.9175,0.9175,0.9191,0.9225,0.9232, 0.9250,0.9256,0.9283,0.9349,0.9384,0.9409,0.9461,0.9498,0.9507,0.9576, 0.9651,0.9653,0.9682,0.9686,0.9703,0.9831,0.9853,0.9854,0.9991, Overall p-value after applying KStest on 269 p-values = 0.421010 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.