RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-08_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 10.8994 0.138253 2 to 25 15.80 14.2633 0.351616 3 to 26 15.77 26.2430 0.929854 4 to 27 16.12 30.4491 0.976717 5 to 28 15.80 19.4703 0.697783 6 to 29 15.78 16.2849 0.496263 7 to 30 15.68 12.9770 0.262277 8 to 31 15.72 18.1790 0.622364 9 to 32 15.63 18.0735 0.615779 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.771600 Tough bday spacings test for dh-ranFile-2015-10-08_11:31: 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 31 65 112 98 75 57 28 11 8 5 (O-E)^2/E 0.1 0.9 0.9 2.1 0.0 0.1 0.5 0.1 1.0 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.186, p= 0.201 RESULTS OF GCD FOR dh-ranFile-2015-10-08_11:31 Euclid's algorithm: p-value, steps to gcd: 0.108820 p-value, dist. of gcd's: 0.824715 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-08_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.595 0.513 0.258 0.564 0.860 0.263 0.860 0.195 Bits 8 to 15---> 0.812 0.953 0.492 0.051 0.643 0.714 0.172 0.661 Bits 16 to 23---> 0.128 0.068 0.749 0.209 0.441 0.271 0.670 0.672 Bits 24 to 31---> 0.516 0.482 0.763 0.610 0.740 0.755 0.183 0.299 KS test for the above 32 p values: 0.356 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-08_11:31, p-values for 5 runs: 0.1250, 0.9044, 0.0043, 0.9182, 0.1806 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-08_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 230 211.4 1.633 1.633 r= 29 5182 5134.0 0.449 2.082 r= 30 22996 23103.0 0.496 2.578 r= 31 11592 11551.5 0.142 2.720 chi-square = 2.720 with df = 3; p-value = 0.563 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-08_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 192 211.4 1.783 1.783 r= 30 5046 5134.0 1.509 3.292 r= 31 23294 23103.0 1.578 4.870 r= 32 11468 11551.5 0.604 5.474 chi-square = 5.474 with df = 3; p-value = 0.860 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-08_11:31 b-rank test for bits 1 to 8, p=0.27017 b-rank test for bits 2 to 9, p=0.01903 b-rank test for bits 3 to 10, p=0.10194 b-rank test for bits 4 to 11, p=0.03172 b-rank test for bits 5 to 12, p=0.12735 b-rank test for bits 6 to 13, p=0.73471 b-rank test for bits 7 to 14, p=0.15778 b-rank test for bits 8 to 15, p=0.76396 b-rank test for bits 9 to 16, p=0.64351 b-rank test for bits 10 to 17, p=0.44663 b-rank test for bits 11 to 18, p=0.99350 b-rank test for bits 12 to 19, p=0.94004 b-rank test for bits 13 to 20, p=0.48823 b-rank test for bits 14 to 21, p=0.15391 b-rank test for bits 15 to 22, p=0.12982 b-rank test for bits 16 to 23, p=0.03630 b-rank test for bits 17 to 24, p=0.18065 b-rank test for bits 18 to 25, p=0.51341 b-rank test for bits 19 to 26, p=0.39888 b-rank test for bits 20 to 27, p=0.17542 b-rank test for bits 21 to 28, p=0.13740 b-rank test for bits 22 to 29, p=0.51017 b-rank test for bits 23 to 30, p=0.78525 b-rank test for bits 24 to 31, p=0.48559 b-rank test for bits 25 to 32, p=0.78258 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 = 0.089391 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-08_11:31 (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 141398 -1.19 0.116103 2 142333 0.99 0.838884 3 142253 0.80 0.789003 4 141868 -0.10 0.461536 5 142139 0.54 0.704232 6 141193 -1.67 0.047098 7 142446 1.25 0.895061 8 141186 -1.69 0.045512 9 141819 -0.21 0.416424 10 142096 0.44 0.668634 11 141649 -0.61 0.271512 12 142408 1.17 0.878014 13 141700 -0.49 0.312389 14 141827 -0.19 0.423730 15 141861 -0.11 0.455047 16 142703 1.85 0.968157 17 141134 -1.81 0.035030 18 141455 -1.06 0.144227 19 142365 1.06 0.856483 20 141229 -1.59 0.055967 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-08_11:31 Bits used No. missing words z-score p-value 23 to 32 142157 0.8540 0.803457 22 to 31 142072 0.5609 0.712578 21 to 30 141569 -1.1736 0.120287 20 to 29 141741 -0.5804 0.280806 19 to 28 141844 -0.2253 0.410882 18 to 27 142233 1.1161 0.867811 17 to 26 142172 0.9058 0.817468 16 to 25 142209 1.0333 0.849279 15 to 24 141834 -0.2598 0.397525 14 to 23 141565 -1.1873 0.117546 13 to 22 141623 -0.9873 0.161737 12 to 21 142464 1.9127 0.972104 11 to 20 141834 -0.2598 0.397525 10 to 19 142441 1.8333 0.966624 9 to 18 141886 -0.0804 0.467940 8 to 17 141922 0.0437 0.517424 7 to 16 141641 -0.9253 0.177411 6 to 15 141351 -1.9253 0.027097 5 to 14 142233 1.1161 0.867811 4 to 13 142262 1.2161 0.888027 3 to 12 142257 1.1989 0.884709 2 to 11 141793 -0.4011 0.344159 1 to 10 141795 -0.3942 0.346701 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-08_11:31 Bits used No. missing words z-score p-value 28 to 32 142197 0.9752 0.835258 27 to 31 141831 -0.2655 0.395302 26 to 30 141435 -1.6079 0.053929 25 to 29 142200 0.9853 0.837767 24 to 28 142253 1.1650 0.877987 23 to 27 141718 -0.6486 0.258306 22 to 26 141659 -0.8486 0.198059 21 to 25 142417 1.7209 0.957367 20 to 24 141839 -0.2384 0.405783 19 to 23 141789 -0.4079 0.341674 18 to 22 142127 0.7379 0.769702 17 to 21 141953 0.1480 0.558842 16 to 20 141529 -1.2893 0.098655 15 to 19 141944 0.1175 0.546778 14 to 18 141770 -0.4723 0.318355 13 to 17 141606 -1.0282 0.151919 12 to 16 141588 -1.0893 0.138021 11 to 15 141764 -0.4926 0.311132 10 to 14 141910 0.0023 0.500906 9 to 13 142002 0.3141 0.623291 8 to 12 141434 -1.6113 0.053558 7 to 11 141712 -0.6689 0.251775 6 to 10 141498 -1.3943 0.081608 5 to 9 141730 -0.6079 0.271628 4 to 8 141389 -1.7638 0.038880 3 to 7 141847 -0.2113 0.416331 2 to 6 142047 0.4667 0.679635 1 to 5 142442 1.8057 0.964514 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-08_11:31 Bits used No. missing words z-score p-value 31 to 32 141871 -0.1131 0.454988 30 to 31 142201 0.8604 0.805211 29 to 30 142334 1.2527 0.894845 28 to 29 141793 -0.3432 0.365740 27 to 28 141622 -0.8476 0.198336 26 to 27 141848 -0.1809 0.428217 25 to 26 142311 1.1849 0.881965 24 to 25 141610 -0.8830 0.188624 23 to 24 142116 0.6096 0.728952 22 to 23 142143 0.6893 0.754680 21 to 22 141484 -1.2547 0.104801 20 to 21 142124 0.6332 0.736713 19 to 20 142080 0.5035 0.692677 18 to 19 141715 -0.5732 0.283240 17 to 18 142289 1.1200 0.868637 16 to 17 142208 0.8810 0.810850 15 to 16 142186 0.8161 0.792789 14 to 15 142274 1.0757 0.858974 13 to 14 141630 -0.8240 0.204975 12 to 13 142207 0.8781 0.810051 11 to 12 141666 -0.7178 0.236444 10 to 11 141927 0.0521 0.520785 9 to 10 141253 -1.9361 0.026429 8 to 9 142257 1.0256 0.847454 7 to 8 142061 0.4474 0.672708 6 to 7 142480 1.6834 0.953850 5 to 6 141837 -0.2134 0.415522 4 to 5 141807 -0.3019 0.381380 3 to 4 142082 0.5094 0.694747 2 to 3 142301 1.1554 0.876030 1 to 2 141741 -0.4965 0.309754 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-08_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2483.17 -0.238 0.405941 Test results for specific bytes for dh-ranFile-2015-10-08_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2543.94 0.621 0.732838 2 to 9 2493.12 -0.097 0.461245 3 to 10 2432.85 -0.950 0.171163 4 to 11 2496.85 -0.045 0.482252 5 to 12 2418.34 -1.155 0.124068 6 to 13 2488.41 -0.164 0.434882 7 to 14 2643.25 2.026 0.978611 8 to 15 2500.05 0.001 0.500266 9 to 16 2454.01 -0.650 0.257734 10 to 17 2466.25 -0.477 0.316579 11 to 18 2514.07 0.199 0.578878 12 to 19 2616.17 1.643 0.949792 13 to 20 2427.81 -1.021 0.153660 14 to 21 2489.96 -0.142 0.443559 15 to 22 2518.61 0.263 0.603769 16 to 23 2672.62 2.441 0.992682 17 to 24 2590.40 1.278 0.899458 18 to 25 2515.13 0.214 0.584739 19 to 26 2643.42 2.028 0.978731 20 to 27 2585.82 1.214 0.887571 21 to 28 2442.41 -0.814 0.207691 22 to 29 2549.62 0.702 0.758555 23 to 30 2440.63 -0.840 0.200570 24 to 31 2337.80 -2.294 0.010901 25 to 32 2477.28 -0.321 0.374001 CDPARK for dh-ranFile-2015-10-08_11:31: 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 3560 1.6895 0.954438 3492 -1.4155 0.078457 3503 -0.9132 0.180558 3471 -2.3744 0.008788 3521 -0.0913 0.463617 3525 0.0913 0.536383 3512 -0.5023 0.307734 3536 0.5936 0.723613 3499 -1.0959 0.136563 3526 0.1370 0.554479 Square side=100, avg. no. parked=3514.50 sample std.=23.65 p-value of the KSTEST for those 10 p-values: 0.409986 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-08_11:31 0.2216,0.8036,0.8173,0.2236,0.5858,0.6300,0.2666,0.6110,0.0920,0.6743, The KS test for those 10 p-values: 0.786513 The 3DSPHERES test for dh-ranFile-2015-10-08_11:31 sample no r^3 equiv. uni. 1 50.200 0.812380 2 55.689 0.843749 3 15.516 0.403809 4 36.305 0.701854 5 24.396 0.556565 6 10.410 0.293193 7 10.799 0.302308 8 1.265 0.041295 9 5.377 0.164084 10 13.351 0.359198 11 12.010 0.329896 12 76.072 0.920796 13 38.538 0.723243 14 6.633 0.198374 15 3.872 0.121082 16 18.581 0.461707 17 22.576 0.528834 18 62.828 0.876839 19 12.251 0.335273 20 11.081 0.308828 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.716705 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-08_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -1.6 0.0 0.8 -0.6 -1.3 0.1 0.3 -0.6 -0.3 -0.3 0.2 -1.0 -0.2 -0.5 0.7 1.2 -0.3 0.9 -1.2 -1.1 0.2 1.3 -0.6 -0.0 1.5 0.4 0.0 0.7 -0.9 1.6 -0.3 -0.6 -0.2 2.0 1.4 0.5 2.1 -0.7 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:35.909861 z-score=-0.664489, p-value=0.265692 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-08_11:31 Test no p-value 1 0.443158 2 0.017124 3 0.898240 4 0.674969 5 0.626846 6 0.675667 7 0.430382 8 0.332584 9 0.293169 10 0.889814 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.853698 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-08_11:31: (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 66564 0.16 66580 0.11 3 25000.00 25139 0.77 25101 0.41 4 6666.67 6661 0.00 6669 0.00 5 1388.89 1339 1.79 1372 0.21 6 238.10 262 2.40 227 0.52 7 34.72 28 1.30 44 2.48 8 4.96 6 0.22 6 0.22 p=0.64523 p=0.31553 Number of rngs required: 688113, p-value: 0.369 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-08_11:31 No. of wins: Observed Expected 98553 98585.9 z-score=-0.147, pvalue=0.44158 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66964 66666.7 1.326 1.326 2 37690 37654.3 0.034 1.360 3 26642 26954.7 3.628 4.988 4 19191 19313.5 0.777 5.765 5 13880 13851.4 0.059 5.824 6 9855 9943.5 0.788 6.612 7 7211 7145.0 0.609 7.221 8 5114 5139.1 0.122 7.344 9 3732 3699.9 0.279 7.623 10 2670 2666.3 0.005 7.628 11 1955 1923.3 0.522 8.149 12 1380 1388.7 0.055 8.204 13 1019 1003.7 0.233 8.437 14 751 726.1 0.851 9.288 15 522 525.8 0.028 9.316 16 384 381.2 0.021 9.338 17 285 276.5 0.259 9.596 18 215 200.8 1.000 10.596 19 141 146.0 0.170 10.766 20 90 106.2 2.475 13.242 21 309 287.1 1.668 14.910 Chisq= 14.91 for 20 degrees of freedom, p= 0.21848 SUMMARY of craptest p-value for no. of wins: 0.441581 p-value for throws/game: 0.218478 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-08_11:31 No. of wins: Observed Expected 98505 98585.9 z-score=-0.362, pvalue=0.35881 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66787 66666.7 0.217 0.217 2 37682 37654.3 0.020 0.238 3 26914 26954.7 0.062 0.299 4 19408 19313.5 0.463 0.762 5 13872 13851.4 0.031 0.792 6 9911 9943.5 0.107 0.899 7 7081 7145.0 0.574 1.473 8 5079 5139.1 0.702 2.175 9 3671 3699.9 0.225 2.400 10 2591 2666.3 2.126 4.526 11 1981 1923.3 1.729 6.256 12 1391 1388.7 0.004 6.259 13 997 1003.7 0.045 6.304 14 740 726.1 0.265 6.569 15 561 525.8 2.352 8.920 16 369 381.2 0.387 9.308 17 298 276.5 1.665 10.973 18 184 200.8 1.410 12.384 19 116 146.0 6.159 18.542 20 105 106.2 0.014 18.556 21 262 287.1 2.197 20.753 Chisq= 20.75 for 20 degrees of freedom, p= 0.58819 SUMMARY of craptest p-value for no. of wins: 0.358808 p-value for throws/game: 0.588191 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0043,0.0088,0.0109,0.0171,0.0190,0.0264,0.0271,0.0317,0.0350,0.0363, 0.0389,0.0413,0.0455,0.0471,0.0511,0.0536,0.0539,0.0560,0.0684,0.0785, 0.0816,0.0894,0.0920,0.0987,0.1019,0.1048,0.1088,0.1161,0.1175,0.1203, 0.1211,0.1241,0.1250,0.1273,0.1276,0.1298,0.1366,0.1374,0.1380,0.1383, 0.1442,0.1519,0.1537,0.1539,0.1578,0.1617,0.1641,0.1712,0.1724,0.1754, 0.1774,0.1806,0.1806,0.1807,0.1827,0.1886,0.1948,0.1981,0.1983,0.1984, 0.2006,0.2006,0.2050,0.2077,0.2088,0.2185,0.2216,0.2236,0.2364,0.2518, 0.2577,0.2580,0.2583,0.2623,0.2629,0.2657,0.2666,0.2702,0.2706,0.2715, 0.2716,0.2808,0.2832,0.2932,0.2932,0.2990,0.3023,0.3077,0.3088,0.3098, 0.3111,0.3124,0.3155,0.3166,0.3184,0.3299,0.3326,0.3353,0.3417,0.3442, 0.3467,0.3516,0.3559,0.3588,0.3592,0.3657,0.3692,0.3740,0.3814,0.3953, 0.3975,0.3975,0.3989,0.4038,0.4058,0.4059,0.4100,0.4109,0.4155,0.4163, 0.4164,0.4237,0.4282,0.4304,0.4349,0.4405,0.4416,0.4432,0.4436,0.4466, 0.4550,0.4550,0.4612,0.4615,0.4617,0.4636,0.4679,0.4818,0.4823,0.4856, 0.4882,0.4918,0.4963,0.5003,0.5009,0.5102,0.5125,0.5134,0.5155,0.5174, 0.5208,0.5288,0.5364,0.5468,0.5545,0.5566,0.5588,0.5631,0.5645,0.5789, 0.5847,0.5858,0.5882,0.5948,0.6038,0.6100,0.6110,0.6158,0.6224,0.6233, 0.6268,0.6300,0.6433,0.6435,0.6452,0.6608,0.6686,0.6700,0.6717,0.6727, 0.6743,0.6750,0.6757,0.6796,0.6927,0.6947,0.6978,0.7019,0.7042,0.7126, 0.7139,0.7167,0.7232,0.7236,0.7290,0.7328,0.7347,0.7367,0.7404,0.7489, 0.7546,0.7547,0.7586,0.7629,0.7640,0.7697,0.7716,0.7826,0.7853,0.7865, 0.7890,0.7928,0.8035,0.8036,0.8052,0.8101,0.8108,0.8120,0.8124,0.8173, 0.8175,0.8247,0.8353,0.8378,0.8389,0.8437,0.8475,0.8493,0.8537,0.8565, 0.8590,0.8598,0.8602,0.8604,0.8678,0.8678,0.8686,0.8760,0.8768,0.8780, 0.8780,0.8820,0.8847,0.8876,0.8880,0.8898,0.8948,0.8951,0.8982,0.8995, 0.9044,0.9182,0.9208,0.9299,0.9400,0.9498,0.9526,0.9539,0.9544,0.9574, 0.9645,0.9666,0.9682,0.9721,0.9767,0.9786,0.9787,0.9927,0.9935, Overall p-value after applying KStest on 269 p-values = 0.762185 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.