RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-29_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 19.0044 0.671723 2 to 25 15.81 17.4232 0.573933 3 to 26 15.98 27.6926 0.951339 4 to 27 15.81 20.2912 0.740396 5 to 28 15.72 17.0193 0.546940 6 to 29 15.90 21.9630 0.813856 7 to 30 15.75 13.9533 0.329596 8 to 31 15.76 21.9880 0.814819 9 to 32 15.84 15.6436 0.450774 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.156320 Tough bday spacings test for dh-ranFile-2018-03-29_22:31: 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 7 42 92 86 93 75 57 22 16 9 1 (O-E)^2/E 0.5 0.8 4.8 1.4 0.2 0.1 0.5 2.0 0.1 0.9 2.3 Birthday Spacings: Sum(O-E)^2/E= 13.580, p= 0.807 RESULTS OF GCD FOR dh-ranFile-2018-03-29_22:31 Euclid's algorithm: p-value, steps to gcd: 0.028839 p-value, dist. of gcd's: 0.488694 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-29_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.897 0.679 0.112 0.036 0.039 0.681 0.733 0.532 Bits 8 to 15---> 0.367 0.299 0.765 0.111 0.287 0.910 0.590 0.300 Bits 16 to 23---> 0.382 0.611 0.516 0.090 0.534 0.682 0.545 0.326 Bits 24 to 31---> 0.759 0.754 0.721 0.239 0.075 0.432 0.575 0.399 KS test for the above 32 p values: 0.511 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-29_22:31, p-values for 5 runs: 0.5889, 0.1054, 0.6982, 0.9515, 0.8482 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-29_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 232 211.4 2.004 2.004 r= 29 5133 5134.0 0.000 2.004 r= 30 23096 23103.0 0.002 2.006 r= 31 11539 11551.5 0.014 2.020 chi-square = 2.020 with df = 3; p-value = 0.432 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-29_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5120 5134.0 0.038 0.093 r= 31 23096 23103.0 0.002 0.096 r= 32 11576 11551.5 0.052 0.148 chi-square = 0.148 with df = 3; p-value = 0.014 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-29_22:31 b-rank test for bits 1 to 8, p=0.25505 b-rank test for bits 2 to 9, p=0.21248 b-rank test for bits 3 to 10, p=0.12927 b-rank test for bits 4 to 11, p=0.87126 b-rank test for bits 5 to 12, p=0.93999 b-rank test for bits 6 to 13, p=0.22198 b-rank test for bits 7 to 14, p=0.75665 b-rank test for bits 8 to 15, p=0.21968 b-rank test for bits 9 to 16, p=0.45243 b-rank test for bits 10 to 17, p=0.07543 b-rank test for bits 11 to 18, p=0.82247 b-rank test for bits 12 to 19, p=0.29529 b-rank test for bits 13 to 20, p=0.03186 b-rank test for bits 14 to 21, p=0.33688 b-rank test for bits 15 to 22, p=0.30750 b-rank test for bits 16 to 23, p=0.12670 b-rank test for bits 17 to 24, p=0.25937 b-rank test for bits 18 to 25, p=0.25903 b-rank test for bits 19 to 26, p=0.59332 b-rank test for bits 20 to 27, p=0.62300 b-rank test for bits 21 to 28, p=0.66633 b-rank test for bits 22 to 29, p=0.76640 b-rank test for bits 23 to 30, p=0.45128 b-rank test for bits 24 to 31, p=0.04958 b-rank test for bits 25 to 32, p=0.80370 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 = 0.257883 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-29_22:31 (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 141379 -1.24 0.107656 2 142120 0.49 0.688718 3 142309 0.93 0.824799 4 142318 0.95 0.830170 5 141552 -0.83 0.201892 6 142422 1.20 0.884508 7 141325 -1.37 0.086086 8 142793 2.06 0.980522 9 141622 -0.67 0.251005 10 141152 -1.77 0.038408 11 142931 2.39 0.991509 12 141902 -0.02 0.493168 13 141181 -1.70 0.044405 14 142087 0.42 0.660972 15 141393 -1.21 0.113836 16 141809 -0.23 0.407331 17 141533 -0.88 0.189626 18 141731 -0.42 0.338464 19 141516 -0.92 0.179049 20 141426 -1.13 0.129391 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-29_22:31 Bits used No. missing words z-score p-value 23 to 32 141728 -0.6253 0.265895 22 to 31 141509 -1.3804 0.083724 21 to 30 141757 -0.5253 0.299696 20 to 29 141605 -1.0494 0.146994 19 to 28 141319 -2.0356 0.020894 18 to 27 141870 -0.1356 0.446061 17 to 26 142424 1.7747 0.962028 16 to 25 142606 2.4023 0.991854 15 to 24 142270 1.2437 0.893193 14 to 23 141564 -1.1908 0.116867 13 to 22 141763 -0.5046 0.306925 12 to 21 142496 2.0230 0.978463 11 to 20 142005 0.3299 0.629261 10 to 19 141853 -0.1942 0.422994 9 to 18 142315 1.3989 0.919073 8 to 17 141921 0.0402 0.516050 7 to 16 141625 -0.9804 0.163432 6 to 15 141360 -1.8942 0.029096 5 to 14 142051 0.4885 0.687408 4 to 13 141940 0.1058 0.542113 3 to 12 142304 1.3609 0.913232 2 to 11 142457 1.8885 0.970522 1 to 10 142188 0.9609 0.831707 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-29_22:31 Bits used No. missing words z-score p-value 28 to 32 141219 -2.3401 0.009639 27 to 31 141848 -0.2079 0.417654 26 to 30 141680 -0.7774 0.218464 25 to 29 142385 1.6124 0.946567 24 to 28 141770 -0.4723 0.318355 23 to 27 141831 -0.2655 0.395302 22 to 26 141928 0.0633 0.525232 21 to 25 141019 -3.0181 0.001272 20 to 24 141944 0.1175 0.546778 19 to 23 142039 0.4396 0.669872 18 to 22 142056 0.4972 0.690471 17 to 21 142875 3.2735 0.999469 16 to 20 141863 -0.1571 0.437602 15 to 19 141544 -1.2384 0.107783 14 to 18 141986 0.2599 0.602529 13 to 17 142132 0.7548 0.774820 12 to 16 142049 0.4735 0.682057 11 to 15 141907 -0.0079 0.496849 10 to 14 142477 1.9243 0.972842 9 to 13 142035 0.4260 0.664946 8 to 12 141743 -0.5638 0.286435 7 to 11 141973 0.2158 0.585440 6 to 10 142246 1.1413 0.873118 5 to 9 142373 1.5718 0.941997 4 to 8 142196 0.9718 0.834416 3 to 7 141865 -0.1503 0.440275 2 to 6 141742 -0.5672 0.285282 1 to 5 142454 1.8463 0.967579 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-29_22:31 Bits used No. missing words z-score p-value 31 to 32 141804 -0.3107 0.378011 30 to 31 141808 -0.2989 0.382505 29 to 30 142516 1.7896 0.963240 28 to 29 141217 -2.0423 0.020562 27 to 28 141698 -0.6234 0.266513 26 to 27 141687 -0.6558 0.255963 25 to 26 142771 2.5418 0.994486 24 to 25 141985 0.2232 0.588316 23 to 24 142115 0.6067 0.727974 22 to 23 141307 -1.7768 0.037802 21 to 22 141799 -0.3255 0.372418 20 to 21 141326 -1.7207 0.042649 19 to 20 141829 -0.2370 0.406343 18 to 19 142357 1.3206 0.906676 17 to 18 141851 -0.1721 0.431693 16 to 17 141807 -0.3019 0.381380 15 to 16 141711 -0.5850 0.279259 14 to 15 141785 -0.3668 0.356901 13 to 14 142491 1.7158 0.956904 12 to 13 141823 -0.2547 0.399493 11 to 12 141786 -0.3638 0.358002 10 to 11 142020 0.3265 0.627962 9 to 10 141881 -0.0836 0.466699 8 to 9 141913 0.0108 0.504319 7 to 8 141814 -0.2812 0.389275 6 to 7 141319 -1.7414 0.040808 5 to 6 142372 1.3648 0.913843 4 to 5 141083 -2.4376 0.007394 3 to 4 142354 1.3117 0.905191 2 to 3 142478 1.6775 0.953277 1 to 2 141808 -0.2989 0.382505 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-29_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2607.23 1.516 0.935297 Test results for specific bytes for dh-ranFile-2018-03-29_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2597.78 1.383 0.916636 2 to 9 2508.64 0.122 0.548622 3 to 10 2507.45 0.105 0.541981 4 to 11 2487.87 -0.172 0.431887 5 to 12 2536.29 0.513 0.696112 6 to 13 2316.34 -2.597 0.004697 7 to 14 2402.41 -1.380 0.083768 8 to 15 2489.22 -0.152 0.439434 9 to 16 2390.25 -1.552 0.060325 10 to 17 2462.09 -0.536 0.295932 11 to 18 2570.35 0.995 0.840115 12 to 19 2571.42 1.010 0.843772 13 to 20 2425.21 -1.058 0.145085 14 to 21 2501.24 0.018 0.507016 15 to 22 2440.48 -0.842 0.199951 16 to 23 2637.59 1.946 0.974162 17 to 24 2607.02 1.514 0.934924 18 to 25 2468.55 -0.445 0.328250 19 to 26 2427.29 -1.028 0.151909 20 to 27 2508.63 0.122 0.548556 21 to 28 2521.41 0.303 0.618951 22 to 29 2602.84 1.454 0.927074 23 to 30 2519.52 0.276 0.608755 24 to 31 2456.54 -0.615 0.269421 25 to 32 2489.97 -0.142 0.443593 CDPARK for dh-ranFile-2018-03-29_22:31: 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 3498 -1.1416 0.126820 3541 0.8219 0.794438 3542 0.8676 0.807188 3470 -2.4201 0.007758 3496 -1.2329 0.108811 3522 -0.0457 0.481790 3500 -1.0502 0.146807 3525 0.0913 0.536383 3504 -0.8676 0.192812 3561 1.7352 0.958644 Square side=100, avg. no. parked=3515.90 sample std.=25.85 p-value of the KSTEST for those 10 p-values: 0.357136 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-29_22:31 0.7215,0.5005,0.1510,0.1876,0.2531,0.9009,0.5969,0.0198,0.8039,0.5064, The KS test for those 10 p-values: 0.964593 The 3DSPHERES test for dh-ranFile-2018-03-29_22:31 sample no r^3 equiv. uni. 1 5.838 0.176838 2 33.624 0.673978 3 1.128 0.036904 4 35.462 0.693359 5 41.077 0.745694 6 11.927 0.328047 7 143.355 0.991591 8 12.820 0.347753 9 1.696 0.054974 10 8.992 0.258976 11 3.221 0.101792 12 7.880 0.231007 13 9.184 0.263721 14 16.268 0.418566 15 28.884 0.618175 16 18.458 0.459504 17 77.591 0.924707 18 80.266 0.931129 19 6.356 0.190936 20 74.197 0.915688 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.733023 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-29_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 2.0 1.1 2.4 0.5 0.4 2.0 1.4 0.4 0.8 1.7 0.0 0.8 -0.2 -0.7 1.0 -2.2 -0.2 -0.4 -0.2 0.2 -0.5 -1.3 -1.1 -0.7 0.4 -0.3 0.1 2.4 -2.0 -0.3 0.6 -1.2 2.3 0.6 0.3 -0.4 -0.4 1.0 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:54.323682 z-score=1.344624, p-value=0.903721 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-29_22:31 Test no p-value 1 0.453959 2 0.009419 3 0.111958 4 0.569489 5 0.318378 6 0.004237 7 0.001123 8 0.002159 9 0.127423 10 0.796822 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000105 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-29_22:31: (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 66487 0.48 66713 0.03 3 25000.00 25084 0.28 24971 0.03 4 6666.67 6787 2.17 6606 0.55 5 1388.89 1358 0.69 1439 1.81 6 238.10 240 0.02 236 0.02 7 34.72 38 0.31 30 0.64 8 4.96 5 0.00 4 0.19 p=0.31666 p=0.22596 Number of rngs required: 689459, p-value: 0.890 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-29_22:31 No. of wins: Observed Expected 98325 98585.9 z-score=-1.167, pvalue=0.12166 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66659 66666.7 0.001 0.001 2 38029 37654.3 3.728 3.729 3 26787 26954.7 1.044 4.773 4 19500 19313.5 1.802 6.575 5 13661 13851.4 2.618 9.192 6 9840 9943.5 1.078 10.271 7 7106 7145.0 0.213 10.484 8 5098 5139.1 0.328 10.812 9 3679 3699.9 0.118 10.930 10 2723 2666.3 1.206 12.135 11 1927 1923.3 0.007 12.142 12 1394 1388.7 0.020 12.162 13 958 1003.7 2.082 14.245 14 725 726.1 0.002 14.246 15 530 525.8 0.033 14.279 16 380 381.2 0.003 14.283 17 259 276.5 1.112 15.395 18 201 200.8 0.000 15.395 19 162 146.0 1.757 17.152 20 113 106.2 0.433 17.586 21 269 287.1 1.143 18.729 Chisq= 18.73 for 20 degrees of freedom, p= 0.46047 SUMMARY of craptest p-value for no. of wins: 0.121663 p-value for throws/game: 0.460474 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-29_22:31 No. of wins: Observed Expected 98811 98585.9 z-score= 1.007, pvalue=0.84302 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66802 66666.7 0.275 0.275 2 37462 37654.3 0.982 1.257 3 26975 26954.7 0.015 1.272 4 19300 19313.5 0.009 1.282 5 13827 13851.4 0.043 1.325 6 9831 9943.5 1.274 2.598 7 7265 7145.0 2.015 4.613 8 5130 5139.1 0.016 4.629 9 3694 3699.9 0.009 4.638 10 2649 2666.3 0.112 4.751 11 1955 1923.3 0.522 5.272 12 1472 1388.7 4.992 10.264 13 1025 1003.7 0.451 10.715 14 716 726.1 0.142 10.857 15 547 525.8 0.852 11.709 16 350 381.2 2.546 14.254 17 266 276.5 0.402 14.656 18 210 200.8 0.419 15.075 19 143 146.0 0.061 15.136 20 95 106.2 1.184 16.320 21 286 287.1 0.004 16.324 Chisq= 16.32 for 20 degrees of freedom, p= 0.30369 SUMMARY of craptest p-value for no. of wins: 0.843024 p-value for throws/game: 0.303692 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0011,0.0013,0.0022,0.0042,0.0047,0.0074,0.0078,0.0094,0.0096, 0.0144,0.0198,0.0206,0.0209,0.0288,0.0291,0.0319,0.0358,0.0369,0.0378, 0.0384,0.0393,0.0408,0.0426,0.0444,0.0496,0.0550,0.0603,0.0749,0.0754, 0.0837,0.0838,0.0861,0.0895,0.1018,0.1054,0.1077,0.1078,0.1088,0.1108, 0.1118,0.1120,0.1138,0.1169,0.1217,0.1267,0.1268,0.1274,0.1293,0.1294, 0.1451,0.1468,0.1470,0.1510,0.1519,0.1563,0.1634,0.1768,0.1790,0.1876, 0.1896,0.1909,0.1928,0.2000,0.2019,0.2125,0.2185,0.2197,0.2220,0.2260, 0.2310,0.2388,0.2510,0.2531,0.2550,0.2560,0.2579,0.2590,0.2590,0.2594, 0.2637,0.2659,0.2665,0.2694,0.2793,0.2853,0.2864,0.2868,0.2953,0.2959, 0.2989,0.2996,0.2997,0.3037,0.3069,0.3075,0.3167,0.3184,0.3184,0.3256, 0.3280,0.3283,0.3296,0.3369,0.3385,0.3478,0.3569,0.3571,0.3580,0.3666, 0.3724,0.3780,0.3814,0.3822,0.3825,0.3825,0.3893,0.3953,0.3987,0.3995, 0.4063,0.4073,0.4177,0.4186,0.4230,0.4317,0.4317,0.4319,0.4322,0.4376, 0.4394,0.4403,0.4436,0.4461,0.4508,0.4513,0.4524,0.4540,0.4595,0.4605, 0.4667,0.4818,0.4887,0.4932,0.4968,0.5005,0.5043,0.5064,0.5070,0.5111, 0.5155,0.5160,0.5252,0.5321,0.5343,0.5364,0.5420,0.5421,0.5446,0.5468, 0.5469,0.5486,0.5486,0.5695,0.5739,0.5746,0.5854,0.5883,0.5889,0.5898, 0.5933,0.5969,0.6025,0.6088,0.6112,0.6182,0.6190,0.6230,0.6280,0.6293, 0.6610,0.6649,0.6663,0.6699,0.6717,0.6740,0.6790,0.6811,0.6820,0.6821, 0.6874,0.6887,0.6905,0.6934,0.6961,0.6982,0.7214,0.7215,0.7280,0.7330, 0.7331,0.7404,0.7457,0.7545,0.7566,0.7586,0.7654,0.7664,0.7748,0.7944, 0.7968,0.8037,0.8039,0.8070,0.8072,0.8139,0.8148,0.8225,0.8248,0.8302, 0.8317,0.8344,0.8401,0.8430,0.8438,0.8482,0.8713,0.8731,0.8845,0.8902, 0.8932,0.8974,0.9009,0.9037,0.9052,0.9067,0.9099,0.9132,0.9138,0.9157, 0.9166,0.9191,0.9247,0.9271,0.9311,0.9349,0.9353,0.9400,0.9420,0.9466, 0.9513,0.9515,0.9533,0.9569,0.9586,0.9620,0.9632,0.9646,0.9676,0.9705, 0.9728,0.9742,0.9785,0.9805,0.9915,0.9916,0.9919,0.9945,0.9995, Overall p-value after applying KStest on 269 p-values = 0.055839 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.