RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-01_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.58 18.5323 0.643970 2 to 25 15.69 18.0083 0.611680 3 to 26 16.08 21.0317 0.775124 4 to 27 16.03 10.2182 0.105791 5 to 28 16.14 14.0236 0.334568 6 to 29 15.69 15.1098 0.412429 7 to 30 15.60 17.3466 0.568866 8 to 31 15.43 23.5034 0.866431 9 to 32 15.49 35.5050 0.994663 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.551313 Tough bday spacings test for dh-ranFile-2017-02-01_06:31: 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 8 36 89 101 87 75 54 27 13 8 2 (O-E)^2/E 0.1 0.0 3.4 0.1 1.2 0.1 0.1 0.3 0.2 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 6.851, p= 0.261 RESULTS OF GCD FOR dh-ranFile-2017-02-01_06:31 Euclid's algorithm: p-value, steps to gcd: 0.595316 p-value, dist. of gcd's: 0.301749 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-01_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.273 0.390 0.137 0.358 0.834 0.293 0.105 0.191 Bits 8 to 15---> 0.255 0.833 0.678 0.341 0.118 0.262 0.455 0.282 Bits 16 to 23---> 0.049 0.611 0.161 0.965 0.443 0.594 0.892 0.702 Bits 24 to 31---> 0.914 0.845 0.259 0.584 0.938 0.918 0.974 0.629 KS test for the above 32 p values: 0.214 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-01_06:31, p-values for 5 runs: 0.1405, 0.4394, 0.7935, 0.9263, 0.4301 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-01_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5059 5134.0 1.096 1.825 r= 30 23177 23103.0 0.237 2.062 r= 31 11565 11551.5 0.016 2.078 chi-square = 2.078 with df = 3; p-value = 0.444 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-01_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5201 5134.0 0.874 1.134 r= 31 23222 23103.0 0.612 1.747 r= 32 11373 11551.5 2.759 4.506 chi-square = 4.506 with df = 3; p-value = 0.788 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-01_06:31 b-rank test for bits 1 to 8, p=0.71092 b-rank test for bits 2 to 9, p=0.76311 b-rank test for bits 3 to 10, p=0.79302 b-rank test for bits 4 to 11, p=0.53525 b-rank test for bits 5 to 12, p=0.91885 b-rank test for bits 6 to 13, p=0.61525 b-rank test for bits 7 to 14, p=0.62930 b-rank test for bits 8 to 15, p=0.44316 b-rank test for bits 9 to 16, p=0.44342 b-rank test for bits 10 to 17, p=0.81089 b-rank test for bits 11 to 18, p=0.02737 b-rank test for bits 12 to 19, p=0.45208 b-rank test for bits 13 to 20, p=0.94680 b-rank test for bits 14 to 21, p=0.95386 b-rank test for bits 15 to 22, p=0.24663 b-rank test for bits 16 to 23, p=0.28990 b-rank test for bits 17 to 24, p=0.18618 b-rank test for bits 18 to 25, p=0.13030 b-rank test for bits 19 to 26, p=0.52590 b-rank test for bits 20 to 27, p=0.92783 b-rank test for bits 21 to 28, p=0.68652 b-rank test for bits 22 to 29, p=0.40466 b-rank test for bits 23 to 30, p=0.77514 b-rank test for bits 24 to 31, p=0.56235 b-rank test for bits 25 to 32, p=0.19422 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 = 0.548966 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-01_06:31 (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 141074 -1.95 0.025487 2 142092 0.43 0.665237 3 141348 -1.31 0.094841 4 141695 -0.50 0.308266 5 141953 0.10 0.540635 6 141307 -1.41 0.079667 7 141373 -1.25 0.105083 8 142030 0.28 0.611005 9 142049 0.33 0.627913 10 141821 -0.21 0.418248 11 141522 -0.90 0.182739 12 142346 1.02 0.846197 13 141827 -0.19 0.423730 14 143303 3.26 0.999436 15 142630 1.68 0.953891 16 142211 0.70 0.759544 17 141745 -0.38 0.350508 18 141953 0.10 0.540635 19 142362 1.06 0.854890 20 142658 1.75 0.959874 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-01_06:31 Bits used No. missing words z-score p-value 23 to 32 141667 -0.8356 0.201684 22 to 31 142060 0.5196 0.698312 21 to 30 141364 -1.8804 0.030024 20 to 29 141824 -0.2942 0.384287 19 to 28 141757 -0.5253 0.299696 18 to 27 141780 -0.4460 0.327811 17 to 26 142227 1.0954 0.863332 16 to 25 141787 -0.4218 0.336575 15 to 24 141837 -0.2494 0.401520 14 to 23 142118 0.7196 0.764100 13 to 22 141498 -1.4184 0.078040 12 to 21 142074 0.5678 0.714924 11 to 20 142269 1.2402 0.892557 10 to 19 142171 0.9023 0.816554 9 to 18 141601 -1.0632 0.143844 8 to 17 142022 0.3885 0.651183 7 to 16 141974 0.2230 0.588232 6 to 15 141817 -0.3184 0.375099 5 to 14 141574 -1.1563 0.123777 4 to 13 141845 -0.2218 0.412224 3 to 12 141637 -0.9391 0.173848 2 to 11 141789 -0.4149 0.339096 1 to 10 141863 -0.1598 0.436536 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-01_06:31 Bits used No. missing words z-score p-value 28 to 32 142186 0.9379 0.825843 27 to 31 142093 0.6226 0.733230 26 to 30 141818 -0.3096 0.378435 25 to 29 141539 -1.2554 0.104675 24 to 28 141851 -0.1977 0.421629 23 to 27 142064 0.5243 0.699967 22 to 26 141932 0.0768 0.530628 21 to 25 142029 0.4057 0.657504 20 to 24 141998 0.3006 0.618131 19 to 23 141666 -0.8248 0.204729 18 to 22 141418 -1.6655 0.047904 17 to 21 141866 -0.1469 0.441613 16 to 20 142124 0.7277 0.766600 15 to 19 141611 -1.0113 0.155939 14 to 18 142206 1.0057 0.842711 13 to 17 142290 1.2904 0.901545 12 to 16 141336 -1.9435 0.025978 11 to 15 141621 -0.9774 0.164188 10 to 14 142337 1.4497 0.926433 9 to 13 141844 -0.2215 0.412368 8 to 12 142538 2.1311 0.983459 7 to 11 141850 -0.2011 0.420303 6 to 10 141120 -2.6757 0.003729 5 to 9 141839 -0.2384 0.405783 4 to 8 141983 0.2497 0.598602 3 to 7 141889 -0.0689 0.472529 2 to 6 141991 0.2768 0.609051 1 to 5 142081 0.5819 0.719694 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-01_06:31 Bits used No. missing words z-score p-value 31 to 32 141749 -0.4729 0.318125 30 to 31 141847 -0.1839 0.427060 29 to 30 142036 0.3737 0.645671 28 to 29 141906 -0.0098 0.496081 27 to 28 141705 -0.6027 0.273340 26 to 27 141794 -0.3402 0.366851 25 to 26 142463 1.6332 0.948791 24 to 25 141652 -0.7591 0.223901 23 to 24 141883 -0.0777 0.469045 22 to 23 141742 -0.4936 0.310795 21 to 22 140854 -3.1131 0.000926 20 to 21 141829 -0.2370 0.406343 19 to 20 142003 0.2763 0.608846 18 to 19 142306 1.1701 0.879023 17 to 18 141420 -1.4435 0.074447 16 to 17 141865 -0.1308 0.447980 15 to 16 141667 -0.7148 0.237355 14 to 15 141114 -2.3461 0.009485 13 to 14 141915 0.0167 0.506672 12 to 13 141939 0.0875 0.534872 11 to 12 141499 -1.2104 0.113060 10 to 11 141652 -0.7591 0.223901 9 to 10 142097 0.5536 0.710073 8 to 9 141682 -0.6706 0.251241 7 to 8 141679 -0.6794 0.248430 6 to 7 141326 -1.7207 0.042649 5 to 6 141352 -1.6440 0.050084 4 to 5 142122 0.6273 0.734784 3 to 4 141940 0.0905 0.536044 2 to 3 141917 0.0226 0.509025 1 to 2 142581 1.9813 0.976223 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-01_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2482.82 -0.243 0.404027 Test results for specific bytes for dh-ranFile-2017-02-01_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2614.50 1.619 0.947299 2 to 9 2431.79 -0.965 0.167355 3 to 10 2528.15 0.398 0.654705 4 to 11 2503.55 0.050 0.520000 5 to 12 2421.95 -1.104 0.134837 6 to 13 2554.98 0.778 0.781581 7 to 14 2508.79 0.124 0.549454 8 to 15 2463.15 -0.521 0.301144 9 to 16 2401.92 -1.387 0.082704 10 to 17 2476.14 -0.337 0.367886 11 to 18 2465.66 -0.486 0.313603 12 to 19 2490.45 -0.135 0.446302 13 to 20 2610.77 1.566 0.941381 14 to 21 2416.77 -1.177 0.119584 15 to 22 2506.17 0.087 0.534794 16 to 23 2391.04 -1.541 0.061661 17 to 24 2330.47 -2.397 0.008254 18 to 25 2345.81 -2.181 0.014609 19 to 26 2595.51 1.351 0.911602 20 to 27 2356.48 -2.030 0.021192 21 to 28 2534.07 0.482 0.685012 22 to 29 2523.25 0.329 0.628856 23 to 30 2605.37 1.490 0.931906 24 to 31 2466.45 -0.474 0.317597 25 to 32 2479.44 -0.291 0.385593 CDPARK for dh-ranFile-2017-02-01_06:31: 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 3519 -0.1826 0.427537 3543 0.9132 0.819442 3538 0.6849 0.753306 3533 0.4566 0.676028 3516 -0.3196 0.374623 3496 -1.2329 0.108811 3524 0.0457 0.518210 3536 0.5936 0.723613 3498 -1.1416 0.126820 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3520.50 sample std.=16.41 p-value of the KSTEST for those 10 p-values: 0.857693 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-01_06:31 0.0309,0.6699,0.2537,0.8345,0.1900,0.5974,0.3612,0.6889,0.1813,0.7157, The KS test for those 10 p-values: 0.797446 The 3DSPHERES test for dh-ranFile-2017-02-01_06:31 sample no r^3 equiv. uni. 1 33.558 0.673263 2 58.247 0.856522 3 63.148 0.878148 4 21.050 0.504246 5 31.105 0.645419 6 6.465 0.193867 7 32.304 0.659322 8 1.038 0.034019 9 139.278 0.990368 10 67.873 0.895903 11 48.787 0.803333 12 32.054 0.656470 13 2.629 0.083912 14 16.903 0.430750 15 5.361 0.163636 16 32.302 0.659293 17 21.844 0.517197 18 1.777 0.057515 19 82.516 0.936106 20 36.274 0.701542 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.365361 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-01_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.6 0.3 0.6 -0.2 -0.8 0.8 -0.2 1.5 -0.8 -0.1 -0.1 0.4 0.7 0.1 -1.1 0.8 1.5 0.4 -0.3 -0.7 -2.8 -0.3 0.6 -0.4 1.8 0.0 0.6 -0.5 -1.1 -0.2 -1.1 0.5 -0.3 0.6 1.0 -0.9 0.2 0.1 -1.3 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:33.609612 z-score=-0.915466, p-value=0.181256 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-01_06:31 Test no p-value 1 0.742984 2 0.137138 3 0.714342 4 0.080108 5 0.519487 6 0.006578 7 0.458009 8 0.000209 9 0.253774 10 0.260701 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.024822 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-01_06:31: (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 66663 0.00 66704 0.02 3 25000.00 25084 0.28 25031 0.04 4 6666.67 6618 0.36 6580 1.13 5 1388.89 1364 0.45 1414 0.45 6 238.10 236 0.02 227 0.52 7 34.72 32 0.21 36 0.05 8 4.96 2 1.77 7 0.84 p=0.20149 p=0.19661 Number of rngs required: 687202, p-value: 0.081 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-01_06:31 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 66725 66666.7 0.051 0.051 2 37475 37654.3 0.854 0.905 3 26897 26954.7 0.124 1.029 4 19381 19313.5 0.236 1.265 5 13963 13851.4 0.899 2.164 6 9980 9943.5 0.134 2.297 7 7225 7145.0 0.895 3.193 8 5109 5139.1 0.176 3.368 9 3720 3699.9 0.110 3.478 10 2619 2666.3 0.839 4.317 11 1898 1923.3 0.334 4.651 12 1382 1388.7 0.033 4.683 13 980 1003.7 0.560 5.244 14 703 726.1 0.737 5.981 15 576 525.8 4.786 10.767 16 378 381.2 0.026 10.793 17 256 276.5 1.526 12.318 18 214 200.8 0.864 13.182 19 141 146.0 0.170 13.352 20 102 106.2 0.167 13.519 21 276 287.1 0.430 13.950 Chisq= 13.95 for 20 degrees of freedom, p= 0.16696 SUMMARY of craptest p-value for no. of wins: 0.299051 p-value for throws/game: 0.166960 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-01_06:31 No. of wins: Observed Expected 98407 98585.9 z-score=-0.800, pvalue=0.21187 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66239 66666.7 2.743 2.743 2 37712 37654.3 0.088 2.832 3 27113 26954.7 0.929 3.761 4 19436 19313.5 0.777 4.539 5 13818 13851.4 0.081 4.619 6 9946 9943.5 0.001 4.620 7 7201 7145.0 0.439 5.058 8 5174 5139.1 0.237 5.296 9 3680 3699.9 0.107 5.402 10 2637 2666.3 0.322 5.724 11 2006 1923.3 3.553 9.278 12 1425 1388.7 0.947 10.224 13 1018 1003.7 0.203 10.428 14 704 726.1 0.675 11.103 15 477 525.8 4.536 15.638 16 381 381.2 0.000 15.638 17 292 276.5 0.864 16.503 18 195 200.8 0.169 16.672 19 151 146.0 0.172 16.844 20 101 106.2 0.256 17.100 21 294 287.1 0.165 17.266 Chisq= 17.27 for 20 degrees of freedom, p= 0.36433 SUMMARY of craptest p-value for no. of wins: 0.211867 p-value for throws/game: 0.364334 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0009,0.0037,0.0066,0.0083,0.0095,0.0146,0.0212,0.0248,0.0255, 0.0260,0.0274,0.0300,0.0309,0.0340,0.0426,0.0479,0.0492,0.0501,0.0575, 0.0617,0.0744,0.0780,0.0797,0.0801,0.0807,0.0827,0.0839,0.0948,0.1045, 0.1047,0.1051,0.1058,0.1088,0.1131,0.1180,0.1196,0.1238,0.1268,0.1303, 0.1348,0.1371,0.1374,0.1405,0.1438,0.1559,0.1607,0.1636,0.1642,0.1670, 0.1674,0.1688,0.1738,0.1813,0.1813,0.1827,0.1862,0.1900,0.1905,0.1939, 0.1942,0.1966,0.2015,0.2017,0.2047,0.2119,0.2138,0.2239,0.2239,0.2374, 0.2466,0.2484,0.2512,0.2537,0.2538,0.2552,0.2590,0.2606,0.2607,0.2619, 0.2731,0.2733,0.2825,0.2899,0.2929,0.2991,0.2997,0.3011,0.3017,0.3083, 0.3108,0.3136,0.3176,0.3181,0.3278,0.3346,0.3366,0.3391,0.3406,0.3505, 0.3584,0.3612,0.3643,0.3654,0.3669,0.3679,0.3746,0.3751,0.3784,0.3843, 0.3856,0.3895,0.4015,0.4040,0.4047,0.4058,0.4063,0.4122,0.4124,0.4124, 0.4182,0.4203,0.4216,0.4237,0.4271,0.4275,0.4301,0.4308,0.4365,0.4394, 0.4416,0.4427,0.4432,0.4434,0.4436,0.4463,0.4480,0.4521,0.4546,0.4580, 0.4690,0.4725,0.4961,0.5042,0.5067,0.5090,0.5172,0.5182,0.5195,0.5200, 0.5259,0.5306,0.5348,0.5349,0.5352,0.5360,0.5406,0.5406,0.5490,0.5495, 0.5513,0.5623,0.5689,0.5839,0.5882,0.5942,0.5953,0.5974,0.5986,0.6088, 0.6091,0.6110,0.6113,0.6117,0.6153,0.6181,0.6279,0.6287,0.6289,0.6293, 0.6440,0.6454,0.6457,0.6512,0.6547,0.6565,0.6575,0.6593,0.6593,0.6652, 0.6699,0.6733,0.6760,0.6779,0.6850,0.6865,0.6889,0.6983,0.7000,0.7015, 0.7023,0.7101,0.7109,0.7143,0.7149,0.7157,0.7197,0.7236,0.7332,0.7348, 0.7430,0.7533,0.7595,0.7631,0.7641,0.7666,0.7751,0.7751,0.7816,0.7882, 0.7930,0.7935,0.7974,0.8033,0.8109,0.8166,0.8194,0.8258,0.8334,0.8338, 0.8345,0.8427,0.8455,0.8462,0.8549,0.8565,0.8577,0.8633,0.8664,0.8781, 0.8790,0.8916,0.8926,0.8959,0.9015,0.9116,0.9135,0.9182,0.9189,0.9263, 0.9264,0.9278,0.9319,0.9361,0.9377,0.9414,0.9468,0.9473,0.9488,0.9539, 0.9539,0.9599,0.9652,0.9742,0.9762,0.9835,0.9904,0.9947,0.9994, Overall p-value after applying KStest on 269 p-values = 0.277569 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.