RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-26_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 15.59 29.1710 0.967019 2 to 25 15.82 17.7229 0.593479 3 to 26 15.48 30.8230 0.979015 4 to 27 15.92 15.2828 0.424882 5 to 28 15.98 22.8352 0.845308 6 to 29 15.67 16.7010 0.525207 7 to 30 15.83 27.3019 0.946214 8 to 31 15.58 13.3512 0.287626 9 to 32 15.72 16.5390 0.514005 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.066846 Tough bday spacings test for dh-ranFile-2016-04-26_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 14 42 63 93 100 69 58 26 19 10 6 (O-E)^2/E 2.6 0.8 1.4 0.2 0.1 1.1 0.7 0.5 1.1 1.7 0.9 Birthday Spacings: Sum(O-E)^2/E= 11.070, p= 0.648 RESULTS OF GCD FOR dh-ranFile-2016-04-26_02:31 Euclid's algorithm: p-value, steps to gcd: 0.107452 p-value, dist. of gcd's: 0.410932 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-26_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.267 0.352 0.317 0.824 0.960 0.921 0.527 0.220 Bits 8 to 15---> 0.915 0.121 0.222 0.780 0.236 0.157 0.418 0.889 Bits 16 to 23---> 0.721 0.811 0.279 0.984 0.583 0.168 0.453 0.120 Bits 24 to 31---> 0.148 0.283 0.592 0.782 0.586 0.738 0.886 0.749 KS test for the above 32 p values: 0.389 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-26_02:31, p-values for 5 runs: 0.1849, 0.6949, 0.3460, 0.4543, 0.4349 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-26_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5082 5134.0 0.527 0.558 r= 30 23116 23103.0 0.007 0.566 r= 31 11588 11551.5 0.115 0.681 chi-square = 0.681 with df = 3; p-value = 0.122 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-26_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5187 5134.0 0.547 0.646 r= 31 23015 23103.0 0.336 0.982 r= 32 11582 11551.5 0.080 1.062 chi-square = 1.062 with df = 3; p-value = 0.214 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-26_02:31 b-rank test for bits 1 to 8, p=0.18836 b-rank test for bits 2 to 9, p=0.07180 b-rank test for bits 3 to 10, p=0.17650 b-rank test for bits 4 to 11, p=0.41820 b-rank test for bits 5 to 12, p=0.39534 b-rank test for bits 6 to 13, p=0.47346 b-rank test for bits 7 to 14, p=0.61455 b-rank test for bits 8 to 15, p=0.10944 b-rank test for bits 9 to 16, p=0.89671 b-rank test for bits 10 to 17, p=0.42980 b-rank test for bits 11 to 18, p=0.51471 b-rank test for bits 12 to 19, p=0.23689 b-rank test for bits 13 to 20, p=0.46946 b-rank test for bits 14 to 21, p=0.97239 b-rank test for bits 15 to 22, p=0.90353 b-rank test for bits 16 to 23, p=0.88201 b-rank test for bits 17 to 24, p=0.52996 b-rank test for bits 18 to 25, p=0.31718 b-rank test for bits 19 to 26, p=0.87691 b-rank test for bits 20 to 27, p=0.37329 b-rank test for bits 21 to 28, p=0.48778 b-rank test for bits 22 to 29, p=0.63450 b-rank test for bits 23 to 30, p=0.65470 b-rank test for bits 24 to 31, p=0.79434 b-rank test for bits 25 to 32, p=0.75584 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 = 0.774547 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-26_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 141835 -0.17 0.431063 2 142224 0.74 0.768894 3 142124 0.50 0.692013 4 141648 -0.61 0.270738 5 141943 0.08 0.531352 6 142030 0.28 0.611005 7 142029 0.28 0.610109 8 142551 1.50 0.933093 9 141927 0.04 0.516466 10 142317 0.95 0.829578 11 142004 0.22 0.587528 12 141895 -0.03 0.486645 13 142774 2.02 0.978322 14 141365 -1.27 0.101722 15 141490 -0.98 0.163607 16 142007 0.23 0.590255 17 141893 -0.04 0.484782 18 141883 -0.06 0.475473 19 142103 0.45 0.674546 20 141828 -0.19 0.424645 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-26_02:31 Bits used No. missing words z-score p-value 23 to 32 141795 -0.3942 0.346701 22 to 31 142425 1.7782 0.962312 21 to 30 141662 -0.8529 0.196868 20 to 29 141855 -0.1873 0.425695 19 to 28 142332 1.4575 0.927508 18 to 27 141870 -0.1356 0.446061 17 to 26 141657 -0.8701 0.192122 16 to 25 142087 0.6127 0.729948 15 to 24 141434 -1.6391 0.050599 14 to 23 141928 0.0644 0.525666 13 to 22 142052 0.4920 0.688628 12 to 21 141893 -0.0563 0.477547 11 to 20 141838 -0.2460 0.402855 10 to 19 142196 0.9885 0.838550 9 to 18 142086 0.6092 0.728806 8 to 17 141801 -0.3736 0.354369 7 to 16 141562 -1.1977 0.115519 6 to 15 142111 0.6954 0.756602 5 to 14 142387 1.6471 0.950235 4 to 13 141912 0.0092 0.503673 3 to 12 141728 -0.6253 0.265895 2 to 11 142224 1.0851 0.861054 1 to 10 141504 -1.3977 0.081103 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-26_02:31 Bits used No. missing words z-score p-value 28 to 32 141803 -0.3604 0.359259 27 to 31 141324 -1.9842 0.023618 26 to 30 141884 -0.0859 0.465787 25 to 29 141807 -0.3469 0.364340 24 to 28 141794 -0.3909 0.347917 23 to 27 141881 -0.0960 0.461747 22 to 26 141361 -1.8587 0.031532 21 to 25 141817 -0.3130 0.377147 20 to 24 142099 0.6429 0.739872 19 to 23 142328 1.4192 0.922083 18 to 22 141875 -0.1164 0.453679 17 to 21 141891 -0.0621 0.475227 16 to 20 141968 0.1989 0.578822 15 to 19 141970 0.2057 0.581472 14 to 18 142027 0.3989 0.655010 13 to 17 142098 0.6396 0.738770 12 to 16 142035 0.4260 0.664946 11 to 15 141719 -0.6452 0.259403 10 to 14 141762 -0.4994 0.308741 9 to 13 142481 1.9379 0.973680 8 to 12 142112 0.6870 0.753964 7 to 11 142268 1.2158 0.887975 6 to 10 142063 0.5209 0.698787 5 to 9 142105 0.6633 0.746427 4 to 8 142407 1.6870 0.954200 3 to 7 141598 -1.0554 0.145631 2 to 6 141651 -0.8757 0.190598 1 to 5 141714 -0.6621 0.253942 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-26_02:31 Bits used No. missing words z-score p-value 31 to 32 141781 -0.3786 0.352509 30 to 31 142329 1.2380 0.892135 29 to 30 142260 1.0344 0.849531 28 to 29 141967 0.1701 0.567541 27 to 28 142709 2.3589 0.990836 26 to 27 142450 1.5949 0.944632 25 to 26 141938 0.0846 0.533699 24 to 25 142166 0.7571 0.775517 23 to 24 141857 -0.1544 0.438661 22 to 23 142688 2.2970 0.989190 21 to 22 141964 0.1613 0.564059 20 to 21 141787 -0.3609 0.359104 19 to 20 142074 0.4858 0.686429 18 to 19 141964 0.1613 0.564059 17 to 18 142204 0.8692 0.807640 16 to 17 142015 0.3117 0.622370 15 to 16 141679 -0.6794 0.248430 14 to 15 142088 0.5271 0.700921 13 to 14 142066 0.4622 0.678014 12 to 13 142727 2.4120 0.992067 11 to 12 141868 -0.1219 0.451482 10 to 11 141699 -0.6204 0.267483 9 to 10 141869 -0.1190 0.452651 8 to 9 141256 -1.9272 0.026976 7 to 8 141411 -1.4700 0.070781 6 to 7 142475 1.6686 0.952406 5 to 6 141419 -1.4464 0.074032 4 to 5 142183 0.8073 0.790249 3 to 4 142156 0.7276 0.766583 2 to 3 142237 0.9666 0.833123 1 to 2 141619 -0.8564 0.195880 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-26_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2396.56 -1.463 0.071754 Test results for specific bytes for dh-ranFile-2016-04-26_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2598.35 1.391 0.917875 2 to 9 2493.26 -0.095 0.462045 3 to 10 2540.41 0.572 0.716181 4 to 11 2490.47 -0.135 0.446418 5 to 12 2614.87 1.625 0.947869 6 to 13 2452.92 -0.666 0.252749 7 to 14 2396.41 -1.465 0.071459 8 to 15 2462.24 -0.534 0.296645 9 to 16 2461.06 -0.551 0.290906 10 to 17 2430.97 -0.976 0.164471 11 to 18 2494.00 -0.085 0.466200 12 to 19 2502.65 0.037 0.514955 13 to 20 2429.82 -0.993 0.160474 14 to 21 2630.15 1.841 0.967158 15 to 22 2476.28 -0.335 0.368648 16 to 23 2490.09 -0.140 0.444279 17 to 24 2496.17 -0.054 0.478393 18 to 25 2540.15 0.568 0.714923 19 to 26 2410.61 -1.264 0.103091 20 to 27 2479.09 -0.296 0.383703 21 to 28 2500.20 0.003 0.501124 22 to 29 2493.09 -0.098 0.461093 23 to 30 2410.21 -1.270 0.102064 24 to 31 2480.24 -0.279 0.389972 25 to 32 2454.11 -0.649 0.258154 CDPARK for dh-ranFile-2016-04-26_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 3502 -0.9589 0.168804 3523 0.0000 0.500000 3543 0.9132 0.819442 3533 0.4566 0.676028 3504 -0.8676 0.192812 3538 0.6849 0.753306 3511 -0.5479 0.291865 3512 -0.5023 0.307734 3563 1.8265 0.966111 3551 1.2785 0.899470 Square side=100, avg. no. parked=3528.00 sample std.=19.81 p-value of the KSTEST for those 10 p-values: 0.817681 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-26_02:31 0.8465,0.5439,0.9622,0.1278,0.4516,0.0947,0.6904,0.1651,0.2491,0.9929, The KS test for those 10 p-values: 0.657094 The 3DSPHERES test for dh-ranFile-2016-04-26_02:31 sample no r^3 equiv. uni. 1 0.703 0.023171 2 16.316 0.419502 3 86.088 0.943278 4 1.554 0.050495 5 28.028 0.607128 6 16.100 0.415309 7 24.673 0.560643 8 82.947 0.937017 9 16.216 0.417571 10 15.991 0.413174 11 0.115 0.003825 12 59.949 0.864433 13 3.601 0.113118 14 11.308 0.314035 15 21.906 0.518186 16 4.925 0.151396 17 1.160 0.037922 18 22.638 0.529800 19 62.497 0.875473 20 6.957 0.206979 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.209853 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-26_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.5 0.8 0.2 0.4 0.1 -0.8 1.5 -0.7 -0.6 -0.5 -0.7 0.6 0.5 -0.6 0.7 -0.9 0.4 -1.7 -0.6 0.3 -0.6 1.7 0.2 -0.2 1.8 0.8 0.0 1.1 0.8 -0.7 -1.6 0.9 0.1 -1.5 -1.0 2.4 0.8 0.5 1.5 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:40.940333 z-score=-0.115619, p-value=0.482599 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-26_02:31 Test no p-value 1 0.806005 2 0.010145 3 0.017542 4 0.837520 5 0.862845 6 0.025377 7 0.015084 8 0.007650 9 0.727735 10 0.464437 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001850 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-26_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 66471 0.57 66426 0.87 3 25000.00 25177 1.25 25168 1.13 4 6666.67 6688 0.07 6702 0.19 5 1388.89 1344 1.45 1403 0.14 6 238.10 276 6.03 269 4.01 7 34.72 39 0.53 25 2.72 8 4.96 4 0.19 6 0.22 p=0.87927 p=0.84152 Number of rngs required: 688988, p-value: 0.750 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-26_02:31 No. of wins: Observed Expected 99074 98585.9 z-score= 2.183, pvalue=0.98549 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67126 66666.7 3.165 3.165 2 37725 37654.3 0.133 3.297 3 26761 26954.7 1.392 4.690 4 19354 19313.5 0.085 4.775 5 13758 13851.4 0.630 5.405 6 9826 9943.5 1.389 6.795 7 7068 7145.0 0.830 7.625 8 5072 5139.1 0.875 8.500 9 3577 3699.9 4.080 12.580 10 2691 2666.3 0.229 12.809 11 1977 1923.3 1.498 14.307 12 1418 1388.7 0.616 14.923 13 1039 1003.7 1.240 16.164 14 740 726.1 0.265 16.428 15 467 525.8 6.583 23.012 16 389 381.2 0.162 23.173 17 273 276.5 0.045 23.218 18 219 200.8 1.644 24.862 19 157 146.0 0.831 25.694 20 97 106.2 0.800 26.493 21 266 287.1 1.553 28.046 Chisq= 28.05 for 20 degrees of freedom, p= 0.89168 SUMMARY of craptest p-value for no. of wins: 0.985491 p-value for throws/game: 0.891681 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-26_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 66488 66666.7 0.479 0.479 2 37610 37654.3 0.052 0.531 3 27063 26954.7 0.435 0.966 4 19526 19313.5 2.339 3.305 5 13783 13851.4 0.338 3.643 6 9939 9943.5 0.002 3.645 7 7103 7145.0 0.247 3.892 8 5212 5139.1 1.035 4.927 9 3678 3699.9 0.129 5.056 10 2651 2666.3 0.088 5.144 11 1888 1923.3 0.649 5.793 12 1384 1388.7 0.016 5.809 13 1013 1003.7 0.086 5.895 14 769 726.1 2.530 8.425 15 526 525.8 0.000 8.425 16 380 381.2 0.003 8.428 17 249 276.5 2.743 11.171 18 199 200.8 0.017 11.187 19 150 146.0 0.110 11.298 20 123 106.2 2.652 13.950 21 266 287.1 1.553 15.503 Chisq= 15.50 for 20 degrees of freedom, p= 0.25306 SUMMARY of craptest p-value for no. of wins: 0.360481 p-value for throws/game: 0.253058 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0019,0.0038,0.0076,0.0101,0.0151,0.0175,0.0232,0.0236,0.0254,0.0270, 0.0315,0.0379,0.0505,0.0506,0.0668,0.0708,0.0715,0.0718,0.0718,0.0740, 0.0811,0.0947,0.1017,0.1021,0.1031,0.1075,0.1094,0.1131,0.1155,0.1205, 0.1205,0.1223,0.1278,0.1456,0.1479,0.1514,0.1573,0.1605,0.1636,0.1645, 0.1651,0.1678,0.1688,0.1765,0.1849,0.1884,0.1906,0.1921,0.1928,0.1959, 0.1969,0.2070,0.2099,0.2138,0.2198,0.2221,0.2362,0.2369,0.2484,0.2491, 0.2527,0.2531,0.2539,0.2582,0.2594,0.2659,0.2668,0.2675,0.2707,0.2794, 0.2828,0.2876,0.2909,0.2919,0.2966,0.3077,0.3087,0.3140,0.3171,0.3172, 0.3460,0.3467,0.3479,0.3519,0.3525,0.3544,0.3591,0.3593,0.3605,0.3643, 0.3686,0.3733,0.3771,0.3837,0.3886,0.3900,0.3953,0.4029,0.4109,0.4132, 0.4153,0.4176,0.4182,0.4182,0.4195,0.4246,0.4249,0.4257,0.4298,0.4311, 0.4349,0.4387,0.4443,0.4461,0.4464,0.4515,0.4516,0.4527,0.4529,0.4537, 0.4543,0.4611,0.4617,0.4620,0.4644,0.4658,0.4662,0.4695,0.4735,0.4752, 0.4755,0.4775,0.4784,0.4826,0.4848,0.4866,0.4878,0.5000,0.5011,0.5037, 0.5140,0.5147,0.5150,0.5165,0.5182,0.5252,0.5257,0.5269,0.5298,0.5300, 0.5314,0.5337,0.5439,0.5606,0.5641,0.5641,0.5675,0.5788,0.5815,0.5826, 0.5856,0.5875,0.5903,0.5919,0.5935,0.6071,0.6101,0.6110,0.6146,0.6224, 0.6345,0.6479,0.6547,0.6550,0.6571,0.6649,0.6745,0.6760,0.6780,0.6864, 0.6886,0.6904,0.6920,0.6949,0.6988,0.7009,0.7149,0.7162,0.7215,0.7277, 0.7288,0.7299,0.7378,0.7388,0.7399,0.7464,0.7487,0.7502,0.7533,0.7540, 0.7558,0.7566,0.7666,0.7689,0.7745,0.7755,0.7799,0.7825,0.7902,0.7943, 0.8060,0.8076,0.8105,0.8177,0.8194,0.8245,0.8296,0.8331,0.8375,0.8386, 0.8415,0.8453,0.8465,0.8495,0.8611,0.8628,0.8644,0.8755,0.8769,0.8793, 0.8820,0.8858,0.8880,0.8887,0.8917,0.8921,0.8967,0.8995,0.9035,0.9147, 0.9179,0.9212,0.9221,0.9275,0.9331,0.9370,0.9433,0.9446,0.9462,0.9479, 0.9502,0.9524,0.9542,0.9596,0.9622,0.9623,0.9661,0.9670,0.9672,0.9724, 0.9737,0.9783,0.9790,0.9838,0.9855,0.9892,0.9908,0.9921,0.9929, Overall p-value after applying KStest on 269 p-values = 0.562298 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.