RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-30_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 44.2810 0.999689 2 to 25 15.61 18.1831 0.622623 3 to 26 15.55 21.0241 0.774787 4 to 27 15.62 29.4251 0.969198 5 to 28 15.95 15.3072 0.426634 6 to 29 15.94 8.9410 0.057906 7 to 30 15.69 19.7218 0.711293 8 to 31 15.74 25.2322 0.910369 9 to 32 15.82 20.3003 0.740842 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.034548 Tough bday spacings test for dh-ranFile-2018-03-30_12:31: 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 5 33 57 95 96 90 56 38 15 13 2 (O-E)^2/E 1.9 0.4 3.6 0.1 0.0 1.8 0.3 2.3 0.0 6.2 1.0 Birthday Spacings: Sum(O-E)^2/E= 17.538, p= 0.937 RESULTS OF GCD FOR dh-ranFile-2018-03-30_12:31 Euclid's algorithm: p-value, steps to gcd: 0.786968 p-value, dist. of gcd's: 0.708098 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-30_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.646 0.122 0.126 0.447 0.617 0.981 0.737 0.996 Bits 8 to 15---> 0.805 0.210 0.524 0.339 0.018 0.560 0.325 0.256 Bits 16 to 23---> 0.848 0.089 0.483 0.417 0.580 0.595 0.854 0.459 Bits 24 to 31---> 0.822 0.572 0.886 0.400 0.671 0.408 0.642 0.790 KS test for the above 32 p values: 0.405 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-30_12:31, p-values for 5 runs: 0.5120, 0.8003, 0.3060, 0.8192, 0.3047 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-30_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 251 211.4 7.411 7.411 r= 29 4985 5134.0 4.325 11.736 r= 30 23184 23103.0 0.284 12.019 r= 31 11580 11551.5 0.070 12.089 chi-square = 12.089 with df = 3; p-value = 0.993 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-30_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 185 211.4 3.301 3.301 r= 30 5153 5134.0 0.070 3.371 r= 31 23047 23103.0 0.136 3.507 r= 32 11615 11551.5 0.349 3.856 chi-square = 3.856 with df = 3; p-value = 0.723 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-30_12:31 b-rank test for bits 1 to 8, p=0.42838 b-rank test for bits 2 to 9, p=0.20865 b-rank test for bits 3 to 10, p=0.42829 b-rank test for bits 4 to 11, p=0.17732 b-rank test for bits 5 to 12, p=0.03320 b-rank test for bits 6 to 13, p=0.00504 b-rank test for bits 7 to 14, p=0.33062 b-rank test for bits 8 to 15, p=0.64598 b-rank test for bits 9 to 16, p=0.40553 b-rank test for bits 10 to 17, p=0.12125 b-rank test for bits 11 to 18, p=0.12580 b-rank test for bits 12 to 19, p=0.14174 b-rank test for bits 13 to 20, p=0.28597 b-rank test for bits 14 to 21, p=0.09721 b-rank test for bits 15 to 22, p=0.95271 b-rank test for bits 16 to 23, p=0.97481 b-rank test for bits 17 to 24, p=0.00270 b-rank test for bits 18 to 25, p=0.63600 b-rank test for bits 19 to 26, p=0.82074 b-rank test for bits 20 to 27, p=0.00299 b-rank test for bits 21 to 28, p=0.48214 b-rank test for bits 22 to 29, p=0.12496 b-rank test for bits 23 to 30, p=0.89158 b-rank test for bits 24 to 31, p=0.06132 b-rank test for bits 25 to 32, p=0.34713 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 = 0.003824 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-30_12:31 (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 141716 -0.45 0.325741 2 141608 -0.70 0.240703 3 141646 -0.62 0.269193 4 141739 -0.40 0.345327 5 141293 -1.44 0.074930 6 141493 -0.97 0.165343 7 141472 -1.02 0.153438 8 141977 0.16 0.562814 9 141728 -0.42 0.335904 10 142059 0.35 0.636717 11 142135 0.53 0.700996 12 142878 2.26 0.988190 13 142172 0.61 0.730298 14 142102 0.45 0.673704 15 142100 0.45 0.672017 16 141676 -0.55 0.292821 17 142106 0.46 0.677066 18 142182 0.64 0.737963 19 141600 -0.72 0.234922 20 142076 0.39 0.651516 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-30_12:31 Bits used No. missing words z-score p-value 23 to 32 142129 0.7575 0.775620 22 to 31 142028 0.4092 0.658806 21 to 30 141788 -0.4184 0.337835 20 to 29 141667 -0.8356 0.201684 19 to 28 141708 -0.6942 0.243765 18 to 27 141675 -0.8080 0.209535 17 to 26 141850 -0.2046 0.418948 16 to 25 142100 0.6575 0.744565 15 to 24 142097 0.6471 0.741229 14 to 23 142215 1.0540 0.854066 13 to 22 142184 0.9471 0.828216 12 to 21 142217 1.0609 0.855639 11 to 20 142081 0.5920 0.723063 10 to 19 141726 -0.6322 0.263637 9 to 18 141816 -0.3218 0.373792 8 to 17 141605 -1.0494 0.146994 7 to 16 142123 0.7368 0.769376 6 to 15 141989 0.2747 0.608236 5 to 14 142171 0.9023 0.816554 4 to 13 142104 0.6713 0.748978 3 to 12 141932 0.0782 0.531155 2 to 11 142239 1.1368 0.872188 1 to 10 142263 1.2196 0.888683 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-30_12:31 Bits used No. missing words z-score p-value 28 to 32 141595 -1.0655 0.143319 27 to 31 142300 1.3243 0.907299 26 to 30 141535 -1.2689 0.102236 25 to 29 142076 0.5650 0.713957 24 to 28 141948 0.1311 0.552146 23 to 27 141826 -0.2825 0.388790 22 to 26 141450 -1.5571 0.059729 21 to 25 142678 2.6057 0.995415 20 to 24 141975 0.2226 0.588081 19 to 23 142092 0.6192 0.732114 18 to 22 142009 0.3379 0.632267 17 to 21 142182 0.9243 0.822336 16 to 20 142037 0.4328 0.667413 15 to 19 141804 -0.3571 0.360527 14 to 18 141802 -0.3638 0.357992 13 to 17 142077 0.5684 0.715109 12 to 16 142201 0.9887 0.838598 11 to 15 141663 -0.8350 0.201854 10 to 14 142076 0.5650 0.713957 9 to 13 141936 0.0904 0.536018 8 to 12 141886 -0.0791 0.468483 7 to 11 142040 0.4429 0.671099 6 to 10 141821 -0.2994 0.382308 5 to 9 142113 0.6904 0.755031 4 to 8 141693 -0.7333 0.231681 3 to 7 142044 0.4565 0.675988 2 to 6 141778 -0.4452 0.328093 1 to 5 141873 -0.1232 0.450993 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-30_12:31 Bits used No. missing words z-score p-value 31 to 32 142372 1.3648 0.913843 30 to 31 141998 0.2616 0.603171 29 to 30 141458 -1.3314 0.091536 28 to 29 141490 -1.2370 0.108051 27 to 28 142047 0.4061 0.657668 26 to 27 142034 0.3678 0.643473 25 to 26 142107 0.5831 0.720086 24 to 25 141890 -0.0570 0.477264 23 to 24 141976 0.1967 0.577956 22 to 23 142321 1.2144 0.887696 21 to 22 141589 -0.9449 0.172348 20 to 21 141907 -0.0069 0.497258 19 to 20 141991 0.2409 0.595189 18 to 19 141779 -0.3845 0.350321 17 to 18 141573 -0.9921 0.160569 16 to 17 141940 0.0905 0.536044 15 to 16 141345 -1.6647 0.047987 14 to 15 141738 -0.5054 0.306640 13 to 14 141951 0.1229 0.548915 12 to 13 142449 1.5919 0.944302 11 to 12 142020 0.3265 0.627962 10 to 11 141770 -0.4110 0.340535 9 to 10 142242 0.9813 0.836784 8 to 9 141660 -0.7355 0.231022 7 to 8 141474 -1.2842 0.099543 6 to 7 142378 1.3825 0.916592 5 to 6 142106 0.5801 0.719092 4 to 5 141650 -0.7650 0.222140 3 to 4 141942 0.0964 0.538387 2 to 3 141443 -1.3756 0.084472 1 to 2 142555 1.9046 0.971586 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-30_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2499.36 -0.009 0.496416 Test results for specific bytes for dh-ranFile-2018-03-30_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2667.59 2.370 0.991108 2 to 9 2516.63 0.235 0.592973 3 to 10 2351.89 -2.095 0.018105 4 to 11 2489.23 -0.152 0.439480 5 to 12 2459.26 -0.576 0.282259 6 to 13 2546.43 0.657 0.744304 7 to 14 2459.01 -0.580 0.281048 8 to 15 2528.45 0.402 0.656309 9 to 16 2667.95 2.375 0.991229 10 to 17 2508.00 0.113 0.545016 11 to 18 2496.89 -0.044 0.482463 12 to 19 2538.35 0.542 0.706216 13 to 20 2500.90 0.013 0.505069 14 to 21 2443.53 -0.799 0.212252 15 to 22 2642.55 2.016 0.978099 16 to 23 2542.59 0.602 0.726539 17 to 24 2394.91 -1.486 0.068614 18 to 25 2454.55 -0.643 0.260207 19 to 26 2462.01 -0.537 0.295531 20 to 27 2455.46 -0.630 0.264372 21 to 28 2532.72 0.463 0.678205 22 to 29 2561.74 0.873 0.808708 23 to 30 2565.65 0.928 0.823396 24 to 31 2457.69 -0.598 0.274783 25 to 32 2539.51 0.559 0.711835 CDPARK for dh-ranFile-2018-03-30_12:31: 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 3568 2.0548 0.980051 3516 -0.3196 0.374623 3531 0.3653 0.642555 3531 0.3653 0.642555 3540 0.7763 0.781201 3518 -0.2283 0.409702 3531 0.3653 0.642555 3535 0.5479 0.708135 3516 -0.3196 0.374623 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3530.50 sample std.=14.92 p-value of the KSTEST for those 10 p-values: 0.227293 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-30_12:31 0.1592,0.7423,0.5799,0.4851,0.6821,0.7322,0.4971,0.1426,0.4954,0.2997, The KS test for those 10 p-values: 0.558456 The 3DSPHERES test for dh-ranFile-2018-03-30_12:31 sample no r^3 equiv. uni. 1 9.954 0.282374 2 0.240 0.007969 3 26.945 0.592679 4 71.175 0.906751 5 24.097 0.552114 6 21.409 0.510142 7 38.002 0.718248 8 10.451 0.294153 9 13.231 0.356639 10 20.346 0.492479 11 65.130 0.885938 12 32.727 0.664090 13 9.631 0.274593 14 21.363 0.509388 15 0.793 0.026083 16 8.584 0.248846 17 57.475 0.852783 18 12.868 0.348806 19 12.857 0.348551 20 0.944 0.030986 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.434296 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-30_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.5 0.1 0.2 0.8 1.6 0.8 2.5 -0.2 -0.9 0.8 0.9 0.3 -0.2 0.5 -0.1 -0.5 1.6 -1.1 0.2 -1.4 -0.2 -0.9 -0.2 -0.7 1.0 -0.3 -0.4 0.8 -0.8 0.3 0.8 -0.5 -1.5 -1.2 0.2 -1.2 -1.3 0.5 -0.1 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:35.997263 z-score=-0.654952, p-value=0.269171 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-30_12:31 Test no p-value 1 0.917125 2 0.838496 3 0.741755 4 0.228248 5 0.276839 6 0.031725 7 0.049641 8 0.444060 9 0.055820 10 0.745560 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.385603 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-30_12:31: (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 66780 0.19 66887 0.73 3 25000.00 24852 0.88 24689 3.87 4 6666.67 6663 0.00 6741 0.83 5 1388.89 1415 0.49 1404 0.16 6 238.10 256 1.35 237 0.01 7 34.72 28 1.30 39 0.53 8 4.96 5 0.00 2 1.77 p=0.35160 p=0.75367 Number of rngs required: 688319, p-value: 0.462 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-30_12:31 No. of wins: Observed Expected 98566 98585.9 z-score=-0.089, pvalue=0.46461 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66545 66666.7 0.222 0.222 2 37491 37654.3 0.708 0.930 3 27072 26954.7 0.510 1.441 4 19380 19313.5 0.229 1.670 5 13844 13851.4 0.004 1.674 6 10037 9943.5 0.878 2.552 7 7103 7145.0 0.247 2.799 8 5255 5139.1 2.615 5.414 9 3703 3699.9 0.003 5.417 10 2687 2666.3 0.161 5.578 11 1928 1923.3 0.011 5.589 12 1340 1388.7 1.711 7.300 13 1012 1003.7 0.068 7.368 14 693 726.1 1.513 8.881 15 516 525.8 0.184 9.065 16 396 381.2 0.579 9.643 17 279 276.5 0.022 9.665 18 182 200.8 1.765 11.431 19 137 146.0 0.553 11.984 20 109 106.2 0.073 12.057 21 291 287.1 0.053 12.109 Chisq= 12.11 for 20 degrees of freedom, p= 0.08773 SUMMARY of craptest p-value for no. of wins: 0.464613 p-value for throws/game: 0.087734 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-30_12:31 No. of wins: Observed Expected 98434 98585.9 z-score=-0.679, pvalue=0.24851 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66954 66666.7 1.238 1.238 2 37743 37654.3 0.209 1.447 3 26618 26954.7 4.207 5.654 4 19312 19313.5 0.000 5.654 5 13793 13851.4 0.246 5.900 6 10056 9943.5 1.272 7.172 7 7062 7145.0 0.965 8.137 8 5036 5139.1 2.067 10.204 9 3744 3699.9 0.526 10.731 10 2729 2666.3 1.475 12.205 11 1920 1923.3 0.006 12.211 12 1417 1388.7 0.575 12.786 13 1034 1003.7 0.914 13.700 14 710 726.1 0.359 14.059 15 516 525.8 0.184 14.243 16 356 381.2 1.660 15.902 17 262 276.5 0.764 16.667 18 200 200.8 0.003 16.670 19 151 146.0 0.172 16.842 20 98 106.2 0.635 17.478 21 289 287.1 0.012 17.490 Chisq= 17.49 for 20 degrees of freedom, p= 0.37905 SUMMARY of craptest p-value for no. of wins: 0.248506 p-value for throws/game: 0.379051 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0030,0.0038,0.0050,0.0080,0.0177,0.0181,0.0261,0.0310,0.0317, 0.0332,0.0345,0.0480,0.0496,0.0558,0.0579,0.0597,0.0613,0.0686,0.0749, 0.0845,0.0877,0.0887,0.0915,0.0972,0.0995,0.1022,0.1081,0.1213,0.1216, 0.1250,0.1258,0.1264,0.1417,0.1426,0.1433,0.1470,0.1534,0.1592,0.1606, 0.1653,0.1723,0.1773,0.2017,0.2019,0.2086,0.2095,0.2100,0.2123,0.2221, 0.2273,0.2282,0.2310,0.2317,0.2349,0.2407,0.2438,0.2485,0.2488,0.2556, 0.2602,0.2636,0.2644,0.2692,0.2692,0.2746,0.2748,0.2768,0.2810,0.2823, 0.2824,0.2860,0.2928,0.2942,0.2955,0.2997,0.3047,0.3060,0.3066,0.3249, 0.3257,0.3281,0.3306,0.3359,0.3378,0.3385,0.3405,0.3453,0.3471,0.3486, 0.3488,0.3503,0.3516,0.3566,0.3580,0.3605,0.3738,0.3746,0.3746,0.3791, 0.3823,0.3856,0.3888,0.4003,0.4049,0.4055,0.4077,0.4097,0.4168,0.4189, 0.4266,0.4275,0.4283,0.4284,0.4343,0.4395,0.4441,0.4472,0.4510,0.4591, 0.4615,0.4646,0.4685,0.4773,0.4821,0.4825,0.4834,0.4851,0.4925,0.4954, 0.4964,0.4971,0.4973,0.5051,0.5094,0.5101,0.5120,0.5240,0.5312,0.5360, 0.5360,0.5384,0.5450,0.5489,0.5521,0.5521,0.5585,0.5600,0.5628,0.5724, 0.5780,0.5799,0.5804,0.5881,0.5927,0.5930,0.5949,0.5952,0.6032,0.6082, 0.6170,0.6226,0.6280,0.6323,0.6360,0.6367,0.6423,0.6426,0.6426,0.6426, 0.6435,0.6460,0.6461,0.6515,0.6563,0.6577,0.6588,0.6641,0.6674,0.6707, 0.6711,0.6720,0.6737,0.6760,0.6771,0.6782,0.6821,0.7010,0.7062,0.7081, 0.7081,0.7113,0.7118,0.7140,0.7140,0.7151,0.7182,0.7191,0.7201,0.7226, 0.7231,0.7265,0.7303,0.7321,0.7322,0.7369,0.7380,0.7408,0.7412,0.7418, 0.7423,0.7443,0.7446,0.7456,0.7490,0.7537,0.7550,0.7694,0.7748,0.7756, 0.7812,0.7870,0.7904,0.8003,0.8049,0.8087,0.8166,0.8192,0.8207,0.8223, 0.8223,0.8234,0.8282,0.8368,0.8385,0.8386,0.8482,0.8528,0.8539,0.8541, 0.8556,0.8722,0.8859,0.8861,0.8877,0.8887,0.8916,0.9068,0.9073,0.9104, 0.9138,0.9166,0.9171,0.9367,0.9443,0.9527,0.9692,0.9716,0.9748,0.9781, 0.9801,0.9814,0.9882,0.9911,0.9912,0.9929,0.9954,0.9955,0.9997, Overall p-value after applying KStest on 269 p-values = 0.472807 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.