RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-25_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.27 24.7001 0.898374 2 to 25 16.06 24.5768 0.895409 3 to 26 15.93 10.0363 0.097918 4 to 27 15.98 16.2959 0.497034 5 to 28 16.13 12.7575 0.247740 6 to 29 15.86 19.5744 0.703423 7 to 30 15.66 20.7867 0.764022 8 to 31 15.75 9.7501 0.086238 9 to 32 15.47 18.5919 0.647547 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.852726 Tough bday spacings test for dh-ranFile-2015-12-25_20:31: 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 33 76 100 99 91 47 19 15 9 4 (O-E)^2/E 0.5 0.4 0.1 0.1 0.0 2.1 0.5 3.9 0.0 0.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.414, p= 0.412 RESULTS OF GCD FOR dh-ranFile-2015-12-25_20:31 Euclid's algorithm: p-value, steps to gcd: 0.399096 p-value, dist. of gcd's: 0.804592 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-25_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.179 0.768 0.631 0.265 0.335 0.084 0.990 0.895 Bits 8 to 15---> 0.905 0.542 0.773 0.070 0.864 0.451 0.206 0.698 Bits 16 to 23---> 0.513 0.631 0.843 0.654 0.521 0.040 0.535 0.747 Bits 24 to 31---> 0.970 0.601 0.166 0.483 0.264 0.245 0.782 0.546 KS test for the above 32 p values: 0.210 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-25_20:31, p-values for 5 runs: 0.9243, 0.7400, 0.2475, 0.6359, 0.1486 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-25_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 187 211.4 2.820 2.820 r= 29 5187 5134.0 0.547 3.367 r= 30 23205 23103.0 0.450 3.817 r= 31 11421 11551.5 1.475 5.292 chi-square = 5.292 with df = 3; p-value = 0.848 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-25_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5063 5134.0 0.982 1.187 r= 31 23190 23103.0 0.327 1.514 r= 32 11529 11551.5 0.044 1.558 chi-square = 1.558 with df = 3; p-value = 0.331 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-25_20:31 b-rank test for bits 1 to 8, p=0.20100 b-rank test for bits 2 to 9, p=0.74268 b-rank test for bits 3 to 10, p=0.05343 b-rank test for bits 4 to 11, p=0.15314 b-rank test for bits 5 to 12, p=0.64653 b-rank test for bits 6 to 13, p=0.21839 b-rank test for bits 7 to 14, p=0.16313 b-rank test for bits 8 to 15, p=0.80309 b-rank test for bits 9 to 16, p=0.94709 b-rank test for bits 10 to 17, p=0.78096 b-rank test for bits 11 to 18, p=0.95369 b-rank test for bits 12 to 19, p=0.51283 b-rank test for bits 13 to 20, p=0.83837 b-rank test for bits 14 to 21, p=0.46079 b-rank test for bits 15 to 22, p=0.23382 b-rank test for bits 16 to 23, p=0.04861 b-rank test for bits 17 to 24, p=0.10930 b-rank test for bits 18 to 25, p=0.46055 b-rank test for bits 19 to 26, p=0.77971 b-rank test for bits 20 to 27, p=0.71127 b-rank test for bits 21 to 28, p=0.66715 b-rank test for bits 22 to 29, p=0.44910 b-rank test for bits 23 to 30, p=0.81219 b-rank test for bits 24 to 31, p=0.69914 b-rank test for bits 25 to 32, p=0.59387 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 = 0.809235 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-25_20:31 (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 141984 0.17 0.569249 2 142202 0.68 0.752952 3 141632 -0.65 0.258503 4 141966 0.13 0.552669 5 141691 -0.51 0.304985 6 142221 0.73 0.766755 7 141875 -0.08 0.468035 8 141383 -1.23 0.109397 9 141986 0.18 0.571084 10 141470 -1.03 0.152335 11 142201 0.68 0.752214 12 141869 -0.09 0.462464 13 142482 1.34 0.909554 14 141615 -0.69 0.245825 15 141819 -0.21 0.416424 16 141346 -1.32 0.094055 17 142714 1.88 0.969951 18 141894 -0.04 0.485714 19 142595 1.60 0.945426 20 142207 0.70 0.756626 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-25_20:31 Bits used No. missing words z-score p-value 23 to 32 141718 -0.6598 0.254704 22 to 31 142185 0.9506 0.829093 21 to 30 141742 -0.5770 0.281970 20 to 29 141479 -1.4839 0.068918 19 to 28 141727 -0.6287 0.264765 18 to 27 141600 -1.0667 0.143064 17 to 26 142099 0.6540 0.743455 16 to 25 141930 0.0713 0.528411 15 to 24 142252 1.1816 0.881322 14 to 23 142129 0.7575 0.775620 13 to 22 142077 0.5782 0.718426 12 to 21 142326 1.4368 0.924612 11 to 20 142369 1.5851 0.943525 10 to 19 141881 -0.0977 0.461089 9 to 18 141390 -1.7908 0.036663 8 to 17 141965 0.1920 0.576115 7 to 16 141885 -0.0839 0.466569 6 to 15 142004 0.3264 0.627957 5 to 14 141043 -2.9873 0.001407 4 to 13 141546 -1.2529 0.105128 3 to 12 142182 0.9402 0.826453 2 to 11 142156 0.8506 0.802500 1 to 10 141692 -0.7494 0.226804 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-25_20:31 Bits used No. missing words z-score p-value 28 to 32 141576 -1.1299 0.129252 27 to 31 141908 -0.0045 0.498201 26 to 30 142207 1.0091 0.843525 25 to 29 142699 2.6768 0.996284 24 to 28 142419 1.7277 0.957979 23 to 27 141377 -1.8045 0.035576 22 to 26 142086 0.5989 0.725374 21 to 25 142253 1.1650 0.877987 20 to 24 142155 0.8328 0.797516 19 to 23 142065 0.5277 0.701145 18 to 22 142275 1.2396 0.892431 17 to 21 142127 0.7379 0.769702 16 to 20 141768 -0.4791 0.315939 15 to 19 141867 -0.1435 0.442951 14 to 18 142241 1.1243 0.869558 13 to 17 142423 1.7413 0.959181 12 to 16 141374 -1.8147 0.034787 11 to 15 141892 -0.0587 0.476577 10 to 14 141871 -0.1299 0.448310 9 to 13 142234 1.1006 0.864459 8 to 12 142086 0.5989 0.725374 7 to 11 142283 1.2667 0.897365 6 to 10 142134 0.7616 0.776849 5 to 9 141970 0.2057 0.581472 4 to 8 141943 0.1141 0.545435 3 to 7 141745 -0.5571 0.288746 2 to 6 141924 0.0497 0.519831 1 to 5 141813 -0.3265 0.372007 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-25_20:31 Bits used No. missing words z-score p-value 31 to 32 142168 0.7630 0.777280 30 to 31 142729 2.4179 0.992195 29 to 30 142074 0.4858 0.686429 28 to 29 142023 0.3353 0.631304 27 to 28 142004 0.2793 0.609978 26 to 27 141212 -2.0570 0.019842 25 to 26 141599 -0.9154 0.179984 24 to 25 142312 1.1878 0.882547 23 to 24 141420 -1.4435 0.074447 22 to 23 142069 0.4710 0.681181 21 to 22 142257 1.0256 0.847454 20 to 21 142004 0.2793 0.609978 19 to 20 141865 -0.1308 0.447980 18 to 19 141854 -0.1632 0.435174 17 to 18 142407 1.4681 0.928955 16 to 17 141576 -0.9833 0.162736 15 to 16 142351 1.3029 0.903689 14 to 15 141809 -0.2960 0.383631 13 to 14 141894 -0.0452 0.481966 12 to 13 142038 0.3796 0.647863 11 to 12 141503 -1.1986 0.115339 10 to 11 141889 -0.0600 0.476090 9 to 10 142735 2.4356 0.992567 8 to 9 141620 -0.8535 0.196696 7 to 8 142229 0.9430 0.827154 6 to 7 141812 -0.2871 0.387014 5 to 6 141839 -0.2075 0.417824 4 to 5 142254 1.0167 0.845358 3 to 4 141948 0.1141 0.545409 2 to 3 141432 -1.4081 0.079558 1 to 2 141309 -1.7709 0.038290 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-25_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2439.59 -0.854 0.196463 Test results for specific bytes for dh-ranFile-2015-12-25_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2451.54 -0.685 0.246589 2 to 9 2527.46 0.388 0.651143 3 to 10 2539.51 0.559 0.711816 4 to 11 2582.02 1.160 0.876956 5 to 12 2532.54 0.460 0.677310 6 to 13 2511.80 0.167 0.566253 7 to 14 2553.75 0.760 0.776408 8 to 15 2484.93 -0.213 0.415623 9 to 16 2592.52 1.308 0.904647 10 to 17 2479.95 -0.284 0.388353 11 to 18 2486.30 -0.194 0.423174 12 to 19 2519.23 0.272 0.607164 13 to 20 2461.37 -0.546 0.292422 14 to 21 2484.06 -0.225 0.410849 15 to 22 2456.00 -0.622 0.266902 16 to 23 2405.13 -1.342 0.089857 17 to 24 2485.23 -0.209 0.417299 18 to 25 2523.75 0.336 0.631508 19 to 26 2523.67 0.335 0.631115 20 to 27 2504.91 0.069 0.527661 21 to 28 2595.33 1.348 0.911190 22 to 29 2486.87 -0.186 0.426365 23 to 30 2544.66 0.632 0.736156 24 to 31 2435.98 -0.905 0.182635 25 to 32 2691.70 2.711 0.996646 CDPARK for dh-ranFile-2015-12-25_20:31: 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 3547 1.0959 0.863437 3499 -1.0959 0.136563 3517 -0.2740 0.392053 3510 -0.5936 0.276387 3522 -0.0457 0.481790 3533 0.4566 0.676028 3548 1.1416 0.873180 3511 -0.5479 0.291865 3509 -0.6393 0.261324 3526 0.1370 0.554479 Square side=100, avg. no. parked=3522.20 sample std.=15.57 p-value of the KSTEST for those 10 p-values: 0.834630 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-25_20:31 0.1224,0.2619,0.1252,0.1294,0.6095,0.7759,0.1322,0.1018,0.0478,0.0508, The KS test for those 10 p-values: 0.001935 The 3DSPHERES test for dh-ranFile-2015-12-25_20:31 sample no r^3 equiv. uni. 1 40.258 0.738656 2 42.207 0.755096 3 38.888 0.726447 4 2.795 0.088945 5 31.814 0.653708 6 53.807 0.833636 7 13.036 0.352425 8 45.563 0.781019 9 40.353 0.739485 10 49.328 0.806849 11 22.031 0.520195 12 43.573 0.766000 13 39.409 0.731160 14 9.472 0.270748 15 32.603 0.662697 16 7.878 0.230948 17 14.830 0.390013 18 81.381 0.933642 19 7.979 0.233535 20 26.154 0.581804 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.121931 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-25_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 1.5 0.3 -2.0 -0.6 -0.4 -0.8 1.0 -1.9 -0.2 -1.9 0.7 -0.5 -0.4 -0.2 -0.7 1.5 -0.7 1.8 -1.5 1.6 0.5 0.9 -0.9 0.2 -0.4 -0.0 1.1 2.1 -0.7 0.4 1.4 -0.4 0.8 -0.8 -0.7 0.8 -0.4 -1.3 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:45.653005 z-score=0.398576, p-value=0.677200 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-25_20:31 Test no p-value 1 0.045844 2 0.298671 3 0.684128 4 0.411434 5 0.019837 6 0.576000 7 0.029267 8 0.195444 9 0.287277 10 0.093903 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.011312 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-25_20:31: (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 66807 0.30 66703 0.02 3 25000.00 24928 0.21 25012 0.01 4 6666.67 6560 1.71 6585 1.00 5 1388.89 1411 0.35 1403 0.14 6 238.10 243 0.10 258 1.66 7 34.72 41 1.14 36 0.05 8 4.96 9 3.29 2 1.77 p=0.68731 p=0.41019 Number of rngs required: 687944, p-value: 0.298 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-25_20:31 No. of wins: Observed Expected 98704 98585.9 z-score= 0.528, pvalue=0.70139 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66805 66666.7 0.287 0.287 2 37649 37654.3 0.001 0.288 3 27117 26954.7 0.977 1.265 4 19234 19313.5 0.327 1.592 5 13851 13851.4 0.000 1.592 6 9970 9943.5 0.070 1.662 7 7051 7145.0 1.237 2.899 8 5126 5139.1 0.033 2.933 9 3639 3699.9 1.001 3.934 10 2621 2666.3 0.770 4.703 11 1800 1923.3 7.908 12.612 12 1447 1388.7 2.444 15.056 13 983 1003.7 0.428 15.483 14 717 726.1 0.115 15.598 15 548 525.8 0.934 16.532 16 381 381.2 0.000 16.533 17 290 276.5 0.655 17.188 18 182 200.8 1.765 18.953 19 148 146.0 0.028 18.981 20 131 106.2 5.783 24.764 21 310 287.1 1.824 26.589 Chisq= 26.59 for 20 degrees of freedom, p= 0.85276 SUMMARY of craptest p-value for no. of wins: 0.701388 p-value for throws/game: 0.852763 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-25_20:31 No. of wins: Observed Expected 98647 98585.9 z-score= 0.273, pvalue=0.60775 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66760 66666.7 0.131 0.131 2 37640 37654.3 0.005 0.136 3 26933 26954.7 0.018 0.154 4 19283 19313.5 0.048 0.202 5 13761 13851.4 0.590 0.792 6 9935 9943.5 0.007 0.799 7 7259 7145.0 1.818 2.617 8 5095 5139.1 0.378 2.995 9 3654 3699.9 0.569 3.564 10 2686 2666.3 0.146 3.709 11 1969 1923.3 1.084 4.794 12 1414 1388.7 0.459 5.253 13 992 1003.7 0.137 5.390 14 686 726.1 2.219 7.609 15 557 525.8 1.847 9.456 16 389 381.2 0.162 9.618 17 288 276.5 0.475 10.093 18 186 200.8 1.095 11.188 19 152 146.0 0.248 11.436 20 106 106.2 0.000 11.436 21 255 287.1 3.592 15.028 Chisq= 15.03 for 20 degrees of freedom, p= 0.22520 SUMMARY of craptest p-value for no. of wins: 0.607750 p-value for throws/game: 0.225199 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0014,0.0019,0.0113,0.0198,0.0198,0.0293,0.0348,0.0356,0.0367,0.0383, 0.0401,0.0458,0.0478,0.0486,0.0508,0.0534,0.0689,0.0697,0.0744,0.0796, 0.0840,0.0862,0.0889,0.0899,0.0939,0.0941,0.0979,0.1018,0.1051,0.1093, 0.1094,0.1153,0.1219,0.1224,0.1252,0.1293,0.1294,0.1322,0.1366,0.1431, 0.1486,0.1523,0.1531,0.1627,0.1631,0.1660,0.1786,0.1800,0.1826,0.1954, 0.1965,0.1967,0.2010,0.2055,0.2096,0.2184,0.2252,0.2268,0.2309,0.2335, 0.2338,0.2448,0.2458,0.2466,0.2475,0.2477,0.2547,0.2585,0.2613,0.2619, 0.2644,0.2648,0.2648,0.2669,0.2707,0.2764,0.2820,0.2873,0.2887,0.2919, 0.2924,0.2984,0.2987,0.3050,0.3159,0.3311,0.3354,0.3524,0.3720,0.3836, 0.3870,0.3884,0.3900,0.3921,0.3991,0.4102,0.4108,0.4114,0.4115,0.4156, 0.4164,0.4173,0.4178,0.4232,0.4264,0.4352,0.4430,0.4480,0.4483,0.4491, 0.4512,0.4605,0.4608,0.4611,0.4625,0.4666,0.4680,0.4761,0.4766,0.4818, 0.4820,0.4827,0.4857,0.4970,0.4982,0.5128,0.5129,0.5198,0.5202,0.5208, 0.5277,0.5284,0.5351,0.5418,0.5454,0.5454,0.5462,0.5527,0.5545,0.5663, 0.5692,0.5711,0.5760,0.5761,0.5815,0.5818,0.5939,0.6009,0.6072,0.6078, 0.6095,0.6100,0.6100,0.6280,0.6306,0.6311,0.6313,0.6314,0.6315,0.6359, 0.6465,0.6475,0.6479,0.6511,0.6536,0.6537,0.6627,0.6672,0.6760,0.6772, 0.6773,0.6812,0.6841,0.6864,0.6873,0.6984,0.6991,0.7011,0.7014,0.7034, 0.7113,0.7118,0.7184,0.7254,0.7254,0.7264,0.7312,0.7362,0.7387,0.7395, 0.7400,0.7427,0.7435,0.7467,0.7522,0.7530,0.7551,0.7566,0.7640,0.7660, 0.7668,0.7682,0.7697,0.7729,0.7756,0.7759,0.7764,0.7768,0.7773,0.7797, 0.7810,0.7810,0.7820,0.7975,0.8025,0.8031,0.8046,0.8068,0.8092,0.8122, 0.8265,0.8272,0.8291,0.8336,0.8346,0.8384,0.8427,0.8435,0.8454,0.8475, 0.8484,0.8527,0.8528,0.8634,0.8640,0.8645,0.8696,0.8732,0.8770,0.8780, 0.8813,0.8825,0.8924,0.8946,0.8954,0.8974,0.8984,0.9037,0.9046,0.9055, 0.9096,0.9112,0.9243,0.9246,0.9290,0.9336,0.9435,0.9454,0.9471,0.9537, 0.9580,0.9592,0.9700,0.9704,0.9899,0.9922,0.9926,0.9963,0.9966, Overall p-value after applying KStest on 269 p-values = 0.344934 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.