RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-27_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.78 22.7532 0.842540 2 to 25 15.76 22.6000 0.837269 3 to 26 15.88 15.2069 0.419421 4 to 27 15.85 18.4292 0.637739 5 to 28 15.57 24.5082 0.893728 6 to 29 15.85 13.8298 0.320892 7 to 30 15.57 32.1851 0.985730 8 to 31 15.64 15.7120 0.455663 9 to 32 16.06 14.4405 0.364286 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.209428 Tough bday spacings test for dh-ranFile-2015-10-27_07:31: 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 44 78 87 101 75 51 28 18 5 5 (O-E)^2/E 0.1 1.5 0.3 1.2 0.1 0.1 0.0 0.1 0.7 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 4.732, p= 0.092 RESULTS OF GCD FOR dh-ranFile-2015-10-27_07:31 Euclid's algorithm: p-value, steps to gcd: 0.656383 p-value, dist. of gcd's: 0.860065 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-27_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.288 0.848 0.728 0.612 0.981 0.232 0.355 0.799 Bits 8 to 15---> 0.083 0.536 0.812 0.771 0.165 0.241 0.656 0.285 Bits 16 to 23---> 0.697 0.836 0.598 0.668 0.235 0.670 0.323 0.009 Bits 24 to 31---> 0.684 0.805 0.950 0.163 0.776 0.253 0.296 0.284 KS test for the above 32 p values: 0.385 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-27_07:31, p-values for 5 runs: 0.1073, 0.6674, 0.5292, 0.7410, 0.4388 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-27_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5183 5134.0 0.467 0.997 r= 30 23091 23103.0 0.006 1.003 r= 31 11504 11551.5 0.196 1.199 chi-square = 1.199 with df = 3; p-value = 0.247 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-27_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5082 5134.0 0.527 1.161 r= 31 23141 23103.0 0.062 1.224 r= 32 11554 11551.5 0.001 1.224 chi-square = 1.224 with df = 3; p-value = 0.253 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-27_07:31 b-rank test for bits 1 to 8, p=0.50312 b-rank test for bits 2 to 9, p=0.03325 b-rank test for bits 3 to 10, p=0.42060 b-rank test for bits 4 to 11, p=0.58405 b-rank test for bits 5 to 12, p=0.33480 b-rank test for bits 6 to 13, p=0.24145 b-rank test for bits 7 to 14, p=0.10888 b-rank test for bits 8 to 15, p=0.17819 b-rank test for bits 9 to 16, p=0.00339 b-rank test for bits 10 to 17, p=0.33262 b-rank test for bits 11 to 18, p=0.84721 b-rank test for bits 12 to 19, p=0.75959 b-rank test for bits 13 to 20, p=0.11104 b-rank test for bits 14 to 21, p=0.71578 b-rank test for bits 15 to 22, p=0.10210 b-rank test for bits 16 to 23, p=0.00601 b-rank test for bits 17 to 24, p=0.59994 b-rank test for bits 18 to 25, p=0.39067 b-rank test for bits 19 to 26, p=0.09967 b-rank test for bits 20 to 27, p=0.19417 b-rank test for bits 21 to 28, p=0.97145 b-rank test for bits 22 to 29, p=0.96019 b-rank test for bits 23 to 30, p=0.44277 b-rank test for bits 24 to 31, p=0.18830 b-rank test for bits 25 to 32, p=0.13814 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 = 0.025521 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-27_07:31 (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 142037 0.30 0.617261 2 141662 -0.58 0.281675 3 141688 -0.52 0.302534 4 142361 1.06 0.854357 5 142148 0.56 0.711455 6 141967 0.13 0.553593 7 141856 -0.12 0.450419 8 142197 0.67 0.749248 9 142471 1.31 0.905293 10 141856 -0.12 0.450419 11 141517 -0.92 0.179661 12 141772 -0.32 0.374157 13 142022 0.26 0.603820 14 141807 -0.24 0.405518 15 142173 0.62 0.731070 16 141592 -0.74 0.229218 17 141627 -0.66 0.254739 18 141629 -0.65 0.256241 19 142103 0.45 0.674546 20 142214 0.71 0.761720 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-27_07:31 Bits used No. missing words z-score p-value 23 to 32 142196 0.9885 0.838550 22 to 31 141919 0.0333 0.513300 21 to 30 142562 2.2506 0.987794 20 to 29 141906 -0.0115 0.495419 19 to 28 141643 -0.9184 0.179210 18 to 27 142035 0.4333 0.667618 17 to 26 142174 0.9127 0.819288 16 to 25 141959 0.1713 0.567997 15 to 24 142205 1.0196 0.846029 14 to 23 141712 -0.6804 0.248110 13 to 22 141652 -0.8873 0.187447 12 to 21 141745 -0.5667 0.285474 11 to 20 141826 -0.2873 0.386924 10 to 19 142038 0.4437 0.671367 9 to 18 141317 -2.0425 0.020550 8 to 17 142090 0.6230 0.733358 7 to 16 142092 0.6299 0.735619 6 to 15 142235 1.1230 0.869281 5 to 14 141373 -1.8494 0.032199 4 to 13 142370 1.5885 0.943915 3 to 12 142342 1.4920 0.932146 2 to 11 141867 -0.1460 0.441974 1 to 10 141577 -1.1460 0.125905 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-27_07:31 Bits used No. missing words z-score p-value 28 to 32 141299 -2.0689 0.019277 27 to 31 141901 -0.0282 0.488737 26 to 30 141603 -1.0384 0.149540 25 to 29 142007 0.3311 0.629710 24 to 28 142099 0.6429 0.739872 23 to 27 141854 -0.1876 0.425611 22 to 26 141813 -0.3265 0.372007 21 to 25 142003 0.3175 0.624578 20 to 24 141679 -0.7808 0.217466 19 to 23 141557 -1.1943 0.116173 18 to 22 141791 -0.4011 0.344166 17 to 21 142221 1.0565 0.854632 16 to 20 141949 0.1345 0.553486 15 to 19 142220 1.0531 0.853857 14 to 18 141894 -0.0520 0.479278 13 to 17 141885 -0.0825 0.467135 12 to 16 141616 -0.9943 0.160029 11 to 15 142133 0.7582 0.775835 10 to 14 142182 0.9243 0.822336 9 to 13 141812 -0.3299 0.370726 8 to 12 141482 -1.4486 0.073728 7 to 11 141602 -1.0418 0.148753 6 to 10 142411 1.7006 0.955489 5 to 9 141947 0.1277 0.550805 4 to 8 141563 -1.1740 0.120198 3 to 7 141902 -0.0248 0.490088 2 to 6 141816 -0.3164 0.375860 1 to 5 141633 -0.9367 0.174453 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-27_07:31 Bits used No. missing words z-score p-value 31 to 32 142018 0.3206 0.625728 30 to 31 141891 -0.0541 0.478439 29 to 30 141788 -0.3579 0.360207 28 to 29 141814 -0.2812 0.389275 27 to 28 141998 0.2616 0.603171 26 to 27 141834 -0.2222 0.412074 25 to 26 142260 1.0344 0.849531 24 to 25 141985 0.2232 0.588316 23 to 24 142311 1.1849 0.881965 22 to 23 142153 0.7188 0.763865 21 to 22 141911 0.0049 0.501965 20 to 21 141380 -1.5614 0.059209 19 to 20 141907 -0.0069 0.497258 18 to 19 141778 -0.3874 0.349229 17 to 18 141381 -1.5585 0.059558 16 to 17 142044 0.3973 0.654411 15 to 16 141648 -0.7709 0.220388 14 to 15 141061 -2.5024 0.006167 13 to 14 142059 0.4415 0.670576 12 to 13 141942 0.0964 0.538387 11 to 12 142020 0.3265 0.627962 10 to 11 141948 0.1141 0.545409 9 to 10 142211 0.8899 0.813235 8 to 9 141634 -0.8122 0.208343 7 to 8 141883 -0.0777 0.469045 6 to 7 141474 -1.2842 0.099543 5 to 6 141874 -0.1042 0.458498 4 to 5 141507 -1.1868 0.117650 3 to 4 141933 0.0698 0.527833 2 to 3 141835 -0.2193 0.413223 1 to 2 142519 1.7984 0.963946 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-27_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2395.34 -1.480 0.069427 Test results for specific bytes for dh-ranFile-2015-10-27_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2400.01 -1.414 0.078665 2 to 9 2619.69 1.693 0.954741 3 to 10 2480.02 -0.283 0.388768 4 to 11 2517.28 0.244 0.596554 5 to 12 2460.35 -0.561 0.287487 6 to 13 2426.99 -1.033 0.150910 7 to 14 2511.03 0.156 0.561975 8 to 15 2481.46 -0.262 0.396565 9 to 16 2404.51 -1.350 0.088442 10 to 17 2453.88 -0.652 0.257108 11 to 18 2544.28 0.626 0.734415 12 to 19 2331.13 -2.388 0.008467 13 to 20 2518.30 0.259 0.602116 14 to 21 2498.21 -0.025 0.489892 15 to 22 2367.42 -1.875 0.030395 16 to 23 2528.64 0.405 0.657284 17 to 24 2407.97 -1.302 0.096542 18 to 25 2388.31 -1.580 0.057108 19 to 26 2571.29 1.008 0.843325 20 to 27 2481.11 -0.267 0.394705 21 to 28 2573.85 1.044 0.851843 22 to 29 2629.05 1.825 0.966000 23 to 30 2567.78 0.958 0.831091 24 to 31 2362.66 -1.942 0.026052 25 to 32 2462.69 -0.528 0.298852 CDPARK for dh-ranFile-2015-10-27_07:31: 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 3524 0.0457 0.518210 3485 -1.7352 0.041356 3531 0.3653 0.642555 3523 0.0000 0.500000 3499 -1.0959 0.136563 3534 0.5023 0.692266 3566 1.9635 0.975204 3526 0.1370 0.554479 3540 0.7763 0.781201 3503 -0.9132 0.180558 Square side=100, avg. no. parked=3523.10 sample std.=21.80 p-value of the KSTEST for those 10 p-values: 0.947612 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-27_07:31 0.1307,0.0895,0.3709,0.7152,0.4404,0.2279,0.3991,0.9073,0.9069,0.2861, The KS test for those 10 p-values: 0.761922 The 3DSPHERES test for dh-ranFile-2015-10-27_07:31 sample no r^3 equiv. uni. 1 47.017 0.791380 2 9.597 0.273784 3 2.587 0.082633 4 35.456 0.693297 5 33.766 0.675521 6 2.060 0.066362 7 24.365 0.556100 8 49.436 0.807539 9 25.591 0.573874 10 11.960 0.328787 11 7.558 0.222708 12 80.281 0.931164 13 11.370 0.315456 14 3.062 0.097043 15 15.018 0.393831 16 14.796 0.389329 17 59.233 0.861160 18 29.405 0.624756 19 0.378 0.012530 20 16.945 0.431536 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.851404 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-27_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 -1.1 -0.7 -0.7 0.7 -0.0 1.3 -2.1 -0.7 0.6 -0.6 -0.7 -0.6 0.8 -0.2 0.2 -0.9 1.3 -1.2 0.1 0.4 0.3 1.3 0.8 -0.9 0.2 0.2 -0.5 -0.2 1.6 0.6 0.5 -0.5 1.3 0.4 0.5 -0.1 0.9 1.5 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:32.977517 z-score=-0.984434, p-value=0.160812 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-27_07:31 Test no p-value 1 0.300560 2 0.611786 3 0.120894 4 0.770880 5 0.488893 6 0.138339 7 0.093134 8 0.922665 9 0.849337 10 0.054063 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.599791 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-27_07:31: (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 66814 0.33 66404 1.03 3 25000.00 24960 0.06 25264 2.79 4 6666.67 6534 2.64 6654 0.02 5 1388.89 1401 0.11 1432 1.34 6 238.10 247 0.33 213 2.65 7 34.72 38 0.31 28 1.30 8 4.96 5 0.00 4 0.19 p=0.29339 p=0.84345 Number of rngs required: 687855, p-value: 0.264 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-27_07:31 No. of wins: Observed Expected 98632 98585.9 z-score= 0.206, pvalue=0.58175 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66596 66666.7 0.075 0.075 2 37451 37654.3 1.098 1.173 3 26985 26954.7 0.034 1.207 4 19453 19313.5 1.008 2.215 5 13710 13851.4 1.444 3.659 6 10019 9943.5 0.573 4.231 7 7111 7145.0 0.162 4.393 8 5166 5139.1 0.141 4.535 9 3634 3699.9 1.173 5.707 10 2779 2666.3 4.764 10.471 11 1924 1923.3 0.000 10.471 12 1413 1388.7 0.424 10.895 13 1058 1003.7 2.936 13.831 14 741 726.1 0.304 14.135 15 552 525.8 1.302 15.437 16 395 381.2 0.503 15.940 17 273 276.5 0.045 15.985 18 224 200.8 2.673 18.659 19 150 146.0 0.110 18.769 20 103 106.2 0.097 18.866 21 263 287.1 2.025 20.892 Chisq= 20.89 for 20 degrees of freedom, p= 0.59646 SUMMARY of craptest p-value for no. of wins: 0.581750 p-value for throws/game: 0.596461 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-27_07:31 No. of wins: Observed Expected 98662 98585.9 z-score= 0.341, pvalue=0.63328 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66673 66666.7 0.001 0.001 2 37564 37654.3 0.217 0.217 3 27001 26954.7 0.079 0.297 4 19340 19313.5 0.036 0.333 5 13929 13851.4 0.435 0.768 6 9801 9943.5 2.043 2.811 7 7222 7145.0 0.829 3.640 8 5026 5139.1 2.488 6.128 9 3749 3699.9 0.653 6.781 10 2723 2666.3 1.206 7.987 11 1952 1923.3 0.427 8.414 12 1305 1388.7 5.049 13.463 13 1010 1003.7 0.039 13.503 14 717 726.1 0.115 13.618 15 557 525.8 1.847 15.465 16 385 381.2 0.039 15.504 17 313 276.5 4.807 20.311 18 196 200.8 0.116 20.427 19 130 146.0 1.750 22.177 20 107 106.2 0.006 22.183 21 300 287.1 0.578 22.761 Chisq= 22.76 for 20 degrees of freedom, p= 0.69934 SUMMARY of craptest p-value for no. of wins: 0.633278 p-value for throws/game: 0.699336 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0034,0.0060,0.0062,0.0085,0.0085,0.0125,0.0193,0.0206,0.0255,0.0261, 0.0304,0.0322,0.0332,0.0414,0.0541,0.0571,0.0592,0.0596,0.0664,0.0694, 0.0737,0.0787,0.0826,0.0828,0.0884,0.0895,0.0917,0.0931,0.0965,0.0970, 0.0995,0.0997,0.1021,0.1073,0.1089,0.1110,0.1162,0.1177,0.1202,0.1209, 0.1259,0.1307,0.1366,0.1381,0.1383,0.1488,0.1495,0.1509,0.1600,0.1608, 0.1625,0.1648,0.1745,0.1782,0.1792,0.1797,0.1806,0.1874,0.1883,0.1942, 0.2083,0.2094,0.2175,0.2204,0.2227,0.2279,0.2292,0.2318,0.2354,0.2412, 0.2415,0.2467,0.2481,0.2527,0.2528,0.2547,0.2562,0.2571,0.2636,0.2738, 0.2817,0.2839,0.2847,0.2855,0.2861,0.2875,0.2878,0.2934,0.2958,0.2989, 0.3006,0.3025,0.3155,0.3209,0.3226,0.3288,0.3326,0.3348,0.3442,0.3492, 0.3548,0.3602,0.3643,0.3707,0.3709,0.3720,0.3742,0.3759,0.3850,0.3869, 0.3888,0.3893,0.3893,0.3907,0.3938,0.3947,0.3966,0.3991,0.4055,0.4121, 0.4132,0.4194,0.4206,0.4256,0.4315,0.4388,0.4404,0.4420,0.4428,0.4504, 0.4504,0.4557,0.4585,0.4671,0.4690,0.4784,0.4793,0.4887,0.4889,0.4899, 0.4901,0.4954,0.4973,0.5000,0.5020,0.5031,0.5133,0.5182,0.5278,0.5292, 0.5362,0.5384,0.5454,0.5508,0.5535,0.5536,0.5545,0.5561,0.5620,0.5680, 0.5739,0.5817,0.5841,0.5883,0.5965,0.5966,0.5977,0.5998,0.5999,0.6021, 0.6032,0.6038,0.6118,0.6123,0.6173,0.6246,0.6248,0.6257,0.6280,0.6297, 0.6333,0.6377,0.6426,0.6544,0.6563,0.6564,0.6573,0.6674,0.6676,0.6676, 0.6699,0.6706,0.6714,0.6745,0.6755,0.6843,0.6923,0.6933,0.6971,0.6993, 0.7115,0.7152,0.7158,0.7284,0.7311,0.7334,0.7344,0.7356,0.7399,0.7410, 0.7492,0.7596,0.7617,0.7619,0.7639,0.7706,0.7709,0.7756,0.7758,0.7812, 0.7914,0.7990,0.8046,0.8075,0.8115,0.8132,0.8193,0.8223,0.8311,0.8362, 0.8373,0.8386,0.8425,0.8433,0.8435,0.8460,0.8472,0.8479,0.8493,0.8495, 0.8514,0.8518,0.8539,0.8544,0.8546,0.8601,0.8612,0.8693,0.8820,0.8937, 0.9053,0.9069,0.9073,0.9227,0.9312,0.9321,0.9439,0.9476,0.9496,0.9547, 0.9555,0.9602,0.9639,0.9660,0.9714,0.9752,0.9813,0.9857,0.9878, Overall p-value after applying KStest on 269 p-values = 0.247796 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.