RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-07_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.82 31.4966 0.982634 2 to 25 15.77 15.9297 0.471178 3 to 26 15.85 12.4358 0.226941 4 to 27 15.81 17.6281 0.587344 5 to 28 15.94 19.3088 0.688902 6 to 29 15.59 19.1502 0.680018 7 to 30 15.68 18.0049 0.611466 8 to 31 15.78 17.6952 0.591689 9 to 32 15.76 10.3633 0.112312 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.587629 Tough bday spacings test for dh-ranFile-2015-07-07_17:31: 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 40 60 103 96 83 65 25 15 5 3 (O-E)^2/E 1.9 0.3 2.4 0.3 0.0 0.3 3.2 0.8 0.0 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 9.853, p= 0.546 RESULTS OF GCD FOR dh-ranFile-2015-07-07_17:31 Euclid's algorithm: p-value, steps to gcd: 0.789163 p-value, dist. of gcd's: 0.507893 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-07_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.185 0.124 0.430 0.648 0.461 0.361 0.691 0.026 Bits 8 to 15---> 0.599 0.945 0.845 0.659 0.700 0.873 0.255 0.558 Bits 16 to 23---> 0.763 0.580 0.651 0.673 0.849 0.052 0.220 0.136 Bits 24 to 31---> 0.903 0.810 0.252 0.301 0.659 0.229 0.995 0.748 KS test for the above 32 p values: 0.285 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-07_17:31, p-values for 5 runs: 0.2388, 0.5053, 0.5003, 0.6290, 0.8795 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-07_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5123 5134.0 0.024 0.171 r= 30 23023 23103.0 0.277 0.448 r= 31 11637 11551.5 0.632 1.081 chi-square = 1.081 with df = 3; p-value = 0.218 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-07_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5167 5134.0 0.212 0.304 r= 31 23179 23103.0 0.250 0.554 r= 32 11447 11551.5 0.946 1.500 chi-square = 1.500 with df = 3; p-value = 0.318 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-07_17:31 b-rank test for bits 1 to 8, p=0.33625 b-rank test for bits 2 to 9, p=0.75219 b-rank test for bits 3 to 10, p=0.61189 b-rank test for bits 4 to 11, p=0.11546 b-rank test for bits 5 to 12, p=0.43652 b-rank test for bits 6 to 13, p=0.21657 b-rank test for bits 7 to 14, p=0.30591 b-rank test for bits 8 to 15, p=0.41560 b-rank test for bits 9 to 16, p=0.77796 b-rank test for bits 10 to 17, p=0.61392 b-rank test for bits 11 to 18, p=0.81296 b-rank test for bits 12 to 19, p=0.01294 b-rank test for bits 13 to 20, p=0.67331 b-rank test for bits 14 to 21, p=0.52022 b-rank test for bits 15 to 22, p=0.18378 b-rank test for bits 16 to 23, p=0.75710 b-rank test for bits 17 to 24, p=0.88314 b-rank test for bits 18 to 25, p=0.76600 b-rank test for bits 19 to 26, p=0.81004 b-rank test for bits 20 to 27, p=0.38353 b-rank test for bits 21 to 28, p=0.38548 b-rank test for bits 22 to 29, p=0.49010 b-rank test for bits 23 to 30, p=0.42509 b-rank test for bits 24 to 31, p=0.46782 b-rank test for bits 25 to 32, p=0.56796 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 = 0.439364 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-07_17:31 (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 143154 2.91 0.998182 2 141779 -0.30 0.380370 3 141327 -1.36 0.086823 4 141540 -0.86 0.194091 5 141590 -0.75 0.227804 6 141943 0.08 0.531352 7 141113 -1.86 0.031401 8 141905 -0.01 0.495964 9 142147 0.56 0.710657 10 141848 -0.14 0.443029 11 141622 -0.67 0.251005 12 141725 -0.43 0.333351 13 141967 0.13 0.553593 14 142212 0.71 0.760271 15 142074 0.38 0.649786 16 141822 -0.20 0.419160 17 142310 0.94 0.825401 18 141154 -1.76 0.038800 19 141436 -1.11 0.134382 20 141636 -0.64 0.261535 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-07_17:31 Bits used No. missing words z-score p-value 23 to 32 141948 0.1333 0.553040 22 to 31 141974 0.2230 0.588232 21 to 30 141875 -0.1184 0.452884 20 to 29 141559 -1.2080 0.113517 19 to 28 141341 -1.9598 0.025012 18 to 27 142502 2.0437 0.979508 17 to 26 141550 -1.2391 0.107660 16 to 25 141746 -0.5632 0.286647 15 to 24 141542 -1.2667 0.102639 14 to 23 142056 0.5058 0.693487 13 to 22 141989 0.2747 0.608236 12 to 21 141690 -0.7563 0.224732 11 to 20 141857 -0.1804 0.428400 10 to 19 141651 -0.8908 0.186520 9 to 18 142301 1.3506 0.911586 8 to 17 142273 1.2540 0.895085 7 to 16 142157 0.8540 0.803457 6 to 15 142170 0.8989 0.815637 5 to 14 142189 0.9644 0.832572 4 to 13 141856 -0.1839 0.427047 3 to 12 141710 -0.6873 0.245933 2 to 11 142086 0.6092 0.728806 1 to 10 141835 -0.2563 0.398856 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-07_17:31 Bits used No. missing words z-score p-value 28 to 32 142105 0.6633 0.746427 27 to 31 141976 0.2260 0.589399 26 to 30 141986 0.2599 0.602529 25 to 29 141829 -0.2723 0.392694 24 to 28 141383 -1.7842 0.037198 23 to 27 141905 -0.0147 0.494145 22 to 26 141896 -0.0452 0.481979 21 to 25 141950 0.1379 0.554826 20 to 24 141921 0.0396 0.515778 19 to 23 142002 0.3141 0.623291 18 to 22 142278 1.2497 0.894301 17 to 21 141644 -0.8994 0.184214 16 to 20 141700 -0.7096 0.238978 15 to 19 142093 0.6226 0.733230 14 to 18 142005 0.3243 0.627147 13 to 17 142152 0.8226 0.794635 12 to 16 142374 1.5752 0.942389 11 to 15 141932 0.0768 0.530628 10 to 14 142224 1.0667 0.856941 9 to 13 141960 0.1718 0.568188 8 to 12 142235 1.1040 0.865196 7 to 11 142114 0.6938 0.756095 6 to 10 142408 1.6904 0.954525 5 to 9 142303 1.3345 0.908976 4 to 8 142294 1.3040 0.903877 3 to 7 141803 -0.3604 0.359259 2 to 6 142016 0.3616 0.641172 1 to 5 141987 0.2633 0.603836 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-07_17:31 Bits used No. missing words z-score p-value 31 to 32 141855 -0.1603 0.436336 30 to 31 141776 -0.3933 0.347048 29 to 30 141807 -0.3019 0.381380 28 to 29 141414 -1.4612 0.071987 27 to 28 142007 0.2881 0.613370 26 to 27 142059 0.4415 0.670576 25 to 26 141965 0.1642 0.565220 24 to 25 142053 0.4238 0.664146 23 to 24 141919 0.0285 0.511378 22 to 23 142334 1.2527 0.894845 21 to 22 141404 -1.4906 0.068027 20 to 21 141968 0.1731 0.568701 19 to 20 141595 -0.9272 0.176904 18 to 19 141728 -0.5349 0.296361 17 to 18 141098 -2.3933 0.008349 16 to 17 141415 -1.4582 0.072393 15 to 16 141998 0.2616 0.603171 14 to 15 141827 -0.2429 0.404056 13 to 14 142267 1.0551 0.854304 12 to 13 142325 1.2262 0.889932 11 to 12 142340 1.2704 0.898031 10 to 11 142331 1.2439 0.893225 9 to 10 141828 -0.2399 0.405199 8 to 9 141647 -0.7738 0.219514 7 to 8 141573 -0.9921 0.160569 6 to 7 141722 -0.5526 0.290270 5 to 6 141461 -1.3225 0.093000 4 to 5 141967 0.1701 0.567541 3 to 4 142199 0.8545 0.803582 2 to 3 142702 2.3383 0.990313 1 to 2 142374 1.3707 0.914767 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-07_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2430.12 -0.988 0.161518 Test results for specific bytes for dh-ranFile-2015-07-07_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2609.85 1.554 0.939855 2 to 9 2535.31 0.499 0.691235 3 to 10 2346.49 -2.171 0.014967 4 to 11 2371.61 -1.816 0.034710 5 to 12 2612.29 1.588 0.943858 6 to 13 2647.79 2.090 0.981694 7 to 14 2593.24 1.319 0.906352 8 to 15 2466.03 -0.480 0.315453 9 to 16 2498.75 -0.018 0.492929 10 to 17 2439.21 -0.860 0.194996 11 to 18 2462.46 -0.531 0.297740 12 to 19 2494.80 -0.074 0.470666 13 to 20 2514.99 0.212 0.583947 14 to 21 2373.11 -1.794 0.036371 15 to 22 2570.53 0.997 0.840736 16 to 23 2496.07 -0.056 0.477863 17 to 24 2393.03 -1.513 0.065175 18 to 25 2461.74 -0.541 0.294218 19 to 26 2573.88 1.045 0.851949 20 to 27 2580.03 1.132 0.871142 21 to 28 2574.40 1.052 0.853638 22 to 29 2542.08 0.595 0.724131 23 to 30 2592.20 1.304 0.903866 24 to 31 2538.74 0.548 0.708128 25 to 32 2606.79 1.510 0.934506 CDPARK for dh-ranFile-2015-07-07_17:31: 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 3539 0.7306 0.767486 3507 -0.7306 0.232514 3536 0.5936 0.723613 3520 -0.1370 0.445521 3487 -1.6438 0.050105 3544 0.9589 0.831196 3493 -1.3699 0.085365 3550 1.2329 0.891189 3536 0.5936 0.723613 3524 0.0457 0.518210 Square side=100, avg. no. parked=3523.60 sample std.=20.55 p-value of the KSTEST for those 10 p-values: 0.858752 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-07_17:31 0.3938,0.5510,0.7018,0.4933,0.6078,0.5464,0.3333,0.6675,0.7021,0.1354, The KS test for those 10 p-values: 0.309765 The 3DSPHERES test for dh-ranFile-2015-07-07_17:31 sample no r^3 equiv. uni. 1 1.844 0.059600 2 15.623 0.405932 3 29.078 0.620633 4 30.525 0.638497 5 16.109 0.415474 6 37.947 0.717730 7 49.304 0.806689 8 20.619 0.497066 9 19.971 0.486084 10 0.076 0.002515 11 13.352 0.359212 12 2.964 0.094062 13 20.574 0.496320 14 21.096 0.505004 15 61.765 0.872396 16 10.794 0.302193 17 14.033 0.373604 18 1.418 0.046178 19 1.813 0.058639 20 8.266 0.240831 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.137035 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-07_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.6 1.8 0.6 -1.4 2.4 -0.1 0.8 -1.6 -0.0 0.3 0.2 -0.6 -0.9 0.4 0.3 1.5 -0.4 1.0 0.7 -0.3 -0.4 -1.0 -1.7 0.5 0.8 0.2 -0.5 0.1 0.1 -1.1 0.9 -0.6 0.1 -0.8 -1.0 -1.6 1.1 0.1 1.0 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:37.102312 z-score=-0.534382, p-value=0.314498 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-07_17:31 Test no p-value 1 0.034088 2 0.219893 3 0.881055 4 0.041654 5 0.451784 6 0.042823 7 0.682886 8 0.203935 9 0.069985 10 0.328876 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.020193 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-07_17:31: (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 66712 0.03 67047 2.17 3 25000.00 25014 0.01 24622 5.72 4 6666.67 6550 2.04 6675 0.01 5 1388.89 1454 3.05 1391 0.00 6 238.10 235 0.04 229 0.35 7 34.72 31 0.40 30 0.64 8 4.96 3 0.77 5 0.00 p=0.61444 p=0.82003 Number of rngs required: 687733, p-value: 0.219 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-07_17:31 No. of wins: Observed Expected 98523 98585.9 z-score=-0.281, pvalue=0.38930 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66461 66666.7 0.634 0.634 2 37820 37654.3 0.729 1.363 3 26963 26954.7 0.003 1.366 4 19438 19313.5 0.803 2.169 5 13870 13851.4 0.025 2.194 6 9849 9943.5 0.899 3.093 7 7177 7145.0 0.143 3.236 8 5133 5139.1 0.007 3.243 9 3654 3699.9 0.569 3.812 10 2646 2666.3 0.155 3.966 11 1981 1923.3 1.729 5.695 12 1408 1388.7 0.267 5.963 13 1035 1003.7 0.975 6.938 14 659 726.1 6.208 13.146 15 575 525.8 4.597 17.742 16 362 381.2 0.962 18.705 17 279 276.5 0.022 18.726 18 177 200.8 2.828 21.554 19 145 146.0 0.007 21.561 20 114 106.2 0.571 22.131 21 254 287.1 3.819 25.950 Chisq= 25.95 for 20 degrees of freedom, p= 0.83255 SUMMARY of craptest p-value for no. of wins: 0.389301 p-value for throws/game: 0.832545 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-07_17:31 No. of wins: Observed Expected 98331 98585.9 z-score=-1.140, pvalue=0.12717 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66722 66666.7 0.046 0.046 2 37554 37654.3 0.267 0.313 3 27222 26954.7 2.650 2.963 4 19250 19313.5 0.209 3.172 5 13774 13851.4 0.433 3.605 6 9895 9943.5 0.237 3.842 7 7085 7145.0 0.504 4.346 8 5110 5139.1 0.164 4.510 9 3669 3699.9 0.257 4.768 10 2725 2666.3 1.292 6.060 11 1919 1923.3 0.010 6.070 12 1353 1388.7 0.920 6.990 13 1069 1003.7 4.246 11.236 14 729 726.1 0.011 11.247 15 557 525.8 1.847 13.094 16 362 381.2 0.962 14.056 17 265 276.5 0.482 14.538 18 183 200.8 1.583 16.121 19 148 146.0 0.028 16.149 20 110 106.2 0.135 16.284 21 299 287.1 0.492 16.776 Chisq= 16.78 for 20 degrees of freedom, p= 0.33252 SUMMARY of craptest p-value for no. of wins: 0.127169 p-value for throws/game: 0.332515 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0025,0.0083,0.0129,0.0150,0.0202,0.0250,0.0256,0.0314,0.0341,0.0347, 0.0364,0.0372,0.0388,0.0417,0.0428,0.0462,0.0501,0.0525,0.0586,0.0596, 0.0652,0.0680,0.0700,0.0720,0.0724,0.0854,0.0868,0.0930,0.0941,0.1026, 0.1077,0.1123,0.1135,0.1155,0.1238,0.1272,0.1344,0.1354,0.1358,0.1370, 0.1606,0.1615,0.1769,0.1838,0.1842,0.1848,0.1865,0.1941,0.1950,0.2039, 0.2166,0.2183,0.2194,0.2195,0.2199,0.2201,0.2247,0.2269,0.2278,0.2289, 0.2325,0.2388,0.2390,0.2408,0.2459,0.2510,0.2521,0.2552,0.2615,0.2847, 0.2866,0.2903,0.2942,0.2964,0.2977,0.3009,0.3022,0.3059,0.3098,0.3145, 0.3155,0.3177,0.3289,0.3325,0.3333,0.3334,0.3362,0.3470,0.3592,0.3593, 0.3612,0.3736,0.3804,0.3814,0.3835,0.3855,0.3893,0.3927,0.3938,0.3989, 0.4041,0.4052,0.4059,0.4155,0.4156,0.4192,0.4251,0.4270,0.4284,0.4296, 0.4363,0.4365,0.4394,0.4430,0.4455,0.4518,0.4529,0.4613,0.4678,0.4707, 0.4712,0.4779,0.4820,0.4861,0.4901,0.4929,0.4933,0.4941,0.4960,0.4963, 0.4971,0.5003,0.5050,0.5053,0.5079,0.5114,0.5158,0.5182,0.5202,0.5306, 0.5314,0.5464,0.5465,0.5510,0.5530,0.5536,0.5548,0.5577,0.5652,0.5675, 0.5680,0.5682,0.5687,0.5804,0.5839,0.5873,0.5876,0.5882,0.5894,0.5917, 0.5987,0.6025,0.6032,0.6038,0.6078,0.6082,0.6115,0.6119,0.6134,0.6139, 0.6144,0.6206,0.6233,0.6271,0.6290,0.6385,0.6412,0.6484,0.6498,0.6512, 0.6587,0.6588,0.6641,0.6675,0.6706,0.6732,0.6733,0.6800,0.6829,0.6889, 0.6911,0.6912,0.6935,0.6995,0.7018,0.7021,0.7081,0.7107,0.7177,0.7236, 0.7236,0.7241,0.7288,0.7332,0.7464,0.7480,0.7522,0.7561,0.7571,0.7603, 0.7632,0.7660,0.7675,0.7780,0.7892,0.7946,0.8035,0.8036,0.8067,0.8096, 0.8100,0.8130,0.8156,0.8200,0.8254,0.8312,0.8325,0.8326,0.8407,0.8452, 0.8491,0.8519,0.8536,0.8543,0.8569,0.8588,0.8652,0.8711,0.8724,0.8727, 0.8795,0.8811,0.8831,0.8899,0.8912,0.8932,0.8943,0.8948,0.8951,0.8980, 0.9035,0.9039,0.9039,0.9064,0.9090,0.9116,0.9148,0.9345,0.9399,0.9424, 0.9439,0.9454,0.9545,0.9795,0.9817,0.9826,0.9903,0.9951,0.9982, Overall p-value after applying KStest on 269 p-values = 0.634076 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.