RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-09_18:31 (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 23.9566 0.879380 2 to 25 15.69 35.0728 0.993914 3 to 26 15.51 18.8193 0.660999 4 to 27 15.80 29.8744 0.972734 5 to 28 16.00 21.1400 0.779909 6 to 29 15.94 8.0683 0.034937 7 to 30 15.57 17.3849 0.571399 8 to 31 15.69 18.6137 0.648847 9 to 32 15.76 15.4494 0.436850 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.093209 Tough bday spacings test for dh-ranFile-2015-12-09_18:31: 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 12 35 68 105 101 78 53 24 11 9 4 (O-E)^2/E 0.9 0.1 0.4 0.5 0.1 0.0 0.0 1.1 1.0 0.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.002, p= 0.109 RESULTS OF GCD FOR dh-ranFile-2015-12-09_18:31 Euclid's algorithm: p-value, steps to gcd: 0.912547 p-value, dist. of gcd's: 0.119772 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-09_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.276 0.349 0.543 0.353 0.670 0.315 0.468 0.687 Bits 8 to 15---> 0.697 0.605 0.647 0.462 0.817 0.464 0.399 0.352 Bits 16 to 23---> 0.534 0.529 0.852 0.262 0.917 0.553 0.201 0.844 Bits 24 to 31---> 0.221 0.952 0.882 0.299 0.369 0.775 0.933 0.835 KS test for the above 32 p values: 0.861 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-09_18:31, p-values for 5 runs: 0.3970, 0.9071, 0.8639, 0.1167, 0.3093 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-09_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5086 5134.0 0.449 0.979 r= 30 23305 23103.0 1.765 2.744 r= 31 11387 11551.5 2.343 5.087 chi-square = 5.087 with df = 3; p-value = 0.834 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-09_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5083 5134.0 0.507 1.020 r= 31 23091 23103.0 0.006 1.026 r= 32 11625 11551.5 0.467 1.494 chi-square = 1.494 with df = 3; p-value = 0.316 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-09_18:31 b-rank test for bits 1 to 8, p=0.47515 b-rank test for bits 2 to 9, p=0.42253 b-rank test for bits 3 to 10, p=0.90152 b-rank test for bits 4 to 11, p=0.54426 b-rank test for bits 5 to 12, p=0.93646 b-rank test for bits 6 to 13, p=0.87676 b-rank test for bits 7 to 14, p=0.17400 b-rank test for bits 8 to 15, p=0.65713 b-rank test for bits 9 to 16, p=0.64448 b-rank test for bits 10 to 17, p=0.07323 b-rank test for bits 11 to 18, p=0.55752 b-rank test for bits 12 to 19, p=0.06990 b-rank test for bits 13 to 20, p=0.22672 b-rank test for bits 14 to 21, p=0.67389 b-rank test for bits 15 to 22, p=0.68829 b-rank test for bits 16 to 23, p=0.85350 b-rank test for bits 17 to 24, p=0.27631 b-rank test for bits 18 to 25, p=0.27961 b-rank test for bits 19 to 26, p=0.46630 b-rank test for bits 20 to 27, p=0.14560 b-rank test for bits 21 to 28, p=0.24125 b-rank test for bits 22 to 29, p=0.31017 b-rank test for bits 23 to 30, p=0.72992 b-rank test for bits 24 to 31, p=0.90844 b-rank test for bits 25 to 32, p=0.29032 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 = 0.955349 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-09_18:31 (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 141598 -0.73 0.233489 2 142349 1.03 0.847852 3 142172 0.61 0.730298 4 142179 0.63 0.735676 5 141384 -1.23 0.109835 6 140853 -2.47 0.006792 7 142082 0.40 0.656686 8 141538 -0.87 0.192808 9 142010 0.24 0.592977 10 141610 -0.70 0.242161 11 141881 -0.07 0.473613 12 142205 0.69 0.755160 13 142397 1.14 0.872735 14 142302 0.92 0.820547 15 141449 -1.08 0.141067 16 141463 -1.04 0.148514 17 141996 0.20 0.580237 18 142193 0.66 0.746264 19 141531 -0.88 0.188362 20 141760 -0.35 0.363582 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-09_18:31 Bits used No. missing words z-score p-value 23 to 32 141612 -1.0253 0.152617 22 to 31 142144 0.8092 0.790802 21 to 30 141918 0.0299 0.511925 20 to 29 141986 0.2644 0.604256 19 to 28 141642 -0.9218 0.178309 18 to 27 141774 -0.4667 0.320373 17 to 26 141797 -0.3873 0.349251 16 to 25 142030 0.4161 0.661333 15 to 24 141813 -0.3322 0.369880 14 to 23 142277 1.2678 0.897570 13 to 22 141491 -1.4425 0.074578 12 to 21 142417 1.7506 0.959991 11 to 20 141617 -1.0080 0.156719 10 to 19 142137 0.7851 0.783793 9 to 18 142438 1.8230 0.965848 8 to 17 141947 0.1299 0.551676 7 to 16 142101 0.6609 0.745672 6 to 15 142049 0.4816 0.684962 5 to 14 141739 -0.5873 0.278486 4 to 13 142296 1.3333 0.908791 3 to 12 141309 -2.0701 0.019221 2 to 11 141719 -0.6563 0.255812 1 to 10 141425 -1.6701 0.047449 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-09_18:31 Bits used No. missing words z-score p-value 28 to 32 142165 0.8667 0.806941 27 to 31 141631 -0.9435 0.172715 26 to 30 142073 0.5548 0.710489 25 to 29 141721 -0.6384 0.261605 24 to 28 141916 0.0226 0.509019 23 to 27 141865 -0.1503 0.440275 22 to 26 142416 1.7175 0.957058 21 to 25 142251 1.1582 0.876610 20 to 24 142035 0.4260 0.664946 19 to 23 142131 0.7514 0.773801 18 to 22 141744 -0.5604 0.287589 17 to 21 142284 1.2701 0.897970 16 to 20 141384 -1.7808 0.037474 15 to 19 141912 0.0091 0.503611 14 to 18 142485 1.9514 0.974497 13 to 17 141770 -0.4723 0.318355 12 to 16 141684 -0.7638 0.222484 11 to 15 142080 0.5785 0.718551 10 to 14 142664 2.5582 0.994739 9 to 13 141949 0.1345 0.553486 8 to 12 142070 0.5446 0.707001 7 to 11 141806 -0.3503 0.363068 6 to 10 141949 0.1345 0.553486 5 to 9 142046 0.4633 0.678421 4 to 8 141745 -0.5571 0.288746 3 to 7 141821 -0.2994 0.382308 2 to 6 142066 0.5311 0.702320 1 to 5 141308 -2.0384 0.020755 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-09_18:31 Bits used No. missing words z-score p-value 31 to 32 141423 -1.4346 0.075700 30 to 31 141808 -0.2989 0.382505 29 to 30 142208 0.8810 0.810850 28 to 29 141320 -1.7384 0.041067 27 to 28 141994 0.2498 0.598615 26 to 27 141737 -0.5083 0.305605 25 to 26 141815 -0.2783 0.390407 24 to 25 141224 -2.0216 0.021608 23 to 24 142029 0.3530 0.637959 22 to 23 142088 0.5271 0.700921 21 to 22 142080 0.5035 0.692677 20 to 21 142227 0.9371 0.825641 19 to 20 141857 -0.1544 0.438661 18 to 19 141942 0.0964 0.538387 17 to 18 142200 0.8574 0.804397 16 to 17 141855 -0.1603 0.436336 15 to 16 141841 -0.2016 0.420129 14 to 15 141811 -0.2901 0.385886 13 to 14 141807 -0.3019 0.381380 12 to 13 141779 -0.3845 0.350321 11 to 12 142925 2.9961 0.998633 10 to 11 142060 0.4445 0.671643 9 to 10 140907 -2.9567 0.001555 8 to 9 142405 1.4622 0.928150 7 to 8 141610 -0.8830 0.188624 6 to 7 141651 -0.7620 0.223019 5 to 6 141967 0.1701 0.567541 4 to 5 141605 -0.8977 0.184665 3 to 4 141783 -0.3727 0.354703 2 to 3 142260 1.0344 0.849531 1 to 2 141789 -0.3550 0.361311 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-09_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2488.86 -0.158 0.437386 Test results for specific bytes for dh-ranFile-2015-12-09_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2478.95 -0.298 0.382968 2 to 9 2519.91 0.282 0.610868 3 to 10 2582.43 1.166 0.878147 4 to 11 2468.80 -0.441 0.329536 5 to 12 2513.57 0.192 0.576120 6 to 13 2503.15 0.045 0.517757 7 to 14 2456.49 -0.615 0.269148 8 to 15 2510.04 0.142 0.556445 9 to 16 2544.42 0.628 0.735043 10 to 17 2627.82 1.808 0.964669 11 to 18 2498.08 -0.027 0.489144 12 to 19 2511.09 0.157 0.562298 13 to 20 2498.89 -0.016 0.493722 14 to 21 2370.54 -1.831 0.033562 15 to 22 2346.30 -2.174 0.014868 16 to 23 2469.84 -0.426 0.334875 17 to 24 2599.74 1.411 0.920806 18 to 25 2557.93 0.819 0.793683 19 to 26 2486.71 -0.188 0.425482 20 to 27 2467.88 -0.454 0.324822 21 to 28 2431.54 -0.968 0.166475 22 to 29 2473.90 -0.369 0.356017 23 to 30 2483.22 -0.237 0.406211 24 to 31 2599.28 1.404 0.919855 25 to 32 2614.38 1.618 0.947126 CDPARK for dh-ranFile-2015-12-09_18:31: 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 3534 0.5023 0.692266 3505 -0.8219 0.205562 3502 -0.9589 0.168804 3515 -0.3653 0.357445 3480 -1.9635 0.024796 3541 0.8219 0.794438 3547 1.0959 0.863437 3492 -1.4155 0.078457 3511 -0.5479 0.291865 3531 0.3653 0.642555 Square side=100, avg. no. parked=3515.80 sample std.=20.86 p-value of the KSTEST for those 10 p-values: 0.566391 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-09_18:31 0.7020,0.1648,0.8603,0.7219,0.8413,0.4483,0.8071,0.8928,0.0140,0.6158, The KS test for those 10 p-values: 0.255370 The 3DSPHERES test for dh-ranFile-2015-12-09_18:31 sample no r^3 equiv. uni. 1 16.197 0.417194 2 24.916 0.564185 3 50.174 0.812217 4 50.002 0.811137 5 22.051 0.520504 6 6.676 0.199522 7 9.086 0.261291 8 1.611 0.052273 9 22.866 0.533364 10 4.171 0.129814 11 19.269 0.473912 12 43.625 0.766407 13 10.888 0.304360 14 15.636 0.406185 15 2.946 0.093539 16 34.358 0.681858 17 22.859 0.533259 18 84.193 0.939579 19 103.616 0.968377 20 167.819 0.996280 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.912537 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-09_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.1 0.6 0.9 0.8 0.5 -0.1 0.2 -1.5 -0.3 0.7 -0.5 -1.3 -1.8 0.5 -0.6 1.6 1.6 1.2 -0.6 0.5 -0.4 -0.7 1.5 1.4 -0.9 -1.0 -2.3 0.1 -0.4 -1.7 -0.1 1.2 -0.5 -0.6 1.3 -1.4 0.2 1.3 0.4 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:43.976077 z-score=0.215608, p-value=0.612123 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-09_18:31 Test no p-value 1 0.407829 2 0.961348 3 0.558458 4 0.741850 5 0.061358 6 0.030533 7 0.538528 8 0.881962 9 0.228642 10 0.581878 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.960499 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-09_18:31: (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 66681 0.00 66434 0.81 3 25000.00 25038 0.06 25093 0.35 4 6666.67 6648 0.05 6764 1.42 5 1388.89 1374 0.16 1456 3.24 6 238.10 216 2.05 215 2.24 7 34.72 37 0.15 33 0.09 8 4.96 5 0.00 4 0.19 p=0.12855 p=0.78529 Number of rngs required: 689094, p-value: 0.788 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-09_18:31 No. of wins: Observed Expected 98676 98585.9 z-score= 0.403, pvalue=0.65659 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66773 66666.7 0.170 0.170 2 37385 37654.3 1.926 2.096 3 27051 26954.7 0.344 2.440 4 19274 19313.5 0.081 2.520 5 13751 13851.4 0.728 3.248 6 10045 9943.5 1.035 4.284 7 7250 7145.0 1.542 5.826 8 5118 5139.1 0.086 5.912 9 3703 3699.9 0.003 5.915 10 2705 2666.3 0.562 6.477 11 1923 1923.3 0.000 6.477 12 1416 1388.7 0.535 7.012 13 1010 1003.7 0.039 7.051 14 708 726.1 0.453 7.504 15 507 525.8 0.675 8.179 16 389 381.2 0.162 8.341 17 273 276.5 0.045 8.386 18 198 200.8 0.040 8.426 19 137 146.0 0.553 8.979 20 98 106.2 0.635 9.614 21 286 287.1 0.004 9.619 Chisq= 9.62 for 20 degrees of freedom, p= 0.02543 SUMMARY of craptest p-value for no. of wins: 0.656587 p-value for throws/game: 0.025427 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-09_18:31 No. of wins: Observed Expected 98712 98585.9 z-score= 0.564, pvalue=0.71368 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66533 66666.7 0.268 0.268 2 37761 37654.3 0.302 0.570 3 26793 26954.7 0.970 1.541 4 19600 19313.5 4.251 5.792 5 13885 13851.4 0.081 5.873 6 10051 9943.5 1.161 7.034 7 6966 7145.0 4.486 11.520 8 5189 5139.1 0.485 12.005 9 3696 3699.9 0.004 12.009 10 2737 2666.3 1.875 13.884 11 1867 1923.3 1.650 15.534 12 1339 1388.7 1.782 17.315 13 1004 1003.7 0.000 17.315 14 721 726.1 0.036 17.352 15 494 525.8 1.927 19.279 16 380 381.2 0.003 19.283 17 280 276.5 0.043 19.326 18 182 200.8 1.765 21.092 19 157 146.0 0.831 21.923 20 94 106.2 1.405 23.328 21 271 287.1 0.904 24.232 Chisq= 24.23 for 20 degrees of freedom, p= 0.76759 SUMMARY of craptest p-value for no. of wins: 0.713683 p-value for throws/game: 0.767592 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0068,0.0140,0.0149,0.0192,0.0208,0.0216,0.0248,0.0254,0.0305, 0.0336,0.0349,0.0375,0.0411,0.0474,0.0523,0.0614,0.0699,0.0732,0.0746, 0.0757,0.0785,0.0932,0.0935,0.1090,0.1098,0.1167,0.1198,0.1285,0.1298, 0.1411,0.1456,0.1485,0.1526,0.1567,0.1648,0.1665,0.1688,0.1727,0.1740, 0.1783,0.1847,0.1884,0.1886,0.1928,0.1995,0.2012,0.2056,0.2212,0.2225, 0.2230,0.2267,0.2286,0.2335,0.2413,0.2422,0.2554,0.2558,0.2613,0.2616, 0.2625,0.2691,0.2758,0.2763,0.2785,0.2796,0.2876,0.2887,0.2903,0.2919, 0.2987,0.3044,0.3056,0.3093,0.3102,0.3148,0.3163,0.3184,0.3204,0.3248, 0.3295,0.3349,0.3493,0.3493,0.3503,0.3517,0.3527,0.3547,0.3560,0.3574, 0.3613,0.3631,0.3636,0.3688,0.3699,0.3814,0.3823,0.3825,0.3830,0.3859, 0.3904,0.3970,0.3993,0.4062,0.4062,0.4078,0.4172,0.4201,0.4225,0.4255, 0.4363,0.4369,0.4374,0.4387,0.4403,0.4483,0.4618,0.4639,0.4663,0.4678, 0.4736,0.4739,0.4752,0.4891,0.4937,0.5036,0.5090,0.5119,0.5178,0.5205, 0.5286,0.5333,0.5334,0.5336,0.5384,0.5385,0.5428,0.5443,0.5517,0.5530, 0.5535,0.5535,0.5564,0.5575,0.5585,0.5623,0.5642,0.5664,0.5675,0.5714, 0.5761,0.5802,0.5819,0.5930,0.5986,0.6043,0.6051,0.6109,0.6121,0.6158, 0.6380,0.6426,0.6445,0.6474,0.6488,0.6566,0.6567,0.6571,0.6610,0.6613, 0.6649,0.6700,0.6716,0.6739,0.6784,0.6819,0.6850,0.6869,0.6883,0.6923, 0.6927,0.6972,0.7009,0.7020,0.7023,0.7070,0.7105,0.7137,0.7186,0.7219, 0.7299,0.7303,0.7350,0.7357,0.7418,0.7457,0.7463,0.7552,0.7664,0.7676, 0.7738,0.7755,0.7799,0.7838,0.7853,0.7877,0.7908,0.7937,0.7944,0.8044, 0.8069,0.8071,0.8108,0.8111,0.8122,0.8170,0.8205,0.8256,0.8345,0.8354, 0.8413,0.8436,0.8479,0.8495,0.8520,0.8535,0.8603,0.8610,0.8634,0.8639, 0.8727,0.8766,0.8768,0.8781,0.8794,0.8820,0.8821,0.8928,0.8976,0.8980, 0.9015,0.9071,0.9084,0.9088,0.9125,0.9125,0.9168,0.9199,0.9208,0.9282, 0.9325,0.9365,0.9396,0.9471,0.9520,0.9553,0.9571,0.9600,0.9605,0.9613, 0.9647,0.9658,0.9684,0.9727,0.9745,0.9939,0.9947,0.9963,0.9986, Overall p-value after applying KStest on 269 p-values = 0.419315 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.