RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-24_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.55 16.0128 0.477074 2 to 25 15.48 33.6048 0.990561 3 to 26 15.68 11.7294 0.183761 4 to 27 15.99 11.6090 0.176787 5 to 28 15.67 16.6744 0.523369 6 to 29 15.93 12.2571 0.215673 7 to 30 15.95 15.2761 0.424400 8 to 31 15.72 20.8885 0.768681 9 to 32 15.80 11.7201 0.183218 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.470205 Tough bday spacings test for dh-ranFile-2016-06-24_02:31: 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 9 31 74 107 99 88 45 30 13 2 2 (O-E)^2/E 0.0 0.9 0.0 0.9 0.0 1.2 1.0 0.0 0.2 3.2 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.502, p= 0.420 RESULTS OF GCD FOR dh-ranFile-2016-06-24_02:31 Euclid's algorithm: p-value, steps to gcd: 0.212101 p-value, dist. of gcd's: 0.936166 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-24_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.032 0.912 0.985 0.670 0.498 0.376 0.900 0.974 Bits 8 to 15---> 0.013 0.542 0.987 0.287 0.862 0.232 0.916 0.504 Bits 16 to 23---> 0.730 0.815 0.751 0.077 0.140 0.546 0.468 0.453 Bits 24 to 31---> 0.217 0.443 0.623 0.645 0.271 0.601 0.382 0.476 KS test for the above 32 p values: 0.376 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-24_02:31, p-values for 5 runs: 0.4926, 0.4016, 0.4257, 0.0798, 0.5144 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-24_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5166 5134.0 0.199 0.299 r= 30 23104 23103.0 0.000 0.299 r= 31 11514 11551.5 0.122 0.421 chi-square = 0.421 with df = 3; p-value = 0.064 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-24_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5201 5134.0 0.874 0.886 r= 31 23104 23103.0 0.000 0.886 r= 32 11482 11551.5 0.418 1.304 chi-square = 1.304 with df = 3; p-value = 0.272 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-24_02:31 b-rank test for bits 1 to 8, p=0.89411 b-rank test for bits 2 to 9, p=0.44486 b-rank test for bits 3 to 10, p=0.25821 b-rank test for bits 4 to 11, p=0.38473 b-rank test for bits 5 to 12, p=0.45536 b-rank test for bits 6 to 13, p=0.82969 b-rank test for bits 7 to 14, p=0.21641 b-rank test for bits 8 to 15, p=0.27365 b-rank test for bits 9 to 16, p=0.05515 b-rank test for bits 10 to 17, p=0.61505 b-rank test for bits 11 to 18, p=0.80749 b-rank test for bits 12 to 19, p=0.71089 b-rank test for bits 13 to 20, p=0.10303 b-rank test for bits 14 to 21, p=0.73306 b-rank test for bits 15 to 22, p=0.78604 b-rank test for bits 16 to 23, p=0.25122 b-rank test for bits 17 to 24, p=0.36970 b-rank test for bits 18 to 25, p=0.89902 b-rank test for bits 19 to 26, p=0.65806 b-rank test for bits 20 to 27, p=0.58002 b-rank test for bits 21 to 28, p=0.42437 b-rank test for bits 22 to 29, p=0.79703 b-rank test for bits 23 to 30, p=0.63746 b-rank test for bits 24 to 31, p=0.36656 b-rank test for bits 25 to 32, p=0.98817 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 = 0.708672 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-24_02:31 (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 142003 0.22 0.586619 2 141931 0.05 0.520190 3 142184 0.64 0.739483 4 141892 -0.04 0.483851 5 141190 -1.68 0.046413 6 142563 1.53 0.936653 7 141860 -0.12 0.454121 8 141593 -0.74 0.229927 9 141845 -0.15 0.440263 10 141978 0.16 0.563734 11 141193 -1.67 0.047098 12 141619 -0.68 0.248778 13 142081 0.40 0.655826 14 142776 2.02 0.978563 15 140978 -2.18 0.014777 16 142280 0.87 0.806769 17 141453 -1.07 0.143169 18 141595 -0.73 0.231348 19 141743 -0.39 0.348778 20 142201 0.68 0.752214 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-24_02:31 Bits used No. missing words z-score p-value 23 to 32 141989 0.2747 0.608236 22 to 31 141820 -0.3080 0.379028 21 to 30 142308 1.3747 0.915392 20 to 29 142252 1.1816 0.881322 19 to 28 141869 -0.1391 0.444698 18 to 27 141951 0.1437 0.557127 17 to 26 142093 0.6333 0.736746 16 to 25 142155 0.8471 0.801541 15 to 24 141288 -2.1425 0.016076 14 to 23 141237 -2.3184 0.010214 13 to 22 141792 -0.4046 0.342891 12 to 21 141857 -0.1804 0.428400 11 to 20 141568 -1.1770 0.119598 10 to 19 141697 -0.7322 0.232032 9 to 18 142044 0.4644 0.678812 8 to 17 141904 -0.0184 0.492668 7 to 16 141685 -0.7736 0.219598 6 to 15 142042 0.4575 0.676338 5 to 14 141677 -0.8011 0.211526 4 to 13 141803 -0.3667 0.356938 3 to 12 142082 0.5954 0.724217 2 to 11 141784 -0.4322 0.332808 1 to 10 141660 -0.8598 0.194961 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-24_02:31 Bits used No. missing words z-score p-value 28 to 32 142326 1.4124 0.921090 27 to 31 142236 1.1074 0.865930 26 to 30 142497 1.9921 0.976820 25 to 29 141215 -2.3537 0.009295 24 to 28 141412 -1.6859 0.045911 23 to 27 141430 -1.6248 0.052098 22 to 26 142223 1.0633 0.856174 21 to 25 141942 0.1107 0.544091 20 to 24 141864 -0.1537 0.438939 19 to 23 141904 -0.0181 0.492792 18 to 22 142067 0.5345 0.703493 17 to 21 141711 -0.6723 0.250695 16 to 20 141540 -1.2520 0.105291 15 to 19 142262 1.1955 0.884053 14 to 18 142078 0.5718 0.716259 13 to 17 141773 -0.4621 0.321992 12 to 16 141754 -0.5265 0.299256 11 to 15 141454 -1.5435 0.061356 10 to 14 141812 -0.3299 0.370726 9 to 13 142220 1.0531 0.853857 8 to 12 141694 -0.7299 0.232716 7 to 11 141948 0.1311 0.552146 6 to 10 142108 0.6735 0.749672 5 to 9 142392 1.6362 0.949098 4 to 8 141494 -1.4079 0.079581 3 to 7 141888 -0.0723 0.471180 2 to 6 142280 1.2565 0.895534 1 to 5 141753 -0.5299 0.298080 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-24_02:31 Bits used No. missing words z-score p-value 31 to 32 142309 1.1790 0.880794 30 to 31 142159 0.7365 0.769284 29 to 30 141834 -0.2222 0.412074 28 to 29 141995 0.2527 0.599755 27 to 28 142190 0.8279 0.796146 26 to 27 141984 0.2203 0.587168 25 to 26 141734 -0.5172 0.302509 24 to 25 141411 -1.4700 0.070781 23 to 24 141506 -1.1898 0.117070 22 to 23 141183 -2.1426 0.016074 21 to 22 142241 0.9784 0.836056 20 to 21 142021 0.3294 0.629077 19 to 20 141942 0.0964 0.538387 18 to 19 141635 -0.8092 0.209191 17 to 18 142196 0.8456 0.801122 16 to 17 141515 -1.1632 0.122371 15 to 16 141540 -1.0895 0.137974 14 to 15 142102 0.5683 0.715101 13 to 14 142122 0.6273 0.734784 12 to 13 141594 -0.9302 0.176140 11 to 12 142115 0.6067 0.727974 10 to 11 142416 1.4946 0.932491 9 to 10 141325 -1.7237 0.042382 8 to 9 141621 -0.8505 0.197515 7 to 8 141981 0.2114 0.583719 6 to 7 141825 -0.2488 0.401773 5 to 6 142222 0.9223 0.821822 4 to 5 141819 -0.2665 0.394942 3 to 4 141714 -0.5762 0.282242 2 to 3 141918 0.0256 0.510202 1 to 2 141215 -2.0482 0.020272 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-24_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2438.73 -0.867 0.193093 Test results for specific bytes for dh-ranFile-2016-06-24_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2470.20 -0.422 0.336695 2 to 9 2465.33 -0.490 0.311955 3 to 10 2550.11 0.709 0.760742 4 to 11 2383.55 -1.647 0.049795 5 to 12 2559.41 0.840 0.799596 6 to 13 2389.54 -1.562 0.059124 7 to 14 2477.01 -0.325 0.372542 8 to 15 2512.90 0.182 0.572392 9 to 16 2541.99 0.594 0.723664 10 to 17 2498.89 -0.016 0.493757 11 to 18 2586.77 1.227 0.890122 12 to 19 2384.43 -1.634 0.051094 13 to 20 2559.20 0.837 0.798773 14 to 21 2487.11 -0.182 0.427695 15 to 22 2534.14 0.483 0.685395 16 to 23 2403.23 -1.369 0.085563 17 to 24 2449.12 -0.720 0.235906 18 to 25 2576.34 1.080 0.859841 19 to 26 2524.35 0.344 0.634715 20 to 27 2506.18 0.087 0.534796 21 to 28 2424.82 -1.063 0.143857 22 to 29 2432.44 -0.955 0.169667 23 to 30 2391.71 -1.531 0.062834 24 to 31 2635.62 1.918 0.972446 25 to 32 2507.02 0.099 0.539528 CDPARK for dh-ranFile-2016-06-24_02:31: 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 3540 0.7763 0.781201 3523 0.0000 0.500000 3507 -0.7306 0.232514 3520 -0.1370 0.445521 3500 -1.0502 0.146807 3504 -0.8676 0.192812 3537 0.6393 0.738676 3482 -1.8721 0.030593 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3514.60 sample std.=16.77 p-value of the KSTEST for those 10 p-values: 0.357217 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-24_02:31 0.0506,0.5279,0.2766,0.0097,0.1621,0.4675,0.5316,0.8629,0.1329,0.4564, The KS test for those 10 p-values: 0.142400 The 3DSPHERES test for dh-ranFile-2016-06-24_02:31 sample no r^3 equiv. uni. 1 59.729 0.863437 2 6.758 0.201696 3 11.108 0.309451 4 31.110 0.645487 5 16.368 0.420497 6 58.862 0.859435 7 34.794 0.686454 8 43.804 0.767793 9 22.003 0.519741 10 87.928 0.946653 11 6.757 0.201660 12 4.936 0.151722 13 28.620 0.614802 14 9.096 0.261555 15 32.071 0.656661 16 101.920 0.966537 17 9.744 0.277320 18 5.002 0.153581 19 15.473 0.402967 20 88.301 0.947312 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.680580 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-24_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.3 -0.4 -1.0 1.2 -1.4 -0.5 0.2 -1.2 0.3 0.9 1.4 1.7 0.8 -0.9 0.2 0.1 0.2 0.4 -0.5 -1.4 0.2 -0.5 0.9 -1.2 -0.5 -2.0 -0.2 0.6 0.6 -0.9 -2.4 2.1 0.0 -0.6 0.6 1.0 -0.1 1.3 -0.1 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:42.614559 z-score=0.067054, p-value=0.555458 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-24_02:31 Test no p-value 1 0.331079 2 0.642678 3 0.892329 4 0.768270 5 0.554090 6 0.705979 7 0.053013 8 0.139892 9 0.360512 10 0.056945 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.844264 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-24_02:31: (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 66740 0.08 66473 0.56 3 25000.00 24924 0.23 25117 0.55 4 6666.67 6674 0.01 6725 0.51 5 1388.89 1372 0.21 1413 0.42 6 238.10 255 1.20 233 0.11 7 34.72 31 0.40 30 0.64 8 4.96 3 0.77 8 1.86 p=0.17852 p=0.41097 Number of rngs required: 689232, p-value: 0.831 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-24_02:31 No. of wins: Observed Expected 98607 98585.9 z-score= 0.095, pvalue=0.53767 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66272 66666.7 2.336 2.336 2 37831 37654.3 0.829 3.165 3 27038 26954.7 0.257 3.423 4 19321 19313.5 0.003 3.426 5 13631 13851.4 3.508 6.933 6 9983 9943.5 0.157 7.090 7 7304 7145.0 3.537 10.627 8 5160 5139.1 0.085 10.712 9 3698 3699.9 0.001 10.713 10 2679 2666.3 0.061 10.774 11 2025 1923.3 5.375 16.148 12 1430 1388.7 1.226 17.374 13 977 1003.7 0.711 18.085 14 759 726.1 1.487 19.572 15 525 525.8 0.001 19.573 16 348 381.2 2.883 22.457 17 270 276.5 0.155 22.611 18 215 200.8 1.000 23.611 19 142 146.0 0.109 23.720 20 125 106.2 3.322 27.042 21 267 287.1 1.409 28.451 Chisq= 28.45 for 20 degrees of freedom, p= 0.90085 SUMMARY of craptest p-value for no. of wins: 0.537667 p-value for throws/game: 0.900855 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-24_02:31 No. of wins: Observed Expected 98814 98585.9 z-score= 1.020, pvalue=0.84623 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66569 66666.7 0.143 0.143 2 37611 37654.3 0.050 0.193 3 26912 26954.7 0.068 0.261 4 19571 19313.5 3.434 3.695 5 13890 13851.4 0.107 3.802 6 9812 9943.5 1.740 5.542 7 7200 7145.0 0.423 5.965 8 5176 5139.1 0.265 6.231 9 3618 3699.9 1.811 8.042 10 2655 2666.3 0.048 8.090 11 1877 1923.3 1.116 9.206 12 1390 1388.7 0.001 9.207 13 1007 1003.7 0.011 9.218 14 783 726.1 4.452 13.670 15 559 525.8 2.092 15.762 16 390 381.2 0.205 15.967 17 303 276.5 2.532 18.499 18 170 200.8 4.733 23.232 19 129 146.0 1.976 25.208 20 113 106.2 0.433 25.641 21 265 287.1 1.703 27.345 Chisq= 27.34 for 20 degrees of freedom, p= 0.87416 SUMMARY of craptest p-value for no. of wins: 0.846226 p-value for throws/game: 0.874156 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0093,0.0097,0.0102,0.0132,0.0148,0.0161,0.0161,0.0203,0.0306,0.0321, 0.0424,0.0459,0.0464,0.0471,0.0498,0.0506,0.0511,0.0521,0.0530,0.0551, 0.0569,0.0591,0.0614,0.0628,0.0640,0.0708,0.0768,0.0796,0.0798,0.0856, 0.1030,0.1053,0.1171,0.1196,0.1224,0.1329,0.1380,0.1399,0.1399,0.1424, 0.1432,0.1439,0.1468,0.1517,0.1536,0.1621,0.1697,0.1761,0.1768,0.1785, 0.1832,0.1838,0.1928,0.1931,0.1950,0.1975,0.2017,0.2017,0.2092,0.2115, 0.2121,0.2157,0.2164,0.2173,0.2196,0.2299,0.2313,0.2320,0.2321,0.2325, 0.2327,0.2359,0.2488,0.2507,0.2512,0.2582,0.2613,0.2616,0.2714,0.2719, 0.2736,0.2766,0.2773,0.2822,0.2874,0.2981,0.2993,0.3025,0.3095,0.3120, 0.3220,0.3311,0.3328,0.3367,0.3429,0.3488,0.3569,0.3572,0.3605,0.3666, 0.3697,0.3707,0.3725,0.3762,0.3762,0.3790,0.3815,0.3847,0.3949,0.4016, 0.4018,0.4030,0.4110,0.4121,0.4201,0.4205,0.4244,0.4244,0.4257,0.4277, 0.4284,0.4389,0.4403,0.4433,0.4447,0.4449,0.4455,0.4531,0.4541,0.4554, 0.4564,0.4675,0.4680,0.4702,0.4712,0.4764,0.4771,0.4839,0.4926,0.4927, 0.4928,0.4938,0.4980,0.5000,0.5040,0.5102,0.5144,0.5182,0.5197,0.5202, 0.5234,0.5279,0.5316,0.5348,0.5377,0.5384,0.5395,0.5419,0.5441,0.5463, 0.5521,0.5541,0.5555,0.5571,0.5637,0.5724,0.5800,0.5837,0.5866,0.5872, 0.5998,0.6006,0.6082,0.6148,0.6150,0.6230,0.6291,0.6347,0.6375,0.6427, 0.6447,0.6455,0.6558,0.6567,0.6581,0.6695,0.6763,0.6788,0.6806,0.6854, 0.6865,0.7035,0.7060,0.7087,0.7109,0.7151,0.7163,0.7237,0.7242,0.7280, 0.7297,0.7331,0.7348,0.7367,0.7387,0.7395,0.7497,0.7512,0.7522,0.7607, 0.7678,0.7683,0.7687,0.7693,0.7812,0.7860,0.7961,0.7970,0.7988,0.7996, 0.8011,0.8015,0.8068,0.8075,0.8154,0.8218,0.8297,0.8315,0.8361,0.8443, 0.8462,0.8539,0.8562,0.8594,0.8598,0.8621,0.8629,0.8634,0.8659,0.8742, 0.8808,0.8813,0.8841,0.8901,0.8923,0.8941,0.8955,0.8990,0.9000,0.9009, 0.9121,0.9154,0.9160,0.9211,0.9325,0.9362,0.9367,0.9467,0.9473,0.9491, 0.9665,0.9724,0.9737,0.9768,0.9786,0.9848,0.9871,0.9882,0.9906, Overall p-value after applying KStest on 269 p-values = 0.553892 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.