RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-07_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.83 13.6228 0.306399 2 to 25 16.11 11.6378 0.178443 3 to 26 15.98 20.3278 0.742195 4 to 27 15.82 20.0838 0.730036 5 to 28 16.11 8.1235 0.036166 6 to 29 15.99 7.4735 0.023451 7 to 30 16.03 19.4290 0.695527 8 to 31 15.85 21.6219 0.800298 9 to 32 15.67 19.9391 0.722642 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.404661 Tough bday spacings test for dh-ranFile-2016-05-07_10:31: 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 15 28 77 102 96 72 44 35 15 12 4 (O-E)^2/E 3.7 2.0 0.2 0.2 0.0 0.5 1.3 0.9 0.0 4.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 13.216, p= 0.788 RESULTS OF GCD FOR dh-ranFile-2016-05-07_10:31 Euclid's algorithm: p-value, steps to gcd: 0.360643 p-value, dist. of gcd's: 0.612918 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-07_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.811 0.274 0.133 0.805 0.510 0.253 0.579 0.272 Bits 8 to 15---> 0.359 0.562 0.257 0.671 0.331 0.415 0.620 0.601 Bits 16 to 23---> 0.677 0.165 0.306 0.817 0.357 0.187 0.558 0.782 Bits 24 to 31---> 0.436 0.267 0.223 0.778 0.625 0.356 0.551 0.730 KS test for the above 32 p values: 0.867 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-07_10:31, p-values for 5 runs: 0.5760, 0.8968, 0.4776, 0.2197, 0.8949 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-07_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 189 211.4 2.377 2.377 r= 29 5080 5134.0 0.568 2.945 r= 30 23008 23103.0 0.391 3.336 r= 31 11723 11551.5 2.545 5.882 chi-square = 5.882 with df = 3; p-value = 0.882 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-07_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 251 211.4 7.411 7.411 r= 30 5251 5134.0 2.666 10.076 r= 31 23043 23103.0 0.156 10.233 r= 32 11455 11551.5 0.807 11.039 chi-square = 11.039 with df = 3; p-value = 0.988 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-07_10:31 b-rank test for bits 1 to 8, p=0.42054 b-rank test for bits 2 to 9, p=0.54716 b-rank test for bits 3 to 10, p=0.34572 b-rank test for bits 4 to 11, p=0.78562 b-rank test for bits 5 to 12, p=0.78446 b-rank test for bits 6 to 13, p=0.11510 b-rank test for bits 7 to 14, p=0.30084 b-rank test for bits 8 to 15, p=0.40046 b-rank test for bits 9 to 16, p=0.94830 b-rank test for bits 10 to 17, p=0.55414 b-rank test for bits 11 to 18, p=0.46042 b-rank test for bits 12 to 19, p=0.13536 b-rank test for bits 13 to 20, p=0.49181 b-rank test for bits 14 to 21, p=0.01074 b-rank test for bits 15 to 22, p=0.20611 b-rank test for bits 16 to 23, p=0.18397 b-rank test for bits 17 to 24, p=0.02614 b-rank test for bits 18 to 25, p=0.56003 b-rank test for bits 19 to 26, p=0.38037 b-rank test for bits 20 to 27, p=0.76959 b-rank test for bits 21 to 28, p=0.30080 b-rank test for bits 22 to 29, p=0.11409 b-rank test for bits 23 to 30, p=0.26249 b-rank test for bits 24 to 31, p=0.06520 b-rank test for bits 25 to 32, p=0.17198 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 = 0.047806 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-07_10:31 (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 142417 1.19 0.882217 2 141484 -0.99 0.160169 3 141720 -0.44 0.329114 4 142034 0.29 0.614583 5 142607 1.63 0.948457 6 141893 -0.04 0.484782 7 142004 0.22 0.587528 8 141648 -0.61 0.270738 9 142198 0.67 0.749991 10 141797 -0.26 0.396486 11 142296 0.90 0.816852 12 141352 -1.30 0.096429 13 141025 -2.07 0.019405 14 141611 -0.70 0.242891 15 141502 -0.95 0.170623 16 141608 -0.70 0.240703 17 141156 -1.76 0.039194 18 141776 -0.31 0.377703 19 141286 -1.46 0.072644 20 141591 -0.74 0.228510 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-07_10:31 Bits used No. missing words z-score p-value 23 to 32 142449 1.8609 0.968623 22 to 31 142355 1.5368 0.937828 21 to 30 142098 0.6506 0.742343 20 to 29 142035 0.4333 0.667618 19 to 28 141738 -0.5908 0.277330 18 to 27 141454 -1.5701 0.058196 17 to 26 141944 0.1196 0.547581 16 to 25 142096 0.6437 0.740112 15 to 24 142240 1.1402 0.872907 14 to 23 142167 0.8885 0.812869 13 to 22 141781 -0.4425 0.329058 12 to 21 141649 -0.8977 0.184676 11 to 20 142275 1.2609 0.896333 10 to 19 141665 -0.8425 0.199749 9 to 18 142087 0.6127 0.729948 8 to 17 141996 0.2989 0.617477 7 to 16 141914 0.0161 0.506424 6 to 15 141428 -1.6598 0.048482 5 to 14 141824 -0.2942 0.384287 4 to 13 141862 -0.1632 0.435178 3 to 12 141962 0.1816 0.572060 2 to 11 142094 0.6368 0.737870 1 to 10 142257 1.1989 0.884709 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-07_10:31 Bits used No. missing words z-score p-value 28 to 32 141620 -0.9808 0.163351 27 to 31 142293 1.3006 0.903298 26 to 30 141810 -0.3367 0.368167 25 to 29 141440 -1.5909 0.055811 24 to 28 141614 -1.0011 0.158385 23 to 27 142369 1.5582 0.940407 22 to 26 141178 -2.4791 0.006586 21 to 25 141410 -1.6926 0.045262 20 to 24 142085 0.5955 0.724243 19 to 23 141735 -0.5909 0.277277 18 to 22 141608 -1.0215 0.153519 17 to 21 141684 -0.7638 0.222484 16 to 20 142233 1.0972 0.863720 15 to 19 141506 -1.3672 0.085778 14 to 18 141906 -0.0113 0.495497 13 to 17 140965 -3.2011 0.000684 12 to 16 141685 -0.7604 0.223496 11 to 15 141471 -1.4859 0.068658 10 to 14 141245 -2.2520 0.012162 9 to 13 142202 0.9921 0.839426 8 to 12 141670 -0.8113 0.208600 7 to 11 141789 -0.4079 0.341674 6 to 10 141821 -0.2994 0.382308 5 to 9 141839 -0.2384 0.405783 4 to 8 141791 -0.4011 0.344166 3 to 7 141779 -0.4418 0.329318 2 to 6 141566 -1.1638 0.122246 1 to 5 141756 -0.5198 0.301615 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-07_10:31 Bits used No. missing words z-score p-value 31 to 32 141483 -1.2576 0.104266 30 to 31 141991 0.2409 0.595189 29 to 30 141572 -0.9951 0.159850 28 to 29 142300 1.1524 0.875426 27 to 28 141929 0.0580 0.523135 26 to 27 141955 0.1347 0.553583 25 to 26 141829 -0.2370 0.406343 24 to 25 141589 -0.9449 0.172348 23 to 24 141620 -0.8535 0.196696 22 to 23 141398 -1.5083 0.065733 21 to 22 142222 0.9223 0.821822 20 to 21 141761 -0.4376 0.330856 19 to 20 141648 -0.7709 0.220388 18 to 19 141860 -0.1455 0.442152 17 to 18 141957 0.1406 0.555915 16 to 17 142152 0.7158 0.762955 15 to 16 141665 -0.7207 0.235536 14 to 15 141760 -0.4405 0.329787 13 to 14 142262 1.0403 0.850905 12 to 13 141543 -1.0806 0.139933 11 to 12 141877 -0.0954 0.462011 10 to 11 141899 -0.0305 0.487845 9 to 10 141806 -0.3048 0.380256 8 to 9 141484 -1.2547 0.104801 7 to 8 141890 -0.0570 0.477264 6 to 7 142140 0.6804 0.751888 5 to 6 141842 -0.1986 0.421283 4 to 5 141833 -0.2252 0.410927 3 to 4 142126 0.6391 0.738636 2 to 3 142121 0.6244 0.733816 1 to 2 141997 0.2586 0.602033 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-07_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2528.54 0.404 0.656741 Test results for specific bytes for dh-ranFile-2016-05-07_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2580.80 1.143 0.873405 2 to 9 2462.43 -0.531 0.297575 3 to 10 2500.25 0.004 0.501427 4 to 11 2563.84 0.903 0.816675 5 to 12 2526.68 0.377 0.647040 6 to 13 2518.41 0.260 0.602700 7 to 14 2508.00 0.113 0.545045 8 to 15 2417.00 -1.174 0.120227 9 to 16 2491.32 -0.123 0.451148 10 to 17 2492.32 -0.109 0.456783 11 to 18 2483.97 -0.227 0.410305 12 to 19 2553.65 0.759 0.775981 13 to 20 2481.40 -0.263 0.396274 14 to 21 2449.97 -0.707 0.239636 15 to 22 2474.30 -0.363 0.358141 16 to 23 2602.09 1.444 0.925605 17 to 24 2533.76 0.477 0.683491 18 to 25 2442.50 -0.813 0.208076 19 to 26 2417.05 -1.173 0.120388 20 to 27 2559.71 0.844 0.800778 21 to 28 2556.14 0.794 0.786383 22 to 29 2461.34 -0.547 0.292299 23 to 30 2577.33 1.094 0.862932 24 to 31 2517.84 0.252 0.599597 25 to 32 2471.26 -0.406 0.342223 CDPARK for dh-ranFile-2016-05-07_10:31: 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 3529 0.2740 0.607947 3542 0.8676 0.807188 3551 1.2785 0.899470 3500 -1.0502 0.146807 3488 -1.5982 0.055002 3555 1.4612 0.928018 3526 0.1370 0.554479 3538 0.6849 0.753306 3564 1.8721 0.969407 Square side=100, avg. no. parked=3532.70 sample std.=22.48 p-value of the KSTEST for those 10 p-values: 0.158911 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-07_10:31 0.1263,0.5969,0.3401,0.9218,0.5031,0.6946,0.9139,0.9047,0.7738,0.1793, The KS test for those 10 p-values: 0.482630 The 3DSPHERES test for dh-ranFile-2016-05-07_10:31 sample no r^3 equiv. uni. 1 59.536 0.862555 2 20.988 0.503213 3 59.393 0.861901 4 5.712 0.173369 5 69.738 0.902179 6 26.331 0.584268 7 17.165 0.435696 8 3.479 0.109504 9 19.846 0.483942 10 47.374 0.793848 11 46.293 0.786286 12 0.745 0.024520 13 27.367 0.598372 14 5.305 0.162068 15 4.436 0.137442 16 6.104 0.184089 17 51.901 0.822723 18 25.387 0.570971 19 0.750 0.024681 20 17.071 0.433936 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.721177 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-07_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 1.8 -1.1 0.8 -1.3 -0.2 -1.2 0.3 -0.8 0.1 0.5 1.0 0.2 -0.5 -2.8 -0.7 -1.0 0.0 1.8 1.3 1.8 0.2 -1.8 -0.4 1.3 0.8 1.2 -1.8 0.2 -0.9 0.8 -0.3 -0.2 0.4 0.2 1.7 -1.6 0.2 0.1 -0.7 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:49.051715 z-score=0.769405, p-value=0.788718 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-07_10:31 Test no p-value 1 0.038484 2 0.989053 3 0.105517 4 0.576424 5 0.256569 6 0.772773 7 0.222379 8 0.067339 9 0.829851 10 0.062105 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.139629 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-07_10:31: (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 66891 0.75 66691 0.01 3 25000.00 24809 1.46 25042 0.07 4 6666.67 6655 0.02 6631 0.19 5 1388.89 1379 0.07 1350 1.09 6 238.10 231 0.21 249 0.50 7 34.72 32 0.21 31 0.40 8 4.96 2 1.77 5 0.00 p=0.39012 p=0.10545 Number of rngs required: 687376, p-value: 0.116 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-07_10:31 No. of wins: Observed Expected 98816 98585.9 z-score= 1.029, pvalue=0.84834 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66706 66666.7 0.023 0.023 2 37743 37654.3 0.209 0.232 3 27016 26954.7 0.139 0.371 4 19573 19313.5 3.488 3.859 5 13755 13851.4 0.671 4.530 6 9939 9943.5 0.002 4.532 7 7023 7145.0 2.084 6.616 8 5017 5139.1 2.900 9.516 9 3627 3699.9 1.435 10.951 10 2649 2666.3 0.112 11.063 11 1930 1923.3 0.023 11.086 12 1416 1388.7 0.535 11.621 13 991 1003.7 0.161 11.782 14 753 726.1 0.994 12.776 15 485 525.8 3.171 15.947 16 388 381.2 0.123 16.070 17 257 276.5 1.381 17.451 18 198 200.8 0.040 17.491 19 140 146.0 0.245 17.736 20 94 106.2 1.405 19.141 21 300 287.1 0.578 19.719 Chisq= 19.72 for 20 degrees of freedom, p= 0.52439 SUMMARY of craptest p-value for no. of wins: 0.848337 p-value for throws/game: 0.524391 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-07_10:31 No. of wins: Observed Expected 98480 98585.9 z-score=-0.473, pvalue=0.31794 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66844 66666.7 0.472 0.472 2 37347 37654.3 2.508 2.980 3 26970 26954.7 0.009 2.989 4 19559 19313.5 3.122 6.110 5 14030 13851.4 2.302 8.413 6 9790 9943.5 2.371 10.783 7 7040 7145.0 1.544 12.327 8 5068 5139.1 0.983 13.310 9 3668 3699.9 0.274 13.585 10 2656 2666.3 0.040 13.624 11 1966 1923.3 0.947 14.571 12 1385 1388.7 0.010 14.581 13 1051 1003.7 2.228 16.809 14 726 726.1 0.000 16.809 15 532 525.8 0.072 16.881 16 372 381.2 0.220 17.101 17 282 276.5 0.108 17.209 18 190 200.8 0.584 17.793 19 149 146.0 0.062 17.855 20 81 106.2 5.986 23.841 21 294 287.1 0.165 24.006 Chisq= 24.01 for 20 degrees of freedom, p= 0.75787 SUMMARY of craptest p-value for no. of wins: 0.317942 p-value for throws/game: 0.757871 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0066,0.0107,0.0122,0.0194,0.0235,0.0245,0.0247,0.0261,0.0362, 0.0385,0.0392,0.0453,0.0478,0.0485,0.0550,0.0558,0.0582,0.0621,0.0652, 0.0657,0.0673,0.0687,0.0726,0.0858,0.0964,0.1043,0.1048,0.1054,0.1055, 0.1095,0.1141,0.1151,0.1164,0.1202,0.1204,0.1222,0.1263,0.1334,0.1354, 0.1374,0.1396,0.1399,0.1468,0.1535,0.1584,0.1589,0.1599,0.1602,0.1621, 0.1634,0.1654,0.1706,0.1720,0.1723,0.1734,0.1784,0.1793,0.1840,0.1841, 0.1847,0.1873,0.1967,0.1997,0.2061,0.2081,0.2086,0.2197,0.2204,0.2224, 0.2225,0.2228,0.2235,0.2285,0.2355,0.2396,0.2407,0.2429,0.2533,0.2566, 0.2570,0.2625,0.2673,0.2707,0.2723,0.2740,0.2773,0.2773,0.2923,0.2976, 0.3008,0.3008,0.3016,0.3057,0.3064,0.3179,0.3291,0.3291,0.3293,0.3298, 0.3309,0.3313,0.3401,0.3417,0.3422,0.3442,0.3457,0.3559,0.3569,0.3581, 0.3589,0.3606,0.3682,0.3777,0.3803,0.3804,0.3823,0.3843,0.3901,0.3963, 0.3965,0.4005,0.4047,0.4058,0.4063,0.4103,0.4109,0.4147,0.4205,0.4213, 0.4339,0.4352,0.4357,0.4358,0.4422,0.4511,0.4568,0.4604,0.4620,0.4773, 0.4776,0.4826,0.4839,0.4848,0.4878,0.4918,0.4955,0.5014,0.5031,0.5032, 0.5064,0.5097,0.5231,0.5244,0.5450,0.5472,0.5476,0.5512,0.5536,0.5541, 0.5545,0.5559,0.5578,0.5600,0.5616,0.5710,0.5721,0.5760,0.5764,0.5794, 0.5843,0.5875,0.5952,0.5969,0.5984,0.5996,0.6013,0.6020,0.6027,0.6079, 0.6129,0.6146,0.6175,0.6202,0.6251,0.6470,0.6567,0.6676,0.6712,0.6775, 0.6835,0.6923,0.6946,0.6955,0.7212,0.7226,0.7242,0.7299,0.7300,0.7304, 0.7338,0.7379,0.7386,0.7401,0.7422,0.7423,0.7500,0.7519,0.7533,0.7579, 0.7630,0.7696,0.7728,0.7738,0.7760,0.7784,0.7819,0.7845,0.7856,0.7863, 0.7864,0.7882,0.7887,0.7938,0.8003,0.8008,0.8050,0.8072,0.8108,0.8129, 0.8167,0.8169,0.8171,0.8218,0.8227,0.8299,0.8394,0.8483,0.8509,0.8619, 0.8626,0.8629,0.8637,0.8669,0.8729,0.8734,0.8754,0.8822,0.8825,0.8847, 0.8949,0.8963,0.8968,0.8995,0.9022,0.9033,0.9047,0.9139,0.9218,0.9256, 0.9280,0.9378,0.9404,0.9483,0.9485,0.9686,0.9694,0.9885,0.9891, Overall p-value after applying KStest on 269 p-values = 0.070051 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.