RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-28_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.89 16.4379 0.506966 2 to 25 15.62 16.3738 0.502495 3 to 26 15.52 14.0626 0.337335 4 to 27 15.94 17.6726 0.590227 5 to 28 15.84 25.1736 0.909110 6 to 29 15.67 21.5607 0.797792 7 to 30 15.81 12.6897 0.243304 8 to 31 15.80 24.6673 0.897591 9 to 32 15.84 11.5656 0.174302 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.845181 Tough bday spacings test for dh-ranFile-2016-05-28_12:31: 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 33 73 106 100 76 53 31 10 7 6 (O-E)^2/E 1.9 0.4 0.0 0.7 0.1 0.1 0.0 0.1 1.6 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 5.682, p= 0.159 RESULTS OF GCD FOR dh-ranFile-2016-05-28_12:31 Euclid's algorithm: p-value, steps to gcd: 0.015284 p-value, dist. of gcd's: 0.401268 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-28_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.728 0.328 0.462 0.811 0.171 0.754 0.928 0.432 Bits 8 to 15---> 0.618 0.293 0.735 0.508 0.953 0.777 0.514 0.924 Bits 16 to 23---> 0.622 0.628 0.748 0.123 0.304 0.484 0.594 0.890 Bits 24 to 31---> 0.107 0.928 0.786 0.752 0.151 0.087 0.000 0.788 KS test for the above 32 p values: 0.711 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-28_12:31, p-values for 5 runs: 0.7691, 0.7372, 0.4611, 0.8830, 0.5708 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-28_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5083 5134.0 0.507 0.941 r= 30 23110 23103.0 0.002 0.943 r= 31 11586 11551.5 0.103 1.046 chi-square = 1.046 with df = 3; p-value = 0.210 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-28_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5156 5134.0 0.094 0.187 r= 31 23159 23103.0 0.136 0.322 r= 32 11478 11551.5 0.468 0.790 chi-square = 0.790 with df = 3; p-value = 0.148 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-28_12:31 b-rank test for bits 1 to 8, p=0.63991 b-rank test for bits 2 to 9, p=0.02431 b-rank test for bits 3 to 10, p=0.20502 b-rank test for bits 4 to 11, p=0.97394 b-rank test for bits 5 to 12, p=0.09687 b-rank test for bits 6 to 13, p=0.62643 b-rank test for bits 7 to 14, p=0.82204 b-rank test for bits 8 to 15, p=0.75492 b-rank test for bits 9 to 16, p=0.66381 b-rank test for bits 10 to 17, p=0.27308 b-rank test for bits 11 to 18, p=0.71467 b-rank test for bits 12 to 19, p=0.83000 b-rank test for bits 13 to 20, p=0.19096 b-rank test for bits 14 to 21, p=0.26077 b-rank test for bits 15 to 22, p=0.43421 b-rank test for bits 16 to 23, p=0.90154 b-rank test for bits 17 to 24, p=0.34445 b-rank test for bits 18 to 25, p=0.71576 b-rank test for bits 19 to 26, p=0.01910 b-rank test for bits 20 to 27, p=0.03823 b-rank test for bits 21 to 28, p=0.85026 b-rank test for bits 22 to 29, p=0.98044 b-rank test for bits 23 to 30, p=0.71823 b-rank test for bits 24 to 31, p=0.10481 b-rank test for bits 25 to 32, p=0.69805 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 = 0.554864 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-28_12:31 (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 142445 1.25 0.894636 2 141800 -0.26 0.399190 3 141991 0.19 0.575666 4 142353 1.04 0.850042 5 142587 1.58 0.943328 6 141983 0.17 0.568331 7 141832 -0.18 0.428310 8 141905 -0.01 0.495964 9 141594 -0.74 0.230637 10 141596 -0.73 0.232060 11 141542 -0.86 0.195378 12 142117 0.49 0.686236 13 142455 1.27 0.898833 14 141779 -0.30 0.380370 15 141784 -0.29 0.384827 16 141981 0.17 0.566493 17 142369 1.07 0.858588 18 141198 -1.66 0.048258 19 141645 -0.62 0.268422 20 141913 0.01 0.503421 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-28_12:31 Bits used No. missing words z-score p-value 23 to 32 141885 -0.0839 0.466569 22 to 31 141908 -0.0046 0.498170 21 to 30 141634 -0.9494 0.171205 20 to 29 141778 -0.4529 0.325324 19 to 28 141452 -1.5770 0.057398 18 to 27 141431 -1.6494 0.049531 17 to 26 141618 -1.0046 0.157548 16 to 25 141712 -0.6804 0.248110 15 to 24 141337 -1.9736 0.024216 14 to 23 141449 -1.5873 0.056217 13 to 22 142180 0.9333 0.824679 12 to 21 142157 0.8540 0.803457 11 to 20 141484 -1.4667 0.071235 10 to 19 141234 -2.3287 0.009937 9 to 18 141916 0.0230 0.509175 8 to 17 142153 0.8402 0.799614 7 to 16 141801 -0.3736 0.354369 6 to 15 141932 0.0782 0.531155 5 to 14 141931 0.0747 0.529783 4 to 13 141673 -0.8149 0.207556 3 to 12 141974 0.2230 0.588232 2 to 11 142727 2.8196 0.997595 1 to 10 142368 1.5816 0.943132 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-28_12:31 Bits used No. missing words z-score p-value 28 to 32 141509 -1.3571 0.087383 27 to 31 141780 -0.4384 0.330546 26 to 30 142045 0.4599 0.677205 25 to 29 141791 -0.4011 0.344166 24 to 28 142210 1.0192 0.845951 23 to 27 141699 -0.7130 0.237928 22 to 26 141987 0.2633 0.603836 21 to 25 141820 -0.3028 0.381016 20 to 24 141766 -0.4859 0.313532 19 to 23 141776 -0.4520 0.325647 18 to 22 142097 0.6362 0.737667 17 to 21 141492 -1.4147 0.078581 16 to 20 141792 -0.3977 0.345415 15 to 19 142326 1.4124 0.921090 14 to 18 141057 -2.8893 0.001931 13 to 17 142421 1.7345 0.958583 12 to 16 142315 1.3752 0.915458 11 to 15 141986 0.2599 0.602529 10 to 14 141558 -1.1909 0.116837 9 to 13 141423 -1.6486 0.049617 8 to 12 142002 0.3141 0.623291 7 to 11 141957 0.1616 0.564187 6 to 10 141961 0.1752 0.569520 5 to 9 141969 0.2023 0.580148 4 to 8 141497 -1.3977 0.081097 3 to 7 142595 2.3243 0.989945 2 to 6 142061 0.5141 0.696421 1 to 5 141366 -1.8418 0.032752 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-28_12:31 Bits used No. missing words z-score p-value 31 to 32 142144 0.6922 0.755607 30 to 31 142091 0.5359 0.703986 29 to 30 141863 -0.1367 0.445647 28 to 29 141761 -0.4376 0.330856 27 to 28 141989 0.2350 0.592901 26 to 27 142499 1.7394 0.959021 25 to 26 141698 -0.6234 0.266513 24 to 25 141661 -0.7325 0.231921 23 to 24 141951 0.1229 0.548915 22 to 23 142728 2.4150 0.992131 21 to 22 141536 -1.1013 0.135390 20 to 21 141546 -1.0718 0.141912 19 to 20 141790 -0.3520 0.362417 18 to 19 141778 -0.3874 0.349229 17 to 18 141999 0.2645 0.604308 16 to 17 141567 -1.0098 0.156290 15 to 16 141778 -0.3874 0.349229 14 to 15 142248 0.9990 0.841109 13 to 14 142164 0.7512 0.773746 12 to 13 141789 -0.3550 0.361311 11 to 12 142001 0.2704 0.606579 10 to 11 142084 0.5153 0.696811 9 to 10 142194 0.8397 0.799471 8 to 9 141879 -0.0895 0.464355 7 to 8 142020 0.3265 0.627962 6 to 7 142019 0.3235 0.626846 5 to 6 142281 1.0964 0.863542 4 to 5 141362 -1.6145 0.053205 3 to 4 141737 -0.5083 0.305605 2 to 3 141805 -0.3078 0.379133 1 to 2 141741 -0.4965 0.309754 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-28_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2442.14 -0.818 0.206588 Test results for specific bytes for dh-ranFile-2016-05-28_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2537.07 0.524 0.699926 2 to 9 2531.04 0.439 0.669649 3 to 10 2506.33 0.089 0.535645 4 to 11 2519.92 0.282 0.610898 5 to 12 2555.36 0.783 0.783177 6 to 13 2589.45 1.265 0.897061 7 to 14 2380.98 -1.683 0.046171 8 to 15 2527.78 0.393 0.652805 9 to 16 2424.63 -1.066 0.143236 10 to 17 2565.81 0.931 0.823979 11 to 18 2514.58 0.206 0.581681 12 to 19 2559.02 0.835 0.798047 13 to 20 2495.61 -0.062 0.475237 14 to 21 2491.80 -0.116 0.453862 15 to 22 2531.67 0.448 0.672889 16 to 23 2438.69 -0.867 0.192974 17 to 24 2538.79 0.549 0.708345 18 to 25 2432.01 -0.961 0.168157 19 to 26 2642.39 2.014 0.977976 20 to 27 2631.96 1.866 0.968996 21 to 28 2498.42 -0.022 0.491095 22 to 29 2512.33 0.174 0.569223 23 to 30 2463.46 -0.517 0.302657 24 to 31 2485.25 -0.209 0.417356 25 to 32 2484.40 -0.221 0.412722 CDPARK for dh-ranFile-2016-05-28_12:31: 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 3498 -1.1416 0.126820 3482 -1.8721 0.030593 3551 1.2785 0.899470 3498 -1.1416 0.126820 3448 -3.4247 0.000308 3514 -0.4110 0.340551 3500 -1.0502 0.146807 3526 0.1370 0.554479 3520 -0.1370 0.445521 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3505.80 sample std.=26.48 p-value of the KSTEST for those 10 p-values: 0.033359 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-28_12:31 0.6428,0.2407,0.5557,0.7071,0.7927,0.3221,0.3354,0.3152,0.1714,0.5948, The KS test for those 10 p-values: 0.539702 The 3DSPHERES test for dh-ranFile-2016-05-28_12:31 sample no r^3 equiv. uni. 1 2.014 0.064924 2 17.239 0.437085 3 32.069 0.656642 4 77.723 0.925037 5 4.418 0.136932 6 8.552 0.248038 7 26.872 0.591694 8 66.271 0.890192 9 24.847 0.563185 10 7.962 0.233091 11 53.579 0.832366 12 1.119 0.036610 13 9.609 0.274065 14 90.437 0.950933 15 11.941 0.328370 16 0.038 0.001274 17 4.741 0.146175 18 27.119 0.595040 19 15.784 0.409106 20 76.569 0.922097 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.635769 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-28_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.4 0.3 -1.3 -1.4 1.9 0.4 -0.8 2.4 0.1 -0.0 1.0 -0.3 0.7 -0.3 -1.5 -2.1 0.2 -1.9 -0.5 0.8 0.6 0.8 1.2 -1.0 2.0 -0.1 0.5 0.6 -0.3 1.2 2.6 0.3 0.1 1.1 0.3 -0.7 0.9 -0.7 -0.6 2.0 -0.1 Chi-square with 42 degrees of freedom:51.701432 z-score=1.058513, p-value=0.854975 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-28_12:31 Test no p-value 1 0.633915 2 0.997500 3 0.043581 4 0.473714 5 0.743555 6 0.914366 7 0.007228 8 0.395319 9 0.094584 10 0.081423 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.206000 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-28_12:31: (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 66747 0.10 66586 0.10 3 25000.00 24697 3.67 25051 0.10 4 6666.67 6900 8.17 6704 0.21 5 1388.89 1374 0.16 1377 0.10 6 238.10 235 0.04 223 0.96 7 34.72 39 0.53 52 8.60 8 4.96 7 0.84 6 0.22 p=0.96428 p=0.88695 Number of rngs required: 688046, p-value: 0.340 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-28_12:31 No. of wins: Observed Expected 98832 98585.9 z-score= 1.101, pvalue=0.86453 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66618 66666.7 0.036 0.036 2 37608 37654.3 0.057 0.093 3 26844 26954.7 0.455 0.547 4 19529 19313.5 2.405 2.953 5 13988 13851.4 1.347 4.300 6 9970 9943.5 0.070 4.370 7 7119 7145.0 0.095 4.465 8 5045 5139.1 1.722 6.187 9 3664 3699.9 0.348 6.534 10 2608 2666.3 1.275 7.809 11 1878 1923.3 1.068 8.877 12 1326 1388.7 2.834 11.712 13 1010 1003.7 0.039 11.751 14 767 726.1 2.299 14.050 15 548 525.8 0.934 14.985 16 384 381.2 0.021 15.006 17 309 276.5 3.810 18.816 18 185 200.8 1.248 20.064 19 178 146.0 7.021 27.085 20 127 106.2 4.067 31.152 21 295 287.1 0.217 31.369 Chisq= 31.37 for 20 degrees of freedom, p= 0.94950 SUMMARY of craptest p-value for no. of wins: 0.864527 p-value for throws/game: 0.949497 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-28_12:31 No. of wins: Observed Expected 98679 98585.9 z-score= 0.417, pvalue=0.66151 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66665 66666.7 0.000 0.000 2 37757 37654.3 0.280 0.280 3 27060 26954.7 0.411 0.691 4 19308 19313.5 0.002 0.693 5 13875 13851.4 0.040 0.733 6 9912 9943.5 0.100 0.833 7 7188 7145.0 0.258 1.091 8 5098 5139.1 0.328 1.420 9 3680 3699.9 0.107 1.526 10 2669 2666.3 0.003 1.529 11 1855 1923.3 2.427 3.957 12 1335 1388.7 2.080 6.036 13 1015 1003.7 0.127 6.163 14 725 726.1 0.002 6.165 15 524 525.8 0.006 6.171 16 352 381.2 2.229 8.401 17 249 276.5 2.743 11.143 18 213 200.8 0.737 11.881 19 146 146.0 0.000 11.881 20 128 106.2 4.468 16.349 21 246 287.1 5.887 22.236 Chisq= 22.24 for 20 degrees of freedom, p= 0.67217 SUMMARY of craptest p-value for no. of wins: 0.661508 p-value for throws/game: 0.672166 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0003,0.0013,0.0019,0.0072,0.0099,0.0153,0.0191,0.0242,0.0243, 0.0306,0.0328,0.0334,0.0366,0.0382,0.0436,0.0462,0.0483,0.0495,0.0496, 0.0532,0.0562,0.0574,0.0649,0.0712,0.0786,0.0811,0.0814,0.0871,0.0874, 0.0946,0.0969,0.1048,0.1069,0.1168,0.1229,0.1268,0.1268,0.1354,0.1369, 0.1419,0.1432,0.1462,0.1468,0.1481,0.1507,0.1563,0.1575,0.1588,0.1682, 0.1712,0.1714,0.1714,0.1743,0.1910,0.1930,0.1954,0.2050,0.2060,0.2066, 0.2076,0.2099,0.2306,0.2319,0.2321,0.2331,0.2379,0.2407,0.2433,0.2480, 0.2481,0.2608,0.2665,0.2684,0.2731,0.2741,0.2934,0.3027,0.3036,0.3056, 0.3098,0.3135,0.3152,0.3221,0.3253,0.3256,0.3282,0.3284,0.3305,0.3309, 0.3354,0.3373,0.3405,0.3406,0.3442,0.3445,0.3454,0.3492,0.3492,0.3544, 0.3613,0.3624,0.3791,0.3804,0.3810,0.3848,0.3953,0.3992,0.4013,0.4091, 0.4127,0.4174,0.4283,0.4325,0.4342,0.4371,0.4455,0.4456,0.4539,0.4611, 0.4623,0.4636,0.4644,0.4666,0.4737,0.4752,0.4839,0.4911,0.4960,0.4982, 0.5025,0.5034,0.5070,0.5081,0.5092,0.5138,0.5298,0.5312,0.5356,0.5397, 0.5489,0.5545,0.5549,0.5557,0.5632,0.5642,0.5665,0.5683,0.5692,0.5695, 0.5708,0.5757,0.5801,0.5817,0.5882,0.5902,0.5917,0.5929,0.5945,0.5948, 0.5950,0.6025,0.6038,0.6043,0.6066,0.6109,0.6182,0.6222,0.6233,0.6264, 0.6268,0.6280,0.6281,0.6339,0.6358,0.6399,0.6428,0.6528,0.6566,0.6615, 0.6638,0.6696,0.6722,0.6729,0.6772,0.6862,0.6964,0.6968,0.6981,0.6999, 0.7040,0.7071,0.7083,0.7105,0.7147,0.7158,0.7182,0.7284,0.7351,0.7372, 0.7377,0.7436,0.7477,0.7518,0.7536,0.7549,0.7556,0.7691,0.7737,0.7775, 0.7832,0.7865,0.7879,0.7927,0.7978,0.7980,0.7995,0.7996,0.8035,0.8111, 0.8220,0.8240,0.8247,0.8300,0.8324,0.8411,0.8452,0.8460,0.8500,0.8503, 0.8550,0.8586,0.8635,0.8645,0.8830,0.8870,0.8902,0.8903,0.8946,0.8971, 0.8976,0.8988,0.8995,0.9015,0.9091,0.9144,0.9155,0.9211,0.9221,0.9243, 0.9250,0.9278,0.9283,0.9431,0.9433,0.9495,0.9509,0.9527,0.9586,0.9590, 0.9643,0.9690,0.9739,0.9780,0.9804,0.9899,0.9921,0.9975,0.9976, Overall p-value after applying KStest on 269 p-values = 0.863026 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.