RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-03_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 15.67 11.2347 0.155893 2 to 25 15.72 16.8282 0.533935 3 to 26 15.93 21.4292 0.792322 4 to 27 15.84 17.7347 0.594243 5 to 28 15.87 16.2989 0.497246 6 to 29 15.68 18.8258 0.661376 7 to 30 15.70 14.0677 0.337699 8 to 31 15.62 14.9748 0.402700 9 to 32 15.69 23.4005 0.863338 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.699614 Tough bday spacings test for dh-ranFile-2017-02-03_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 10 39 76 95 90 62 70 40 10 4 4 (O-E)^2/E 0.1 0.2 0.1 0.1 0.6 3.3 6.2 3.5 1.6 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 16.653, p= 0.918 RESULTS OF GCD FOR dh-ranFile-2017-02-03_12:31 Euclid's algorithm: p-value, steps to gcd: 0.938619 p-value, dist. of gcd's: 0.350542 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-03_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.402 0.903 0.143 0.218 0.342 0.281 0.919 0.868 Bits 8 to 15---> 0.988 0.672 0.401 0.286 0.263 0.800 0.849 0.401 Bits 16 to 23---> 0.649 0.838 0.031 0.736 0.697 0.304 0.359 0.638 Bits 24 to 31---> 0.030 0.328 0.151 0.698 0.075 0.921 0.999 0.956 KS test for the above 32 p values: 0.544 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-03_12:31, p-values for 5 runs: 0.7933, 0.1286, 0.3820, 0.2987, 0.4643 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-03_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5149 5134.0 0.044 0.075 r= 30 22913 23103.0 1.563 1.639 r= 31 11724 11551.5 2.575 4.214 chi-square = 4.214 with df = 3; p-value = 0.761 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-03_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5160 5134.0 0.132 0.861 r= 31 23069 23103.0 0.050 0.911 r= 32 11572 11551.5 0.036 0.947 chi-square = 0.947 with df = 3; p-value = 0.186 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-03_12:31 b-rank test for bits 1 to 8, p=0.28140 b-rank test for bits 2 to 9, p=0.40040 b-rank test for bits 3 to 10, p=0.21443 b-rank test for bits 4 to 11, p=0.53412 b-rank test for bits 5 to 12, p=0.56979 b-rank test for bits 6 to 13, p=0.83866 b-rank test for bits 7 to 14, p=0.16417 b-rank test for bits 8 to 15, p=0.40607 b-rank test for bits 9 to 16, p=0.14096 b-rank test for bits 10 to 17, p=0.39161 b-rank test for bits 11 to 18, p=0.57831 b-rank test for bits 12 to 19, p=0.43851 b-rank test for bits 13 to 20, p=0.29692 b-rank test for bits 14 to 21, p=0.99146 b-rank test for bits 15 to 22, p=0.99742 b-rank test for bits 16 to 23, p=0.87836 b-rank test for bits 17 to 24, p=0.94303 b-rank test for bits 18 to 25, p=0.43861 b-rank test for bits 19 to 26, p=0.45330 b-rank test for bits 20 to 27, p=0.53722 b-rank test for bits 21 to 28, p=0.32525 b-rank test for bits 22 to 29, p=0.15700 b-rank test for bits 23 to 30, p=0.59720 b-rank test for bits 24 to 31, p=0.37786 b-rank test for bits 25 to 32, p=0.67331 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 = 0.325331 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-03_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 141904 -0.01 0.495032 2 141895 -0.03 0.486645 3 142306 0.93 0.822985 4 142427 1.21 0.886766 5 141651 -0.60 0.273063 6 141979 0.16 0.564654 7 142109 0.47 0.679578 8 141900 -0.02 0.491304 9 142433 1.22 0.889435 10 142445 1.25 0.894636 11 141460 -1.05 0.146897 12 141413 -1.16 0.123096 13 142027 0.27 0.608315 14 141939 0.07 0.527634 15 141604 -0.71 0.237803 16 141268 -1.50 0.067010 17 141026 -2.06 0.019516 18 142288 0.88 0.811852 19 142349 1.03 0.847852 20 141373 -1.25 0.105083 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-03_12:31 Bits used No. missing words z-score p-value 23 to 32 141842 -0.2322 0.408202 22 to 31 141981 0.2471 0.597599 21 to 30 141786 -0.4253 0.335318 20 to 29 142107 0.6816 0.752261 19 to 28 142449 1.8609 0.968623 18 to 27 141747 -0.5598 0.287822 17 to 26 141819 -0.3115 0.377717 16 to 25 141784 -0.4322 0.332808 15 to 24 142028 0.4092 0.658806 14 to 23 141982 0.2506 0.598933 13 to 22 141435 -1.6356 0.050960 12 to 21 142471 1.9368 0.973615 11 to 20 142186 0.9540 0.829967 10 to 19 142030 0.4161 0.661333 9 to 18 141946 0.1264 0.550312 8 to 17 141518 -1.3494 0.088602 7 to 16 142066 0.5402 0.705485 6 to 15 141557 -1.2149 0.112196 5 to 14 141910 0.0023 0.500922 4 to 13 142314 1.3954 0.918554 3 to 12 141712 -0.6804 0.248110 2 to 11 141433 -1.6425 0.050241 1 to 10 141740 -0.5839 0.279645 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-03_12:31 Bits used No. missing words z-score p-value 28 to 32 141659 -0.8486 0.198059 27 to 31 142108 0.6735 0.749672 26 to 30 141497 -1.3977 0.081097 25 to 29 141910 0.0023 0.500906 24 to 28 142220 1.0531 0.853857 23 to 27 142161 0.8531 0.803203 22 to 26 141641 -0.9096 0.181519 21 to 25 141941 0.1074 0.542747 20 to 24 142068 0.5379 0.704665 19 to 23 141932 0.0768 0.530628 18 to 22 141721 -0.6384 0.261605 17 to 21 142053 0.4870 0.686877 16 to 20 142134 0.7616 0.776849 15 to 19 141700 -0.7096 0.238978 14 to 18 141817 -0.3130 0.377147 13 to 17 141973 0.2158 0.585440 12 to 16 141500 -1.3876 0.082636 11 to 15 141706 -0.6893 0.245332 10 to 14 141489 -1.4248 0.077101 9 to 13 142472 1.9074 0.971763 8 to 12 142647 2.5006 0.993800 7 to 11 141723 -0.6316 0.263815 6 to 10 141616 -0.9943 0.160029 5 to 9 141386 -1.7740 0.038032 4 to 8 141943 0.1141 0.545435 3 to 7 141985 0.2565 0.601221 2 to 6 142202 0.9921 0.839426 1 to 5 141737 -0.5842 0.279553 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-03_12:31 Bits used No. missing words z-score p-value 31 to 32 141835 -0.2193 0.413223 30 to 31 141505 -1.1927 0.116491 29 to 30 141564 -1.0187 0.154179 28 to 29 141832 -0.2281 0.409780 27 to 28 141850 -0.1750 0.430534 26 to 27 141947 0.1111 0.544240 25 to 26 142158 0.7335 0.768385 24 to 25 142033 0.3648 0.642373 23 to 24 141957 0.1406 0.555915 22 to 23 142042 0.3914 0.652233 21 to 22 142218 0.9105 0.818729 20 to 21 142123 0.6303 0.735749 19 to 20 141788 -0.3579 0.360207 18 to 19 142284 1.1052 0.865468 17 to 18 141705 -0.6027 0.273340 16 to 17 142573 1.9577 0.974869 15 to 16 142258 1.0285 0.848149 14 to 15 141529 -1.1219 0.130949 13 to 14 141394 -1.5201 0.064237 12 to 13 142292 1.1288 0.870513 11 to 12 142005 0.2822 0.611110 10 to 11 141803 -0.3137 0.376891 9 to 10 142272 1.0698 0.857651 8 to 9 141484 -1.2547 0.104801 7 to 8 142046 0.4032 0.656583 6 to 7 142317 1.2026 0.885428 5 to 6 142568 1.9430 0.973991 4 to 5 141872 -0.1101 0.456158 3 to 4 141727 -0.5378 0.295342 2 to 3 141806 -0.3048 0.380256 1 to 2 142471 1.6568 0.951224 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-03_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2602.57 1.451 0.926543 Test results for specific bytes for dh-ranFile-2017-02-03_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2555.46 0.784 0.783592 2 to 9 2531.51 0.446 0.672040 3 to 10 2413.86 -1.218 0.111584 4 to 11 2436.22 -0.902 0.183514 5 to 12 2612.98 1.598 0.944957 6 to 13 2631.52 1.860 0.968554 7 to 14 2518.50 0.262 0.603211 8 to 15 2538.34 0.542 0.706157 9 to 16 2541.12 0.582 0.719548 10 to 17 2582.61 1.168 0.878652 11 to 18 2585.43 1.208 0.886498 12 to 19 2415.91 -1.189 0.117181 13 to 20 2442.89 -0.808 0.209630 14 to 21 2598.30 1.390 0.917766 15 to 22 2592.02 1.301 0.903422 16 to 23 2558.16 0.823 0.794614 17 to 24 2453.20 -0.662 0.254018 18 to 25 2507.69 0.109 0.543296 19 to 26 2575.58 1.069 0.857446 20 to 27 2481.72 -0.259 0.397977 21 to 28 2515.79 0.223 0.588345 22 to 29 2471.89 -0.398 0.345473 23 to 30 2386.55 -1.604 0.054316 24 to 31 2457.39 -0.603 0.273396 25 to 32 2506.95 0.098 0.539150 CDPARK for dh-ranFile-2017-02-03_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 3529 0.2740 0.607947 3526 0.1370 0.554479 3537 0.6393 0.738676 3518 -0.2283 0.409702 3531 0.3653 0.642555 3541 0.8219 0.794438 3523 0.0000 0.500000 3543 0.9132 0.819442 3548 1.1416 0.873180 3510 -0.5936 0.276387 Square side=100, avg. no. parked=3530.60 sample std.=11.27 p-value of the KSTEST for those 10 p-values: 0.193187 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-03_12:31 0.4620,0.4901,0.9696,0.3682,0.3852,0.4409,0.2999,0.8040,0.8751,0.4987, The KS test for those 10 p-values: 0.373284 The 3DSPHERES test for dh-ranFile-2017-02-03_12:31 sample no r^3 equiv. uni. 1 7.889 0.231230 2 13.198 0.355931 3 4.070 0.126857 4 1.269 0.041428 5 14.964 0.392737 6 18.979 0.468816 7 26.546 0.587227 8 83.246 0.937642 9 0.788 0.025935 10 19.528 0.478438 11 13.033 0.352376 12 16.078 0.414870 13 5.269 0.161069 14 10.624 0.298222 15 74.322 0.916037 16 12.456 0.339785 17 13.390 0.360020 18 42.670 0.758853 19 2.402 0.076948 20 9.678 0.275743 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.080482 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-03_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.3 -1.6 -1.2 1.4 0.6 1.1 0.8 0.4 -1.0 0.5 0.4 -0.3 -0.3 -0.9 -0.2 -1.2 -0.4 3.0 -0.3 -1.5 0.0 1.6 -1.0 -0.9 1.0 0.8 -0.3 2.4 -1.2 -1.8 0.8 -0.8 -0.2 0.4 -0.2 1.1 1.3 -0.7 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:47.044570 z-score=0.550408, p-value=0.726386 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-03_12:31 Test no p-value 1 0.145633 2 0.520548 3 0.094371 4 0.248093 5 0.560116 6 0.452701 7 0.537177 8 0.626044 9 0.773111 10 0.823242 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.793814 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-03_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 66538 0.25 66732 0.06 3 25000.00 25118 0.56 25069 0.19 4 6666.67 6664 0.00 6597 0.73 5 1388.89 1430 1.22 1351 1.03 6 238.10 213 2.65 211 3.08 7 34.72 32 0.21 33 0.09 8 4.96 4 0.19 6 0.22 p=0.46477 p=0.50673 Number of rngs required: 689469, p-value: 0.892 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-03_12:31 No. of wins: Observed Expected 98872 98585.9 z-score= 1.280, pvalue=0.89969 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67231 66666.7 4.777 4.777 2 37388 37654.3 1.884 6.661 3 26750 26954.7 1.555 8.216 4 19238 19313.5 0.295 8.511 5 14082 13851.4 3.838 12.349 6 9849 9943.5 0.899 13.248 7 7038 7145.0 1.603 14.851 8 5210 5139.1 0.979 15.830 9 3665 3699.9 0.329 16.158 10 2657 2666.3 0.032 16.191 11 1903 1923.3 0.215 16.406 12 1408 1388.7 0.267 16.673 13 1003 1003.7 0.001 16.673 14 711 726.1 0.316 16.989 15 514 525.8 0.266 17.256 16 376 381.2 0.070 17.325 17 267 276.5 0.329 17.654 18 199 200.8 0.017 17.671 19 135 146.0 0.827 18.497 20 94 106.2 1.405 19.902 21 282 287.1 0.091 19.993 Chisq= 19.99 for 20 degrees of freedom, p= 0.54165 SUMMARY of craptest p-value for no. of wins: 0.899691 p-value for throws/game: 0.541648 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-03_12:31 No. of wins: Observed Expected 98750 98585.9 z-score= 0.734, pvalue=0.76857 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66764 66666.7 0.142 0.142 2 37803 37654.3 0.587 0.729 3 26879 26954.7 0.213 0.942 4 19166 19313.5 1.126 2.068 5 13943 13851.4 0.605 2.673 6 10009 9943.5 0.431 3.104 7 7155 7145.0 0.014 3.118 8 5092 5139.1 0.431 3.549 9 3576 3699.9 4.147 7.696 10 2691 2666.3 0.229 7.925 11 1891 1923.3 0.543 8.468 12 1392 1388.7 0.008 8.476 13 1009 1003.7 0.028 8.504 14 693 726.1 1.513 10.016 15 551 525.8 1.204 11.221 16 396 381.2 0.579 11.799 17 272 276.5 0.075 11.874 18 200 200.8 0.003 11.877 19 134 146.0 0.984 12.861 20 127 106.2 4.067 16.928 21 257 287.1 3.159 20.087 Chisq= 20.09 for 20 degrees of freedom, p= 0.54748 SUMMARY of craptest p-value for no. of wins: 0.768567 p-value for throws/game: 0.547483 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0195,0.0259,0.0303,0.0310,0.0380,0.0414,0.0502,0.0510,0.0543,0.0642, 0.0670,0.0751,0.0769,0.0771,0.0805,0.0811,0.0826,0.0886,0.0944,0.1048, 0.1051,0.1116,0.1122,0.1165,0.1172,0.1231,0.1269,0.1286,0.1309,0.1410, 0.1428,0.1456,0.1469,0.1514,0.1542,0.1559,0.1570,0.1600,0.1611,0.1642, 0.1815,0.1835,0.1860,0.1932,0.1981,0.2096,0.2144,0.2180,0.2312,0.2378, 0.2390,0.2453,0.2481,0.2481,0.2540,0.2616,0.2632,0.2638,0.2731,0.2733, 0.2734,0.2757,0.2764,0.2796,0.2796,0.2806,0.2814,0.2859,0.2878,0.2953, 0.2969,0.2982,0.2987,0.2999,0.3040,0.3253,0.3253,0.3279,0.3328,0.3353, 0.3377,0.3398,0.3423,0.3455,0.3505,0.3524,0.3559,0.3588,0.3600,0.3602, 0.3682,0.3733,0.3769,0.3771,0.3777,0.3779,0.3803,0.3820,0.3852,0.3916, 0.3927,0.3980,0.4004,0.4011,0.4011,0.4023,0.4027,0.4061,0.4082,0.4097, 0.4098,0.4132,0.4149,0.4305,0.4385,0.4386,0.4409,0.4527,0.4533,0.4562, 0.4620,0.4643,0.4648,0.4688,0.4784,0.4866,0.4901,0.4913,0.4950,0.4972, 0.4987,0.5000,0.5009,0.5009,0.5067,0.5205,0.5276,0.5306,0.5339,0.5341, 0.5372,0.5372,0.5392,0.5416,0.5427,0.5433,0.5437,0.5442,0.5454,0.5475, 0.5503,0.5545,0.5559,0.5601,0.5647,0.5698,0.5783,0.5854,0.5872,0.5883, 0.5942,0.5972,0.5976,0.5989,0.6012,0.6032,0.6079,0.6083,0.6111,0.6260, 0.6383,0.6424,0.6426,0.6493,0.6522,0.6566,0.6588,0.6613,0.6614,0.6720, 0.6720,0.6733,0.6796,0.6869,0.6968,0.6977,0.6996,0.7047,0.7055,0.7062, 0.7195,0.7264,0.7357,0.7365,0.7387,0.7497,0.7523,0.7589,0.7607,0.7684, 0.7686,0.7731,0.7768,0.7836,0.7923,0.7933,0.7938,0.7944,0.7946,0.7998, 0.8032,0.8040,0.8119,0.8187,0.8194,0.8230,0.8232,0.8300,0.8379,0.8387, 0.8394,0.8479,0.8481,0.8495,0.8539,0.8574,0.8577,0.8633,0.8655,0.8681, 0.8705,0.8732,0.8751,0.8784,0.8787,0.8854,0.8865,0.8868,0.8894,0.8924, 0.8946,0.8997,0.9031,0.9034,0.9160,0.9176,0.9178,0.9186,0.9191,0.9210, 0.9265,0.9376,0.9386,0.9430,0.9450,0.9512,0.9559,0.9686,0.9686,0.9696, 0.9718,0.9736,0.9740,0.9749,0.9880,0.9915,0.9938,0.9974,0.9994, Overall p-value after applying KStest on 269 p-values = 0.316604 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.