RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-26_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.72 15.5811 0.446297 2 to 25 15.87 13.0036 0.264052 3 to 26 15.76 34.6793 0.993147 4 to 27 16.08 12.7965 0.250304 5 to 28 15.81 14.9666 0.402114 6 to 29 16.25 36.4143 0.995963 7 to 30 15.69 12.2064 0.212521 8 to 31 15.77 18.6325 0.649974 9 to 32 16.03 12.0087 0.200387 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.181016 Tough bday spacings test for dh-ranFile-2016-08-26_07:31: 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 3 38 81 82 115 80 44 30 10 12 5 (O-E)^2/E 4.1 0.1 0.8 2.5 3.1 0.0 1.3 0.0 1.6 4.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 18.101, p= 0.947 RESULTS OF GCD FOR dh-ranFile-2016-08-26_07:31 Euclid's algorithm: p-value, steps to gcd: 0.446753 p-value, dist. of gcd's: 0.002324 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-26_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.318 0.089 0.544 0.250 0.258 0.982 0.112 0.282 Bits 8 to 15---> 0.228 0.447 0.076 0.662 0.325 0.256 0.583 0.417 Bits 16 to 23---> 0.349 0.273 0.580 0.093 0.878 0.081 0.315 0.102 Bits 24 to 31---> 0.425 0.043 0.039 0.139 0.214 0.760 0.557 0.708 KS test for the above 32 p values: 0.994 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-26_07:31, p-values for 5 runs: 0.1298, 0.5700, 0.3311, 0.0358, 0.2438 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-26_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5136 5134.0 0.001 0.984 r= 30 23069 23103.0 0.050 1.034 r= 31 11598 11551.5 0.187 1.221 chi-square = 1.221 with df = 3; p-value = 0.252 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-26_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5081 5134.0 0.547 0.549 r= 31 23265 23103.0 1.135 1.684 r= 32 11442 11551.5 1.038 2.723 chi-square = 2.723 with df = 3; p-value = 0.564 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-26_07:31 b-rank test for bits 1 to 8, p=0.83204 b-rank test for bits 2 to 9, p=0.00597 b-rank test for bits 3 to 10, p=0.08656 b-rank test for bits 4 to 11, p=0.05204 b-rank test for bits 5 to 12, p=0.86381 b-rank test for bits 6 to 13, p=0.97234 b-rank test for bits 7 to 14, p=0.65254 b-rank test for bits 8 to 15, p=0.92554 b-rank test for bits 9 to 16, p=0.22393 b-rank test for bits 10 to 17, p=0.79636 b-rank test for bits 11 to 18, p=0.77685 b-rank test for bits 12 to 19, p=0.44866 b-rank test for bits 13 to 20, p=0.51003 b-rank test for bits 14 to 21, p=0.07726 b-rank test for bits 15 to 22, p=0.39300 b-rank test for bits 16 to 23, p=0.51283 b-rank test for bits 17 to 24, p=0.34126 b-rank test for bits 18 to 25, p=0.87133 b-rank test for bits 19 to 26, p=0.42958 b-rank test for bits 20 to 27, p=0.82632 b-rank test for bits 21 to 28, p=0.00443 b-rank test for bits 22 to 29, p=0.29692 b-rank test for bits 23 to 30, p=0.06962 b-rank test for bits 24 to 31, p=0.73464 b-rank test for bits 25 to 32, p=0.21849 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 = 0.469521 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-26_07:31 (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 141757 -0.36 0.360954 2 142402 1.15 0.875154 3 141932 0.05 0.521121 4 141697 -0.50 0.309913 5 141937 0.06 0.525774 6 142180 0.63 0.736439 7 142209 0.70 0.758087 8 142576 1.56 0.940341 9 142553 1.50 0.933697 10 142463 1.29 0.902102 11 141572 -0.79 0.215303 12 142381 1.10 0.864776 13 141303 -1.42 0.078291 14 142601 1.62 0.946958 15 141448 -1.08 0.140545 16 142406 1.16 0.877066 17 141984 0.17 0.569249 18 141462 -1.05 0.147974 19 142068 0.37 0.644579 20 142083 0.41 0.657545 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-26_07:31 Bits used No. missing words z-score p-value 23 to 32 142016 0.3678 0.643499 22 to 31 141864 -0.1563 0.437894 21 to 30 141764 -0.5011 0.308137 20 to 29 141646 -0.9080 0.181930 19 to 28 142181 0.9368 0.825568 18 to 27 141861 -0.1667 0.433821 17 to 26 141390 -1.7908 0.036663 16 to 25 141661 -0.8563 0.195913 15 to 24 142022 0.3885 0.651183 14 to 23 142123 0.7368 0.769376 13 to 22 141713 -0.6770 0.249203 12 to 21 141656 -0.8736 0.191181 11 to 20 141722 -0.6460 0.259151 10 to 19 142198 0.9954 0.840233 9 to 18 142282 1.2851 0.900616 8 to 17 141513 -1.3667 0.085867 7 to 16 141623 -0.9873 0.161737 6 to 15 142014 0.3609 0.640925 5 to 14 141789 -0.4149 0.339096 4 to 13 141793 -0.4011 0.344159 3 to 12 141315 -2.0494 0.020211 2 to 11 141775 -0.4632 0.321608 1 to 10 141765 -0.4977 0.309351 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-26_07:31 Bits used No. missing words z-score p-value 28 to 32 142226 1.0735 0.858467 27 to 31 141923 0.0463 0.518480 26 to 30 142102 0.6531 0.743160 25 to 29 142344 1.4735 0.929686 24 to 28 142482 1.9413 0.973886 23 to 27 142784 2.9650 0.998487 22 to 26 141993 0.2836 0.611652 21 to 25 141974 0.2192 0.586761 20 to 24 141648 -0.8859 0.187845 19 to 23 142156 0.8362 0.798470 18 to 22 141730 -0.6079 0.271628 17 to 21 142247 1.1446 0.873822 16 to 20 142216 1.0396 0.850728 15 to 19 141503 -1.3774 0.084196 14 to 18 141960 0.1718 0.568188 13 to 17 142288 1.2836 0.900364 12 to 16 141974 0.2192 0.586761 11 to 15 141549 -1.2215 0.110956 10 to 14 141937 0.0938 0.537365 9 to 13 141512 -1.3469 0.089009 8 to 12 141683 -0.7672 0.221475 7 to 11 141955 0.1548 0.561516 6 to 10 141828 -0.2757 0.391391 5 to 9 142402 1.6701 0.952547 4 to 8 141395 -1.7435 0.040624 3 to 7 141996 0.2938 0.615543 2 to 6 142144 0.7955 0.786836 1 to 5 142453 1.8429 0.967332 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-26_07:31 Bits used No. missing words z-score p-value 31 to 32 142115 0.6067 0.727974 30 to 31 142374 1.3707 0.914767 29 to 30 142125 0.6362 0.737675 28 to 29 141650 -0.7650 0.222140 27 to 28 142128 0.6450 0.740551 26 to 27 141873 -0.1072 0.457328 25 to 26 141995 0.2527 0.599755 24 to 25 142389 1.4150 0.921459 23 to 24 141949 0.1170 0.546578 22 to 23 141720 -0.5585 0.288253 21 to 22 141522 -1.1426 0.126609 20 to 21 141878 -0.0924 0.463183 19 to 20 142325 1.2262 0.889932 18 to 19 142015 0.3117 0.622370 17 to 18 141729 -0.5319 0.297381 16 to 17 141793 -0.3432 0.365740 15 to 16 141738 -0.5054 0.306640 14 to 15 141946 0.1082 0.543070 13 to 14 141316 -1.7502 0.040039 12 to 13 141941 0.0934 0.537216 11 to 12 142211 0.8899 0.813235 10 to 11 141723 -0.5496 0.291281 9 to 10 141051 -2.5319 0.005672 8 to 9 141019 -2.6263 0.004315 7 to 8 142115 0.6067 0.727974 6 to 7 141701 -0.6145 0.269428 5 to 6 142063 0.4533 0.674835 4 to 5 142191 0.8309 0.796981 3 to 4 142282 1.0993 0.864186 2 to 3 142168 0.7630 0.777280 1 to 2 141910 0.0020 0.500789 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-26_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2500.19 0.003 0.501099 Test results for specific bytes for dh-ranFile-2016-08-26_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2445.72 -0.768 0.221349 2 to 9 2403.91 -1.359 0.087081 3 to 10 2497.76 -0.032 0.487347 4 to 11 2528.23 0.399 0.655150 5 to 12 2503.19 0.045 0.517965 6 to 13 2564.64 0.914 0.819685 7 to 14 2487.34 -0.179 0.428944 8 to 15 2605.87 1.497 0.932826 9 to 16 2507.24 0.102 0.540790 10 to 17 2564.98 0.919 0.820945 11 to 18 2496.78 -0.046 0.481823 12 to 19 2510.32 0.146 0.558031 13 to 20 2431.89 -0.963 0.167727 14 to 21 2593.27 1.319 0.906424 15 to 22 2400.57 -1.406 0.079835 16 to 23 2501.65 0.023 0.509325 17 to 24 2449.88 -0.709 0.239233 18 to 25 2566.18 0.936 0.825350 19 to 26 2660.20 2.266 0.988262 20 to 27 2518.71 0.265 0.604326 21 to 28 2513.09 0.185 0.573454 22 to 29 2584.74 1.198 0.884621 23 to 30 2408.67 -1.292 0.098254 24 to 31 2536.17 0.512 0.695512 25 to 32 2414.04 -1.216 0.112065 CDPARK for dh-ranFile-2016-08-26_07:31: 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 3530 0.3196 0.625377 3492 -1.4155 0.078457 3497 -1.1872 0.117571 3508 -0.6849 0.246694 3531 0.3653 0.642555 3511 -0.5479 0.291865 3524 0.0457 0.518210 3532 0.4110 0.659449 3501 -1.0046 0.157553 3558 1.5982 0.944998 Square side=100, avg. no. parked=3518.40 sample std.=19.23 p-value of the KSTEST for those 10 p-values: 0.680773 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-26_07:31 0.3625,0.0058,0.3556,0.8659,0.2593,0.6052,0.6292,0.2655,0.6828,0.5128, The KS test for those 10 p-values: 0.634528 The 3DSPHERES test for dh-ranFile-2016-08-26_07:31 sample no r^3 equiv. uni. 1 28.755 0.616527 2 16.802 0.428831 3 22.216 0.523140 4 34.239 0.680593 5 28.017 0.606988 6 4.375 0.135700 7 0.736 0.024233 8 19.609 0.479851 9 6.708 0.200362 10 93.833 0.956184 11 48.332 0.800326 12 3.095 0.098018 13 6.033 0.182179 14 3.741 0.117227 15 64.081 0.881876 16 14.823 0.389875 17 5.496 0.167387 18 3.484 0.109643 19 58.925 0.859727 20 4.478 0.138648 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.276260 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-26_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 2.0 -0.1 0.1 -1.2 0.0 -1.2 1.6 1.3 1.9 -0.8 -0.3 2.1 -1.2 -0.2 -0.7 -0.1 0.8 0.6 0.1 -0.5 -0.9 -0.2 -1.3 0.0 -1.2 0.6 1.5 -0.4 -0.3 0.5 -1.1 -2.7 -0.4 0.4 -0.7 -1.7 -0.4 1.0 -1.3 0.0 -0.1 Chi-square with 42 degrees of freedom:46.233271 z-score=0.461888, p-value=0.698278 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-26_07:31 Test no p-value 1 0.793486 2 0.610604 3 0.293830 4 0.965300 5 0.509500 6 0.338233 7 0.378295 8 0.355422 9 0.157270 10 0.869013 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.854015 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-26_07:31: (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 66593 0.08 66690 0.01 3 25000.00 25179 1.28 24923 0.24 4 6666.67 6560 1.71 6721 0.44 5 1388.89 1384 0.02 1396 0.04 6 238.10 242 0.06 227 0.52 7 34.72 35 0.00 36 0.05 8 4.96 6 0.22 6 0.22 p=0.23901 p=0.04096 Number of rngs required: 687710, p-value: 0.212 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-26_07:31 No. of wins: Observed Expected 98475 98585.9 z-score=-0.496, pvalue=0.31001 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66366 66666.7 1.356 1.356 2 37439 37654.3 1.231 2.587 3 27285 26954.7 4.047 6.634 4 19307 19313.5 0.002 6.636 5 14024 13851.4 2.150 8.786 6 10054 9943.5 1.227 10.013 7 7239 7145.0 1.236 11.249 8 5096 5139.1 0.361 11.610 9 3673 3699.9 0.195 11.805 10 2666 2666.3 0.000 11.805 11 1941 1923.3 0.162 11.968 12 1411 1388.7 0.357 12.325 13 942 1003.7 3.795 16.119 14 686 726.1 2.219 18.338 15 493 525.8 2.050 20.389 16 359 381.2 1.287 21.676 17 296 276.5 1.369 23.045 18 213 200.8 0.737 23.783 19 132 146.0 1.340 25.122 20 104 106.2 0.046 25.169 21 274 287.1 0.599 25.768 Chisq= 25.77 for 20 degrees of freedom, p= 0.82638 SUMMARY of craptest p-value for no. of wins: 0.310009 p-value for throws/game: 0.826378 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-26_07:31 No. of wins: Observed Expected 98704 98585.9 z-score= 0.528, pvalue=0.70139 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66421 66666.7 0.905 0.905 2 37511 37654.3 0.546 1.451 3 26680 26954.7 2.800 4.251 4 19465 19313.5 1.189 5.440 5 14000 13851.4 1.594 7.034 6 10022 9943.5 0.619 7.653 7 7228 7145.0 0.964 8.616 8 5107 5139.1 0.200 8.817 9 3816 3699.9 3.645 12.462 10 2665 2666.3 0.001 12.463 11 1917 1923.3 0.021 12.483 12 1413 1388.7 0.424 12.907 13 1057 1003.7 2.829 15.736 14 733 726.1 0.065 15.801 15 517 525.8 0.148 15.949 16 392 381.2 0.309 16.258 17 292 276.5 0.864 17.122 18 197 200.8 0.073 17.195 19 169 146.0 3.629 20.824 20 85 106.2 4.237 25.061 21 313 287.1 2.334 27.395 Chisq= 27.40 for 20 degrees of freedom, p= 0.87550 SUMMARY of craptest p-value for no. of wins: 0.701388 p-value for throws/game: 0.875497 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0043,0.0044,0.0057,0.0058,0.0060,0.0202,0.0242,0.0358,0.0367, 0.0386,0.0400,0.0406,0.0410,0.0430,0.0520,0.0696,0.0760,0.0773,0.0783, 0.0785,0.0798,0.0814,0.0842,0.0859,0.0866,0.0871,0.0885,0.0890,0.0927, 0.0980,0.0983,0.1020,0.1096,0.1110,0.1118,0.1121,0.1172,0.1176,0.1266, 0.1298,0.1357,0.1386,0.1392,0.1405,0.1480,0.1573,0.1576,0.1617,0.1674, 0.1677,0.1810,0.1819,0.1822,0.1878,0.1912,0.1959,0.2004,0.2004,0.2116, 0.2125,0.2141,0.2153,0.2185,0.2213,0.2215,0.2221,0.2239,0.2279,0.2390, 0.2392,0.2438,0.2467,0.2492,0.2498,0.2503,0.2521,0.2556,0.2580,0.2592, 0.2593,0.2641,0.2655,0.2694,0.2716,0.2728,0.2763,0.2820,0.2883,0.2913, 0.2919,0.2938,0.2969,0.2974,0.3066,0.3081,0.3094,0.3099,0.3100,0.3148, 0.3179,0.3216,0.3251,0.3311,0.3382,0.3391,0.3413,0.3442,0.3495,0.3554, 0.3556,0.3610,0.3625,0.3657,0.3783,0.3899,0.3914,0.3930,0.4021,0.4171, 0.4250,0.4288,0.4289,0.4296,0.4338,0.4379,0.4463,0.4468,0.4471,0.4487, 0.4573,0.4632,0.4695,0.4799,0.4818,0.4873,0.5008,0.5011,0.5093,0.5095, 0.5100,0.5128,0.5128,0.5180,0.5182,0.5185,0.5211,0.5231,0.5258,0.5372, 0.5374,0.5408,0.5431,0.5442,0.5466,0.5572,0.5580,0.5615,0.5636,0.5682, 0.5692,0.5700,0.5735,0.5801,0.5834,0.5868,0.5868,0.5998,0.6043,0.6052, 0.6070,0.6106,0.6117,0.6155,0.6165,0.6224,0.6254,0.6292,0.6345,0.6409, 0.6426,0.6435,0.6446,0.6500,0.6512,0.6525,0.6552,0.6575,0.6594,0.6617, 0.6748,0.6806,0.6808,0.6828,0.6955,0.6983,0.7014,0.7085,0.7280,0.7280, 0.7346,0.7364,0.7377,0.7406,0.7432,0.7581,0.7600,0.7694,0.7768,0.7773, 0.7868,0.7935,0.7964,0.7970,0.7985,0.8003,0.8132,0.8197,0.8209,0.8253, 0.8256,0.8263,0.8264,0.8320,0.8402,0.8507,0.8540,0.8585,0.8597,0.8638, 0.8642,0.8648,0.8659,0.8690,0.8713,0.8738,0.8752,0.8755,0.8771,0.8785, 0.8819,0.8846,0.8899,0.9004,0.9006,0.9021,0.9064,0.9148,0.9215,0.9255, 0.9297,0.9328,0.9337,0.9403,0.9450,0.9467,0.9470,0.9525,0.9562,0.9653, 0.9673,0.9723,0.9739,0.9818,0.9883,0.9931,0.9936,0.9960,0.9985, Overall p-value after applying KStest on 269 p-values = 0.395385 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.