RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-05_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.48 18.8963 0.665482 2 to 25 15.77 32.6086 0.987370 3 to 26 15.94 16.6408 0.521051 4 to 27 15.84 21.3031 0.786973 5 to 28 15.77 11.8543 0.191119 6 to 29 15.60 16.3855 0.503313 7 to 30 15.87 11.3598 0.162740 8 to 31 15.73 15.8825 0.467819 9 to 32 15.64 12.7385 0.246495 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.880010 Tough bday spacings test for dh-ranFile-2016-01-05_14:31: 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 13 49 79 102 90 71 50 32 12 2 0 (O-E)^2/E 1.6 4.2 0.4 0.2 0.6 0.7 0.1 0.2 0.6 3.2 4.1 Birthday Spacings: Sum(O-E)^2/E= 15.783, p= 0.894 RESULTS OF GCD FOR dh-ranFile-2016-01-05_14:31 Euclid's algorithm: p-value, steps to gcd: 0.305222 p-value, dist. of gcd's: 0.353150 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-05_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.647 0.513 0.677 0.686 0.472 0.127 0.127 0.642 Bits 8 to 15---> 0.750 0.460 0.930 0.806 0.018 0.055 0.700 0.731 Bits 16 to 23---> 0.518 0.296 0.810 0.718 0.910 0.396 0.483 0.822 Bits 24 to 31---> 0.432 0.217 0.585 0.831 0.573 0.401 0.180 0.219 KS test for the above 32 p values: 0.408 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-05_14:31, p-values for 5 runs: 0.6644, 0.4868, 0.3422, 0.4071, 0.2268 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-05_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5174 5134.0 0.311 0.746 r= 30 22910 23103.0 1.613 2.359 r= 31 11695 11551.5 1.782 4.141 chi-square = 4.141 with df = 3; p-value = 0.753 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-05_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5022 5134.0 2.444 2.716 r= 31 23101 23103.0 0.000 2.716 r= 32 11658 11551.5 0.981 3.697 chi-square = 3.697 with df = 3; p-value = 0.704 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-05_14:31 b-rank test for bits 1 to 8, p=0.22287 b-rank test for bits 2 to 9, p=0.20960 b-rank test for bits 3 to 10, p=0.53315 b-rank test for bits 4 to 11, p=0.33226 b-rank test for bits 5 to 12, p=0.26092 b-rank test for bits 6 to 13, p=0.21995 b-rank test for bits 7 to 14, p=0.10840 b-rank test for bits 8 to 15, p=0.01103 b-rank test for bits 9 to 16, p=0.62544 b-rank test for bits 10 to 17, p=0.26399 b-rank test for bits 11 to 18, p=0.65178 b-rank test for bits 12 to 19, p=0.34802 b-rank test for bits 13 to 20, p=0.79888 b-rank test for bits 14 to 21, p=0.96850 b-rank test for bits 15 to 22, p=0.18371 b-rank test for bits 16 to 23, p=0.82765 b-rank test for bits 17 to 24, p=0.95653 b-rank test for bits 18 to 25, p=0.36478 b-rank test for bits 19 to 26, p=0.22204 b-rank test for bits 20 to 27, p=0.31774 b-rank test for bits 21 to 28, p=0.86699 b-rank test for bits 22 to 29, p=0.52256 b-rank test for bits 23 to 30, p=0.05754 b-rank test for bits 24 to 31, p=0.58113 b-rank test for bits 25 to 32, p=0.41452 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 = 0.367030 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-05_14:31 (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 141929 0.05 0.518328 2 142020 0.26 0.602018 3 142026 0.27 0.607417 4 141945 0.08 0.533210 5 142169 0.61 0.727977 6 142018 0.25 0.600214 7 141494 -0.97 0.165924 8 141979 0.16 0.564654 9 142136 0.53 0.701806 10 141899 -0.02 0.490372 11 140832 -2.52 0.005916 12 142187 0.65 0.741754 13 141908 -0.00 0.498760 14 142411 1.17 0.879427 15 142531 1.45 0.926819 16 141382 -1.23 0.108960 17 141753 -0.37 0.357460 18 141772 -0.32 0.374157 19 141983 0.17 0.568331 20 141714 -0.46 0.324059 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-05_14:31 Bits used No. missing words z-score p-value 23 to 32 142208 1.0299 0.848471 22 to 31 141840 -0.2391 0.405526 21 to 30 141511 -1.3736 0.084790 20 to 29 141817 -0.3184 0.375099 19 to 28 141660 -0.8598 0.194961 18 to 27 142246 1.1609 0.877165 17 to 26 142346 1.5058 0.933935 16 to 25 142036 0.4368 0.668869 15 to 24 141961 0.1782 0.570706 14 to 23 142265 1.2264 0.889985 13 to 22 142019 0.3782 0.647349 12 to 21 142187 0.9575 0.830838 11 to 20 142342 1.4920 0.932146 10 to 19 142075 0.5713 0.716094 9 to 18 142172 0.9058 0.817468 8 to 17 141714 -0.6736 0.250298 7 to 16 142279 1.2747 0.898797 6 to 15 141361 -1.8908 0.029326 5 to 14 141847 -0.2149 0.414911 4 to 13 141438 -1.6253 0.052052 3 to 12 141539 -1.2770 0.100801 2 to 11 141330 -1.9977 0.022875 1 to 10 141936 0.0920 0.536637 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-05_14:31 Bits used No. missing words z-score p-value 28 to 32 141999 0.3040 0.619423 27 to 31 142232 1.0938 0.862978 26 to 30 141958 0.1650 0.565521 25 to 29 141695 -0.7265 0.233753 24 to 28 141819 -0.3062 0.379725 23 to 27 141667 -0.8215 0.205693 22 to 26 141572 -1.1435 0.126417 21 to 25 141803 -0.3604 0.359259 20 to 24 142468 1.8938 0.970874 19 to 23 141647 -0.8893 0.186933 18 to 22 141803 -0.3604 0.359259 17 to 21 142037 0.4328 0.667413 16 to 20 142430 1.7650 0.961217 15 to 19 141753 -0.5299 0.298080 14 to 18 142019 0.3718 0.644965 13 to 17 141712 -0.6689 0.251775 12 to 16 141578 -1.1232 0.130686 11 to 15 142152 0.8226 0.794635 10 to 14 141705 -0.6926 0.244267 9 to 13 141868 -0.1401 0.444290 8 to 12 141726 -0.6215 0.267149 7 to 11 141749 -0.5435 0.293396 6 to 10 141503 -1.3774 0.084196 5 to 9 142007 0.3311 0.629710 4 to 8 141539 -1.2554 0.104675 3 to 7 141693 -0.7333 0.231681 2 to 6 141914 0.0158 0.506315 1 to 5 141846 -0.2147 0.415009 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-05_14:31 Bits used No. missing words z-score p-value 31 to 32 141079 -2.4494 0.007156 30 to 31 141576 -0.9833 0.162736 29 to 30 142143 0.6893 0.754680 28 to 29 141438 -1.3904 0.082211 27 to 28 142018 0.3206 0.625728 26 to 27 142380 1.3884 0.917493 25 to 26 142467 1.6450 0.950020 24 to 25 141850 -0.1750 0.430534 23 to 24 141705 -0.6027 0.273340 22 to 23 142330 1.2409 0.892681 21 to 22 141862 -0.1396 0.444482 20 to 21 142204 0.8692 0.807640 19 to 20 142537 1.8515 0.967954 18 to 19 142028 0.3501 0.636853 17 to 18 141348 -1.6558 0.048877 16 to 17 142247 0.9961 0.840394 15 to 16 142264 1.0462 0.852271 14 to 15 142161 0.7424 0.771074 13 to 14 141556 -1.0423 0.148643 12 to 13 141902 -0.0216 0.491375 11 to 12 141745 -0.4847 0.313927 10 to 11 141851 -0.1721 0.431693 9 to 10 141828 -0.2399 0.405199 8 to 9 141815 -0.2783 0.390407 7 to 8 141948 0.1141 0.545409 6 to 7 142398 1.4415 0.925279 5 to 6 141932 0.0669 0.526659 4 to 5 141799 -0.3255 0.372418 3 to 4 142015 0.3117 0.622370 2 to 3 141720 -0.5585 0.288253 1 to 2 142004 0.2793 0.609978 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-05_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2520.47 0.290 0.613917 Test results for specific bytes for dh-ranFile-2016-01-05_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2439.31 -0.858 0.195373 2 to 9 2518.46 0.261 0.603001 3 to 10 2496.94 -0.043 0.482746 4 to 11 2475.89 -0.341 0.366545 5 to 12 2416.88 -1.176 0.119886 6 to 13 2463.23 -0.520 0.301513 7 to 14 2465.85 -0.483 0.314569 8 to 15 2401.97 -1.386 0.082822 9 to 16 2591.75 1.298 0.902774 10 to 17 2450.07 -0.706 0.240045 11 to 18 2590.36 1.278 0.899366 12 to 19 2546.06 0.651 0.742590 13 to 20 2433.40 -0.942 0.173136 14 to 21 2587.46 1.237 0.891925 15 to 22 2529.34 0.415 0.660893 16 to 23 2520.15 0.285 0.612141 17 to 24 2642.63 2.017 0.978156 18 to 25 2726.55 3.204 0.999322 19 to 26 2474.31 -0.363 0.358172 20 to 27 2544.12 0.624 0.733656 21 to 28 2465.62 -0.486 0.313399 22 to 29 2508.65 0.122 0.548660 23 to 30 2445.79 -0.767 0.221644 24 to 31 2596.54 1.365 0.913916 25 to 32 2599.40 1.406 0.920090 CDPARK for dh-ranFile-2016-01-05_14:31: 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 3522 -0.0457 0.481790 3525 0.0913 0.536383 3519 -0.1826 0.427537 3520 -0.1370 0.445521 3537 0.6393 0.738676 3468 -2.5114 0.006012 3524 0.0457 0.518210 3486 -1.6895 0.045562 3518 -0.2283 0.409702 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3513.10 sample std.=19.46 p-value of the KSTEST for those 10 p-values: 0.167547 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-05_14:31 0.2661,0.4328,0.2982,0.4858,0.5442,0.7013,0.1851,0.1067,0.8559,0.3667, The KS test for those 10 p-values: 0.536528 The 3DSPHERES test for dh-ranFile-2016-01-05_14:31 sample no r^3 equiv. uni. 1 3.273 0.103353 2 5.273 0.161189 3 1.605 0.052104 4 3.982 0.124298 5 20.227 0.490458 6 49.452 0.807641 7 68.546 0.898214 8 28.171 0.608996 9 151.436 0.993577 10 57.063 0.850745 11 8.598 0.249197 12 25.003 0.565451 13 16.313 0.419440 14 2.636 0.084129 15 37.793 0.716283 16 12.264 0.335558 17 20.908 0.501893 18 0.030 0.001006 19 31.067 0.644979 20 14.021 0.373354 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.642877 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-05_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 -1.1 -1.3 0.1 -1.7 1.3 0.1 1.8 1.1 0.4 1.3 -0.6 -1.5 -0.6 0.5 0.3 0.0 -0.1 -0.1 -1.5 0.8 -0.2 1.1 -0.9 -0.3 0.3 0.7 -0.4 -0.8 1.1 -1.3 0.3 0.9 0.1 -1.6 1.0 -0.4 0.1 -0.7 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:33.711326 z-score=-0.904368, p-value=0.184666 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-05_14:31 Test no p-value 1 0.273399 2 0.454785 3 0.001563 4 0.688369 5 0.726691 6 0.068800 7 0.034775 8 0.151685 9 0.412466 10 0.554263 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.078369 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-05_14:31: (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 66675 0.00 66792 0.24 3 25000.00 24808 1.47 25004 0.00 4 6666.67 6805 2.87 6614 0.42 5 1388.89 1405 0.19 1324 3.03 6 238.10 265 3.04 231 0.21 7 34.72 37 0.15 28 1.30 8 4.96 4 0.19 6 0.22 p=0.75512 p=0.50812 Number of rngs required: 688705, p-value: 0.636 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-05_14:31 No. of wins: Observed Expected 98720 98585.9 z-score= 0.600, pvalue=0.72573 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66683 66666.7 0.004 0.004 2 37783 37654.3 0.440 0.444 3 26719 26954.7 2.062 2.505 4 19329 19313.5 0.013 2.518 5 13814 13851.4 0.101 2.619 6 9789 9943.5 2.402 5.021 7 7218 7145.0 0.745 5.766 8 5330 5139.1 7.093 12.860 9 3700 3699.9 0.000 12.860 10 2611 2666.3 1.147 14.006 11 1980 1923.3 1.670 15.676 12 1428 1388.7 1.110 16.786 13 1041 1003.7 1.385 18.171 14 703 726.1 0.737 18.909 15 529 525.8 0.019 18.928 16 365 381.2 0.684 19.612 17 268 276.5 0.264 19.876 18 189 200.8 0.697 20.572 19 127 146.0 2.469 23.041 20 114 106.2 0.571 23.612 21 280 287.1 0.176 23.788 Chisq= 23.79 for 20 degrees of freedom, p= 0.74823 SUMMARY of craptest p-value for no. of wins: 0.725733 p-value for throws/game: 0.748229 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-05_14:31 No. of wins: Observed Expected 98873 98585.9 z-score= 1.284, pvalue=0.90048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66983 66666.7 1.501 1.501 2 37885 37654.3 1.413 2.914 3 26986 26954.7 0.036 2.950 4 18954 19313.5 6.690 9.641 5 13964 13851.4 0.915 10.556 6 9837 9943.5 1.142 11.697 7 7125 7145.0 0.056 11.754 8 5077 5139.1 0.750 12.503 9 3567 3699.9 4.771 17.275 10 2658 2666.3 0.026 17.300 11 1955 1923.3 0.522 17.822 12 1376 1388.7 0.117 17.939 13 1010 1003.7 0.039 17.978 14 711 726.1 0.316 18.294 15 539 525.8 0.330 18.623 16 396 381.2 0.579 19.202 17 262 276.5 0.764 19.966 18 188 200.8 0.820 20.786 19 156 146.0 0.687 21.473 20 100 106.2 0.364 21.837 21 271 287.1 0.904 22.741 Chisq= 22.74 for 20 degrees of freedom, p= 0.69832 SUMMARY of craptest p-value for no. of wins: 0.900475 p-value for throws/game: 0.698317 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0010,0.0016,0.0059,0.0060,0.0072,0.0110,0.0179,0.0229,0.0293,0.0348, 0.0456,0.0489,0.0521,0.0521,0.0555,0.0575,0.0688,0.0784,0.0822,0.0828, 0.0841,0.0842,0.0848,0.1008,0.1034,0.1047,0.1067,0.1084,0.1090,0.1199, 0.1243,0.1264,0.1265,0.1273,0.1307,0.1486,0.1517,0.1612,0.1627,0.1627, 0.1659,0.1675,0.1731,0.1800,0.1837,0.1847,0.1851,0.1869,0.1911,0.1950, 0.1954,0.2057,0.2096,0.2171,0.2187,0.2199,0.2216,0.2220,0.2229,0.2268, 0.2317,0.2338,0.2400,0.2443,0.2465,0.2492,0.2503,0.2518,0.2609,0.2640, 0.2661,0.2671,0.2733,0.2734,0.2883,0.2934,0.2961,0.2981,0.2982,0.3015, 0.3052,0.3077,0.3134,0.3139,0.3146,0.3177,0.3241,0.3323,0.3356,0.3422, 0.3480,0.3532,0.3575,0.3582,0.3593,0.3593,0.3648,0.3665,0.3667,0.3670, 0.3724,0.3734,0.3742,0.3751,0.3797,0.3904,0.3962,0.4007,0.4052,0.4055, 0.4071,0.4076,0.4097,0.4125,0.4145,0.4149,0.4150,0.4194,0.4275,0.4305, 0.4315,0.4317,0.4328,0.4443,0.4445,0.4455,0.4548,0.4603,0.4678,0.4721, 0.4818,0.4827,0.4834,0.4858,0.4868,0.4904,0.4905,0.4914,0.4988,0.5019, 0.5033,0.5063,0.5081,0.5125,0.5177,0.5182,0.5183,0.5211,0.5226,0.5267, 0.5331,0.5332,0.5364,0.5365,0.5366,0.5442,0.5454,0.5487,0.5543,0.5647, 0.5655,0.5655,0.5683,0.5707,0.5726,0.5811,0.5845,0.6002,0.6020,0.6030, 0.6074,0.6090,0.6100,0.6121,0.6139,0.6194,0.6224,0.6254,0.6257,0.6297, 0.6360,0.6369,0.6418,0.6429,0.6450,0.6450,0.6473,0.6473,0.6518,0.6609, 0.6644,0.6655,0.6674,0.6689,0.6770,0.6859,0.6884,0.6983,0.6996,0.7013, 0.7018,0.7039,0.7161,0.7163,0.7181,0.7257,0.7267,0.7280,0.7311,0.7337, 0.7387,0.7418,0.7426,0.7482,0.7504,0.7534,0.7547,0.7551,0.7711,0.7870, 0.7946,0.7989,0.8058,0.8076,0.8076,0.8105,0.8175,0.8220,0.8277,0.8308, 0.8311,0.8404,0.8485,0.8507,0.8523,0.8559,0.8630,0.8670,0.8772,0.8794, 0.8800,0.8900,0.8919,0.8927,0.8940,0.8982,0.8988,0.8994,0.9005,0.9028, 0.9103,0.9139,0.9175,0.9201,0.9253,0.9268,0.9303,0.9321,0.9339,0.9500, 0.9565,0.9612,0.9680,0.9685,0.9709,0.9782,0.9874,0.9936,0.9993, Overall p-value after applying KStest on 269 p-values = 0.431938 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.