RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-07_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.00 12.6041 0.237742 2 to 25 15.55 24.5819 0.895534 3 to 26 15.69 15.0192 0.405900 4 to 27 15.79 18.8679 0.663834 5 to 28 15.96 15.6022 0.447813 6 to 29 15.56 44.8177 0.999741 7 to 30 15.89 15.5940 0.447220 8 to 31 15.96 21.5967 0.799270 9 to 32 15.75 26.5791 0.935463 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.107539 Tough bday spacings test for dh-ranFile-2016-02-07_04:31: 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 41 78 107 90 63 59 29 15 6 2 (O-E)^2/E 0.1 0.5 0.3 0.9 0.6 2.9 0.9 0.0 0.0 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 7.376, p= 0.310 RESULTS OF GCD FOR dh-ranFile-2016-02-07_04:31 Euclid's algorithm: p-value, steps to gcd: 0.795415 p-value, dist. of gcd's: 0.652828 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-07_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.796 0.103 0.197 0.781 0.297 0.488 0.410 0.492 Bits 8 to 15---> 0.794 0.655 0.969 0.759 0.604 0.928 0.608 0.895 Bits 16 to 23---> 0.512 0.705 0.349 0.921 0.258 0.001 0.827 0.649 Bits 24 to 31---> 0.776 0.362 0.833 0.843 0.642 0.621 0.976 0.717 KS test for the above 32 p values: 0.971 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-07_04:31, p-values for 5 runs: 0.9427, 0.3290, 0.2082, 0.5558, 0.1878 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-07_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 211 211.4 0.001 0.001 r= 29 5210 5134.0 1.125 1.126 r= 30 23045 23103.0 0.146 1.271 r= 31 11534 11551.5 0.027 1.298 chi-square = 1.298 with df = 3; p-value = 0.270 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-07_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 225 211.4 0.873 0.873 r= 30 5072 5134.0 0.749 1.622 r= 31 23269 23103.0 1.192 2.814 r= 32 11434 11551.5 1.196 4.009 chi-square = 4.009 with df = 3; p-value = 0.740 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-07_04:31 b-rank test for bits 1 to 8, p=0.74704 b-rank test for bits 2 to 9, p=0.95554 b-rank test for bits 3 to 10, p=0.72965 b-rank test for bits 4 to 11, p=0.05394 b-rank test for bits 5 to 12, p=0.64078 b-rank test for bits 6 to 13, p=0.04709 b-rank test for bits 7 to 14, p=0.10173 b-rank test for bits 8 to 15, p=0.01538 b-rank test for bits 9 to 16, p=0.80709 b-rank test for bits 10 to 17, p=0.66399 b-rank test for bits 11 to 18, p=0.59304 b-rank test for bits 12 to 19, p=0.82952 b-rank test for bits 13 to 20, p=0.08385 b-rank test for bits 14 to 21, p=0.76054 b-rank test for bits 15 to 22, p=0.56344 b-rank test for bits 16 to 23, p=0.24472 b-rank test for bits 17 to 24, p=0.35350 b-rank test for bits 18 to 25, p=0.18255 b-rank test for bits 19 to 26, p=0.20259 b-rank test for bits 20 to 27, p=0.80237 b-rank test for bits 21 to 28, p=0.77972 b-rank test for bits 22 to 29, p=0.96697 b-rank test for bits 23 to 30, p=0.87076 b-rank test for bits 24 to 31, p=0.27821 b-rank test for bits 25 to 32, p=0.33029 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 = 0.684524 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-07_04:31 (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 141813 -0.23 0.410962 2 141859 -0.12 0.453195 3 141643 -0.62 0.266883 4 141706 -0.48 0.317369 5 141784 -0.29 0.384827 6 142144 0.55 0.708255 7 142395 1.13 0.871759 8 142811 2.11 0.982428 9 142176 0.62 0.733378 10 140853 -2.47 0.006792 11 141999 0.21 0.582975 12 141280 -1.47 0.070727 13 141888 -0.05 0.480126 14 141651 -0.60 0.273063 15 142092 0.43 0.665237 16 141761 -0.35 0.364459 17 141146 -1.78 0.037254 18 142316 0.95 0.828985 19 142549 1.49 0.932485 20 141926 0.04 0.515534 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-07_04:31 Bits used No. missing words z-score p-value 23 to 32 142172 0.9058 0.817468 22 to 31 141919 0.0333 0.513300 21 to 30 141675 -0.8080 0.209535 20 to 29 141539 -1.2770 0.100801 19 to 28 142378 1.6161 0.946964 18 to 27 141920 0.0368 0.514675 17 to 26 141656 -0.8736 0.191181 16 to 25 142126 0.7471 0.772510 15 to 24 141791 -0.4080 0.341624 14 to 23 141945 0.1230 0.548947 13 to 22 142123 0.7368 0.769376 12 to 21 142027 0.4058 0.657540 11 to 20 142240 1.1402 0.872907 10 to 19 141797 -0.3873 0.349251 9 to 18 141590 -1.1011 0.135418 8 to 17 141929 0.0678 0.527039 7 to 16 141942 0.1127 0.544848 6 to 15 142170 0.8989 0.815637 5 to 14 141938 0.0989 0.539376 4 to 13 141623 -0.9873 0.161737 3 to 12 141678 -0.7977 0.212525 2 to 11 141367 -1.8701 0.030735 1 to 10 142560 2.2437 0.987574 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-07_04:31 Bits used No. missing words z-score p-value 28 to 32 141808 -0.3435 0.365614 27 to 31 141786 -0.4181 0.337949 26 to 30 141623 -0.9706 0.165871 25 to 29 141934 0.0836 0.533324 24 to 28 141503 -1.3774 0.084196 23 to 27 141812 -0.3299 0.370726 22 to 26 142018 0.3684 0.643702 21 to 25 141997 0.2972 0.616838 20 to 24 141547 -1.2282 0.109679 19 to 23 142068 0.5379 0.704665 18 to 22 141145 -2.5909 0.004786 17 to 21 142013 0.3514 0.637365 16 to 20 141727 -0.6181 0.268265 15 to 19 141954 0.1514 0.560179 14 to 18 141695 -0.7265 0.233753 13 to 17 141573 -1.1401 0.127122 12 to 16 141613 -1.0045 0.157567 11 to 15 142080 0.5785 0.718551 10 to 14 141819 -0.3062 0.379725 9 to 13 141831 -0.2655 0.395302 8 to 12 141567 -1.1604 0.122935 7 to 11 141532 -1.2791 0.100434 6 to 10 142078 0.5718 0.716259 5 to 9 141943 0.1141 0.545435 4 to 8 142177 0.9074 0.817891 3 to 7 142110 0.6802 0.751823 2 to 6 141830 -0.2689 0.393998 1 to 5 142522 2.0768 0.981092 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-07_04:31 Bits used No. missing words z-score p-value 31 to 32 141759 -0.4435 0.328720 30 to 31 142174 0.7807 0.782522 29 to 30 141976 0.1967 0.577956 28 to 29 142169 0.7660 0.778158 27 to 28 141048 -2.5408 0.005530 26 to 27 141439 -1.3874 0.082659 25 to 26 141679 -0.6794 0.248430 24 to 25 141352 -1.6440 0.050084 23 to 24 141547 -1.0688 0.142575 22 to 23 142145 0.6952 0.756532 21 to 22 141659 -0.7384 0.230125 20 to 21 141932 0.0669 0.526659 19 to 20 141918 0.0256 0.510202 18 to 19 141791 -0.3491 0.363524 17 to 18 141875 -0.1013 0.459669 16 to 17 141662 -0.7296 0.232821 15 to 16 141956 0.1377 0.554749 14 to 15 142450 1.5949 0.944632 13 to 14 141964 0.1613 0.564059 12 to 13 141623 -0.8446 0.199158 11 to 12 142068 0.4681 0.680127 10 to 11 142336 1.2586 0.895915 9 to 10 141625 -0.8387 0.200810 8 to 9 142071 0.4769 0.683284 7 to 8 142018 0.3206 0.625728 6 to 7 142653 2.1937 0.985872 5 to 6 142185 0.8132 0.791944 4 to 5 141761 -0.4376 0.330856 3 to 4 141300 -1.7974 0.036133 2 to 3 141681 -0.6735 0.250302 1 to 2 142439 1.5624 0.940909 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-07_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2444.64 -0.783 0.216851 Test results for specific bytes for dh-ranFile-2016-02-07_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2582.62 1.168 0.878678 2 to 9 2461.86 -0.539 0.294814 3 to 10 2463.08 -0.522 0.300787 4 to 11 2565.04 0.920 0.821161 5 to 12 2614.78 1.623 0.947729 6 to 13 2400.56 -1.406 0.079821 7 to 14 2420.23 -1.128 0.129637 8 to 15 2436.06 -0.904 0.182937 9 to 16 2525.01 0.354 0.638207 10 to 17 2569.84 0.988 0.838354 11 to 18 2463.27 -0.519 0.301731 12 to 19 2439.38 -0.857 0.195625 13 to 20 2510.05 0.142 0.556537 14 to 21 2602.40 1.448 0.926218 15 to 22 2443.22 -0.803 0.210985 16 to 23 2507.92 0.112 0.544592 17 to 24 2449.22 -0.718 0.236330 18 to 25 2389.12 -1.568 0.058438 19 to 26 2450.31 -0.703 0.241120 20 to 27 2632.97 1.880 0.969975 21 to 28 2445.90 -0.765 0.222127 22 to 29 2586.82 1.228 0.890239 23 to 30 2527.16 0.384 0.649545 24 to 31 2461.45 -0.545 0.292822 25 to 32 2491.07 -0.126 0.449736 CDPARK for dh-ranFile-2016-02-07_04:31: 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 3538 0.6849 0.753306 3518 -0.2283 0.409702 3573 2.2831 0.988788 3501 -1.0046 0.157553 3538 0.6849 0.753306 3494 -1.3242 0.092718 3488 -1.5982 0.055002 3554 1.4155 0.921543 3521 -0.0913 0.463617 3482 -1.8721 0.030593 Square side=100, avg. no. parked=3520.70 sample std.=28.49 p-value of the KSTEST for those 10 p-values: 0.439396 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-07_04:31 0.7691,0.9057,0.5703,0.1978,0.7857,0.6363,0.9414,0.7748,0.4144,0.9402, The KS test for those 10 p-values: 0.051090 The 3DSPHERES test for dh-ranFile-2016-02-07_04:31 sample no r^3 equiv. uni. 1 36.923 0.707928 2 41.275 0.747370 3 17.152 0.435462 4 52.833 0.828144 5 25.294 0.569645 6 0.523 0.017282 7 42.035 0.753692 8 7.060 0.209691 9 44.199 0.770834 10 5.932 0.179407 11 47.245 0.792959 12 15.526 0.404014 13 44.933 0.776371 14 2.732 0.087041 15 11.012 0.307228 16 49.639 0.808837 17 67.515 0.894652 18 12.837 0.348117 19 43.558 0.765886 20 60.266 0.865860 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.269904 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-07_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 0.1 -0.8 -0.2 0.7 -1.7 0.8 -2.4 0.4 1.6 0.3 -0.3 1.4 1.4 0.4 0.8 -0.2 -0.9 -1.0 0.6 1.3 -1.0 0.2 -1.6 -0.6 -1.0 -1.5 -2.1 0.3 -0.5 0.8 -0.6 1.2 -0.2 -1.6 -0.5 0.8 0.9 -0.1 1.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:47.054157 z-score=0.551454, p-value=0.726708 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-07_04:31 Test no p-value 1 0.113967 2 0.156007 3 0.165164 4 0.708650 5 0.745143 6 0.035582 7 0.043085 8 0.180816 9 0.034943 10 0.051760 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000690 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-07_04:31: (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 66597 0.07 66508 0.38 3 25000.00 25078 0.24 25213 1.81 4 6666.67 6675 0.01 6686 0.06 5 1388.89 1376 0.12 1320 3.42 6 238.10 239 0.00 229 0.35 7 34.72 32 0.21 40 0.80 8 4.96 2 1.77 3 0.77 p=0.12369 p=0.73032 Number of rngs required: 689583, p-value: 0.915 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-07_04:31 No. of wins: Observed Expected 98463 98585.9 z-score=-0.549, pvalue=0.29133 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66309 66666.7 1.919 1.919 2 37981 37654.3 2.834 4.753 3 27045 26954.7 0.302 5.055 4 19130 19313.5 1.743 6.798 5 13797 13851.4 0.214 7.012 6 10005 9943.5 0.380 7.392 7 7144 7145.0 0.000 7.392 8 5199 5139.1 0.699 8.091 9 3771 3699.9 1.368 9.458 10 2650 2666.3 0.100 9.558 11 1917 1923.3 0.021 9.579 12 1427 1388.7 1.054 10.633 13 995 1003.7 0.076 10.709 14 748 726.1 0.658 11.367 15 558 525.8 1.967 13.334 16 344 381.2 3.621 16.955 17 272 276.5 0.075 17.030 18 190 200.8 0.584 17.614 19 147 146.0 0.007 17.621 20 107 106.2 0.006 17.626 21 264 287.1 1.861 19.487 Chisq= 19.49 for 20 degrees of freedom, p= 0.50961 SUMMARY of craptest p-value for no. of wins: 0.291333 p-value for throws/game: 0.509612 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-07_04:31 No. of wins: Observed Expected 98428 98585.9 z-score=-0.706, pvalue=0.24008 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66599 66666.7 0.069 0.069 2 37549 37654.3 0.295 0.363 3 26726 26954.7 1.941 2.304 4 19541 19313.5 2.681 4.985 5 13914 13851.4 0.283 5.268 6 9906 9943.5 0.142 5.409 7 7156 7145.0 0.017 5.426 8 5219 5139.1 1.243 6.669 9 3755 3699.9 0.822 7.491 10 2608 2666.3 1.275 8.766 11 1991 1923.3 2.381 11.147 12 1359 1388.7 0.637 11.784 13 1056 1003.7 2.724 14.507 14 708 726.1 0.453 14.960 15 578 525.8 5.175 20.135 16 335 381.2 5.588 25.723 17 291 276.5 0.756 26.479 18 192 200.8 0.388 26.868 19 130 146.0 1.750 28.618 20 100 106.2 0.364 28.981 21 287 287.1 0.000 28.981 Chisq= 28.98 for 20 degrees of freedom, p= 0.91187 SUMMARY of craptest p-value for no. of wins: 0.240083 p-value for throws/game: 0.911874 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0014,0.0048,0.0055,0.0068,0.0154,0.0173,0.0306,0.0307,0.0349, 0.0356,0.0361,0.0373,0.0431,0.0471,0.0501,0.0511,0.0518,0.0539,0.0550, 0.0584,0.0707,0.0798,0.0827,0.0839,0.0842,0.0870,0.0927,0.1004,0.1008, 0.1017,0.1029,0.1075,0.1097,0.1140,0.1229,0.1237,0.1271,0.1296,0.1354, 0.1426,0.1560,0.1576,0.1576,0.1617,0.1652,0.1659,0.1794,0.1808,0.1826, 0.1829,0.1878,0.1912,0.1956,0.1968,0.1978,0.1992,0.2008,0.2026,0.2082, 0.2095,0.2097,0.2110,0.2125,0.2169,0.2221,0.2301,0.2328,0.2338,0.2363, 0.2377,0.2401,0.2411,0.2447,0.2484,0.2503,0.2584,0.2669,0.2683,0.2699, 0.2704,0.2731,0.2782,0.2913,0.2928,0.2948,0.2972,0.3008,0.3017,0.3072, 0.3105,0.3174,0.3287,0.3290,0.3303,0.3309,0.3379,0.3416,0.3481,0.3487, 0.3493,0.3535,0.3616,0.3635,0.3645,0.3656,0.3707,0.3797,0.3848,0.3940, 0.3953,0.4040,0.4059,0.4097,0.4101,0.4110,0.4144,0.4355,0.4394,0.4472, 0.4478,0.4497,0.4532,0.4597,0.4636,0.4801,0.4879,0.4922,0.5096,0.5102, 0.5123,0.5133,0.5147,0.5155,0.5267,0.5270,0.5333,0.5394,0.5446,0.5448, 0.5454,0.5489,0.5547,0.5558,0.5565,0.5602,0.5634,0.5641,0.5696,0.5703, 0.5780,0.5830,0.5930,0.6043,0.6078,0.6168,0.6215,0.6257,0.6363,0.6374, 0.6382,0.6408,0.6422,0.6437,0.6488,0.6495,0.6528,0.6553,0.6575,0.6638, 0.6640,0.6652,0.6801,0.6833,0.6845,0.7047,0.7051,0.7079,0.7083,0.7086, 0.7163,0.7173,0.7186,0.7267,0.7296,0.7303,0.7334,0.7395,0.7451,0.7470, 0.7474,0.7518,0.7533,0.7533,0.7537,0.7565,0.7592,0.7605,0.7659,0.7691, 0.7694,0.7708,0.7725,0.7748,0.7763,0.7764,0.7782,0.7797,0.7814,0.7825, 0.7857,0.7919,0.7930,0.7935,0.7954,0.7965,0.7993,0.8024,0.8071,0.8088, 0.8156,0.8175,0.8179,0.8212,0.8268,0.8281,0.8290,0.8295,0.8332,0.8384, 0.8433,0.8659,0.8708,0.8718,0.8729,0.8787,0.8902,0.8947,0.8953,0.8955, 0.8959,0.9057,0.9119,0.9155,0.9212,0.9215,0.9262,0.9275,0.9325,0.9355, 0.9402,0.9409,0.9414,0.9427,0.9446,0.9470,0.9477,0.9555,0.9670,0.9695, 0.9700,0.9711,0.9756,0.9811,0.9824,0.9859,0.9876,0.9888,0.9997, Overall p-value after applying KStest on 269 p-values = 0.580425 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.