RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-13_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 20.3888 0.745172 2 to 25 16.05 17.7224 0.593447 3 to 26 16.00 18.3093 0.630418 4 to 27 15.98 10.9269 0.139659 5 to 28 15.77 16.1996 0.490265 6 to 29 15.67 15.5523 0.444234 7 to 30 15.78 20.5136 0.751194 8 to 31 16.10 11.3221 0.160662 9 to 32 16.05 11.4349 0.166917 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.651288 Tough bday spacings test for dh-ranFile-2015-07-13_20:31: 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 16 32 75 103 100 65 48 38 14 5 4 (O-E)^2/E 5.1 0.6 0.0 0.3 0.1 2.2 0.3 2.3 0.1 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 11.340, p= 0.668 RESULTS OF GCD FOR dh-ranFile-2015-07-13_20:31 Euclid's algorithm: p-value, steps to gcd: 0.459275 p-value, dist. of gcd's: 0.537015 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-13_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.207 0.020 0.410 0.769 0.154 0.295 0.211 0.702 Bits 8 to 15---> 0.737 0.524 0.678 0.923 0.624 0.661 0.949 0.905 Bits 16 to 23---> 0.198 0.401 0.588 0.172 0.477 0.048 0.924 0.252 Bits 24 to 31---> 0.334 0.729 0.380 0.899 0.628 0.834 0.221 0.754 KS test for the above 32 p values: 0.072 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-13_20:31, p-values for 5 runs: 0.5809, 0.6026, 0.9263, 0.8793, 0.1490 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-13_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5133 5134.0 0.000 0.195 r= 30 23135 23103.0 0.044 0.239 r= 31 11527 11551.5 0.052 0.291 chi-square = 0.291 with df = 3; p-value = 0.038 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-13_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 240 211.4 3.864 3.864 r= 30 5176 5134.0 0.343 4.207 r= 31 23097 23103.0 0.002 4.209 r= 32 11487 11551.5 0.360 4.569 chi-square = 4.569 with df = 3; p-value = 0.794 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-13_20:31 b-rank test for bits 1 to 8, p=0.49314 b-rank test for bits 2 to 9, p=0.49249 b-rank test for bits 3 to 10, p=0.08319 b-rank test for bits 4 to 11, p=0.47898 b-rank test for bits 5 to 12, p=0.23845 b-rank test for bits 6 to 13, p=0.74659 b-rank test for bits 7 to 14, p=0.16885 b-rank test for bits 8 to 15, p=0.60034 b-rank test for bits 9 to 16, p=0.57309 b-rank test for bits 10 to 17, p=0.70833 b-rank test for bits 11 to 18, p=0.65292 b-rank test for bits 12 to 19, p=0.50303 b-rank test for bits 13 to 20, p=0.00399 b-rank test for bits 14 to 21, p=0.69924 b-rank test for bits 15 to 22, p=0.36780 b-rank test for bits 16 to 23, p=0.20364 b-rank test for bits 17 to 24, p=0.12847 b-rank test for bits 18 to 25, p=0.97974 b-rank test for bits 19 to 26, p=0.67975 b-rank test for bits 20 to 27, p=0.21684 b-rank test for bits 21 to 28, p=0.82551 b-rank test for bits 22 to 29, p=0.87657 b-rank test for bits 23 to 30, p=0.04194 b-rank test for bits 24 to 31, p=0.57883 b-rank test for bits 25 to 32, p=0.53702 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 = 0.749021 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-13_20:31 (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 141127 -1.83 0.033784 2 142233 0.76 0.775247 3 141580 -0.77 0.220809 4 141498 -0.96 0.168263 5 142539 1.47 0.929380 6 141934 0.06 0.522982 7 141576 -0.78 0.218046 8 141711 -0.46 0.321543 9 141406 -1.18 0.119797 10 142418 1.19 0.882678 11 142245 0.78 0.783561 12 141619 -0.68 0.248778 13 142444 1.25 0.894209 14 142011 0.24 0.593884 15 141890 -0.05 0.481989 16 142164 0.60 0.724086 17 141571 -0.79 0.214621 18 142032 0.29 0.612795 19 141862 -0.11 0.455973 20 142186 0.65 0.740998 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-13_20:31 Bits used No. missing words z-score p-value 23 to 32 142107 0.6816 0.752261 22 to 31 142013 0.3575 0.639635 21 to 30 141976 0.2299 0.590914 20 to 29 142079 0.5851 0.720749 19 to 28 141497 -1.4218 0.077538 18 to 27 141971 0.2127 0.584202 17 to 26 141858 -0.1770 0.429754 16 to 25 141996 0.2989 0.617477 15 to 24 142018 0.3747 0.646067 14 to 23 142264 1.2230 0.889335 13 to 22 142345 1.5023 0.933492 12 to 21 141946 0.1264 0.550312 11 to 20 141988 0.2713 0.606911 10 to 19 141918 0.0299 0.511925 9 to 18 142495 2.0196 0.978285 8 to 17 141913 0.0127 0.505049 7 to 16 142066 0.5402 0.705485 6 to 15 142141 0.7989 0.787815 5 to 14 142035 0.4333 0.667618 4 to 13 142025 0.3989 0.655003 3 to 12 141825 -0.2908 0.385605 2 to 11 141854 -0.1908 0.424344 1 to 10 141927 0.0609 0.524293 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-13_20:31 Bits used No. missing words z-score p-value 28 to 32 141983 0.2497 0.598602 27 to 31 142110 0.6802 0.751823 26 to 30 141894 -0.0520 0.479278 25 to 29 142058 0.5040 0.692857 24 to 28 141806 -0.3503 0.363068 23 to 27 141816 -0.3164 0.375860 22 to 26 142115 0.6972 0.757157 21 to 25 141715 -0.6587 0.255030 20 to 24 142025 0.3921 0.652509 19 to 23 141682 -0.7706 0.220469 18 to 22 141532 -1.2791 0.100434 17 to 21 142210 1.0192 0.845951 16 to 20 141835 -0.2520 0.400534 15 to 19 141812 -0.3299 0.370726 14 to 18 141454 -1.5435 0.061356 13 to 17 141838 -0.2418 0.404469 12 to 16 141877 -0.1096 0.456366 11 to 15 141682 -0.7706 0.220469 10 to 14 142378 1.5887 0.943937 9 to 13 142081 0.5819 0.719694 8 to 12 142015 0.3582 0.639905 7 to 11 142094 0.6260 0.734343 6 to 10 141894 -0.0520 0.479278 5 to 9 141658 -0.8520 0.197116 4 to 8 141778 -0.4452 0.328093 3 to 7 142334 1.4396 0.925004 2 to 6 142325 1.4091 0.920590 1 to 5 141929 0.0667 0.526581 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-13_20:31 Bits used No. missing words z-score p-value 31 to 32 142231 0.9489 0.828659 30 to 31 142038 0.3796 0.647863 29 to 30 141826 -0.2458 0.402914 28 to 29 141769 -0.4140 0.339454 27 to 28 141721 -0.5555 0.289261 26 to 27 141909 -0.0010 0.499612 25 to 26 141801 -0.3196 0.374652 24 to 25 141855 -0.1603 0.436336 23 to 24 141849 -0.1780 0.429375 22 to 23 142230 0.9459 0.827908 21 to 22 141864 -0.1337 0.446813 20 to 21 141753 -0.4612 0.322345 19 to 20 141791 -0.3491 0.363524 18 to 19 141617 -0.8623 0.194253 17 to 18 141869 -0.1190 0.452651 16 to 17 142318 1.2055 0.885998 15 to 16 141705 -0.6027 0.273340 14 to 15 141977 0.1996 0.579110 13 to 14 141625 -0.8387 0.200810 12 to 13 141649 -0.7679 0.221263 11 to 12 141856 -0.1573 0.437498 10 to 11 141758 -0.4464 0.327654 9 to 10 141601 -0.9095 0.181536 8 to 9 142076 0.4917 0.688517 7 to 8 142276 1.0816 0.860290 6 to 7 141606 -0.8948 0.185453 5 to 6 142058 0.4386 0.669508 4 to 5 141681 -0.6735 0.250302 3 to 4 141647 -0.7738 0.219514 2 to 3 141328 -1.7148 0.043188 1 to 2 142033 0.3648 0.642373 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-13_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2547.10 0.666 0.747307 Test results for specific bytes for dh-ranFile-2015-07-13_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2539.76 0.562 0.713059 2 to 9 2608.99 1.541 0.938379 3 to 10 2677.39 2.509 0.993940 4 to 11 2435.45 -0.913 0.180670 5 to 12 2522.41 0.317 0.624368 6 to 13 2504.07 0.058 0.522956 7 to 14 2419.51 -1.138 0.127508 8 to 15 2364.45 -1.917 0.027617 9 to 16 2473.27 -0.378 0.352712 10 to 17 2576.38 1.080 0.859971 11 to 18 2449.33 -0.717 0.236814 12 to 19 2430.58 -0.982 0.163123 13 to 20 2588.52 1.252 0.894683 14 to 21 2617.39 1.660 0.951560 15 to 22 2454.17 -0.648 0.258444 16 to 23 2376.52 -1.746 0.040378 17 to 24 2461.22 -0.548 0.291696 18 to 25 2647.87 2.091 0.981748 19 to 26 2473.07 -0.381 0.351673 20 to 27 2459.41 -0.574 0.282974 21 to 28 2449.87 -0.709 0.239186 22 to 29 2493.40 -0.093 0.462793 23 to 30 2511.86 0.168 0.566583 24 to 31 2531.77 0.449 0.673371 25 to 32 2448.88 -0.723 0.234864 CDPARK for dh-ranFile-2015-07-13_20:31: 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 3512 -0.5023 0.307734 3548 1.1416 0.873180 3524 0.0457 0.518210 3546 1.0502 0.853193 3528 0.2283 0.590298 3529 0.2740 0.607947 3503 -0.9132 0.180558 3527 0.1826 0.572463 3492 -1.4155 0.078457 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3521.70 sample std.=17.09 p-value of the KSTEST for those 10 p-values: 0.940321 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-13_20:31 0.9844,0.0196,0.0434,0.8668,0.4345,0.3452,0.8891,0.7363,0.7228,0.9276, The KS test for those 10 p-values: 0.198513 The 3DSPHERES test for dh-ranFile-2015-07-13_20:31 sample no r^3 equiv. uni. 1 33.501 0.672641 2 12.726 0.345714 3 125.175 0.984586 4 9.671 0.275574 5 60.093 0.865085 6 19.778 0.482778 7 49.722 0.809366 8 74.445 0.916383 9 61.713 0.872176 10 26.797 0.590667 11 20.190 0.489819 12 41.937 0.752884 13 28.895 0.618323 14 0.373 0.012356 15 29.152 0.621576 16 15.334 0.400175 17 87.545 0.945967 18 23.474 0.542720 19 18.295 0.456551 20 30.385 0.636817 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.106573 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-13_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.9 -0.8 -0.1 2.7 1.4 0.4 0.2 0.5 -0.1 -0.8 -1.0 -0.2 0.8 -0.6 0.1 1.0 -0.2 -0.1 0.3 -1.0 -1.5 0.2 0.6 1.8 -1.0 -0.8 0.4 1.2 0.3 -0.4 -0.7 0.6 0.5 -1.0 -0.1 -0.5 3.0 0.1 -0.1 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:40.863258 z-score=-0.124029, p-value=0.479193 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-13_20:31 Test no p-value 1 0.278372 2 0.038055 3 0.516708 4 0.461642 5 0.185920 6 0.097635 7 0.503677 8 0.167401 9 0.357771 10 0.267495 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.029533 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-13_20:31: (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 66566 0.15 66456 0.67 3 25000.00 25166 1.10 25205 1.68 4 6666.67 6687 0.06 6698 0.15 5 1388.89 1315 3.93 1358 0.69 6 238.10 230 0.28 242 0.06 7 34.72 33 0.09 35 0.00 8 4.96 2 1.77 5 0.00 p=0.71237 p=0.22281 Number of rngs required: 687559, p-value: 0.164 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-13_20:31 No. of wins: Observed Expected 98625 98585.9 z-score= 0.175, pvalue=0.56949 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66665 66666.7 0.000 0.000 2 37452 37654.3 1.087 1.087 3 27091 26954.7 0.689 1.776 4 19443 19313.5 0.869 2.645 5 13848 13851.4 0.001 2.646 6 10051 9943.5 1.161 3.807 7 7030 7145.0 1.852 5.659 8 5125 5139.1 0.039 5.697 9 3686 3699.9 0.052 5.749 10 2725 2666.3 1.292 7.042 11 1859 1923.3 2.152 9.193 12 1322 1388.7 3.207 12.401 13 1037 1003.7 1.104 13.504 14 751 726.1 0.851 14.355 15 504 525.8 0.907 15.262 16 379 381.2 0.012 15.274 17 293 276.5 0.980 16.254 18 179 200.8 2.373 18.627 19 136 146.0 0.683 19.310 20 106 106.2 0.000 19.310 21 318 287.1 3.323 22.633 Chisq= 22.63 for 20 degrees of freedom, p= 0.69282 SUMMARY of craptest p-value for no. of wins: 0.569485 p-value for throws/game: 0.692822 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-13_20:31 No. of wins: Observed Expected 99109 98585.9 z-score= 2.340, pvalue=0.99035 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66899 66666.7 0.810 0.810 2 37532 37654.3 0.397 1.207 3 26948 26954.7 0.002 1.209 4 19308 19313.5 0.002 1.210 5 13836 13851.4 0.017 1.227 6 9938 9943.5 0.003 1.231 7 7077 7145.0 0.648 1.878 8 5149 5139.1 0.019 1.897 9 3738 3699.9 0.393 2.290 10 2687 2666.3 0.161 2.451 11 1886 1923.3 0.725 3.176 12 1364 1388.7 0.441 3.616 13 1040 1003.7 1.312 4.928 14 726 726.1 0.000 4.928 15 500 525.8 1.269 6.198 16 368 381.2 0.454 6.651 17 268 276.5 0.264 6.915 18 214 200.8 0.864 7.779 19 129 146.0 1.976 9.755 20 90 106.2 2.475 12.230 21 303 287.1 0.879 13.109 Chisq= 13.11 for 20 degrees of freedom, p= 0.12735 SUMMARY of craptest p-value for no. of wins: 0.990353 p-value for throws/game: 0.127348 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0040,0.0124,0.0196,0.0199,0.0276,0.0295,0.0338,0.0381,0.0383,0.0404, 0.0419,0.0432,0.0434,0.0484,0.0614,0.0724,0.0775,0.0785,0.0832,0.0976, 0.1004,0.1066,0.1198,0.1273,0.1275,0.1285,0.1397,0.1490,0.1541,0.1607, 0.1631,0.1641,0.1669,0.1674,0.1683,0.1688,0.1721,0.1806,0.1807,0.1815, 0.1855,0.1859,0.1943,0.1971,0.1981,0.1985,0.2008,0.2036,0.2068,0.2107, 0.2146,0.2168,0.2180,0.2195,0.2205,0.2205,0.2205,0.2208,0.2213,0.2228, 0.2349,0.2368,0.2384,0.2392,0.2467,0.2488,0.2503,0.2516,0.2550,0.2584, 0.2675,0.2733,0.2756,0.2784,0.2830,0.2893,0.2917,0.2951,0.3077,0.3215, 0.3223,0.3277,0.3281,0.3335,0.3395,0.3452,0.3457,0.3517,0.3527,0.3578, 0.3631,0.3635,0.3678,0.3707,0.3747,0.3759,0.3795,0.3856,0.4002,0.4005, 0.4005,0.4029,0.4045,0.4096,0.4243,0.4294,0.4298,0.4345,0.4363,0.4375, 0.4442,0.4468,0.4527,0.4560,0.4564,0.4566,0.4593,0.4616,0.4628,0.4774, 0.4790,0.4792,0.4793,0.4793,0.4820,0.4828,0.4898,0.4903,0.4925,0.4931, 0.4996,0.5030,0.5037,0.5050,0.5119,0.5167,0.5182,0.5230,0.5230,0.5235, 0.5243,0.5266,0.5370,0.5370,0.5427,0.5503,0.5666,0.5695,0.5725,0.5731, 0.5788,0.5791,0.5809,0.5842,0.5882,0.5903,0.5907,0.5909,0.5934,0.5939, 0.5986,0.6003,0.6026,0.6069,0.6079,0.6128,0.6175,0.6183,0.6216,0.6237, 0.6244,0.6280,0.6304,0.6368,0.6396,0.6399,0.6424,0.6461,0.6479,0.6513, 0.6525,0.6529,0.6550,0.6608,0.6676,0.6684,0.6695,0.6726,0.6734,0.6778, 0.6797,0.6885,0.6928,0.6929,0.6992,0.7019,0.7055,0.7083,0.7124,0.7131, 0.7197,0.7207,0.7228,0.7241,0.7288,0.7343,0.7363,0.7374,0.7410,0.7452, 0.7466,0.7473,0.7490,0.7512,0.7518,0.7523,0.7529,0.7543,0.7572,0.7688, 0.7752,0.7836,0.7878,0.7938,0.8094,0.8255,0.8279,0.8287,0.8335,0.8460, 0.8532,0.8600,0.8603,0.8651,0.8668,0.8722,0.8732,0.8766,0.8793,0.8827, 0.8860,0.8891,0.8893,0.8942,0.8947,0.8995,0.9054,0.9164,0.9206,0.9229, 0.9243,0.9250,0.9263,0.9276,0.9294,0.9335,0.9384,0.9403,0.9439,0.9460, 0.9491,0.9516,0.9783,0.9797,0.9817,0.9844,0.9846,0.9904,0.9939, Overall p-value after applying KStest on 269 p-values = 0.377253 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.