RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-26_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 15.52 18.2907 0.629274 2 to 25 15.64 26.8235 0.939292 3 to 26 15.57 19.6465 0.707290 4 to 27 15.97 23.8669 0.876903 5 to 28 16.04 15.4397 0.436158 6 to 29 15.72 10.7383 0.130157 7 to 30 15.74 23.3228 0.860965 8 to 31 15.89 26.1627 0.928453 9 to 32 15.66 15.3556 0.430115 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.144532 Tough bday spacings test for dh-ranFile-2015-11-26_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 9 45 67 102 97 78 51 35 13 3 0 (O-E)^2/E 0.0 1.9 0.5 0.2 0.0 0.0 0.0 0.9 0.2 2.0 4.1 Birthday Spacings: Sum(O-E)^2/E= 9.869, p= 0.548 RESULTS OF GCD FOR dh-ranFile-2015-11-26_20:31 Euclid's algorithm: p-value, steps to gcd: 0.434960 p-value, dist. of gcd's: 0.857766 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-26_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.530 0.660 0.298 0.472 0.667 0.155 0.891 0.414 Bits 8 to 15---> 0.583 0.313 0.410 0.026 0.707 0.334 0.080 0.568 Bits 16 to 23---> 0.849 0.657 0.707 0.312 0.744 0.304 0.346 0.789 Bits 24 to 31---> 0.496 0.533 0.187 0.965 0.982 0.066 0.543 0.998 KS test for the above 32 p values: 0.219 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-26_20:31, p-values for 5 runs: 0.9049, 0.0500, 0.3177, 0.4254, 0.6216 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-26_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5172 5134.0 0.281 0.486 r= 30 23022 23103.0 0.284 0.770 r= 31 11588 11551.5 0.115 0.886 chi-square = 0.886 with df = 3; p-value = 0.171 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-26_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 190 211.4 2.170 2.170 r= 30 5183 5134.0 0.467 2.637 r= 31 23157 23103.0 0.126 2.763 r= 32 11470 11551.5 0.575 3.339 chi-square = 3.339 with df = 3; p-value = 0.658 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-26_20:31 b-rank test for bits 1 to 8, p=0.19661 b-rank test for bits 2 to 9, p=0.94477 b-rank test for bits 3 to 10, p=0.90070 b-rank test for bits 4 to 11, p=0.70670 b-rank test for bits 5 to 12, p=0.24650 b-rank test for bits 6 to 13, p=0.73802 b-rank test for bits 7 to 14, p=0.13986 b-rank test for bits 8 to 15, p=0.78076 b-rank test for bits 9 to 16, p=0.87894 b-rank test for bits 10 to 17, p=0.49332 b-rank test for bits 11 to 18, p=0.22669 b-rank test for bits 12 to 19, p=0.72588 b-rank test for bits 13 to 20, p=0.51974 b-rank test for bits 14 to 21, p=0.94938 b-rank test for bits 15 to 22, p=0.34220 b-rank test for bits 16 to 23, p=0.23273 b-rank test for bits 17 to 24, p=0.26761 b-rank test for bits 18 to 25, p=0.66807 b-rank test for bits 19 to 26, p=0.72321 b-rank test for bits 20 to 27, p=0.19813 b-rank test for bits 21 to 28, p=0.09772 b-rank test for bits 22 to 29, p=0.14365 b-rank test for bits 23 to 30, p=0.42195 b-rank test for bits 24 to 31, p=0.97257 b-rank test for bits 25 to 32, p=0.58205 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 = 0.769924 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-26_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 141854 -0.13 0.448570 2 142137 0.53 0.702616 3 141628 -0.66 0.255490 4 141932 0.05 0.521121 5 142444 1.25 0.894209 6 141500 -0.96 0.169441 7 141968 0.14 0.554516 8 142168 0.60 0.727201 9 141611 -0.70 0.242891 10 142200 0.68 0.751474 11 141570 -0.79 0.213939 12 141512 -0.93 0.176615 13 141907 -0.01 0.497828 14 142646 1.72 0.957392 15 142118 0.49 0.687065 16 141516 -0.92 0.179049 17 142673 1.78 0.962811 18 141837 -0.17 0.432900 19 141789 -0.28 0.389300 20 141596 -0.73 0.232060 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-26_20:31 Bits used No. missing words z-score p-value 23 to 32 142164 0.8782 0.810075 22 to 31 142144 0.8092 0.790802 21 to 30 141849 -0.2080 0.417601 20 to 29 141998 0.3058 0.620106 19 to 28 142336 1.4713 0.929392 18 to 27 141907 -0.0080 0.496795 17 to 26 141448 -1.5908 0.055828 16 to 25 141995 0.2954 0.616161 15 to 24 141792 -0.4046 0.342891 14 to 23 141808 -0.3494 0.363389 13 to 22 141687 -0.7667 0.221643 12 to 21 141867 -0.1460 0.441974 11 to 20 141796 -0.3908 0.347975 10 to 19 141618 -1.0046 0.157548 9 to 18 141463 -1.5391 0.061894 8 to 17 142266 1.2299 0.890632 7 to 16 141606 -1.0460 0.147789 6 to 15 141682 -0.7839 0.216550 5 to 14 141744 -0.5701 0.284304 4 to 13 142031 0.4196 0.662594 3 to 12 142229 1.1023 0.864837 2 to 11 141998 0.3058 0.620106 1 to 10 142222 1.0782 0.859522 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-26_20:31 Bits used No. missing words z-score p-value 28 to 32 142186 0.9379 0.825843 27 to 31 141606 -1.0282 0.151919 26 to 30 141907 -0.0079 0.496849 25 to 29 142335 1.4429 0.925483 24 to 28 141752 -0.5333 0.296905 23 to 27 141427 -1.6350 0.051023 22 to 26 141586 -1.0960 0.136532 21 to 25 141753 -0.5299 0.298080 20 to 24 141680 -0.7774 0.218464 19 to 23 141759 -0.5096 0.305168 18 to 22 141946 0.1243 0.549463 17 to 21 142259 1.1853 0.882055 16 to 20 142099 0.6429 0.739872 15 to 19 142417 1.7209 0.957367 14 to 18 141961 0.1752 0.569520 13 to 17 142252 1.1616 0.877300 12 to 16 142047 0.4667 0.679635 11 to 15 142168 0.8768 0.809715 10 to 14 142076 0.5650 0.713957 9 to 13 141429 -1.6282 0.051737 8 to 12 141978 0.2328 0.592034 7 to 11 142151 0.8192 0.793670 6 to 10 141787 -0.4147 0.339189 5 to 9 141878 -0.1062 0.457711 4 to 8 141698 -0.7164 0.236881 3 to 7 142590 2.3074 0.989483 2 to 6 141639 -0.9164 0.179736 1 to 5 142130 0.7480 0.772780 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-26_20:31 Bits used No. missing words z-score p-value 31 to 32 141942 0.0964 0.538387 30 to 31 141835 -0.2193 0.413223 29 to 30 142118 0.6155 0.730903 28 to 29 141723 -0.5496 0.291281 27 to 28 141470 -1.2960 0.097495 26 to 27 142355 1.3147 0.905688 25 to 26 142072 0.4799 0.684334 24 to 25 141835 -0.2193 0.413223 23 to 24 141971 0.1819 0.572176 22 to 23 142113 0.6008 0.726012 21 to 22 142179 0.7955 0.786835 20 to 21 141745 -0.4847 0.313927 19 to 20 141815 -0.2783 0.390407 18 to 19 142384 1.4002 0.919274 17 to 18 142306 1.1701 0.879023 16 to 17 141845 -0.1898 0.424747 15 to 16 142231 0.9489 0.828659 14 to 15 141985 0.2232 0.588316 13 to 14 141651 -0.7620 0.223019 12 to 13 141584 -0.9597 0.168609 11 to 12 141734 -0.5172 0.302509 10 to 11 142628 2.1200 0.982996 9 to 10 141340 -1.6794 0.046533 8 to 9 141858 -0.1514 0.439824 7 to 8 142033 0.3648 0.642373 6 to 7 141779 -0.3845 0.350321 5 to 6 141288 -1.8328 0.033414 4 to 5 141606 -0.8948 0.185453 3 to 4 141836 -0.2163 0.414372 2 to 3 142273 1.0728 0.858314 1 to 2 142038 0.3796 0.647863 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-26_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2423.05 -1.088 0.138249 Test results for specific bytes for dh-ranFile-2015-11-26_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2599.56 1.408 0.920424 2 to 9 2571.53 1.012 0.844145 3 to 10 2524.84 0.351 0.637327 4 to 11 2537.37 0.529 0.701445 5 to 12 2444.17 -0.789 0.214911 6 to 13 2412.19 -1.242 0.107157 7 to 14 2536.66 0.518 0.697923 8 to 15 2462.62 -0.529 0.298553 9 to 16 2454.27 -0.647 0.258889 10 to 17 2453.68 -0.655 0.256231 11 to 18 2528.17 0.398 0.654851 12 to 19 2511.54 0.163 0.564825 13 to 20 2528.22 0.399 0.655076 14 to 21 2575.99 1.075 0.858729 15 to 22 2549.65 0.702 0.758700 16 to 23 2555.55 0.786 0.783952 17 to 24 2443.70 -0.796 0.212969 18 to 25 2490.82 -0.130 0.448359 19 to 26 2435.43 -0.913 0.180568 20 to 27 2545.13 0.638 0.738320 21 to 28 2406.99 -1.315 0.094188 22 to 29 2373.99 -1.782 0.037376 23 to 30 2363.56 -1.930 0.026833 24 to 31 2598.73 1.396 0.918680 25 to 32 2420.15 -1.129 0.129397 CDPARK for dh-ranFile-2015-11-26_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 3533 0.4566 0.676028 3520 -0.1370 0.445521 3512 -0.5023 0.307734 3506 -0.7763 0.218799 3505 -0.8219 0.205562 3509 -0.6393 0.261324 3539 0.7306 0.767486 3522 -0.0457 0.481790 3519 -0.1826 0.427537 3534 0.5023 0.692266 Square side=100, avg. no. parked=3519.90 sample std.=11.56 p-value of the KSTEST for those 10 p-values: 0.423047 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-26_20:31 0.2164,0.6186,0.8651,0.1193,0.7218,0.3230,0.4681,0.7534,0.6684,0.8862, The KS test for those 10 p-values: 0.749289 The 3DSPHERES test for dh-ranFile-2015-11-26_20:31 sample no r^3 equiv. uni. 1 31.133 0.645754 2 8.245 0.240299 3 30.868 0.642608 4 19.280 0.474114 5 31.994 0.655776 6 32.274 0.658970 7 36.520 0.703981 8 5.828 0.176551 9 18.326 0.457115 10 29.875 0.630587 11 12.746 0.346133 12 24.073 0.551766 13 33.001 0.667137 14 18.794 0.465519 15 3.859 0.120692 16 55.666 0.843632 17 123.392 0.983642 18 27.846 0.604730 19 24.284 0.554912 20 15.153 0.396551 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.188301 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-26_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 2.0 0.3 0.2 -0.2 -0.5 0.3 -2.4 -0.4 0.7 -1.2 0.9 -0.9 1.9 0.7 -0.5 0.7 -1.1 -1.0 -0.2 -0.9 -0.0 0.3 1.7 1.3 0.8 -1.6 -0.5 1.0 0.7 1.2 -1.1 1.2 -0.4 -0.3 -2.3 -1.7 -2.0 -1.8 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:53.326307 z-score=1.235801, p-value=0.887010 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-26_20:31 Test no p-value 1 0.263649 2 0.582587 3 0.599043 4 0.387032 5 0.085199 6 0.709569 7 0.375704 8 0.000041 9 0.016311 10 0.316938 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.040484 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-26_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 66659 0.00 66773 0.17 3 25000.00 25071 0.20 24901 0.39 4 6666.67 6610 0.48 6690 0.08 5 1388.89 1395 0.03 1345 1.39 6 238.10 228 0.43 239 0.00 7 34.72 35 0.00 46 3.66 8 4.96 1 3.16 5 0.00 p=0.36426 p=0.54223 Number of rngs required: 688001, p-value: 0.322 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-26_20:31 No. of wins: Observed Expected 98565 98585.9 z-score=-0.093, pvalue=0.46284 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66373 66666.7 1.294 1.294 2 37434 37654.3 1.289 2.583 3 26956 26954.7 0.000 2.583 4 19386 19313.5 0.272 2.855 5 14055 13851.4 2.992 5.847 6 9917 9943.5 0.071 5.918 7 7270 7145.0 2.186 8.104 8 5179 5139.1 0.310 8.414 9 3715 3699.9 0.062 8.476 10 2690 2666.3 0.211 8.687 11 1917 1923.3 0.021 8.708 12 1313 1388.7 4.131 12.839 13 1046 1003.7 1.781 14.620 14 735 726.1 0.108 14.728 15 543 525.8 0.560 15.288 16 388 381.2 0.123 15.411 17 266 276.5 0.402 15.813 18 219 200.8 1.644 17.457 19 162 146.0 1.757 19.214 20 120 106.2 1.789 21.003 21 316 287.1 2.906 23.909 Chisq= 23.91 for 20 degrees of freedom, p= 0.75362 SUMMARY of craptest p-value for no. of wins: 0.462836 p-value for throws/game: 0.753621 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-26_20:31 No. of wins: Observed Expected 99074 98585.9 z-score= 2.183, pvalue=0.98549 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66800 66666.7 0.267 0.267 2 37942 37654.3 2.198 2.465 3 26795 26954.7 0.947 3.411 4 19301 19313.5 0.008 3.419 5 13712 13851.4 1.403 4.822 6 9939 9943.5 0.002 4.825 7 7093 7145.0 0.379 5.203 8 4973 5139.1 5.367 10.570 9 3798 3699.9 2.603 13.173 10 2653 2666.3 0.066 13.239 11 1917 1923.3 0.021 13.260 12 1403 1388.7 0.146 13.407 13 1018 1003.7 0.203 13.610 14 739 726.1 0.228 13.838 15 539 525.8 0.330 14.167 16 394 381.2 0.433 14.600 17 276 276.5 0.001 14.601 18 217 200.8 1.302 15.903 19 154 146.0 0.440 16.343 20 92 106.2 1.902 18.246 21 245 287.1 6.177 24.423 Chisq= 24.42 for 20 degrees of freedom, p= 0.77561 SUMMARY of craptest p-value for no. of wins: 0.985491 p-value for throws/game: 0.775608 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0163,0.0264,0.0268,0.0334,0.0374,0.0405,0.0465,0.0500,0.0510, 0.0517,0.0558,0.0619,0.0664,0.0801,0.0852,0.0942,0.0975,0.0977,0.1072, 0.1193,0.1207,0.1294,0.1302,0.1365,0.1382,0.1399,0.1437,0.1445,0.1478, 0.1519,0.1545,0.1575,0.1686,0.1694,0.1711,0.1766,0.1766,0.1790,0.1797, 0.1806,0.1855,0.1868,0.1883,0.1966,0.1981,0.2056,0.2130,0.2139,0.2149, 0.2164,0.2166,0.2185,0.2188,0.2188,0.2216,0.2230,0.2267,0.2321,0.2327, 0.2369,0.2403,0.2429,0.2465,0.2555,0.2562,0.2589,0.2613,0.2636,0.2676, 0.2843,0.2913,0.2969,0.2981,0.2982,0.2986,0.3025,0.3036,0.3052,0.3077, 0.3118,0.3130,0.3139,0.3169,0.3177,0.3216,0.3230,0.3345,0.3392,0.3422, 0.3429,0.3459,0.3461,0.3480,0.3503,0.3634,0.3643,0.3757,0.3870,0.3893, 0.3904,0.3966,0.4097,0.4132,0.4132,0.4137,0.4144,0.4176,0.4220,0.4230, 0.4247,0.4254,0.4275,0.4301,0.4329,0.4350,0.4362,0.4398,0.4420,0.4455, 0.4484,0.4486,0.4571,0.4577,0.4628,0.4655,0.4681,0.4719,0.4741,0.4818, 0.4933,0.4958,0.4968,0.4968,0.4978,0.5197,0.5211,0.5303,0.5329,0.5384, 0.5422,0.5426,0.5479,0.5495,0.5518,0.5545,0.5549,0.5648,0.5681,0.5695, 0.5722,0.5821,0.5826,0.5833,0.5883,0.5920,0.5990,0.6047,0.6162,0.6186, 0.6201,0.6201,0.6216,0.6293,0.6306,0.6373,0.6424,0.6426,0.6458,0.6479, 0.6549,0.6551,0.6558,0.6570,0.6577,0.6590,0.6601,0.6626,0.6669,0.6671, 0.6681,0.6684,0.6760,0.6796,0.6843,0.6871,0.6923,0.6979,0.7014,0.7026, 0.7040,0.7066,0.7067,0.7068,0.7073,0.7096,0.7140,0.7218,0.7232,0.7259, 0.7260,0.7272,0.7309,0.7380,0.7383,0.7399,0.7441,0.7493,0.7515,0.7534, 0.7536,0.7587,0.7675,0.7699,0.7728,0.7756,0.7808,0.7840,0.7868,0.7887, 0.7908,0.7937,0.8097,0.8101,0.8258,0.8287,0.8436,0.8441,0.8487,0.8578, 0.8583,0.8587,0.8595,0.8610,0.8648,0.8651,0.8769,0.8773,0.8789,0.8790, 0.8821,0.8862,0.8870,0.8906,0.8909,0.8942,0.9007,0.9049,0.9057,0.9187, 0.9193,0.9204,0.9255,0.9285,0.9294,0.9393,0.9448,0.9494,0.9574,0.9574, 0.9628,0.9652,0.9726,0.9819,0.9830,0.9836,0.9855,0.9895,0.9978, Overall p-value after applying KStest on 269 p-values = 0.466083 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.