RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-12_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 23.0743 0.853153 2 to 25 15.89 12.7915 0.249971 3 to 26 15.62 20.2824 0.739959 4 to 27 15.89 20.8892 0.768713 5 to 28 15.85 13.3171 0.285288 6 to 29 15.85 12.5946 0.237127 7 to 30 15.79 15.5221 0.442069 8 to 31 15.58 14.0157 0.334009 9 to 32 15.69 23.4273 0.864151 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.691515 Tough bday spacings test for dh-ranFile-2016-01-12_16:31: 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 39 70 114 95 72 48 29 14 8 1 (O-E)^2/E 0.1 0.2 0.1 2.7 0.1 0.5 0.3 0.0 0.1 0.3 2.3 Birthday Spacings: Sum(O-E)^2/E= 6.655, p= 0.242 RESULTS OF GCD FOR dh-ranFile-2016-01-12_16:31 Euclid's algorithm: p-value, steps to gcd: 0.068653 p-value, dist. of gcd's: 0.462551 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-12_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.486 0.710 0.977 0.636 0.251 0.229 0.322 0.749 Bits 8 to 15---> 0.868 0.467 0.378 0.636 0.918 0.762 0.618 0.957 Bits 16 to 23---> 0.351 0.088 0.186 0.776 0.908 0.851 0.905 0.073 Bits 24 to 31---> 0.164 0.757 0.681 0.909 0.415 0.494 0.040 0.009 KS test for the above 32 p values: 0.453 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-12_16:31, p-values for 5 runs: 0.9283, 0.6295, 0.8031, 0.7325, 0.8527 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-12_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5185 5134.0 0.506 1.807 r= 30 22948 23103.0 1.041 2.848 r= 31 11639 11551.5 0.662 3.510 chi-square = 3.510 with df = 3; p-value = 0.681 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-12_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5144 5134.0 0.019 0.768 r= 31 23020 23103.0 0.299 1.067 r= 32 11612 11551.5 0.317 1.383 chi-square = 1.383 with df = 3; p-value = 0.291 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-12_16:31 b-rank test for bits 1 to 8, p=0.37433 b-rank test for bits 2 to 9, p=0.27907 b-rank test for bits 3 to 10, p=0.78024 b-rank test for bits 4 to 11, p=0.03230 b-rank test for bits 5 to 12, p=0.34405 b-rank test for bits 6 to 13, p=0.44151 b-rank test for bits 7 to 14, p=0.73880 b-rank test for bits 8 to 15, p=0.25238 b-rank test for bits 9 to 16, p=0.09771 b-rank test for bits 10 to 17, p=0.60399 b-rank test for bits 11 to 18, p=0.61777 b-rank test for bits 12 to 19, p=0.82370 b-rank test for bits 13 to 20, p=0.62241 b-rank test for bits 14 to 21, p=0.85730 b-rank test for bits 15 to 22, p=0.39024 b-rank test for bits 16 to 23, p=0.54685 b-rank test for bits 17 to 24, p=0.92477 b-rank test for bits 18 to 25, p=0.98011 b-rank test for bits 19 to 26, p=0.99048 b-rank test for bits 20 to 27, p=0.02607 b-rank test for bits 21 to 28, p=0.95270 b-rank test for bits 22 to 29, p=0.28824 b-rank test for bits 23 to 30, p=0.12993 b-rank test for bits 24 to 31, p=0.43727 b-rank test for bits 25 to 32, p=0.82444 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 = 0.797185 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-12_16:31 (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 142758 1.98 0.976309 2 142146 0.55 0.709857 3 142402 1.15 0.875154 4 141624 -0.67 0.252495 5 141961 0.12 0.548045 6 142155 0.57 0.717015 7 142172 0.61 0.730298 8 142091 0.42 0.664386 9 141508 -0.94 0.174203 10 141209 -1.64 0.050890 11 141724 -0.43 0.332502 12 142115 0.48 0.684577 13 141729 -0.42 0.336756 14 142466 1.30 0.903308 15 141801 -0.25 0.400093 16 141605 -0.71 0.238526 17 141470 -1.03 0.152335 18 141257 -1.52 0.063737 19 142841 2.18 0.985252 20 141458 -1.05 0.145825 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-12_16:31 Bits used No. missing words z-score p-value 23 to 32 141658 -0.8667 0.193066 22 to 31 141942 0.1127 0.544848 21 to 30 142061 0.5230 0.699513 20 to 29 141966 0.1954 0.577466 19 to 28 141862 -0.1632 0.435178 18 to 27 141994 0.2920 0.614844 17 to 26 141941 0.1092 0.543481 16 to 25 142084 0.6023 0.726516 15 to 24 142674 2.6368 0.995815 14 to 23 141716 -0.6667 0.252496 13 to 22 141871 -0.1322 0.447424 12 to 21 142425 1.7782 0.962312 11 to 20 142130 0.7609 0.776651 10 to 19 142278 1.2713 0.898185 9 to 18 141596 -1.0804 0.139971 8 to 17 142182 0.9402 0.826453 7 to 16 141559 -1.2080 0.113517 6 to 15 141942 0.1127 0.544848 5 to 14 142300 1.3471 0.911032 4 to 13 141678 -0.7977 0.212525 3 to 12 141792 -0.4046 0.342891 2 to 11 142041 0.4540 0.675098 1 to 10 142693 2.7023 0.996557 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-12_16:31 Bits used No. missing words z-score p-value 28 to 32 142127 0.7379 0.769702 27 to 31 142079 0.5752 0.717406 26 to 30 141901 -0.0282 0.488737 25 to 29 142157 0.8396 0.799422 24 to 28 141875 -0.1164 0.453679 23 to 27 141712 -0.6689 0.251775 22 to 26 142195 0.9684 0.833571 21 to 25 141726 -0.6215 0.267149 20 to 24 142194 0.9650 0.832723 19 to 23 141790 -0.4045 0.342919 18 to 22 141765 -0.4893 0.312331 17 to 21 142498 1.9955 0.977005 16 to 20 141684 -0.7638 0.222484 15 to 19 141725 -0.6248 0.266036 14 to 18 141935 0.0870 0.534671 13 to 17 141798 -0.3774 0.352942 12 to 16 141939 0.1006 0.540057 11 to 15 141840 -0.2350 0.407098 10 to 14 142132 0.7548 0.774820 9 to 13 142315 1.3752 0.915458 8 to 12 142257 1.1785 0.880710 7 to 11 142137 0.7718 0.779873 6 to 10 142407 1.6870 0.954200 5 to 9 142088 0.6057 0.727630 4 to 8 142027 0.3989 0.655010 3 to 7 141714 -0.6621 0.253942 2 to 6 141277 -2.1435 0.016037 1 to 5 141751 -0.5367 0.295733 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-12_16:31 Bits used No. missing words z-score p-value 31 to 32 142387 1.4091 0.920591 30 to 31 141751 -0.4671 0.320232 29 to 30 141706 -0.5998 0.274322 28 to 29 141861 -0.1426 0.443316 27 to 28 142070 0.4740 0.682233 26 to 27 142191 0.8309 0.796981 25 to 26 142771 2.5418 0.994486 24 to 25 142055 0.4297 0.666295 23 to 24 142270 1.0639 0.856318 22 to 23 142010 0.2970 0.616752 21 to 22 142166 0.7571 0.775517 20 to 21 141396 -1.5142 0.064982 19 to 20 141574 -0.9892 0.161289 18 to 19 141859 -0.1485 0.440988 17 to 18 142180 0.7984 0.787691 16 to 17 142471 1.6568 0.951224 15 to 16 141859 -0.1485 0.440988 14 to 15 141846 -0.1868 0.425903 13 to 14 141964 0.1613 0.564059 12 to 13 141937 0.0816 0.532527 11 to 12 141927 0.0521 0.520785 10 to 11 141881 -0.0836 0.466699 9 to 10 141803 -0.3137 0.376891 8 to 9 143087 3.4740 0.999744 7 to 8 141604 -0.9007 0.183880 6 to 7 141431 -1.4110 0.079122 5 to 6 141917 0.0226 0.509025 4 to 5 141910 0.0020 0.500789 3 to 4 142521 1.8043 0.964411 2 to 3 141460 -1.3255 0.092510 1 to 2 141416 -1.4553 0.072800 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-12_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2531.84 0.450 0.673755 Test results for specific bytes for dh-ranFile-2016-01-12_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2372.63 -1.801 0.035827 2 to 9 2476.39 -0.334 0.369230 3 to 10 2598.46 1.392 0.918111 4 to 11 2523.44 0.331 0.629853 5 to 12 2447.76 -0.739 0.230002 6 to 13 2447.55 -0.742 0.229121 7 to 14 2616.27 1.644 0.949949 8 to 15 2597.49 1.379 0.916000 9 to 16 2507.40 0.105 0.541673 10 to 17 2486.28 -0.194 0.423066 11 to 18 2454.19 -0.648 0.258547 12 to 19 2556.46 0.799 0.787712 13 to 20 2484.41 -0.220 0.412764 14 to 21 2634.63 1.904 0.971544 15 to 22 2451.97 -0.679 0.248513 16 to 23 2560.78 0.860 0.804970 17 to 24 2568.40 0.967 0.833306 18 to 25 2571.58 1.012 0.844315 19 to 26 2577.73 1.099 0.864184 20 to 27 2412.17 -1.242 0.107111 21 to 28 2402.63 -1.377 0.084252 22 to 29 2563.29 0.895 0.814611 23 to 30 2494.06 -0.084 0.466525 24 to 31 2460.49 -0.559 0.288144 25 to 32 2501.13 0.016 0.506376 CDPARK for dh-ranFile-2016-01-12_16:31: 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 3554 1.4155 0.921543 3530 0.3196 0.625377 3537 0.6393 0.738676 3536 0.5936 0.723613 3535 0.5479 0.708135 3539 0.7306 0.767486 3531 0.3653 0.642555 3534 0.5023 0.692266 3527 0.1826 0.572463 Square side=100, avg. no. parked=3533.50 sample std.=9.97 p-value of the KSTEST for those 10 p-values: 0.041793 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-12_16:31 0.3917,0.1042,0.7976,0.6868,0.3421,0.9979,0.7346,0.6292,0.7874,0.6788, The KS test for those 10 p-values: 0.232674 The 3DSPHERES test for dh-ranFile-2016-01-12_16:31 sample no r^3 equiv. uni. 1 87.840 0.946497 2 71.470 0.907664 3 77.126 0.923532 4 20.166 0.489418 5 5.767 0.174891 6 2.363 0.075756 7 62.681 0.876234 8 35.365 0.692360 9 100.051 0.964387 10 15.463 0.402766 11 18.160 0.454106 12 47.972 0.797913 13 37.550 0.713970 14 29.636 0.627629 15 108.583 0.973202 16 83.369 0.937898 17 18.677 0.463442 18 58.016 0.855413 19 34.916 0.687722 20 39.788 0.734531 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.005096 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-12_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 2.6 0.8 0.2 0.4 1.1 -0.3 -1.4 1.6 0.7 -0.7 -0.6 2.1 0.5 0.8 0.0 -1.9 -0.8 2.4 -0.9 -0.6 -0.4 0.4 -0.7 -0.0 -0.3 -2.3 -0.1 -0.9 0.8 1.7 2.3 -2.2 1.5 0.9 0.2 0.3 -0.7 0.1 0.4 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:57.721935 z-score=1.715404, p-value=0.946234 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-12_16:31 Test no p-value 1 0.155222 2 0.077997 3 0.012258 4 0.668660 5 0.213015 6 0.598505 7 0.709640 8 0.203280 9 0.871320 10 0.235362 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.221766 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-12_16:31: (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 66766 0.15 66731 0.06 3 25000.00 24873 0.65 24984 0.01 4 6666.67 6690 0.08 6598 0.71 5 1388.89 1386 0.01 1388 0.00 6 238.10 250 0.60 245 0.20 7 34.72 33 0.09 50 6.72 8 4.96 1 3.16 3 0.77 p=0.42018 p=0.79497 Number of rngs required: 689526, p-value: 0.904 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-12_16:31 No. of wins: Observed Expected 98172 98585.9 z-score=-1.851, pvalue=0.03208 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66586 66666.7 0.098 0.098 2 37922 37654.3 1.903 2.000 3 26872 26954.7 0.254 2.254 4 19278 19313.5 0.065 2.320 5 13964 13851.4 0.915 3.235 6 10000 9943.5 0.321 3.555 7 7119 7145.0 0.095 3.650 8 5044 5139.1 1.759 5.409 9 3622 3699.9 1.639 7.047 10 2591 2666.3 2.126 9.174 11 1904 1923.3 0.194 9.368 12 1402 1388.7 0.127 9.495 13 978 1003.7 0.659 10.154 14 752 726.1 0.921 11.074 15 567 525.8 3.222 14.297 16 393 381.2 0.368 14.665 17 283 276.5 0.151 14.816 18 215 200.8 1.000 15.816 19 152 146.0 0.248 16.064 20 90 106.2 2.475 18.539 21 266 287.1 1.553 20.092 Chisq= 20.09 for 20 degrees of freedom, p= 0.54782 SUMMARY of craptest p-value for no. of wins: 0.032084 p-value for throws/game: 0.547817 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-12_16:31 No. of wins: Observed Expected 98501 98585.9 z-score=-0.380, pvalue=0.35214 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66972 66666.7 1.398 1.398 2 37761 37654.3 0.302 1.701 3 26839 26954.7 0.497 2.198 4 19239 19313.5 0.287 2.485 5 13812 13851.4 0.112 2.597 6 9950 9943.5 0.004 2.601 7 7184 7145.0 0.213 2.814 8 5135 5139.1 0.003 2.817 9 3659 3699.9 0.451 3.268 10 2670 2666.3 0.005 3.273 11 1826 1923.3 4.925 8.199 12 1367 1388.7 0.340 8.539 13 947 1003.7 3.205 11.744 14 758 726.1 1.398 13.141 15 496 525.8 1.693 14.834 16 354 381.2 1.934 16.768 17 297 276.5 1.514 18.282 18 217 200.8 1.302 19.584 19 136 146.0 0.683 20.267 20 108 106.2 0.030 20.297 21 273 287.1 0.694 20.991 Chisq= 20.99 for 20 degrees of freedom, p= 0.60233 SUMMARY of craptest p-value for no. of wins: 0.352145 p-value for throws/game: 0.602330 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0051,0.0094,0.0123,0.0160,0.0261,0.0321,0.0323,0.0358,0.0400,0.0418, 0.0509,0.0637,0.0650,0.0687,0.0728,0.0728,0.0758,0.0780,0.0791,0.0843, 0.0882,0.0925,0.0977,0.1042,0.1071,0.1135,0.1299,0.1400,0.1458,0.1523, 0.1552,0.1613,0.1639,0.1742,0.1749,0.1839,0.1855,0.1931,0.2033,0.2125, 0.2130,0.2218,0.2225,0.2286,0.2291,0.2300,0.2327,0.2354,0.2371,0.2385, 0.2425,0.2485,0.2500,0.2506,0.2518,0.2524,0.2525,0.2525,0.2539,0.2585, 0.2660,0.2671,0.2743,0.2791,0.2853,0.2881,0.2882,0.2906,0.2957,0.3077, 0.3123,0.3202,0.3218,0.3325,0.3340,0.3368,0.3421,0.3429,0.3429,0.3440, 0.3514,0.3521,0.3529,0.3692,0.3743,0.3769,0.3783,0.3902,0.3917,0.4001, 0.4028,0.4071,0.4128,0.4147,0.4202,0.4231,0.4259,0.4352,0.4373,0.4410, 0.4410,0.4415,0.4421,0.4433,0.4474,0.4525,0.4537,0.4541,0.4626,0.4634, 0.4665,0.4667,0.4669,0.4858,0.4887,0.4894,0.4942,0.5008,0.5064,0.5090, 0.5208,0.5325,0.5347,0.5401,0.5417,0.5435,0.5448,0.5448,0.5468,0.5478, 0.5480,0.5641,0.5725,0.5775,0.5985,0.6023,0.6040,0.6148,0.6168,0.6178, 0.6178,0.6224,0.6254,0.6276,0.6292,0.6295,0.6299,0.6360,0.6363,0.6426, 0.6550,0.6644,0.6663,0.6687,0.6738,0.6751,0.6788,0.6805,0.6812,0.6822, 0.6846,0.6868,0.6877,0.6915,0.6923,0.6924,0.6995,0.7081,0.7096,0.7099, 0.7101,0.7140,0.7170,0.7174,0.7236,0.7265,0.7276,0.7303,0.7325,0.7345, 0.7346,0.7387,0.7388,0.7400,0.7494,0.7570,0.7621,0.7675,0.7687,0.7697, 0.7748,0.7755,0.7756,0.7767,0.7799,0.7802,0.7874,0.7877,0.7877,0.7950, 0.7970,0.7972,0.7976,0.7979,0.7994,0.8031,0.8050,0.8146,0.8237,0.8244, 0.8265,0.8327,0.8333,0.8336,0.8443,0.8515,0.8527,0.8532,0.8554,0.8563, 0.8573,0.8642,0.8642,0.8682,0.8713,0.8752,0.8762,0.8807,0.8982,0.9033, 0.9045,0.9054,0.9077,0.9080,0.9093,0.9110,0.9155,0.9160,0.9177,0.9181, 0.9206,0.9215,0.9235,0.9248,0.9283,0.9379,0.9462,0.9465,0.9499,0.9512, 0.9527,0.9542,0.9572,0.9623,0.9644,0.9644,0.9715,0.9732,0.9763,0.9770, 0.9771,0.9801,0.9853,0.9905,0.9945,0.9958,0.9966,0.9979,0.9997, Overall p-value after applying KStest on 269 p-values = 0.004374 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.