RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-26_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.90 15.4794 0.439006 2 to 25 15.59 23.3730 0.862505 3 to 26 15.73 20.3274 0.742175 4 to 27 15.71 20.5361 0.752270 5 to 28 15.73 14.1407 0.342879 6 to 29 15.91 9.0440 0.061128 7 to 30 15.81 20.1870 0.735222 8 to 31 15.82 29.9852 0.973548 9 to 32 16.18 14.3251 0.356032 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.605338 Tough bday spacings test for dh-ranFile-2017-01-26_11:31: 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 12 33 71 98 96 81 46 38 16 6 3 (O-E)^2/E 0.9 0.4 0.1 0.0 0.0 0.1 0.7 2.3 0.1 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 4.855, p= 0.099 RESULTS OF GCD FOR dh-ranFile-2017-01-26_11:31 Euclid's algorithm: p-value, steps to gcd: 0.385330 p-value, dist. of gcd's: 0.765677 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-26_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.090 0.111 0.448 0.642 0.451 0.181 0.545 0.304 Bits 8 to 15---> 0.304 0.638 0.868 0.394 0.188 0.965 0.519 0.011 Bits 16 to 23---> 0.907 0.709 0.075 0.718 0.476 0.007 0.382 0.435 Bits 24 to 31---> 0.872 0.619 0.502 0.661 0.155 0.038 0.751 0.993 KS test for the above 32 p values: 0.245 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-26_11:31, p-values for 5 runs: 0.2293, 0.7551, 0.7987, 0.5465, 0.3932 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-26_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5138 5134.0 0.003 0.064 r= 30 23189 23103.0 0.320 0.384 r= 31 11458 11551.5 0.757 1.141 chi-square = 1.141 with df = 3; p-value = 0.233 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-26_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 211 211.4 0.001 0.001 r= 30 5051 5134.0 1.342 1.343 r= 31 23234 23103.0 0.742 2.085 r= 32 11504 11551.5 0.196 2.281 chi-square = 2.281 with df = 3; p-value = 0.484 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-26_11:31 b-rank test for bits 1 to 8, p=0.81415 b-rank test for bits 2 to 9, p=0.29713 b-rank test for bits 3 to 10, p=0.00443 b-rank test for bits 4 to 11, p=0.77183 b-rank test for bits 5 to 12, p=0.60187 b-rank test for bits 6 to 13, p=0.70668 b-rank test for bits 7 to 14, p=0.03015 b-rank test for bits 8 to 15, p=0.68410 b-rank test for bits 9 to 16, p=0.37192 b-rank test for bits 10 to 17, p=0.75022 b-rank test for bits 11 to 18, p=0.57844 b-rank test for bits 12 to 19, p=0.79311 b-rank test for bits 13 to 20, p=0.90079 b-rank test for bits 14 to 21, p=0.12123 b-rank test for bits 15 to 22, p=0.60583 b-rank test for bits 16 to 23, p=0.31900 b-rank test for bits 17 to 24, p=0.56878 b-rank test for bits 18 to 25, p=0.46809 b-rank test for bits 19 to 26, p=0.86383 b-rank test for bits 20 to 27, p=0.66653 b-rank test for bits 21 to 28, p=0.57414 b-rank test for bits 22 to 29, p=0.90219 b-rank test for bits 23 to 30, p=0.13383 b-rank test for bits 24 to 31, p=0.59793 b-rank test for bits 25 to 32, p=0.79816 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 = 0.259496 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-26_11:31 (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 141823 -0.20 0.420073 2 141813 -0.23 0.410962 3 141975 0.15 0.560972 4 141285 -1.46 0.072322 5 141378 -1.24 0.107224 6 141580 -0.77 0.220809 7 141353 -1.30 0.096829 8 141984 0.17 0.569249 9 142482 1.34 0.909554 10 142225 0.74 0.769605 11 142195 0.67 0.747759 12 142046 0.32 0.625259 13 141197 -1.66 0.048024 14 141649 -0.61 0.271512 15 142163 0.59 0.723305 16 142166 0.60 0.725646 17 141684 -0.53 0.299280 18 142204 0.69 0.754425 19 142870 2.24 0.987602 20 142573 1.55 0.939505 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-26_11:31 Bits used No. missing words z-score p-value 23 to 32 141710 -0.6873 0.245933 22 to 31 141781 -0.4425 0.329058 21 to 30 142115 0.7092 0.760902 20 to 29 141609 -1.0356 0.150190 19 to 28 141889 -0.0701 0.472056 18 to 27 141290 -2.1356 0.016355 17 to 26 141698 -0.7287 0.233085 16 to 25 141746 -0.5632 0.286647 15 to 24 141884 -0.0873 0.465199 14 to 23 141721 -0.6494 0.258036 13 to 22 141896 -0.0460 0.481669 12 to 21 142222 1.0782 0.859522 11 to 20 141477 -1.4908 0.068008 10 to 19 141603 -1.0563 0.145413 9 to 18 142121 0.7299 0.767273 8 to 17 142025 0.3989 0.655003 7 to 16 141707 -0.6977 0.242686 6 to 15 141541 -1.2701 0.102024 5 to 14 141573 -1.1598 0.123074 4 to 13 141968 0.2023 0.580163 3 to 12 141520 -1.3425 0.089714 2 to 11 141964 0.1885 0.574764 1 to 10 141534 -1.2942 0.097791 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-26_11:31 Bits used No. missing words z-score p-value 28 to 32 141733 -0.5977 0.275010 27 to 31 142092 0.6192 0.732114 26 to 30 141549 -1.2215 0.110956 25 to 29 141608 -1.0215 0.153519 24 to 28 141719 -0.6452 0.259403 23 to 27 141866 -0.1469 0.441613 22 to 26 141183 -2.4621 0.006906 21 to 25 141738 -0.5808 0.280695 20 to 24 142121 0.7175 0.763475 19 to 23 141912 0.0091 0.503611 18 to 22 142154 0.8294 0.796558 17 to 21 141921 0.0396 0.515778 16 to 20 141718 -0.6486 0.258306 15 to 19 141730 -0.6079 0.271628 14 to 18 142017 0.3650 0.642438 13 to 17 141631 -0.9435 0.172715 12 to 16 141891 -0.0621 0.475227 11 to 15 142220 1.0531 0.853857 10 to 14 141921 0.0396 0.515778 9 to 13 142240 1.1209 0.868838 8 to 12 141640 -0.9130 0.180626 7 to 11 141847 -0.2113 0.416331 6 to 10 141899 -0.0350 0.486033 5 to 9 142003 0.3175 0.624578 4 to 8 141949 0.1345 0.553486 3 to 7 141745 -0.5571 0.288746 2 to 6 141782 -0.4316 0.333006 1 to 5 141988 0.2667 0.605141 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-26_11:31 Bits used No. missing words z-score p-value 31 to 32 141413 -1.4641 0.071583 30 to 31 141857 -0.1544 0.438661 29 to 30 141693 -0.6381 0.261691 28 to 29 141293 -1.8181 0.034526 27 to 28 141742 -0.4936 0.310795 26 to 27 142217 0.9076 0.817950 25 to 26 141568 -1.0069 0.156998 24 to 25 141974 0.1908 0.575646 23 to 24 141503 -1.1986 0.115339 22 to 23 142074 0.4858 0.686429 21 to 22 142256 1.0226 0.846758 20 to 21 141607 -0.8918 0.186242 19 to 20 141684 -0.6647 0.253124 18 to 19 142347 1.2911 0.901659 17 to 18 141392 -1.5260 0.063499 16 to 17 142316 1.1996 0.884856 15 to 16 141955 0.1347 0.553583 14 to 15 141677 -0.6853 0.246565 13 to 14 141642 -0.7886 0.215178 12 to 13 141460 -1.3255 0.092510 11 to 12 142519 1.7984 0.963946 10 to 11 141131 -2.2960 0.010839 9 to 10 141904 -0.0157 0.493728 8 to 9 141740 -0.4995 0.308714 7 to 8 141626 -0.8358 0.201639 6 to 7 141793 -0.3432 0.365740 5 to 6 142059 0.4415 0.670576 4 to 5 142070 0.4740 0.682233 3 to 4 142175 0.7837 0.783388 2 to 3 142208 0.8810 0.810850 1 to 2 142121 0.6244 0.733816 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-26_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2439.25 -0.859 0.195131 Test results for specific bytes for dh-ranFile-2017-01-26_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2479.27 -0.293 0.384711 2 to 9 2489.98 -0.142 0.443654 3 to 10 2606.86 1.511 0.934630 4 to 11 2486.87 -0.186 0.426355 5 to 12 2510.61 0.150 0.559657 6 to 13 2455.38 -0.631 0.264021 7 to 14 2605.29 1.489 0.931757 8 to 15 2507.56 0.107 0.542598 9 to 16 2611.67 1.579 0.942855 10 to 17 2406.93 -1.316 0.094060 11 to 18 2580.80 1.143 0.873414 12 to 19 2585.87 1.214 0.887711 13 to 20 2502.57 0.036 0.514516 14 to 21 2518.73 0.265 0.604445 15 to 22 2464.29 -0.505 0.306760 16 to 23 2554.18 0.766 0.778217 17 to 24 2327.22 -2.444 0.007272 18 to 25 2525.61 0.362 0.641383 19 to 26 2453.62 -0.656 0.255938 20 to 27 2476.94 -0.326 0.372191 21 to 28 2323.83 -2.491 0.006363 22 to 29 2599.90 1.413 0.921143 23 to 30 2421.75 -1.107 0.134233 24 to 31 2585.42 1.208 0.886471 25 to 32 2577.34 1.094 0.862958 CDPARK for dh-ranFile-2017-01-26_11:31: 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 3516 -0.3196 0.374623 3519 -0.1826 0.427537 3527 0.1826 0.572463 3542 0.8676 0.807188 3545 1.0046 0.842447 3484 -1.7808 0.037471 3554 1.4155 0.921543 3491 -1.4612 0.071982 3474 -2.2374 0.012629 3569 2.1005 0.982156 Square side=100, avg. no. parked=3522.10 sample std.=29.90 p-value of the KSTEST for those 10 p-values: 0.387654 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-26_11:31 0.0295,0.1014,0.0982,0.1240,0.1967,0.4240,0.5546,0.0467,0.9803,0.7870, The KS test for those 10 p-values: 0.045634 The 3DSPHERES test for dh-ranFile-2017-01-26_11:31 sample no r^3 equiv. uni. 1 113.615 0.977340 2 10.396 0.292876 3 36.529 0.704073 4 63.734 0.880505 5 5.427 0.165481 6 0.177 0.005873 7 0.915 0.030035 8 8.032 0.234876 9 22.297 0.524429 10 29.818 0.629881 11 97.875 0.961707 12 32.175 0.657842 13 9.673 0.275613 14 9.205 0.264234 15 15.149 0.396474 16 0.462 0.015266 17 30.657 0.640090 18 53.825 0.833734 19 31.725 0.652682 20 19.387 0.475984 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.728606 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-26_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 -1.3 -1.7 0.7 -3.2 -0.8 -0.2 1.2 -1.5 -1.6 -0.3 1.1 -0.3 0.7 -0.1 -0.1 -1.6 -0.1 0.9 1.5 0.7 0.5 -1.1 2.0 -2.1 -0.0 1.8 -0.1 -1.1 0.8 1.1 0.1 -1.3 0.5 -1.4 -0.5 -1.0 -0.8 -1.3 -0.6 0.0 2.7 Chi-square with 42 degrees of freedom:62.717515 z-score=2.260466, p-value=0.979283 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-26_11:31 Test no p-value 1 0.680451 2 0.338613 3 0.917263 4 0.039184 5 0.662043 6 0.971791 7 0.485407 8 0.297251 9 0.368905 10 0.329705 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.887507 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-26_11:31: (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 66970 1.38 66803 0.28 3 25000.00 24803 1.55 24839 1.04 4 6666.67 6596 0.75 6706 0.23 5 1388.89 1351 1.03 1380 0.06 6 238.10 236 0.02 233 0.11 7 34.72 35 0.00 36 0.05 8 4.96 8 1.86 2 1.77 p=0.64050 p=0.25966 Number of rngs required: 686959, p-value: 0.045 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-26_11:31 No. of wins: Observed Expected 98487 98585.9 z-score=-0.442, pvalue=0.32919 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66653 66666.7 0.003 0.003 2 37586 37654.3 0.124 0.127 3 27159 26954.7 1.548 1.675 4 19271 19313.5 0.093 1.768 5 13717 13851.4 1.304 3.073 6 10070 9943.5 1.608 4.681 7 7141 7145.0 0.002 4.683 8 5172 5139.1 0.211 4.894 9 3722 3699.9 0.132 5.026 10 2563 2666.3 4.002 9.028 11 1885 1923.3 0.764 9.792 12 1386 1388.7 0.005 9.798 13 1023 1003.7 0.371 10.168 14 750 726.1 0.784 10.952 15 477 525.8 4.536 15.488 16 402 381.2 1.140 16.628 17 292 276.5 0.864 17.493 18 221 200.8 2.026 19.518 19 122 146.0 3.940 23.459 20 109 106.2 0.073 23.532 21 279 287.1 0.229 23.761 Chisq= 23.76 for 20 degrees of freedom, p= 0.74702 SUMMARY of craptest p-value for no. of wins: 0.329189 p-value for throws/game: 0.747015 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-26_11:31 No. of wins: Observed Expected 97901 98585.9 z-score=-3.063, pvalue=0.00110 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66542 66666.7 0.233 0.233 2 37691 37654.3 0.036 0.269 3 26866 26954.7 0.292 0.561 4 19268 19313.5 0.107 0.668 5 13958 13851.4 0.820 1.488 6 9901 9943.5 0.182 1.670 7 7238 7145.0 1.210 2.880 8 5111 5139.1 0.153 3.033 9 3766 3699.9 1.182 4.215 10 2658 2666.3 0.026 4.241 11 1933 1923.3 0.049 4.290 12 1392 1388.7 0.008 4.298 13 992 1003.7 0.137 4.434 14 742 726.1 0.346 4.781 15 522 525.8 0.028 4.809 16 387 381.2 0.090 4.898 17 264 276.5 0.569 5.467 18 194 200.8 0.232 5.699 19 155 146.0 0.557 6.256 20 116 106.2 0.901 7.157 21 304 287.1 0.993 8.151 Chisq= 8.15 for 20 degrees of freedom, p= 0.00918 SUMMARY of craptest p-value for no. of wins: 0.001095 p-value for throws/game: 0.009176 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0044,0.0059,0.0064,0.0069,0.0072,0.0073,0.0092,0.0105,0.0108, 0.0126,0.0153,0.0164,0.0295,0.0300,0.0301,0.0345,0.0375,0.0380,0.0392, 0.0452,0.0456,0.0467,0.0480,0.0611,0.0635,0.0680,0.0716,0.0720,0.0723, 0.0753,0.0897,0.0902,0.0925,0.0941,0.0968,0.0978,0.0982,0.0994,0.1014, 0.1020,0.1072,0.1110,0.1110,0.1153,0.1212,0.1231,0.1240,0.1338,0.1342, 0.1454,0.1502,0.1535,0.1553,0.1570,0.1655,0.1727,0.1806,0.1807,0.1862, 0.1884,0.1951,0.1967,0.2016,0.2152,0.2208,0.2293,0.2328,0.2331,0.2349, 0.2427,0.2449,0.2459,0.2466,0.2531,0.2559,0.2580,0.2583,0.2594,0.2595, 0.2597,0.2617,0.2640,0.2642,0.2715,0.2716,0.2750,0.2756,0.2807,0.2866, 0.2887,0.2929,0.2971,0.2973,0.2993,0.3038,0.3044,0.3068,0.3087,0.3108, 0.3190,0.3291,0.3292,0.3297,0.3330,0.3386,0.3429,0.3560,0.3657,0.3689, 0.3719,0.3722,0.3746,0.3820,0.3847,0.3853,0.3877,0.3932,0.3940,0.3965, 0.4110,0.4163,0.4201,0.4240,0.4264,0.4275,0.4354,0.4387,0.4390,0.4416, 0.4437,0.4477,0.4506,0.4652,0.4681,0.4721,0.4752,0.4755,0.4760,0.4817, 0.4838,0.4854,0.4860,0.4937,0.5015,0.5036,0.5145,0.5158,0.5158,0.5186, 0.5244,0.5426,0.5452,0.5465,0.5535,0.5536,0.5546,0.5597,0.5610,0.5688, 0.5692,0.5725,0.5741,0.5748,0.5756,0.5784,0.5802,0.5979,0.6019,0.6044, 0.6051,0.6053,0.6058,0.6191,0.6246,0.6253,0.6299,0.6379,0.6401,0.6405, 0.6414,0.6416,0.6424,0.6527,0.6550,0.6578,0.6615,0.6620,0.6665,0.6706, 0.6805,0.6822,0.6841,0.6864,0.7041,0.7067,0.7091,0.7180,0.7233,0.7256, 0.7286,0.7321,0.7338,0.7352,0.7422,0.7470,0.7478,0.7502,0.7506,0.7523, 0.7544,0.7551,0.7609,0.7635,0.7657,0.7673,0.7696,0.7718,0.7782,0.7834, 0.7870,0.7931,0.7966,0.7982,0.7987,0.8072,0.8108,0.8141,0.8180,0.8337, 0.8424,0.8468,0.8539,0.8595,0.8625,0.8630,0.8638,0.8681,0.8688,0.8723, 0.8734,0.8805,0.8849,0.8865,0.8875,0.8877,0.9008,0.9017,0.9022,0.9067, 0.9096,0.9173,0.9211,0.9215,0.9318,0.9346,0.9395,0.9429,0.9617,0.9639, 0.9646,0.9718,0.9735,0.9773,0.9793,0.9803,0.9822,0.9876,0.9927, Overall p-value after applying KStest on 269 p-values = 0.078217 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.