RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-18_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.56 23.1562 0.855767 2 to 25 15.88 18.3074 0.630297 3 to 26 15.68 12.4095 0.225268 4 to 27 15.77 14.7634 0.387481 5 to 28 15.89 34.1101 0.991874 6 to 29 15.65 19.2231 0.684120 7 to 30 15.78 17.2620 0.563246 8 to 31 15.60 25.1918 0.909503 9 to 32 15.65 14.5624 0.373034 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.320155 Tough bday spacings test for dh-ranFile-2017-01-18_17:31: 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 35 71 106 89 89 51 36 11 2 1 (O-E)^2/E 0.0 0.1 0.1 0.7 0.8 1.5 0.0 1.3 1.0 3.2 2.3 Birthday Spacings: Sum(O-E)^2/E= 11.006, p= 0.643 RESULTS OF GCD FOR dh-ranFile-2017-01-18_17:31 Euclid's algorithm: p-value, steps to gcd: 0.001243 p-value, dist. of gcd's: 0.601703 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-18_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.586 0.562 0.151 0.420 0.559 0.506 0.282 0.489 Bits 8 to 15---> 0.701 0.924 0.558 0.079 0.160 0.706 0.558 0.622 Bits 16 to 23---> 0.932 0.523 0.884 0.290 0.936 0.925 0.045 0.192 Bits 24 to 31---> 0.513 0.664 0.929 0.972 0.606 0.473 0.143 0.258 KS test for the above 32 p values: 0.530 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-18_17:31, p-values for 5 runs: 0.8944, 0.7184, 0.8204, 0.0837, 0.1639 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-18_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5055 5134.0 1.216 1.833 r= 30 23231 23103.0 0.709 2.541 r= 31 11514 11551.5 0.122 2.663 chi-square = 2.663 with df = 3; p-value = 0.553 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-18_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5173 5134.0 0.296 1.045 r= 31 23159 23103.0 0.136 1.180 r= 32 11444 11551.5 1.001 2.181 chi-square = 2.181 with df = 3; p-value = 0.464 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-18_17:31 b-rank test for bits 1 to 8, p=0.53752 b-rank test for bits 2 to 9, p=0.80925 b-rank test for bits 3 to 10, p=0.58153 b-rank test for bits 4 to 11, p=0.73188 b-rank test for bits 5 to 12, p=0.96989 b-rank test for bits 6 to 13, p=0.92240 b-rank test for bits 7 to 14, p=0.51735 b-rank test for bits 8 to 15, p=0.50004 b-rank test for bits 9 to 16, p=0.58088 b-rank test for bits 10 to 17, p=0.18838 b-rank test for bits 11 to 18, p=0.44269 b-rank test for bits 12 to 19, p=0.75577 b-rank test for bits 13 to 20, p=0.05070 b-rank test for bits 14 to 21, p=0.82338 b-rank test for bits 15 to 22, p=0.15358 b-rank test for bits 16 to 23, p=0.22320 b-rank test for bits 17 to 24, p=0.52702 b-rank test for bits 18 to 25, p=0.52713 b-rank test for bits 19 to 26, p=0.52913 b-rank test for bits 20 to 27, p=0.23260 b-rank test for bits 21 to 28, p=0.70087 b-rank test for bits 22 to 29, p=0.87214 b-rank test for bits 23 to 30, p=0.65696 b-rank test for bits 24 to 31, p=0.38935 b-rank test for bits 25 to 32, p=0.68767 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 = 0.338462 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-18_17:31 (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 141419 -1.15 0.125974 2 141450 -1.07 0.141591 3 142555 1.51 0.934296 4 142576 1.56 0.940341 5 141536 -0.87 0.191532 6 141564 -0.81 0.209878 7 141741 -0.39 0.347051 8 142227 0.74 0.771023 9 142074 0.38 0.649786 10 141525 -0.90 0.184602 11 141414 -1.16 0.123572 12 141701 -0.49 0.313217 13 143136 2.87 0.997922 14 142136 0.53 0.701806 15 141006 -2.11 0.017404 16 141777 -0.31 0.378591 17 142564 1.53 0.936942 18 142228 0.74 0.771730 19 141400 -1.19 0.117019 20 142434 1.23 0.889875 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-18_17:31 Bits used No. missing words z-score p-value 23 to 32 141857 -0.1804 0.428400 22 to 31 141901 -0.0287 0.488542 21 to 30 142473 1.9437 0.974034 20 to 29 142076 0.5747 0.717261 19 to 28 141330 -1.9977 0.022875 18 to 27 142361 1.5575 0.940322 17 to 26 141714 -0.6736 0.250298 16 to 25 141875 -0.1184 0.452884 15 to 24 141885 -0.0839 0.466569 14 to 23 141364 -1.8804 0.030024 13 to 22 141984 0.2575 0.601597 12 to 21 142178 0.9264 0.822894 11 to 20 141393 -1.7804 0.037501 10 to 19 142049 0.4816 0.684962 9 to 18 142068 0.5471 0.707858 8 to 17 142360 1.5540 0.939912 7 to 16 142171 0.9023 0.816554 6 to 15 142063 0.5299 0.701908 5 to 14 141966 0.1954 0.577466 4 to 13 141684 -0.7770 0.218579 3 to 12 141859 -0.1736 0.431109 2 to 11 142082 0.5954 0.724217 1 to 10 141912 0.0092 0.503673 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-18_17:31 Bits used No. missing words z-score p-value 28 to 32 141777 -0.4486 0.326869 27 to 31 141776 -0.4520 0.325647 26 to 30 142021 0.3785 0.647486 25 to 29 141745 -0.5571 0.288746 24 to 28 141799 -0.3740 0.354202 23 to 27 141876 -0.1130 0.455022 22 to 26 141512 -1.3469 0.089009 21 to 25 142263 1.1989 0.884713 20 to 24 141807 -0.3469 0.364340 19 to 23 141547 -1.2282 0.109679 18 to 22 141876 -0.1130 0.455022 17 to 21 141969 0.2023 0.580148 16 to 20 141715 -0.6587 0.255030 15 to 19 141849 -0.2045 0.418978 14 to 18 141519 -1.3232 0.092892 13 to 17 141167 -2.5164 0.005928 12 to 16 141846 -0.2147 0.415009 11 to 15 142160 0.8497 0.802262 10 to 14 142047 0.4667 0.679635 9 to 13 141924 0.0497 0.519831 8 to 12 142010 0.3413 0.633544 7 to 11 142474 1.9141 0.972199 6 to 10 141776 -0.4520 0.325647 5 to 9 141410 -1.6926 0.045262 4 to 8 142358 1.5209 0.935859 3 to 7 142128 0.7413 0.770730 2 to 6 142022 0.3819 0.648744 1 to 5 142646 2.4972 0.993741 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-18_17:31 Bits used No. missing words z-score p-value 31 to 32 142311 1.1849 0.881965 30 to 31 142408 1.4710 0.929355 29 to 30 141889 -0.0600 0.476090 28 to 29 142401 1.4504 0.926520 27 to 28 141915 0.0167 0.506672 26 to 27 141885 -0.0718 0.471393 25 to 26 142382 1.3943 0.918388 24 to 25 141973 0.1878 0.574490 23 to 24 141753 -0.4612 0.322345 22 to 23 141540 -1.0895 0.137974 21 to 22 141928 0.0551 0.521960 20 to 21 142463 1.6332 0.948791 19 to 20 141933 0.0698 0.527833 18 to 19 142153 0.7188 0.763865 17 to 18 141679 -0.6794 0.248430 16 to 17 141553 -1.0511 0.146602 15 to 16 142428 1.5300 0.936992 14 to 15 142533 1.8397 0.967096 13 to 14 142232 0.9518 0.829408 12 to 13 141972 0.1849 0.573333 11 to 12 142528 1.8250 0.965998 10 to 11 141017 -2.6322 0.004241 9 to 10 142088 0.5271 0.700921 8 to 9 141500 -1.2075 0.113627 7 to 8 141470 -1.2960 0.097495 6 to 7 141876 -0.0983 0.460840 5 to 6 141391 -1.5290 0.063133 4 to 5 141622 -0.8476 0.198336 3 to 4 142432 1.5418 0.938439 2 to 3 142650 2.1849 0.985551 1 to 2 141884 -0.0747 0.470219 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-18_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2496.12 -0.055 0.478107 Test results for specific bytes for dh-ranFile-2017-01-18_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2578.34 1.108 0.866059 2 to 9 2477.79 -0.314 0.376714 3 to 10 2540.26 0.569 0.715426 4 to 11 2507.01 0.099 0.539505 5 to 12 2609.22 1.545 0.938777 6 to 13 2471.95 -0.397 0.345786 7 to 14 2543.34 0.613 0.730022 8 to 15 2516.37 0.232 0.591553 9 to 16 2465.35 -0.490 0.312036 10 to 17 2448.77 -0.725 0.234362 11 to 18 2511.45 0.162 0.564339 12 to 19 2444.99 -0.778 0.218283 13 to 20 2556.55 0.800 0.788075 14 to 21 2435.42 -0.913 0.180559 15 to 22 2374.15 -1.780 0.037560 16 to 23 2526.82 0.379 0.647753 17 to 24 2453.81 -0.653 0.256789 18 to 25 2426.07 -1.046 0.147892 19 to 26 2446.93 -0.751 0.226475 20 to 27 2520.96 0.296 0.616520 21 to 28 2513.66 0.193 0.576606 22 to 29 2429.63 -0.995 0.159827 23 to 30 2474.79 -0.357 0.360710 24 to 31 2388.48 -1.577 0.057377 25 to 32 2336.09 -2.318 0.010225 CDPARK for dh-ranFile-2017-01-18_17:31: 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 3540 0.7763 0.781201 3518 -0.2283 0.409702 3537 0.6393 0.738676 3525 0.0913 0.536383 3533 0.4566 0.676028 3516 -0.3196 0.374623 3542 0.8676 0.807188 3551 1.2785 0.899470 3520 -0.1370 0.445521 3523 0.0000 0.500000 Square side=100, avg. no. parked=3530.50 sample std.=11.20 p-value of the KSTEST for those 10 p-values: 0.193325 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-18_17:31 0.7009,0.0290,0.6399,0.6038,0.7588,0.8256,0.0075,0.4207,0.4194,0.3952, The KS test for those 10 p-values: 0.492515 The 3DSPHERES test for dh-ranFile-2017-01-18_17:31 sample no r^3 equiv. uni. 1 47.748 0.796399 2 78.774 0.927618 3 10.663 0.299134 4 87.276 0.945480 5 3.637 0.114162 6 14.331 0.379794 7 40.830 0.743592 8 5.127 0.157081 9 44.135 0.770346 10 3.283 0.103647 11 114.715 0.978156 12 63.377 0.879074 13 15.857 0.410554 14 2.478 0.079282 15 61.378 0.870742 16 23.938 0.549739 17 19.448 0.477052 18 43.483 0.765293 19 6.752 0.201538 20 2.630 0.083928 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.602658 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-18_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.6 0.9 0.5 -2.2 -2.2 -2.2 1.9 -0.6 0.8 -2.4 -1.0 -0.5 1.4 0.6 0.9 1.0 0.1 -0.3 0.7 -0.2 0.2 1.7 -0.8 -1.6 0.0 -0.6 0.0 0.5 -1.8 -0.9 0.1 2.2 -0.1 -0.7 -1.6 0.2 0.9 -1.3 0.1 1.0 -1.1 Chi-square with 42 degrees of freedom:55.150828 z-score=1.434873, p-value=0.916012 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-18_17:31 Test no p-value 1 0.019946 2 0.171954 3 0.260111 4 0.833301 5 0.110967 6 0.232540 7 0.154070 8 0.293619 9 0.922775 10 0.742692 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.170000 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-18_17:31: (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 66508 0.38 66423 0.89 3 25000.00 25210 1.76 25190 1.44 4 6666.67 6655 0.02 6672 0.00 5 1388.89 1367 0.35 1393 0.01 6 238.10 220 1.38 267 3.51 7 34.72 32 0.21 51 7.63 8 4.96 7 0.84 3 0.77 p=0.44775 p=0.97322 Number of rngs required: 688077, p-value: 0.354 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-18_17:31 No. of wins: Observed Expected 98394 98585.9 z-score=-0.858, pvalue=0.19542 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66760 66666.7 0.131 0.131 2 37515 37654.3 0.515 0.646 3 26785 26954.7 1.069 1.715 4 19409 19313.5 0.473 2.188 5 13789 13851.4 0.281 2.469 6 9939 9943.5 0.002 2.471 7 7154 7145.0 0.011 2.482 8 5238 5139.1 1.904 4.387 9 3722 3699.9 0.132 4.519 10 2643 2666.3 0.204 4.723 11 2041 1923.3 7.199 11.922 12 1379 1388.7 0.068 11.990 13 938 1003.7 4.302 16.293 14 753 726.1 0.994 17.286 15 559 525.8 2.092 19.378 16 372 381.2 0.220 19.597 17 287 276.5 0.396 19.993 18 216 200.8 1.146 21.139 19 149 146.0 0.062 21.201 20 82 106.2 5.521 26.722 21 270 287.1 1.020 27.742 Chisq= 27.74 for 20 degrees of freedom, p= 0.88435 SUMMARY of craptest p-value for no. of wins: 0.195418 p-value for throws/game: 0.884352 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-18_17:31 No. of wins: Observed Expected 98543 98585.9 z-score=-0.192, pvalue=0.42399 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66812 66666.7 0.317 0.317 2 37346 37654.3 2.525 2.841 3 27105 26954.7 0.838 3.679 4 19222 19313.5 0.433 4.112 5 13906 13851.4 0.215 4.327 6 9928 9943.5 0.024 4.352 7 7149 7145.0 0.002 4.354 8 5063 5139.1 1.126 5.480 9 3750 3699.9 0.679 6.159 10 2672 2666.3 0.012 6.171 11 1978 1923.3 1.554 7.725 12 1367 1388.7 0.340 8.066 13 994 1003.7 0.094 8.160 14 755 726.1 1.147 9.307 15 533 525.8 0.098 9.404 16 366 381.2 0.602 10.007 17 272 276.5 0.075 10.081 18 219 200.8 1.644 11.725 19 153 146.0 0.337 12.062 20 115 106.2 0.727 12.789 21 295 287.1 0.217 13.005 Chisq= 13.01 for 20 degrees of freedom, p= 0.12285 SUMMARY of craptest p-value for no. of wins: 0.423993 p-value for throws/game: 0.122850 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0042,0.0059,0.0075,0.0102,0.0174,0.0199,0.0229,0.0290,0.0300, 0.0375,0.0376,0.0450,0.0453,0.0507,0.0574,0.0631,0.0793,0.0793,0.0837, 0.0839,0.0890,0.0929,0.0975,0.1036,0.1097,0.1110,0.1136,0.1142,0.1170, 0.1229,0.1236,0.1260,0.1380,0.1416,0.1427,0.1466,0.1479,0.1509,0.1536, 0.1541,0.1571,0.1596,0.1598,0.1639,0.1700,0.1720,0.1806,0.1846,0.1884, 0.1915,0.1921,0.1933,0.1954,0.1983,0.2015,0.2099,0.2183,0.2186,0.2232, 0.2253,0.2265,0.2325,0.2326,0.2344,0.2484,0.2503,0.2550,0.2568,0.2580, 0.2601,0.2822,0.2887,0.2897,0.2936,0.2991,0.3120,0.3132,0.3202,0.3223, 0.3256,0.3256,0.3269,0.3385,0.3458,0.3471,0.3537,0.3542,0.3607,0.3643, 0.3730,0.3746,0.3767,0.3786,0.3798,0.3875,0.3894,0.3952,0.4097,0.4106, 0.4150,0.4190,0.4194,0.4199,0.4207,0.4240,0.4284,0.4311,0.4427,0.4455, 0.4477,0.4529,0.4550,0.4550,0.4608,0.4643,0.4666,0.4702,0.4714,0.4730, 0.4761,0.4771,0.4781,0.4885,0.4894,0.4925,0.5000,0.5000,0.5037,0.5061, 0.5067,0.5130,0.5174,0.5198,0.5220,0.5232,0.5270,0.5271,0.5278,0.5291, 0.5297,0.5364,0.5375,0.5395,0.5497,0.5535,0.5582,0.5583,0.5585,0.5619, 0.5632,0.5643,0.5733,0.5745,0.5766,0.5775,0.5801,0.5809,0.5815,0.5858, 0.5916,0.6016,0.6017,0.6027,0.6038,0.6055,0.6165,0.6217,0.6303,0.6335, 0.6399,0.6429,0.6475,0.6478,0.6487,0.6498,0.6570,0.6636,0.6760,0.6796, 0.6841,0.6850,0.6877,0.7007,0.7009,0.7009,0.7009,0.7018,0.7019,0.7065, 0.7079,0.7154,0.7173,0.7184,0.7242,0.7300,0.7319,0.7387,0.7427,0.7436, 0.7558,0.7588,0.7639,0.7653,0.7703,0.7707,0.7710,0.7717,0.7812,0.7881, 0.7964,0.8023,0.8072,0.8092,0.8166,0.8204,0.8229,0.8234,0.8256,0.8294, 0.8333,0.8558,0.8661,0.8707,0.8721,0.8791,0.8820,0.8840,0.8844,0.8847, 0.8899,0.8944,0.8995,0.9095,0.9160,0.9184,0.9224,0.9228,0.9239,0.9245, 0.9265,0.9276,0.9292,0.9294,0.9323,0.9343,0.9359,0.9363,0.9369,0.9370, 0.9384,0.9388,0.9399,0.9403,0.9403,0.9455,0.9488,0.9660,0.9671,0.9699, 0.9722,0.9725,0.9732,0.9740,0.9782,0.9856,0.9919,0.9937,0.9979, Overall p-value after applying KStest on 269 p-values = 0.559366 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.