RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-07_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.78 15.7161 0.455958 2 to 25 15.81 12.3194 0.219576 3 to 26 16.01 11.0875 0.148019 4 to 27 15.64 17.7468 0.595019 5 to 28 15.94 18.5145 0.642899 6 to 29 15.85 14.9513 0.401011 7 to 30 15.71 13.7260 0.313606 8 to 31 15.95 16.1123 0.484115 9 to 32 15.49 12.5043 0.231314 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.208056 Tough bday spacings test for dh-ranFile-2015-07-07_14:31: 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 15 41 67 98 87 79 53 36 19 3 2 (O-E)^2/E 3.7 0.5 0.5 0.0 1.2 0.0 0.0 1.3 1.1 2.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 11.445, p= 0.676 RESULTS OF GCD FOR dh-ranFile-2015-07-07_14:31 Euclid's algorithm: p-value, steps to gcd: 0.431374 p-value, dist. of gcd's: 0.179280 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-07_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.339 0.342 0.617 0.425 0.963 0.044 0.359 0.262 Bits 8 to 15---> 0.726 0.838 0.386 0.719 0.500 0.806 0.586 0.152 Bits 16 to 23---> 0.110 0.236 0.018 0.163 0.016 0.244 0.921 0.505 Bits 24 to 31---> 0.317 0.647 0.889 0.299 0.570 0.995 0.312 0.581 KS test for the above 32 p values: 0.221 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-07_14:31, p-values for 5 runs: 0.2899, 0.5065, 0.5796, 0.7455, 0.6322 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-07_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 4956 5134.0 6.172 6.204 r= 30 23338 23103.0 2.389 8.593 r= 31 11492 11551.5 0.307 8.900 chi-square = 8.900 with df = 3; p-value = 0.969 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-07_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5146 5134.0 0.028 1.633 r= 31 23132 23103.0 0.036 1.669 r= 32 11529 11551.5 0.044 1.713 chi-square = 1.713 with df = 3; p-value = 0.366 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-07_14:31 b-rank test for bits 1 to 8, p=0.49909 b-rank test for bits 2 to 9, p=0.76814 b-rank test for bits 3 to 10, p=0.14948 b-rank test for bits 4 to 11, p=0.20106 b-rank test for bits 5 to 12, p=0.62824 b-rank test for bits 6 to 13, p=0.75996 b-rank test for bits 7 to 14, p=0.54144 b-rank test for bits 8 to 15, p=0.51738 b-rank test for bits 9 to 16, p=0.81136 b-rank test for bits 10 to 17, p=0.28398 b-rank test for bits 11 to 18, p=0.68579 b-rank test for bits 12 to 19, p=0.37446 b-rank test for bits 13 to 20, p=0.28321 b-rank test for bits 14 to 21, p=0.28134 b-rank test for bits 15 to 22, p=0.06990 b-rank test for bits 16 to 23, p=0.39608 b-rank test for bits 17 to 24, p=0.46672 b-rank test for bits 18 to 25, p=0.44738 b-rank test for bits 19 to 26, p=0.61217 b-rank test for bits 20 to 27, p=0.03700 b-rank test for bits 21 to 28, p=0.11384 b-rank test for bits 22 to 29, p=0.34588 b-rank test for bits 23 to 30, p=0.35558 b-rank test for bits 24 to 31, p=0.03279 b-rank test for bits 25 to 32, p=0.73577 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 = 0.171229 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-07_14:31 (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 142423 1.20 0.884962 2 141927 0.04 0.516466 3 142094 0.43 0.666937 4 141310 -1.40 0.080711 5 140308 -3.74 0.000091 6 142207 0.70 0.756626 7 141953 0.10 0.540635 8 141574 -0.78 0.216672 9 142009 0.23 0.592070 10 142702 1.85 0.967989 11 142364 1.06 0.855953 12 142070 0.38 0.646317 13 140981 -2.17 0.015042 14 142152 0.57 0.714638 15 141496 -0.97 0.167091 16 141422 -1.14 0.127431 17 142678 1.80 0.963749 18 141597 -0.73 0.232774 19 142019 0.26 0.601117 20 141632 -0.65 0.258503 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-07_14:31 Bits used No. missing words z-score p-value 23 to 32 142009 0.3437 0.634460 22 to 31 142339 1.4816 0.930779 21 to 30 141726 -0.6322 0.263637 20 to 29 141475 -1.4977 0.067107 19 to 28 141974 0.2230 0.588232 18 to 27 141841 -0.2356 0.406864 17 to 26 141788 -0.4184 0.337835 16 to 25 141771 -0.4770 0.316681 15 to 24 142187 0.9575 0.830838 14 to 23 141897 -0.0425 0.483043 13 to 22 142152 0.8368 0.798646 12 to 21 142086 0.6092 0.728806 11 to 20 141890 -0.0667 0.473428 10 to 19 141708 -0.6942 0.243765 9 to 18 142009 0.3437 0.634460 8 to 17 142474 1.9471 0.974241 7 to 16 142126 0.7471 0.772510 6 to 15 142246 1.1609 0.877165 5 to 14 141873 -0.1253 0.450153 4 to 13 141713 -0.6770 0.249203 3 to 12 141391 -1.7873 0.036941 2 to 11 141822 -0.3011 0.381655 1 to 10 141423 -1.6770 0.046771 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-07_14:31 Bits used No. missing words z-score p-value 28 to 32 141713 -0.6655 0.252857 27 to 31 142214 1.0328 0.849147 26 to 30 141754 -0.5265 0.299256 25 to 29 141619 -0.9842 0.162516 24 to 28 142636 2.4633 0.993117 23 to 27 142008 0.3345 0.630989 22 to 26 142170 0.8836 0.811551 21 to 25 141725 -0.6248 0.266036 20 to 24 142168 0.8768 0.809715 19 to 23 141916 0.0226 0.509019 18 to 22 141989 0.2701 0.606446 17 to 21 141920 0.0362 0.514426 16 to 20 142063 0.5209 0.698787 15 to 19 141738 -0.5808 0.280695 14 to 18 141845 -0.2181 0.413688 13 to 17 142218 1.0463 0.852298 12 to 16 141970 0.2057 0.581472 11 to 15 141506 -1.3672 0.085778 10 to 14 142119 0.7107 0.761379 9 to 13 142463 1.8768 0.969731 8 to 12 141898 -0.0384 0.484682 7 to 11 142369 1.5582 0.940407 6 to 10 141947 0.1277 0.550805 5 to 9 142536 2.1243 0.983178 4 to 8 142076 0.5650 0.713957 3 to 7 141578 -1.1232 0.130686 2 to 6 142269 1.2192 0.888620 1 to 5 141811 -0.3333 0.369446 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-07_14:31 Bits used No. missing words z-score p-value 31 to 32 143288 4.0669 0.999976 30 to 31 142282 1.0993 0.864186 29 to 30 142162 0.7453 0.771967 28 to 29 142150 0.7099 0.761130 27 to 28 141969 0.1760 0.569860 26 to 27 141846 -0.1868 0.425903 25 to 26 141768 -0.4169 0.338375 24 to 25 141769 -0.4140 0.339454 23 to 24 141919 0.0285 0.511378 22 to 23 142457 1.6155 0.946904 21 to 22 141646 -0.7768 0.218643 20 to 21 141593 -0.9331 0.175377 19 to 20 142084 0.5153 0.696811 18 to 19 141718 -0.5644 0.286243 17 to 18 141831 -0.2311 0.408633 16 to 17 141816 -0.2753 0.391539 15 to 16 141928 0.0551 0.521960 14 to 15 141968 0.1731 0.568701 13 to 14 142037 0.3766 0.646767 12 to 13 141555 -1.0452 0.147960 11 to 12 141771 -0.4081 0.341617 10 to 11 142080 0.5035 0.692677 9 to 10 141442 -1.3786 0.084016 8 to 9 141796 -0.3343 0.369074 7 to 8 141705 -0.6027 0.273340 6 to 7 142213 0.8958 0.814815 5 to 6 142131 0.6539 0.743410 4 to 5 141534 -1.1072 0.134111 3 to 4 142112 0.5978 0.725029 2 to 3 142094 0.5447 0.707037 1 to 2 142193 0.8368 0.798643 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-07_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2474.84 -0.356 0.360988 Test results for specific bytes for dh-ranFile-2015-07-07_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2488.30 -0.165 0.434280 2 to 9 2489.45 -0.149 0.440712 3 to 10 2576.39 1.080 0.860008 4 to 11 2482.47 -0.248 0.402113 5 to 12 2500.17 0.002 0.500954 6 to 13 2482.60 -0.246 0.402812 7 to 14 2436.11 -0.903 0.183136 8 to 15 2447.05 -0.749 0.226990 9 to 16 2619.66 1.692 0.954696 10 to 17 2507.83 0.111 0.544059 11 to 18 2364.77 -1.912 0.027907 12 to 19 2494.04 -0.084 0.466436 13 to 20 2560.34 0.853 0.803281 14 to 21 2560.89 0.861 0.805416 15 to 22 2541.67 0.589 0.722194 16 to 23 2470.09 -0.423 0.336176 17 to 24 2599.56 1.408 0.920427 18 to 25 2531.00 0.438 0.669464 19 to 26 2422.29 -1.099 0.135874 20 to 27 2501.46 0.021 0.508224 21 to 28 2566.65 0.943 0.827053 22 to 29 2522.94 0.324 0.627200 23 to 30 2409.66 -1.278 0.100693 24 to 31 2600.85 1.426 0.923101 25 to 32 2514.30 0.202 0.580133 CDPARK for dh-ranFile-2015-07-07_14:31: 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 3535 0.5479 0.708135 3519 -0.1826 0.427537 3524 0.0457 0.518210 3503 -0.9132 0.180558 3495 -1.2785 0.100530 3507 -0.7306 0.232514 3523 0.0000 0.500000 3505 -0.8219 0.205562 3510 -0.5936 0.276387 3529 0.2740 0.607947 Square side=100, avg. no. parked=3515.00 sample std.=12.21 p-value of the KSTEST for those 10 p-values: 0.208492 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-07_14:31 0.6826,0.5135,0.6268,0.0045,0.0389,0.8172,0.2476,0.3865,0.1750,0.3525, The KS test for those 10 p-values: 0.303642 The 3DSPHERES test for dh-ranFile-2015-07-07_14:31 sample no r^3 equiv. uni. 1 12.120 0.332351 2 19.082 0.470635 3 57.799 0.854361 4 12.950 0.350575 5 8.494 0.246582 6 31.566 0.650833 7 16.284 0.418884 8 31.481 0.649836 9 40.903 0.744217 10 16.364 0.420424 11 51.869 0.822530 12 3.475 0.109376 13 15.001 0.393492 14 119.556 0.981411 15 9.105 0.261778 16 19.970 0.486061 17 22.096 0.521227 18 78.321 0.926517 19 13.536 0.363136 20 0.955 0.031342 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.827500 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-07_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 -0.8 -1.0 0.6 1.0 -0.3 0.1 -0.7 -0.3 1.3 0.9 0.2 1.4 1.3 0.6 1.0 0.7 -1.2 -0.9 -1.0 -0.3 0.2 -2.3 -1.6 0.9 -0.2 0.3 -0.3 -1.6 -1.2 -1.8 0.9 0.4 -1.3 0.1 -0.2 0.8 0.9 -0.1 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:36.681095 z-score=-0.580340, p-value=0.296945 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-07_14:31 Test no p-value 1 0.299973 2 0.297948 3 0.017239 4 0.486422 5 0.746174 6 0.124664 7 0.836096 8 0.126518 9 0.006666 10 0.158886 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.035418 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-07_14:31: (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 66718 0.04 66521 0.32 3 25000.00 24947 0.11 25108 0.47 4 6666.67 6587 0.95 6705 0.22 5 1388.89 1457 3.34 1363 0.48 6 238.10 262 2.40 264 2.82 7 34.72 19 7.12 35 0.00 8 4.96 9 3.29 3 0.77 p=0.99160 p=0.46680 Number of rngs required: 688569, p-value: 0.576 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-07_14:31 No. of wins: Observed Expected 98679 98585.9 z-score= 0.417, pvalue=0.66151 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66556 66666.7 0.184 0.184 2 37794 37654.3 0.518 0.702 3 26821 26954.7 0.663 1.365 4 19148 19313.5 1.418 2.783 5 13721 13851.4 1.228 4.011 6 9879 9943.5 0.419 4.430 7 7242 7145.0 1.316 5.746 8 5161 5139.1 0.094 5.840 9 3851 3699.9 6.174 12.013 10 2712 2666.3 0.783 12.797 11 1964 1923.3 0.860 13.657 12 1364 1388.7 0.441 14.097 13 1032 1003.7 0.797 14.894 14 760 726.1 1.579 16.473 15 537 525.8 0.237 16.710 16 405 381.2 1.492 18.203 17 298 276.5 1.665 19.868 18 202 200.8 0.007 19.875 19 157 146.0 0.831 20.706 20 115 106.2 0.727 21.433 21 281 287.1 0.130 21.563 Chisq= 21.56 for 20 degrees of freedom, p= 0.63531 SUMMARY of craptest p-value for no. of wins: 0.661508 p-value for throws/game: 0.635306 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-07_14:31 No. of wins: Observed Expected 98582 98585.9 z-score=-0.017, pvalue=0.49312 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66671 66666.7 0.000 0.000 2 37850 37654.3 1.017 1.017 3 26836 26954.7 0.523 1.540 4 19186 19313.5 0.841 2.381 5 13736 13851.4 0.962 3.343 6 10098 9943.5 2.399 5.742 7 7148 7145.0 0.001 5.744 8 5089 5139.1 0.488 6.231 9 3653 3699.9 0.594 6.825 10 2679 2666.3 0.061 6.886 11 1910 1923.3 0.092 6.978 12 1427 1388.7 1.054 8.032 13 1031 1003.7 0.742 8.774 14 749 726.1 0.720 9.493 15 544 525.8 0.627 10.121 16 345 381.2 3.429 13.550 17 267 276.5 0.329 13.879 18 188 200.8 0.820 14.698 19 153 146.0 0.337 15.035 20 121 106.2 2.058 17.093 21 319 287.1 3.541 20.635 Chisq= 20.63 for 20 degrees of freedom, p= 0.58109 SUMMARY of craptest p-value for no. of wins: 0.493115 p-value for throws/game: 0.581087 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0045,0.0067,0.0150,0.0162,0.0172,0.0177,0.0279,0.0313,0.0328, 0.0354,0.0369,0.0370,0.0389,0.0435,0.0468,0.0671,0.0699,0.0807,0.0840, 0.0858,0.1005,0.1007,0.1094,0.1103,0.1138,0.1247,0.1265,0.1274,0.1307, 0.1341,0.1359,0.1480,0.1480,0.1495,0.1518,0.1589,0.1625,0.1632,0.1671, 0.1712,0.1750,0.1754,0.1793,0.1806,0.1831,0.2011,0.2056,0.2081,0.2085, 0.2167,0.2186,0.2196,0.2207,0.2270,0.2313,0.2325,0.2328,0.2363,0.2438, 0.2439,0.2466,0.2476,0.2492,0.2529,0.2585,0.2618,0.2619,0.2636,0.2660, 0.2733,0.2764,0.2807,0.2813,0.2832,0.2840,0.2862,0.2899,0.2969,0.2979, 0.2993,0.2993,0.3000,0.3036,0.3124,0.3136,0.3167,0.3170,0.3324,0.3362, 0.3378,0.3384,0.3392,0.3395,0.3416,0.3419,0.3459,0.3506,0.3525,0.3556, 0.3592,0.3610,0.3631,0.3659,0.3691,0.3694,0.3745,0.3817,0.3862,0.3865, 0.3915,0.3935,0.3961,0.4010,0.4021,0.4028,0.4069,0.4086,0.4137,0.4189, 0.4204,0.4246,0.4259,0.4275,0.4314,0.4343,0.4407,0.4474,0.4502,0.4560, 0.4664,0.4667,0.4668,0.4706,0.4734,0.4830,0.4841,0.4847,0.4861,0.4864, 0.4931,0.4991,0.5000,0.5001,0.5010,0.5054,0.5065,0.5082,0.5090,0.5114, 0.5135,0.5144,0.5165,0.5174,0.5182,0.5212,0.5220,0.5406,0.5414,0.5441, 0.5508,0.5687,0.5699,0.5701,0.5757,0.5796,0.5801,0.5806,0.5811,0.5815, 0.5856,0.5882,0.5921,0.5950,0.6011,0.6064,0.6079,0.6122,0.6172,0.6268, 0.6272,0.6282,0.6310,0.6322,0.6345,0.6345,0.6353,0.6429,0.6463,0.6468, 0.6469,0.6498,0.6508,0.6615,0.6669,0.6695,0.6761,0.6826,0.6858,0.6927, 0.6968,0.6988,0.7070,0.7081,0.7140,0.7146,0.7192,0.7222,0.7250,0.7259, 0.7288,0.7358,0.7434,0.7442,0.7455,0.7462,0.7566,0.7600,0.7611,0.7614, 0.7681,0.7720,0.7725,0.7986,0.7986,0.8033,0.8054,0.8057,0.8097,0.8114, 0.8116,0.8148,0.8172,0.8225,0.8271,0.8275,0.8308,0.8361,0.8384,0.8491, 0.8523,0.8544,0.8560,0.8600,0.8642,0.8772,0.8850,0.8886,0.8888,0.9204, 0.9208,0.9231,0.9265,0.9308,0.9404,0.9469,0.9547,0.9634,0.9637,0.9680, 0.9693,0.9697,0.9742,0.9814,0.9832,0.9916,0.9931,0.9951,1.0000, Overall p-value after applying KStest on 269 p-values = 0.154571 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.