RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-31_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.62 24.8409 0.901673 2 to 25 15.59 21.4950 0.795072 3 to 26 15.56 26.2705 0.930328 4 to 27 15.40 24.5738 0.895336 5 to 28 15.58 19.6742 0.708767 6 to 29 15.61 25.6709 0.919330 7 to 30 15.89 17.1308 0.554460 8 to 31 15.33 27.8556 0.953346 9 to 32 15.85 17.8248 0.600029 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.001435 Tough bday spacings test for dh-ranFile-2016-12-31_23:31: 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 32 57 113 90 72 59 31 20 9 8 (O-E)^2/E 0.0 0.6 3.6 2.4 0.6 0.5 0.9 0.1 1.8 0.9 3.8 Birthday Spacings: Sum(O-E)^2/E= 15.076, p= 0.871 RESULTS OF GCD FOR dh-ranFile-2016-12-31_23:31 Euclid's algorithm: p-value, steps to gcd: 0.115685 p-value, dist. of gcd's: 0.291713 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-31_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.928 0.481 0.608 0.098 0.498 0.276 0.457 0.938 Bits 8 to 15---> 0.586 0.096 0.389 0.126 0.242 0.162 0.789 0.050 Bits 16 to 23---> 0.759 0.138 0.050 0.329 0.394 0.718 0.906 0.924 Bits 24 to 31---> 0.870 0.925 0.517 0.931 0.345 0.656 0.106 0.750 KS test for the above 32 p values: 0.184 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-31_23:31, p-values for 5 runs: 0.0260, 0.5204, 0.5999, 0.3633, 0.7376 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-31_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5144 5134.0 0.019 0.021 r= 30 22998 23103.0 0.478 0.499 r= 31 11646 11551.5 0.773 1.271 chi-square = 1.271 with df = 3; p-value = 0.264 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-31_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5197 5134.0 0.773 0.912 r= 31 23142 23103.0 0.066 0.977 r= 32 11455 11551.5 0.807 1.784 chi-square = 1.784 with df = 3; p-value = 0.382 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-31_23:31 b-rank test for bits 1 to 8, p=0.88256 b-rank test for bits 2 to 9, p=0.83440 b-rank test for bits 3 to 10, p=0.64292 b-rank test for bits 4 to 11, p=0.48833 b-rank test for bits 5 to 12, p=0.78648 b-rank test for bits 6 to 13, p=0.98753 b-rank test for bits 7 to 14, p=0.99400 b-rank test for bits 8 to 15, p=0.87984 b-rank test for bits 9 to 16, p=0.55276 b-rank test for bits 10 to 17, p=0.82789 b-rank test for bits 11 to 18, p=0.82211 b-rank test for bits 12 to 19, p=0.69657 b-rank test for bits 13 to 20, p=0.83589 b-rank test for bits 14 to 21, p=0.90950 b-rank test for bits 15 to 22, p=0.37607 b-rank test for bits 16 to 23, p=0.28666 b-rank test for bits 17 to 24, p=0.34388 b-rank test for bits 18 to 25, p=0.09333 b-rank test for bits 19 to 26, p=0.12717 b-rank test for bits 20 to 27, p=0.69236 b-rank test for bits 21 to 28, p=0.34177 b-rank test for bits 22 to 29, p=0.35285 b-rank test for bits 23 to 30, p=0.66084 b-rank test for bits 24 to 31, p=0.09904 b-rank test for bits 25 to 32, p=0.60650 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 = 0.100554 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-31_23:31 (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 141808 -0.24 0.406425 2 141415 -1.15 0.124050 3 142379 1.10 0.863758 4 141612 -0.69 0.243623 5 141509 -0.94 0.174804 6 141422 -1.14 0.127431 7 141589 -0.75 0.227099 8 141759 -0.35 0.362705 9 141441 -1.09 0.136927 10 141625 -0.66 0.253242 11 142041 0.31 0.620822 12 142118 0.49 0.687065 13 141689 -0.51 0.303350 14 141798 -0.26 0.397387 15 140875 -2.42 0.007832 16 142104 0.45 0.675387 17 141733 -0.41 0.340175 18 141775 -0.31 0.376816 19 141439 -1.10 0.135905 20 141841 -0.16 0.436579 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-31_23:31 Bits used No. missing words z-score p-value 23 to 32 141884 -0.0873 0.465199 22 to 31 141378 -1.8322 0.033463 21 to 30 141777 -0.4563 0.324083 20 to 29 141655 -0.8770 0.190243 19 to 28 142031 0.4196 0.662594 18 to 27 142199 0.9989 0.841069 17 to 26 142038 0.4437 0.671367 16 to 25 141754 -0.5356 0.296110 15 to 24 141954 0.1540 0.561209 14 to 23 141729 -0.6218 0.267028 13 to 22 141549 -1.2425 0.107023 12 to 21 141493 -1.4356 0.075555 11 to 20 141648 -0.9011 0.183758 10 to 19 141673 -0.8149 0.207556 9 to 18 142243 1.1506 0.875049 8 to 17 141534 -1.2942 0.097791 7 to 16 141996 0.2989 0.617477 6 to 15 141835 -0.2563 0.398856 5 to 14 141789 -0.4149 0.339096 4 to 13 141438 -1.6253 0.052052 3 to 12 141759 -0.5184 0.302097 2 to 11 141498 -1.4184 0.078040 1 to 10 141697 -0.7322 0.232032 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-31_23:31 Bits used No. missing words z-score p-value 28 to 32 142157 0.8396 0.799422 27 to 31 141960 0.1718 0.568188 26 to 30 142302 1.3311 0.908419 25 to 29 141920 0.0362 0.514426 24 to 28 141532 -1.2791 0.100434 23 to 27 141644 -0.8994 0.184214 22 to 26 141347 -1.9062 0.028312 21 to 25 141731 -0.6045 0.272753 20 to 24 141638 -0.9198 0.178848 19 to 23 141946 0.1243 0.549463 18 to 22 141657 -0.8554 0.196177 17 to 21 142230 1.0870 0.861485 16 to 20 141687 -0.7537 0.225526 15 to 19 141519 -1.3232 0.092892 14 to 18 142240 1.1209 0.868838 13 to 17 141989 0.2701 0.606446 12 to 16 141535 -1.2689 0.102236 11 to 15 142155 0.8328 0.797516 10 to 14 141974 0.2192 0.586761 9 to 13 142064 0.5243 0.699967 8 to 12 141998 0.3006 0.618131 7 to 11 142014 0.3548 0.638635 6 to 10 141976 0.2260 0.589399 5 to 9 141764 -0.4926 0.311132 4 to 8 142051 0.4802 0.684471 3 to 7 141858 -0.1740 0.430933 2 to 6 141269 -2.1706 0.014980 1 to 5 141644 -0.8994 0.184214 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-31_23:31 Bits used No. missing words z-score p-value 31 to 32 141527 -1.1278 0.129699 30 to 31 141547 -1.0688 0.142575 29 to 30 141830 -0.2340 0.407488 28 to 29 141700 -0.6175 0.268455 27 to 28 142173 0.7778 0.781653 26 to 27 141947 0.1111 0.544240 25 to 26 142226 0.9341 0.824882 24 to 25 142641 2.1583 0.984548 23 to 24 142008 0.2911 0.614498 22 to 23 141626 -0.8358 0.201639 21 to 22 143095 3.4976 0.999765 20 to 21 141732 -0.5231 0.300453 19 to 20 141611 -0.8800 0.189422 18 to 19 141980 0.2085 0.582568 17 to 18 141514 -1.1662 0.121774 16 to 17 141750 -0.4700 0.319178 15 to 16 142070 0.4740 0.682233 14 to 15 142392 1.4238 0.922749 13 to 14 141896 -0.0393 0.484317 12 to 13 141975 0.1937 0.576801 11 to 12 142251 1.0079 0.843243 10 to 11 141657 -0.7443 0.228337 9 to 10 141715 -0.5732 0.283240 8 to 9 142005 0.2822 0.611110 7 to 8 141388 -1.5378 0.062043 6 to 7 141922 0.0374 0.514907 5 to 6 142113 0.6008 0.726012 4 to 5 142396 1.4356 0.924443 3 to 4 141484 -1.2547 0.104801 2 to 3 141635 -0.8092 0.209191 1 to 2 141237 -1.9833 0.023668 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-31_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2577.32 1.094 0.862919 Test results for specific bytes for dh-ranFile-2016-12-31_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2527.59 0.390 0.651818 2 to 9 2541.67 0.589 0.722162 3 to 10 2583.65 1.183 0.881607 4 to 11 2524.76 0.350 0.636878 5 to 12 2505.03 0.071 0.528365 6 to 13 2562.46 0.883 0.811463 7 to 14 2443.76 -0.795 0.213194 8 to 15 2407.65 -1.306 0.095779 9 to 16 2562.58 0.885 0.811916 10 to 17 2491.40 -0.122 0.451625 11 to 18 2525.76 0.364 0.642197 12 to 19 2547.24 0.668 0.747938 13 to 20 2520.24 0.286 0.612648 14 to 21 2498.24 -0.025 0.490082 15 to 22 2553.87 0.762 0.776909 16 to 23 2395.62 -1.476 0.069945 17 to 24 2507.29 0.103 0.541048 18 to 25 2451.33 -0.688 0.245649 19 to 26 2538.18 0.540 0.705405 20 to 27 2527.69 0.392 0.652316 21 to 28 2371.80 -1.813 0.034911 22 to 29 2412.15 -1.242 0.107058 23 to 30 2432.76 -0.951 0.170808 24 to 31 2491.97 -0.114 0.454811 25 to 32 2506.50 0.092 0.536642 CDPARK for dh-ranFile-2016-12-31_23:31: 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 3528 0.2283 0.590298 3541 0.8219 0.794438 3492 -1.4155 0.078457 3531 0.3653 0.642555 3526 0.1370 0.554479 3505 -0.8219 0.205562 3551 1.2785 0.899470 3529 0.2740 0.607947 3556 1.5068 0.934075 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3526.50 sample std.=19.45 p-value of the KSTEST for those 10 p-values: 0.830799 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-31_23:31 0.7124,0.3182,0.4462,0.8065,0.7387,0.6746,0.5101,0.3468,0.6183,0.5060, The KS test for those 10 p-values: 0.240985 The 3DSPHERES test for dh-ranFile-2016-12-31_23:31 sample no r^3 equiv. uni. 1 57.263 0.851738 2 2.696 0.085934 3 25.040 0.565981 4 6.980 0.207583 5 15.864 0.410685 6 7.421 0.219150 7 19.004 0.469244 8 16.805 0.428892 9 29.244 0.622730 10 27.220 0.596401 11 22.027 0.520131 12 5.771 0.174988 13 28.232 0.609793 14 5.998 0.181215 15 40.423 0.740097 16 16.619 0.425343 17 2.187 0.070311 18 57.759 0.854166 19 2.644 0.084369 20 27.195 0.596059 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.356177 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-31_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 1.1 1.2 -0.7 0.9 -0.4 -1.0 -0.2 -0.3 1.4 0.1 -0.0 -0.5 0.3 -1.2 0.3 0.6 0.6 0.9 -0.2 -0.1 0.8 -0.8 -0.5 -0.2 -2.4 -0.0 -0.5 0.4 0.7 0.8 -0.1 0.5 -0.8 -0.7 1.0 -0.4 -1.6 2.1 1.6 1.0 0.8 Chi-square with 42 degrees of freedom:33.762122 z-score=-0.898826, p-value=0.186381 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-31_23:31 Test no p-value 1 0.181653 2 0.313974 3 0.947776 4 0.067963 5 0.281007 6 0.368366 7 0.651673 8 0.139987 9 0.387167 10 0.174206 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.132787 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-31_23:31: (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 66435 0.81 66882 0.70 3 25000.00 25158 1.00 24754 2.42 4 6666.67 6700 0.17 6752 1.09 5 1388.89 1431 1.28 1340 1.72 6 238.10 228 0.43 235 0.04 7 34.72 39 0.53 33 0.09 8 4.96 8 1.86 3 0.77 p=0.58415 p=0.66307 Number of rngs required: 688154, p-value: 0.387 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-31_23:31 No. of wins: Observed Expected 98678 98585.9 z-score= 0.412, pvalue=0.65987 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66912 66666.7 0.903 0.903 2 37537 37654.3 0.366 1.268 3 27206 26954.7 2.342 3.611 4 19106 19313.5 2.229 5.839 5 13767 13851.4 0.515 6.354 6 10017 9943.5 0.543 6.896 7 7112 7145.0 0.153 7.049 8 5159 5139.1 0.077 7.126 9 3654 3699.9 0.569 7.695 10 2678 2666.3 0.051 7.746 11 1900 1923.3 0.283 8.029 12 1333 1388.7 2.237 10.266 13 980 1003.7 0.560 10.827 14 707 726.1 0.505 11.331 15 540 525.8 0.382 11.713 16 390 381.2 0.205 11.918 17 261 276.5 0.873 12.791 18 231 200.8 4.532 17.324 19 138 146.0 0.437 17.761 20 114 106.2 0.571 18.331 21 258 287.1 2.952 21.283 Chisq= 21.28 for 20 degrees of freedom, p= 0.61937 SUMMARY of craptest p-value for no. of wins: 0.659871 p-value for throws/game: 0.619372 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-31_23:31 No. of wins: Observed Expected 98130 98585.9 z-score=-2.039, pvalue=0.02073 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66560 66666.7 0.171 0.171 2 37676 37654.3 0.012 0.183 3 26913 26954.7 0.065 0.248 4 19335 19313.5 0.024 0.272 5 13863 13851.4 0.010 0.281 6 9994 9943.5 0.256 0.537 7 7230 7145.0 1.011 1.548 8 5198 5139.1 0.676 2.224 9 3616 3699.9 1.901 4.125 10 2685 2666.3 0.131 4.256 11 1920 1923.3 0.006 4.262 12 1338 1388.7 1.854 6.116 13 1008 1003.7 0.018 6.134 14 748 726.1 0.658 6.792 15 552 525.8 1.302 8.094 16 390 381.2 0.205 8.299 17 281 276.5 0.072 8.371 18 176 200.8 3.070 11.441 19 146 146.0 0.000 11.441 20 94 106.2 1.405 12.846 21 277 287.1 0.356 13.202 Chisq= 13.20 for 20 degrees of freedom, p= 0.13146 SUMMARY of craptest p-value for no. of wins: 0.020732 p-value for throws/game: 0.131458 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0014,0.0078,0.0150,0.0207,0.0237,0.0260,0.0283,0.0335,0.0349,0.0495, 0.0497,0.0521,0.0620,0.0680,0.0699,0.0703,0.0756,0.0780,0.0785,0.0844, 0.0859,0.0929,0.0933,0.0958,0.0962,0.0978,0.0984,0.0990,0.1004,0.1006, 0.1022,0.1048,0.1057,0.1070,0.1071,0.1157,0.1218,0.1241,0.1264,0.1272, 0.1274,0.1297,0.1315,0.1328,0.1359,0.1369,0.1377,0.1400,0.1426,0.1617, 0.1708,0.1742,0.1748,0.1750,0.1788,0.1812,0.1817,0.1838,0.1842,0.1842, 0.1843,0.1864,0.1894,0.1902,0.1962,0.2016,0.2056,0.2076,0.2076,0.2092, 0.2132,0.2188,0.2191,0.2255,0.2271,0.2283,0.2320,0.2410,0.2416,0.2436, 0.2456,0.2532,0.2641,0.2670,0.2685,0.2728,0.2755,0.2810,0.2832,0.2867, 0.2917,0.2961,0.3005,0.3021,0.3034,0.3111,0.3140,0.3182,0.3192,0.3241, 0.3287,0.3391,0.3402,0.3418,0.3439,0.3452,0.3468,0.3528,0.3562,0.3627, 0.3633,0.3684,0.3761,0.3768,0.3816,0.3872,0.3872,0.3893,0.3940,0.3974, 0.3989,0.4064,0.4075,0.4107,0.4253,0.4289,0.4309,0.4366,0.4462,0.4516, 0.4548,0.4574,0.4652,0.4692,0.4814,0.4843,0.4883,0.4901,0.4984,0.5060, 0.5101,0.5144,0.5149,0.5171,0.5201,0.5204,0.5284,0.5366,0.5410,0.5442, 0.5495,0.5528,0.5545,0.5545,0.5612,0.5660,0.5682,0.5768,0.5826,0.5841, 0.5861,0.5868,0.5894,0.5903,0.5961,0.5964,0.5999,0.6000,0.6064,0.6065, 0.6079,0.6085,0.6098,0.6111,0.6126,0.6145,0.6175,0.6181,0.6183,0.6194, 0.6208,0.6227,0.6369,0.6386,0.6422,0.6426,0.6429,0.6517,0.6518,0.6523, 0.6559,0.6599,0.6608,0.6626,0.6631,0.6714,0.6746,0.6754,0.6822,0.6845, 0.6871,0.6924,0.6966,0.7000,0.7054,0.7088,0.7124,0.7180,0.7222,0.7260, 0.7376,0.7387,0.7401,0.7479,0.7500,0.7591,0.7769,0.7817,0.7865,0.7893, 0.7944,0.7951,0.7975,0.7994,0.8065,0.8115,0.8119,0.8221,0.8249,0.8279, 0.8308,0.8344,0.8359,0.8411,0.8432,0.8517,0.8542,0.8615,0.8629,0.8638, 0.8688,0.8696,0.8707,0.8750,0.8798,0.8816,0.8826,0.8953,0.8995,0.9017, 0.9057,0.9084,0.9095,0.9193,0.9227,0.9240,0.9244,0.9255,0.9281,0.9303, 0.9307,0.9341,0.9384,0.9478,0.9533,0.9845,0.9875,0.9940,0.9998, Overall p-value after applying KStest on 269 p-values = 0.097261 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.