RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-22_07:31 (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 22.6654 0.839537 2 to 25 15.45 18.3088 0.630383 3 to 26 15.50 26.6278 0.936242 4 to 27 15.87 10.7036 0.128450 5 to 28 16.06 5.3203 0.003289 6 to 29 15.87 12.3010 0.218423 7 to 30 15.56 22.0706 0.817981 8 to 31 15.96 10.7292 0.129710 9 to 32 15.53 16.6689 0.522993 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.584881 Tough bday spacings test for dh-ranFile-2017-01-22_07:31: 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 31 73 96 95 78 66 26 14 10 1 (O-E)^2/E 0.1 0.9 0.0 0.0 0.1 0.0 3.7 0.5 0.1 1.7 2.3 Birthday Spacings: Sum(O-E)^2/E= 9.330, p= 0.499 RESULTS OF GCD FOR dh-ranFile-2017-01-22_07:31 Euclid's algorithm: p-value, steps to gcd: 0.477892 p-value, dist. of gcd's: 0.749263 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-22_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.314 0.805 0.847 0.258 0.225 0.936 0.248 0.251 Bits 8 to 15---> 0.158 0.031 0.414 0.838 0.811 0.872 0.468 0.477 Bits 16 to 23---> 0.882 0.574 0.288 0.925 0.349 0.139 0.670 0.418 Bits 24 to 31---> 0.458 0.419 0.887 0.248 0.440 0.859 0.805 0.685 KS test for the above 32 p values: 0.529 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-22_07:31, p-values for 5 runs: 0.5204, 0.6762, 0.0919, 0.3417, 0.8051 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-22_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5142 5134.0 0.012 0.432 r= 30 22999 23103.0 0.469 0.901 r= 31 11657 11551.5 0.963 1.864 chi-square = 1.864 with df = 3; p-value = 0.399 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-22_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5257 5134.0 2.946 3.695 r= 31 22948 23103.0 1.041 4.736 r= 32 11571 11551.5 0.033 4.768 chi-square = 4.768 with df = 3; p-value = 0.810 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-22_07:31 b-rank test for bits 1 to 8, p=0.40284 b-rank test for bits 2 to 9, p=0.68428 b-rank test for bits 3 to 10, p=0.12779 b-rank test for bits 4 to 11, p=0.24752 b-rank test for bits 5 to 12, p=0.47743 b-rank test for bits 6 to 13, p=0.95316 b-rank test for bits 7 to 14, p=0.72051 b-rank test for bits 8 to 15, p=0.88019 b-rank test for bits 9 to 16, p=0.10025 b-rank test for bits 10 to 17, p=0.94126 b-rank test for bits 11 to 18, p=0.34967 b-rank test for bits 12 to 19, p=0.93255 b-rank test for bits 13 to 20, p=0.58534 b-rank test for bits 14 to 21, p=0.93333 b-rank test for bits 15 to 22, p=0.76088 b-rank test for bits 16 to 23, p=0.55235 b-rank test for bits 17 to 24, p=0.49082 b-rank test for bits 18 to 25, p=0.16555 b-rank test for bits 19 to 26, p=0.47828 b-rank test for bits 20 to 27, p=0.59039 b-rank test for bits 21 to 28, p=0.91322 b-rank test for bits 22 to 29, p=0.25471 b-rank test for bits 23 to 30, p=0.94888 b-rank test for bits 24 to 31, p=0.02466 b-rank test for bits 25 to 32, p=0.82950 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 = 0.263026 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-22_07:31 (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 142145 0.55 0.709057 2 142729 1.92 0.972261 3 142489 1.35 0.912191 4 141362 -1.28 0.100482 5 142119 0.49 0.687892 6 142280 0.87 0.806769 7 142482 1.34 0.909554 8 142436 1.23 0.890752 9 141309 -1.40 0.080362 10 142443 1.25 0.893782 11 141735 -0.41 0.341889 12 141490 -0.98 0.163607 13 141351 -1.30 0.096030 14 140844 -2.49 0.006404 15 141699 -0.49 0.311563 16 142213 0.71 0.760996 17 142198 0.67 0.749991 18 141885 -0.06 0.477334 19 142504 1.39 0.917647 20 141530 -0.89 0.187732 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-22_07:31 Bits used No. missing words z-score p-value 23 to 32 141966 0.1954 0.577466 22 to 31 141900 -0.0322 0.487167 21 to 30 142391 1.6609 0.951636 20 to 29 142264 1.2230 0.889335 19 to 28 142421 1.7644 0.961166 18 to 27 141466 -1.5287 0.063166 17 to 26 141758 -0.5218 0.300895 16 to 25 141469 -1.5184 0.064459 15 to 24 141643 -0.9184 0.179210 14 to 23 142037 0.4402 0.670119 13 to 22 142105 0.6747 0.750075 12 to 21 142450 1.8644 0.968866 11 to 20 142231 1.1092 0.866330 10 to 19 141587 -1.1115 0.133180 9 to 18 142110 0.6920 0.755521 8 to 17 141662 -0.8529 0.196868 7 to 16 142178 0.9264 0.822894 6 to 15 142266 1.2299 0.890632 5 to 14 141795 -0.3942 0.346701 4 to 13 141848 -0.2115 0.416255 3 to 12 142142 0.8023 0.788813 2 to 11 141664 -0.8460 0.198786 1 to 10 141533 -1.2977 0.097197 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-22_07:31 Bits used No. missing words z-score p-value 28 to 32 142104 0.6599 0.745341 27 to 31 141304 -2.0520 0.020086 26 to 30 142230 1.0870 0.861485 25 to 29 142257 1.1785 0.880710 24 to 28 141891 -0.0621 0.475227 23 to 27 142420 1.7311 0.958282 22 to 26 141980 0.2396 0.594664 21 to 25 141677 -0.7876 0.215477 20 to 24 141687 -0.7537 0.225526 19 to 23 142709 2.7107 0.996643 18 to 22 141745 -0.5571 0.288746 17 to 21 141617 -0.9909 0.160855 16 to 20 141977 0.2294 0.590717 15 to 19 142008 0.3345 0.630989 14 to 18 142278 1.2497 0.894301 13 to 17 141678 -0.7842 0.216470 12 to 16 141554 -1.2045 0.114197 11 to 15 141925 0.0531 0.521181 10 to 14 142146 0.8023 0.788802 9 to 13 141915 0.0192 0.507667 8 to 12 141737 -0.5842 0.279553 7 to 11 141868 -0.1401 0.444290 6 to 10 142066 0.5311 0.702320 5 to 9 141500 -1.3876 0.082636 4 to 8 142086 0.5989 0.725374 3 to 7 141696 -0.7232 0.234793 2 to 6 142004 0.3209 0.625863 1 to 5 142288 1.2836 0.900364 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-22_07:31 Bits used No. missing words z-score p-value 31 to 32 142049 0.4120 0.659832 30 to 31 142324 1.2232 0.889376 29 to 30 141901 -0.0246 0.490198 28 to 29 142411 1.4799 0.930544 27 to 28 141749 -0.4729 0.318125 26 to 27 141464 -1.3137 0.094481 25 to 26 142362 1.3353 0.909113 24 to 25 141545 -1.0747 0.141250 23 to 24 141872 -0.1101 0.456158 22 to 23 141789 -0.3550 0.361311 21 to 22 142250 1.0049 0.842534 20 to 21 141251 -1.9420 0.026070 19 to 20 141680 -0.6765 0.249365 18 to 19 142572 1.9548 0.974695 17 to 18 141859 -0.1485 0.440988 16 to 17 141873 -0.1072 0.457328 15 to 16 141614 -0.8712 0.191828 14 to 15 141863 -0.1367 0.445647 13 to 14 141685 -0.6617 0.254069 12 to 13 141838 -0.2104 0.416673 11 to 12 141596 -0.9243 0.177671 10 to 11 142180 0.7984 0.787691 9 to 10 141854 -0.1632 0.435174 8 to 9 142122 0.6273 0.734784 7 to 8 141716 -0.5703 0.284239 6 to 7 141913 0.0108 0.504319 5 to 6 141364 -1.6086 0.053847 4 to 5 141920 0.0315 0.512555 3 to 4 141809 -0.2960 0.383631 2 to 3 141593 -0.9331 0.175377 1 to 2 142162 0.7453 0.771967 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-22_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2421.35 -1.112 0.133004 Test results for specific bytes for dh-ranFile-2017-01-22_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2452.46 -0.672 0.250679 2 to 9 2516.03 0.227 0.589676 3 to 10 2422.21 -1.100 0.135630 4 to 11 2445.27 -0.774 0.219465 5 to 12 2472.49 -0.389 0.348627 6 to 13 2528.99 0.410 0.659097 7 to 14 2344.58 -2.198 0.013974 8 to 15 2480.46 -0.276 0.391150 9 to 16 2672.72 2.443 0.992708 10 to 17 2574.83 1.058 0.855037 11 to 18 2509.55 0.135 0.553723 12 to 19 2639.53 1.973 0.975767 13 to 20 2522.85 0.323 0.626688 14 to 21 2443.49 -0.799 0.212088 15 to 22 2517.69 0.250 0.598799 16 to 23 2551.32 0.726 0.766001 17 to 24 2279.30 -3.121 0.000901 18 to 25 2548.69 0.689 0.754437 19 to 26 2404.40 -1.352 0.088194 20 to 27 2400.91 -1.401 0.080564 21 to 28 2622.47 1.732 0.958363 22 to 29 2601.68 1.438 0.924788 23 to 30 2579.82 1.129 0.870505 24 to 31 2430.27 -0.986 0.162034 25 to 32 2450.29 -0.703 0.241029 CDPARK for dh-ranFile-2017-01-22_07:31: 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 3527 0.1826 0.572463 3509 -0.6393 0.261324 3526 0.1370 0.554479 3520 -0.1370 0.445521 3529 0.2740 0.607947 3500 -1.0502 0.146807 3506 -0.7763 0.218799 3569 2.1005 0.982156 3514 -0.4110 0.340551 3547 1.0959 0.863437 Square side=100, avg. no. parked=3524.70 sample std.=19.57 p-value of the KSTEST for those 10 p-values: 0.886437 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-22_07:31 0.8355,0.5717,0.5621,0.6113,0.6847,0.3181,0.4455,0.0601,0.5176,0.9072, The KS test for those 10 p-values: 0.636333 The 3DSPHERES test for dh-ranFile-2017-01-22_07:31 sample no r^3 equiv. uni. 1 22.136 0.521863 2 1.300 0.042400 3 17.857 0.448563 4 5.292 0.161729 5 3.857 0.120640 6 33.435 0.671925 7 17.016 0.432883 8 4.654 0.143687 9 3.407 0.107353 10 0.807 0.026532 11 17.546 0.442821 12 23.637 0.545199 13 10.593 0.297484 14 15.372 0.400938 15 40.703 0.742504 16 18.782 0.465304 17 6.214 0.187094 18 14.057 0.374105 19 0.092 0.003068 20 25.752 0.576167 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.013918 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-22_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 1.8 -0.6 1.1 -0.5 1.4 -2.0 0.1 1.0 1.0 -0.7 0.3 0.9 -0.5 -1.3 1.9 0.5 -0.3 -0.1 -1.4 -1.2 0.3 1.6 -0.5 -0.2 0.6 -0.0 -0.0 -1.2 -0.4 -1.0 -0.1 1.4 0.3 0.5 -0.5 -2.3 0.2 -1.2 1.0 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:42.198331 z-score=0.021640, p-value=0.537604 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-22_07:31 Test no p-value 1 0.033203 2 0.318744 3 0.131727 4 0.003263 5 0.000423 6 0.847596 7 0.045640 8 0.227888 9 0.293923 10 0.553278 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001192 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-22_07:31: (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 66817 0.34 66578 0.12 3 25000.00 24869 0.69 25116 0.54 4 6666.67 6683 0.04 6655 0.02 5 1388.89 1362 0.52 1372 0.21 6 238.10 234 0.07 244 0.15 7 34.72 31 0.40 32 0.21 8 4.96 3 0.77 2 1.77 p=0.17009 p=0.19216 Number of rngs required: 687630, p-value: 0.186 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-22_07:31 No. of wins: Observed Expected 98960 98585.9 z-score= 1.673, pvalue=0.95287 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66878 66666.7 0.670 0.670 2 37610 37654.3 0.052 0.722 3 26868 26954.7 0.279 1.001 4 19329 19313.5 0.013 1.014 5 13971 13851.4 1.032 2.046 6 9983 9943.5 0.157 2.203 7 7021 7145.0 2.153 4.355 8 4929 5139.1 8.587 12.943 9 3672 3699.9 0.210 13.153 10 2679 2666.3 0.061 13.213 11 1886 1923.3 0.725 13.938 12 1385 1388.7 0.010 13.948 13 1033 1003.7 0.854 14.802 14 778 726.1 3.704 18.506 15 514 525.8 0.266 18.772 16 413 381.2 2.661 21.434 17 267 276.5 0.329 21.763 18 210 200.8 0.419 22.181 19 167 146.0 3.025 25.207 20 103 106.2 0.097 25.304 21 304 287.1 0.993 26.297 Chisq= 26.30 for 20 degrees of freedom, p= 0.84378 SUMMARY of craptest p-value for no. of wins: 0.952874 p-value for throws/game: 0.843779 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-22_07:31 No. of wins: Observed Expected 98909 98585.9 z-score= 1.445, pvalue=0.92581 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66996 66666.7 1.627 1.627 2 37418 37654.3 1.483 3.110 3 26822 26954.7 0.654 3.764 4 19121 19313.5 1.918 5.682 5 13878 13851.4 0.051 5.733 6 10140 9943.5 3.881 9.614 7 7155 7145.0 0.014 9.628 8 5147 5139.1 0.012 9.640 9 3709 3699.9 0.023 9.663 10 2621 2666.3 0.770 10.432 11 1914 1923.3 0.045 10.478 12 1327 1388.7 2.745 13.222 13 1046 1003.7 1.781 15.004 14 737 726.1 0.162 15.166 15 541 525.8 0.437 15.604 16 377 381.2 0.045 15.649 17 293 276.5 0.980 16.628 18 212 200.8 0.621 17.250 19 140 146.0 0.245 17.495 20 109 106.2 0.073 17.568 21 297 287.1 0.340 17.908 Chisq= 17.91 for 20 degrees of freedom, p= 0.40656 SUMMARY of craptest p-value for no. of wins: 0.925810 p-value for throws/game: 0.406564 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0009,0.0012,0.0031,0.0033,0.0033,0.0064,0.0139,0.0140,0.0201, 0.0247,0.0261,0.0265,0.0307,0.0332,0.0424,0.0456,0.0538,0.0601,0.0632, 0.0645,0.0804,0.0806,0.0826,0.0882,0.0919,0.0945,0.0960,0.0972,0.1002, 0.1005,0.1074,0.1142,0.1206,0.1278,0.1284,0.1297,0.1317,0.1330,0.1332, 0.1356,0.1394,0.1413,0.1437,0.1468,0.1578,0.1609,0.1617,0.1620,0.1636, 0.1655,0.1701,0.1754,0.1777,0.1792,0.1856,0.1871,0.1877,0.1918,0.1922, 0.1969,0.1988,0.2121,0.2155,0.2165,0.2184,0.2188,0.2195,0.2247,0.2255, 0.2279,0.2348,0.2410,0.2475,0.2480,0.2481,0.2494,0.2507,0.2507,0.2541, 0.2547,0.2576,0.2613,0.2630,0.2796,0.2842,0.2877,0.2887,0.2939,0.2975, 0.3009,0.3116,0.3141,0.3181,0.3181,0.3187,0.3406,0.3417,0.3419,0.3467, 0.3486,0.3486,0.3497,0.3613,0.3741,0.3836,0.3912,0.3988,0.4009,0.4028, 0.4066,0.4141,0.4163,0.4167,0.4183,0.4194,0.4329,0.4352,0.4397,0.4410, 0.4428,0.4443,0.4455,0.4455,0.4456,0.4486,0.4562,0.4573,0.4582,0.4653, 0.4685,0.4752,0.4773,0.4774,0.4774,0.4779,0.4783,0.4872,0.4902,0.4908, 0.4989,0.5043,0.5077,0.5126,0.5176,0.5204,0.5212,0.5219,0.5230,0.5287, 0.5376,0.5452,0.5523,0.5533,0.5537,0.5545,0.5621,0.5717,0.5725,0.5745, 0.5762,0.5775,0.5849,0.5853,0.5897,0.5904,0.5907,0.5947,0.5988,0.6079, 0.6113,0.6259,0.6267,0.6304,0.6310,0.6363,0.6591,0.6598,0.6696,0.6701, 0.6719,0.6762,0.6843,0.6847,0.6847,0.6879,0.7023,0.7091,0.7205,0.7254, 0.7348,0.7425,0.7453,0.7493,0.7500,0.7501,0.7544,0.7555,0.7609,0.7610, 0.7660,0.7720,0.7877,0.7888,0.7888,0.8048,0.8048,0.8051,0.8068,0.8104, 0.8110,0.8180,0.8229,0.8295,0.8355,0.8376,0.8395,0.8425,0.8438,0.8471, 0.8476,0.8550,0.8595,0.8615,0.8634,0.8663,0.8705,0.8720,0.8802,0.8807, 0.8825,0.8864,0.8867,0.8893,0.8894,0.8906,0.8908,0.8938,0.8943,0.9004, 0.9072,0.9091,0.9096,0.9122,0.9132,0.9176,0.9246,0.9248,0.9258,0.9305, 0.9325,0.9333,0.9356,0.9362,0.9413,0.9489,0.9516,0.9529,0.9532,0.9583, 0.9584,0.9612,0.9689,0.9723,0.9747,0.9758,0.9822,0.9927,0.9966, Overall p-value after applying KStest on 269 p-values = 0.372125 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.