RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-24_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.86 11.3691 0.163254 2 to 25 15.62 25.6664 0.919243 3 to 26 15.59 25.8266 0.922322 4 to 27 15.76 18.1124 0.618215 5 to 28 15.76 10.3293 0.110766 6 to 29 15.51 32.7570 0.987902 7 to 30 15.78 20.2384 0.737780 8 to 31 15.90 22.7574 0.842682 9 to 32 15.93 11.8711 0.192121 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.188014 Tough bday spacings test for dh-ranFile-2016-06-24_22:31: 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 33 72 79 104 91 50 30 12 11 3 (O-E)^2/E 3.7 0.4 0.0 3.6 0.4 2.1 0.1 0.0 0.6 2.9 0.3 Birthday Spacings: Sum(O-E)^2/E= 14.035, p= 0.829 RESULTS OF GCD FOR dh-ranFile-2016-06-24_22:31 Euclid's algorithm: p-value, steps to gcd: 0.283684 p-value, dist. of gcd's: 0.293717 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-24_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.730 0.204 0.037 0.935 0.837 0.998 0.794 0.022 Bits 8 to 15---> 0.964 0.165 0.451 0.962 0.119 0.802 0.587 0.284 Bits 16 to 23---> 0.813 0.790 0.636 0.246 0.549 0.391 0.341 0.751 Bits 24 to 31---> 0.433 0.646 0.704 0.532 0.299 0.504 0.174 0.599 KS test for the above 32 p values: 0.231 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-24_22:31, p-values for 5 runs: 0.6024, 0.4143, 0.4748, 0.4649, 0.0752 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-24_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5252 5134.0 2.712 3.047 r= 30 22999 23103.0 0.469 3.515 r= 31 11546 11551.5 0.003 3.518 chi-square = 3.518 with df = 3; p-value = 0.682 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-24_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 194 211.4 1.435 1.435 r= 30 5093 5134.0 0.328 1.763 r= 31 23079 23103.0 0.025 1.788 r= 32 11634 11551.5 0.589 2.377 chi-square = 2.377 with df = 3; p-value = 0.502 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-24_22:31 b-rank test for bits 1 to 8, p=0.72040 b-rank test for bits 2 to 9, p=0.22931 b-rank test for bits 3 to 10, p=0.83420 b-rank test for bits 4 to 11, p=0.58882 b-rank test for bits 5 to 12, p=0.21798 b-rank test for bits 6 to 13, p=0.34396 b-rank test for bits 7 to 14, p=0.52181 b-rank test for bits 8 to 15, p=0.14719 b-rank test for bits 9 to 16, p=0.09862 b-rank test for bits 10 to 17, p=0.05196 b-rank test for bits 11 to 18, p=0.71284 b-rank test for bits 12 to 19, p=0.49355 b-rank test for bits 13 to 20, p=0.75628 b-rank test for bits 14 to 21, p=0.11112 b-rank test for bits 15 to 22, p=0.39913 b-rank test for bits 16 to 23, p=0.43424 b-rank test for bits 17 to 24, p=0.61671 b-rank test for bits 18 to 25, p=0.66909 b-rank test for bits 19 to 26, p=0.71363 b-rank test for bits 20 to 27, p=0.40831 b-rank test for bits 21 to 28, p=0.74724 b-rank test for bits 22 to 29, p=0.31514 b-rank test for bits 23 to 30, p=0.15051 b-rank test for bits 24 to 31, p=0.61650 b-rank test for bits 25 to 32, p=0.13710 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 = 0.306139 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-24_22:31 (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 141533 -0.88 0.189626 2 142280 0.87 0.806769 3 141712 -0.46 0.322381 4 141905 -0.01 0.495964 5 141502 -0.95 0.170623 6 141676 -0.55 0.292821 7 142212 0.71 0.760271 8 141071 -1.96 0.025073 9 142270 0.84 0.800298 10 141672 -0.55 0.289615 11 141929 0.05 0.518328 12 141526 -0.90 0.185225 13 142742 1.95 0.974142 14 141384 -1.23 0.109835 15 140741 -2.73 0.003169 16 141177 -1.71 0.043536 17 142295 0.90 0.816232 18 140759 -2.69 0.003597 19 141859 -0.12 0.453195 20 141491 -0.98 0.164184 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-24_22:31 Bits used No. missing words z-score p-value 23 to 32 142069 0.5506 0.709041 22 to 31 141789 -0.4149 0.339096 21 to 30 141864 -0.1563 0.437894 20 to 29 141669 -0.8287 0.203630 19 to 28 142378 1.6161 0.946964 18 to 27 141936 0.0920 0.536637 17 to 26 142214 1.0506 0.853276 16 to 25 142203 1.0127 0.844388 15 to 24 141949 0.1368 0.554403 14 to 23 141642 -0.9218 0.178309 13 to 22 141567 -1.1804 0.118911 12 to 21 142033 0.4264 0.665109 11 to 20 141665 -0.8425 0.199749 10 to 19 141882 -0.0942 0.462459 9 to 18 141958 0.1678 0.566641 8 to 17 142421 1.7644 0.961166 7 to 16 142031 0.4196 0.662594 6 to 15 142222 1.0782 0.859522 5 to 14 142327 1.4402 0.925100 4 to 13 142712 2.7678 0.997178 3 to 12 142176 0.9196 0.821097 2 to 11 141911 0.0058 0.502297 1 to 10 142254 1.1885 0.882685 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-24_22:31 Bits used No. missing words z-score p-value 28 to 32 142044 0.4565 0.675988 27 to 31 141566 -1.1638 0.122246 26 to 30 141757 -0.5164 0.302797 25 to 29 142089 0.6091 0.728755 24 to 28 142279 1.2531 0.894919 23 to 27 142285 1.2735 0.898572 22 to 26 142072 0.5514 0.709328 21 to 25 142165 0.8667 0.806941 20 to 24 141749 -0.5435 0.293396 19 to 23 141541 -1.2486 0.105910 18 to 22 141866 -0.1469 0.441613 17 to 21 141746 -0.5537 0.289905 16 to 20 141982 0.2463 0.597290 15 to 19 142079 0.5752 0.717406 14 to 18 142103 0.6565 0.744252 13 to 17 141870 -0.1333 0.446969 12 to 16 142203 0.9955 0.840251 11 to 15 141672 -0.8045 0.210552 10 to 14 141989 0.2701 0.606446 9 to 13 142188 0.9446 0.827580 8 to 12 141866 -0.1469 0.441613 7 to 11 142498 1.9955 0.977005 6 to 10 141960 0.1718 0.568188 5 to 9 141698 -0.7164 0.236881 4 to 8 141801 -0.3672 0.356727 3 to 7 142012 0.3480 0.636093 2 to 6 141412 -1.6859 0.045911 1 to 5 141687 -0.7537 0.225526 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-24_22:31 Bits used No. missing words z-score p-value 31 to 32 141907 -0.0069 0.497258 30 to 31 142078 0.4976 0.690600 29 to 30 141836 -0.2163 0.414372 28 to 29 142794 2.6096 0.995468 27 to 28 141587 -0.9508 0.170846 26 to 27 141707 -0.5968 0.275306 25 to 26 142142 0.6863 0.753751 24 to 25 142509 1.7689 0.961548 23 to 24 142213 0.8958 0.814815 22 to 23 142545 1.8751 0.969613 21 to 22 142251 1.0079 0.843243 20 to 21 141404 -1.4906 0.068027 19 to 20 142323 1.2203 0.888818 18 to 19 141637 -0.8033 0.210891 17 to 18 141922 0.0374 0.514907 16 to 17 141839 -0.2075 0.417824 15 to 16 142040 0.3855 0.650051 14 to 15 141999 0.2645 0.604308 13 to 14 142200 0.8574 0.804397 12 to 13 142301 1.1554 0.876030 11 to 12 141361 -1.6175 0.052886 10 to 11 141857 -0.1544 0.438661 9 to 10 141815 -0.2783 0.390407 8 to 9 142502 1.7483 0.959793 7 to 8 141716 -0.5703 0.284239 6 to 7 142091 0.5359 0.703986 5 to 6 141434 -1.4022 0.080435 4 to 5 142184 0.8102 0.791098 3 to 4 141864 -0.1337 0.446813 2 to 3 142033 0.3648 0.642373 1 to 2 142086 0.5212 0.698869 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-24_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2525.86 0.366 0.642726 Test results for specific bytes for dh-ranFile-2016-06-24_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2609.61 1.550 0.939449 2 to 9 2428.37 -1.013 0.155516 3 to 10 2650.82 2.133 0.983532 4 to 11 2468.90 -0.440 0.330012 5 to 12 2401.47 -1.393 0.081741 6 to 13 2568.68 0.971 0.834299 7 to 14 2445.60 -0.769 0.220868 8 to 15 2498.21 -0.025 0.489906 9 to 16 2530.87 0.437 0.668770 10 to 17 2667.25 2.365 0.990993 11 to 18 2686.30 2.635 0.995790 12 to 19 2444.76 -0.781 0.217350 13 to 20 2423.87 -1.077 0.140814 14 to 21 2539.39 0.557 0.711277 15 to 22 2538.76 0.548 0.708227 16 to 23 2535.16 0.497 0.690502 17 to 24 2392.72 -1.517 0.064614 18 to 25 2578.86 1.115 0.867637 19 to 26 2602.68 1.452 0.926773 20 to 27 2673.56 2.455 0.992947 21 to 28 2552.40 0.741 0.770681 22 to 29 2566.63 0.942 0.826988 23 to 30 2559.99 0.848 0.801892 24 to 31 2506.82 0.096 0.538423 25 to 32 2379.50 -1.704 0.044176 CDPARK for dh-ranFile-2016-06-24_22:31: 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 3514 -0.4110 0.340551 3509 -0.6393 0.261324 3514 -0.4110 0.340551 3521 -0.0913 0.463617 3476 -2.1461 0.015932 3487 -1.6438 0.050105 3545 1.0046 0.842447 3549 1.1872 0.882429 3519 -0.1826 0.427537 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3514.60 sample std.=21.11 p-value of the KSTEST for those 10 p-values: 0.307559 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-24_22:31 0.2002,0.8716,0.6551,0.4699,0.8438,0.1908,0.4744,0.2920,0.3497,0.7402, The KS test for those 10 p-values: 0.879955 The 3DSPHERES test for dh-ranFile-2016-06-24_22:31 sample no r^3 equiv. uni. 1 23.505 0.543194 2 29.168 0.621776 3 88.904 0.948360 4 53.211 0.830294 5 22.960 0.534818 6 12.971 0.351035 7 32.469 0.661179 8 7.839 0.229955 9 50.562 0.814632 10 3.790 0.118693 11 29.874 0.630571 12 74.319 0.916030 13 85.658 0.942459 14 10.012 0.283747 15 53.350 0.831078 16 160.108 0.995189 17 38.561 0.723448 18 17.429 0.440651 19 3.431 0.108071 20 6.664 0.199186 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.311129 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-24_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 0.6 -0.7 0.6 -1.4 -0.3 -1.5 0.0 -1.0 0.3 0.7 0.5 -1.2 0.1 0.5 0.5 1.3 0.3 -0.9 0.0 0.4 -0.6 0.6 -0.9 1.0 0.5 -0.3 -0.9 -0.4 -0.5 -1.5 0.2 -1.7 -0.9 -1.0 -1.4 -0.4 1.3 -0.7 -0.6 2.0 -0.1 Chi-square with 42 degrees of freedom:32.808172 z-score=-1.002911, p-value=0.155558 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-24_22:31 Test no p-value 1 0.349690 2 0.738993 3 0.722891 4 0.607414 5 0.136297 6 0.340104 7 0.550534 8 0.199188 9 0.775209 10 0.034586 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.785714 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-24_22:31: (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 66643 0.01 66638 0.01 3 25000.00 25068 0.18 25118 0.56 4 6666.67 6612 0.45 6551 2.01 5 1388.89 1392 0.01 1394 0.02 6 238.10 240 0.02 262 2.40 7 34.72 40 0.80 35 0.00 8 4.96 4 0.19 1 3.16 p=0.05128 p=0.77331 Number of rngs required: 688172, p-value: 0.395 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-24_22:31 No. of wins: Observed Expected 98752 98585.9 z-score= 0.743, pvalue=0.77128 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66818 66666.7 0.344 0.344 2 37557 37654.3 0.252 0.595 3 27073 26954.7 0.519 1.114 4 19455 19313.5 1.037 2.151 5 13810 13851.4 0.124 2.275 6 9747 9943.5 3.885 6.160 7 7109 7145.0 0.182 6.342 8 5074 5139.1 0.824 7.166 9 3614 3699.9 1.993 9.158 10 2757 2666.3 3.086 12.244 11 1907 1923.3 0.139 12.382 12 1391 1388.7 0.004 12.386 13 1025 1003.7 0.451 12.837 14 736 726.1 0.134 12.971 15 565 525.8 2.917 15.888 16 372 381.2 0.220 16.108 17 262 276.5 0.764 16.872 18 211 200.8 0.515 17.387 19 141 146.0 0.170 17.558 20 100 106.2 0.364 17.921 21 276 287.1 0.430 18.352 Chisq= 18.35 for 20 degrees of freedom, p= 0.43574 SUMMARY of craptest p-value for no. of wins: 0.771284 p-value for throws/game: 0.435735 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-24_22:31 No. of wins: Observed Expected 98637 98585.9 z-score= 0.229, pvalue=0.59046 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66390 66666.7 1.148 1.148 2 37566 37654.3 0.207 1.355 3 26901 26954.7 0.107 1.462 4 19732 19313.5 9.070 10.532 5 13834 13851.4 0.022 10.554 6 9908 9943.5 0.127 10.681 7 7192 7145.0 0.309 10.990 8 5131 5139.1 0.013 11.003 9 3659 3699.9 0.451 11.454 10 2719 2666.3 1.042 12.496 11 1912 1923.3 0.067 12.563 12 1421 1388.7 0.749 13.312 13 1005 1003.7 0.002 13.314 14 742 726.1 0.346 13.660 15 516 525.8 0.184 13.844 16 357 381.2 1.530 15.374 17 280 276.5 0.043 15.418 18 203 200.8 0.023 15.441 19 136 146.0 0.683 16.124 20 115 106.2 0.727 16.851 21 281 287.1 0.130 16.981 Chisq= 16.98 for 20 degrees of freedom, p= 0.34578 SUMMARY of craptest p-value for no. of wins: 0.590462 p-value for throws/game: 0.345778 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0032,0.0036,0.0159,0.0221,0.0251,0.0346,0.0369,0.0435,0.0442,0.0459, 0.0501,0.0513,0.0520,0.0529,0.0646,0.0680,0.0752,0.0804,0.0817,0.0986, 0.1059,0.1081,0.1098,0.1108,0.1111,0.1187,0.1189,0.1191,0.1222,0.1363, 0.1371,0.1408,0.1472,0.1505,0.1555,0.1556,0.1633,0.1642,0.1646,0.1706, 0.1708,0.1744,0.1783,0.1852,0.1880,0.1896,0.1908,0.1921,0.1992,0.1992, 0.1997,0.2002,0.2036,0.2044,0.2106,0.2109,0.2173,0.2180,0.2209,0.2255, 0.2293,0.2300,0.2309,0.2369,0.2460,0.2613,0.2753,0.2837,0.2837,0.2842, 0.2842,0.2896,0.2899,0.2920,0.2928,0.2934,0.2937,0.2986,0.3028,0.3061, 0.3076,0.3077,0.3111,0.3151,0.3224,0.3300,0.3391,0.3401,0.3406,0.3406, 0.3413,0.3440,0.3458,0.3497,0.3497,0.3510,0.3567,0.3904,0.3914,0.3952, 0.3991,0.4083,0.4143,0.4144,0.4178,0.4275,0.4328,0.4342,0.4357,0.4379, 0.4387,0.4407,0.4416,0.4416,0.4468,0.4470,0.4511,0.4532,0.4625,0.4636, 0.4649,0.4699,0.4744,0.4748,0.4899,0.4936,0.4960,0.4973,0.5020,0.5023, 0.5044,0.5149,0.5183,0.5218,0.5317,0.5348,0.5366,0.5384,0.5432,0.5488, 0.5505,0.5544,0.5666,0.5682,0.5873,0.5888,0.5905,0.5973,0.5995,0.6024, 0.6043,0.6064,0.6074,0.6165,0.6167,0.6182,0.6218,0.6306,0.6361,0.6364, 0.6424,0.6427,0.6465,0.6501,0.6551,0.6612,0.6626,0.6651,0.6688,0.6691, 0.6760,0.6816,0.6905,0.6906,0.6989,0.7040,0.7042,0.7082,0.7090,0.7093, 0.7113,0.7128,0.7136,0.7174,0.7204,0.7229,0.7234,0.7288,0.7297,0.7378, 0.7390,0.7402,0.7443,0.7472,0.7511,0.7538,0.7563,0.7603,0.7707,0.7713, 0.7733,0.7752,0.7857,0.7901,0.7911,0.7943,0.8003,0.8018,0.8019,0.8044, 0.8068,0.8069,0.8131,0.8146,0.8148,0.8162,0.8211,0.8270,0.8276,0.8286, 0.8303,0.8311,0.8342,0.8343,0.8367,0.8403,0.8424,0.8427,0.8432,0.8438, 0.8444,0.8533,0.8595,0.8676,0.8716,0.8760,0.8800,0.8824,0.8827,0.8888, 0.8949,0.8986,0.9160,0.9192,0.9223,0.9251,0.9268,0.9349,0.9394,0.9425, 0.9470,0.9484,0.9598,0.9612,0.9615,0.9623,0.9641,0.9696,0.9741,0.9770, 0.9835,0.9879,0.9910,0.9929,0.9952,0.9955,0.9958,0.9972,0.9976, Overall p-value after applying KStest on 269 p-values = 0.330990 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.