RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-12_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 24.8019 0.900767 2 to 25 15.59 11.3810 0.163914 3 to 26 15.63 15.8262 0.463810 4 to 27 15.60 12.7367 0.246377 5 to 28 15.86 9.8465 0.090078 6 to 29 15.95 11.5770 0.174954 7 to 30 16.11 22.6277 0.838231 8 to 31 15.60 21.2439 0.784430 9 to 32 15.74 18.8806 0.664573 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.916021 Tough bday spacings test for dh-ranFile-2015-12-12_20:31: 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 11 33 74 103 109 74 45 28 17 3 3 (O-E)^2/E 0.4 0.4 0.0 0.3 1.3 0.2 1.0 0.1 0.3 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 6.187, p= 0.201 RESULTS OF GCD FOR dh-ranFile-2015-12-12_20:31 Euclid's algorithm: p-value, steps to gcd: 0.260907 p-value, dist. of gcd's: 0.714885 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-12_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.511 0.753 0.076 0.734 0.838 0.322 0.709 0.760 Bits 8 to 15---> 0.378 0.912 0.821 0.348 0.604 0.535 0.968 0.884 Bits 16 to 23---> 0.535 0.069 0.607 0.873 0.105 0.696 0.778 0.690 Bits 24 to 31---> 0.944 0.517 0.807 0.769 0.665 0.598 0.182 0.015 KS test for the above 32 p values: 0.929 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-12_20:31, p-values for 5 runs: 0.8180, 0.5183, 0.6752, 0.6600, 0.4461 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-12_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5140 5134.0 0.007 0.202 r= 30 23181 23103.0 0.263 0.465 r= 31 11474 11551.5 0.520 0.985 chi-square = 0.985 with df = 3; p-value = 0.195 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-12_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 197 211.4 0.983 0.983 r= 30 5115 5134.0 0.070 1.054 r= 31 23007 23103.0 0.399 1.453 r= 32 11681 11551.5 1.451 2.904 chi-square = 2.904 with df = 3; p-value = 0.593 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-12_20:31 b-rank test for bits 1 to 8, p=0.24959 b-rank test for bits 2 to 9, p=0.10522 b-rank test for bits 3 to 10, p=0.49030 b-rank test for bits 4 to 11, p=0.33350 b-rank test for bits 5 to 12, p=0.03397 b-rank test for bits 6 to 13, p=0.11312 b-rank test for bits 7 to 14, p=0.34379 b-rank test for bits 8 to 15, p=0.50265 b-rank test for bits 9 to 16, p=0.27639 b-rank test for bits 10 to 17, p=0.76156 b-rank test for bits 11 to 18, p=0.63604 b-rank test for bits 12 to 19, p=0.33529 b-rank test for bits 13 to 20, p=0.49091 b-rank test for bits 14 to 21, p=0.03991 b-rank test for bits 15 to 22, p=0.15953 b-rank test for bits 16 to 23, p=0.28471 b-rank test for bits 17 to 24, p=0.36627 b-rank test for bits 18 to 25, p=0.24008 b-rank test for bits 19 to 26, p=0.07995 b-rank test for bits 20 to 27, p=0.61005 b-rank test for bits 21 to 28, p=0.85714 b-rank test for bits 22 to 29, p=0.71509 b-rank test for bits 23 to 30, p=0.23401 b-rank test for bits 24 to 31, p=0.92940 b-rank test for bits 25 to 32, p=0.78633 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 = 0.132994 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-12_20:31 (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 142769 2.01 0.977709 2 141873 -0.08 0.466177 3 142251 0.80 0.787650 4 142166 0.60 0.725646 5 141632 -0.65 0.258503 6 141304 -1.41 0.078634 7 141504 -0.95 0.171811 8 141720 -0.44 0.329114 9 141651 -0.60 0.273063 10 142369 1.07 0.858588 11 142112 0.47 0.682082 12 142741 1.94 0.974001 13 142098 0.44 0.670328 14 141934 0.06 0.522982 15 141424 -1.13 0.128408 16 141943 0.08 0.531352 17 142157 0.58 0.718594 18 142511 1.41 0.920104 19 142109 0.47 0.679578 20 141623 -0.67 0.251749 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-12_20:31 Bits used No. missing words z-score p-value 23 to 32 142461 1.9023 0.971435 22 to 31 142556 2.2299 0.987123 21 to 30 141826 -0.2873 0.386924 20 to 29 142192 0.9747 0.835151 19 to 28 142268 1.2368 0.891918 18 to 27 141251 -2.2701 0.011601 17 to 26 142058 0.5127 0.695904 16 to 25 141972 0.2161 0.585547 15 to 24 142209 1.0333 0.849279 14 to 23 142577 2.3023 0.989341 13 to 22 142309 1.3782 0.915925 12 to 21 142771 2.9713 0.998517 11 to 20 142137 0.7851 0.783793 10 to 19 142157 0.8540 0.803457 9 to 18 141810 -0.3425 0.365981 8 to 17 142110 0.6920 0.755521 7 to 16 141887 -0.0770 0.469312 6 to 15 142155 0.8471 0.801541 5 to 14 142156 0.8506 0.802500 4 to 13 141313 -2.0563 0.019876 3 to 12 141593 -1.0908 0.137682 2 to 11 142180 0.9333 0.824679 1 to 10 141985 0.2609 0.602927 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-12_20:31 Bits used No. missing words z-score p-value 28 to 32 142249 1.1514 0.875221 27 to 31 142383 1.6057 0.945826 26 to 30 141505 -1.3706 0.085248 25 to 29 142045 0.4599 0.677205 24 to 28 142075 0.5616 0.712803 23 to 27 142194 0.9650 0.832723 22 to 26 142432 1.7718 0.961783 21 to 25 141643 -0.9028 0.183312 20 to 24 142492 1.9752 0.975875 19 to 23 142008 0.3345 0.630989 18 to 22 141520 -1.3198 0.093457 17 to 21 141836 -0.2486 0.401844 16 to 20 141760 -0.5062 0.306357 15 to 19 141532 -1.2791 0.100434 14 to 18 141649 -0.8825 0.188760 13 to 17 142066 0.5311 0.702320 12 to 16 142087 0.6023 0.726503 11 to 15 141751 -0.5367 0.295733 10 to 14 141716 -0.6554 0.256119 9 to 13 141783 -0.4282 0.334239 8 to 12 141569 -1.1537 0.124320 7 to 11 141495 -1.4045 0.080084 6 to 10 142336 1.4463 0.925959 5 to 9 142301 1.3277 0.907861 4 to 8 141879 -0.1028 0.459056 3 to 7 141973 0.2158 0.585440 2 to 6 142262 1.1955 0.884053 1 to 5 142155 0.8328 0.797516 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-12_20:31 Bits used No. missing words z-score p-value 31 to 32 141748 -0.4759 0.317073 30 to 31 142113 0.6008 0.726012 29 to 30 140907 -2.9567 0.001555 28 to 29 142080 0.5035 0.692677 27 to 28 142293 1.1318 0.871134 26 to 27 141778 -0.3874 0.349229 25 to 26 142134 0.6627 0.746253 24 to 25 141646 -0.7768 0.218643 23 to 24 141804 -0.3107 0.378011 22 to 23 141405 -1.4877 0.068415 21 to 22 141765 -0.4258 0.335144 20 to 21 142015 0.3117 0.622370 19 to 20 141823 -0.2547 0.399493 18 to 19 142143 0.6893 0.754680 17 to 18 141924 0.0433 0.517259 16 to 17 142353 1.3088 0.904692 15 to 16 141822 -0.2576 0.398354 14 to 15 142219 0.9135 0.819505 13 to 14 141870 -0.1160 0.453819 12 to 13 141738 -0.5054 0.306640 11 to 12 141840 -0.2045 0.418976 10 to 11 141225 -2.0187 0.021761 9 to 10 141924 0.0433 0.517259 8 to 9 141039 -2.5673 0.005124 7 to 8 141819 -0.2665 0.394942 6 to 7 142653 2.1937 0.985872 5 to 6 142281 1.0964 0.863542 4 to 5 141533 -1.1101 0.133474 3 to 4 141864 -0.1337 0.446813 2 to 3 141937 0.0816 0.532527 1 to 2 142098 0.5565 0.711082 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-12_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2625.40 1.773 0.961918 Test results for specific bytes for dh-ranFile-2015-12-12_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2499.76 -0.003 0.498658 2 to 9 2419.36 -1.140 0.127062 3 to 10 2462.69 -0.528 0.298851 4 to 11 2513.61 0.192 0.576312 5 to 12 2449.80 -0.710 0.238864 6 to 13 2528.23 0.399 0.655160 7 to 14 2457.87 -0.596 0.275652 8 to 15 2310.75 -2.676 0.003721 9 to 16 2512.57 0.178 0.570559 10 to 17 2630.20 1.841 0.967214 11 to 18 2489.69 -0.146 0.442025 12 to 19 2448.52 -0.728 0.233298 13 to 20 2524.03 0.340 0.633020 14 to 21 2579.92 1.130 0.870814 15 to 22 2522.85 0.323 0.626694 16 to 23 2425.00 -1.061 0.144422 17 to 24 2616.51 1.648 0.950287 18 to 25 2575.69 1.070 0.857790 19 to 26 2531.88 0.451 0.673975 20 to 27 2462.71 -0.527 0.298973 21 to 28 2422.89 -1.090 0.137753 22 to 29 2561.69 0.872 0.808528 23 to 30 2505.04 0.071 0.528419 24 to 31 2406.21 -1.326 0.092346 25 to 32 2506.43 0.091 0.536224 CDPARK for dh-ranFile-2015-12-12_20:31: 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 3504 -0.8676 0.192812 3551 1.2785 0.899470 3513 -0.4566 0.323972 3502 -0.9589 0.168804 3495 -1.2785 0.100530 3541 0.8219 0.794438 3529 0.2740 0.607947 3525 0.0913 0.536383 3537 0.6393 0.738676 3522 -0.0457 0.481790 Square side=100, avg. no. parked=3521.90 sample std.=17.37 p-value of the KSTEST for those 10 p-values: 0.989492 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-12_20:31 0.8706,0.6971,0.8981,0.7421,0.3028,0.7809,0.7056,0.6672,0.4476,0.0517, The KS test for those 10 p-values: 0.250933 The 3DSPHERES test for dh-ranFile-2015-12-12_20:31 sample no r^3 equiv. uni. 1 16.675 0.426397 2 7.455 0.220036 3 49.031 0.804921 4 25.003 0.565449 5 1.739 0.056306 6 13.624 0.364996 7 16.516 0.423366 8 108.908 0.973491 9 31.198 0.646518 10 19.696 0.481359 11 3.206 0.101342 12 56.471 0.847768 13 211.366 0.999129 14 1.919 0.061949 15 12.147 0.332967 16 34.643 0.684865 17 27.049 0.594090 18 27.017 0.593664 19 9.754 0.277564 20 16.863 0.429997 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.806837 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-12_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.9 -1.3 0.6 0.9 -0.2 0.1 -0.8 0.2 -1.4 1.6 -1.6 1.1 0.5 -0.8 0.5 -0.5 0.2 0.1 1.0 -1.5 -0.6 -1.0 0.4 0.5 1.2 1.0 1.1 -2.3 -1.0 0.5 1.4 0.9 -0.2 1.0 1.5 0.5 0.8 1.3 -0.1 3.9 1.0 0.8 Chi-square with 42 degrees of freedom:54.542878 z-score=1.368540, p-value=0.907113 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-12_20:31 Test no p-value 1 0.053495 2 0.095923 3 0.611715 4 0.642374 5 0.020675 6 0.824677 7 0.020078 8 0.001646 9 0.067957 10 0.146236 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000546 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-12_20:31: (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 66753 0.11 66626 0.02 3 25000.00 24964 0.05 25187 1.40 4 6666.67 6548 2.11 6614 0.42 5 1388.89 1456 3.24 1354 0.88 6 238.10 233 0.11 197 7.09 7 34.72 40 0.80 19 7.12 8 4.96 5 0.00 2 1.77 p=0.62332 p=0.99529 Number of rngs required: 687912, p-value: 0.286 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-12_20:31 No. of wins: Observed Expected 98612 98585.9 z-score= 0.117, pvalue=0.54654 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67064 66666.7 2.368 2.368 2 37720 37654.3 0.115 2.483 3 26886 26954.7 0.175 2.658 4 19141 19313.5 1.540 4.198 5 13853 13851.4 0.000 4.198 6 9919 9943.5 0.061 4.259 7 7031 7145.0 1.820 6.078 8 5084 5139.1 0.590 6.669 9 3648 3699.9 0.727 7.396 10 2712 2666.3 0.783 8.179 11 1893 1923.3 0.478 8.657 12 1413 1388.7 0.424 9.081 13 1019 1003.7 0.233 9.314 14 720 726.1 0.052 9.366 15 483 525.8 3.490 12.855 16 387 381.2 0.090 12.945 17 287 276.5 0.396 13.341 18 190 200.8 0.584 13.925 19 175 146.0 5.767 19.692 20 101 106.2 0.256 19.948 21 274 287.1 0.599 20.547 Chisq= 20.55 for 20 degrees of freedom, p= 0.57578 SUMMARY of craptest p-value for no. of wins: 0.546538 p-value for throws/game: 0.575781 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-12_20:31 No. of wins: Observed Expected 98381 98585.9 z-score=-0.916, pvalue=0.17977 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66589 66666.7 0.090 0.090 2 37574 37654.3 0.171 0.262 3 27178 26954.7 1.849 2.111 4 19355 19313.5 0.089 2.200 5 13762 13851.4 0.577 2.778 6 9990 9943.5 0.217 2.995 7 7012 7145.0 2.477 5.471 8 5269 5139.1 3.285 8.756 9 3707 3699.9 0.014 8.770 10 2678 2666.3 0.051 8.821 11 1907 1923.3 0.139 8.960 12 1346 1388.7 1.315 10.275 13 1028 1003.7 0.588 10.863 14 700 726.1 0.941 11.804 15 532 525.8 0.072 11.876 16 360 381.2 1.174 13.050 17 279 276.5 0.022 13.072 18 214 200.8 0.864 13.936 19 146 146.0 0.000 13.936 20 111 106.2 0.216 14.151 21 263 287.1 2.025 16.176 Chisq= 16.18 for 20 degrees of freedom, p= 0.29438 SUMMARY of craptest p-value for no. of wins: 0.179769 p-value for throws/game: 0.294381 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0016,0.0016,0.0037,0.0051,0.0116,0.0147,0.0199,0.0201,0.0207, 0.0218,0.0340,0.0399,0.0517,0.0535,0.0563,0.0619,0.0680,0.0684,0.0686, 0.0764,0.0786,0.0800,0.0801,0.0852,0.0901,0.0923,0.0935,0.0959,0.1004, 0.1005,0.1013,0.1052,0.1053,0.1131,0.1243,0.1271,0.1284,0.1330,0.1335, 0.1377,0.1378,0.1444,0.1462,0.1595,0.1639,0.1688,0.1718,0.1750,0.1798, 0.1815,0.1833,0.1888,0.1928,0.1951,0.2007,0.2186,0.2200,0.2333,0.2340, 0.2389,0.2401,0.2464,0.2496,0.2509,0.2517,0.2561,0.2585,0.2609,0.2731, 0.2757,0.2764,0.2776,0.2847,0.2857,0.2944,0.2957,0.2989,0.2990,0.3028, 0.3064,0.3066,0.3171,0.3223,0.3240,0.3291,0.3330,0.3335,0.3342,0.3351, 0.3353,0.3438,0.3483,0.3492,0.3650,0.3660,0.3663,0.3780,0.3780,0.3869, 0.3949,0.3984,0.3995,0.4018,0.4190,0.4234,0.4264,0.4300,0.4420,0.4461, 0.4468,0.4476,0.4538,0.4591,0.4638,0.4662,0.4693,0.4814,0.4818,0.4903, 0.4909,0.4987,0.5027,0.5105,0.5168,0.5173,0.5173,0.5183,0.5230,0.5284, 0.5314,0.5325,0.5350,0.5352,0.5362,0.5364,0.5465,0.5654,0.5706,0.5758, 0.5763,0.5854,0.5855,0.5934,0.5937,0.5941,0.5977,0.6029,0.6043,0.6070, 0.6079,0.6100,0.6117,0.6224,0.6233,0.6267,0.6310,0.6330,0.6360,0.6424, 0.6465,0.6552,0.6600,0.6646,0.6650,0.6672,0.6703,0.6740,0.6752,0.6772, 0.6796,0.6821,0.6849,0.6901,0.6927,0.6957,0.6959,0.6971,0.7023,0.7056, 0.7091,0.7111,0.7128,0.7149,0.7151,0.7186,0.7256,0.7260,0.7265,0.7344, 0.7387,0.7421,0.7463,0.7534,0.7547,0.7555,0.7605,0.7616,0.7686,0.7778, 0.7809,0.7838,0.7844,0.7863,0.7877,0.7944,0.7975,0.8015,0.8025,0.8035, 0.8049,0.8068,0.8071,0.8085,0.8180,0.8195,0.8207,0.8247,0.8247,0.8327, 0.8352,0.8380,0.8382,0.8478,0.8493,0.8571,0.8578,0.8586,0.8635,0.8706, 0.8708,0.8711,0.8731,0.8752,0.8836,0.8841,0.8919,0.8981,0.8995,0.9008, 0.9047,0.9071,0.9079,0.9118,0.9159,0.9160,0.9201,0.9260,0.9286,0.9294, 0.9444,0.9458,0.9503,0.9618,0.9619,0.9672,0.9682,0.9714,0.9735,0.9740, 0.9759,0.9777,0.9859,0.9871,0.9893,0.9895,0.9953,0.9985,0.9991, Overall p-value after applying KStest on 269 p-values = 0.290437 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.