RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 13.8789 0.324345 2 to 25 16.01 12.6227 0.238942 3 to 26 15.46 24.6877 0.898079 4 to 27 15.59 31.1543 0.980874 5 to 28 16.06 18.2260 0.625280 6 to 29 15.83 16.3589 0.501450 7 to 30 15.61 28.0011 0.955075 8 to 31 15.77 20.0943 0.730568 9 to 32 15.59 16.1306 0.485403 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.226465 Tough bday spacings test for dh-ranFile-2018-07-07_17:31: 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 32 59 106 106 72 58 31 14 5 2 (O-E)^2/E 3.7 0.6 2.8 0.7 0.7 0.5 0.7 0.1 0.1 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 11.205, p= 0.658 RESULTS OF GCD FOR dh-ranFile-2018-07-07_17:31 Euclid's algorithm: p-value, steps to gcd: 0.164700 p-value, dist. of gcd's: 0.198908 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.927 0.571 0.193 0.044 0.670 0.454 0.726 0.185 Bits 8 to 15---> 0.724 0.291 0.344 0.647 0.532 0.525 0.763 0.579 Bits 16 to 23---> 0.239 0.824 0.257 0.969 0.718 0.709 0.238 0.959 Bits 24 to 31---> 0.701 0.085 0.449 0.860 0.244 0.459 0.171 0.438 KS test for the above 32 p values: 0.159 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_17:31, p-values for 5 runs: 0.7727, 0.6835, 0.6176, 0.6471, 0.6207 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5138 5134.0 0.003 0.031 r= 30 23210 23103.0 0.495 0.526 r= 31 11443 11551.5 1.020 1.545 chi-square = 1.545 with df = 3; p-value = 0.328 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5242 5134.0 2.271 2.410 r= 31 23093 23103.0 0.004 2.415 r= 32 11459 11551.5 0.741 3.156 chi-square = 3.156 with df = 3; p-value = 0.632 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_17:31 b-rank test for bits 1 to 8, p=0.54976 b-rank test for bits 2 to 9, p=0.39969 b-rank test for bits 3 to 10, p=0.20722 b-rank test for bits 4 to 11, p=0.80720 b-rank test for bits 5 to 12, p=0.15133 b-rank test for bits 6 to 13, p=0.52646 b-rank test for bits 7 to 14, p=0.37957 b-rank test for bits 8 to 15, p=0.21561 b-rank test for bits 9 to 16, p=0.57907 b-rank test for bits 10 to 17, p=0.80972 b-rank test for bits 11 to 18, p=0.93430 b-rank test for bits 12 to 19, p=0.92992 b-rank test for bits 13 to 20, p=0.19483 b-rank test for bits 14 to 21, p=0.38698 b-rank test for bits 15 to 22, p=0.53047 b-rank test for bits 16 to 23, p=0.17578 b-rank test for bits 17 to 24, p=0.16048 b-rank test for bits 18 to 25, p=0.37173 b-rank test for bits 19 to 26, p=0.59696 b-rank test for bits 20 to 27, p=0.21193 b-rank test for bits 21 to 28, p=0.26805 b-rank test for bits 22 to 29, p=0.79595 b-rank test for bits 23 to 30, p=0.74920 b-rank test for bits 24 to 31, p=0.29947 b-rank test for bits 25 to 32, p=0.34532 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 = 0.364565 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_17:31 (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 143101 2.78 0.997318 2 141857 -0.12 0.451344 3 141525 -0.90 0.184602 4 142319 0.96 0.830760 5 141370 -1.26 0.103814 6 141878 -0.07 0.470823 7 141832 -0.18 0.428310 8 142265 0.83 0.797015 9 142205 0.69 0.755160 10 141964 0.13 0.550820 11 142888 2.29 0.988891 12 142939 2.41 0.991931 13 141420 -1.14 0.126458 14 142577 1.56 0.940617 15 141582 -0.76 0.222198 16 141955 0.11 0.542489 17 141370 -1.26 0.103814 18 142396 1.14 0.872247 19 142341 1.01 0.843411 20 142214 0.71 0.761720 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-07_17:31 Bits used No. missing words z-score p-value 23 to 32 141871 -0.1322 0.447424 22 to 31 142194 0.9816 0.836857 21 to 30 142304 1.3609 0.913232 20 to 29 142034 0.4299 0.666365 19 to 28 141966 0.1954 0.577466 18 to 27 141961 0.1782 0.570706 17 to 26 141788 -0.4184 0.337835 16 to 25 141722 -0.6460 0.259151 15 to 24 141750 -0.5494 0.291361 14 to 23 141638 -0.9356 0.174734 13 to 22 141934 0.0851 0.533897 12 to 21 141543 -1.2632 0.103257 11 to 20 142164 0.8782 0.810075 10 to 19 141594 -1.0873 0.138442 9 to 18 141711 -0.6839 0.247020 8 to 17 142038 0.4437 0.671367 7 to 16 141924 0.0506 0.520172 6 to 15 140951 -3.3046 0.000476 5 to 14 142168 0.8920 0.813794 4 to 13 141827 -0.2839 0.388245 3 to 12 141994 0.2920 0.614844 2 to 11 141761 -0.5115 0.304507 1 to 10 141868 -0.1425 0.443336 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-07_17:31 Bits used No. missing words z-score p-value 28 to 32 142255 1.1718 0.879354 27 to 31 141926 0.0565 0.522532 26 to 30 141428 -1.6316 0.051379 25 to 29 141607 -1.0248 0.152718 24 to 28 142201 0.9887 0.838598 23 to 27 141732 -0.6011 0.273881 22 to 26 142220 1.0531 0.853857 21 to 25 141751 -0.5367 0.295733 20 to 24 142230 1.0870 0.861485 19 to 23 141433 -1.6147 0.053190 18 to 22 141907 -0.0079 0.496849 17 to 21 142213 1.0294 0.848352 16 to 20 141557 -1.1943 0.116173 15 to 19 142134 0.7616 0.776849 14 to 18 141805 -0.3537 0.361797 13 to 17 141937 0.0938 0.537365 12 to 16 141781 -0.4350 0.331775 11 to 15 141955 0.1548 0.561516 10 to 14 141839 -0.2384 0.405783 9 to 13 141919 0.0328 0.513075 8 to 12 141957 0.1616 0.564187 7 to 11 141412 -1.6859 0.045911 6 to 10 142084 0.5921 0.723109 5 to 9 142257 1.1785 0.880710 4 to 8 141821 -0.2994 0.382308 3 to 7 141834 -0.2554 0.399224 2 to 6 141696 -0.7232 0.234793 1 to 5 141947 0.1277 0.550805 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-07_17:31 Bits used No. missing words z-score p-value 31 to 32 141340 -1.6794 0.046533 30 to 31 141638 -0.8004 0.211744 29 to 30 142138 0.6745 0.750017 28 to 29 142022 0.3324 0.630191 27 to 28 141930 0.0610 0.524310 26 to 27 142266 1.0521 0.853629 25 to 26 141644 -0.7827 0.216906 24 to 25 141680 -0.6765 0.249365 23 to 24 141738 -0.5054 0.306640 22 to 23 141882 -0.0806 0.467872 21 to 22 142390 1.4179 0.921891 20 to 21 141928 0.0551 0.521960 19 to 20 142647 2.1760 0.985223 18 to 19 142101 0.5654 0.714099 17 to 18 141791 -0.3491 0.363524 16 to 17 141887 -0.0659 0.473741 15 to 16 141996 0.2557 0.600895 14 to 15 141482 -1.2606 0.103734 13 to 14 142032 0.3619 0.641271 12 to 13 142778 2.5624 0.994803 11 to 12 142240 0.9754 0.835326 10 to 11 142651 2.1878 0.985659 9 to 10 141470 -1.2960 0.097495 8 to 9 141703 -0.6086 0.271381 7 to 8 141511 -1.1750 0.119994 6 to 7 142328 1.2350 0.891588 5 to 6 141950 0.1200 0.547747 4 to 5 142533 1.8397 0.967096 3 to 4 141932 0.0669 0.526659 2 to 3 141527 -1.1278 0.129699 1 to 2 141616 -0.8653 0.193443 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2509.72 0.138 0.554684 Test results for specific bytes for dh-ranFile-2018-07-07_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2499.32 -0.010 0.496178 2 to 9 2552.64 0.744 0.771706 3 to 10 2601.16 1.431 0.923721 4 to 11 2492.58 -0.105 0.458202 5 to 12 2549.48 0.700 0.757965 6 to 13 2429.46 -0.998 0.159223 7 to 14 2517.30 0.245 0.596631 8 to 15 2628.34 1.815 0.965238 9 to 16 2636.68 1.933 0.973383 10 to 17 2588.19 1.247 0.893840 11 to 18 2487.83 -0.172 0.431659 12 to 19 2603.44 1.463 0.928246 13 to 20 2378.30 -1.721 0.042622 14 to 21 2465.76 -0.484 0.314133 15 to 22 2582.34 1.165 0.877893 16 to 23 2463.18 -0.521 0.301274 17 to 24 2525.42 0.360 0.640397 18 to 25 2342.81 -2.223 0.013108 19 to 26 2565.45 0.926 0.822680 20 to 27 2462.61 -0.529 0.298483 21 to 28 2478.88 -0.299 0.382591 22 to 29 2498.64 -0.019 0.492340 23 to 30 2719.07 3.098 0.999026 24 to 31 2520.75 0.293 0.615385 25 to 32 2578.90 1.116 0.867741 CDPARK for dh-ranFile-2018-07-07_17:31: 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 3536 0.5936 0.723613 3525 0.0913 0.536383 3507 -0.7306 0.232514 3536 0.5936 0.723613 3533 0.4566 0.676028 3526 0.1370 0.554479 3541 0.8219 0.794438 3521 -0.0913 0.463617 3539 0.7306 0.767486 3505 -0.8219 0.205562 Square side=100, avg. no. parked=3526.90 sample std.=12.10 p-value of the KSTEST for those 10 p-values: 0.339792 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_17:31 0.2257,0.5386,0.4097,0.1347,0.5142,0.4217,0.0466,0.7754,0.2461,0.9317, The KS test for those 10 p-values: 0.731393 The 3DSPHERES test for dh-ranFile-2018-07-07_17:31 sample no r^3 equiv. uni. 1 13.386 0.359947 2 183.442 0.997790 3 41.911 0.752674 4 56.311 0.846957 5 9.023 0.259742 6 0.383 0.012695 7 1.386 0.045139 8 1.034 0.033871 9 11.623 0.321199 10 55.370 0.842081 11 10.892 0.304467 12 80.386 0.931405 13 36.031 0.699112 14 20.969 0.502900 15 24.926 0.564331 16 7.183 0.212924 17 31.362 0.648449 18 29.359 0.624178 19 12.623 0.343460 20 93.700 0.955990 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.813543 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.9 0.3 -0.8 1.2 -0.6 -0.8 1.9 -0.2 -1.3 -0.7 -0.1 -0.0 0.8 0.8 -2.0 0.1 -0.5 -0.5 0.8 -0.1 0.6 0.1 0.4 0.1 2.0 0.8 -1.7 -0.5 -1.3 0.5 1.4 0.0 0.3 -1.5 1.1 -0.5 1.1 0.1 2.1 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:39.136095 z-score=-0.312478, p-value=0.402595 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-07_17:31 Test no p-value 1 0.762065 2 0.159095 3 0.015807 4 0.306101 5 0.079340 6 0.044747 7 0.010970 8 0.536171 9 0.086351 10 0.755468 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.005567 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_17:31: (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 66779 0.19 66695 0.01 3 25000.00 24808 1.47 24850 0.90 4 6666.67 6750 1.04 6727 0.55 5 1388.89 1402 0.12 1416 0.53 6 238.10 219 1.53 267 3.51 7 34.72 40 0.80 39 0.53 8 4.96 1 3.16 5 0.00 p=0.78476 p=0.57951 Number of rngs required: 688714, p-value: 0.640 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_17:31 No. of wins: Observed Expected 98704 98585.9 z-score= 0.528, pvalue=0.70139 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66741 66666.7 0.083 0.083 2 37581 37654.3 0.143 0.226 3 27118 26954.7 0.989 1.215 4 19078 19313.5 2.871 4.085 5 13879 13851.4 0.055 4.140 6 9978 9943.5 0.119 4.260 7 7050 7145.0 1.264 5.523 8 5093 5139.1 0.413 5.936 9 3704 3699.9 0.005 5.941 10 2732 2666.3 1.619 7.560 11 1909 1923.3 0.107 7.667 12 1379 1388.7 0.068 7.735 13 1048 1003.7 1.954 9.689 14 755 726.1 1.147 10.836 15 542 525.8 0.497 11.333 16 390 381.2 0.205 11.538 17 272 276.5 0.075 11.613 18 200 200.8 0.003 11.616 19 152 146.0 0.248 11.864 20 105 106.2 0.014 11.878 21 294 287.1 0.165 12.043 Chisq= 12.04 for 20 degrees of freedom, p= 0.08542 SUMMARY of craptest p-value for no. of wins: 0.701388 p-value for throws/game: 0.085420 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_17:31 No. of wins: Observed Expected 98625 98585.9 z-score= 0.175, pvalue=0.56949 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66486 66666.7 0.490 0.490 2 37711 37654.3 0.085 0.575 3 26987 26954.7 0.039 0.614 4 19236 19313.5 0.311 0.924 5 13862 13851.4 0.008 0.932 6 9908 9943.5 0.127 1.059 7 7344 7145.0 5.541 6.600 8 5062 5139.1 1.156 7.756 9 3726 3699.9 0.185 7.941 10 2685 2666.3 0.131 8.072 11 1900 1923.3 0.283 8.355 12 1410 1388.7 0.325 8.680 13 991 1003.7 0.161 8.842 14 731 726.1 0.033 8.874 15 529 525.8 0.019 8.893 16 379 381.2 0.012 8.905 17 274 276.5 0.023 8.929 18 224 200.8 2.673 11.602 19 167 146.0 3.025 14.627 20 98 106.2 0.635 15.263 21 290 287.1 0.029 15.292 Chisq= 15.29 for 20 degrees of freedom, p= 0.24051 SUMMARY of craptest p-value for no. of wins: 0.569485 p-value for throws/game: 0.240511 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0056,0.0110,0.0127,0.0131,0.0158,0.0339,0.0426,0.0441,0.0447, 0.0451,0.0459,0.0465,0.0466,0.0514,0.0532,0.0793,0.0846,0.0854,0.0864, 0.0975,0.1033,0.1037,0.1038,0.1038,0.1162,0.1200,0.1265,0.1297,0.1347, 0.1384,0.1513,0.1527,0.1591,0.1592,0.1592,0.1605,0.1647,0.1710,0.1747, 0.1758,0.1846,0.1855,0.1930,0.1934,0.1948,0.1989,0.2056,0.2072,0.2117, 0.2119,0.2129,0.2156,0.2169,0.2222,0.2257,0.2265,0.2325,0.2348,0.2385, 0.2388,0.2389,0.2405,0.2438,0.2461,0.2470,0.2494,0.2572,0.2592,0.2597, 0.2680,0.2714,0.2739,0.2911,0.2914,0.2957,0.2985,0.2995,0.3013,0.3045, 0.3045,0.3061,0.3066,0.3141,0.3212,0.3243,0.3282,0.3318,0.3378,0.3398, 0.3435,0.3440,0.3453,0.3599,0.3618,0.3635,0.3646,0.3717,0.3796,0.3823, 0.3826,0.3870,0.3882,0.3992,0.3997,0.4026,0.4058,0.4097,0.4217,0.4283, 0.4317,0.4378,0.4433,0.4474,0.4488,0.4513,0.4540,0.4582,0.4592,0.4636, 0.4679,0.4708,0.4737,0.4854,0.4923,0.4962,0.4968,0.5014,0.5029,0.5131, 0.5142,0.5202,0.5220,0.5225,0.5243,0.5247,0.5265,0.5267,0.5305,0.5321, 0.5339,0.5362,0.5364,0.5374,0.5386,0.5425,0.5477,0.5498,0.5508,0.5508, 0.5545,0.5547,0.5615,0.5642,0.5643,0.5695,0.5707,0.5707,0.5775,0.5787, 0.5791,0.5795,0.5966,0.5970,0.6009,0.6148,0.6154,0.6176,0.6207,0.6242, 0.6253,0.6302,0.6318,0.6399,0.6404,0.6413,0.6471,0.6471,0.6484,0.6582, 0.6664,0.6701,0.6714,0.6760,0.6835,0.6991,0.7013,0.7014,0.7086,0.7141, 0.7183,0.7231,0.7236,0.7236,0.7239,0.7259,0.7306,0.7314,0.7492,0.7500, 0.7527,0.7552,0.7555,0.7580,0.7617,0.7621,0.7630,0.7675,0.7717,0.7727, 0.7754,0.7768,0.7848,0.7944,0.7959,0.7970,0.8072,0.8097,0.8101,0.8135, 0.8138,0.8227,0.8245,0.8308,0.8353,0.8369,0.8386,0.8421,0.8434,0.8470, 0.8484,0.8536,0.8539,0.8603,0.8615,0.8677,0.8722,0.8779,0.8794,0.8807, 0.8916,0.8938,0.8981,0.9132,0.9219,0.9237,0.9275,0.9282,0.9299,0.9314, 0.9317,0.9343,0.9406,0.9551,0.9560,0.9592,0.9652,0.9671,0.9688,0.9734, 0.9809,0.9852,0.9857,0.9889,0.9919,0.9948,0.9973,0.9978,0.9990, Overall p-value after applying KStest on 269 p-values = 0.812152 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.