RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-25_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 15.97 21.2829 0.786110 2 to 25 15.91 20.9380 0.770922 3 to 26 15.80 20.5679 0.753785 4 to 27 15.87 17.6645 0.589701 5 to 28 15.75 11.4859 0.169782 6 to 29 16.02 15.5692 0.445444 7 to 30 15.89 20.8915 0.768818 8 to 31 15.99 17.2809 0.564504 9 to 32 15.90 19.2254 0.684249 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.169197 Tough bday spacings test for dh-ranFile-2016-03-25_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 14 32 91 103 93 76 43 23 11 7 7 (O-E)^2/E 2.6 0.6 4.3 0.3 0.2 0.1 1.6 1.5 1.0 0.0 2.1 Birthday Spacings: Sum(O-E)^2/E= 14.295, p= 0.840 RESULTS OF GCD FOR dh-ranFile-2016-03-25_20:31 Euclid's algorithm: p-value, steps to gcd: 0.310312 p-value, dist. of gcd's: 0.077868 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-25_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.416 0.415 0.040 0.143 0.911 0.112 0.892 0.299 Bits 8 to 15---> 0.022 0.656 0.264 0.017 0.206 0.507 0.048 0.878 Bits 16 to 23---> 0.841 0.260 0.495 0.878 0.553 0.009 0.049 0.498 Bits 24 to 31---> 0.708 0.748 0.686 0.035 0.189 0.111 0.405 0.256 KS test for the above 32 p values: 0.973 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-25_20:31, p-values for 5 runs: 0.5447, 0.3978, 0.8941, 0.0720, 0.9308 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-25_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5147 5134.0 0.033 0.368 r= 30 23124 23103.0 0.019 0.387 r= 31 11526 11551.5 0.056 0.443 chi-square = 0.443 with df = 3; p-value = 0.069 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-25_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5237 5134.0 2.066 2.918 r= 31 23032 23103.0 0.218 3.136 r= 32 11533 11551.5 0.030 3.166 chi-square = 3.166 with df = 3; p-value = 0.633 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-25_20:31 b-rank test for bits 1 to 8, p=0.94720 b-rank test for bits 2 to 9, p=0.72404 b-rank test for bits 3 to 10, p=0.43576 b-rank test for bits 4 to 11, p=0.38353 b-rank test for bits 5 to 12, p=0.33409 b-rank test for bits 6 to 13, p=0.39525 b-rank test for bits 7 to 14, p=0.11384 b-rank test for bits 8 to 15, p=0.65733 b-rank test for bits 9 to 16, p=0.46961 b-rank test for bits 10 to 17, p=0.36733 b-rank test for bits 11 to 18, p=0.54700 b-rank test for bits 12 to 19, p=0.88438 b-rank test for bits 13 to 20, p=0.82067 b-rank test for bits 14 to 21, p=0.02970 b-rank test for bits 15 to 22, p=0.79664 b-rank test for bits 16 to 23, p=0.12134 b-rank test for bits 17 to 24, p=0.28344 b-rank test for bits 18 to 25, p=0.12018 b-rank test for bits 19 to 26, p=0.96656 b-rank test for bits 20 to 27, p=0.65403 b-rank test for bits 21 to 28, p=0.75672 b-rank test for bits 22 to 29, p=0.45852 b-rank test for bits 23 to 30, p=0.26662 b-rank test for bits 24 to 31, p=0.23514 b-rank test for bits 25 to 32, p=0.47405 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 = 0.965768 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-25_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 142253 0.80 0.789003 2 142501 1.38 0.916577 3 142220 0.73 0.766039 4 141133 -1.81 0.034850 5 141812 -0.23 0.410054 6 142168 0.60 0.727201 7 142201 0.68 0.752214 8 141872 -0.09 0.465249 9 142051 0.33 0.629680 10 141460 -1.05 0.146897 11 143207 3.03 0.998785 12 141771 -0.32 0.373272 13 141578 -0.77 0.219425 14 141203 -1.65 0.049440 15 141266 -1.50 0.066406 16 142624 1.67 0.952520 17 142144 0.55 0.708255 18 141796 -0.26 0.395586 19 142586 1.58 0.943062 20 142133 0.52 0.699371 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-25_20:31 Bits used No. missing words z-score p-value 23 to 32 141939 0.1023 0.540745 22 to 31 142074 0.5678 0.714924 21 to 30 142008 0.3402 0.633163 20 to 29 142067 0.5437 0.706673 19 to 28 141932 0.0782 0.531155 18 to 27 142084 0.6023 0.726516 17 to 26 141886 -0.0804 0.467940 16 to 25 142206 1.0230 0.846846 15 to 24 142030 0.4161 0.661333 14 to 23 142264 1.2230 0.889335 13 to 22 141697 -0.7322 0.232032 12 to 21 142049 0.4816 0.684962 11 to 20 141881 -0.0977 0.461089 10 to 19 142203 1.0127 0.844388 9 to 18 142031 0.4196 0.662594 8 to 17 141756 -0.5287 0.298498 7 to 16 142051 0.4885 0.687408 6 to 15 141707 -0.6977 0.242686 5 to 14 142027 0.4058 0.657540 4 to 13 141403 -1.7460 0.040408 3 to 12 141872 -0.1287 0.448788 2 to 11 141911 0.0058 0.502297 1 to 10 141955 0.1575 0.562568 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-25_20:31 Bits used No. missing words z-score p-value 28 to 32 141701 -0.7062 0.240031 27 to 31 141503 -1.3774 0.084196 26 to 30 142107 0.6701 0.748593 25 to 29 141468 -1.4960 0.067322 24 to 28 142025 0.3921 0.652509 23 to 27 142184 0.9311 0.824095 22 to 26 141867 -0.1435 0.442951 21 to 25 141260 -2.2011 0.013864 20 to 24 142231 1.0904 0.862233 19 to 23 141882 -0.0926 0.463093 18 to 22 141917 0.0260 0.510371 17 to 21 141680 -0.7774 0.218464 16 to 20 141768 -0.4791 0.315939 15 to 19 142237 1.1107 0.866661 14 to 18 141907 -0.0079 0.496849 13 to 17 141764 -0.4926 0.311132 12 to 16 141673 -0.8011 0.211532 11 to 15 142319 1.3887 0.917540 10 to 14 142525 2.0870 0.981557 9 to 13 141955 0.1548 0.561516 8 to 12 141763 -0.4960 0.309935 7 to 11 141702 -0.7028 0.241086 6 to 10 142233 1.0972 0.863720 5 to 9 142043 0.4531 0.674768 4 to 8 141775 -0.4554 0.324427 3 to 7 142252 1.1616 0.877300 2 to 6 142529 2.1006 0.982161 1 to 5 142139 0.7785 0.781875 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-25_20:31 Bits used No. missing words z-score p-value 31 to 32 142433 1.5447 0.938797 30 to 31 141548 -1.0659 0.143241 29 to 30 141940 0.0905 0.536044 28 to 29 142267 1.0551 0.854304 27 to 28 141674 -0.6942 0.243782 26 to 27 142159 0.7365 0.769284 25 to 26 142401 1.4504 0.926520 24 to 25 141871 -0.1131 0.454988 23 to 24 141589 -0.9449 0.172348 22 to 23 142053 0.4238 0.664146 21 to 22 141833 -0.2252 0.410927 20 to 21 142136 0.6686 0.748138 19 to 20 141226 -2.0157 0.021914 18 to 19 141651 -0.7620 0.223019 17 to 18 141894 -0.0452 0.481966 16 to 17 141798 -0.3284 0.371302 15 to 16 142002 0.2734 0.607713 14 to 15 141504 -1.1957 0.115914 13 to 14 142298 1.1465 0.874210 12 to 13 141682 -0.6706 0.251241 11 to 12 141667 -0.7148 0.237355 10 to 11 142056 0.4327 0.667367 9 to 10 142086 0.5212 0.698869 8 to 9 141549 -1.0629 0.143909 7 to 8 141736 -0.5113 0.304571 6 to 7 141378 -1.5673 0.058517 5 to 6 142305 1.1672 0.878429 4 to 5 141752 -0.4641 0.321288 3 to 4 142071 0.4769 0.683284 2 to 3 141624 -0.8417 0.199983 1 to 2 142006 0.2852 0.612240 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-25_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2542.12 0.596 0.724297 Test results for specific bytes for dh-ranFile-2016-03-25_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2493.06 -0.098 0.460899 2 to 9 2500.95 0.013 0.505367 3 to 10 2447.43 -0.743 0.228619 4 to 11 2563.24 0.894 0.814417 5 to 12 2412.87 -1.232 0.108947 6 to 13 2456.39 -0.617 0.268696 7 to 14 2526.24 0.371 0.644694 8 to 15 2566.53 0.941 0.826608 9 to 16 2491.72 -0.117 0.453373 10 to 17 2572.73 1.029 0.848161 11 to 18 2477.22 -0.322 0.373653 12 to 19 2473.78 -0.371 0.355390 13 to 20 2552.47 0.742 0.770963 14 to 21 2666.40 2.353 0.990696 15 to 22 2497.00 -0.042 0.483062 16 to 23 2494.80 -0.074 0.470692 17 to 24 2518.11 0.256 0.601051 18 to 25 2595.17 1.346 0.910824 19 to 26 2402.07 -1.385 0.083046 20 to 27 2551.61 0.730 0.767252 21 to 28 2503.52 0.050 0.519838 22 to 29 2517.22 0.244 0.596198 23 to 30 2557.62 0.815 0.792444 24 to 31 2524.52 0.347 0.635624 25 to 32 2566.32 0.938 0.825840 CDPARK for dh-ranFile-2016-03-25_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 3502 -0.9589 0.168804 3566 1.9635 0.975204 3485 -1.7352 0.041356 3481 -1.9178 0.027568 3497 -1.1872 0.117571 3515 -0.3653 0.357445 3536 0.5936 0.723613 3510 -0.5936 0.276387 3569 2.1005 0.982156 3511 -0.5479 0.291865 Square side=100, avg. no. parked=3517.20 sample std.=29.15 p-value of the KSTEST for those 10 p-values: 0.130536 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-25_20:31 0.9974,0.7780,0.0980,0.0079,0.3023,0.6495,0.5422,0.1916,0.4066,0.3845, The KS test for those 10 p-values: 0.585582 The 3DSPHERES test for dh-ranFile-2016-03-25_20:31 sample no r^3 equiv. uni. 1 78.791 0.927658 2 24.738 0.561590 3 20.963 0.502798 4 14.450 0.382255 5 12.706 0.345263 6 53.864 0.833949 7 89.310 0.949055 8 25.220 0.568576 9 32.406 0.660476 10 5.954 0.180011 11 35.878 0.697582 12 9.375 0.268381 13 36.150 0.700312 14 19.417 0.476512 15 12.553 0.341918 16 7.375 0.217935 17 17.080 0.434101 18 11.275 0.313276 19 9.668 0.275487 20 74.380 0.916201 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.511973 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-25_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.8 -1.4 -0.5 -0.6 1.4 1.7 -1.1 0.3 -0.3 -0.1 -0.9 -0.8 -1.5 -0.1 0.4 0.3 0.7 1.3 -1.5 -0.6 1.6 0.3 2.2 0.6 -0.3 -1.1 0.7 0.0 -0.9 -2.7 2.0 -0.4 -2.0 0.1 0.3 -0.1 -1.2 -0.1 0.1 -1.0 1.8 Chi-square with 42 degrees of freedom:50.261013 z-score=0.901350, p-value=0.821195 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-25_20:31 Test no p-value 1 0.000708 2 0.584479 3 0.289006 4 0.824001 5 0.704505 6 0.379085 7 0.158813 8 0.864096 9 0.653628 10 0.721270 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.611144 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-25_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 66710 0.03 66859 0.55 3 25000.00 24928 0.21 24889 0.49 4 6666.67 6650 0.04 6546 2.18 5 1388.89 1407 0.24 1443 2.11 6 238.10 272 4.83 215 2.24 7 34.72 27 1.72 44 2.48 8 4.96 5 0.00 3 0.77 p=0.68451 p=0.90639 Number of rngs required: 687323, p-value: 0.105 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-25_20:31 No. of wins: Observed Expected 98565 98585.9 z-score=-0.093, pvalue=0.46284 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66621 66666.7 0.031 0.031 2 37839 37654.3 0.906 0.937 3 26893 26954.7 0.141 1.078 4 19336 19313.5 0.026 1.105 5 13807 13851.4 0.142 1.247 6 9986 9943.5 0.181 1.428 7 7018 7145.0 2.258 3.687 8 5078 5139.1 0.726 4.413 9 3692 3699.9 0.017 4.429 10 2722 2666.3 1.164 5.593 11 1907 1923.3 0.139 5.732 12 1362 1388.7 0.515 6.246 13 1028 1003.7 0.588 6.834 14 736 726.1 0.134 6.968 15 533 525.8 0.098 7.066 16 392 381.2 0.309 7.374 17 295 276.5 1.232 8.607 18 195 200.8 0.169 8.776 19 158 146.0 0.989 9.765 20 103 106.2 0.097 9.862 21 299 287.1 0.492 10.354 Chisq= 10.35 for 20 degrees of freedom, p= 0.03872 SUMMARY of craptest p-value for no. of wins: 0.462836 p-value for throws/game: 0.038717 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-25_20:31 No. of wins: Observed Expected 98209 98585.9 z-score=-1.686, pvalue=0.04594 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66481 66666.7 0.517 0.517 2 37796 37654.3 0.533 1.050 3 26797 26954.7 0.923 1.973 4 19198 19313.5 0.690 2.663 5 13915 13851.4 0.292 2.955 6 9939 9943.5 0.002 2.957 7 7221 7145.0 0.808 3.765 8 5321 5139.1 6.440 10.206 9 3679 3699.9 0.118 10.323 10 2682 2666.3 0.092 10.416 11 1890 1923.3 0.578 10.993 12 1410 1388.7 0.325 11.319 13 1032 1003.7 0.797 12.116 14 766 726.1 2.188 14.304 15 514 525.8 0.266 14.570 16 340 381.2 4.443 19.013 17 283 276.5 0.151 19.164 18 205 200.8 0.087 19.251 19 143 146.0 0.061 19.312 20 112 106.2 0.315 19.627 21 276 287.1 0.430 20.057 Chisq= 20.06 for 20 degrees of freedom, p= 0.54562 SUMMARY of craptest p-value for no. of wins: 0.045943 p-value for throws/game: 0.545620 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0079,0.0088,0.0139,0.0166,0.0219,0.0219,0.0276,0.0297,0.0346, 0.0349,0.0387,0.0399,0.0404,0.0414,0.0459,0.0484,0.0486,0.0494,0.0585, 0.0664,0.0673,0.0689,0.0720,0.0779,0.0830,0.0842,0.0980,0.1045,0.1089, 0.1107,0.1123,0.1138,0.1159,0.1176,0.1202,0.1213,0.1305,0.1430,0.1432, 0.1439,0.1469,0.1588,0.1688,0.1692,0.1698,0.1723,0.1800,0.1887,0.1916, 0.2000,0.2063,0.2115,0.2179,0.2185,0.2194,0.2230,0.2286,0.2320,0.2351, 0.2374,0.2400,0.2411,0.2427,0.2438,0.2512,0.2559,0.2597,0.2638,0.2666, 0.2684,0.2687,0.2755,0.2764,0.2834,0.2890,0.2919,0.2985,0.2992,0.3023, 0.3046,0.3099,0.3103,0.3111,0.3133,0.3159,0.3213,0.3244,0.3341,0.3419, 0.3453,0.3554,0.3574,0.3673,0.3713,0.3733,0.3737,0.3791,0.3823,0.3835, 0.3845,0.3953,0.3956,0.3978,0.4053,0.4066,0.4101,0.4109,0.4155,0.4157, 0.4341,0.4358,0.4430,0.4454,0.4488,0.4534,0.4550,0.4585,0.4609,0.4611, 0.4628,0.4631,0.4652,0.4679,0.4696,0.4707,0.4741,0.4765,0.4820,0.4831, 0.4945,0.4968,0.4978,0.5023,0.5028,0.5054,0.5065,0.5104,0.5120,0.5198, 0.5312,0.5360,0.5407,0.5422,0.5447,0.5456,0.5470,0.5531,0.5615,0.5616, 0.5626,0.5645,0.5686,0.5845,0.5856,0.5897,0.5962,0.6011,0.6077,0.6111, 0.6122,0.6297,0.6332,0.6332,0.6356,0.6447,0.6495,0.6525,0.6536,0.6540, 0.6563,0.6573,0.6575,0.6605,0.6613,0.6626,0.6641,0.6674,0.6748,0.6833, 0.6842,0.6845,0.6850,0.6859,0.6874,0.6976,0.6989,0.6994,0.7003,0.7045, 0.7067,0.7083,0.7083,0.7149,0.7213,0.7236,0.7240,0.7243,0.7265,0.7272, 0.7481,0.7484,0.7486,0.7522,0.7538,0.7567,0.7660,0.7673,0.7688,0.7693, 0.7709,0.7710,0.7780,0.7819,0.7861,0.7890,0.7924,0.7966,0.8144,0.8207, 0.8212,0.8240,0.8241,0.8258,0.8266,0.8339,0.8400,0.8407,0.8444,0.8468, 0.8482,0.8543,0.8622,0.8637,0.8641,0.8667,0.8742,0.8773,0.8775,0.8781, 0.8784,0.8844,0.8893,0.8917,0.8941,0.9064,0.9108,0.9115,0.9162,0.9166, 0.9175,0.9265,0.9277,0.9308,0.9388,0.9431,0.9472,0.9491,0.9525,0.9658, 0.9666,0.9733,0.9752,0.9816,0.9822,0.9822,0.9907,0.9974,0.9988, Overall p-value after applying KStest on 269 p-values = 0.980275 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.