RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-10_13:31 (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 21.1794 0.781632 2 to 25 15.92 14.4173 0.362627 3 to 26 15.71 31.5840 0.983059 4 to 27 15.74 19.9693 0.724200 5 to 28 16.06 18.6615 0.651697 6 to 29 15.75 15.4069 0.433803 7 to 30 15.94 24.8495 0.901871 8 to 31 15.93 17.1206 0.553773 9 to 32 15.51 23.0263 0.851605 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.078555 Tough bday spacings test for dh-ranFile-2016-04-10_13:31: 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 3 37 75 99 106 76 42 35 17 7 3 (O-E)^2/E 4.1 0.0 0.0 0.0 0.7 0.1 2.0 0.9 0.3 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.449, p= 0.415 RESULTS OF GCD FOR dh-ranFile-2016-04-10_13:31 Euclid's algorithm: p-value, steps to gcd: 0.726541 p-value, dist. of gcd's: 0.325526 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-10_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.758 0.857 0.585 0.777 0.164 0.100 0.567 0.481 Bits 8 to 15---> 0.609 0.070 0.551 0.759 0.134 0.717 0.282 0.697 Bits 16 to 23---> 0.023 0.362 0.548 0.877 0.764 0.935 0.493 0.127 Bits 24 to 31---> 0.052 0.865 0.389 0.269 0.662 0.231 0.903 0.838 KS test for the above 32 p values: 0.127 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-10_13:31, p-values for 5 runs: 0.7239, 0.8146, 0.7781, 0.5442, 0.3292 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-10_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5244 5134.0 2.356 2.551 r= 30 23199 23103.0 0.399 2.950 r= 31 11352 11551.5 3.446 6.396 chi-square = 6.396 with df = 3; p-value = 0.906 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-10_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5168 5134.0 0.225 0.430 r= 31 23139 23103.0 0.056 0.486 r= 32 11475 11551.5 0.507 0.993 chi-square = 0.993 with df = 3; p-value = 0.197 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-10_13:31 b-rank test for bits 1 to 8, p=0.26638 b-rank test for bits 2 to 9, p=0.09272 b-rank test for bits 3 to 10, p=0.45863 b-rank test for bits 4 to 11, p=0.76588 b-rank test for bits 5 to 12, p=0.68826 b-rank test for bits 6 to 13, p=0.75025 b-rank test for bits 7 to 14, p=0.33918 b-rank test for bits 8 to 15, p=0.64879 b-rank test for bits 9 to 16, p=0.71758 b-rank test for bits 10 to 17, p=0.55096 b-rank test for bits 11 to 18, p=0.70214 b-rank test for bits 12 to 19, p=0.30606 b-rank test for bits 13 to 20, p=0.29573 b-rank test for bits 14 to 21, p=0.47554 b-rank test for bits 15 to 22, p=0.08528 b-rank test for bits 16 to 23, p=0.06802 b-rank test for bits 17 to 24, p=0.17465 b-rank test for bits 18 to 25, p=0.58015 b-rank test for bits 19 to 26, p=0.49272 b-rank test for bits 20 to 27, p=0.35844 b-rank test for bits 21 to 28, p=0.69176 b-rank test for bits 22 to 29, p=0.39452 b-rank test for bits 23 to 30, p=0.50092 b-rank test for bits 24 to 31, p=0.39618 b-rank test for bits 25 to 32, p=0.74307 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 = 0.224131 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-10_13:31 (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 141594 -0.74 0.230637 2 142135 0.53 0.700996 3 142245 0.78 0.783561 4 142433 1.22 0.889435 5 142303 0.92 0.821159 6 142442 1.24 0.893353 7 141609 -0.70 0.241431 8 141688 -0.52 0.302534 9 141884 -0.06 0.476404 10 141916 0.02 0.506217 11 141862 -0.11 0.455973 12 142000 0.21 0.583886 13 142322 0.96 0.832523 14 141761 -0.35 0.364459 15 141607 -0.71 0.239976 16 142398 1.14 0.873222 17 141353 -1.30 0.096829 18 142378 1.10 0.863247 19 142249 0.79 0.786292 20 141378 -1.24 0.107224 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-10_13:31 Bits used No. missing words z-score p-value 23 to 32 141608 -1.0391 0.149386 22 to 31 141970 0.2092 0.582857 21 to 30 142336 1.4713 0.929392 20 to 29 141905 -0.0149 0.494044 19 to 28 142095 0.6402 0.738992 18 to 27 141767 -0.4908 0.311786 17 to 26 141757 -0.5253 0.299696 16 to 25 141941 0.1092 0.543481 15 to 24 141685 -0.7736 0.219598 14 to 23 141920 0.0368 0.514675 13 to 22 141720 -0.6529 0.256923 12 to 21 141856 -0.1839 0.427047 11 to 20 142045 0.4678 0.680046 10 to 19 142457 1.8885 0.970522 9 to 18 142363 1.5644 0.941136 8 to 17 141602 -1.0598 0.144627 7 to 16 142211 1.0402 0.850886 6 to 15 142061 0.5230 0.699513 5 to 14 141804 -0.3632 0.358225 4 to 13 142033 0.4264 0.665109 3 to 12 141890 -0.0667 0.473428 2 to 11 141994 0.2920 0.614844 1 to 10 142256 1.1954 0.884037 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-10_13:31 Bits used No. missing words z-score p-value 28 to 32 141964 0.1853 0.573512 27 to 31 141722 -0.6350 0.262709 26 to 30 141986 0.2599 0.602529 25 to 29 141848 -0.2079 0.417654 24 to 28 141870 -0.1333 0.446969 23 to 27 141605 -1.0316 0.151123 22 to 26 142160 0.8497 0.802262 21 to 25 141817 -0.3130 0.377147 20 to 24 142005 0.3243 0.627147 19 to 23 141719 -0.6452 0.259403 18 to 22 142061 0.5141 0.696421 17 to 21 141706 -0.6893 0.245332 16 to 20 141885 -0.0825 0.467135 15 to 19 141731 -0.6045 0.272753 14 to 18 141648 -0.8859 0.187845 13 to 17 141765 -0.4893 0.312331 12 to 16 141930 0.0701 0.527930 11 to 15 141687 -0.7537 0.225526 10 to 14 141339 -1.9333 0.026598 9 to 13 142054 0.4904 0.688077 8 to 12 141689 -0.7469 0.227568 7 to 11 141928 0.0633 0.525232 6 to 10 142435 1.7819 0.962620 5 to 9 141900 -0.0316 0.487385 4 to 8 142201 0.9887 0.838598 3 to 7 141991 0.2768 0.609051 2 to 6 141774 -0.4587 0.323208 1 to 5 142011 0.3446 0.634819 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-10_13:31 Bits used No. missing words z-score p-value 31 to 32 141963 0.1583 0.562897 30 to 31 141304 -1.7856 0.037079 29 to 30 141775 -0.3963 0.345959 28 to 29 142180 0.7984 0.787691 27 to 28 141844 -0.1927 0.423592 26 to 27 141537 -1.0983 0.136033 25 to 26 141544 -1.0777 0.140591 24 to 25 142016 0.3147 0.623490 23 to 24 141703 -0.6086 0.271381 22 to 23 142083 0.5123 0.695780 21 to 22 141677 -0.6853 0.246565 20 to 21 142367 1.3501 0.911501 19 to 20 142431 1.5388 0.938080 18 to 19 141816 -0.2753 0.391539 17 to 18 142347 1.2911 0.901659 16 to 17 142081 0.5064 0.693713 15 to 16 141957 0.1406 0.555915 14 to 15 141436 -1.3963 0.081319 13 to 14 141811 -0.2901 0.385886 12 to 13 142638 2.1495 0.984201 11 to 12 141507 -1.1868 0.117650 10 to 11 141867 -0.1249 0.450314 9 to 10 141819 -0.2665 0.394942 8 to 9 141165 -2.1957 0.014058 7 to 8 142544 1.8722 0.969409 6 to 7 141641 -0.7915 0.214316 5 to 6 141883 -0.0777 0.469045 4 to 5 141502 -1.2016 0.114766 3 to 4 141879 -0.0895 0.464355 2 to 3 141737 -0.5083 0.305605 1 to 2 141680 -0.6765 0.249365 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-10_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2436.55 -0.897 0.184774 Test results for specific bytes for dh-ranFile-2016-04-10_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2521.55 0.305 0.619737 2 to 9 2577.04 1.089 0.862027 3 to 10 2495.34 -0.066 0.473737 4 to 11 2476.52 -0.332 0.369915 5 to 12 2547.77 0.676 0.750339 6 to 13 2483.90 -0.228 0.409920 7 to 14 2509.21 0.130 0.551814 8 to 15 2591.20 1.290 0.901444 9 to 16 2435.59 -0.911 0.181184 10 to 17 2646.62 2.073 0.980936 11 to 18 2428.95 -1.005 0.157497 12 to 19 2486.32 -0.193 0.423305 13 to 20 2548.70 0.689 0.754501 14 to 21 2473.50 -0.375 0.353895 15 to 22 2719.62 3.106 0.999052 16 to 23 2379.79 -1.700 0.044561 17 to 24 2438.60 -0.868 0.192615 18 to 25 2517.37 0.246 0.597018 19 to 26 2461.96 -0.538 0.295304 20 to 27 2576.13 1.077 0.859181 21 to 28 2508.33 0.118 0.546882 22 to 29 2408.55 -1.293 0.097955 23 to 30 2541.26 0.584 0.720238 24 to 31 2481.11 -0.267 0.394660 25 to 32 2490.68 -0.132 0.447586 CDPARK for dh-ranFile-2016-04-10_13:31: 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 3569 2.1005 0.982156 3546 1.0502 0.853193 3509 -0.6393 0.261324 3491 -1.4612 0.071982 3531 0.3653 0.642555 3500 -1.0502 0.146807 3497 -1.1872 0.117571 3487 -1.6438 0.050105 3547 1.0959 0.863437 3512 -0.5023 0.307734 Square side=100, avg. no. parked=3518.90 sample std.=26.38 p-value of the KSTEST for those 10 p-values: 0.324546 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-10_13:31 0.1147,0.6282,0.1966,0.4625,0.6922,0.5067,0.5222,0.7912,0.7000,0.9387, The KS test for those 10 p-values: 0.720480 The 3DSPHERES test for dh-ranFile-2016-04-10_13:31 sample no r^3 equiv. uni. 1 9.398 0.268939 2 36.123 0.700033 3 11.336 0.314668 4 31.542 0.650553 5 37.391 0.712454 6 0.750 0.024700 7 114.130 0.977726 8 30.779 0.641552 9 36.477 0.703559 10 7.348 0.217252 11 13.324 0.358613 12 0.939 0.030802 13 22.619 0.529508 14 64.461 0.883363 15 14.318 0.379521 16 0.013 0.000432 17 0.023 0.000766 18 5.015 0.153938 19 35.497 0.693710 20 13.210 0.356175 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.111885 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-10_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 0.3 -0.1 0.1 0.4 -1.6 1.0 0.4 1.3 -1.2 -1.3 -0.6 -0.1 0.3 0.1 1.5 0.7 0.9 -1.5 0.1 0.4 -0.2 -0.7 0.2 -0.6 -0.7 -1.0 0.0 0.5 1.3 -1.2 0.5 1.6 0.3 0.2 -0.7 3.0 0.1 0.4 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:38.028768 z-score=-0.433297, p-value=0.354071 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-10_13:31 Test no p-value 1 0.713590 2 0.089083 3 0.550699 4 0.020465 5 0.042604 6 0.618315 7 0.018852 8 0.263446 9 0.003902 10 0.439521 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.004045 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-10_13:31: (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 66769 0.16 66774 0.17 3 25000.00 24982 0.01 24977 0.02 4 6666.67 6588 0.93 6574 1.29 5 1388.89 1349 1.15 1389 0.00 6 238.10 275 5.72 241 0.04 7 34.72 35 0.00 41 1.14 8 4.96 1 3.16 3 0.77 p=0.91550 p=0.24647 Number of rngs required: 687199, p-value: 0.080 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-10_13:31 No. of wins: Observed Expected 98920 98585.9 z-score= 1.494, pvalue=0.93247 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67000 66666.7 1.667 1.667 2 37698 37654.3 0.051 1.717 3 26922 26954.7 0.040 1.757 4 19357 19313.5 0.098 1.855 5 13756 13851.4 0.657 2.513 6 9917 9943.5 0.071 2.583 7 7166 7145.0 0.062 2.645 8 5066 5139.1 1.039 3.684 9 3594 3699.9 3.029 6.713 10 2657 2666.3 0.032 6.746 11 1947 1923.3 0.291 7.037 12 1353 1388.7 0.920 7.957 13 997 1003.7 0.045 8.002 14 742 726.1 0.346 8.348 15 507 525.8 0.675 9.023 16 367 381.2 0.525 9.548 17 268 276.5 0.264 9.812 18 180 200.8 2.160 11.972 19 126 146.0 2.736 14.708 20 103 106.2 0.097 14.805 21 277 287.1 0.356 15.162 Chisq= 15.16 for 20 degrees of freedom, p= 0.23291 SUMMARY of craptest p-value for no. of wins: 0.932474 p-value for throws/game: 0.232910 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-10_13:31 No. of wins: Observed Expected 98924 98585.9 z-score= 1.512, pvalue=0.93478 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66999 66666.7 1.657 1.657 2 37700 37654.3 0.055 1.712 3 26874 26954.7 0.242 1.954 4 19251 19313.5 0.202 2.156 5 13758 13851.4 0.630 2.786 6 9914 9943.5 0.088 2.874 7 7119 7145.0 0.095 2.969 8 5090 5139.1 0.469 3.437 9 3702 3699.9 0.001 3.438 10 2644 2666.3 0.186 3.625 11 1896 1923.3 0.388 4.013 12 1435 1388.7 1.541 5.554 13 1005 1003.7 0.002 5.556 14 743 726.1 0.391 5.947 15 542 525.8 0.497 6.444 16 370 381.2 0.326 6.770 17 262 276.5 0.764 7.535 18 177 200.8 2.828 10.362 19 131 146.0 1.538 11.900 20 95 106.2 1.184 13.085 21 293 287.1 0.121 13.205 Chisq= 13.21 for 20 degrees of freedom, p= 0.13159 SUMMARY of craptest p-value for no. of wins: 0.934780 p-value for throws/game: 0.131594 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0008,0.0039,0.0040,0.0141,0.0189,0.0205,0.0234,0.0247,0.0266, 0.0308,0.0371,0.0426,0.0446,0.0501,0.0521,0.0680,0.0698,0.0720,0.0786, 0.0802,0.0813,0.0853,0.0891,0.0927,0.0968,0.0980,0.1001,0.1072,0.1119, 0.1147,0.1148,0.1176,0.1177,0.1265,0.1268,0.1316,0.1345,0.1360,0.1406, 0.1446,0.1468,0.1494,0.1511,0.1539,0.1575,0.1640,0.1746,0.1812,0.1848, 0.1878,0.1926,0.1966,0.1970,0.2143,0.2173,0.2196,0.2241,0.2255,0.2276, 0.2306,0.2306,0.2329,0.2400,0.2414,0.2453,0.2465,0.2466,0.2494,0.2569, 0.2594,0.2613,0.2627,0.2634,0.2664,0.2685,0.2689,0.2714,0.2728,0.2822, 0.2953,0.2957,0.2997,0.3025,0.3056,0.3061,0.3077,0.3118,0.3123,0.3147, 0.3232,0.3245,0.3255,0.3292,0.3392,0.3460,0.3539,0.3541,0.3562,0.3582, 0.3584,0.3586,0.3618,0.3626,0.3645,0.3699,0.3771,0.3795,0.3859,0.3893, 0.3915,0.3945,0.3947,0.3949,0.3962,0.4099,0.4149,0.4177,0.4233,0.4236, 0.4270,0.4338,0.4395,0.4470,0.4476,0.4503,0.4560,0.4586,0.4625,0.4644, 0.4671,0.4690,0.4734,0.4737,0.4755,0.4764,0.4808,0.4874,0.4927,0.4933, 0.4940,0.5009,0.5062,0.5067,0.5147,0.5222,0.5252,0.5279,0.5295,0.5435, 0.5442,0.5469,0.5475,0.5507,0.5510,0.5512,0.5518,0.5538,0.5559,0.5629, 0.5672,0.5735,0.5801,0.5829,0.5839,0.5846,0.5970,0.6025,0.6090,0.6091, 0.6148,0.6183,0.6197,0.6235,0.6271,0.6282,0.6348,0.6416,0.6426,0.6488, 0.6506,0.6517,0.6621,0.6651,0.6800,0.6881,0.6883,0.6918,0.6922,0.6937, 0.6937,0.6958,0.6964,0.6971,0.6995,0.7000,0.7000,0.7010,0.7021,0.7036, 0.7125,0.7136,0.7174,0.7176,0.7202,0.7205,0.7239,0.7242,0.7265,0.7390, 0.7431,0.7503,0.7503,0.7545,0.7579,0.7586,0.7643,0.7659,0.7772,0.7781, 0.7816,0.7836,0.7863,0.7877,0.7912,0.8023,0.8146,0.8212,0.8325,0.8380, 0.8386,0.8509,0.8516,0.8532,0.8566,0.8592,0.8620,0.8632,0.8634,0.8651, 0.8732,0.8774,0.8834,0.8840,0.8894,0.8934,0.9014,0.9017,0.9019,0.9028, 0.9061,0.9115,0.9155,0.9294,0.9325,0.9348,0.9349,0.9381,0.9387,0.9411, 0.9626,0.9694,0.9705,0.9777,0.9809,0.9822,0.9831,0.9842,0.9991, Overall p-value after applying KStest on 269 p-values = 0.565189 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.