RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-16_14:31 (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 20.1636 0.734053 2 to 25 16.06 19.4629 0.697383 3 to 26 15.96 12.1674 0.210106 4 to 27 15.79 15.6292 0.449742 5 to 28 15.88 20.4235 0.746856 6 to 29 15.78 18.2928 0.629402 7 to 30 15.80 21.1470 0.780215 8 to 31 15.79 14.2355 0.349636 9 to 32 15.68 20.7788 0.763659 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.238121 Tough bday spacings test for dh-ranFile-2016-02-16_14:31: 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 7 39 78 85 91 83 60 33 17 7 0 (O-E)^2/E 0.5 0.2 0.3 1.6 0.5 0.3 1.2 0.4 0.3 0.0 4.1 Birthday Spacings: Sum(O-E)^2/E= 9.311, p= 0.497 RESULTS OF GCD FOR dh-ranFile-2016-02-16_14:31 Euclid's algorithm: p-value, steps to gcd: 0.247273 p-value, dist. of gcd's: 0.330014 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-16_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.193 0.089 0.887 0.391 0.575 0.396 0.691 0.748 Bits 8 to 15---> 0.938 0.995 0.657 0.298 0.430 0.905 0.711 0.400 Bits 16 to 23---> 0.304 0.492 0.572 0.040 0.323 0.356 0.122 0.911 Bits 24 to 31---> 0.959 0.497 0.320 0.970 0.638 0.376 0.305 0.976 KS test for the above 32 p values: 0.682 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-16_14:31, p-values for 5 runs: 0.6918, 0.9160, 0.8378, 0.2240, 0.5936 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-16_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5301 5134.0 5.432 5.636 r= 30 23072 23103.0 0.042 5.678 r= 31 11409 11551.5 1.758 7.437 chi-square = 7.437 with df = 3; p-value = 0.941 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-16_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5195 5134.0 0.725 1.060 r= 31 23076 23103.0 0.032 1.091 r= 32 11526 11551.5 0.056 1.148 chi-square = 1.148 with df = 3; p-value = 0.234 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-16_14:31 b-rank test for bits 1 to 8, p=0.68852 b-rank test for bits 2 to 9, p=0.20055 b-rank test for bits 3 to 10, p=0.09119 b-rank test for bits 4 to 11, p=0.30168 b-rank test for bits 5 to 12, p=0.71250 b-rank test for bits 6 to 13, p=0.18393 b-rank test for bits 7 to 14, p=0.73585 b-rank test for bits 8 to 15, p=0.84443 b-rank test for bits 9 to 16, p=0.95742 b-rank test for bits 10 to 17, p=0.91975 b-rank test for bits 11 to 18, p=0.96917 b-rank test for bits 12 to 19, p=0.61862 b-rank test for bits 13 to 20, p=0.32007 b-rank test for bits 14 to 21, p=0.55591 b-rank test for bits 15 to 22, p=0.41221 b-rank test for bits 16 to 23, p=0.69939 b-rank test for bits 17 to 24, p=0.82403 b-rank test for bits 18 to 25, p=0.99929 b-rank test for bits 19 to 26, p=0.09031 b-rank test for bits 20 to 27, p=0.66631 b-rank test for bits 21 to 28, p=0.56408 b-rank test for bits 22 to 29, p=0.27731 b-rank test for bits 23 to 30, p=0.18412 b-rank test for bits 24 to 31, p=0.48633 b-rank test for bits 25 to 32, p=0.42933 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 = 0.594146 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-16_14:31 (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 141867 -0.10 0.460608 2 142591 1.59 0.944385 3 141637 -0.64 0.262295 4 141857 -0.12 0.451344 5 142651 1.73 0.958441 6 141058 -1.99 0.023346 7 141914 0.01 0.504353 8 141489 -0.98 0.163030 9 141814 -0.22 0.411871 10 142313 0.94 0.827199 11 142389 1.12 0.868797 12 141380 -1.24 0.108090 13 142236 0.76 0.777342 14 142116 0.48 0.685407 15 142052 0.33 0.630562 16 141495 -0.97 0.166507 17 141774 -0.32 0.375929 18 141868 -0.10 0.461536 19 141384 -1.23 0.109835 20 142354 1.04 0.850586 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-16_14:31 Bits used No. missing words z-score p-value 23 to 32 142194 0.9816 0.836857 22 to 31 142011 0.3506 0.637051 21 to 30 142174 0.9127 0.819288 20 to 29 142092 0.6299 0.735619 19 to 28 141985 0.2609 0.602927 18 to 27 141826 -0.2873 0.386924 17 to 26 142016 0.3678 0.643499 16 to 25 141380 -1.8253 0.033980 15 to 24 141617 -1.0080 0.156719 14 to 23 142038 0.4437 0.671367 13 to 22 141953 0.1506 0.559849 12 to 21 141623 -0.9873 0.161737 11 to 20 141868 -0.1425 0.443336 10 to 19 141846 -0.2184 0.413567 9 to 18 141712 -0.6804 0.248110 8 to 17 141752 -0.5425 0.293731 7 to 16 142628 2.4782 0.993397 6 to 15 142352 1.5264 0.936551 5 to 14 141603 -1.0563 0.145413 4 to 13 141949 0.1368 0.554403 3 to 12 142433 1.8058 0.964522 2 to 11 141743 -0.5736 0.283136 1 to 10 141419 -1.6908 0.045438 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-16_14:31 Bits used No. missing words z-score p-value 28 to 32 142069 0.5413 0.705834 27 to 31 141865 -0.1503 0.440275 26 to 30 142470 1.9006 0.971321 25 to 29 142545 2.1548 0.984412 24 to 28 141626 -0.9604 0.168417 23 to 27 141814 -0.3232 0.373290 22 to 26 142284 1.2701 0.897970 21 to 25 141356 -1.8757 0.030349 20 to 24 142069 0.5413 0.705834 19 to 23 142457 1.8565 0.968309 18 to 22 142090 0.6124 0.729877 17 to 21 141871 -0.1299 0.448310 16 to 20 141931 0.0735 0.529279 15 to 19 141658 -0.8520 0.197116 14 to 18 141904 -0.0181 0.492792 13 to 17 142054 0.4904 0.688077 12 to 16 141954 0.1514 0.560179 11 to 15 141815 -0.3198 0.374574 10 to 14 141679 -0.7808 0.217466 9 to 13 142469 1.8972 0.971098 8 to 12 141557 -1.1943 0.116173 7 to 11 142182 0.9243 0.822336 6 to 10 141735 -0.5909 0.277277 5 to 9 142022 0.3819 0.648744 4 to 8 141586 -1.0960 0.136532 3 to 7 142032 0.4158 0.661233 2 to 6 141972 0.2124 0.584118 1 to 5 141676 -0.7909 0.214487 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-16_14:31 Bits used No. missing words z-score p-value 31 to 32 141508 -1.1839 0.118233 30 to 31 142090 0.5329 0.702966 29 to 30 142034 0.3678 0.643473 28 to 29 141722 -0.5526 0.290270 27 to 28 142023 0.3353 0.631304 26 to 27 142174 0.7807 0.782522 25 to 26 141446 -1.3668 0.085851 24 to 25 141698 -0.6234 0.266513 23 to 24 141570 -1.0010 0.158420 22 to 23 142044 0.3973 0.654411 21 to 22 141894 -0.0452 0.481966 20 to 21 142171 0.7719 0.779910 19 to 20 142071 0.4769 0.683284 18 to 19 141754 -0.4582 0.323404 17 to 18 142873 2.8427 0.997763 16 to 17 141540 -1.0895 0.137974 15 to 16 141362 -1.6145 0.053205 14 to 15 142060 0.4445 0.671643 13 to 14 142011 0.2999 0.617878 12 to 13 141352 -1.6440 0.050084 11 to 12 142235 0.9607 0.831643 10 to 11 142476 1.6716 0.952698 9 to 10 141523 -1.1396 0.127223 8 to 9 142202 0.8633 0.806023 7 to 8 142404 1.4592 0.927745 6 to 7 141872 -0.1101 0.456158 5 to 6 141974 0.1908 0.575646 4 to 5 142132 0.6568 0.744359 3 to 4 141641 -0.7915 0.214316 2 to 3 142446 1.5831 0.943300 1 to 2 141909 -0.0010 0.499612 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-16_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2396.46 -1.464 0.071568 Test results for specific bytes for dh-ranFile-2016-02-16_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2514.52 0.205 0.581365 2 to 9 2390.09 -1.554 0.060043 3 to 10 2603.31 1.461 0.927990 4 to 11 2483.68 -0.231 0.408720 5 to 12 2406.44 -1.323 0.092892 6 to 13 2519.84 0.281 0.610464 7 to 14 2486.21 -0.195 0.422699 8 to 15 2569.02 0.976 0.835499 9 to 16 2504.35 0.061 0.524512 10 to 17 2587.72 1.241 0.892616 11 to 18 2466.45 -0.475 0.317568 12 to 19 2541.06 0.581 0.719277 13 to 20 2594.68 1.339 0.909715 14 to 21 2541.41 0.586 0.720956 15 to 22 2490.78 -0.130 0.448155 16 to 23 2550.10 0.708 0.760674 17 to 24 2604.53 1.478 0.930328 18 to 25 2492.97 -0.099 0.460411 19 to 26 2471.99 -0.396 0.346004 20 to 27 2425.47 -1.054 0.145938 21 to 28 2497.08 -0.041 0.483539 22 to 29 2466.89 -0.468 0.319800 23 to 30 2587.36 1.235 0.891674 24 to 31 2633.65 1.890 0.970631 25 to 32 2589.06 1.259 0.896065 CDPARK for dh-ranFile-2016-02-16_14:31: 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 3537 0.6393 0.738676 3515 -0.3653 0.357445 3524 0.0457 0.518210 3564 1.8721 0.969407 3496 -1.2329 0.108811 3562 1.7808 0.962529 3506 -0.7763 0.218799 3488 -1.5982 0.055002 3517 -0.2740 0.392053 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3521.10 sample std.=24.79 p-value of the KSTEST for those 10 p-values: 0.602216 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-16_14:31 0.8867,0.1193,0.6065,0.0956,0.0702,0.7762,0.4810,0.7035,0.5175,0.2053, The KS test for those 10 p-values: 0.782918 The 3DSPHERES test for dh-ranFile-2016-02-16_14:31 sample no r^3 equiv. uni. 1 16.058 0.414490 2 23.608 0.544768 3 1.935 0.062464 4 54.596 0.837951 5 15.214 0.397789 6 2.970 0.094255 7 32.118 0.657202 8 61.591 0.871654 9 4.365 0.135405 10 81.441 0.933776 11 35.981 0.698614 12 13.643 0.365408 13 4.672 0.144223 14 99.391 0.963594 15 6.775 0.202160 16 43.353 0.764275 17 0.236 0.007823 18 13.800 0.368724 19 101.781 0.966383 20 80.491 0.931645 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.600219 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-16_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 1.3 -0.1 -0.1 -0.5 1.6 -0.8 1.3 2.0 0.0 0.4 -0.2 -0.9 -0.8 -0.1 0.3 1.9 -1.3 -0.7 1.0 -0.5 -1.1 0.5 -0.5 0.0 1.3 -1.0 -0.1 0.4 -0.5 -0.9 0.7 0.0 0.7 1.3 -1.7 0.3 -1.7 -1.6 1.0 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:41.739751 z-score=-0.028395, p-value=0.517709 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-16_14:31 Test no p-value 1 0.027282 2 0.482998 3 0.105046 4 0.050257 5 0.000594 6 0.103991 7 0.810150 8 0.570295 9 0.621864 10 0.099249 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.006434 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-16_14:31: (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 66810 0.31 66748 0.10 3 25000.00 25012 0.01 24790 1.76 4 6666.67 6498 4.27 6747 0.97 5 1388.89 1402 0.12 1413 0.42 6 238.10 239 0.00 250 0.60 7 34.72 35 0.00 41 1.14 8 4.96 3 0.77 10 5.12 p=0.51677 p=0.87958 Number of rngs required: 689636, p-value: 0.925 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-16_14:31 No. of wins: Observed Expected 98327 98585.9 z-score=-1.158, pvalue=0.12348 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66700 66666.7 0.017 0.017 2 37277 37654.3 3.781 3.798 3 27141 26954.7 1.287 5.085 4 19351 19313.5 0.073 5.158 5 13984 13851.4 1.269 6.427 6 10025 9943.5 0.667 7.094 7 7125 7145.0 0.056 7.150 8 5144 5139.1 0.005 7.155 9 3650 3699.9 0.672 7.827 10 2681 2666.3 0.081 7.908 11 1938 1923.3 0.112 8.020 12 1381 1388.7 0.043 8.063 13 1003 1003.7 0.001 8.064 14 720 726.1 0.052 8.116 15 544 525.8 0.627 8.743 16 398 381.2 0.745 9.488 17 255 276.5 1.678 11.166 18 184 200.8 1.410 12.576 19 134 146.0 0.984 13.560 20 95 106.2 1.184 14.744 21 270 287.1 1.020 15.764 Chisq= 15.76 for 20 degrees of freedom, p= 0.26885 SUMMARY of craptest p-value for no. of wins: 0.123480 p-value for throws/game: 0.268854 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-16_14:31 No. of wins: Observed Expected 98672 98585.9 z-score= 0.385, pvalue=0.64998 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66729 66666.7 0.058 0.058 2 37710 37654.3 0.082 0.141 3 26806 26954.7 0.821 0.961 4 19147 19313.5 1.435 2.396 5 14108 13851.4 4.753 7.149 6 9869 9943.5 0.559 7.708 7 7149 7145.0 0.002 7.710 8 5043 5139.1 1.796 9.506 9 3680 3699.9 0.107 9.613 10 2747 2666.3 2.443 12.055 11 1884 1923.3 0.804 12.859 12 1429 1388.7 1.167 14.027 13 1025 1003.7 0.451 14.478 14 754 726.1 1.069 15.547 15 507 525.8 0.675 16.222 16 375 381.2 0.099 16.321 17 272 276.5 0.075 16.395 18 217 200.8 1.302 17.697 19 143 146.0 0.061 17.758 20 112 106.2 0.315 18.073 21 294 287.1 0.165 18.238 Chisq= 18.24 for 20 degrees of freedom, p= 0.42830 SUMMARY of craptest p-value for no. of wins: 0.649983 p-value for throws/game: 0.428298 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0064,0.0078,0.0233,0.0273,0.0303,0.0340,0.0401,0.0454,0.0501, 0.0503,0.0532,0.0550,0.0600,0.0625,0.0702,0.0716,0.0859,0.0892,0.0903, 0.0912,0.0929,0.0943,0.0956,0.0992,0.1040,0.1050,0.1081,0.1088,0.1098, 0.1162,0.1182,0.1193,0.1217,0.1235,0.1272,0.1354,0.1365,0.1380,0.1442, 0.1454,0.1459,0.1567,0.1584,0.1617,0.1630,0.1665,0.1684,0.1688,0.1839, 0.1841,0.1928,0.1971,0.2005,0.2022,0.2053,0.2101,0.2143,0.2145,0.2175, 0.2188,0.2240,0.2344,0.2381,0.2473,0.2481,0.2623,0.2665,0.2689,0.2773, 0.2773,0.2831,0.2903,0.2937,0.2977,0.3017,0.3035,0.3049,0.3176,0.3197, 0.3198,0.3201,0.3229,0.3234,0.3300,0.3460,0.3496,0.3561,0.3574,0.3654, 0.3687,0.3733,0.3746,0.3758,0.3759,0.3869,0.3907,0.3921,0.3957,0.3978, 0.3996,0.4087,0.4119,0.4122,0.4136,0.4145,0.4227,0.4283,0.4293,0.4297, 0.4403,0.4433,0.4482,0.4483,0.4497,0.4513,0.4562,0.4604,0.4606,0.4615, 0.4810,0.4820,0.4830,0.4835,0.4863,0.4918,0.4928,0.4972,0.4974,0.4996, 0.5044,0.5168,0.5175,0.5177,0.5182,0.5245,0.5293,0.5448,0.5544,0.5559, 0.5598,0.5602,0.5641,0.5703,0.5719,0.5754,0.5756,0.5814,0.5841,0.5936, 0.5941,0.6002,0.6022,0.6029,0.6065,0.6105,0.6179,0.6186,0.6219,0.6294, 0.6306,0.6313,0.6371,0.6376,0.6435,0.6435,0.6487,0.6500,0.6544,0.6572, 0.6572,0.6612,0.6663,0.6714,0.6716,0.6820,0.6833,0.6854,0.6881,0.6885, 0.6906,0.6918,0.6974,0.6986,0.6994,0.7030,0.7035,0.7058,0.7058,0.7108, 0.7125,0.7193,0.7210,0.7299,0.7341,0.7356,0.7359,0.7387,0.7444,0.7469, 0.7476,0.7607,0.7637,0.7643,0.7762,0.7773,0.7799,0.7802,0.7825,0.7829, 0.8060,0.8101,0.8193,0.8223,0.8240,0.8272,0.8316,0.8355,0.8369,0.8378, 0.8380,0.8444,0.8506,0.8688,0.8717,0.8796,0.8867,0.8867,0.8917,0.8926, 0.8961,0.8980,0.9053,0.9097,0.9113,0.9160,0.9197,0.9249,0.9277,0.9280, 0.9303,0.9316,0.9338,0.9366,0.9383,0.9408,0.9433,0.9444,0.9527,0.9574, 0.9584,0.9591,0.9625,0.9636,0.9645,0.9664,0.9683,0.9692,0.9694,0.9704, 0.9706,0.9711,0.9713,0.9765,0.9844,0.9934,0.9949,0.9978,0.9993, Overall p-value after applying KStest on 269 p-values = 0.333357 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.