RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 8.6216 0.048608 2 to 25 15.85 14.9237 0.399019 3 to 26 15.81 20.5792 0.754321 4 to 27 15.65 14.1127 0.340890 5 to 28 15.61 17.6675 0.589898 6 to 29 15.90 13.8140 0.319780 7 to 30 15.56 29.2281 0.967521 8 to 31 15.64 15.3573 0.430234 9 to 32 15.46 32.7263 0.987794 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.619202 Tough bday spacings test for dh-ranFile-2018-06-30_11:31: 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 13 37 70 108 92 78 53 30 9 5 5 (O-E)^2/E 1.6 0.0 0.1 1.1 0.3 0.0 0.0 0.0 2.3 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.135, p= 0.196 RESULTS OF GCD FOR dh-ranFile-2018-06-30_11:31 Euclid's algorithm: p-value, steps to gcd: 0.697698 p-value, dist. of gcd's: 0.852722 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.959 0.409 0.070 0.840 0.985 0.474 0.671 0.149 Bits 8 to 15---> 0.310 0.168 0.040 0.686 0.082 0.442 0.644 0.842 Bits 16 to 23---> 0.249 0.776 0.347 0.064 0.201 0.545 0.477 0.160 Bits 24 to 31---> 0.298 0.149 0.280 0.140 0.736 0.515 0.792 0.025 KS test for the above 32 p values: 0.781 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_11:31, p-values for 5 runs: 0.3212, 0.8379, 0.3297, 0.9639, 0.5944 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5220 5134.0 1.440 1.468 r= 30 23068 23103.0 0.053 1.521 r= 31 11503 11551.5 0.204 1.725 chi-square = 1.725 with df = 3; p-value = 0.369 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5261 5134.0 3.141 3.336 r= 31 22966 23103.0 0.813 4.149 r= 32 11568 11551.5 0.024 4.172 chi-square = 4.172 with df = 3; p-value = 0.757 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_11:31 b-rank test for bits 1 to 8, p=0.26576 b-rank test for bits 2 to 9, p=0.85387 b-rank test for bits 3 to 10, p=0.99926 b-rank test for bits 4 to 11, p=0.72190 b-rank test for bits 5 to 12, p=0.45595 b-rank test for bits 6 to 13, p=0.23664 b-rank test for bits 7 to 14, p=0.76775 b-rank test for bits 8 to 15, p=0.93273 b-rank test for bits 9 to 16, p=0.54261 b-rank test for bits 10 to 17, p=0.33589 b-rank test for bits 11 to 18, p=0.90906 b-rank test for bits 12 to 19, p=0.68646 b-rank test for bits 13 to 20, p=0.12743 b-rank test for bits 14 to 21, p=0.15269 b-rank test for bits 15 to 22, p=0.10966 b-rank test for bits 16 to 23, p=0.18749 b-rank test for bits 17 to 24, p=0.73823 b-rank test for bits 18 to 25, p=0.09547 b-rank test for bits 19 to 26, p=0.87540 b-rank test for bits 20 to 27, p=0.28092 b-rank test for bits 21 to 28, p=0.21844 b-rank test for bits 22 to 29, p=0.52477 b-rank test for bits 23 to 30, p=0.02819 b-rank test for bits 24 to 31, p=0.99397 b-rank test for bits 25 to 32, p=0.06427 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 = 0.430441 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_11:31 (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 142585 1.58 0.942794 2 142328 0.98 0.836013 3 141985 0.18 0.570167 4 141963 0.13 0.549895 5 141097 -1.90 0.028850 6 142674 1.79 0.963000 7 142025 0.27 0.606519 8 142130 0.52 0.696928 9 142548 1.49 0.932179 10 141961 0.12 0.548045 11 141685 -0.52 0.300092 12 142058 0.35 0.635840 13 141938 0.07 0.526704 14 142166 0.60 0.725646 15 141983 0.17 0.568331 16 142472 1.31 0.905686 17 142193 0.66 0.746264 18 142377 1.09 0.862734 19 141421 -1.14 0.126944 20 141771 -0.32 0.373272 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-30_11:31 Bits used No. missing words z-score p-value 23 to 32 141389 -1.7942 0.036387 22 to 31 141517 -1.3529 0.088050 21 to 30 141851 -0.2011 0.420295 20 to 29 142150 0.8299 0.796701 19 to 28 141838 -0.2460 0.402855 18 to 27 141803 -0.3667 0.356938 17 to 26 141466 -1.5287 0.063166 16 to 25 141584 -1.1218 0.130968 15 to 24 141836 -0.2529 0.400187 14 to 23 141632 -0.9563 0.169458 13 to 22 141882 -0.0942 0.462459 12 to 21 141926 0.0575 0.522920 11 to 20 141752 -0.5425 0.293731 10 to 19 141857 -0.1804 0.428400 9 to 18 141640 -0.9287 0.176516 8 to 17 142160 0.8644 0.806310 7 to 16 141373 -1.8494 0.032199 6 to 15 141696 -0.7356 0.230981 5 to 14 141405 -1.7391 0.041011 4 to 13 141504 -1.3977 0.081103 3 to 12 141927 0.0609 0.524293 2 to 11 141803 -0.3667 0.356938 1 to 10 141968 0.2023 0.580163 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-30_11:31 Bits used No. missing words z-score p-value 28 to 32 142870 3.2565 0.999436 27 to 31 142065 0.5277 0.701145 26 to 30 141678 -0.7842 0.216470 25 to 29 141518 -1.3265 0.092330 24 to 28 142343 1.4701 0.929228 23 to 27 141809 -0.3401 0.366890 22 to 26 141942 0.1107 0.544091 21 to 25 142042 0.4497 0.673547 20 to 24 141548 -1.2248 0.110316 19 to 23 141720 -0.6418 0.260503 18 to 22 141861 -0.1638 0.434932 17 to 21 142731 2.7853 0.997326 16 to 20 141699 -0.7130 0.237928 15 to 19 142071 0.5480 0.708166 14 to 18 141772 -0.4655 0.320778 13 to 17 141707 -0.6859 0.246399 12 to 16 142150 0.8158 0.792702 11 to 15 141553 -1.2079 0.113543 10 to 14 141968 0.1989 0.578822 9 to 13 141707 -0.6859 0.246399 8 to 12 141796 -0.3842 0.350426 7 to 11 141868 -0.1401 0.444290 6 to 10 141993 0.2836 0.611652 5 to 9 141749 -0.5435 0.293396 4 to 8 142255 1.1718 0.879354 3 to 7 141941 0.1074 0.542747 2 to 6 141750 -0.5401 0.294564 1 to 5 141334 -1.9503 0.025572 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-30_11:31 Bits used No. missing words z-score p-value 31 to 32 142671 2.2468 0.987674 30 to 31 141785 -0.3668 0.356901 29 to 30 141974 0.1908 0.575646 28 to 29 141931 0.0639 0.525484 27 to 28 141559 -1.0334 0.150703 26 to 27 142270 1.0639 0.856318 25 to 26 142004 0.2793 0.609978 24 to 25 141994 0.2498 0.598615 23 to 24 141934 0.0728 0.529007 22 to 23 141642 -0.7886 0.215178 21 to 22 141491 -1.2340 0.108599 20 to 21 141987 0.2291 0.590610 19 to 20 141915 0.0167 0.506672 18 to 19 141472 -1.2901 0.098515 17 to 18 140606 -3.8446 0.000060 16 to 17 142359 1.3265 0.907656 15 to 16 141788 -0.3579 0.360207 14 to 15 141360 -1.6204 0.052569 13 to 14 142371 1.3619 0.913379 12 to 13 141534 -1.1072 0.134111 11 to 12 141613 -0.8741 0.191024 10 to 11 141914 0.0138 0.505496 9 to 10 142161 0.7424 0.771074 8 to 9 141662 -0.7296 0.232821 7 to 8 142145 0.6952 0.756532 6 to 7 141712 -0.5821 0.280252 5 to 6 141865 -0.1308 0.447980 4 to 5 142087 0.5241 0.699896 3 to 4 141889 -0.0600 0.476090 2 to 3 141980 0.2085 0.582568 1 to 2 142326 1.2291 0.890486 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2319.26 -2.556 0.005293 Test results for specific bytes for dh-ranFile-2018-06-30_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2460.03 -0.565 0.285943 2 to 9 2505.29 0.075 0.529793 3 to 10 2326.78 -2.450 0.007148 4 to 11 2342.37 -2.229 0.012902 5 to 12 2573.08 1.033 0.849309 6 to 13 2496.72 -0.046 0.481493 7 to 14 2270.56 -3.245 0.000588 8 to 15 2519.51 0.276 0.608671 9 to 16 2461.73 -0.541 0.294156 10 to 17 2777.64 3.926 0.999957 11 to 18 2545.66 0.646 0.740765 12 to 19 2503.45 0.049 0.519444 13 to 20 2503.24 0.046 0.518287 14 to 21 2441.90 -0.822 0.205625 15 to 22 2557.68 0.816 0.792664 16 to 23 2505.60 0.079 0.531536 17 to 24 2449.13 -0.719 0.235927 18 to 25 2668.00 2.376 0.991245 19 to 26 2412.92 -1.232 0.109061 20 to 27 2505.02 0.071 0.528276 21 to 28 2526.96 0.381 0.648507 22 to 29 2375.35 -1.763 0.038961 23 to 30 2447.96 -0.736 0.230900 24 to 31 2534.10 0.482 0.685190 25 to 32 2485.20 -0.209 0.417120 CDPARK for dh-ranFile-2018-06-30_11:31: 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 3530 0.3196 0.625377 3520 -0.1370 0.445521 3535 0.5479 0.708135 3525 0.0913 0.536383 3542 0.8676 0.807188 3516 -0.3196 0.374623 3524 0.0457 0.518210 3520 -0.1370 0.445521 3518 -0.2283 0.409702 3507 -0.7306 0.232514 Square side=100, avg. no. parked=3523.70 sample std.=9.50 p-value of the KSTEST for those 10 p-values: 0.292264 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_11:31 0.0409,0.6359,0.8961,0.8161,0.9585,0.9248,0.2999,0.6052,0.1027,0.2312, The KS test for those 10 p-values: 0.615603 The 3DSPHERES test for dh-ranFile-2018-06-30_11:31 sample no r^3 equiv. uni. 1 28.907 0.618475 2 14.262 0.378360 3 8.959 0.258161 4 26.145 0.581680 5 25.081 0.566567 6 15.197 0.397440 7 7.457 0.220084 8 40.198 0.738136 9 57.271 0.851775 10 4.651 0.143624 11 22.091 0.521148 12 6.389 0.191819 13 24.404 0.556680 14 47.722 0.796227 15 31.159 0.646064 16 28.423 0.612269 17 48.808 0.803466 18 34.931 0.687877 19 9.440 0.269975 20 2.637 0.084144 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.523871 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.5 -0.8 1.4 1.3 0.1 -1.4 0.4 -1.9 2.4 -0.2 0.4 1.1 0.1 -1.1 -2.2 -0.5 -0.3 0.2 0.1 0.5 0.3 1.0 -0.6 -0.0 0.2 1.2 1.0 -0.8 0.2 1.0 0.4 0.0 -0.9 -1.0 1.9 0.3 -0.7 0.1 -0.7 -1.3 0.0 1.8 Chi-square with 42 degrees of freedom:43.593910 z-score=0.173910, p-value=0.596521 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-30_11:31 Test no p-value 1 0.578352 2 0.296728 3 0.008832 4 0.140254 5 0.065133 6 0.004057 7 0.451826 8 0.597472 9 0.990448 10 0.391783 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.061076 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_11:31: (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 66891 0.75 66511 0.36 3 25000.00 24827 1.20 25151 0.91 4 6666.67 6617 0.37 6625 0.26 5 1388.89 1387 0.00 1436 1.60 6 238.10 233 0.11 236 0.02 7 34.72 42 1.53 37 0.15 8 4.96 2 1.77 3 0.77 p=0.54550 p=0.33369 Number of rngs required: 689383, p-value: 0.872 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_11:31 No. of wins: Observed Expected 98458 98585.9 z-score=-0.572, pvalue=0.28371 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66417 66666.7 0.935 0.935 2 37695 37654.3 0.044 0.979 3 27083 26954.7 0.610 1.589 4 19243 19313.5 0.257 1.846 5 13940 13851.4 0.566 2.413 6 10085 9943.5 2.012 4.425 7 7056 7145.0 1.109 5.534 8 5058 5139.1 1.279 6.813 9 3714 3699.9 0.054 6.867 10 2764 2666.3 3.580 10.448 11 1846 1923.3 3.109 13.557 12 1426 1388.7 1.000 14.556 13 998 1003.7 0.033 14.589 14 712 726.1 0.275 14.864 15 565 525.8 2.917 17.781 16 386 381.2 0.062 17.843 17 267 276.5 0.329 18.172 18 188 200.8 0.820 18.992 19 148 146.0 0.028 19.019 20 114 106.2 0.571 19.590 21 295 287.1 0.217 19.807 Chisq= 19.81 for 20 degrees of freedom, p= 0.52992 SUMMARY of craptest p-value for no. of wins: 0.283709 p-value for throws/game: 0.529916 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_11:31 No. of wins: Observed Expected 98713 98585.9 z-score= 0.569, pvalue=0.71520 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66658 66666.7 0.001 0.001 2 37468 37654.3 0.922 0.923 3 26749 26954.7 1.570 2.493 4 19653 19313.5 5.969 8.463 5 13722 13851.4 1.209 9.672 6 10078 9943.5 1.818 11.490 7 7118 7145.0 0.102 11.592 8 5191 5139.1 0.525 12.117 9 3718 3699.9 0.089 12.206 10 2643 2666.3 0.204 12.409 11 1931 1923.3 0.031 12.440 12 1380 1388.7 0.055 12.495 13 978 1003.7 0.659 13.154 14 771 726.1 2.771 15.925 15 541 525.8 0.437 16.362 16 392 381.2 0.309 16.671 17 270 276.5 0.155 16.826 18 192 200.8 0.388 17.214 19 149 146.0 0.062 17.276 20 110 106.2 0.135 17.411 21 288 287.1 0.003 17.414 Chisq= 17.41 for 20 degrees of freedom, p= 0.37404 SUMMARY of craptest p-value for no. of wins: 0.715203 p-value for throws/game: 0.374044 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0006,0.0041,0.0053,0.0071,0.0088,0.0129,0.0252,0.0256,0.0282, 0.0289,0.0322,0.0364,0.0390,0.0403,0.0409,0.0410,0.0486,0.0526,0.0611, 0.0632,0.0642,0.0643,0.0651,0.0704,0.0811,0.0817,0.0841,0.0880,0.0923, 0.0955,0.0985,0.1027,0.1086,0.1091,0.1097,0.1103,0.1135,0.1269,0.1274, 0.1310,0.1341,0.1402,0.1403,0.1436,0.1486,0.1492,0.1507,0.1527,0.1596, 0.1680,0.1695,0.1765,0.1875,0.1910,0.1918,0.1962,0.2010,0.2056,0.2152, 0.2165,0.2184,0.2201,0.2309,0.2310,0.2312,0.2325,0.2328,0.2359,0.2366, 0.2379,0.2464,0.2464,0.2487,0.2582,0.2605,0.2658,0.2700,0.2798,0.2803, 0.2809,0.2837,0.2859,0.2923,0.2934,0.2937,0.2942,0.2946,0.2967,0.2977, 0.2999,0.3001,0.3101,0.3198,0.3208,0.3212,0.3297,0.3337,0.3359,0.3409, 0.3473,0.3504,0.3569,0.3569,0.3569,0.3602,0.3669,0.3686,0.3733,0.3740, 0.3746,0.3784,0.3918,0.3974,0.3990,0.4002,0.4029,0.4086,0.4097,0.4171, 0.4203,0.4284,0.4302,0.4304,0.4349,0.4424,0.4443,0.4455,0.4455,0.4480, 0.4518,0.4560,0.4625,0.4741,0.4761,0.4772,0.4815,0.5055,0.5067,0.5154, 0.5182,0.5183,0.5194,0.5211,0.5229,0.5239,0.5243,0.5248,0.5255,0.5267, 0.5283,0.5290,0.5298,0.5299,0.5315,0.5364,0.5426,0.5427,0.5441,0.5455, 0.5455,0.5480,0.5499,0.5567,0.5666,0.5683,0.5702,0.5756,0.5784,0.5788, 0.5802,0.5817,0.5826,0.5899,0.5906,0.5944,0.5965,0.5975,0.5986,0.6052, 0.6065,0.6087,0.6100,0.6117,0.6123,0.6156,0.6185,0.6192,0.6254,0.6358, 0.6359,0.6444,0.6461,0.6485,0.6709,0.6735,0.6852,0.6859,0.6865,0.6879, 0.6969,0.6977,0.6999,0.7011,0.7081,0.7082,0.7152,0.7219,0.7256,0.7358, 0.7381,0.7382,0.7408,0.7463,0.7543,0.7565,0.7566,0.7677,0.7711,0.7759, 0.7814,0.7915,0.7927,0.7927,0.7962,0.7967,0.8035,0.8063,0.8072,0.8161, 0.8360,0.8379,0.8402,0.8425,0.8493,0.8518,0.8527,0.8539,0.8563,0.8627, 0.8724,0.8754,0.8794,0.8905,0.8961,0.9057,0.9077,0.9091,0.9134,0.9248, 0.9292,0.9322,0.9327,0.9428,0.9585,0.9588,0.9630,0.9639,0.9675,0.9851, 0.9877,0.9878,0.9904,0.9912,0.9940,0.9973,0.9993,0.9994,1.0000, Overall p-value after applying KStest on 269 p-values = 0.117753 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.