RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-20_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.57 24.5986 0.895939 2 to 25 15.70 14.5865 0.374759 3 to 26 15.52 30.3692 0.976198 4 to 27 16.04 8.3806 0.042284 5 to 28 15.65 15.2390 0.421730 6 to 29 16.10 18.5483 0.644936 7 to 30 16.02 7.7412 0.028229 8 to 31 15.99 19.0815 0.676124 9 to 32 15.90 17.8399 0.600994 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.746015 Tough bday spacings test for dh-ranFile-2016-02-20_09:31: 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 9 46 75 91 100 78 50 22 15 4 10 (O-E)^2/E 0.0 2.4 0.0 0.5 0.1 0.0 0.1 2.0 0.0 1.0 8.7 Birthday Spacings: Sum(O-E)^2/E= 14.760, p= 0.859 RESULTS OF GCD FOR dh-ranFile-2016-02-20_09:31 Euclid's algorithm: p-value, steps to gcd: 0.829777 p-value, dist. of gcd's: 0.696343 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-20_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.147 0.311 0.701 0.729 0.726 0.171 0.607 0.763 Bits 8 to 15---> 0.736 0.127 0.239 0.459 0.596 0.075 0.389 0.399 Bits 16 to 23---> 0.327 0.532 0.530 0.655 0.720 0.173 0.189 0.420 Bits 24 to 31---> 0.795 0.814 0.706 0.504 0.216 0.251 0.686 0.966 KS test for the above 32 p values: 0.570 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-20_09:31, p-values for 5 runs: 0.3403, 0.4172, 0.7256, 0.1489, 0.9130 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-20_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 232 211.4 2.004 2.004 r= 29 5197 5134.0 0.773 2.777 r= 30 23075 23103.0 0.034 2.811 r= 31 11496 11551.5 0.267 3.077 chi-square = 3.077 with df = 3; p-value = 0.620 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-20_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 198 211.4 0.852 0.852 r= 30 5151 5134.0 0.056 0.908 r= 31 23020 23103.0 0.299 1.206 r= 32 11631 11551.5 0.547 1.753 chi-square = 1.753 with df = 3; p-value = 0.375 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-20_09:31 b-rank test for bits 1 to 8, p=0.03069 b-rank test for bits 2 to 9, p=0.16489 b-rank test for bits 3 to 10, p=0.01202 b-rank test for bits 4 to 11, p=0.22739 b-rank test for bits 5 to 12, p=0.88666 b-rank test for bits 6 to 13, p=0.07294 b-rank test for bits 7 to 14, p=0.68449 b-rank test for bits 8 to 15, p=0.81749 b-rank test for bits 9 to 16, p=0.90360 b-rank test for bits 10 to 17, p=0.38884 b-rank test for bits 11 to 18, p=0.02458 b-rank test for bits 12 to 19, p=0.84098 b-rank test for bits 13 to 20, p=0.38326 b-rank test for bits 14 to 21, p=0.24098 b-rank test for bits 15 to 22, p=0.42995 b-rank test for bits 16 to 23, p=0.89644 b-rank test for bits 17 to 24, p=0.81156 b-rank test for bits 18 to 25, p=0.73232 b-rank test for bits 19 to 26, p=0.81755 b-rank test for bits 20 to 27, p=0.29966 b-rank test for bits 21 to 28, p=0.65648 b-rank test for bits 22 to 29, p=0.65688 b-rank test for bits 23 to 30, p=0.58132 b-rank test for bits 24 to 31, p=0.45792 b-rank test for bits 25 to 32, p=0.61112 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 = 0.748205 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-20_09:31 (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 142378 1.10 0.863247 2 141680 -0.54 0.296042 3 141683 -0.53 0.298469 4 141487 -0.99 0.161882 5 142135 0.53 0.700996 6 141854 -0.13 0.448570 7 142501 1.38 0.916577 8 141716 -0.45 0.325741 9 142407 1.16 0.877541 10 142092 0.43 0.665237 11 141993 0.20 0.577496 12 142356 1.04 0.851670 13 141645 -0.62 0.268422 14 142223 0.73 0.768182 15 141918 0.02 0.508081 16 141589 -0.75 0.227099 17 142105 0.46 0.676227 18 142368 1.07 0.858063 19 141549 -0.84 0.199924 20 141579 -0.77 0.220117 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-20_09:31 Bits used No. missing words z-score p-value 23 to 32 142066 0.5402 0.705485 22 to 31 141724 -0.6391 0.261389 21 to 30 142301 1.3506 0.911586 20 to 29 142114 0.7058 0.759831 19 to 28 142312 1.3885 0.917510 18 to 27 142176 0.9196 0.821097 17 to 26 142400 1.6920 0.954674 16 to 25 141619 -1.0011 0.158380 15 to 24 141792 -0.4046 0.342891 14 to 23 142215 1.0540 0.854066 13 to 22 141831 -0.2701 0.393540 12 to 21 141994 0.2920 0.614844 11 to 20 141586 -1.1149 0.132440 10 to 19 142140 0.7954 0.786814 9 to 18 142001 0.3161 0.624038 8 to 17 141992 0.2851 0.612204 7 to 16 141624 -0.9839 0.162583 6 to 15 141923 0.0471 0.518798 5 to 14 141922 0.0437 0.517424 4 to 13 141811 -0.3391 0.367279 3 to 12 142251 1.1782 0.880636 2 to 11 141901 -0.0287 0.488542 1 to 10 141786 -0.4253 0.335318 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-20_09:31 Bits used No. missing words z-score p-value 28 to 32 142186 0.9379 0.825843 27 to 31 141870 -0.1333 0.446969 26 to 30 141939 0.1006 0.540057 25 to 29 142042 0.4497 0.673547 24 to 28 142037 0.4328 0.667413 23 to 27 142169 0.8802 0.810635 22 to 26 141738 -0.5808 0.280695 21 to 25 142312 1.3650 0.913871 20 to 24 141695 -0.7265 0.233753 19 to 23 141992 0.2802 0.610352 18 to 22 142400 1.6633 0.951873 17 to 21 142005 0.3243 0.627147 16 to 20 142060 0.5107 0.695236 15 to 19 142458 1.8599 0.968550 14 to 18 141655 -0.8621 0.194306 13 to 17 141691 -0.7401 0.229619 12 to 16 141838 -0.2418 0.404469 11 to 15 141994 0.2870 0.612950 10 to 14 141697 -0.7198 0.235836 9 to 13 141604 -1.0350 0.150331 8 to 12 141809 -0.3401 0.366890 7 to 11 141829 -0.2723 0.392694 6 to 10 142197 0.9752 0.835258 5 to 9 141685 -0.7604 0.223496 4 to 8 141485 -1.4384 0.075159 3 to 7 141888 -0.0723 0.471180 2 to 6 141802 -0.3638 0.357992 1 to 5 141304 -2.0520 0.020086 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-20_09:31 Bits used No. missing words z-score p-value 31 to 32 141723 -0.5496 0.291281 30 to 31 142016 0.3147 0.623490 29 to 30 141892 -0.0511 0.479615 28 to 29 142210 0.8869 0.812442 27 to 28 141960 0.1495 0.559408 26 to 27 142314 1.1937 0.883706 25 to 26 141937 0.0816 0.532527 24 to 25 141972 0.1849 0.573333 23 to 24 142123 0.6303 0.735749 22 to 23 142337 1.2616 0.896447 21 to 22 141972 0.1849 0.573333 20 to 21 141980 0.2085 0.582568 19 to 20 142605 2.0521 0.979921 18 to 19 142221 0.9194 0.821052 17 to 18 142001 0.2704 0.606579 16 to 17 142456 1.6126 0.946584 15 to 16 141141 -2.2665 0.011712 14 to 15 142257 1.0256 0.847454 13 to 14 141937 0.0816 0.532527 12 to 13 141696 -0.6293 0.264579 11 to 12 142106 0.5801 0.719092 10 to 11 142027 0.3471 0.635745 9 to 10 141943 0.0993 0.539559 8 to 9 141507 -1.1868 0.117650 7 to 8 142152 0.7158 0.762955 6 to 7 141974 0.1908 0.575646 5 to 6 141436 -1.3963 0.081319 4 to 5 141751 -0.4671 0.320232 3 to 4 141705 -0.6027 0.273340 2 to 3 142087 0.5241 0.699896 1 to 2 141810 -0.2930 0.384758 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-20_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2627.01 1.796 0.963774 Test results for specific bytes for dh-ranFile-2016-02-20_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2465.97 -0.481 0.315175 2 to 9 2634.29 1.899 0.971226 3 to 10 2513.99 0.198 0.578398 4 to 11 2462.94 -0.524 0.300125 5 to 12 2570.66 0.999 0.841167 6 to 13 2684.24 2.605 0.995413 7 to 14 2560.14 0.851 0.802479 8 to 15 2429.26 -1.000 0.158550 9 to 16 2475.35 -0.349 0.363673 10 to 17 2406.61 -1.321 0.093299 11 to 18 2452.16 -0.676 0.249363 12 to 19 2539.08 0.553 0.709770 13 to 20 2382.57 -1.661 0.048383 14 to 21 2521.36 0.302 0.618728 15 to 22 2431.15 -0.974 0.165108 16 to 23 2502.54 0.036 0.514353 17 to 24 2547.56 0.673 0.749405 18 to 25 2576.71 1.085 0.861016 19 to 26 2597.21 1.375 0.915400 20 to 27 2559.10 0.836 0.798354 21 to 28 2462.99 -0.523 0.300343 22 to 29 2445.79 -0.767 0.221628 23 to 30 2484.85 -0.214 0.415157 24 to 31 2574.55 1.054 0.854117 25 to 32 2630.01 1.839 0.967018 CDPARK for dh-ranFile-2016-02-20_09:31: 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 3577 2.4658 0.993164 3502 -0.9589 0.168804 3547 1.0959 0.863437 3496 -1.2329 0.108811 3499 -1.0959 0.136563 3532 0.4110 0.659449 3505 -0.8219 0.205562 3510 -0.5936 0.276387 3520 -0.1370 0.445521 3533 0.4566 0.676028 Square side=100, avg. no. parked=3522.10 sample std.=24.32 p-value of the KSTEST for those 10 p-values: 0.648940 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-20_09:31 0.6700,0.2609,0.9185,0.4745,0.8566,0.2590,0.3595,0.2975,0.7653,0.5490, The KS test for those 10 p-values: 0.758467 The 3DSPHERES test for dh-ranFile-2016-02-20_09:31 sample no r^3 equiv. uni. 1 15.028 0.394034 2 8.684 0.251341 3 19.955 0.485804 4 0.403 0.013360 5 23.076 0.536614 6 31.654 0.651858 7 22.920 0.534197 8 13.211 0.356208 9 5.781 0.175283 10 27.794 0.604055 11 67.396 0.894233 12 20.657 0.497711 13 4.134 0.128739 14 25.631 0.574452 15 9.437 0.269890 16 6.218 0.187184 17 18.910 0.467593 18 35.101 0.689649 19 29.654 0.627850 20 48.566 0.801877 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.402073 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-20_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.4 -0.5 -0.8 0.9 0.7 0.7 0.3 0.1 0.2 0.6 0.0 0.6 -0.3 -0.2 0.8 -0.6 -0.3 -2.0 0.7 0.8 -0.0 -0.8 -0.5 -0.3 -1.0 1.5 0.2 -0.6 0.7 1.2 -0.1 0.0 -0.6 -0.5 1.0 -1.0 0.9 -1.3 0.1 1.0 1.8 Chi-square with 42 degrees of freedom:26.056125 z-score=-1.739619, p-value=0.025511 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-20_09:31 Test no p-value 1 0.161900 2 0.052241 3 0.051577 4 0.013236 5 0.296439 6 0.000424 7 0.749860 8 0.324145 9 0.125232 10 0.511228 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001300 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-20_09:31: (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 66851 0.51 66832 0.41 3 25000.00 24837 1.06 24881 0.57 4 6666.67 6615 0.40 6644 0.08 5 1388.89 1414 0.45 1375 0.14 6 238.10 248 0.41 225 0.72 7 34.72 30 0.64 34 0.01 8 4.96 4 0.19 8 1.86 p=0.27828 p=0.29504 Number of rngs required: 687748, p-value: 0.225 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-20_09:31 No. of wins: Observed Expected 98284 98585.9 z-score=-1.350, pvalue=0.08849 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66262 66666.7 2.456 2.456 2 37965 37654.3 2.563 5.020 3 27145 26954.7 1.343 6.363 4 19260 19313.5 0.148 6.511 5 13714 13851.4 1.363 7.874 6 9935 9943.5 0.007 7.881 7 7137 7145.0 0.009 7.890 8 5168 5139.1 0.163 8.053 9 3617 3699.9 1.856 9.909 10 2691 2666.3 0.229 10.138 11 1943 1923.3 0.201 10.339 12 1356 1388.7 0.772 11.111 13 1083 1003.7 6.263 17.374 14 791 726.1 5.793 23.167 15 538 525.8 0.281 23.449 16 336 381.2 5.348 28.797 17 289 276.5 0.561 29.359 18 209 200.8 0.332 29.691 19 153 146.0 0.337 30.028 20 113 106.2 0.433 30.461 21 295 287.1 0.217 30.678 Chisq= 30.68 for 20 degrees of freedom, p= 0.94041 SUMMARY of craptest p-value for no. of wins: 0.088494 p-value for throws/game: 0.940413 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-20_09:31 No. of wins: Observed Expected 98816 98585.9 z-score= 1.029, pvalue=0.84834 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66729 66666.7 0.058 0.058 2 37586 37654.3 0.124 0.182 3 27027 26954.7 0.194 0.376 4 19216 19313.5 0.492 0.868 5 13840 13851.4 0.009 0.877 6 9843 9943.5 1.017 1.894 7 7204 7145.0 0.487 2.381 8 5147 5139.1 0.012 2.393 9 3796 3699.9 2.498 4.891 10 2663 2666.3 0.004 4.895 11 1955 1923.3 0.522 5.416 12 1370 1388.7 0.253 5.669 13 993 1003.7 0.114 5.784 14 713 726.1 0.238 6.021 15 553 525.8 1.403 7.425 16 350 381.2 2.546 9.971 17 286 276.5 0.324 10.294 18 167 200.8 5.699 15.993 19 131 146.0 1.538 17.531 20 111 106.2 0.216 17.747 21 320 287.1 3.767 21.513 Chisq= 21.51 for 20 degrees of freedom, p= 0.63251 SUMMARY of craptest p-value for no. of wins: 0.848337 p-value for throws/game: 0.632505 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0013,0.0117,0.0120,0.0132,0.0134,0.0201,0.0246,0.0255,0.0282, 0.0307,0.0423,0.0484,0.0516,0.0522,0.0729,0.0752,0.0753,0.0813,0.0885, 0.0933,0.1088,0.1177,0.1252,0.1275,0.1287,0.1324,0.1366,0.1468,0.1489, 0.1503,0.1584,0.1585,0.1619,0.1619,0.1626,0.1649,0.1651,0.1688,0.1710, 0.1734,0.1753,0.1872,0.1895,0.1943,0.1999,0.2056,0.2158,0.2201,0.2216, 0.2235,0.2246,0.2271,0.2274,0.2296,0.2338,0.2358,0.2393,0.2410,0.2494, 0.2513,0.2513,0.2590,0.2609,0.2614,0.2646,0.2684,0.2699,0.2733,0.2764, 0.2783,0.2807,0.2913,0.2950,0.2960,0.2964,0.2975,0.2985,0.2997,0.3001, 0.3003,0.3107,0.3152,0.3202,0.3241,0.3257,0.3266,0.3353,0.3403,0.3429, 0.3562,0.3580,0.3595,0.3637,0.3669,0.3673,0.3748,0.3748,0.3833,0.3848, 0.3887,0.3888,0.3927,0.3935,0.3940,0.3993,0.4021,0.4045,0.4152,0.4172, 0.4200,0.4217,0.4300,0.4455,0.4470,0.4486,0.4579,0.4591,0.4676,0.4712, 0.4745,0.4796,0.4858,0.4885,0.4977,0.5043,0.5081,0.5112,0.5144,0.5174, 0.5188,0.5296,0.5323,0.5325,0.5325,0.5342,0.5366,0.5396,0.5401,0.5490, 0.5594,0.5704,0.5733,0.5733,0.5745,0.5756,0.5775,0.5784,0.5813,0.5826, 0.5964,0.6010,0.6041,0.6066,0.6070,0.6104,0.6111,0.6122,0.6130,0.6148, 0.6187,0.6202,0.6235,0.6240,0.6271,0.6278,0.6325,0.6357,0.6449,0.6489, 0.6519,0.6548,0.6565,0.6569,0.6594,0.6652,0.6674,0.6700,0.6735,0.6760, 0.6761,0.6762,0.6845,0.6865,0.6896,0.6952,0.6963,0.6999,0.7010,0.7014, 0.7055,0.7057,0.7098,0.7191,0.7198,0.7256,0.7259,0.7290,0.7323,0.7357, 0.7365,0.7460,0.7482,0.7494,0.7499,0.7585,0.7598,0.7630,0.7630,0.7653, 0.7682,0.7868,0.7952,0.7984,0.8019,0.8025,0.8106,0.8116,0.8124,0.8140, 0.8175,0.8175,0.8211,0.8211,0.8258,0.8298,0.8353,0.8410,0.8412,0.8475, 0.8483,0.8517,0.8541,0.8541,0.8566,0.8581,0.8589,0.8610,0.8632,0.8634, 0.8775,0.8806,0.8837,0.8867,0.8942,0.8959,0.8964,0.8964,0.9036,0.9116, 0.9130,0.9139,0.9154,0.9166,0.9175,0.9185,0.9404,0.9466,0.9519,0.9547, 0.9638,0.9660,0.9670,0.9686,0.9712,0.9762,0.9799,0.9932,0.9954, Overall p-value after applying KStest on 269 p-values = 0.480089 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.