RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-06_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 16.04 11.0714 0.147170 2 to 25 15.84 19.6608 0.708054 3 to 26 15.73 20.9478 0.771364 4 to 27 15.82 12.6221 0.238904 5 to 28 15.84 21.4256 0.792172 6 to 29 16.03 15.6421 0.450665 7 to 30 15.52 20.2046 0.736101 8 to 31 15.63 17.9627 0.608802 9 to 32 15.59 18.5534 0.645238 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.437771 Tough bday spacings test for dh-ranFile-2015-10-06_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 12 34 71 103 97 78 50 28 13 7 7 (O-E)^2/E 0.9 0.2 0.1 0.3 0.0 0.0 0.1 0.1 0.2 0.0 2.1 Birthday Spacings: Sum(O-E)^2/E= 4.003, p= 0.053 RESULTS OF GCD FOR dh-ranFile-2015-10-06_20:31 Euclid's algorithm: p-value, steps to gcd: 0.820873 p-value, dist. of gcd's: 0.073211 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-06_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.113 0.853 0.942 0.144 0.224 0.389 0.936 0.840 Bits 8 to 15---> 1.000 0.845 1.000 0.838 0.457 0.700 0.447 0.834 Bits 16 to 23---> 0.437 0.486 0.048 0.655 0.807 0.589 0.769 0.175 Bits 24 to 31---> 0.229 0.131 0.768 0.001 0.111 0.878 0.180 0.378 KS test for the above 32 p values: 0.797 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-06_20:31, p-values for 5 runs: 0.1406, 0.4920, 0.4225, 0.7946, 0.4425 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-06_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5230 5134.0 1.795 2.308 r= 30 23140 23103.0 0.059 2.367 r= 31 11429 11551.5 1.300 3.667 chi-square = 3.667 with df = 3; p-value = 0.700 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-06_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 195 211.4 1.275 1.275 r= 30 5135 5134.0 0.000 1.275 r= 31 23182 23103.0 0.270 1.545 r= 32 11488 11551.5 0.349 1.894 chi-square = 1.894 with df = 3; p-value = 0.405 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-06_20:31 b-rank test for bits 1 to 8, p=0.36008 b-rank test for bits 2 to 9, p=0.81711 b-rank test for bits 3 to 10, p=0.31252 b-rank test for bits 4 to 11, p=0.90365 b-rank test for bits 5 to 12, p=0.03624 b-rank test for bits 6 to 13, p=0.46893 b-rank test for bits 7 to 14, p=0.90338 b-rank test for bits 8 to 15, p=0.45777 b-rank test for bits 9 to 16, p=0.45174 b-rank test for bits 10 to 17, p=0.00754 b-rank test for bits 11 to 18, p=0.26115 b-rank test for bits 12 to 19, p=0.89803 b-rank test for bits 13 to 20, p=0.67785 b-rank test for bits 14 to 21, p=0.58459 b-rank test for bits 15 to 22, p=0.75181 b-rank test for bits 16 to 23, p=0.93453 b-rank test for bits 17 to 24, p=0.35637 b-rank test for bits 18 to 25, p=0.47495 b-rank test for bits 19 to 26, p=0.86948 b-rank test for bits 20 to 27, p=0.47854 b-rank test for bits 21 to 28, p=0.17807 b-rank test for bits 22 to 29, p=0.74286 b-rank test for bits 23 to 30, p=0.78027 b-rank test for bits 24 to 31, p=0.13290 b-rank test for bits 25 to 32, p=0.79868 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 = 0.613084 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-06_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 141540 -0.86 0.194091 2 141710 -0.47 0.320706 3 141863 -0.11 0.456900 4 141806 -0.24 0.404613 5 142242 0.78 0.781499 6 142291 0.89 0.813737 7 140856 -2.46 0.006927 8 142461 1.29 0.901292 9 141077 -1.94 0.025906 10 141870 -0.09 0.463392 11 142326 0.97 0.834855 12 141437 -1.10 0.134889 13 141151 -1.77 0.038214 14 142044 0.31 0.623486 15 141865 -0.10 0.458753 16 141907 -0.01 0.497828 17 142081 0.40 0.655826 18 141574 -0.78 0.216672 19 142885 2.28 0.988684 20 142443 1.25 0.893782 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-06_20:31 Bits used No. missing words z-score p-value 23 to 32 141825 -0.2908 0.385605 22 to 31 142010 0.3471 0.635756 21 to 30 142028 0.4092 0.658806 20 to 29 141663 -0.8494 0.197826 19 to 28 142494 2.0161 0.978105 18 to 27 141606 -1.0460 0.147789 17 to 26 141797 -0.3873 0.349251 16 to 25 141822 -0.3011 0.381655 15 to 24 141484 -1.4667 0.071235 14 to 23 142474 1.9471 0.974241 13 to 22 142268 1.2368 0.891918 12 to 21 142061 0.5230 0.699513 11 to 20 141926 0.0575 0.522920 10 to 19 142562 2.2506 0.987794 9 to 18 141945 0.1230 0.548947 8 to 17 141198 -2.4529 0.007086 7 to 16 141162 -2.5770 0.004983 6 to 15 142157 0.8540 0.803457 5 to 14 141648 -0.9011 0.183758 4 to 13 141494 -1.4322 0.076047 3 to 12 142038 0.4437 0.671367 2 to 11 141507 -1.3873 0.082668 1 to 10 141695 -0.7391 0.229933 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-06_20:31 Bits used No. missing words z-score p-value 28 to 32 141635 -0.9299 0.176203 27 to 31 142282 1.2633 0.896757 26 to 30 141710 -0.6757 0.249617 25 to 29 141960 0.1718 0.568188 24 to 28 141654 -0.8655 0.193375 23 to 27 142184 0.9311 0.824095 22 to 26 142033 0.4192 0.662473 21 to 25 141707 -0.6859 0.246399 20 to 24 141388 -1.7672 0.038596 19 to 23 141435 -1.6079 0.053929 18 to 22 141966 0.1921 0.576169 17 to 21 142080 0.5785 0.718551 16 to 20 142371 1.5650 0.941207 15 to 19 141939 0.1006 0.540057 14 to 18 142228 1.0802 0.859982 13 to 17 142000 0.3074 0.620714 12 to 16 141911 0.0057 0.502258 11 to 15 142260 1.1887 0.882723 10 to 14 142386 1.6158 0.946935 9 to 13 141465 -1.5062 0.066008 8 to 12 141860 -0.1672 0.433598 7 to 11 141744 -0.5604 0.287589 6 to 10 141499 -1.3909 0.082120 5 to 9 142287 1.2802 0.899769 4 to 8 141976 0.2260 0.589399 3 to 7 141787 -0.4147 0.339189 2 to 6 141954 0.1514 0.560179 1 to 5 142125 0.7311 0.767636 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-06_20:31 Bits used No. missing words z-score p-value 31 to 32 142452 1.6008 0.945289 30 to 31 141852 -0.1691 0.432853 29 to 30 141893 -0.0482 0.480790 28 to 29 142078 0.4976 0.690600 27 to 28 142221 0.9194 0.821052 26 to 27 141441 -1.3815 0.083562 25 to 26 141416 -1.4553 0.072800 24 to 25 142183 0.8073 0.790249 23 to 24 141766 -0.4228 0.336220 22 to 23 142265 1.0492 0.852951 21 to 22 141804 -0.3107 0.378011 20 to 21 141950 0.1200 0.547747 19 to 20 141427 -1.4228 0.077397 18 to 19 141877 -0.0954 0.462011 17 to 18 142098 0.5565 0.711082 16 to 17 141906 -0.0098 0.496081 15 to 16 142104 0.5742 0.717100 14 to 15 141663 -0.7266 0.233724 13 to 14 141798 -0.3284 0.371302 12 to 13 141928 0.0551 0.521960 11 to 12 142255 1.0197 0.846059 10 to 11 141861 -0.1426 0.443316 9 to 10 141691 -0.6440 0.259774 8 to 9 141786 -0.3638 0.358002 7 to 8 141839 -0.2075 0.417824 6 to 7 141788 -0.3579 0.360207 5 to 6 141871 -0.1131 0.454988 4 to 5 141727 -0.5378 0.295342 3 to 4 141964 0.1613 0.564059 2 to 3 141983 0.2173 0.586019 1 to 2 141616 -0.8653 0.193443 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-06_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2534.33 0.485 0.686331 Test results for specific bytes for dh-ranFile-2015-10-06_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2518.41 0.260 0.602712 2 to 9 2431.90 -0.963 0.167768 3 to 10 2399.33 -1.424 0.077269 4 to 11 2428.84 -1.006 0.157133 5 to 12 2395.76 -1.474 0.070208 6 to 13 2501.64 0.023 0.509268 7 to 14 2516.69 0.236 0.593282 8 to 15 2527.15 0.384 0.649493 9 to 16 2446.54 -0.756 0.224819 10 to 17 2486.06 -0.197 0.421833 11 to 18 2613.03 1.598 0.945033 12 to 19 2545.46 0.643 0.739850 13 to 20 2572.16 1.020 0.846248 14 to 21 2412.64 -1.235 0.108324 15 to 22 2455.50 -0.629 0.264559 16 to 23 2667.37 2.367 0.991034 17 to 24 2510.16 0.144 0.557149 18 to 25 2345.17 -2.190 0.014278 19 to 26 2534.75 0.491 0.688420 20 to 27 2549.26 0.697 0.756968 21 to 28 2397.50 -1.450 0.073581 22 to 29 2491.25 -0.124 0.450774 23 to 30 2474.02 -0.367 0.356673 24 to 31 2601.41 1.434 0.924236 25 to 32 2605.16 1.487 0.931510 CDPARK for dh-ranFile-2015-10-06_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 3509 -0.6393 0.261324 3489 -1.5525 0.060270 3526 0.1370 0.554479 3507 -0.7306 0.232514 3524 0.0457 0.518210 3494 -1.3242 0.092718 3532 0.4110 0.659449 3492 -1.4155 0.078457 3496 -1.2329 0.108811 3513 -0.4566 0.323972 Square side=100, avg. no. parked=3508.20 sample std.=14.63 p-value of the KSTEST for those 10 p-values: 0.029836 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-06_20:31 0.0112,0.6353,0.5297,0.7338,0.3282,0.0027,0.7470,0.3555,0.8488,0.3917, The KS test for those 10 p-values: 0.351325 The 3DSPHERES test for dh-ranFile-2015-10-06_20:31 sample no r^3 equiv. uni. 1 0.285 0.009467 2 62.481 0.875408 3 10.201 0.288249 4 1.286 0.041967 5 29.832 0.630051 6 14.429 0.381808 7 29.256 0.622881 8 18.622 0.462452 9 43.683 0.766853 10 59.756 0.863560 11 132.284 0.987838 12 43.919 0.768685 13 16.784 0.428493 14 53.882 0.834047 15 57.327 0.852053 16 36.682 0.705573 17 10.317 0.291008 18 12.112 0.332171 19 24.237 0.554211 20 13.033 0.352369 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.601658 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-06_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.8 -0.4 -0.3 0.9 1.0 0.8 0.6 -0.9 0.7 1.4 -0.4 -0.6 1.5 -1.9 1.3 2.2 -0.9 -0.3 -0.8 -1.5 0.1 -0.2 -0.9 -1.0 -1.0 1.9 0.0 -0.5 1.0 0.8 1.1 -1.2 -0.1 -0.1 0.0 0.2 -1.6 -1.3 -0.6 1.0 -1.1 Chi-square with 42 degrees of freedom:41.833565 z-score=-0.018160, p-value=0.521796 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-06_20:31 Test no p-value 1 0.341252 2 0.559941 3 0.001040 4 0.450162 5 0.447534 6 0.972276 7 0.084206 8 0.831307 9 0.000840 10 0.799404 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.096768 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-06_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 66857 0.54 66533 0.27 3 25000.00 24802 1.57 25204 1.66 4 6666.67 6656 0.02 6580 1.13 5 1388.89 1395 0.03 1406 0.21 6 238.10 242 0.06 233 0.11 7 34.72 44 2.48 39 0.53 8 4.96 3 0.77 4 0.19 p=0.51545 p=0.33586 Number of rngs required: 689332, p-value: 0.859 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-06_20:31 No. of wins: Observed Expected 98499 98585.9 z-score=-0.388, pvalue=0.34883 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66859 66666.7 0.555 0.555 2 37391 37654.3 1.841 2.396 3 26825 26954.7 0.624 3.021 4 19542 19313.5 2.704 5.725 5 13809 13851.4 0.130 5.855 6 9963 9943.5 0.038 5.893 7 7223 7145.0 0.851 6.744 8 5188 5139.1 0.466 7.210 9 3686 3699.9 0.052 7.262 10 2655 2666.3 0.048 7.310 11 1816 1923.3 5.989 13.299 12 1398 1388.7 0.062 13.361 13 1017 1003.7 0.176 13.537 14 684 726.1 2.446 15.982 15 543 525.8 0.560 16.542 16 363 381.2 0.864 17.407 17 284 276.5 0.201 17.608 18 201 200.8 0.000 17.608 19 160 146.0 1.346 18.954 20 109 106.2 0.073 19.027 21 284 287.1 0.034 19.061 Chisq= 19.06 for 20 degrees of freedom, p= 0.48211 SUMMARY of craptest p-value for no. of wins: 0.348830 p-value for throws/game: 0.482106 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-06_20:31 No. of wins: Observed Expected 98749 98585.9 z-score= 0.730, pvalue=0.76720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66779 66666.7 0.189 0.189 2 37789 37654.3 0.482 0.671 3 27082 26954.7 0.601 1.272 4 19202 19313.5 0.643 1.915 5 13716 13851.4 1.324 3.239 6 10079 9943.5 1.845 5.084 7 6998 7145.0 3.025 8.110 8 5065 5139.1 1.068 9.177 9 3628 3699.9 1.396 10.573 10 2618 2666.3 0.875 11.448 11 1881 1923.3 0.932 12.380 12 1404 1388.7 0.168 12.547 13 1013 1003.7 0.086 12.633 14 741 726.1 0.304 12.937 15 560 525.8 2.220 15.157 16 402 381.2 1.140 16.298 17 295 276.5 1.232 17.530 18 224 200.8 2.673 20.203 19 128 146.0 2.216 22.419 20 121 106.2 2.058 24.477 21 275 287.1 0.511 24.988 Chisq= 24.99 for 20 degrees of freedom, p= 0.79810 SUMMARY of craptest p-value for no. of wins: 0.767202 p-value for throws/game: 0.798100 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0010,0.0013,0.0027,0.0050,0.0069,0.0071,0.0075,0.0095,0.0112, 0.0143,0.0259,0.0298,0.0362,0.0382,0.0386,0.0420,0.0484,0.0528,0.0539, 0.0603,0.0660,0.0702,0.0712,0.0728,0.0732,0.0736,0.0760,0.0773,0.0774, 0.0785,0.0821,0.0827,0.0836,0.0842,0.0927,0.0968,0.1083,0.1088,0.1114, 0.1132,0.1311,0.1329,0.1349,0.1406,0.1439,0.1472,0.1478,0.1571,0.1678, 0.1753,0.1762,0.1781,0.1802,0.1838,0.1934,0.1934,0.1941,0.1978,0.2167, 0.2242,0.2248,0.2295,0.2299,0.2325,0.2337,0.2389,0.2464,0.2496,0.2598, 0.2612,0.2613,0.2646,0.2876,0.2882,0.2910,0.2953,0.3125,0.3207,0.3240, 0.3282,0.3322,0.3359,0.3362,0.3392,0.3413,0.3488,0.3493,0.3513,0.3524, 0.3555,0.3564,0.3567,0.3580,0.3601,0.3602,0.3713,0.3780,0.3783,0.3817, 0.3818,0.3856,0.3892,0.3917,0.4046,0.4054,0.4178,0.4218,0.4225,0.4285, 0.4329,0.4336,0.4370,0.4378,0.4425,0.4433,0.4474,0.4475,0.4502,0.4507, 0.4508,0.4517,0.4550,0.4569,0.4569,0.4578,0.4588,0.4620,0.4625,0.4634, 0.4689,0.4750,0.4785,0.4808,0.4821,0.4860,0.4920,0.4961,0.4978,0.5023, 0.5093,0.5154,0.5182,0.5218,0.5220,0.5229,0.5297,0.5401,0.5477,0.5489, 0.5542,0.5545,0.5571,0.5599,0.5602,0.5641,0.5682,0.5762,0.5846,0.5860, 0.5885,0.5894,0.5933,0.6017,0.6027,0.6088,0.6131,0.6207,0.6229,0.6235, 0.6301,0.6353,0.6358,0.6452,0.6495,0.6549,0.6558,0.6588,0.6594,0.6625, 0.6714,0.6779,0.6863,0.6884,0.6906,0.6995,0.6999,0.7002,0.7056,0.7081, 0.7111,0.7171,0.7186,0.7338,0.7361,0.7399,0.7429,0.7470,0.7518,0.7570, 0.7669,0.7672,0.7676,0.7680,0.7685,0.7687,0.7714,0.7803,0.7815,0.7902, 0.7922,0.7946,0.7969,0.7981,0.7987,0.7994,0.8035,0.8071,0.8137,0.8171, 0.8209,0.8211,0.8241,0.8313,0.8340,0.8344,0.8349,0.8382,0.8400,0.8449, 0.8461,0.8462,0.8488,0.8521,0.8527,0.8530,0.8594,0.8600,0.8636,0.8695, 0.8754,0.8782,0.8827,0.8919,0.8938,0.8968,0.8980,0.8998,0.9013,0.9034, 0.9036,0.9242,0.9315,0.9345,0.9355,0.9412,0.9422,0.9450,0.9453,0.9469, 0.9723,0.9742,0.9781,0.9878,0.9878,0.9887,0.9910,0.9995,1.0000, Overall p-value after applying KStest on 269 p-values = 0.442466 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.