RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-16_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.68 29.9207 0.973078 2 to 25 15.77 11.9269 0.195456 3 to 26 15.78 14.5895 0.374975 4 to 27 15.76 8.2789 0.039786 5 to 28 15.91 20.8407 0.766503 6 to 29 15.72 30.7906 0.978824 7 to 30 15.84 16.6513 0.521779 8 to 31 15.49 18.5657 0.645980 9 to 32 15.98 15.7829 0.460726 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.682482 Tough bday spacings test for dh-ranFile-2015-08-16_19:31: 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 10 42 72 86 91 89 53 34 15 6 2 (O-E)^2/E 0.1 0.8 0.0 1.4 0.5 1.5 0.0 0.6 0.0 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.973, p= 0.182 RESULTS OF GCD FOR dh-ranFile-2015-08-16_19:31 Euclid's algorithm: p-value, steps to gcd: 0.286499 p-value, dist. of gcd's: 0.119385 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-16_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.379 0.815 0.145 0.247 0.530 0.215 0.903 0.416 Bits 8 to 15---> 0.771 0.449 0.197 0.896 0.471 0.752 0.163 0.868 Bits 16 to 23---> 0.972 0.819 0.553 0.026 0.928 0.531 0.392 0.679 Bits 24 to 31---> 0.441 0.069 0.210 0.601 0.616 0.632 0.699 0.804 KS test for the above 32 p values: 0.197 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-16_19:31, p-values for 5 runs: 0.0005, 0.3817, 0.8828, 0.3988, 0.2294 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-16_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5150 5134.0 0.050 0.051 r= 30 23068 23103.0 0.053 0.105 r= 31 11570 11551.5 0.030 0.134 chi-square = 0.134 with df = 3; p-value = 0.013 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-16_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5209 5134.0 1.095 2.101 r= 31 23002 23103.0 0.442 2.543 r= 32 11563 11551.5 0.011 2.554 chi-square = 2.554 with df = 3; p-value = 0.534 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-16_19:31 b-rank test for bits 1 to 8, p=0.59334 b-rank test for bits 2 to 9, p=0.04709 b-rank test for bits 3 to 10, p=0.01211 b-rank test for bits 4 to 11, p=0.43188 b-rank test for bits 5 to 12, p=0.78024 b-rank test for bits 6 to 13, p=0.48411 b-rank test for bits 7 to 14, p=0.18836 b-rank test for bits 8 to 15, p=0.85841 b-rank test for bits 9 to 16, p=0.60749 b-rank test for bits 10 to 17, p=0.50820 b-rank test for bits 11 to 18, p=0.38912 b-rank test for bits 12 to 19, p=0.36643 b-rank test for bits 13 to 20, p=0.75652 b-rank test for bits 14 to 21, p=0.19597 b-rank test for bits 15 to 22, p=0.81558 b-rank test for bits 16 to 23, p=0.65232 b-rank test for bits 17 to 24, p=0.20987 b-rank test for bits 18 to 25, p=0.34794 b-rank test for bits 19 to 26, p=0.26196 b-rank test for bits 20 to 27, p=0.47479 b-rank test for bits 21 to 28, p=0.80295 b-rank test for bits 22 to 29, p=0.82343 b-rank test for bits 23 to 30, p=0.53751 b-rank test for bits 24 to 31, p=0.34335 b-rank test for bits 25 to 32, p=0.36780 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 = 0.526462 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-16_19:31 (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 142740 1.94 0.973860 2 141672 -0.55 0.289615 3 142641 1.71 0.956322 4 142078 0.39 0.653242 5 142558 1.52 0.935188 6 142232 0.75 0.774546 7 142596 1.60 0.945684 8 140689 -2.85 0.002177 9 143145 2.89 0.998056 10 141419 -1.15 0.125974 11 141718 -0.45 0.327426 12 141656 -0.59 0.276961 13 142191 0.66 0.744765 14 141480 -1.00 0.157905 15 142417 1.19 0.882217 16 141473 -1.02 0.153992 17 141980 0.17 0.565574 18 142376 1.09 0.862221 19 141655 -0.59 0.276180 20 142135 0.53 0.700996 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-16_19:31 Bits used No. missing words z-score p-value 23 to 32 142223 1.0816 0.860289 22 to 31 141580 -1.1356 0.128058 21 to 30 142073 0.5644 0.713752 20 to 29 142046 0.4713 0.681278 19 to 28 142387 1.6471 0.950235 18 to 27 141658 -0.8667 0.193066 17 to 26 141648 -0.9011 0.183758 16 to 25 141578 -1.1425 0.126620 15 to 24 142035 0.4333 0.667618 14 to 23 141757 -0.5253 0.299696 13 to 22 142220 1.0713 0.857977 12 to 21 141527 -1.3184 0.093688 11 to 20 141805 -0.3598 0.359514 10 to 19 142110 0.6920 0.755521 9 to 18 141958 0.1678 0.566641 8 to 17 142148 0.8230 0.794746 7 to 16 141927 0.0609 0.524293 6 to 15 141663 -0.8494 0.197826 5 to 14 141467 -1.5253 0.063595 4 to 13 142153 0.8402 0.799614 3 to 12 141319 -2.0356 0.020894 2 to 11 141403 -1.7460 0.040408 1 to 10 142430 1.7954 0.963706 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-16_19:31 Bits used No. missing words z-score p-value 28 to 32 141977 0.2294 0.590717 27 to 31 141673 -0.8011 0.211532 26 to 30 141453 -1.5469 0.060946 25 to 29 141798 -0.3774 0.352942 24 to 28 142069 0.5413 0.705834 23 to 27 141830 -0.2689 0.393998 22 to 26 141911 0.0057 0.502258 21 to 25 142428 1.7582 0.960644 20 to 24 141692 -0.7367 0.230649 19 to 23 141858 -0.1740 0.430933 18 to 22 141262 -2.1943 0.014106 17 to 21 141759 -0.5096 0.305168 16 to 20 141855 -0.1842 0.426940 15 to 19 142210 1.0192 0.845951 14 to 18 142046 0.4633 0.678421 13 to 17 141844 -0.2215 0.412368 12 to 16 141537 -1.2621 0.103450 11 to 15 141715 -0.6587 0.255030 10 to 14 141554 -1.2045 0.114197 9 to 13 142410 1.6972 0.955169 8 to 12 141518 -1.3265 0.092330 7 to 11 141546 -1.2316 0.109044 6 to 10 141632 -0.9401 0.173583 5 to 9 141858 -0.1740 0.430933 4 to 8 141398 -1.7333 0.041519 3 to 7 141673 -0.8011 0.211532 2 to 6 141794 -0.3909 0.347917 1 to 5 141941 0.1074 0.542747 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-16_19:31 Bits used No. missing words z-score p-value 31 to 32 141722 -0.5526 0.290270 30 to 31 142533 1.8397 0.967096 29 to 30 141804 -0.3107 0.378011 28 to 29 141495 -1.2222 0.110814 27 to 28 141583 -0.9626 0.167868 26 to 27 141808 -0.2989 0.382505 25 to 26 141481 -1.2635 0.103203 24 to 25 142176 0.7866 0.784253 23 to 24 142599 2.0344 0.979046 22 to 23 142445 1.5801 0.942963 21 to 22 142200 0.8574 0.804397 20 to 21 141688 -0.6529 0.256913 19 to 20 141973 0.1878 0.574490 18 to 19 141935 0.0757 0.530180 17 to 18 141351 -1.6470 0.049780 16 to 17 141967 0.1701 0.567541 15 to 16 141626 -0.8358 0.201639 14 to 15 142210 0.8869 0.812442 13 to 14 141723 -0.5496 0.291281 12 to 13 141626 -0.8358 0.201639 11 to 12 141962 0.1554 0.561735 10 to 11 141819 -0.2665 0.394942 9 to 10 141358 -1.6263 0.051938 8 to 9 141833 -0.2252 0.410927 7 to 8 142252 1.0108 0.843950 6 to 7 141943 0.0993 0.539559 5 to 6 141830 -0.2340 0.407488 4 to 5 141851 -0.1721 0.431693 3 to 4 141460 -1.3255 0.092510 2 to 3 142167 0.7601 0.776399 1 to 2 141510 -1.1780 0.119405 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-16_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2435.92 -0.906 0.182398 Test results for specific bytes for dh-ranFile-2015-08-16_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2562.18 0.879 0.810386 2 to 9 2515.80 0.223 0.588387 3 to 10 2545.03 0.637 0.737862 4 to 11 2418.39 -1.154 0.124207 5 to 12 2490.20 -0.139 0.444880 6 to 13 2513.48 0.191 0.575608 7 to 14 2397.29 -1.453 0.073171 8 to 15 2426.07 -1.046 0.147894 9 to 16 2423.39 -1.083 0.139324 10 to 17 2546.30 0.655 0.743703 11 to 18 2697.60 2.795 0.997401 12 to 19 2524.63 0.348 0.636226 13 to 20 2440.97 -0.835 0.201910 14 to 21 2493.65 -0.090 0.464214 15 to 22 2497.89 -0.030 0.488106 16 to 23 2549.57 0.701 0.758337 17 to 24 2494.07 -0.084 0.466571 18 to 25 2406.67 -1.320 0.093433 19 to 26 2627.10 1.797 0.963869 20 to 27 2484.49 -0.219 0.413187 21 to 28 2541.61 0.588 0.721889 22 to 29 2540.52 0.573 0.716701 23 to 30 2542.51 0.601 0.726152 24 to 31 2520.99 0.297 0.616709 25 to 32 2553.64 0.759 0.775939 CDPARK for dh-ranFile-2015-08-16_19:31: 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 3507 -0.7306 0.232514 3512 -0.5023 0.307734 3516 -0.3196 0.374623 3515 -0.3653 0.357445 3538 0.6849 0.753306 3512 -0.5023 0.307734 3513 -0.4566 0.323972 3506 -0.7763 0.218799 3549 1.1872 0.882429 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3518.70 sample std.=13.16 p-value of the KSTEST for those 10 p-values: 0.191615 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-16_19:31 0.6684,0.8998,0.5468,0.7882,0.7565,0.1423,0.5361,0.3267,0.2668,0.5497, The KS test for those 10 p-values: 0.736021 The 3DSPHERES test for dh-ranFile-2015-08-16_19:31 sample no r^3 equiv. uni. 1 6.011 0.181563 2 11.046 0.308024 3 0.906 0.029741 4 11.529 0.319073 5 9.162 0.263171 6 91.581 0.952769 7 78.255 0.926355 8 65.852 0.888647 9 21.857 0.517406 10 22.158 0.522216 11 12.938 0.350321 12 96.686 0.960159 13 12.042 0.330616 14 41.154 0.746349 15 12.766 0.346589 16 9.082 0.261216 17 45.148 0.777968 18 34.228 0.680483 19 50.683 0.815373 20 22.982 0.535169 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.713216 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-16_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.9 0.1 0.3 -0.5 1.0 -1.1 1.7 -1.9 -0.8 0.4 -0.0 0.6 0.5 -0.3 -0.6 0.0 1.3 -0.5 -0.2 0.5 -0.1 -0.5 -0.1 -0.8 0.9 0.2 1.3 -1.4 -0.8 1.7 -0.3 -1.1 -0.4 -0.9 -1.2 -1.4 0.2 0.1 1.5 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:34.243978 z-score=-0.846251, p-value=0.203046 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-16_19:31 Test no p-value 1 0.223698 2 0.257736 3 0.783223 4 0.151018 5 0.571615 6 0.444325 7 0.502419 8 0.291103 9 0.792868 10 0.270331 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.440205 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-16_19:31: (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 66704 0.02 66422 0.90 3 25000.00 25123 0.61 25159 1.01 4 6666.67 6543 2.29 6706 0.23 5 1388.89 1356 0.78 1432 1.34 6 238.10 230 0.28 246 0.26 7 34.72 31 0.40 29 0.94 8 4.96 12 9.99 5 0.00 p=0.97419 p=0.41512 Number of rngs required: 687772, p-value: 0.233 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-16_19:31 No. of wins: Observed Expected 98497 98585.9 z-score=-0.397, pvalue=0.34553 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66454 66666.7 0.678 0.678 2 37813 37654.3 0.669 1.347 3 26916 26954.7 0.056 1.403 4 19317 19313.5 0.001 1.403 5 13750 13851.4 0.743 2.146 6 10068 9943.5 1.558 3.704 7 7141 7145.0 0.002 3.706 8 5129 5139.1 0.020 3.726 9 3645 3699.9 0.814 4.539 10 2742 2666.3 2.149 6.689 11 1909 1923.3 0.107 6.795 12 1408 1388.7 0.267 7.063 13 1002 1003.7 0.003 7.066 14 770 726.1 2.649 9.715 15 535 525.8 0.160 9.874 16 403 381.2 1.253 11.127 17 261 276.5 0.873 12.000 18 191 200.8 0.481 12.481 19 146 146.0 0.000 12.481 20 104 106.2 0.046 12.527 21 296 287.1 0.275 12.802 Chisq= 12.80 for 20 degrees of freedom, p= 0.11430 SUMMARY of craptest p-value for no. of wins: 0.345526 p-value for throws/game: 0.114301 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-16_19:31 No. of wins: Observed Expected 98635 98585.9 z-score= 0.220, pvalue=0.58698 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66667 66666.7 0.000 0.000 2 37405 37654.3 1.651 1.651 3 27264 26954.7 3.548 5.199 4 19383 19313.5 0.250 5.450 5 13658 13851.4 2.701 8.151 6 9868 9943.5 0.574 8.724 7 7266 7145.0 2.048 10.773 8 5244 5139.1 2.142 12.915 9 3663 3699.9 0.367 13.282 10 2647 2666.3 0.140 13.422 11 1973 1923.3 1.283 14.705 12 1381 1388.7 0.043 14.748 13 1020 1003.7 0.264 15.012 14 718 726.1 0.091 15.103 15 551 525.8 1.204 16.308 16 366 381.2 0.602 16.910 17 241 276.5 4.567 21.477 18 193 200.8 0.305 21.783 19 137 146.0 0.553 22.335 20 111 106.2 0.216 22.551 21 244 287.1 6.474 29.025 Chisq= 29.03 for 20 degrees of freedom, p= 0.91273 SUMMARY of craptest p-value for no. of wins: 0.586982 p-value for throws/game: 0.912735 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0022,0.0121,0.0126,0.0141,0.0209,0.0257,0.0297,0.0398,0.0404, 0.0415,0.0471,0.0498,0.0519,0.0609,0.0636,0.0690,0.0732,0.0923,0.0925, 0.0934,0.0937,0.1032,0.1035,0.1090,0.1108,0.1142,0.1143,0.1194,0.1194, 0.1242,0.1260,0.1266,0.1281,0.1393,0.1423,0.1446,0.1479,0.1510,0.1540, 0.1579,0.1633,0.1679,0.1736,0.1816,0.1824,0.1824,0.1838,0.1884,0.1916, 0.1931,0.1955,0.1960,0.1966,0.1968,0.1978,0.2016,0.2016,0.2019,0.2030, 0.2099,0.2100,0.2115,0.2115,0.2151,0.2188,0.2237,0.2294,0.2306,0.2325, 0.2331,0.2472,0.2550,0.2569,0.2577,0.2612,0.2620,0.2632,0.2668,0.2703, 0.2762,0.2770,0.2865,0.2896,0.2903,0.2911,0.2913,0.2997,0.3052,0.3077, 0.3077,0.3080,0.3191,0.3240,0.3267,0.3274,0.3306,0.3434,0.3455,0.3466, 0.3479,0.3479,0.3503,0.3529,0.3574,0.3595,0.3664,0.3678,0.3746,0.3750, 0.3780,0.3793,0.3817,0.3825,0.3891,0.3917,0.3940,0.3949,0.3988,0.4075, 0.4109,0.4124,0.4132,0.4151,0.4157,0.4269,0.4275,0.4309,0.4309,0.4317, 0.4319,0.4402,0.4410,0.4443,0.4449,0.4494,0.4607,0.4642,0.4666,0.4709, 0.4748,0.4841,0.4881,0.5023,0.5024,0.5082,0.5174,0.5218,0.5222,0.5243, 0.5265,0.5300,0.5302,0.5315,0.5345,0.5352,0.5361,0.5375,0.5396,0.5427, 0.5468,0.5497,0.5532,0.5617,0.5656,0.5666,0.5675,0.5716,0.5745,0.5756, 0.5870,0.5884,0.5907,0.5933,0.6005,0.6075,0.6164,0.6167,0.6320,0.6362, 0.6460,0.6523,0.6532,0.6676,0.6684,0.6784,0.6790,0.6805,0.6813,0.6825, 0.6993,0.7010,0.7058,0.7132,0.7138,0.7167,0.7219,0.7262,0.7360,0.7379, 0.7437,0.7448,0.7463,0.7516,0.7533,0.7555,0.7565,0.7565,0.7583,0.7665, 0.7713,0.7745,0.7759,0.7764,0.7780,0.7802,0.7832,0.7843,0.7882,0.7929, 0.7947,0.7996,0.8029,0.8040,0.8044,0.8104,0.8124,0.8146,0.8154,0.8156, 0.8187,0.8234,0.8440,0.8460,0.8580,0.8584,0.8603,0.8622,0.8677,0.8822, 0.8824,0.8828,0.8886,0.8963,0.8998,0.9034,0.9127,0.9264,0.9283,0.9352, 0.9430,0.9457,0.9502,0.9528,0.9552,0.9563,0.9602,0.9606,0.9637,0.9639, 0.9671,0.9715,0.9731,0.9739,0.9742,0.9788,0.9790,0.9974,0.9981, Overall p-value after applying KStest on 269 p-values = 0.373859 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.