RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-20_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.97 15.6256 0.449487 2 to 25 15.50 17.6171 0.586630 3 to 26 15.99 17.0962 0.552130 4 to 27 15.63 17.3511 0.569162 5 to 28 15.46 29.8417 0.972490 6 to 29 15.68 13.5944 0.304426 7 to 30 15.91 24.1867 0.885549 8 to 31 15.87 13.2644 0.281685 9 to 32 15.77 20.9663 0.772200 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.456895 Tough bday spacings test for dh-ranFile-2015-07-20_12:31: 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 44 72 102 103 72 46 27 18 5 4 (O-E)^2/E 0.5 1.5 0.0 0.2 0.3 0.5 0.7 0.3 0.7 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.995, p= 0.108 RESULTS OF GCD FOR dh-ranFile-2015-07-20_12:31 Euclid's algorithm: p-value, steps to gcd: 0.132751 p-value, dist. of gcd's: 0.336850 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-20_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.873 0.055 0.233 0.174 0.689 0.853 0.574 0.588 Bits 8 to 15---> 0.034 0.224 0.244 0.258 0.635 0.736 0.004 0.949 Bits 16 to 23---> 0.625 0.013 0.350 0.731 0.241 0.798 0.591 0.146 Bits 24 to 31---> 0.635 0.504 0.104 0.732 0.960 0.679 0.171 0.415 KS test for the above 32 p values: 0.436 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-20_12:31, p-values for 5 runs: 0.8879, 0.3366, 0.6244, 0.4608, 0.3673 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-20_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5202 5134.0 0.900 1.414 r= 30 23072 23103.0 0.042 1.455 r= 31 11525 11551.5 0.061 1.516 chi-square = 1.516 with df = 3; p-value = 0.322 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-20_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 246 211.4 5.657 5.657 r= 30 5154 5134.0 0.078 5.734 r= 31 23123 23103.0 0.017 5.752 r= 32 11477 11551.5 0.481 6.232 chi-square = 6.232 with df = 3; p-value = 0.899 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-20_12:31 b-rank test for bits 1 to 8, p=0.82162 b-rank test for bits 2 to 9, p=0.35942 b-rank test for bits 3 to 10, p=0.42839 b-rank test for bits 4 to 11, p=0.87955 b-rank test for bits 5 to 12, p=0.21332 b-rank test for bits 6 to 13, p=0.94656 b-rank test for bits 7 to 14, p=0.23394 b-rank test for bits 8 to 15, p=0.09217 b-rank test for bits 9 to 16, p=0.06813 b-rank test for bits 10 to 17, p=0.30868 b-rank test for bits 11 to 18, p=0.66197 b-rank test for bits 12 to 19, p=0.88454 b-rank test for bits 13 to 20, p=0.36938 b-rank test for bits 14 to 21, p=0.07892 b-rank test for bits 15 to 22, p=0.17946 b-rank test for bits 16 to 23, p=0.77062 b-rank test for bits 17 to 24, p=0.42157 b-rank test for bits 18 to 25, p=0.65636 b-rank test for bits 19 to 26, p=0.00824 b-rank test for bits 20 to 27, p=0.62414 b-rank test for bits 21 to 28, p=0.57597 b-rank test for bits 22 to 29, p=0.80587 b-rank test for bits 23 to 30, p=0.91834 b-rank test for bits 24 to 31, p=0.66577 b-rank test for bits 25 to 32, p=0.45220 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 = 0.995825 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-20_12:31 (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 141645 -0.62 0.268422 2 142242 0.78 0.781499 3 141860 -0.12 0.454121 4 141806 -0.24 0.404613 5 142052 0.33 0.630562 6 141909 -0.00 0.499692 7 141789 -0.28 0.389300 8 140919 -2.31 0.010338 9 141421 -1.14 0.126944 10 141514 -0.92 0.177830 11 141928 0.04 0.517397 12 142187 0.65 0.741754 13 141236 -1.57 0.057836 14 141808 -0.24 0.406425 15 142058 0.35 0.635840 16 142402 1.15 0.875154 17 141386 -1.22 0.110715 18 141994 0.20 0.578410 19 142375 1.09 0.861706 20 142130 0.52 0.696928 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-20_12:31 Bits used No. missing words z-score p-value 23 to 32 141830 -0.2736 0.392215 22 to 31 141821 -0.3046 0.380341 21 to 30 141836 -0.2529 0.400187 20 to 29 142075 0.5713 0.716094 19 to 28 141694 -0.7425 0.228887 18 to 27 142131 0.7644 0.777679 17 to 26 141243 -2.2977 0.010790 16 to 25 141201 -2.4425 0.007293 15 to 24 141810 -0.3425 0.365981 14 to 23 141567 -1.1804 0.118911 13 to 22 141202 -2.4391 0.007363 12 to 21 141518 -1.3494 0.088602 11 to 20 141922 0.0437 0.517424 10 to 19 141810 -0.3425 0.365981 9 to 18 141659 -0.8632 0.194012 8 to 17 141820 -0.3080 0.379028 7 to 16 141953 0.1506 0.559849 6 to 15 141744 -0.5701 0.284304 5 to 14 141526 -1.3218 0.093113 4 to 13 141775 -0.4632 0.321608 3 to 12 141986 0.2644 0.604256 2 to 11 141725 -0.6356 0.262512 1 to 10 141659 -0.8632 0.194012 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-20_12:31 Bits used No. missing words z-score p-value 28 to 32 142227 1.0768 0.859226 27 to 31 142165 0.8667 0.806941 26 to 30 142216 1.0396 0.850728 25 to 29 142008 0.3345 0.630989 24 to 28 141637 -0.9232 0.177964 23 to 27 141550 -1.2181 0.111599 22 to 26 141959 0.1684 0.566855 21 to 25 142194 0.9650 0.832723 20 to 24 142134 0.7616 0.776849 19 to 23 142038 0.4362 0.668643 18 to 22 142097 0.6362 0.737667 17 to 21 141682 -0.7706 0.220469 16 to 20 141722 -0.6350 0.262709 15 to 19 141454 -1.5435 0.061356 14 to 18 142558 2.1989 0.986057 13 to 17 141481 -1.4520 0.073256 12 to 16 141992 0.2802 0.610352 11 to 15 141772 -0.4655 0.320778 10 to 14 141286 -2.1130 0.017301 9 to 13 142099 0.6429 0.739872 8 to 12 141985 0.2565 0.601221 7 to 11 141571 -1.1469 0.125715 6 to 10 142172 0.8904 0.813376 5 to 9 141956 0.1582 0.562852 4 to 8 142074 0.5582 0.711647 3 to 7 141655 -0.8621 0.194306 2 to 6 141705 -0.6926 0.244267 1 to 5 141630 -0.9469 0.171850 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-20_12:31 Bits used No. missing words z-score p-value 31 to 32 141719 -0.5614 0.287247 30 to 31 142232 0.9518 0.829408 29 to 30 141411 -1.4700 0.070781 28 to 29 141834 -0.2222 0.412074 27 to 28 142134 0.6627 0.746253 26 to 27 142348 1.2940 0.902169 25 to 26 141963 0.1583 0.562897 24 to 25 142047 0.4061 0.657668 23 to 24 142050 0.4150 0.660913 22 to 23 141904 -0.0157 0.493728 21 to 22 141529 -1.1219 0.130949 20 to 21 142551 1.8928 0.970810 19 to 20 141824 -0.2517 0.400632 18 to 19 142047 0.4061 0.657668 17 to 18 141515 -1.1632 0.122371 16 to 17 141568 -1.0069 0.156998 15 to 16 142247 0.9961 0.840394 14 to 15 141891 -0.0541 0.478439 13 to 14 141766 -0.4228 0.336220 12 to 13 142001 0.2704 0.606579 11 to 12 141686 -0.6588 0.255015 10 to 11 142130 0.6509 0.742459 9 to 10 141821 -0.2606 0.397216 8 to 9 141881 -0.0836 0.466699 7 to 8 142292 1.1288 0.870513 6 to 7 141714 -0.5762 0.282242 5 to 6 141805 -0.3078 0.379133 4 to 5 140870 -3.0659 0.001085 3 to 4 142195 0.8427 0.800298 2 to 3 141544 -1.0777 0.140591 1 to 2 142037 0.3766 0.646767 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-20_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2498.39 -0.023 0.490890 Test results for specific bytes for dh-ranFile-2015-07-20_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2376.36 -1.749 0.040187 2 to 9 2597.84 1.384 0.916770 3 to 10 2495.71 -0.061 0.475837 4 to 11 2504.44 0.063 0.525028 5 to 12 2463.06 -0.522 0.300680 6 to 13 2533.18 0.469 0.680562 7 to 14 2531.95 0.452 0.674325 8 to 15 2538.12 0.539 0.705066 9 to 16 2443.68 -0.796 0.212876 10 to 17 2611.42 1.576 0.942461 11 to 18 2484.34 -0.221 0.412360 12 to 19 2627.46 1.803 0.964276 13 to 20 2399.19 -1.426 0.076979 14 to 21 2438.22 -0.874 0.191130 15 to 22 2638.57 1.960 0.974979 16 to 23 2435.86 -0.907 0.182167 17 to 24 2431.70 -0.966 0.167062 18 to 25 2498.84 -0.016 0.493456 19 to 26 2464.22 -0.506 0.306434 20 to 27 2593.84 1.327 0.907755 21 to 28 2468.84 -0.441 0.329712 22 to 29 2721.02 3.126 0.999113 23 to 30 2333.16 -2.360 0.009150 24 to 31 2512.13 0.172 0.568122 25 to 32 2486.51 -0.191 0.424358 CDPARK for dh-ranFile-2015-07-20_12:31: 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 3516 -0.3196 0.374623 3539 0.7306 0.767486 3532 0.4110 0.659449 3493 -1.3699 0.085365 3524 0.0457 0.518210 3491 -1.4612 0.071982 3556 1.5068 0.934075 3509 -0.6393 0.261324 3504 -0.8676 0.192812 3526 0.1370 0.554479 Square side=100, avg. no. parked=3519.00 sample std.=19.51 p-value of the KSTEST for those 10 p-values: 0.907500 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-20_12:31 0.6320,0.7702,0.0793,0.5197,0.1610,0.4289,0.0982,0.5280,0.4506,0.6899, The KS test for those 10 p-values: 0.554224 The 3DSPHERES test for dh-ranFile-2015-07-20_12:31 sample no r^3 equiv. uni. 1 44.404 0.772391 2 62.352 0.874869 3 62.431 0.875197 4 22.282 0.524188 5 139.628 0.990479 6 46.943 0.790861 7 8.058 0.235556 8 10.261 0.289675 9 27.773 0.603775 10 36.672 0.705476 11 105.429 0.970231 12 25.388 0.570990 13 46.161 0.785338 14 6.402 0.192160 15 35.102 0.689653 16 16.798 0.428751 17 2.774 0.088328 18 92.548 0.954268 19 40.816 0.743477 20 24.833 0.562977 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.066232 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-20_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -0.4 0.8 1.2 0.4 -0.8 0.8 -2.7 0.7 -0.1 -0.2 0.2 0.2 0.3 0.8 2.0 0.1 -1.3 0.5 -0.6 -0.4 0.5 -1.0 -0.4 -0.6 -0.3 0.1 -1.3 -0.5 -0.4 -1.0 0.1 2.4 2.4 0.4 0.5 -1.7 -0.4 0.4 -0.6 0.0 2.7 Chi-square with 42 degrees of freedom:46.700732 z-score=0.512892, p-value=0.714672 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-20_12:31 Test no p-value 1 0.012266 2 0.279077 3 0.787434 4 0.027571 5 0.146283 6 0.159142 7 0.009830 8 0.198274 9 0.179890 10 0.726674 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002880 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-20_12:31: (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 66761 0.13 66582 0.11 3 25000.00 24865 0.73 25110 0.48 4 6666.67 6666 0.00 6646 0.06 5 1388.89 1426 0.99 1419 0.65 6 238.10 249 0.50 210 3.32 7 34.72 31 0.40 28 1.30 8 4.96 1 3.16 4 0.19 p=0.56707 p=0.58903 Number of rngs required: 687880, p-value: 0.273 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-20_12:31 No. of wins: Observed Expected 98610 98585.9 z-score= 0.108, pvalue=0.54299 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66528 66666.7 0.288 0.288 2 37760 37654.3 0.297 0.585 3 26840 26954.7 0.488 1.073 4 19485 19313.5 1.524 2.597 5 13863 13851.4 0.010 2.607 6 9854 9943.5 0.806 3.413 7 7251 7145.0 1.572 4.985 8 5107 5139.1 0.200 5.185 9 3678 3699.9 0.129 5.314 10 2663 2666.3 0.004 5.318 11 1902 1923.3 0.237 5.555 12 1368 1388.7 0.310 5.865 13 1055 1003.7 2.620 8.485 14 698 726.1 1.091 9.575 15 589 525.8 7.587 17.163 16 377 381.2 0.045 17.208 17 259 276.5 1.112 18.320 18 211 200.8 0.515 18.835 19 119 146.0 4.988 23.823 20 116 106.2 0.901 24.725 21 277 287.1 0.356 25.081 Chisq= 25.08 for 20 degrees of freedom, p= 0.80165 SUMMARY of craptest p-value for no. of wins: 0.542992 p-value for throws/game: 0.801653 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-20_12:31 No. of wins: Observed Expected 98431 98585.9 z-score=-0.693, pvalue=0.24427 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66398 66666.7 1.083 1.083 2 37892 37654.3 1.500 2.583 3 26987 26954.7 0.039 2.622 4 19179 19313.5 0.936 3.558 5 13953 13851.4 0.745 4.303 6 9962 9943.5 0.034 4.337 7 7040 7145.0 1.544 5.881 8 5169 5139.1 0.174 6.055 9 3813 3699.9 3.459 9.514 10 2627 2666.3 0.579 10.094 11 1913 1923.3 0.055 10.149 12 1393 1388.7 0.013 10.162 13 1077 1003.7 5.351 15.513 14 701 726.1 0.870 16.383 15 492 525.8 2.177 18.561 16 394 381.2 0.433 18.994 17 280 276.5 0.043 19.037 18 216 200.8 1.146 20.183 19 136 146.0 0.683 20.866 20 89 106.2 2.790 23.656 21 289 287.1 0.012 23.669 Chisq= 23.67 for 20 degrees of freedom, p= 0.74283 SUMMARY of craptest p-value for no. of wins: 0.244275 p-value for throws/game: 0.742829 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0029,0.0041,0.0073,0.0074,0.0082,0.0091,0.0098,0.0103,0.0108, 0.0123,0.0129,0.0173,0.0276,0.0342,0.0402,0.0547,0.0578,0.0614,0.0662, 0.0681,0.0708,0.0720,0.0733,0.0770,0.0789,0.0793,0.0854,0.0883,0.0886, 0.0922,0.0931,0.0982,0.1039,0.1085,0.1107,0.1116,0.1189,0.1224,0.1257, 0.1269,0.1309,0.1328,0.1406,0.1463,0.1464,0.1570,0.1591,0.1610,0.1671, 0.1713,0.1718,0.1740,0.1778,0.1780,0.1795,0.1799,0.1822,0.1911,0.1922, 0.1928,0.1940,0.1940,0.1943,0.1983,0.2129,0.2133,0.2205,0.2236,0.2289, 0.2328,0.2339,0.2356,0.2408,0.2436,0.2443,0.2443,0.2550,0.2577,0.2613, 0.2625,0.2627,0.2684,0.2732,0.2791,0.2817,0.2822,0.2843,0.2872,0.2897, 0.3007,0.3044,0.3064,0.3087,0.3208,0.3215,0.3216,0.3297,0.3362,0.3366, 0.3369,0.3501,0.3594,0.3660,0.3660,0.3673,0.3694,0.3746,0.3790,0.3791, 0.3803,0.3893,0.3922,0.3972,0.4002,0.4006,0.4046,0.4064,0.4121,0.4124, 0.4153,0.4216,0.4244,0.4284,0.4288,0.4289,0.4356,0.4495,0.4506,0.4522, 0.4541,0.4569,0.4608,0.4667,0.4758,0.4784,0.4909,0.4935,0.4937,0.4997, 0.5040,0.5174,0.5174,0.5182,0.5197,0.5242,0.5250,0.5280,0.5430,0.5521, 0.5542,0.5545,0.5598,0.5629,0.5629,0.5630,0.5669,0.5671,0.5681,0.5692, 0.5710,0.5745,0.5760,0.5784,0.5866,0.5880,0.5890,0.5910,0.6012,0.6038, 0.6043,0.6066,0.6104,0.6241,0.6244,0.6247,0.6306,0.6310,0.6320,0.6347, 0.6353,0.6358,0.6468,0.6564,0.6577,0.6577,0.6594,0.6609,0.6620,0.6658, 0.6686,0.6743,0.6794,0.6806,0.6894,0.6897,0.6899,0.6969,0.7051,0.7055, 0.7116,0.7147,0.7161,0.7267,0.7308,0.7319,0.7360,0.7377,0.7399,0.7418, 0.7425,0.7428,0.7435,0.7463,0.7675,0.7702,0.7706,0.7722,0.7724,0.7768, 0.7777,0.7815,0.7853,0.7874,0.7909,0.7978,0.8003,0.8017,0.8059,0.8069, 0.8134,0.8216,0.8294,0.8327,0.8404,0.8507,0.8531,0.8592,0.8617,0.8705, 0.8725,0.8749,0.8752,0.8752,0.8795,0.8845,0.8855,0.8879,0.8992,0.9022, 0.9075,0.9078,0.9168,0.9183,0.9341,0.9425,0.9466,0.9493,0.9543,0.9597, 0.9643,0.9702,0.9708,0.9725,0.9750,0.9861,0.9905,0.9958,0.9991, Overall p-value after applying KStest on 269 p-values = 0.176221 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.