RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-09_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.72 14.0053 0.333275 2 to 25 15.98 23.4658 0.865307 3 to 26 15.99 14.3230 0.355877 4 to 27 15.52 27.6450 0.950739 5 to 28 15.70 21.7100 0.803869 6 to 29 15.82 18.8498 0.662777 7 to 30 15.56 25.0299 0.905959 8 to 31 15.83 16.3860 0.503344 9 to 32 15.70 22.9299 0.848455 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.069161 Tough bday spacings test for dh-ranFile-2015-08-09_21:31: 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 4 31 63 120 100 70 54 32 17 4 5 (O-E)^2/E 2.9 0.9 1.4 5.1 0.1 0.8 0.1 0.2 0.3 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 12.996, p= 0.776 RESULTS OF GCD FOR dh-ranFile-2015-08-09_21:31 Euclid's algorithm: p-value, steps to gcd: 0.832235 p-value, dist. of gcd's: 0.795696 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-09_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.826 0.401 0.719 0.391 0.685 0.737 0.422 0.857 Bits 8 to 15---> 0.425 0.864 0.816 0.618 0.978 0.346 0.315 0.926 Bits 16 to 23---> 0.255 0.760 0.832 0.391 0.813 0.716 0.653 0.176 Bits 24 to 31---> 0.925 0.706 0.274 0.996 0.905 0.330 0.830 0.127 KS test for the above 32 p values: 0.982 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-09_21:31, p-values for 5 runs: 0.6336, 0.8193, 0.7487, 0.3734, 0.2216 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-09_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5149 5134.0 0.044 0.053 r= 30 23159 23103.0 0.136 0.189 r= 31 11482 11551.5 0.418 0.607 chi-square = 0.607 with df = 3; p-value = 0.105 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-09_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5219 5134.0 1.407 1.755 r= 31 22984 23103.0 0.613 2.369 r= 32 11577 11551.5 0.056 2.425 chi-square = 2.425 with df = 3; p-value = 0.511 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-09_21:31 b-rank test for bits 1 to 8, p=0.03358 b-rank test for bits 2 to 9, p=0.28475 b-rank test for bits 3 to 10, p=0.11813 b-rank test for bits 4 to 11, p=0.71976 b-rank test for bits 5 to 12, p=0.49477 b-rank test for bits 6 to 13, p=0.55003 b-rank test for bits 7 to 14, p=0.77512 b-rank test for bits 8 to 15, p=0.43007 b-rank test for bits 9 to 16, p=0.18397 b-rank test for bits 10 to 17, p=0.23993 b-rank test for bits 11 to 18, p=0.93579 b-rank test for bits 12 to 19, p=0.84838 b-rank test for bits 13 to 20, p=0.24394 b-rank test for bits 14 to 21, p=0.30470 b-rank test for bits 15 to 22, p=0.84082 b-rank test for bits 16 to 23, p=0.54329 b-rank test for bits 17 to 24, p=0.95893 b-rank test for bits 18 to 25, p=0.82689 b-rank test for bits 19 to 26, p=0.05476 b-rank test for bits 20 to 27, p=0.82648 b-rank test for bits 21 to 28, p=0.44641 b-rank test for bits 22 to 29, p=0.06513 b-rank test for bits 23 to 30, p=0.60795 b-rank test for bits 24 to 31, p=0.72588 b-rank test for bits 25 to 32, p=0.30650 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 = 0.993371 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-09_21:31 (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 141960 0.12 0.547120 2 142295 0.90 0.816232 3 141662 -0.58 0.281675 4 142025 0.27 0.606519 5 141437 -1.10 0.134889 6 141894 -0.04 0.485714 7 141127 -1.83 0.033784 8 141357 -1.29 0.098440 9 142065 0.36 0.641965 10 142080 0.40 0.654966 11 141442 -1.09 0.137440 12 142688 1.82 0.965569 13 141602 -0.72 0.236360 14 141653 -0.60 0.274619 15 142267 0.84 0.798332 16 141884 -0.06 0.476404 17 141505 -0.94 0.172407 18 141662 -0.58 0.281675 19 142040 0.31 0.619933 20 141819 -0.21 0.416424 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-09_21:31 Bits used No. missing words z-score p-value 23 to 32 141534 -1.2942 0.097791 22 to 31 141593 -1.0908 0.137682 21 to 30 141668 -0.8322 0.202656 20 to 29 141600 -1.0667 0.143064 19 to 28 141545 -1.2563 0.104502 18 to 27 142051 0.4885 0.687408 17 to 26 141939 0.1023 0.540745 16 to 25 141974 0.2230 0.588232 15 to 24 141768 -0.4873 0.313007 14 to 23 141485 -1.4632 0.071705 13 to 22 141836 -0.2529 0.400187 12 to 21 141996 0.2989 0.617477 11 to 20 142169 0.8954 0.814717 10 to 19 141639 -0.9322 0.175624 9 to 18 142107 0.6816 0.752261 8 to 17 141451 -1.5804 0.057002 7 to 16 141832 -0.2667 0.394867 6 to 15 141988 0.2713 0.606911 5 to 14 141625 -0.9804 0.163432 4 to 13 141602 -1.0598 0.144627 3 to 12 141982 0.2506 0.598933 2 to 11 142219 1.0678 0.857201 1 to 10 141924 0.0506 0.520172 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-09_21:31 Bits used No. missing words z-score p-value 28 to 32 142015 0.3582 0.639905 27 to 31 142153 0.8260 0.795598 26 to 30 142288 1.2836 0.900364 25 to 29 142110 0.6802 0.751823 24 to 28 141584 -1.1028 0.135054 23 to 27 141833 -0.2587 0.397916 22 to 26 141374 -1.8147 0.034787 21 to 25 141822 -0.2960 0.383602 20 to 24 141832 -0.2621 0.396609 19 to 23 141795 -0.3876 0.349171 18 to 22 141962 0.1785 0.570852 17 to 21 141944 0.1175 0.546778 16 to 20 141790 -0.4045 0.342919 15 to 19 141681 -0.7740 0.219465 14 to 18 141006 -3.0621 0.001099 13 to 17 142141 0.7853 0.783868 12 to 16 142338 1.4531 0.926905 11 to 15 142036 0.4294 0.666180 10 to 14 141881 -0.0960 0.461747 9 to 13 141610 -1.0147 0.155130 8 to 12 142014 0.3548 0.638635 7 to 11 142365 1.5446 0.938784 6 to 10 142170 0.8836 0.811551 5 to 9 141597 -1.0587 0.144858 4 to 8 141491 -1.4181 0.078086 3 to 7 141268 -2.1740 0.014853 2 to 6 142308 1.3514 0.911720 1 to 5 141477 -1.4655 0.071389 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-09_21:31 Bits used No. missing words z-score p-value 31 to 32 141262 -1.9095 0.028097 30 to 31 141706 -0.5998 0.274322 29 to 30 141813 -0.2842 0.388144 28 to 29 141525 -1.1337 0.128457 27 to 28 141892 -0.0511 0.479615 26 to 27 141963 0.1583 0.562897 25 to 26 142063 0.4533 0.674835 24 to 25 142343 1.2793 0.899598 23 to 24 142033 0.3648 0.642373 22 to 23 141933 0.0698 0.527833 21 to 22 142455 1.6096 0.946262 20 to 21 142317 1.2026 0.885428 19 to 20 142123 0.6303 0.735749 18 to 19 141572 -0.9951 0.159850 17 to 18 142121 0.6244 0.733816 16 to 17 142094 0.5447 0.707037 15 to 16 142026 0.3442 0.634637 14 to 15 141638 -0.8004 0.211744 13 to 14 142259 1.0315 0.848841 12 to 13 142009 0.2940 0.615626 11 to 12 142345 1.2852 0.900632 10 to 11 141913 0.0108 0.504319 9 to 10 141773 -0.4022 0.343786 8 to 9 141450 -1.3550 0.087716 7 to 8 141374 -1.5791 0.057151 6 to 7 141915 0.0167 0.506672 5 to 6 141792 -0.3461 0.364632 4 to 5 141700 -0.6175 0.268455 3 to 4 141709 -0.5909 0.277279 2 to 3 142653 2.1937 0.985872 1 to 2 142194 0.8397 0.799471 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-09_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2652.22 2.153 0.984332 Test results for specific bytes for dh-ranFile-2015-08-09_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2531.24 0.442 0.670692 2 to 9 2518.69 0.264 0.604259 3 to 10 2365.06 -1.908 0.028178 4 to 11 2499.23 -0.011 0.495665 5 to 12 2481.93 -0.256 0.399152 6 to 13 2351.67 -2.098 0.017968 7 to 14 2418.99 -1.146 0.125981 8 to 15 2594.27 1.333 0.908761 9 to 16 2568.01 0.962 0.831929 10 to 17 2457.65 -0.599 0.274596 11 to 18 2486.06 -0.197 0.421869 12 to 19 2371.19 -1.822 0.034249 13 to 20 2505.19 0.073 0.529230 14 to 21 2573.50 1.039 0.850686 15 to 22 2608.30 1.532 0.937193 16 to 23 2518.07 0.256 0.600841 17 to 24 2396.76 -1.460 0.072145 18 to 25 2423.04 -1.088 0.138206 19 to 26 2498.05 -0.028 0.489024 20 to 27 2461.01 -0.551 0.290657 21 to 28 2424.30 -1.071 0.142190 22 to 29 2448.46 -0.729 0.233031 23 to 30 2512.84 0.182 0.572066 24 to 31 2521.92 0.310 0.621742 25 to 32 2576.47 1.081 0.860248 CDPARK for dh-ranFile-2015-08-09_21:31: 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 3527 0.1826 0.572463 3562 1.7808 0.962529 3527 0.1826 0.572463 3512 -0.5023 0.307734 3491 -1.4612 0.071982 3558 1.5982 0.944998 3516 -0.3196 0.374623 3528 0.2283 0.590298 3487 -1.6438 0.050105 3534 0.5023 0.692266 Square side=100, avg. no. parked=3524.20 sample std.=23.24 p-value of the KSTEST for those 10 p-values: 0.863441 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-09_21:31 0.3450,0.4996,0.5427,0.5519,0.7515,0.3818,0.2413,0.1305,0.7701,0.6936, The KS test for those 10 p-values: 0.633380 The 3DSPHERES test for dh-ranFile-2015-08-09_21:31 sample no r^3 equiv. uni. 1 11.163 0.310713 2 63.920 0.881241 3 6.839 0.203853 4 116.358 0.979320 5 99.568 0.963809 6 58.028 0.855471 7 15.267 0.398853 8 9.788 0.278380 9 36.393 0.702725 10 9.534 0.272255 11 35.867 0.697467 12 20.728 0.498900 13 33.802 0.675906 14 61.904 0.872988 15 23.514 0.543338 16 99.620 0.963871 17 0.431 0.014276 18 21.672 0.514422 19 54.709 0.838561 20 14.686 0.387080 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.221033 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-09_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 1.3 0.1 -0.5 0.9 1.7 1.3 -1.0 0.7 -2.1 0.7 -0.4 1.8 1.2 -0.8 0.0 -1.0 0.5 -1.0 0.2 0.5 -1.9 -0.7 0.3 0.1 -0.3 1.3 0.8 0.0 2.6 -0.4 -0.2 -1.1 -0.1 -1.3 2.4 -0.7 -0.7 1.3 0.4 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:49.169802 z-score=0.782290, p-value=0.792058 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-09_21:31 Test no p-value 1 0.091167 2 0.542535 3 0.014512 4 0.391444 5 0.081692 6 0.044729 7 0.011938 8 0.018494 9 0.887954 10 0.080247 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000146 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-09_21:31: (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 66665 0.00 66648 0.01 3 25000.00 24941 0.14 25142 0.81 4 6666.67 6765 1.45 6623 0.29 5 1388.89 1356 0.78 1335 2.09 6 238.10 240 0.02 219 1.53 7 34.72 26 2.19 28 1.30 8 4.96 6 0.22 4 0.19 p=0.42922 p=0.59956 Number of rngs required: 687597, p-value: 0.175 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-09_21:31 No. of wins: Observed Expected 98764 98585.9 z-score= 0.797, pvalue=0.78720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66602 66666.7 0.063 0.063 2 37488 37654.3 0.735 0.797 3 26934 26954.7 0.016 0.813 4 19339 19313.5 0.034 0.847 5 13915 13851.4 0.292 1.139 6 9931 9943.5 0.016 1.155 7 7178 7145.0 0.152 1.307 8 5061 5139.1 1.186 2.493 9 3768 3699.9 1.255 3.748 10 2695 2666.3 0.309 4.057 11 1981 1923.3 1.729 5.786 12 1451 1388.7 2.791 8.577 13 974 1003.7 0.880 9.457 14 746 726.1 0.543 10.000 15 486 525.8 3.018 13.018 16 351 381.2 2.385 15.403 17 314 276.5 5.074 20.477 18 208 200.8 0.256 20.733 19 167 146.0 3.025 23.759 20 106 106.2 0.000 23.759 21 305 287.1 1.114 24.873 Chisq= 24.87 for 20 degrees of freedom, p= 0.79368 SUMMARY of craptest p-value for no. of wins: 0.787203 p-value for throws/game: 0.793684 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-09_21:31 No. of wins: Observed Expected 98544 98585.9 z-score=-0.187, pvalue=0.42575 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66488 66666.7 0.479 0.479 2 37942 37654.3 2.198 2.677 3 26919 26954.7 0.047 2.724 4 19178 19313.5 0.950 3.674 5 13707 13851.4 1.506 5.180 6 9878 9943.5 0.432 5.612 7 7277 7145.0 2.438 8.050 8 5216 5139.1 1.152 9.201 9 3688 3699.9 0.038 9.239 10 2636 2666.3 0.344 9.584 11 1999 1923.3 2.977 12.561 12 1381 1388.7 0.043 12.604 13 1007 1003.7 0.011 12.615 14 740 726.1 0.265 12.879 15 503 525.8 0.992 13.871 16 439 381.2 8.780 22.651 17 253 276.5 2.004 24.655 18 197 200.8 0.073 24.728 19 159 146.0 1.160 25.888 20 103 106.2 0.097 25.985 21 290 287.1 0.029 26.014 Chisq= 26.01 for 20 degrees of freedom, p= 0.83467 SUMMARY of craptest p-value for no. of wins: 0.425746 p-value for throws/game: 0.834666 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0011,0.0119,0.0143,0.0145,0.0149,0.0180,0.0185,0.0281,0.0282, 0.0336,0.0338,0.0342,0.0348,0.0447,0.0501,0.0548,0.0570,0.0572,0.0651, 0.0692,0.0714,0.0717,0.0720,0.0721,0.0781,0.0802,0.0817,0.0877,0.0912, 0.0978,0.0984,0.1045,0.1052,0.1181,0.1260,0.1272,0.1285,0.1305,0.1349, 0.1351,0.1374,0.1377,0.1382,0.1422,0.1431,0.1446,0.1449,0.1551,0.1599, 0.1634,0.1724,0.1754,0.1756,0.1758,0.1840,0.2027,0.2039,0.2117,0.2195, 0.2210,0.2216,0.2330,0.2364,0.2399,0.2413,0.2439,0.2550,0.2685,0.2723, 0.2743,0.2743,0.2746,0.2746,0.2773,0.2784,0.2817,0.2817,0.2847,0.2907, 0.3047,0.3065,0.3077,0.3107,0.3130,0.3151,0.3295,0.3333,0.3429,0.3438, 0.3450,0.3456,0.3492,0.3559,0.3646,0.3734,0.3746,0.3818,0.3836,0.3871, 0.3881,0.3912,0.3912,0.3914,0.3949,0.3966,0.3979,0.3989,0.3992,0.4002, 0.4007,0.4164,0.4218,0.4219,0.4251,0.4257,0.4292,0.4301,0.4464,0.4617, 0.4764,0.4796,0.4857,0.4890,0.4948,0.4957,0.4989,0.4996,0.5033,0.5043, 0.5067,0.5110,0.5144,0.5202,0.5278,0.5292,0.5407,0.5425,0.5427,0.5433, 0.5433,0.5468,0.5471,0.5500,0.5519,0.5629,0.5709,0.5721,0.5725,0.5725, 0.5882,0.5903,0.5989,0.5996,0.6008,0.6043,0.6065,0.6069,0.6079,0.6156, 0.6175,0.6184,0.6199,0.6217,0.6334,0.6336,0.6346,0.6386,0.6399,0.6420, 0.6424,0.6527,0.6550,0.6628,0.6662,0.6707,0.6748,0.6759,0.6851,0.6874, 0.6923,0.6936,0.6975,0.7027,0.7062,0.7070,0.7156,0.7191,0.7198,0.7259, 0.7338,0.7357,0.7367,0.7487,0.7515,0.7518,0.7523,0.7600,0.7701,0.7751, 0.7761,0.7839,0.7872,0.7921,0.7937,0.7956,0.7957,0.7983,0.7995,0.8039, 0.8116,0.8133,0.8147,0.8162,0.8163,0.8193,0.8260,0.8265,0.8269,0.8304, 0.8316,0.8319,0.8322,0.8347,0.8386,0.8408,0.8484,0.8485,0.8488,0.8507, 0.8555,0.8571,0.8572,0.8602,0.8634,0.8636,0.8653,0.8730,0.8812,0.8854, 0.8880,0.8996,0.9004,0.9006,0.9052,0.9060,0.9088,0.9117,0.9252,0.9261, 0.9269,0.9358,0.9372,0.9388,0.9450,0.9463,0.9507,0.9589,0.9625,0.9638, 0.9639,0.9656,0.9778,0.9793,0.9823,0.9843,0.9859,0.9934,0.9961, Overall p-value after applying KStest on 269 p-values = 0.765152 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.