RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-26_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.41 22.2521 0.824784 2 to 25 15.78 23.8576 0.876645 3 to 26 15.79 16.9820 0.544416 4 to 27 15.85 16.8796 0.537446 5 to 28 15.76 5.5231 0.004141 6 to 29 16.02 27.1405 0.943961 7 to 30 15.91 27.2126 0.944977 8 to 31 15.83 10.9898 0.142904 9 to 32 15.70 16.5930 0.517745 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.271161 Tough bday spacings test for dh-ranFile-2015-10-26_07:31: 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 39 64 105 96 78 61 28 11 7 2 (O-E)^2/E 0.0 0.2 1.2 0.5 0.0 0.0 1.5 0.1 1.0 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.617, p= 0.154 RESULTS OF GCD FOR dh-ranFile-2015-10-26_07:31 Euclid's algorithm: p-value, steps to gcd: 0.522957 p-value, dist. of gcd's: 0.665595 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-26_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.490 0.204 0.840 0.243 0.948 0.862 0.502 0.205 Bits 8 to 15---> 0.170 0.503 0.797 0.937 0.908 0.010 0.802 0.236 Bits 16 to 23---> 0.454 0.296 0.730 0.751 0.627 0.749 0.122 0.731 Bits 24 to 31---> 0.065 0.083 0.927 0.682 0.629 0.322 0.084 0.399 KS test for the above 32 p values: 0.047 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-26_07:31, p-values for 5 runs: 0.3279, 0.7008, 0.7601, 0.3376, 0.0001 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-26_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5197 5134.0 0.773 0.828 r= 30 22948 23103.0 1.041 1.869 r= 31 11647 11551.5 0.789 2.658 chi-square = 2.658 with df = 3; p-value = 0.553 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-26_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5033 5134.0 1.987 1.999 r= 31 23230 23103.0 0.698 2.697 r= 32 11524 11551.5 0.066 2.762 chi-square = 2.762 with df = 3; p-value = 0.570 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-26_07:31 b-rank test for bits 1 to 8, p=0.12376 b-rank test for bits 2 to 9, p=0.36823 b-rank test for bits 3 to 10, p=0.85763 b-rank test for bits 4 to 11, p=0.69284 b-rank test for bits 5 to 12, p=0.41570 b-rank test for bits 6 to 13, p=0.31290 b-rank test for bits 7 to 14, p=0.96040 b-rank test for bits 8 to 15, p=0.79968 b-rank test for bits 9 to 16, p=0.18575 b-rank test for bits 10 to 17, p=0.72217 b-rank test for bits 11 to 18, p=0.70466 b-rank test for bits 12 to 19, p=0.39982 b-rank test for bits 13 to 20, p=0.70230 b-rank test for bits 14 to 21, p=0.92599 b-rank test for bits 15 to 22, p=0.50087 b-rank test for bits 16 to 23, p=0.67629 b-rank test for bits 17 to 24, p=0.07689 b-rank test for bits 18 to 25, p=0.84345 b-rank test for bits 19 to 26, p=0.63408 b-rank test for bits 20 to 27, p=0.62033 b-rank test for bits 21 to 28, p=0.01283 b-rank test for bits 22 to 29, p=0.66128 b-rank test for bits 23 to 30, p=0.53423 b-rank test for bits 24 to 31, p=0.25321 b-rank test for bits 25 to 32, p=0.31048 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 = 0.804877 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-26_07:31 (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 141479 -1.01 0.157342 2 141955 0.11 0.542489 3 142304 0.92 0.821769 4 142060 0.35 0.637593 5 141983 0.17 0.568331 6 142170 0.61 0.728752 7 140974 -2.19 0.014432 8 141225 -1.60 0.054921 9 141633 -0.65 0.259259 10 142360 1.05 0.853822 11 141290 -1.45 0.073944 12 142135 0.53 0.700996 13 142548 1.49 0.932179 14 142267 0.84 0.798332 15 142519 1.42 0.922844 16 141719 -0.44 0.328270 17 141650 -0.61 0.272287 18 141652 -0.60 0.273841 19 141888 -0.05 0.480126 20 140602 -3.05 0.001127 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-26_07:31 Bits used No. missing words z-score p-value 23 to 32 142455 1.8816 0.970056 22 to 31 141622 -0.9908 0.160893 21 to 30 141988 0.2713 0.606911 20 to 29 142316 1.4023 0.919589 19 to 28 142233 1.1161 0.867811 18 to 27 142097 0.6471 0.741229 17 to 26 141758 -0.5218 0.300895 16 to 25 141921 0.0402 0.516050 15 to 24 141872 -0.1287 0.448788 14 to 23 142038 0.4437 0.671367 13 to 22 142167 0.8885 0.812869 12 to 21 141937 0.0954 0.538007 11 to 20 141563 -1.1942 0.116192 10 to 19 141707 -0.6977 0.242686 9 to 18 141822 -0.3011 0.381655 8 to 17 141629 -0.9667 0.166858 7 to 16 141990 0.2782 0.609560 6 to 15 142033 0.4264 0.665109 5 to 14 141820 -0.3080 0.379028 4 to 13 141996 0.2989 0.617477 3 to 12 141649 -0.8977 0.184676 2 to 11 142055 0.5023 0.692275 1 to 10 142070 0.5540 0.710222 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-26_07:31 Bits used No. missing words z-score p-value 28 to 32 141622 -0.9740 0.165028 27 to 31 141626 -0.9604 0.168417 26 to 30 141676 -0.7909 0.214487 25 to 29 142134 0.7616 0.776849 24 to 28 141788 -0.4113 0.340431 23 to 27 142107 0.6701 0.748593 22 to 26 142165 0.8667 0.806941 21 to 25 141740 -0.5740 0.282984 20 to 24 141650 -0.8791 0.189678 19 to 23 141832 -0.2621 0.396609 18 to 22 141907 -0.0079 0.496849 17 to 21 142119 0.7107 0.761379 16 to 20 142296 1.3107 0.905028 15 to 19 142025 0.3921 0.652509 14 to 18 142214 1.0328 0.849147 13 to 17 142133 0.7582 0.775835 12 to 16 141400 -1.7265 0.042125 11 to 15 141912 0.0091 0.503611 10 to 14 142188 0.9446 0.827580 9 to 13 141885 -0.0825 0.467135 8 to 12 142052 0.4836 0.685675 7 to 11 142231 1.0904 0.862233 6 to 10 142125 0.7311 0.767636 5 to 9 141792 -0.3977 0.345415 4 to 8 141477 -1.4655 0.071389 3 to 7 141842 -0.2282 0.409731 2 to 6 142209 1.0158 0.845145 1 to 5 142341 1.4633 0.928306 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-26_07:31 Bits used No. missing words z-score p-value 31 to 32 141399 -1.5054 0.066111 30 to 31 141703 -0.6086 0.271381 29 to 30 142216 0.9046 0.817170 28 to 29 141918 0.0256 0.510202 27 to 28 141555 -1.0452 0.147960 26 to 27 141978 0.2026 0.580263 25 to 26 142310 1.1819 0.881381 24 to 25 142635 2.1406 0.983848 23 to 24 141819 -0.2665 0.394942 22 to 23 141268 -1.8918 0.029257 21 to 22 141572 -0.9951 0.159850 20 to 21 141582 -0.9656 0.167128 19 to 20 142439 1.5624 0.940909 18 to 19 142216 0.9046 0.817170 17 to 18 142794 2.6096 0.995468 16 to 17 141465 -1.3107 0.094978 15 to 16 142047 0.4061 0.657668 14 to 15 142435 1.5506 0.939507 13 to 14 141320 -1.7384 0.041067 12 to 13 141980 0.2085 0.582568 11 to 12 141840 -0.2045 0.418976 10 to 11 141590 -0.9420 0.173102 9 to 10 141815 -0.2783 0.390407 8 to 9 141338 -1.6853 0.045962 7 to 8 141886 -0.0688 0.472566 6 to 7 142319 1.2085 0.886566 5 to 6 141991 0.2409 0.595189 4 to 5 141720 -0.5585 0.288253 3 to 4 141072 -2.4700 0.006756 2 to 3 141934 0.0728 0.529007 1 to 2 142347 1.2911 0.901659 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-26_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2508.12 0.115 0.545740 Test results for specific bytes for dh-ranFile-2015-10-26_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2475.36 -0.348 0.363757 2 to 9 2512.06 0.171 0.567730 3 to 10 2542.03 0.594 0.723894 4 to 11 2389.49 -1.563 0.059052 5 to 12 2502.75 0.039 0.515498 6 to 13 2486.24 -0.195 0.422835 7 to 14 2425.08 -1.059 0.144690 8 to 15 2541.10 0.581 0.719463 9 to 16 2567.75 0.958 0.831018 10 to 17 2460.07 -0.565 0.286124 11 to 18 2461.66 -0.542 0.293842 12 to 19 2596.52 1.365 0.913878 13 to 20 2359.15 -1.992 0.023187 14 to 21 2451.59 -0.685 0.246775 15 to 22 2553.53 0.757 0.775501 16 to 23 2533.53 0.474 0.682320 17 to 24 2523.50 0.332 0.630210 18 to 25 2436.18 -0.902 0.183398 19 to 26 2480.67 -0.273 0.392271 20 to 27 2442.50 -0.813 0.208061 21 to 28 2617.76 1.665 0.952079 22 to 29 2520.04 0.283 0.611587 23 to 30 2520.88 0.295 0.616091 24 to 31 2456.75 -0.612 0.270404 25 to 32 2534.73 0.491 0.688351 CDPARK for dh-ranFile-2015-10-26_07:31: 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 3497 -1.1872 0.117571 3531 0.3653 0.642555 3522 -0.0457 0.481790 3491 -1.4612 0.071982 3514 -0.4110 0.340551 3525 0.0913 0.536383 3539 0.7306 0.767486 3530 0.3196 0.625377 3552 1.3242 0.907282 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3521.00 sample std.=17.75 p-value of the KSTEST for those 10 p-values: 0.982619 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-26_07:31 0.5150,0.7424,0.0576,0.1257,0.8558,0.9779,0.8472,0.5382,0.8855,0.8582, The KS test for those 10 p-values: 0.121330 The 3DSPHERES test for dh-ranFile-2015-10-26_07:31 sample no r^3 equiv. uni. 1 32.526 0.661833 2 41.787 0.751646 3 1.060 0.034702 4 59.889 0.864165 5 28.949 0.619010 6 44.888 0.776032 7 9.436 0.269862 8 4.080 0.127164 9 3.942 0.123120 10 46.761 0.789593 11 3.387 0.106751 12 10.285 0.290252 13 170.794 0.996631 14 36.493 0.703717 15 17.058 0.433681 16 83.968 0.939125 17 28.084 0.607863 18 1.924 0.062116 19 30.118 0.633565 20 12.171 0.333487 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.879573 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-26_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 1.8 -0.1 -1.0 -0.2 -2.0 -0.7 1.5 0.4 0.9 0.8 2.2 0.5 -0.9 -0.1 -0.3 -0.8 0.0 -0.9 0.6 -1.7 1.2 -1.1 -0.5 -0.5 0.9 0.1 -0.3 1.2 0.6 1.9 -1.1 1.5 -0.6 -0.5 0.6 0.0 -0.7 1.3 0.4 1.6 0.0 0.8 Chi-square with 42 degrees of freedom:44.665162 z-score=0.290793, p-value=0.639569 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-26_07:31 Test no p-value 1 0.004768 2 0.326170 3 0.178680 4 0.089781 5 0.383101 6 0.239730 7 0.006858 8 0.962212 9 0.051905 10 0.084172 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001074 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-26_07:31: (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 66758 0.13 66243 2.69 3 25000.00 24992 0.00 25176 1.24 4 6666.67 6617 0.37 6870 6.20 5 1388.89 1345 1.39 1396 0.04 6 238.10 245 0.20 259 1.84 7 34.72 34 0.01 51 7.63 8 4.96 8 1.86 4 0.19 p=0.31833 p=0.99702 Number of rngs required: 689505, p-value: 0.900 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-26_07:31 No. of wins: Observed Expected 98409 98585.9 z-score=-0.791, pvalue=0.21447 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66528 66666.7 0.288 0.288 2 37786 37654.3 0.460 0.749 3 27122 26954.7 1.038 1.787 4 19488 19313.5 1.577 3.364 5 13513 13851.4 8.268 11.633 6 9940 9943.5 0.001 11.634 7 7062 7145.0 0.965 12.599 8 5157 5139.1 0.063 12.661 9 3702 3699.9 0.001 12.662 10 2619 2666.3 0.839 13.501 11 1944 1923.3 0.222 13.724 12 1388 1388.7 0.000 13.724 13 1024 1003.7 0.410 14.134 14 745 726.1 0.490 14.624 15 538 525.8 0.281 14.905 16 372 381.2 0.220 15.125 17 290 276.5 0.655 15.780 18 234 200.8 5.479 21.258 19 147 146.0 0.007 21.266 20 102 106.2 0.167 21.433 21 299 287.1 0.492 21.925 Chisq= 21.92 for 20 degrees of freedom, p= 0.65540 SUMMARY of craptest p-value for no. of wins: 0.214468 p-value for throws/game: 0.655400 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-26_07:31 No. of wins: Observed Expected 98293 98585.9 z-score=-1.310, pvalue=0.09513 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66819 66666.7 0.348 0.348 2 37396 37654.3 1.772 2.120 3 27102 26954.7 0.805 2.925 4 19233 19313.5 0.335 3.260 5 13918 13851.4 0.320 3.580 6 10062 9943.5 1.411 4.991 7 7153 7145.0 0.009 5.000 8 5046 5139.1 1.686 6.686 9 3693 3699.9 0.013 6.699 10 2748 2666.3 2.504 9.202 11 1920 1923.3 0.006 9.208 12 1352 1388.7 0.972 10.180 13 949 1003.7 2.983 13.163 14 759 726.1 1.487 14.649 15 497 525.8 1.581 16.231 16 358 381.2 1.406 17.637 17 248 276.5 2.945 20.582 18 206 200.8 0.133 20.715 19 162 146.0 1.757 22.472 20 89 106.2 2.790 25.263 21 290 287.1 0.029 25.292 Chisq= 25.29 for 20 degrees of freedom, p= 0.80950 SUMMARY of craptest p-value for no. of wins: 0.095126 p-value for throws/game: 0.809499 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0011,0.0011,0.0041,0.0048,0.0068,0.0069,0.0102,0.0128,0.0144, 0.0232,0.0293,0.0347,0.0411,0.0421,0.0460,0.0471,0.0519,0.0549,0.0576, 0.0591,0.0621,0.0648,0.0661,0.0714,0.0720,0.0739,0.0769,0.0834,0.0841, 0.0842,0.0898,0.0950,0.0951,0.1068,0.1162,0.1176,0.1213,0.1220,0.1231, 0.1238,0.1257,0.1272,0.1429,0.1447,0.1480,0.1536,0.1573,0.1599,0.1609, 0.1650,0.1669,0.1671,0.1684,0.1697,0.1731,0.1787,0.1834,0.1847,0.1858, 0.1897,0.2042,0.2050,0.2081,0.2145,0.2145,0.2355,0.2397,0.2427,0.2429, 0.2468,0.2532,0.2593,0.2613,0.2699,0.2704,0.2712,0.2714,0.2723,0.2738, 0.2830,0.2861,0.2883,0.2903,0.2938,0.2958,0.3009,0.3105,0.3129,0.3183, 0.3216,0.3262,0.3279,0.3283,0.3335,0.3376,0.3404,0.3406,0.3454,0.3638, 0.3682,0.3790,0.3817,0.3831,0.3904,0.3923,0.3949,0.3966,0.3986,0.3998, 0.4097,0.4157,0.4190,0.4228,0.4337,0.4488,0.4537,0.4671,0.4726,0.4801, 0.4818,0.4904,0.4968,0.5009,0.5020,0.5028,0.5036,0.5102,0.5150,0.5155, 0.5160,0.5177,0.5230,0.5290,0.5342,0.5364,0.5374,0.5380,0.5382,0.5425, 0.5444,0.5457,0.5525,0.5677,0.5683,0.5703,0.5803,0.5826,0.5952,0.6069, 0.6079,0.6096,0.6116,0.6161,0.6175,0.6190,0.6203,0.6254,0.6270,0.6291, 0.6302,0.6336,0.6341,0.6376,0.6396,0.6426,0.6525,0.6554,0.6577,0.6613, 0.6618,0.6651,0.6656,0.6714,0.6763,0.6823,0.6824,0.6857,0.6884,0.6923, 0.6928,0.7008,0.7010,0.7023,0.7037,0.7047,0.7102,0.7195,0.7222,0.7239, 0.7288,0.7298,0.7312,0.7412,0.7424,0.7486,0.7494,0.7512,0.7516,0.7601, 0.7614,0.7675,0.7676,0.7755,0.7758,0.7760,0.7768,0.7896,0.7974,0.7983, 0.7997,0.8015,0.8049,0.8069,0.8095,0.8129,0.8172,0.8172,0.8218,0.8248, 0.8276,0.8310,0.8401,0.8435,0.8451,0.8472,0.8491,0.8538,0.8558,0.8576, 0.8582,0.8617,0.8622,0.8642,0.8678,0.8766,0.8796,0.8814,0.8855,0.8866, 0.9001,0.9017,0.9050,0.9073,0.9084,0.9139,0.9196,0.9228,0.9260,0.9273, 0.9283,0.9322,0.9373,0.9391,0.9395,0.9409,0.9440,0.9450,0.9484,0.9521, 0.9604,0.9622,0.9701,0.9779,0.9826,0.9838,0.9955,0.9966,0.9970, Overall p-value after applying KStest on 269 p-values = 0.398250 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.