RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-15_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 15.64 15.4706 0.438377 2 to 25 15.66 9.2502 0.067917 3 to 26 15.86 10.8495 0.135719 4 to 27 15.89 7.3699 0.021765 5 to 28 15.73 14.1424 0.343003 6 to 29 15.90 15.9133 0.470014 7 to 30 15.86 13.2266 0.279108 8 to 31 15.82 11.8321 0.189807 9 to 32 15.81 31.0521 0.980317 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.086877 Tough bday spacings test for dh-ranFile-2017-01-15_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 7 33 92 84 102 70 63 30 10 6 3 (O-E)^2/E 0.5 0.4 4.8 1.9 0.2 0.8 2.3 0.0 1.6 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.841, p= 0.767 RESULTS OF GCD FOR dh-ranFile-2017-01-15_21:31 Euclid's algorithm: p-value, steps to gcd: 0.645097 p-value, dist. of gcd's: 0.267012 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-15_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.378 0.234 0.342 0.448 0.720 0.268 0.865 0.293 Bits 8 to 15---> 0.374 0.243 0.666 0.523 0.673 0.225 0.102 0.654 Bits 16 to 23---> 0.294 0.134 0.943 0.383 0.026 0.146 0.880 0.993 Bits 24 to 31---> 0.677 0.722 0.146 0.653 0.108 0.494 0.522 0.595 KS test for the above 32 p values: 0.402 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-15_21:31, p-values for 5 runs: 0.9207, 0.9246, 0.9703, 0.1416, 0.1747 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-15_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5206 5134.0 1.009 1.444 r= 30 22932 23103.0 1.266 2.710 r= 31 11641 11551.5 0.693 3.403 chi-square = 3.403 with df = 3; p-value = 0.666 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-15_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5169 5134.0 0.238 0.443 r= 31 23052 23103.0 0.113 0.556 r= 32 11561 11551.5 0.008 0.564 chi-square = 0.564 with df = 3; p-value = 0.095 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-15_21:31 b-rank test for bits 1 to 8, p=0.70197 b-rank test for bits 2 to 9, p=0.11281 b-rank test for bits 3 to 10, p=0.49604 b-rank test for bits 4 to 11, p=0.72722 b-rank test for bits 5 to 12, p=0.24927 b-rank test for bits 6 to 13, p=0.08033 b-rank test for bits 7 to 14, p=0.92816 b-rank test for bits 8 to 15, p=0.82989 b-rank test for bits 9 to 16, p=0.05753 b-rank test for bits 10 to 17, p=0.48916 b-rank test for bits 11 to 18, p=0.94811 b-rank test for bits 12 to 19, p=0.01168 b-rank test for bits 13 to 20, p=0.12931 b-rank test for bits 14 to 21, p=0.21839 b-rank test for bits 15 to 22, p=0.29001 b-rank test for bits 16 to 23, p=0.92249 b-rank test for bits 17 to 24, p=0.44064 b-rank test for bits 18 to 25, p=0.54519 b-rank test for bits 19 to 26, p=0.61646 b-rank test for bits 20 to 27, p=0.44517 b-rank test for bits 21 to 28, p=0.91337 b-rank test for bits 22 to 29, p=0.14818 b-rank test for bits 23 to 30, p=0.84451 b-rank test for bits 24 to 31, p=0.16951 b-rank test for bits 25 to 32, p=0.29707 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 = 0.730354 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-15_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 142069 0.37 0.645448 2 141885 -0.06 0.477334 3 141786 -0.29 0.386614 4 141641 -0.63 0.265350 5 141865 -0.10 0.458753 6 141990 0.19 0.574750 7 141706 -0.48 0.317369 8 142425 1.20 0.885867 9 141349 -1.31 0.095236 10 142206 0.69 0.755894 11 142512 1.41 0.920450 12 142178 0.63 0.734911 13 142432 1.22 0.888993 14 141412 -1.16 0.122621 15 142196 0.67 0.748504 16 142338 1.00 0.841723 17 142095 0.43 0.667786 18 141917 0.02 0.507149 19 141955 0.11 0.542489 20 141426 -1.13 0.129391 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-15_21:31 Bits used No. missing words z-score p-value 23 to 32 141878 -0.1080 0.456984 22 to 31 141764 -0.5011 0.308137 21 to 30 142354 1.5333 0.937405 20 to 29 141816 -0.3218 0.373792 19 to 28 141355 -1.9115 0.027971 18 to 27 141960 0.1747 0.569352 17 to 26 141877 -0.1115 0.455617 16 to 25 141610 -1.0322 0.150996 15 to 24 142261 1.2127 0.887369 14 to 23 142192 0.9747 0.835151 13 to 22 142356 1.5402 0.938249 12 to 21 141904 -0.0184 0.492668 11 to 20 141720 -0.6529 0.256923 10 to 19 142008 0.3402 0.633163 9 to 18 141976 0.2299 0.590914 8 to 17 141414 -1.7080 0.043815 7 to 16 141680 -0.7908 0.214532 6 to 15 142239 1.1368 0.872188 5 to 14 141445 -1.6011 0.054673 4 to 13 142022 0.3885 0.651183 3 to 12 141831 -0.2701 0.393540 2 to 11 142096 0.6437 0.740112 1 to 10 142017 0.3713 0.644784 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-15_21:31 Bits used No. missing words z-score p-value 28 to 32 142046 0.4633 0.678421 27 to 31 141691 -0.7401 0.229619 26 to 30 142133 0.7582 0.775835 25 to 29 141975 0.2226 0.588081 24 to 28 142125 0.7311 0.767636 23 to 27 141958 0.1650 0.565521 22 to 26 141911 0.0057 0.502258 21 to 25 141917 0.0260 0.510371 20 to 24 142374 1.5752 0.942389 19 to 23 141988 0.2667 0.605141 18 to 22 141758 -0.5130 0.303982 17 to 21 142237 1.1107 0.866661 16 to 20 142068 0.5379 0.704665 15 to 19 141385 -1.7774 0.037752 14 to 18 141298 -2.0723 0.019119 13 to 17 141841 -0.2316 0.408414 12 to 16 142060 0.5107 0.695236 11 to 15 141811 -0.3333 0.369446 10 to 14 141691 -0.7401 0.229619 9 to 13 142080 0.5785 0.718551 8 to 12 142318 1.3853 0.917023 7 to 11 141718 -0.6486 0.258306 6 to 10 142112 0.6870 0.753964 5 to 9 142213 1.0294 0.848352 4 to 8 141708 -0.6825 0.247470 3 to 7 141634 -0.9333 0.175327 2 to 6 142049 0.4735 0.682057 1 to 5 142091 0.6158 0.730997 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-15_21:31 Bits used No. missing words z-score p-value 31 to 32 141725 -0.5437 0.293308 30 to 31 141606 -0.8948 0.185453 29 to 30 141633 -0.8151 0.207498 28 to 29 141833 -0.2252 0.410927 27 to 28 141964 0.1613 0.564059 26 to 27 141498 -1.2134 0.112496 25 to 26 141465 -1.3107 0.094978 24 to 25 141739 -0.5024 0.307676 23 to 24 142607 2.0580 0.980206 22 to 23 142225 0.9312 0.824120 21 to 22 141602 -0.9066 0.182315 20 to 21 141783 -0.3727 0.354703 19 to 20 142390 1.4179 0.921891 18 to 19 141946 0.1082 0.543070 17 to 18 142421 1.5094 0.934395 16 to 17 141450 -1.3550 0.087716 15 to 16 142117 0.6126 0.729928 14 to 15 141716 -0.5703 0.284239 13 to 14 142089 0.5300 0.701944 12 to 13 142095 0.5477 0.708051 11 to 12 142915 2.9666 0.998494 10 to 11 142566 1.9371 0.973632 9 to 10 142084 0.5153 0.696811 8 to 9 142159 0.7365 0.769284 7 to 8 141307 -1.7768 0.037802 6 to 7 142171 0.7719 0.779910 5 to 6 141559 -1.0334 0.150703 4 to 5 142299 1.1495 0.874819 3 to 4 141925 0.0462 0.518434 2 to 3 141717 -0.5673 0.285240 1 to 2 142426 1.5241 0.936258 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-15_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2493.26 -0.095 0.462043 Test results for specific bytes for dh-ranFile-2017-01-15_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2537.07 0.524 0.699962 2 to 9 2556.96 0.806 0.789742 3 to 10 2447.91 -0.737 0.230661 4 to 11 2460.83 -0.554 0.289828 5 to 12 2615.91 1.639 0.949415 6 to 13 2481.07 -0.268 0.394447 7 to 14 2456.81 -0.611 0.270655 8 to 15 2464.63 -0.500 0.308455 9 to 16 2526.17 0.370 0.644336 10 to 17 2487.75 -0.173 0.431239 11 to 18 2548.64 0.688 0.754252 12 to 19 2484.61 -0.218 0.413857 13 to 20 2494.57 -0.077 0.469406 14 to 21 2459.06 -0.579 0.281316 15 to 22 2524.68 0.349 0.636489 16 to 23 2538.21 0.540 0.705547 17 to 24 2576.93 1.088 0.861677 18 to 25 2310.25 -2.684 0.003643 19 to 26 2486.84 -0.186 0.426160 20 to 27 2457.29 -0.604 0.272907 21 to 28 2554.62 0.772 0.780086 22 to 29 2386.10 -1.611 0.053611 23 to 30 2503.41 0.048 0.519251 24 to 31 2365.64 -1.900 0.028707 25 to 32 2355.47 -2.044 0.020479 CDPARK for dh-ranFile-2017-01-15_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 3492 -1.4155 0.078457 3520 -0.1370 0.445521 3535 0.5479 0.708135 3520 -0.1370 0.445521 3500 -1.0502 0.146807 3547 1.0959 0.863437 3496 -1.2329 0.108811 3543 0.9132 0.819442 3530 0.3196 0.625377 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3520.20 sample std.=18.29 p-value of the KSTEST for those 10 p-values: 0.900051 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-15_21:31 0.5153,0.1981,0.1033,0.5481,0.3191,0.0897,0.5065,0.6044,0.4833,0.0134, The KS test for those 10 p-values: 0.097748 The 3DSPHERES test for dh-ranFile-2017-01-15_21:31 sample no r^3 equiv. uni. 1 23.004 0.535504 2 3.060 0.096972 3 41.129 0.746136 4 24.052 0.551450 5 2.106 0.067788 6 0.419 0.013866 7 5.895 0.178389 8 69.980 0.902964 9 27.026 0.593777 10 8.131 0.237406 11 14.211 0.377311 12 35.739 0.696174 13 42.656 0.758737 14 13.487 0.362094 15 169.707 0.996507 16 41.432 0.748691 17 25.990 0.579512 18 46.688 0.789078 19 22.063 0.520705 20 49.041 0.804988 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.811807 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-15_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.6 0.1 2.7 -0.5 -1.0 0.5 -0.5 0.8 0.6 -0.7 0.5 -0.8 0.6 -0.7 0.6 0.9 0.5 -0.9 0.6 -1.9 -0.7 -0.8 2.3 0.5 -0.7 -1.2 1.9 0.8 1.6 -0.9 -1.9 -0.7 -0.8 -0.4 -1.7 1.0 0.2 -0.4 0.4 0.9 -1.0 0.8 Chi-square with 42 degrees of freedom:49.080429 z-score=0.772538, p-value=0.789534 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-15_21:31 Test no p-value 1 0.041056 2 0.578359 3 0.402480 4 0.972786 5 0.219619 6 0.339569 7 0.633756 8 0.683455 9 0.580693 10 0.138005 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.903408 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-15_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 66770 0.16 66721 0.04 3 25000.00 24969 0.04 25004 0.00 4 6666.67 6626 0.25 6615 0.40 5 1388.89 1363 0.48 1389 0.00 6 238.10 231 0.21 220 1.38 7 34.72 34 0.01 45 3.04 8 4.96 6 0.22 5 0.00 p=0.03256 p=0.43872 Number of rngs required: 688872, p-value: 0.706 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-15_21:31 No. of wins: Observed Expected 98480 98585.9 z-score=-0.473, pvalue=0.31794 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66722 66666.7 0.046 0.046 2 37263 37654.3 4.067 4.113 3 27258 26954.7 3.412 7.525 4 19167 19313.5 1.111 8.635 5 13955 13851.4 0.775 9.410 6 10018 9943.5 0.558 9.968 7 7204 7145.0 0.487 10.454 8 5119 5139.1 0.078 10.533 9 3664 3699.9 0.348 10.880 10 2645 2666.3 0.170 11.050 11 1963 1923.3 0.818 11.869 12 1381 1388.7 0.043 11.912 13 995 1003.7 0.076 11.988 14 707 726.1 0.505 12.492 15 530 525.8 0.033 12.525 16 414 381.2 2.831 15.356 17 271 276.5 0.111 15.467 18 204 200.8 0.050 15.517 19 144 146.0 0.027 15.544 20 103 106.2 0.097 15.642 21 273 287.1 0.694 16.335 Chisq= 16.34 for 20 degrees of freedom, p= 0.30438 SUMMARY of craptest p-value for no. of wins: 0.317942 p-value for throws/game: 0.304384 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-15_21:31 No. of wins: Observed Expected 98278 98585.9 z-score=-1.377, pvalue=0.08427 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66505 66666.7 0.392 0.392 2 37590 37654.3 0.110 0.502 3 27055 26954.7 0.373 0.875 4 19076 19313.5 2.920 3.795 5 13959 13851.4 0.836 4.630 6 10014 9943.5 0.499 5.129 7 7128 7145.0 0.041 5.170 8 5250 5139.1 2.394 7.564 9 3805 3699.9 2.988 10.552 10 2608 2666.3 1.275 11.826 11 1923 1923.3 0.000 11.826 12 1386 1388.7 0.005 11.832 13 1015 1003.7 0.127 11.959 14 721 726.1 0.036 11.995 15 490 525.8 2.442 14.437 16 399 381.2 0.836 15.273 17 294 276.5 1.102 16.376 18 217 200.8 1.302 17.678 19 152 146.0 0.248 17.926 20 109 106.2 0.073 17.999 21 304 287.1 0.993 18.992 Chisq= 18.99 for 20 degrees of freedom, p= 0.47763 SUMMARY of craptest p-value for no. of wins: 0.084268 p-value for throws/game: 0.477634 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0036,0.0117,0.0134,0.0139,0.0191,0.0205,0.0218,0.0258,0.0280,0.0287, 0.0326,0.0378,0.0378,0.0411,0.0438,0.0536,0.0547,0.0575,0.0678,0.0679, 0.0785,0.0803,0.0843,0.0869,0.0877,0.0897,0.0950,0.0952,0.0954,0.0970, 0.0977,0.1023,0.1033,0.1077,0.1088,0.1125,0.1128,0.1226,0.1293,0.1294, 0.1336,0.1357,0.1380,0.1416,0.1455,0.1460,0.1468,0.1482,0.1507,0.1510, 0.1695,0.1747,0.1753,0.1784,0.1823,0.1855,0.1898,0.1981,0.2075,0.2145, 0.2184,0.2196,0.2250,0.2296,0.2296,0.2307,0.2344,0.2374,0.2426,0.2475, 0.2493,0.2569,0.2583,0.2653,0.2670,0.2677,0.2707,0.2729,0.2791,0.2813, 0.2842,0.2852,0.2898,0.2900,0.2929,0.2933,0.2936,0.2971,0.3040,0.3044, 0.3077,0.3081,0.3085,0.3174,0.3179,0.3191,0.3396,0.3425,0.3430,0.3547, 0.3621,0.3694,0.3738,0.3743,0.3773,0.3780,0.3828,0.3866,0.3935,0.3944, 0.4017,0.4025,0.4084,0.4109,0.4139,0.4262,0.4275,0.4312,0.4384,0.4387, 0.4406,0.4452,0.4455,0.4455,0.4480,0.4556,0.4570,0.4588,0.4620,0.4694, 0.4700,0.4773,0.4776,0.4833,0.4892,0.4927,0.4942,0.4960,0.5023,0.5065, 0.5071,0.5104,0.5153,0.5184,0.5193,0.5207,0.5221,0.5230,0.5355,0.5425, 0.5431,0.5452,0.5481,0.5515,0.5641,0.5655,0.5694,0.5748,0.5784,0.5795, 0.5807,0.5881,0.5909,0.5938,0.5953,0.6044,0.6051,0.6165,0.6254,0.6332, 0.6338,0.6365,0.6443,0.6448,0.6451,0.6454,0.6512,0.6533,0.6543,0.6655, 0.6665,0.6678,0.6726,0.6774,0.6784,0.6821,0.6835,0.6952,0.6962,0.6968, 0.7000,0.7019,0.7020,0.7047,0.7055,0.7056,0.7081,0.7081,0.7186,0.7198, 0.7219,0.7272,0.7299,0.7304,0.7310,0.7349,0.7401,0.7461,0.7485,0.7487, 0.7540,0.7543,0.7559,0.7587,0.7673,0.7676,0.7693,0.7758,0.7799,0.7801, 0.7891,0.7895,0.7897,0.8050,0.8118,0.8194,0.8241,0.8299,0.8352,0.8417, 0.8445,0.8484,0.8617,0.8634,0.8646,0.8667,0.8722,0.8748,0.8799,0.8859, 0.8874,0.8890,0.9001,0.9030,0.9034,0.9134,0.9170,0.9205,0.9207,0.9219, 0.9225,0.9246,0.9282,0.9344,0.9363,0.9374,0.9382,0.9424,0.9430,0.9481, 0.9494,0.9703,0.9728,0.9736,0.9802,0.9803,0.9930,0.9965,0.9985, Overall p-value after applying KStest on 269 p-values = 0.787292 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.