RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-30_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.71 22.1476 0.820891 2 to 25 15.82 12.4756 0.229478 3 to 26 15.72 30.5004 0.977046 4 to 27 15.72 15.0694 0.409515 5 to 28 16.06 13.0025 0.263984 6 to 29 15.24 37.3926 0.997024 7 to 30 15.81 6.9112 0.015331 8 to 31 16.03 9.9118 0.092732 9 to 32 15.79 11.3945 0.164661 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.175804 Tough bday spacings test for dh-ranFile-2016-09-30_14:31: 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 36 75 97 92 87 48 29 17 4 6 (O-E)^2/E 0.0 0.0 0.0 0.0 0.3 1.0 0.3 0.0 0.3 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 3.990, p= 0.052 RESULTS OF GCD FOR dh-ranFile-2016-09-30_14:31 Euclid's algorithm: p-value, steps to gcd: 0.393102 p-value, dist. of gcd's: 0.225800 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-30_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.546 0.813 0.247 0.323 0.134 0.786 0.844 0.721 Bits 8 to 15---> 0.038 0.879 0.779 0.649 0.726 0.428 0.403 0.278 Bits 16 to 23---> 0.845 0.085 0.609 0.200 0.192 0.949 0.016 0.236 Bits 24 to 31---> 0.848 0.758 0.707 0.106 0.065 0.517 0.563 0.594 KS test for the above 32 p values: 0.133 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-30_14:31, p-values for 5 runs: 0.9045, 0.4736, 0.1669, 0.3212, 0.3258 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-30_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 174 211.4 6.622 6.622 r= 29 5149 5134.0 0.044 6.666 r= 30 23133 23103.0 0.039 6.705 r= 31 11544 11551.5 0.005 6.710 chi-square = 6.710 with df = 3; p-value = 0.918 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-30_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5221 5134.0 1.474 1.483 r= 31 23098 23103.0 0.001 1.485 r= 32 11471 11551.5 0.561 2.046 chi-square = 2.046 with df = 3; p-value = 0.437 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-30_14:31 b-rank test for bits 1 to 8, p=0.81624 b-rank test for bits 2 to 9, p=0.90048 b-rank test for bits 3 to 10, p=0.04518 b-rank test for bits 4 to 11, p=0.11926 b-rank test for bits 5 to 12, p=0.23633 b-rank test for bits 6 to 13, p=0.28820 b-rank test for bits 7 to 14, p=0.75878 b-rank test for bits 8 to 15, p=0.70817 b-rank test for bits 9 to 16, p=0.03646 b-rank test for bits 10 to 17, p=0.13389 b-rank test for bits 11 to 18, p=0.00763 b-rank test for bits 12 to 19, p=0.10795 b-rank test for bits 13 to 20, p=0.18587 b-rank test for bits 14 to 21, p=0.64445 b-rank test for bits 15 to 22, p=0.09614 b-rank test for bits 16 to 23, p=0.30650 b-rank test for bits 17 to 24, p=0.32093 b-rank test for bits 18 to 25, p=0.56231 b-rank test for bits 19 to 26, p=0.45331 b-rank test for bits 20 to 27, p=0.69968 b-rank test for bits 21 to 28, p=0.82914 b-rank test for bits 22 to 29, p=0.84575 b-rank test for bits 23 to 30, p=0.62066 b-rank test for bits 24 to 31, p=0.08806 b-rank test for bits 25 to 32, p=0.26972 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 = 0.106306 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-30_14:31 (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 141892 -0.04 0.483851 2 141973 0.15 0.559129 3 141971 0.14 0.557285 4 141799 -0.26 0.398288 5 142489 1.35 0.912191 6 141876 -0.08 0.468964 7 142335 0.99 0.840024 8 142467 1.30 0.903707 9 142245 0.78 0.783561 10 141697 -0.50 0.309913 11 141881 -0.07 0.473613 12 141259 -1.52 0.064323 13 142550 1.50 0.932789 14 141842 -0.16 0.437499 15 141698 -0.49 0.310737 16 141677 -0.54 0.293624 17 141292 -1.44 0.074600 18 141832 -0.18 0.428310 19 142325 0.97 0.834274 20 142269 0.84 0.799644 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-30_14:31 Bits used No. missing words z-score p-value 23 to 32 141725 -0.6356 0.262512 22 to 31 141088 -2.8322 0.002312 21 to 30 141948 0.1333 0.553040 20 to 29 141611 -1.0287 0.151805 19 to 28 142135 0.7782 0.781766 18 to 27 141819 -0.3115 0.377717 17 to 26 142221 1.0747 0.858751 16 to 25 142243 1.1506 0.875049 15 to 24 141906 -0.0115 0.495419 14 to 23 142057 0.5092 0.694696 13 to 22 142426 1.7816 0.962594 12 to 21 141922 0.0437 0.517424 11 to 20 142157 0.8540 0.803457 10 to 19 142187 0.9575 0.830838 9 to 18 141509 -1.3804 0.083724 8 to 17 142462 1.9058 0.971659 7 to 16 141714 -0.6736 0.250298 6 to 15 141719 -0.6563 0.255812 5 to 14 141927 0.0609 0.524293 4 to 13 141772 -0.4736 0.317910 3 to 12 141735 -0.6011 0.273874 2 to 11 142313 1.3920 0.918034 1 to 10 142402 1.6989 0.955327 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-30_14:31 Bits used No. missing words z-score p-value 28 to 32 141908 -0.0045 0.498201 27 to 31 142054 0.4904 0.688077 26 to 30 141890 -0.0655 0.473878 25 to 29 141785 -0.4215 0.336711 24 to 28 142109 0.6768 0.750749 23 to 27 142023 0.3853 0.650001 22 to 26 141965 0.1887 0.574841 21 to 25 141610 -1.0147 0.155130 20 to 24 141927 0.0599 0.523882 19 to 23 142165 0.8667 0.806941 18 to 22 141961 0.1752 0.569520 17 to 21 141476 -1.4689 0.070928 16 to 20 142260 1.1887 0.882723 15 to 19 142067 0.5345 0.703493 14 to 18 141866 -0.1469 0.441613 13 to 17 141987 0.2633 0.603836 12 to 16 141664 -0.8316 0.202810 11 to 15 141405 -1.7096 0.043671 10 to 14 142137 0.7718 0.779873 9 to 13 141619 -0.9842 0.162516 8 to 12 141970 0.2057 0.581472 7 to 11 141818 -0.3096 0.378435 6 to 10 141989 0.2701 0.606446 5 to 9 141755 -0.5232 0.300434 4 to 8 141965 0.1887 0.574841 3 to 7 142192 0.9582 0.831020 2 to 6 142479 1.9311 0.973264 1 to 5 141950 0.1379 0.554826 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-30_14:31 Bits used No. missing words z-score p-value 31 to 32 141813 -0.2842 0.388144 30 to 31 142259 1.0315 0.848841 29 to 30 141810 -0.2930 0.384758 28 to 29 141777 -0.3904 0.348137 27 to 28 141571 -0.9980 0.159134 26 to 27 142335 1.2557 0.895381 25 to 26 142075 0.4887 0.687474 24 to 25 141951 0.1229 0.548915 23 to 24 142077 0.4946 0.689559 22 to 23 141327 -1.7178 0.042918 21 to 22 142104 0.5742 0.717100 20 to 21 142176 0.7866 0.784253 19 to 20 142513 1.7807 0.962522 18 to 19 142171 0.7719 0.779910 17 to 18 142193 0.8368 0.798643 16 to 17 142031 0.3589 0.640168 15 to 16 141892 -0.0511 0.479615 14 to 15 142046 0.4032 0.656583 13 to 14 141792 -0.3461 0.364632 12 to 13 142108 0.5860 0.721078 11 to 12 142301 1.1554 0.876030 10 to 11 142293 1.1318 0.871134 9 to 10 141751 -0.4671 0.320232 8 to 9 141760 -0.4405 0.329787 7 to 8 142173 0.7778 0.781653 6 to 7 142039 0.3825 0.648958 5 to 6 141973 0.1878 0.574490 4 to 5 142409 1.4740 0.929753 3 to 4 142513 1.7807 0.962522 2 to 3 142300 1.1524 0.875426 1 to 2 142176 0.7866 0.784253 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-30_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2528.50 0.403 0.656569 Test results for specific bytes for dh-ranFile-2016-09-30_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2523.04 0.326 0.627744 2 to 9 2488.46 -0.163 0.435191 3 to 10 2618.25 1.672 0.952768 4 to 11 2533.81 0.478 0.683724 5 to 12 2530.42 0.430 0.666485 6 to 13 2442.60 -0.812 0.208470 7 to 14 2517.48 0.247 0.597601 8 to 15 2447.39 -0.744 0.228425 9 to 16 2587.50 1.237 0.892025 10 to 17 2488.61 -0.161 0.435993 11 to 18 2516.93 0.239 0.594629 12 to 19 2460.18 -0.563 0.286688 13 to 20 2494.06 -0.084 0.466535 14 to 21 2426.03 -1.046 0.147764 15 to 22 2387.60 -1.590 0.055958 16 to 23 2450.47 -0.700 0.241835 17 to 24 2428.99 -1.004 0.157643 18 to 25 2517.02 0.241 0.595124 19 to 26 2616.53 1.648 0.950328 20 to 27 2562.79 0.888 0.812721 21 to 28 2533.03 0.467 0.679806 22 to 29 2444.43 -0.786 0.215953 23 to 30 2540.11 0.567 0.714731 24 to 31 2511.00 0.156 0.561820 25 to 32 2494.62 -0.076 0.469668 CDPARK for dh-ranFile-2016-09-30_14:31: 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 3495 -1.2785 0.100530 3528 0.2283 0.590298 3517 -0.2740 0.392053 3548 1.1416 0.873180 3507 -0.7306 0.232514 3547 1.0959 0.863437 3522 -0.0457 0.481790 3530 0.3196 0.625377 3535 0.5479 0.708135 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3523.80 sample std.=16.39 p-value of the KSTEST for those 10 p-values: 0.969553 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-30_14:31 0.0750,0.0610,0.2567,0.2065,0.2095,0.4484,0.0797,0.6470,0.2438,0.9749, The KS test for those 10 p-values: 0.048475 The 3DSPHERES test for dh-ranFile-2016-09-30_14:31 sample no r^3 equiv. uni. 1 0.636 0.020976 2 6.223 0.187345 3 6.938 0.206481 4 36.997 0.708650 5 102.996 0.967717 6 44.609 0.773944 7 63.624 0.880065 8 2.093 0.067403 9 47.593 0.795349 10 24.051 0.551439 11 38.628 0.724072 12 22.663 0.530192 13 61.210 0.870013 14 7.609 0.224013 15 16.059 0.414504 16 68.245 0.897187 17 30.554 0.638852 18 19.697 0.481369 19 21.959 0.519040 20 61.303 0.870419 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.501213 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-30_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.1 -0.4 -1.4 1.0 0.4 -1.0 0.6 -0.2 -0.8 0.8 0.0 0.1 0.2 0.6 0.4 0.5 -0.1 0.2 0.1 -1.2 -0.6 -1.1 0.2 -0.2 0.5 0.5 0.0 0.5 -0.4 0.8 0.4 -2.3 -0.2 0.1 -0.3 -1.4 -1.0 0.1 1.5 -1.3 0.0 -0.1 Chi-square with 42 degrees of freedom:26.740173 z-score=-1.664984, p-value=0.032223 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-30_14:31 Test no p-value 1 0.062210 2 0.533874 3 0.005783 4 0.055720 5 0.004566 6 0.275335 7 0.073903 8 0.788465 9 0.021033 10 0.832280 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000708 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-30_14:31: (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 66783 0.20 66955 1.25 3 25000.00 25008 0.00 24863 0.75 4 6666.67 6512 3.59 6482 5.12 5 1388.89 1425 0.94 1412 0.38 6 238.10 229 0.35 246 0.26 7 34.72 38 0.31 35 0.00 8 4.96 4 0.19 6 0.22 p=0.52767 p=0.76047 Number of rngs required: 687367, p-value: 0.114 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-30_14:31 No. of wins: Observed Expected 98640 98585.9 z-score= 0.242, pvalue=0.59567 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66703 66666.7 0.020 0.020 2 37467 37654.3 0.932 0.952 3 27168 26954.7 1.687 2.639 4 19620 19313.5 4.865 7.504 5 13856 13851.4 0.002 7.506 6 9968 9943.5 0.060 7.566 7 6989 7145.0 3.407 10.973 8 5123 5139.1 0.050 11.023 9 3629 3699.9 1.357 12.381 10 2640 2666.3 0.259 12.640 11 1880 1923.3 0.976 13.616 12 1302 1388.7 5.418 19.034 13 957 1003.7 2.174 21.208 14 765 726.1 2.080 23.288 15 544 525.8 0.627 23.915 16 392 381.2 0.309 24.224 17 292 276.5 0.864 25.088 18 197 200.8 0.073 25.161 19 139 146.0 0.334 25.496 20 93 106.2 1.644 27.140 21 276 287.1 0.430 27.570 Chisq= 27.57 for 20 degrees of freedom, p= 0.88003 SUMMARY of craptest p-value for no. of wins: 0.595669 p-value for throws/game: 0.880025 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-30_14:31 No. of wins: Observed Expected 98656 98585.9 z-score= 0.314, pvalue=0.62313 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66417 66666.7 0.935 0.935 2 37678 37654.3 0.015 0.950 3 26940 26954.7 0.008 0.958 4 19626 19313.5 5.058 6.016 5 14045 13851.4 2.705 8.721 6 9891 9943.5 0.278 8.999 7 7043 7145.0 1.457 10.455 8 5111 5139.1 0.153 10.609 9 3609 3699.9 2.232 12.840 10 2601 2666.3 1.599 14.439 11 1950 1923.3 0.370 14.809 12 1405 1388.7 0.190 15.000 13 939 1003.7 4.173 19.172 14 786 726.1 4.935 24.107 15 528 525.8 0.009 24.116 16 388 381.2 0.123 24.239 17 305 276.5 2.929 27.168 18 194 200.8 0.232 27.400 19 155 146.0 0.557 27.957 20 95 106.2 1.184 29.141 21 294 287.1 0.165 29.306 Chisq= 29.31 for 20 degrees of freedom, p= 0.91810 SUMMARY of craptest p-value for no. of wins: 0.623131 p-value for throws/game: 0.918097 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0007,0.0023,0.0046,0.0058,0.0076,0.0153,0.0156,0.0210,0.0210,0.0322, 0.0365,0.0377,0.0429,0.0437,0.0452,0.0485,0.0522,0.0557,0.0560,0.0610, 0.0622,0.0643,0.0648,0.0674,0.0709,0.0739,0.0746,0.0750,0.0797,0.0837, 0.0853,0.0881,0.0927,0.0961,0.1005,0.1057,0.1063,0.1080,0.1143,0.1193, 0.1332,0.1336,0.1339,0.1478,0.1518,0.1551,0.1576,0.1591,0.1625,0.1647, 0.1669,0.1758,0.1859,0.1873,0.1922,0.2002,0.2028,0.2065,0.2065,0.2085, 0.2095,0.2160,0.2240,0.2258,0.2284,0.2295,0.2325,0.2356,0.2363,0.2418, 0.2438,0.2469,0.2503,0.2558,0.2567,0.2613,0.2625,0.2640,0.2697,0.2739, 0.2753,0.2783,0.2867,0.2882,0.2936,0.3004,0.3065,0.3099,0.3107,0.3179, 0.3202,0.3209,0.3212,0.3228,0.3258,0.3298,0.3367,0.3481,0.3646,0.3777, 0.3784,0.3848,0.3881,0.3921,0.3931,0.3983,0.4026,0.4095,0.4145,0.4280, 0.4283,0.4352,0.4360,0.4371,0.4375,0.4416,0.4484,0.4533,0.4665,0.4690, 0.4697,0.4736,0.4736,0.4739,0.4796,0.4814,0.4818,0.4839,0.4954,0.4982, 0.5012,0.5167,0.5174,0.5190,0.5239,0.5243,0.5277,0.5302,0.5339,0.5463, 0.5489,0.5514,0.5530,0.5548,0.5573,0.5591,0.5618,0.5623,0.5629,0.5695, 0.5745,0.5748,0.5748,0.5815,0.5903,0.5939,0.5946,0.5951,0.5957,0.5976, 0.6038,0.6064,0.6090,0.6207,0.6231,0.6254,0.6277,0.6389,0.6402,0.6445, 0.6470,0.6485,0.6490,0.6500,0.6566,0.6566,0.6665,0.6798,0.6837,0.6875, 0.6881,0.6896,0.6947,0.6997,0.7035,0.7067,0.7081,0.7082,0.7087,0.7147, 0.7171,0.7211,0.7213,0.7241,0.7261,0.7507,0.7582,0.7588,0.7605,0.7739, 0.7790,0.7799,0.7799,0.7817,0.7818,0.7836,0.7843,0.7843,0.7856,0.7885, 0.7953,0.7986,0.7996,0.8035,0.8069,0.8127,0.8131,0.8162,0.8209,0.8291, 0.8308,0.8310,0.8323,0.8343,0.8400,0.8439,0.8454,0.8458,0.8477,0.8488, 0.8588,0.8634,0.8700,0.8704,0.8711,0.8732,0.8750,0.8754,0.8760,0.8789, 0.8800,0.8801,0.8827,0.8920,0.8954,0.8972,0.9005,0.9037,0.9045,0.9122, 0.9180,0.9181,0.9183,0.9298,0.9328,0.9492,0.9503,0.9528,0.9553,0.9625, 0.9625,0.9626,0.9677,0.9696,0.9717,0.9733,0.9749,0.9770,0.9970, Overall p-value after applying KStest on 269 p-values = 0.682463 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.