RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-16_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.70 15.3563 0.430169 2 to 25 15.73 17.0185 0.546884 3 to 26 15.88 7.0865 0.017599 4 to 27 15.89 5.4775 0.003936 5 to 28 16.01 14.7119 0.383778 6 to 29 15.73 22.2361 0.824192 7 to 30 15.78 13.9003 0.325856 8 to 31 15.85 18.8405 0.662236 9 to 32 15.92 9.3621 0.071788 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.125949 Tough bday spacings test for dh-ranFile-2016-04-16_23:31: 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 37 72 93 93 84 50 35 12 9 6 (O-E)^2/E 0.0 0.0 0.0 0.2 0.2 0.4 0.1 0.9 0.6 0.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 4.257, p= 0.065 RESULTS OF GCD FOR dh-ranFile-2016-04-16_23:31 Euclid's algorithm: p-value, steps to gcd: 0.639921 p-value, dist. of gcd's: 0.537365 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-16_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.483 0.436 0.911 0.174 0.542 0.846 0.751 0.020 Bits 8 to 15---> 0.373 0.222 0.363 0.640 0.169 0.362 0.491 0.136 Bits 16 to 23---> 0.899 0.389 0.732 0.801 0.968 0.136 0.874 0.556 Bits 24 to 31---> 0.407 0.256 0.381 0.725 0.235 0.887 0.648 0.280 KS test for the above 32 p values: 0.102 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-16_23:31, p-values for 5 runs: 0.8199, 0.5736, 0.4927, 0.5491, 0.9036 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-16_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5040 5134.0 1.721 1.733 r= 30 23148 23103.0 0.087 1.821 r= 31 11599 11551.5 0.195 2.016 chi-square = 2.016 with df = 3; p-value = 0.431 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-16_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5119 5134.0 0.044 0.075 r= 31 23064 23103.0 0.066 0.141 r= 32 11603 11551.5 0.229 0.371 chi-square = 0.371 with df = 3; p-value = 0.054 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-16_23:31 b-rank test for bits 1 to 8, p=0.29328 b-rank test for bits 2 to 9, p=0.10034 b-rank test for bits 3 to 10, p=0.77030 b-rank test for bits 4 to 11, p=0.31851 b-rank test for bits 5 to 12, p=0.59552 b-rank test for bits 6 to 13, p=0.56506 b-rank test for bits 7 to 14, p=0.14092 b-rank test for bits 8 to 15, p=0.36106 b-rank test for bits 9 to 16, p=0.76119 b-rank test for bits 10 to 17, p=0.52359 b-rank test for bits 11 to 18, p=0.58592 b-rank test for bits 12 to 19, p=0.09413 b-rank test for bits 13 to 20, p=0.13328 b-rank test for bits 14 to 21, p=0.92253 b-rank test for bits 15 to 22, p=0.46080 b-rank test for bits 16 to 23, p=0.69816 b-rank test for bits 17 to 24, p=0.34869 b-rank test for bits 18 to 25, p=0.15579 b-rank test for bits 19 to 26, p=0.77672 b-rank test for bits 20 to 27, p=0.38143 b-rank test for bits 21 to 28, p=0.44365 b-rank test for bits 22 to 29, p=0.12883 b-rank test for bits 23 to 30, p=0.00542 b-rank test for bits 24 to 31, p=0.34585 b-rank test for bits 25 to 32, p=0.72321 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 = 0.275174 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-16_23:31 (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 141925 0.04 0.514603 2 142180 0.63 0.736439 3 142065 0.36 0.641965 4 141567 -0.80 0.211903 5 142136 0.53 0.701806 6 142944 2.42 0.992185 7 142085 0.41 0.659260 8 142183 0.64 0.738724 9 141680 -0.54 0.296042 10 141783 -0.30 0.383935 11 142113 0.48 0.682915 12 141795 -0.27 0.394686 13 141527 -0.89 0.185850 14 142011 0.24 0.593884 15 141244 -1.55 0.060031 16 141731 -0.42 0.338464 17 141800 -0.26 0.399190 18 141324 -1.37 0.085720 19 141165 -1.74 0.041010 20 142188 0.65 0.742508 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-16_23:31 Bits used No. missing words z-score p-value 23 to 32 141671 -0.8218 0.205588 22 to 31 142105 0.6747 0.750075 21 to 30 141706 -0.7011 0.241609 20 to 29 141359 -1.8977 0.028868 19 to 28 141723 -0.6425 0.260269 18 to 27 142066 0.5402 0.705485 17 to 26 142065 0.5368 0.704295 16 to 25 141705 -0.7046 0.240534 15 to 24 142172 0.9058 0.817468 14 to 23 141564 -1.1908 0.116867 13 to 22 141349 -1.9322 0.026669 12 to 21 141402 -1.7494 0.040110 11 to 20 141602 -1.0598 0.144627 10 to 19 141974 0.2230 0.588232 9 to 18 141574 -1.1563 0.123777 8 to 17 141850 -0.2046 0.418948 7 to 16 142049 0.4816 0.684962 6 to 15 141814 -0.3287 0.371182 5 to 14 141486 -1.4598 0.072178 4 to 13 142113 0.7023 0.758757 3 to 12 142175 0.9161 0.820194 2 to 11 142032 0.4230 0.663852 1 to 10 141990 0.2782 0.609560 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-16_23:31 Bits used No. missing words z-score p-value 28 to 32 141812 -0.3299 0.370726 27 to 31 141909 -0.0011 0.499554 26 to 30 142124 0.7277 0.766600 25 to 29 141814 -0.3232 0.373290 24 to 28 142027 0.3989 0.655010 23 to 27 141921 0.0396 0.515778 22 to 26 142418 1.7243 0.957674 21 to 25 141906 -0.0113 0.495497 20 to 24 141812 -0.3299 0.370726 19 to 23 141934 0.0836 0.533324 18 to 22 142264 1.2023 0.885371 17 to 21 142071 0.5480 0.708166 16 to 20 141805 -0.3537 0.361797 15 to 19 141850 -0.2011 0.420303 14 to 18 141746 -0.5537 0.289905 13 to 17 141661 -0.8418 0.199951 12 to 16 141089 -2.7808 0.002711 11 to 15 142153 0.8260 0.795598 10 to 14 142126 0.7345 0.768670 9 to 13 142459 1.8633 0.968789 8 to 12 141897 -0.0418 0.483330 7 to 11 142009 0.3379 0.632267 6 to 10 141820 -0.3028 0.381016 5 to 9 141787 -0.4147 0.339189 4 to 8 142312 1.3650 0.913871 3 to 7 141808 -0.3435 0.365614 2 to 6 142326 1.4124 0.921090 1 to 5 141706 -0.6893 0.245332 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-16_23:31 Bits used No. missing words z-score p-value 31 to 32 142119 0.6185 0.731876 30 to 31 142479 1.6804 0.953564 29 to 30 141737 -0.5083 0.305605 28 to 29 141259 -1.9184 0.027532 27 to 28 142017 0.3176 0.624610 26 to 27 141487 -1.2458 0.106417 25 to 26 142103 0.5713 0.716101 24 to 25 141976 0.1967 0.577956 23 to 24 141724 -0.5467 0.292294 22 to 23 141941 0.0934 0.537216 21 to 22 141895 -0.0423 0.483141 20 to 21 142366 1.3471 0.911027 19 to 20 142043 0.3943 0.653323 18 to 19 141942 0.0964 0.538387 17 to 18 141754 -0.4582 0.323404 16 to 17 141659 -0.7384 0.230125 15 to 16 142125 0.6362 0.737675 14 to 15 141655 -0.7502 0.226556 13 to 14 142054 0.4268 0.665221 12 to 13 142223 0.9253 0.822590 11 to 12 141970 0.1790 0.571018 10 to 11 141694 -0.6352 0.262652 9 to 10 142107 0.5831 0.720086 8 to 9 142250 1.0049 0.842534 7 to 8 141570 -1.0010 0.158420 6 to 7 142268 1.0580 0.854978 5 to 6 142435 1.5506 0.939507 4 to 5 142456 1.6126 0.946584 3 to 4 141952 0.1259 0.550083 2 to 3 141911 0.0049 0.501965 1 to 2 141725 -0.5437 0.293308 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-16_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2451.83 -0.681 0.247875 Test results for specific bytes for dh-ranFile-2016-04-16_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2631.14 1.855 0.968170 2 to 9 2525.34 0.358 0.639984 3 to 10 2551.42 0.727 0.766451 4 to 11 2573.79 1.044 0.851664 5 to 12 2466.78 -0.470 0.319259 6 to 13 2503.30 0.047 0.518627 7 to 14 2547.34 0.670 0.748421 8 to 15 2487.45 -0.177 0.429581 9 to 16 2489.76 -0.145 0.442439 10 to 17 2427.08 -1.031 0.151226 11 to 18 2497.34 -0.038 0.484985 12 to 19 2507.15 0.101 0.540263 13 to 20 2409.45 -1.281 0.100179 14 to 21 2525.26 0.357 0.639531 15 to 22 2496.58 -0.048 0.480733 16 to 23 2441.54 -0.827 0.204198 17 to 24 2540.20 0.568 0.715148 18 to 25 2461.76 -0.541 0.294306 19 to 26 2453.25 -0.661 0.254278 20 to 27 2427.14 -1.030 0.151412 21 to 28 2419.30 -1.141 0.126867 22 to 29 2494.21 -0.082 0.467358 23 to 30 2463.45 -0.517 0.302624 24 to 31 2550.28 0.711 0.761473 25 to 32 2353.90 -2.066 0.019409 CDPARK for dh-ranFile-2016-04-16_23:31: 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 3548 1.1416 0.873180 3515 -0.3653 0.357445 3540 0.7763 0.781201 3548 1.1416 0.873180 3531 0.3653 0.642555 3546 1.0502 0.853193 3525 0.0913 0.536383 3526 0.1370 0.554479 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3529.20 sample std.=16.70 p-value of the KSTEST for those 10 p-values: 0.382653 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-16_23:31 0.2620,0.1844,0.8891,0.5891,0.2839,0.7037,0.2462,0.6841,0.9870,0.6870, The KS test for those 10 p-values: 0.684151 The 3DSPHERES test for dh-ranFile-2016-04-16_23:31 sample no r^3 equiv. uni. 1 45.159 0.778053 2 9.720 0.276739 3 53.728 0.833196 4 9.314 0.266886 5 23.152 0.537795 6 20.335 0.492288 7 71.255 0.907000 8 5.077 0.155686 9 4.168 0.129711 10 53.253 0.830536 11 20.617 0.497040 12 41.682 0.750776 13 35.289 0.691586 14 5.112 0.156681 15 28.459 0.612729 16 80.594 0.931878 17 5.426 0.165449 18 27.782 0.603898 19 9.946 0.282188 20 6.285 0.189014 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.851881 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-16_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 1.3 0.8 0.0 -1.5 -1.2 -0.4 1.0 -0.8 -0.3 -0.4 -2.0 1.8 1.0 0.1 1.0 -0.4 0.1 -0.1 0.3 -0.0 -0.9 0.2 -0.9 0.2 -0.0 0.9 -0.1 -0.1 -0.9 -0.1 0.0 0.8 0.2 1.5 0.7 -1.7 -1.2 -0.7 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:32.353604 z-score=-1.052508, p-value=0.141936 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-16_23:31 Test no p-value 1 0.021538 2 0.422465 3 0.248179 4 0.389806 5 0.913009 6 0.137832 7 0.390921 8 0.253135 9 0.165510 10 0.616737 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.179050 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-16_23:31: (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 66642 0.01 66389 1.16 3 25000.00 25063 0.16 25187 1.40 4 6666.67 6601 0.65 6717 0.38 5 1388.89 1417 0.57 1422 0.79 6 238.10 240 0.02 253 0.93 7 34.72 34 0.01 27 1.72 8 4.96 2 1.77 4 0.19 p=0.21410 p=0.63654 Number of rngs required: 689043, p-value: 0.770 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-16_23:31 No. of wins: Observed Expected 98638 98585.9 z-score= 0.233, pvalue=0.59220 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66780 66666.7 0.193 0.193 2 37641 37654.3 0.005 0.197 3 27129 26954.7 1.127 1.324 4 19314 19313.5 0.000 1.324 5 13717 13851.4 1.304 2.629 6 9914 9943.5 0.088 2.716 7 7053 7145.0 1.185 3.902 8 5281 5139.1 3.920 7.821 9 3717 3699.9 0.079 7.901 10 2610 2666.3 1.189 9.089 11 1922 1923.3 0.001 9.090 12 1413 1388.7 0.424 9.514 13 945 1003.7 3.435 12.949 14 702 726.1 0.803 13.751 15 486 525.8 3.018 16.769 16 399 381.2 0.836 17.605 17 265 276.5 0.482 18.087 18 184 200.8 1.410 19.497 19 134 146.0 0.984 20.481 20 89 106.2 2.790 23.271 21 305 287.1 1.114 24.385 Chisq= 24.39 for 20 degrees of freedom, p= 0.77403 SUMMARY of craptest p-value for no. of wins: 0.592200 p-value for throws/game: 0.774029 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-16_23:31 No. of wins: Observed Expected 98500 98585.9 z-score=-0.384, pvalue=0.35049 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66821 66666.7 0.357 0.357 2 37521 37654.3 0.472 0.829 3 26852 26954.7 0.392 1.221 4 19319 19313.5 0.002 1.222 5 13887 13851.4 0.091 1.314 6 9891 9943.5 0.278 1.591 7 7104 7145.0 0.236 1.827 8 5055 5139.1 1.375 3.202 9 3806 3699.9 3.045 6.247 10 2685 2666.3 0.131 6.378 11 1912 1923.3 0.067 6.445 12 1437 1388.7 1.677 8.122 13 1018 1003.7 0.203 8.325 14 749 726.1 0.720 9.045 15 533 525.8 0.098 9.143 16 373 381.2 0.174 9.317 17 264 276.5 0.569 9.885 18 204 200.8 0.050 9.935 19 155 146.0 0.557 10.492 20 119 106.2 1.539 12.031 21 295 287.1 0.217 12.248 Chisq= 12.25 for 20 degrees of freedom, p= 0.09271 SUMMARY of craptest p-value for no. of wins: 0.350486 p-value for throws/game: 0.092715 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0039,0.0054,0.0176,0.0194,0.0199,0.0215,0.0267,0.0275,0.0289, 0.0401,0.0410,0.0538,0.0600,0.0650,0.0718,0.0722,0.0785,0.0857,0.0927, 0.0941,0.1002,0.1003,0.1017,0.1064,0.1169,0.1238,0.1259,0.1269,0.1288, 0.1297,0.1333,0.1355,0.1359,0.1378,0.1409,0.1419,0.1446,0.1512,0.1514, 0.1557,0.1558,0.1567,0.1584,0.1654,0.1655,0.1694,0.1743,0.1791,0.1844, 0.1858,0.1890,0.2000,0.2042,0.2056,0.2119,0.2141,0.2221,0.2266,0.2301, 0.2351,0.2405,0.2416,0.2453,0.2462,0.2479,0.2482,0.2531,0.2543,0.2560, 0.2603,0.2620,0.2627,0.2669,0.2752,0.2767,0.2802,0.2822,0.2839,0.2899, 0.2923,0.2933,0.2933,0.2943,0.2960,0.3026,0.3056,0.3185,0.3193,0.3234, 0.3259,0.3385,0.3392,0.3459,0.3487,0.3505,0.3574,0.3611,0.3618,0.3621, 0.3630,0.3656,0.3707,0.3707,0.3712,0.3733,0.3733,0.3806,0.3810,0.3814, 0.3827,0.3838,0.3839,0.3887,0.3898,0.3909,0.3947,0.3992,0.4071,0.4189, 0.4203,0.4225,0.4296,0.4302,0.4309,0.4365,0.4424,0.4437,0.4608,0.4636, 0.4674,0.4807,0.4831,0.4833,0.4833,0.4850,0.4905,0.4923,0.4927,0.4955, 0.4970,0.4996,0.5020,0.5146,0.5158,0.5186,0.5236,0.5333,0.5364,0.5372, 0.5374,0.5378,0.5384,0.5403,0.5423,0.5469,0.5491,0.5501,0.5545,0.5562, 0.5651,0.5710,0.5736,0.5780,0.5859,0.5882,0.5891,0.5922,0.5939,0.5955, 0.6039,0.6096,0.6127,0.6167,0.6246,0.6323,0.6365,0.6395,0.6399,0.6400, 0.6404,0.6420,0.6426,0.6477,0.6533,0.6550,0.6593,0.6622,0.6639,0.6652, 0.6829,0.6841,0.6842,0.6850,0.6870,0.6916,0.6982,0.7018,0.7037,0.7043, 0.7055,0.7082,0.7151,0.7161,0.7201,0.7232,0.7254,0.7319,0.7324,0.7364, 0.7377,0.7387,0.7425,0.7484,0.7501,0.7506,0.7508,0.7588,0.7612,0.7615, 0.7665,0.7666,0.7687,0.7701,0.7703,0.7740,0.7767,0.7781,0.7812,0.7956, 0.8006,0.8175,0.8199,0.8202,0.8226,0.8242,0.8305,0.8332,0.8425,0.8460, 0.8517,0.8519,0.8532,0.8550,0.8732,0.8732,0.8737,0.8854,0.8873,0.8891, 0.8994,0.9036,0.9070,0.9109,0.9110,0.9130,0.9139,0.9211,0.9225,0.9319, 0.9395,0.9466,0.9536,0.9577,0.9682,0.9683,0.9688,0.9870,0.9922, Overall p-value after applying KStest on 269 p-values = 0.168546 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.