RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-27_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.63 20.9546 0.771673 2 to 25 15.90 26.8208 0.939251 3 to 26 15.74 13.2825 0.282923 4 to 27 15.72 25.2273 0.910263 5 to 28 15.80 12.8148 0.251504 6 to 29 15.53 17.9561 0.608387 7 to 30 15.98 12.6252 0.239110 8 to 31 15.73 21.8776 0.810528 9 to 32 15.59 26.1399 0.928052 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.170387 Tough bday spacings test for dh-ranFile-2016-02-27_22:31: 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 13 46 74 104 86 76 41 35 15 6 4 (O-E)^2/E 1.6 2.4 0.0 0.4 1.4 0.1 2.4 0.9 0.0 0.1 0.0 Birthday Spacings: Sum(O-E)^2/E= 9.222, p= 0.489 RESULTS OF GCD FOR dh-ranFile-2016-02-27_22:31 Euclid's algorithm: p-value, steps to gcd: 0.631770 p-value, dist. of gcd's: 0.718789 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-27_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.552 0.696 0.198 0.768 0.695 0.784 0.557 0.146 Bits 8 to 15---> 0.962 0.296 0.716 0.368 0.742 0.214 0.142 0.495 Bits 16 to 23---> 0.368 0.647 0.217 0.302 0.817 0.184 0.616 0.306 Bits 24 to 31---> 0.527 0.667 0.516 0.799 0.601 0.098 0.964 0.657 KS test for the above 32 p values: 0.526 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-27_22:31, p-values for 5 runs: 0.6536, 0.6068, 0.4888, 0.9707, 0.5072 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-27_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5155 5134.0 0.086 0.434 r= 30 22997 23103.0 0.487 0.921 r= 31 11628 11551.5 0.506 1.427 chi-square = 1.427 with df = 3; p-value = 0.301 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-27_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5189 5134.0 0.589 0.601 r= 31 23021 23103.0 0.291 0.892 r= 32 11577 11551.5 0.056 0.948 chi-square = 0.948 with df = 3; p-value = 0.186 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-27_22:31 b-rank test for bits 1 to 8, p=0.89196 b-rank test for bits 2 to 9, p=0.06045 b-rank test for bits 3 to 10, p=0.56407 b-rank test for bits 4 to 11, p=0.37810 b-rank test for bits 5 to 12, p=0.84286 b-rank test for bits 6 to 13, p=0.35692 b-rank test for bits 7 to 14, p=0.77983 b-rank test for bits 8 to 15, p=0.29854 b-rank test for bits 9 to 16, p=0.21987 b-rank test for bits 10 to 17, p=0.88477 b-rank test for bits 11 to 18, p=0.08349 b-rank test for bits 12 to 19, p=0.07880 b-rank test for bits 13 to 20, p=0.41627 b-rank test for bits 14 to 21, p=0.84159 b-rank test for bits 15 to 22, p=0.76151 b-rank test for bits 16 to 23, p=0.63466 b-rank test for bits 17 to 24, p=0.81252 b-rank test for bits 18 to 25, p=0.83623 b-rank test for bits 19 to 26, p=0.33192 b-rank test for bits 20 to 27, p=0.67619 b-rank test for bits 21 to 28, p=0.58554 b-rank test for bits 22 to 29, p=0.15038 b-rank test for bits 23 to 30, p=0.73958 b-rank test for bits 24 to 31, p=0.02929 b-rank test for bits 25 to 32, p=0.23713 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 = 0.837648 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-27_22:31 (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 142021 0.26 0.602920 2 141603 -0.72 0.237081 3 142472 1.31 0.905686 4 141904 -0.01 0.495032 5 142219 0.72 0.765322 6 142426 1.21 0.886317 7 142009 0.23 0.592070 8 142548 1.49 0.932179 9 141553 -0.83 0.202550 10 141670 -0.56 0.288019 11 142212 0.71 0.760271 12 142104 0.45 0.675387 13 142083 0.41 0.657545 14 142288 0.88 0.811852 15 141475 -1.01 0.155103 16 141980 0.17 0.565574 17 142031 0.28 0.611900 18 141653 -0.60 0.274619 19 142442 1.24 0.893353 20 142516 1.42 0.921825 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-27_22:31 Bits used No. missing words z-score p-value 23 to 32 141519 -1.3460 0.089157 22 to 31 141886 -0.0804 0.467940 21 to 30 141467 -1.5253 0.063595 20 to 29 142569 2.2747 0.988539 19 to 28 142056 0.5058 0.693487 18 to 27 141936 0.0920 0.536637 17 to 26 141856 -0.1839 0.427047 16 to 25 142086 0.6092 0.728806 15 to 24 142314 1.3954 0.918554 14 to 23 142146 0.8161 0.792780 13 to 22 142052 0.4920 0.688628 12 to 21 142193 0.9782 0.836006 11 to 20 141728 -0.6253 0.265895 10 to 19 141959 0.1713 0.567997 9 to 18 141507 -1.3873 0.082668 8 to 17 141342 -1.9563 0.025214 7 to 16 141715 -0.6701 0.251396 6 to 15 142284 1.2920 0.901815 5 to 14 141658 -0.8667 0.193066 4 to 13 142120 0.7264 0.766218 3 to 12 142158 0.8575 0.804411 2 to 11 142086 0.6092 0.728806 1 to 10 142243 1.1506 0.875049 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-27_22:31 Bits used No. missing words z-score p-value 28 to 32 142059 0.5074 0.694048 27 to 31 141847 -0.2113 0.416331 26 to 30 141915 0.0192 0.507667 25 to 29 142268 1.2158 0.887975 24 to 28 142040 0.4429 0.671099 23 to 27 142288 1.2836 0.900364 22 to 26 142321 1.3955 0.918566 21 to 25 141808 -0.3435 0.365614 20 to 24 142123 0.7243 0.765561 19 to 23 141810 -0.3367 0.368167 18 to 22 142144 0.7955 0.786836 17 to 21 141665 -0.8282 0.203768 16 to 20 142257 1.1785 0.880710 15 to 19 142274 1.2362 0.891802 14 to 18 141937 0.0938 0.537365 13 to 17 141758 -0.5130 0.303982 12 to 16 141999 0.3040 0.619423 11 to 15 142103 0.6565 0.744252 10 to 14 141784 -0.4248 0.335474 9 to 13 141783 -0.4282 0.334239 8 to 12 142125 0.7311 0.767636 7 to 11 141865 -0.1503 0.440275 6 to 10 142195 0.9684 0.833571 5 to 9 141850 -0.2011 0.420303 4 to 8 141724 -0.6282 0.264924 3 to 7 141825 -0.2859 0.387491 2 to 6 142419 1.7277 0.957979 1 to 5 141886 -0.0791 0.468483 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-27_22:31 Bits used No. missing words z-score p-value 31 to 32 141574 -0.9892 0.161289 30 to 31 142179 0.7955 0.786835 29 to 30 141675 -0.6912 0.244708 28 to 29 142162 0.7453 0.771967 27 to 28 141822 -0.2576 0.398354 26 to 27 142075 0.4887 0.687474 25 to 26 142489 1.7099 0.956362 24 to 25 142540 1.8604 0.968584 23 to 24 142340 1.2704 0.898031 22 to 23 141545 -1.0747 0.141250 21 to 22 142131 0.6539 0.743410 20 to 21 141669 -0.7089 0.239182 19 to 20 142177 0.7896 0.785116 18 to 19 141265 -1.9007 0.028672 17 to 18 141957 0.1406 0.555915 16 to 17 141966 0.1672 0.566381 15 to 16 142421 1.5094 0.934395 14 to 15 141574 -0.9892 0.161289 13 to 14 141939 0.0875 0.534872 12 to 13 142037 0.3766 0.646767 11 to 12 141680 -0.6765 0.249365 10 to 11 142076 0.4917 0.688517 9 to 10 141418 -1.4494 0.073620 8 to 9 141924 0.0433 0.517259 7 to 8 141604 -0.9007 0.183880 6 to 7 141836 -0.2163 0.414372 5 to 6 141861 -0.1426 0.443316 4 to 5 142380 1.3884 0.917493 3 to 4 142285 1.1082 0.866106 2 to 3 142079 0.5005 0.691639 1 to 2 141554 -1.0482 0.147280 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-27_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2503.46 0.049 0.519522 Test results for specific bytes for dh-ranFile-2016-02-27_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2476.89 -0.327 0.371892 2 to 9 2465.85 -0.483 0.314549 3 to 10 2448.22 -0.732 0.231986 4 to 11 2526.74 0.378 0.647341 5 to 12 2494.40 -0.079 0.468450 6 to 13 2516.34 0.231 0.591397 7 to 14 2553.71 0.760 0.776252 8 to 15 2375.73 -1.757 0.039418 9 to 16 2570.75 1.001 0.841479 10 to 17 2498.35 -0.023 0.490670 11 to 18 2496.13 -0.055 0.478195 12 to 19 2534.86 0.493 0.689011 13 to 20 2557.36 0.811 0.791378 14 to 21 2420.34 -1.127 0.129963 15 to 22 2497.52 -0.035 0.486013 16 to 23 2453.15 -0.663 0.253788 17 to 24 2482.15 -0.253 0.400327 18 to 25 2406.30 -1.325 0.092559 19 to 26 2610.80 1.567 0.941431 20 to 27 2543.86 0.620 0.732464 21 to 28 2422.32 -1.099 0.135982 22 to 29 2567.98 0.961 0.831821 23 to 30 2431.09 -0.975 0.164881 24 to 31 2465.03 -0.495 0.310439 25 to 32 2571.77 1.015 0.844955 CDPARK for dh-ranFile-2016-02-27_22:31: 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 3540 0.7763 0.781201 3483 -1.8265 0.033889 3499 -1.0959 0.136563 3513 -0.4566 0.323972 3522 -0.0457 0.481790 3502 -0.9589 0.168804 3573 2.2831 0.988788 3552 1.3242 0.907282 3537 0.6393 0.738676 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3523.70 sample std.=25.67 p-value of the KSTEST for those 10 p-values: 0.919681 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-27_22:31 0.2005,0.2164,0.3536,0.1836,0.3280,0.8459,0.4832,0.7688,0.7242,0.0584, The KS test for those 10 p-values: 0.573227 The 3DSPHERES test for dh-ranFile-2016-02-27_22:31 sample no r^3 equiv. uni. 1 0.198 0.006574 2 66.545 0.891191 3 7.952 0.232846 4 31.928 0.655024 5 3.121 0.098795 6 32.916 0.666191 7 94.896 0.957710 8 14.583 0.384990 9 33.519 0.672834 10 22.831 0.532810 11 19.816 0.483416 12 26.458 0.586022 13 7.758 0.227866 14 46.326 0.786518 15 5.466 0.166559 16 17.444 0.440918 17 15.511 0.403718 18 35.089 0.689516 19 11.030 0.307642 20 1.595 0.051762 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.879340 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-27_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -1.2 -1.3 0.8 1.2 -0.4 1.8 0.6 -0.6 -0.2 -0.5 0.1 -0.5 -0.3 1.7 0.5 1.7 0.8 -0.6 2.3 -1.7 -1.3 -1.8 -0.2 -1.9 -0.0 0.2 -1.2 -0.7 -1.0 -0.4 0.8 0.7 2.1 0.8 -0.1 0.5 -1.3 -0.4 -0.7 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:49.682460 z-score=0.838225, p-value=0.806134 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-27_22:31 Test no p-value 1 0.003016 2 0.999135 3 0.764803 4 0.565317 5 0.419742 6 0.689581 7 0.791573 8 0.512209 9 0.464322 10 0.388622 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.319291 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-27_22:31: (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 66852 0.52 66639 0.01 3 25000.00 24727 2.98 24987 0.01 4 6666.67 6797 2.55 6754 1.14 5 1388.89 1357 0.73 1310 4.48 6 238.10 218 1.70 263 2.61 7 34.72 41 1.14 40 0.80 8 4.96 7 0.84 6 0.22 p=0.89297 p=0.84101 Number of rngs required: 687970, p-value: 0.309 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-27_22:31 No. of wins: Observed Expected 98319 98585.9 z-score=-1.194, pvalue=0.11633 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66545 66666.7 0.222 0.222 2 37674 37654.3 0.010 0.232 3 26896 26954.7 0.128 0.360 4 19383 19313.5 0.250 0.611 5 13775 13851.4 0.422 1.032 6 9988 9943.5 0.199 1.231 7 7148 7145.0 0.001 1.232 8 5193 5139.1 0.566 1.798 9 3672 3699.9 0.210 2.008 10 2691 2666.3 0.229 2.237 11 1881 1923.3 0.932 3.169 12 1410 1388.7 0.325 3.494 13 1041 1003.7 1.385 4.879 14 718 726.1 0.091 4.970 15 551 525.8 1.204 6.174 16 433 381.2 7.053 13.228 17 267 276.5 0.329 13.557 18 186 200.8 1.095 14.652 19 148 146.0 0.028 14.680 20 102 106.2 0.167 14.847 21 298 287.1 0.413 15.260 Chisq= 15.26 for 20 degrees of freedom, p= 0.23864 SUMMARY of craptest p-value for no. of wins: 0.116328 p-value for throws/game: 0.238645 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-27_22:31 No. of wins: Observed Expected 98730 98585.9 z-score= 0.645, pvalue=0.74043 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66531 66666.7 0.276 0.276 2 37548 37654.3 0.300 0.576 3 26980 26954.7 0.024 0.600 4 19244 19313.5 0.250 0.850 5 14077 13851.4 3.674 4.524 6 9974 9943.5 0.093 4.617 7 7227 7145.0 0.940 5.557 8 5163 5139.1 0.111 5.669 9 3665 3699.9 0.329 5.997 10 2706 2666.3 0.591 6.588 11 1919 1923.3 0.010 6.598 12 1334 1388.7 2.158 8.756 13 1021 1003.7 0.298 9.054 14 766 726.1 2.188 11.242 15 494 525.8 1.927 13.169 16 394 381.2 0.433 13.602 17 252 276.5 2.178 15.780 18 177 200.8 2.828 18.607 19 148 146.0 0.028 18.635 20 90 106.2 2.475 21.111 21 290 287.1 0.029 21.140 Chisq= 21.14 for 20 degrees of freedom, p= 0.61105 SUMMARY of craptest p-value for no. of wins: 0.740434 p-value for throws/game: 0.611046 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0030,0.0066,0.0252,0.0287,0.0293,0.0339,0.0394,0.0518,0.0584,0.0604, 0.0636,0.0736,0.0788,0.0827,0.0835,0.0892,0.0926,0.0979,0.0988,0.1163, 0.1300,0.1360,0.1366,0.1413,0.1422,0.1458,0.1473,0.1504,0.1551,0.1613, 0.1613,0.1649,0.1666,0.1688,0.1704,0.1836,0.1839,0.1839,0.1863,0.1931, 0.1984,0.2005,0.2026,0.2038,0.2139,0.2164,0.2172,0.2199,0.2279,0.2320, 0.2328,0.2371,0.2371,0.2386,0.2391,0.2392,0.2447,0.2494,0.2514,0.2515, 0.2538,0.2649,0.2659,0.2746,0.2829,0.2880,0.2956,0.2985,0.3008,0.3020, 0.3040,0.3060,0.3076,0.3089,0.3104,0.3145,0.3193,0.3240,0.3280,0.3319, 0.3342,0.3355,0.3536,0.3569,0.3656,0.3680,0.3682,0.3683,0.3719,0.3746, 0.3781,0.3850,0.3875,0.3886,0.3984,0.4003,0.4037,0.4144,0.4163,0.4163, 0.4197,0.4203,0.4270,0.4403,0.4409,0.4433,0.4643,0.4679,0.4684,0.4685, 0.4782,0.4818,0.4832,0.4834,0.4860,0.4888,0.4889,0.4907,0.4949,0.4950, 0.5072,0.5077,0.5122,0.5159,0.5173,0.5195,0.5261,0.5268,0.5328,0.5349, 0.5366,0.5374,0.5515,0.5559,0.5569,0.5641,0.5653,0.5656,0.5664,0.5680, 0.5732,0.5855,0.5860,0.5914,0.5921,0.6013,0.6029,0.6068,0.6084,0.6110, 0.6119,0.6157,0.6194,0.6318,0.6347,0.6468,0.6472,0.6473,0.6536,0.6550, 0.6567,0.6575,0.6662,0.6673,0.6711,0.6728,0.6754,0.6762,0.6875,0.6885, 0.6886,0.6890,0.6895,0.6896,0.6916,0.6935,0.6940,0.6947,0.6963,0.7165, 0.7188,0.7242,0.7288,0.7288,0.7325,0.7387,0.7396,0.7404,0.7416,0.7434, 0.7443,0.7603,0.7615,0.7648,0.7653,0.7656,0.7662,0.7676,0.7685,0.7688, 0.7717,0.7720,0.7763,0.7798,0.7812,0.7842,0.7851,0.7865,0.7868,0.7868, 0.7914,0.7916,0.7928,0.7987,0.8044,0.8061,0.8105,0.8119,0.8125,0.8170, 0.8318,0.8336,0.8360,0.8362,0.8376,0.8410,0.8415,0.8416,0.8429,0.8450, 0.8459,0.8661,0.8750,0.8793,0.8807,0.8848,0.8863,0.8880,0.8912,0.8918, 0.8920,0.8930,0.8934,0.8980,0.9004,0.9018,0.9057,0.9073,0.9103,0.9175, 0.9186,0.9186,0.9197,0.9218,0.9281,0.9322,0.9344,0.9393,0.9414,0.9564, 0.9577,0.9580,0.9617,0.9637,0.9686,0.9707,0.9885,0.9888,0.9991, Overall p-value after applying KStest on 269 p-values = 0.045872 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.