RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-19_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 7.8744 0.030840 2 to 25 15.65 28.9376 0.964894 3 to 26 15.81 12.7786 0.249121 4 to 27 15.58 26.3441 0.931584 5 to 28 15.95 12.5251 0.232647 6 to 29 16.01 15.9861 0.475182 7 to 30 15.61 27.3556 0.946946 8 to 31 15.90 20.3309 0.742347 9 to 32 15.65 28.1754 0.957070 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.089004 Tough bday spacings test for dh-ranFile-2017-01-19_10:31: 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 10 36 61 104 92 72 59 34 20 5 7 (O-E)^2/E 0.1 0.0 2.1 0.4 0.3 0.5 0.9 0.6 1.8 0.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 9.148, p= 0.482 RESULTS OF GCD FOR dh-ranFile-2017-01-19_10:31 Euclid's algorithm: p-value, steps to gcd: 0.535762 p-value, dist. of gcd's: 0.228293 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-19_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.753 0.203 0.733 0.929 0.302 0.976 0.055 0.820 Bits 8 to 15---> 0.975 0.848 0.897 0.991 0.295 0.634 0.100 0.753 Bits 16 to 23---> 0.850 0.610 0.619 0.498 0.554 0.965 0.260 0.298 Bits 24 to 31---> 0.224 0.742 0.821 0.456 0.080 0.329 0.357 0.111 KS test for the above 32 p values: 0.729 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-19_10:31, p-values for 5 runs: 0.2043, 0.0907, 0.7859, 0.3614, 0.8870 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-19_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 236 211.4 2.858 2.858 r= 29 5140 5134.0 0.007 2.865 r= 30 23098 23103.0 0.001 2.866 r= 31 11526 11551.5 0.056 2.923 chi-square = 2.923 with df = 3; p-value = 0.596 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-19_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5123 5134.0 0.024 0.458 r= 31 23056 23103.0 0.096 0.554 r= 32 11600 11551.5 0.203 0.757 chi-square = 0.757 with df = 3; p-value = 0.140 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-19_10:31 b-rank test for bits 1 to 8, p=0.63208 b-rank test for bits 2 to 9, p=0.37072 b-rank test for bits 3 to 10, p=0.50733 b-rank test for bits 4 to 11, p=0.36325 b-rank test for bits 5 to 12, p=0.32278 b-rank test for bits 6 to 13, p=0.13217 b-rank test for bits 7 to 14, p=0.31801 b-rank test for bits 8 to 15, p=0.02809 b-rank test for bits 9 to 16, p=0.64764 b-rank test for bits 10 to 17, p=0.58229 b-rank test for bits 11 to 18, p=0.44689 b-rank test for bits 12 to 19, p=0.32827 b-rank test for bits 13 to 20, p=0.30596 b-rank test for bits 14 to 21, p=0.05941 b-rank test for bits 15 to 22, p=0.05299 b-rank test for bits 16 to 23, p=0.50679 b-rank test for bits 17 to 24, p=0.79237 b-rank test for bits 18 to 25, p=0.44866 b-rank test for bits 19 to 26, p=0.08181 b-rank test for bits 20 to 27, p=0.37518 b-rank test for bits 21 to 28, p=0.15038 b-rank test for bits 22 to 29, p=0.60017 b-rank test for bits 23 to 30, p=0.46677 b-rank test for bits 24 to 31, p=0.83074 b-rank test for bits 25 to 32, p=0.01300 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 = 0.033448 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-19_10:31 (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 142304 0.92 0.821769 2 142555 1.51 0.934296 3 141632 -0.65 0.258503 4 141768 -0.33 0.370621 5 141966 0.13 0.552669 6 142203 0.69 0.753689 7 141313 -1.39 0.081765 8 141848 -0.14 0.443029 9 141736 -0.40 0.342747 10 141402 -1.19 0.117939 11 141108 -1.87 0.030585 12 142207 0.70 0.756626 13 141205 -1.65 0.049920 14 142004 0.22 0.587528 15 141673 -0.55 0.290415 16 141461 -1.05 0.147435 17 141230 -1.59 0.056231 18 141344 -1.32 0.093273 19 141519 -0.91 0.180888 20 143187 2.99 0.998583 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-19_10:31 Bits used No. missing words z-score p-value 23 to 32 141808 -0.3494 0.363389 22 to 31 141623 -0.9873 0.161737 21 to 30 142198 0.9954 0.840233 20 to 29 141551 -1.2356 0.108300 19 to 28 142352 1.5264 0.936551 18 to 27 141618 -1.0046 0.157548 17 to 26 142325 1.4333 0.924120 16 to 25 142130 0.7609 0.776651 15 to 24 141858 -0.1770 0.429754 14 to 23 142186 0.9540 0.829967 13 to 22 141630 -0.9632 0.167722 12 to 21 141601 -1.0632 0.143844 11 to 20 141588 -1.1080 0.133923 10 to 19 142238 1.1333 0.871465 9 to 18 141271 -2.2011 0.013863 8 to 17 142143 0.8058 0.789809 7 to 16 141909 -0.0011 0.499546 6 to 15 142011 0.3506 0.637051 5 to 14 141910 0.0023 0.500922 4 to 13 142239 1.1368 0.872188 3 to 12 141733 -0.6080 0.271582 2 to 11 142348 1.5127 0.934816 1 to 10 141954 0.1540 0.561209 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-19_10:31 Bits used No. missing words z-score p-value 28 to 32 141734 -0.5943 0.276143 27 to 31 142171 0.8870 0.812465 26 to 30 141442 -1.5842 0.056578 25 to 29 141889 -0.0689 0.472529 24 to 28 142285 1.2735 0.898572 23 to 27 141536 -1.2655 0.102842 22 to 26 142102 0.6531 0.743160 21 to 25 142274 1.2362 0.891802 20 to 24 142004 0.3209 0.625863 19 to 23 142157 0.8396 0.799422 18 to 22 141639 -0.9164 0.179736 17 to 21 142139 0.7785 0.781875 16 to 20 141887 -0.0757 0.469831 15 to 19 142086 0.5989 0.725374 14 to 18 142183 0.9277 0.823217 13 to 17 142302 1.3311 0.908419 12 to 16 141921 0.0396 0.515778 11 to 15 142186 0.9379 0.825843 10 to 14 141564 -1.1706 0.120878 9 to 13 141939 0.1006 0.540057 8 to 12 142621 2.4124 0.992077 7 to 11 141917 0.0260 0.510371 6 to 10 142076 0.5650 0.713957 5 to 9 142092 0.6192 0.732114 4 to 8 141566 -1.1638 0.122246 3 to 7 141575 -1.1333 0.128540 2 to 6 141714 -0.6621 0.253942 1 to 5 141752 -0.5333 0.296905 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-19_10:31 Bits used No. missing words z-score p-value 31 to 32 142287 1.1141 0.867376 30 to 31 141643 -0.7856 0.216041 29 to 30 142305 1.1672 0.878429 28 to 29 141481 -1.2635 0.103203 27 to 28 142246 0.9931 0.839676 26 to 27 142369 1.3560 0.912444 25 to 26 142153 0.7188 0.763865 24 to 25 142270 1.0639 0.856318 23 to 24 141787 -0.3609 0.359104 22 to 23 141718 -0.5644 0.286243 21 to 22 142319 1.2085 0.886566 20 to 21 142141 0.6834 0.752821 19 to 20 142397 1.4386 0.924862 18 to 19 142432 1.5418 0.938439 17 to 18 142192 0.8338 0.797813 16 to 17 141434 -1.4022 0.080435 15 to 16 141386 -1.5437 0.061325 14 to 15 142152 0.7158 0.762955 13 to 14 141905 -0.0128 0.494905 12 to 13 142049 0.4120 0.659832 11 to 12 141978 0.2026 0.580263 10 to 11 142102 0.5683 0.715101 9 to 10 141572 -0.9951 0.159850 8 to 9 142013 0.3058 0.620126 7 to 8 142325 1.2262 0.889932 6 to 7 141588 -0.9479 0.171596 5 to 6 142132 0.6568 0.744359 4 to 5 141686 -0.6588 0.255015 3 to 4 142397 1.4386 0.924862 2 to 3 141662 -0.7296 0.232821 1 to 2 141951 0.1229 0.548915 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-19_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2343.61 -2.212 0.013492 Test results for specific bytes for dh-ranFile-2017-01-19_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2412.56 -1.237 0.108109 2 to 9 2478.53 -0.304 0.380678 3 to 10 2585.36 1.207 0.886323 4 to 11 2649.91 2.120 0.983000 5 to 12 2469.56 -0.431 0.333415 6 to 13 2500.99 0.014 0.505596 7 to 14 2657.08 2.221 0.986840 8 to 15 2501.08 0.015 0.506089 9 to 16 2517.47 0.247 0.597582 10 to 17 2564.47 0.912 0.819032 11 to 18 2465.71 -0.485 0.313865 12 to 19 2413.25 -1.227 0.109948 13 to 20 2455.53 -0.629 0.264716 14 to 21 2534.10 0.482 0.685171 15 to 22 2583.87 1.186 0.882221 16 to 23 2664.44 2.326 0.989980 17 to 24 2555.87 0.790 0.785251 18 to 25 2512.66 0.179 0.571046 19 to 26 2476.37 -0.334 0.369109 20 to 27 2449.20 -0.718 0.236270 21 to 28 2525.12 0.355 0.638817 22 to 29 2583.34 1.179 0.880714 23 to 30 2372.48 -1.803 0.035662 24 to 31 2640.63 1.989 0.976642 25 to 32 2493.89 -0.086 0.465571 CDPARK for dh-ranFile-2017-01-19_10:31: 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 3503 -0.9132 0.180558 3502 -0.9589 0.168804 3495 -1.2785 0.100530 3574 2.3288 0.990064 3505 -0.8219 0.205562 3527 0.1826 0.572463 3559 1.6438 0.949895 3518 -0.2283 0.409702 3533 0.4566 0.676028 3532 0.4110 0.659449 Square side=100, avg. no. parked=3524.80 sample std.=24.57 p-value of the KSTEST for those 10 p-values: 0.733380 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-19_10:31 0.9109,0.3363,0.6848,0.1237,0.1198,0.9993,0.3377,0.9012,0.8409,0.2250, The KS test for those 10 p-values: 0.333261 The 3DSPHERES test for dh-ranFile-2017-01-19_10:31 sample no r^3 equiv. uni. 1 53.446 0.831621 2 0.569 0.018794 3 7.469 0.220384 4 11.096 0.309172 5 19.865 0.484268 6 1.281 0.041810 7 1.083 0.035454 8 29.132 0.621326 9 76.287 0.921362 10 17.663 0.444996 11 41.748 0.751325 12 35.031 0.688918 13 13.832 0.369385 14 9.014 0.259526 15 19.657 0.480672 16 6.334 0.190324 17 11.638 0.321538 18 10.525 0.295898 19 51.071 0.817748 20 46.394 0.787000 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.610566 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-19_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.8 -0.1 0.5 -0.4 -1.1 -0.2 0.4 1.8 -0.5 0.3 0.6 -0.2 -1.5 1.5 -1.6 -0.1 -0.4 1.1 1.9 -0.5 -0.9 -0.6 -0.9 1.5 -0.1 -1.1 -1.3 0.7 0.1 1.8 1.5 -0.0 -1.2 -0.1 -0.3 0.7 0.2 0.1 -0.1 -1.3 0.0 0.8 Chi-square with 42 degrees of freedom:39.253000 z-score=-0.299722, p-value=0.407766 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-19_10:31 Test no p-value 1 0.003136 2 0.336599 3 0.188152 4 0.012877 5 0.087027 6 0.050114 7 0.035304 8 0.276687 9 0.305531 10 0.012674 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000007 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-19_10:31: (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 66728 0.06 66570 0.14 3 25000.00 25024 0.02 25123 0.61 4 6666.67 6603 0.61 6657 0.01 5 1388.89 1388 0.00 1380 0.06 6 238.10 225 0.72 236 0.02 7 34.72 24 3.31 26 2.19 8 4.96 7 0.84 7 0.84 p=0.52543 p=0.30490 Number of rngs required: 687530, p-value: 0.156 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-19_10:31 No. of wins: Observed Expected 98534 98585.9 z-score=-0.232, pvalue=0.40829 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66436 66666.7 0.798 0.798 2 37875 37654.3 1.293 2.091 3 27040 26954.7 0.270 2.361 4 19247 19313.5 0.229 2.590 5 13787 13851.4 0.300 2.889 6 9999 9943.5 0.309 3.199 7 7248 7145.0 1.484 4.683 8 5032 5139.1 2.231 6.914 9 3723 3699.9 0.145 7.058 10 2579 2666.3 2.858 9.917 11 1979 1923.3 1.611 11.528 12 1389 1388.7 0.000 11.528 13 984 1003.7 0.387 11.915 14 734 726.1 0.085 12.000 15 554 525.8 1.508 13.509 16 400 381.2 0.932 14.441 17 285 276.5 0.259 14.700 18 178 200.8 2.595 17.295 19 131 146.0 1.538 18.833 20 112 106.2 0.315 19.148 21 288 287.1 0.003 19.151 Chisq= 19.15 for 20 degrees of freedom, p= 0.48796 SUMMARY of craptest p-value for no. of wins: 0.408292 p-value for throws/game: 0.487963 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-19_10:31 No. of wins: Observed Expected 98442 98585.9 z-score=-0.643, pvalue=0.25998 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66752 66666.7 0.109 0.109 2 37619 37654.3 0.033 0.142 3 26789 26954.7 1.019 1.161 4 19368 19313.5 0.154 1.315 5 13914 13851.4 0.283 1.598 6 10060 9943.5 1.364 2.962 7 7219 7145.0 0.766 3.728 8 5145 5139.1 0.007 3.735 9 3587 3699.9 3.443 7.178 10 2661 2666.3 0.011 7.188 11 1877 1923.3 1.116 8.304 12 1351 1388.7 1.026 9.330 13 1072 1003.7 4.646 13.975 14 713 726.1 0.238 14.213 15 496 525.8 1.693 15.906 16 387 381.2 0.090 15.996 17 243 276.5 4.068 20.064 18 213 200.8 0.737 20.801 19 136 146.0 0.683 21.484 20 108 106.2 0.030 21.514 21 290 287.1 0.029 21.543 Chisq= 21.54 for 20 degrees of freedom, p= 0.63418 SUMMARY of craptest p-value for no. of wins: 0.259976 p-value for throws/game: 0.634185 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0031,0.0127,0.0129,0.0130,0.0135,0.0139,0.0188,0.0281,0.0306, 0.0308,0.0334,0.0353,0.0355,0.0357,0.0418,0.0499,0.0501,0.0530,0.0547, 0.0562,0.0566,0.0594,0.0613,0.0800,0.0804,0.0818,0.0818,0.0870,0.0890, 0.0907,0.0933,0.1001,0.1005,0.1028,0.1032,0.1081,0.1083,0.1099,0.1112, 0.1179,0.1198,0.1209,0.1222,0.1237,0.1285,0.1322,0.1339,0.1403,0.1438, 0.1474,0.1504,0.1559,0.1575,0.1599,0.1617,0.1677,0.1688,0.1716,0.1797, 0.1806,0.1809,0.1882,0.1903,0.2035,0.2043,0.2056,0.2160,0.2204,0.2235, 0.2250,0.2283,0.2326,0.2328,0.2363,0.2491,0.2539,0.2550,0.2585,0.2595, 0.2595,0.2600,0.2647,0.2716,0.2761,0.2767,0.2862,0.2904,0.2947,0.2959, 0.2969,0.2981,0.3017,0.3049,0.3055,0.3060,0.3092,0.3139,0.3180,0.3215, 0.3228,0.3283,0.3287,0.3333,0.3334,0.3363,0.3366,0.3377,0.3427,0.3569, 0.3591,0.3614,0.3633,0.3634,0.3691,0.3694,0.3706,0.3707,0.3752,0.3807, 0.4078,0.4083,0.4097,0.4298,0.4430,0.4450,0.4469,0.4487,0.4558,0.4656, 0.4668,0.4698,0.4725,0.4752,0.4807,0.4819,0.4843,0.4880,0.4949,0.4982, 0.4995,0.5009,0.5056,0.5061,0.5068,0.5073,0.5104,0.5158,0.5254,0.5358, 0.5401,0.5489,0.5527,0.5535,0.5612,0.5710,0.5725,0.5803,0.5823,0.5875, 0.5963,0.5976,0.6002,0.6104,0.6106,0.6191,0.6201,0.6213,0.6259,0.6321, 0.6337,0.6342,0.6371,0.6388,0.6476,0.6594,0.6598,0.6760,0.6848,0.6852, 0.6889,0.7140,0.7151,0.7254,0.7291,0.7321,0.7330,0.7334,0.7417,0.7423, 0.7432,0.7444,0.7513,0.7528,0.7528,0.7530,0.7537,0.7566,0.7630,0.7639, 0.7767,0.7819,0.7853,0.7859,0.7870,0.7898,0.7924,0.7978,0.7994,0.8125, 0.8177,0.8190,0.8198,0.8208,0.8218,0.8232,0.8258,0.8300,0.8307,0.8316, 0.8397,0.8402,0.8409,0.8478,0.8501,0.8563,0.8674,0.8715,0.8722,0.8784, 0.8807,0.8822,0.8863,0.8866,0.8870,0.8899,0.8918,0.8975,0.8986,0.9012, 0.9084,0.9109,0.9124,0.9214,0.9241,0.9249,0.9249,0.9286,0.9316,0.9343, 0.9348,0.9366,0.9384,0.9469,0.9499,0.9571,0.9647,0.9649,0.9745,0.9757, 0.9766,0.9830,0.9868,0.9900,0.9901,0.9912,0.9921,0.9986,0.9993, Overall p-value after applying KStest on 269 p-values = 0.169807 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.