RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-09_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.81 17.0888 0.551632 2 to 25 15.76 17.8833 0.603760 3 to 26 15.75 6.6508 0.012364 4 to 27 15.82 12.5668 0.235334 5 to 28 15.84 16.3619 0.501660 6 to 29 15.56 32.3272 0.986301 7 to 30 15.98 13.1615 0.274690 8 to 31 15.99 17.4434 0.575259 9 to 32 15.55 24.0652 0.882327 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.831470 Tough bday spacings test for dh-ranFile-2016-12-09_19:31: 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 6 36 84 90 88 77 56 31 17 10 5 (O-E)^2/E 1.1 0.0 1.6 0.6 1.0 0.0 0.3 0.1 0.3 1.7 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.844, p= 0.260 RESULTS OF GCD FOR dh-ranFile-2016-12-09_19:31 Euclid's algorithm: p-value, steps to gcd: 0.385481 p-value, dist. of gcd's: 0.609662 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-09_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.777 0.348 0.139 0.061 0.249 0.770 0.506 0.563 Bits 8 to 15---> 0.124 0.641 0.770 0.919 0.529 0.579 0.801 0.379 Bits 16 to 23---> 0.740 0.001 0.242 0.163 0.308 0.824 0.594 0.957 Bits 24 to 31---> 0.281 0.195 0.399 0.249 0.914 0.304 0.446 0.326 KS test for the above 32 p values: 0.219 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-09_19:31, p-values for 5 runs: 0.0594, 0.2424, 0.0563, 0.4699, 0.4754 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-09_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5150 5134.0 0.050 0.110 r= 30 23106 23103.0 0.000 0.111 r= 31 11529 11551.5 0.044 0.155 chi-square = 0.155 with df = 3; p-value = 0.015 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-09_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 192 211.4 1.783 1.783 r= 30 5097 5134.0 0.267 2.050 r= 31 22997 23103.0 0.487 2.537 r= 32 11714 11551.5 2.285 4.822 chi-square = 4.822 with df = 3; p-value = 0.815 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-09_19:31 b-rank test for bits 1 to 8, p=0.95156 b-rank test for bits 2 to 9, p=0.65806 b-rank test for bits 3 to 10, p=0.42502 b-rank test for bits 4 to 11, p=0.36004 b-rank test for bits 5 to 12, p=0.26537 b-rank test for bits 6 to 13, p=0.89780 b-rank test for bits 7 to 14, p=0.22548 b-rank test for bits 8 to 15, p=0.52369 b-rank test for bits 9 to 16, p=0.51416 b-rank test for bits 10 to 17, p=0.47230 b-rank test for bits 11 to 18, p=0.86969 b-rank test for bits 12 to 19, p=0.89646 b-rank test for bits 13 to 20, p=0.88257 b-rank test for bits 14 to 21, p=0.10899 b-rank test for bits 15 to 22, p=0.42132 b-rank test for bits 16 to 23, p=0.37026 b-rank test for bits 17 to 24, p=0.02213 b-rank test for bits 18 to 25, p=0.57856 b-rank test for bits 19 to 26, p=0.40928 b-rank test for bits 20 to 27, p=0.10620 b-rank test for bits 21 to 28, p=0.40281 b-rank test for bits 22 to 29, p=0.72070 b-rank test for bits 23 to 30, p=0.98319 b-rank test for bits 24 to 31, p=0.99672 b-rank test for bits 25 to 32, p=0.98833 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 = 0.208312 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-09_19:31 (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 142315 0.95 0.828391 2 142710 1.87 0.969308 3 142689 1.82 0.965747 4 142523 1.43 0.924187 5 142451 1.27 0.897169 6 142358 1.05 0.852749 7 142051 0.33 0.629680 8 141448 -1.08 0.140545 9 142536 1.46 0.928428 10 142226 0.74 0.770315 11 142056 0.34 0.634083 12 141883 -0.06 0.475473 13 142211 0.70 0.759544 14 141305 -1.41 0.078977 15 142234 0.76 0.775947 16 141582 -0.76 0.222198 17 141690 -0.51 0.304167 18 142668 1.77 0.961852 19 141944 0.08 0.532281 20 141992 0.19 0.576581 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-09_19:31 Bits used No. missing words z-score p-value 23 to 32 141231 -2.3391 0.009666 22 to 31 141542 -1.2667 0.102639 21 to 30 141783 -0.4356 0.331556 20 to 29 141966 0.1954 0.577466 19 to 28 142162 0.8713 0.808198 18 to 27 141996 0.2989 0.617477 17 to 26 142101 0.6609 0.745672 16 to 25 141390 -1.7908 0.036663 15 to 24 142041 0.4540 0.675098 14 to 23 141865 -0.1529 0.439254 13 to 22 142229 1.1023 0.864837 12 to 21 141824 -0.2942 0.384287 11 to 20 142507 2.0609 0.980345 10 to 19 141916 0.0230 0.509175 9 to 18 141785 -0.4287 0.334062 8 to 17 141741 -0.5804 0.280806 7 to 16 142049 0.4816 0.684962 6 to 15 141917 0.0264 0.510550 5 to 14 141618 -1.0046 0.157548 4 to 13 141846 -0.2184 0.413567 3 to 12 141845 -0.2218 0.412224 2 to 11 141819 -0.3115 0.377717 1 to 10 142303 1.3575 0.912686 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-09_19:31 Bits used No. missing words z-score p-value 28 to 32 141998 0.3006 0.618131 27 to 31 142001 0.3107 0.622003 26 to 30 141849 -0.2045 0.418978 25 to 29 141721 -0.6384 0.261605 24 to 28 141797 -0.3808 0.351683 23 to 27 141792 -0.3977 0.345415 22 to 26 142308 1.3514 0.911720 21 to 25 142027 0.3989 0.655010 20 to 24 142281 1.2599 0.896147 19 to 23 141911 0.0057 0.502258 18 to 22 142152 0.8226 0.794635 17 to 21 142322 1.3989 0.919076 16 to 20 141935 0.0870 0.534671 15 to 19 142244 1.1345 0.871702 14 to 18 141638 -0.9198 0.178848 13 to 17 141452 -1.5503 0.060538 12 to 16 141957 0.1616 0.564187 11 to 15 141648 -0.8859 0.187845 10 to 14 142029 0.4057 0.657504 9 to 13 141493 -1.4113 0.079080 8 to 12 142058 0.5040 0.692857 7 to 11 142030 0.4091 0.658749 6 to 10 142107 0.6701 0.748593 5 to 9 141763 -0.4960 0.309935 4 to 8 141937 0.0938 0.537365 3 to 7 142196 0.9718 0.834416 2 to 6 141754 -0.5265 0.299256 1 to 5 141717 -0.6520 0.257212 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-09_19:31 Bits used No. missing words z-score p-value 31 to 32 142423 1.5153 0.935146 30 to 31 142263 1.0433 0.851589 29 to 30 141640 -0.7945 0.213457 28 to 29 142253 1.0138 0.844655 27 to 28 142061 0.4474 0.672708 26 to 27 141998 0.2616 0.603171 25 to 26 141764 -0.4287 0.334070 24 to 25 141666 -0.7178 0.236444 23 to 24 141980 0.2085 0.582568 22 to 23 141925 0.0462 0.518434 21 to 22 142387 1.4091 0.920591 20 to 21 141785 -0.3668 0.356901 19 to 20 141755 -0.4553 0.324464 18 to 19 142272 1.0698 0.857651 17 to 18 141640 -0.7945 0.213457 16 to 17 141471 -1.2930 0.098004 15 to 16 142382 1.3943 0.918388 14 to 15 141881 -0.0836 0.466699 13 to 14 142080 0.5035 0.692677 12 to 13 142304 1.1642 0.877832 11 to 12 141744 -0.4877 0.312882 10 to 11 142250 1.0049 0.842534 9 to 10 142099 0.5595 0.712089 8 to 9 142651 2.1878 0.985659 7 to 8 141858 -0.1514 0.439824 6 to 7 142145 0.6952 0.756532 5 to 6 142621 2.0993 0.982106 4 to 5 141353 -1.6411 0.050389 3 to 4 141908 -0.0039 0.498435 2 to 3 141968 0.1731 0.568701 1 to 2 142014 0.3088 0.621248 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-09_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2482.31 -0.250 0.401224 Test results for specific bytes for dh-ranFile-2016-12-09_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2484.51 -0.219 0.413276 2 to 9 2510.82 0.153 0.560784 3 to 10 2433.77 -0.937 0.174464 4 to 11 2414.78 -1.205 0.114068 5 to 12 2564.55 0.913 0.819339 6 to 13 2589.52 1.266 0.897233 7 to 14 2466.30 -0.477 0.316825 8 to 15 2512.36 0.175 0.569379 9 to 16 2543.79 0.619 0.732156 10 to 17 2486.50 -0.191 0.424307 11 to 18 2476.90 -0.327 0.371940 12 to 19 2480.60 -0.274 0.391898 13 to 20 2421.99 -1.103 0.134976 14 to 21 2478.70 -0.301 0.381603 15 to 22 2488.78 -0.159 0.436947 16 to 23 2493.48 -0.092 0.463252 17 to 24 2453.94 -0.651 0.257417 18 to 25 2521.73 0.307 0.620688 19 to 26 2501.64 0.023 0.509259 20 to 27 2475.32 -0.349 0.363528 21 to 28 2524.20 0.342 0.633936 22 to 29 2510.00 0.141 0.556258 23 to 30 2535.05 0.496 0.689927 24 to 31 2395.94 -1.472 0.070557 25 to 32 2541.79 0.591 0.722757 CDPARK for dh-ranFile-2016-12-09_19:31: 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 3497 -1.1872 0.117571 3510 -0.5936 0.276387 3498 -1.1416 0.126820 3536 0.5936 0.723613 3495 -1.2785 0.100530 3535 0.5479 0.708135 3489 -1.5525 0.060270 3545 1.0046 0.842447 3522 -0.0457 0.481790 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3513.60 sample std.=18.76 p-value of the KSTEST for those 10 p-values: 0.206698 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-09_19:31 0.2767,0.6177,0.5144,0.9031,0.4098,0.1706,0.0980,0.3741,0.4500,0.0976, The KS test for those 10 p-values: 0.361919 The 3DSPHERES test for dh-ranFile-2016-12-09_19:31 sample no r^3 equiv. uni. 1 11.001 0.306989 2 44.646 0.774222 3 7.675 0.225741 4 2.150 0.069152 5 35.440 0.693128 6 9.208 0.264293 7 31.927 0.655008 8 16.199 0.417234 9 2.341 0.075060 10 34.517 0.683539 11 17.902 0.449395 12 3.700 0.116036 13 37.860 0.716909 14 15.094 0.395368 15 2.591 0.082750 16 13.354 0.359252 17 43.388 0.764553 18 8.542 0.247786 19 8.988 0.258890 20 18.944 0.468185 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.149622 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-09_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 -0.8 0.8 -0.2 0.3 -1.3 0.8 -0.5 -0.7 -0.2 0.6 -0.6 -0.0 0.4 -0.3 -1.2 -0.9 1.4 0.2 -0.6 0.3 -0.7 -0.2 -1.0 2.1 1.4 1.4 2.1 0.9 -1.0 0.7 0.3 -1.1 0.1 -0.1 -0.9 0.2 1.3 0.4 -0.6 0.0 1.8 Chi-square with 42 degrees of freedom:34.992314 z-score=-0.764601, p-value=0.230278 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-09_19:31 Test no p-value 1 0.271704 2 0.511824 3 0.007825 4 0.003916 5 0.234500 6 0.115095 7 0.007012 8 0.876146 9 0.108760 10 0.761574 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003785 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-09_19:31: (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 66617 0.04 66614 0.04 3 25000.00 25029 0.03 25030 0.04 4 6666.67 6723 0.48 6671 0.00 5 1388.89 1361 0.56 1394 0.02 6 238.10 228 0.43 250 0.60 7 34.72 40 0.80 33 0.09 8 4.96 1 3.16 7 0.84 p=0.51845 p=0.04878 Number of rngs required: 687747, p-value: 0.224 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-09_19:31 No. of wins: Observed Expected 98926 98585.9 z-score= 1.521, pvalue=0.93591 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66328 66666.7 1.720 1.720 2 37600 37654.3 0.078 1.799 3 26869 26954.7 0.273 2.071 4 19436 19313.5 0.777 2.849 5 13937 13851.4 0.529 3.378 6 9932 9943.5 0.013 3.391 7 7334 7145.0 4.998 8.389 8 5015 5139.1 2.995 11.385 9 3757 3699.9 0.882 12.267 10 2689 2666.3 0.193 12.460 11 1891 1923.3 0.543 13.004 12 1411 1388.7 0.357 13.360 13 1069 1003.7 4.246 17.607 14 737 726.1 0.162 17.769 15 525 525.8 0.001 17.771 16 404 381.2 1.370 19.140 17 253 276.5 2.004 21.144 18 207 200.8 0.190 21.334 19 173 146.0 4.999 26.333 20 116 106.2 0.901 27.234 21 317 287.1 3.111 30.345 Chisq= 30.35 for 20 degrees of freedom, p= 0.93555 SUMMARY of craptest p-value for no. of wins: 0.935909 p-value for throws/game: 0.935552 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-09_19:31 No. of wins: Observed Expected 98676 98585.9 z-score= 0.403, pvalue=0.65659 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66759 66666.7 0.128 0.128 2 37493 37654.3 0.691 0.819 3 27104 26954.7 0.827 1.646 4 19345 19313.5 0.051 1.697 5 13822 13851.4 0.062 1.760 6 9928 9943.5 0.024 1.784 7 7213 7145.0 0.647 2.431 8 4942 5139.1 7.557 9.988 9 3673 3699.9 0.195 10.183 10 2699 2666.3 0.401 10.584 11 1959 1923.3 0.662 11.246 12 1455 1388.7 3.161 14.407 13 945 1003.7 3.435 17.842 14 738 726.1 0.194 18.035 15 494 525.8 1.927 19.963 16 390 381.2 0.205 20.168 17 288 276.5 0.475 20.643 18 207 200.8 0.190 20.833 19 140 146.0 0.245 21.078 20 108 106.2 0.030 21.108 21 298 287.1 0.413 21.521 Chisq= 21.52 for 20 degrees of freedom, p= 0.63294 SUMMARY of craptest p-value for no. of wins: 0.656587 p-value for throws/game: 0.632935 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0038,0.0039,0.0070,0.0078,0.0097,0.0124,0.0155,0.0221,0.0367, 0.0488,0.0504,0.0563,0.0594,0.0603,0.0605,0.0606,0.0692,0.0706,0.0751, 0.0790,0.0791,0.0827,0.0976,0.0980,0.0980,0.1005,0.1026,0.1062,0.1088, 0.1090,0.1141,0.1151,0.1160,0.1176,0.1241,0.1268,0.1350,0.1386,0.1405, 0.1496,0.1575,0.1633,0.1706,0.1745,0.1788,0.1878,0.1948,0.2067,0.2083, 0.2135,0.2135,0.2187,0.2222,0.2243,0.2255,0.2257,0.2303,0.2345,0.2353, 0.2364,0.2416,0.2424,0.2478,0.2488,0.2489,0.2572,0.2574,0.2589,0.2599, 0.2613,0.2616,0.2643,0.2654,0.2717,0.2747,0.2764,0.2767,0.2808,0.2812, 0.2993,0.3036,0.3042,0.3070,0.3080,0.3099,0.3129,0.3168,0.3245,0.3257, 0.3316,0.3341,0.3341,0.3454,0.3479,0.3517,0.3569,0.3593,0.3600,0.3619, 0.3635,0.3703,0.3719,0.3741,0.3777,0.3794,0.3816,0.3843,0.3855,0.3919, 0.3954,0.3987,0.4012,0.4028,0.4093,0.4098,0.4122,0.4133,0.4136,0.4172, 0.4190,0.4213,0.4243,0.4250,0.4369,0.4393,0.4398,0.4455,0.4494,0.4500, 0.4633,0.4667,0.4682,0.4699,0.4723,0.4754,0.4755,0.4818,0.4984,0.5017, 0.5023,0.5064,0.5092,0.5093,0.5106,0.5118,0.5142,0.5144,0.5184,0.5185, 0.5237,0.5292,0.5323,0.5347,0.5374,0.5516,0.5563,0.5608,0.5625,0.5642, 0.5687,0.5694,0.5753,0.5766,0.5775,0.5786,0.5795,0.5826,0.5941,0.6032, 0.6038,0.6097,0.6175,0.6177,0.6181,0.6207,0.6212,0.6220,0.6297,0.6329, 0.6339,0.6341,0.6412,0.6550,0.6550,0.6566,0.6575,0.6581,0.6587,0.6727, 0.6751,0.6835,0.6850,0.6899,0.6927,0.6929,0.6931,0.7081,0.7121,0.7169, 0.7207,0.7228,0.7236,0.7322,0.7405,0.7457,0.7486,0.7565,0.7595,0.7616, 0.7646,0.7698,0.7701,0.7703,0.7742,0.7759,0.7771,0.7946,0.8010,0.8082, 0.8147,0.8193,0.8245,0.8284,0.8315,0.8344,0.8424,0.8425,0.8447,0.8516, 0.8527,0.8577,0.8648,0.8697,0.8717,0.8761,0.8778,0.8823,0.8826,0.8961, 0.8965,0.8972,0.8972,0.8978,0.9031,0.9117,0.9127,0.9140,0.9184,0.9190, 0.9191,0.9206,0.9242,0.9284,0.9351,0.9356,0.9359,0.9516,0.9567,0.9619, 0.9657,0.9693,0.9803,0.9821,0.9832,0.9857,0.9863,0.9883,0.9967, Overall p-value after applying KStest on 269 p-values = 0.699722 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.