RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-20_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 17.8462 0.601396 2 to 25 15.83 23.9470 0.879118 3 to 26 15.80 16.7888 0.531236 4 to 27 15.70 15.2907 0.425447 5 to 28 15.97 8.9744 0.058937 6 to 29 15.82 21.5170 0.795987 7 to 30 15.96 14.4168 0.362592 8 to 31 15.93 19.2198 0.683936 9 to 32 15.68 13.2087 0.277895 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.965486 Tough bday spacings test for dh-ranFile-2016-06-20_12:31: 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 18 35 60 106 93 85 38 40 17 5 3 (O-E)^2/E 8.5 0.1 2.4 0.7 0.2 0.6 3.8 3.5 0.3 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 20.849, p= 0.978 RESULTS OF GCD FOR dh-ranFile-2016-06-20_12:31 Euclid's algorithm: p-value, steps to gcd: 0.165683 p-value, dist. of gcd's: 0.498791 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-20_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.258 0.386 0.989 0.832 0.201 0.250 0.235 0.434 Bits 8 to 15---> 0.729 0.549 0.379 0.688 0.978 0.589 0.794 0.034 Bits 16 to 23---> 0.138 0.119 0.946 0.126 0.071 0.468 0.152 0.696 Bits 24 to 31---> 0.192 0.762 0.524 0.997 0.228 0.462 0.496 0.569 KS test for the above 32 p values: 0.318 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-20_12:31, p-values for 5 runs: 0.6763, 0.3366, 0.7939, 0.8386, 0.8655 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-20_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 214 211.4 0.032 0.032 r= 29 5245 5134.0 2.399 2.431 r= 30 22940 23103.0 1.151 3.582 r= 31 11601 11551.5 0.212 3.794 chi-square = 3.794 with df = 3; p-value = 0.715 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-20_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 182 211.4 4.093 4.093 r= 30 5101 5134.0 0.212 4.306 r= 31 23169 23103.0 0.188 4.494 r= 32 11548 11551.5 0.001 4.495 chi-square = 4.495 with df = 3; p-value = 0.787 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-20_12:31 b-rank test for bits 1 to 8, p=0.22791 b-rank test for bits 2 to 9, p=0.49971 b-rank test for bits 3 to 10, p=0.82080 b-rank test for bits 4 to 11, p=0.77651 b-rank test for bits 5 to 12, p=0.43798 b-rank test for bits 6 to 13, p=0.31734 b-rank test for bits 7 to 14, p=0.73200 b-rank test for bits 8 to 15, p=0.72383 b-rank test for bits 9 to 16, p=0.49762 b-rank test for bits 10 to 17, p=0.63449 b-rank test for bits 11 to 18, p=0.39884 b-rank test for bits 12 to 19, p=0.41852 b-rank test for bits 13 to 20, p=0.82326 b-rank test for bits 14 to 21, p=0.57109 b-rank test for bits 15 to 22, p=0.59657 b-rank test for bits 16 to 23, p=0.45541 b-rank test for bits 17 to 24, p=0.85256 b-rank test for bits 18 to 25, p=0.58713 b-rank test for bits 19 to 26, p=0.95237 b-rank test for bits 20 to 27, p=0.83045 b-rank test for bits 21 to 28, p=0.05840 b-rank test for bits 22 to 29, p=0.65052 b-rank test for bits 23 to 30, p=0.15777 b-rank test for bits 24 to 31, p=0.45613 b-rank test for bits 25 to 32, p=0.82385 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 = 0.173316 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-20_12:31 (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 142274 0.85 0.802902 2 141886 -0.05 0.478265 3 142094 0.43 0.666937 4 142453 1.27 0.898003 5 142463 1.29 0.902102 6 142399 1.14 0.873707 7 141966 0.13 0.552669 8 141612 -0.69 0.243623 9 141229 -1.59 0.055967 10 141855 -0.13 0.449494 11 141998 0.21 0.582063 12 141414 -1.16 0.123572 13 141859 -0.12 0.453195 14 142654 1.74 0.959060 15 142460 1.29 0.900885 16 142509 1.40 0.919408 17 141533 -0.88 0.189626 18 141457 -1.06 0.145291 19 142324 0.97 0.833691 20 142255 0.81 0.790351 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-20_12:31 Bits used No. missing words z-score p-value 23 to 32 141785 -0.4287 0.334062 22 to 31 141808 -0.3494 0.363389 21 to 30 141645 -0.9115 0.181021 20 to 29 141539 -1.2770 0.100801 19 to 28 141829 -0.2770 0.390890 18 to 27 141974 0.2230 0.588232 17 to 26 142288 1.3058 0.904183 16 to 25 141840 -0.2391 0.405526 15 to 24 142033 0.4264 0.665109 14 to 23 141944 0.1196 0.547581 13 to 22 141736 -0.5977 0.275024 12 to 21 141743 -0.5736 0.283136 11 to 20 141385 -1.8080 0.035301 10 to 19 142371 1.5920 0.944304 9 to 18 141783 -0.4356 0.331556 8 to 17 141902 -0.0253 0.489918 7 to 16 141466 -1.5287 0.063166 6 to 15 141131 -2.6839 0.003638 5 to 14 142089 0.6196 0.732224 4 to 13 141961 0.1782 0.570706 3 to 12 141867 -0.1460 0.441974 2 to 11 141862 -0.1632 0.435178 1 to 10 142526 2.1264 0.983267 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-20_12:31 Bits used No. missing words z-score p-value 28 to 32 142150 0.8158 0.792702 27 to 31 141920 0.0362 0.514426 26 to 30 142451 1.8362 0.966834 25 to 29 142085 0.5955 0.724243 24 to 28 141725 -0.6248 0.266036 23 to 27 142620 2.4091 0.992003 22 to 26 142095 0.6294 0.735453 21 to 25 141901 -0.0282 0.488737 20 to 24 141905 -0.0147 0.494145 19 to 23 141839 -0.2384 0.405783 18 to 22 142362 1.5345 0.937544 17 to 21 142062 0.5175 0.697605 16 to 20 141956 0.1582 0.562852 15 to 19 142058 0.5040 0.692857 14 to 18 141886 -0.0791 0.468483 13 to 17 142109 0.6768 0.750749 12 to 16 141930 0.0701 0.527930 11 to 15 141803 -0.3604 0.359259 10 to 14 142294 1.3040 0.903877 9 to 13 141413 -1.6825 0.046238 8 to 12 141559 -1.1876 0.117504 7 to 11 141857 -0.1774 0.429601 6 to 10 142174 0.8972 0.815190 5 to 9 141814 -0.3232 0.373290 4 to 8 142083 0.5887 0.721973 3 to 7 141739 -0.5774 0.281838 2 to 6 141154 -2.5604 0.005227 1 to 5 141656 -0.8587 0.195240 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-20_12:31 Bits used No. missing words z-score p-value 31 to 32 141891 -0.0541 0.478439 30 to 31 141884 -0.0747 0.470219 29 to 30 141361 -1.6175 0.052886 28 to 29 141991 0.2409 0.595189 27 to 28 142425 1.5212 0.935889 26 to 27 141834 -0.2222 0.412074 25 to 26 141494 -1.2252 0.110257 24 to 25 142395 1.4327 0.924022 23 to 24 141671 -0.7030 0.241016 22 to 23 141537 -1.0983 0.136033 21 to 22 141683 -0.6676 0.252182 20 to 21 140711 -3.5349 0.000204 19 to 20 141554 -1.0482 0.147280 18 to 19 141514 -1.1662 0.121774 17 to 18 142084 0.5153 0.696811 16 to 17 142004 0.2793 0.609978 15 to 16 141755 -0.4553 0.324464 14 to 15 141476 -1.2783 0.100579 13 to 14 141853 -0.1662 0.434014 12 to 13 142135 0.6657 0.747196 11 to 12 141684 -0.6647 0.253124 10 to 11 142456 1.6126 0.946584 9 to 10 141892 -0.0511 0.479615 8 to 9 141885 -0.0718 0.471393 7 to 8 141601 -0.9095 0.181536 6 to 7 141922 0.0374 0.514907 5 to 6 141429 -1.4169 0.078256 4 to 5 142024 0.3383 0.632416 3 to 4 142315 1.1967 0.884282 2 to 3 141774 -0.3992 0.344872 1 to 2 141941 0.0934 0.537216 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-20_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2580.97 1.145 0.873909 Test results for specific bytes for dh-ranFile-2016-06-20_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2336.81 -2.308 0.010502 2 to 9 2482.80 -0.243 0.403918 3 to 10 2498.29 -0.024 0.490361 4 to 11 2694.85 2.756 0.997071 5 to 12 2457.41 -0.602 0.273474 6 to 13 2497.38 -0.037 0.485246 7 to 14 2369.39 -1.847 0.032370 8 to 15 2489.10 -0.154 0.438758 9 to 16 2419.65 -1.136 0.127900 10 to 17 2403.47 -1.365 0.086112 11 to 18 2452.12 -0.677 0.249162 12 to 19 2532.83 0.464 0.678757 13 to 20 2573.65 1.042 0.851179 14 to 21 2383.04 -1.654 0.049053 15 to 22 2495.00 -0.071 0.471832 16 to 23 2392.24 -1.524 0.063765 17 to 24 2571.28 1.008 0.843292 18 to 25 2489.27 -0.152 0.439688 19 to 26 2436.03 -0.905 0.182826 20 to 27 2533.05 0.467 0.679868 21 to 28 2385.43 -1.620 0.052594 22 to 29 2579.66 1.126 0.870021 23 to 30 2575.33 1.065 0.856649 24 to 31 2579.80 1.129 0.870455 25 to 32 2519.93 0.282 0.610959 CDPARK for dh-ranFile-2016-06-20_12:31: 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 3522 -0.0457 0.481790 3528 0.2283 0.590298 3517 -0.2740 0.392053 3570 2.1461 0.984068 3520 -0.1370 0.445521 3524 0.0457 0.518210 3524 0.0457 0.518210 3528 0.2283 0.590298 3532 0.4110 0.659449 3526 0.1370 0.554479 Square side=100, avg. no. parked=3529.10 sample std.=14.23 p-value of the KSTEST for those 10 p-values: 0.112681 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-20_12:31 0.7887,0.8054,0.4328,0.6313,0.6862,0.9863,0.8232,0.4617,0.7626,0.2077, The KS test for those 10 p-values: 0.118266 The 3DSPHERES test for dh-ranFile-2016-06-20_12:31 sample no r^3 equiv. uni. 1 33.944 0.677439 2 22.032 0.520202 3 10.888 0.304376 4 40.862 0.743873 5 36.310 0.701900 6 32.329 0.659604 7 0.952 0.031225 8 26.038 0.580182 9 42.903 0.760712 10 18.794 0.465524 11 24.718 0.561292 12 85.157 0.941490 13 5.924 0.179180 14 5.894 0.178385 15 71.527 0.907841 16 3.680 0.115450 17 3.156 0.099854 18 35.158 0.690235 19 17.864 0.448698 20 49.565 0.808367 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.863733 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-20_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.3 0.2 -0.5 0.4 0.2 -0.0 0.3 -0.0 -0.9 -0.7 0.5 -0.8 1.0 -0.6 -1.1 0.2 -2.2 -0.3 1.5 0.2 -1.0 2.5 1.8 0.5 0.5 0.4 0.8 -1.7 0.7 -0.7 0.7 1.1 -1.3 1.9 0.0 0.2 0.5 -0.7 0.9 -1.0 0.8 Chi-square with 42 degrees of freedom:38.614715 z-score=-0.369365, p-value=0.379626 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-20_12:31 Test no p-value 1 0.373984 2 0.016506 3 0.250637 4 0.220296 5 0.129931 6 0.021800 7 0.696811 8 0.627445 9 0.598097 10 0.367920 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.087122 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-20_12:31: (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 66927 1.02 66967 1.35 3 25000.00 24741 2.68 24765 2.21 4 6666.67 6682 0.04 6659 0.01 5 1388.89 1374 0.16 1330 2.50 6 238.10 249 0.50 242 0.06 7 34.72 22 4.66 30 0.64 8 4.96 4 0.19 6 0.22 p=0.83948 p=0.67837 Number of rngs required: 687262, p-value: 0.092 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-20_12:31 No. of wins: Observed Expected 98617 98585.9 z-score= 0.139, pvalue=0.55539 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66632 66666.7 0.018 0.018 2 37864 37654.3 1.168 1.186 3 26773 26954.7 1.225 2.411 4 19245 19313.5 0.243 2.654 5 13839 13851.4 0.011 2.665 6 9894 9943.5 0.247 2.912 7 7100 7145.0 0.284 3.195 8 5073 5139.1 0.849 4.045 9 3803 3699.9 2.875 6.920 10 2721 2666.3 1.122 8.042 11 1926 1923.3 0.004 8.046 12 1484 1388.7 6.534 14.580 13 1013 1003.7 0.086 14.666 14 700 726.1 0.941 15.607 15 528 525.8 0.009 15.616 16 427 381.2 5.515 21.131 17 238 276.5 5.371 26.502 18 214 200.8 0.864 27.366 19 139 146.0 0.334 27.700 20 94 106.2 1.405 29.105 21 293 287.1 0.121 29.225 Chisq= 29.23 for 20 degrees of freedom, p= 0.91659 SUMMARY of craptest p-value for no. of wins: 0.555387 p-value for throws/game: 0.916586 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-20_12:31 No. of wins: Observed Expected 98490 98585.9 z-score=-0.429, pvalue=0.33406 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66517 66666.7 0.336 0.336 2 37566 37654.3 0.207 0.543 3 26964 26954.7 0.003 0.546 4 19308 19313.5 0.002 0.548 5 13840 13851.4 0.009 0.557 6 9887 9943.5 0.322 0.879 7 7340 7145.0 5.320 6.199 8 5094 5139.1 0.395 6.595 9 3775 3699.9 1.526 8.120 10 2705 2666.3 0.562 8.682 11 1894 1923.3 0.447 9.129 12 1423 1388.7 0.845 9.975 13 1031 1003.7 0.742 10.716 14 720 726.1 0.052 10.768 15 551 525.8 1.204 11.973 16 369 381.2 0.387 12.360 17 291 276.5 0.756 13.116 18 202 200.8 0.007 13.123 19 150 146.0 0.110 13.233 20 102 106.2 0.167 13.401 21 271 287.1 0.904 14.305 Chisq= 14.30 for 20 degrees of freedom, p= 0.18530 SUMMARY of craptest p-value for no. of wins: 0.334058 p-value for throws/game: 0.185297 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0036,0.0052,0.0105,0.0165,0.0218,0.0312,0.0324,0.0336,0.0353, 0.0462,0.0491,0.0526,0.0529,0.0560,0.0584,0.0589,0.0632,0.0638,0.0706, 0.0783,0.0861,0.0871,0.0920,0.0999,0.1006,0.1008,0.1103,0.1127,0.1155, 0.1175,0.1183,0.1190,0.1218,0.1236,0.1260,0.1279,0.1299,0.1360,0.1380, 0.1453,0.1473,0.1521,0.1578,0.1657,0.1733,0.1784,0.1792,0.1810,0.1815, 0.1828,0.1853,0.1896,0.1924,0.1952,0.2008,0.2077,0.2203,0.2279,0.2282, 0.2351,0.2410,0.2436,0.2492,0.2498,0.2506,0.2522,0.2531,0.2580,0.2660, 0.2735,0.2750,0.2779,0.2818,0.2831,0.3044,0.3173,0.3179,0.3245,0.3316, 0.3341,0.3341,0.3366,0.3449,0.3593,0.3626,0.3634,0.3679,0.3733,0.3740, 0.3794,0.3796,0.3858,0.3909,0.3921,0.3988,0.4039,0.4055,0.4058,0.4121, 0.4185,0.4254,0.4296,0.4328,0.4336,0.4340,0.4352,0.4380,0.4388,0.4397, 0.4420,0.4455,0.4487,0.4495,0.4532,0.4554,0.4561,0.4616,0.4617,0.4655, 0.4684,0.4685,0.4702,0.4714,0.4718,0.4783,0.4784,0.4796,0.4818,0.4852, 0.4887,0.4899,0.4904,0.4941,0.4956,0.4976,0.4988,0.4997,0.5144,0.5149, 0.5182,0.5182,0.5202,0.5244,0.5279,0.5312,0.5372,0.5476,0.5492,0.5527, 0.5545,0.5554,0.5613,0.5629,0.5694,0.5707,0.5711,0.5802,0.5821,0.5871, 0.5882,0.5893,0.5903,0.5903,0.5952,0.5966,0.5981,0.6014,0.6100,0.6110, 0.6274,0.6313,0.6324,0.6345,0.6505,0.6594,0.6596,0.6651,0.6669,0.6763, 0.6774,0.6784,0.6788,0.6799,0.6839,0.6862,0.6884,0.6902,0.6929,0.6960, 0.6968,0.6968,0.6976,0.7019,0.7154,0.7220,0.7238,0.7242,0.7288,0.7320, 0.7322,0.7355,0.7439,0.7472,0.7507,0.7607,0.7619,0.7626,0.7765,0.7873, 0.7887,0.7904,0.7927,0.7936,0.7939,0.7960,0.8029,0.8054,0.8084,0.8152, 0.8208,0.8232,0.8233,0.8238,0.8304,0.8325,0.8337,0.8386,0.8395,0.8433, 0.8512,0.8526,0.8566,0.8637,0.8655,0.8700,0.8705,0.8737,0.8739,0.8791, 0.8843,0.8980,0.9009,0.9021,0.9039,0.9042,0.9078,0.9166,0.9194,0.9240, 0.9359,0.9375,0.9415,0.9443,0.9462,0.9466,0.9524,0.9591,0.9655,0.9668, 0.9778,0.9781,0.9833,0.9841,0.9863,0.9887,0.9920,0.9971,0.9974, Overall p-value after applying KStest on 269 p-values = 0.874152 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.