RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-18_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 15.91 12.7968 0.250319 2 to 25 15.77 15.2287 0.420986 3 to 26 15.73 17.7103 0.592668 4 to 27 15.59 25.1825 0.909301 5 to 28 15.64 15.3398 0.428976 6 to 29 15.62 19.7140 0.710883 7 to 30 15.73 19.0746 0.675734 8 to 31 15.39 26.8345 0.939460 9 to 32 15.78 14.6350 0.378249 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.500178 Tough bday spacings test for dh-ranFile-2015-11-18_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 7 37 67 111 97 82 53 28 11 6 1 (O-E)^2/E 0.5 0.0 0.5 1.8 0.0 0.2 0.0 0.1 1.0 0.1 2.3 Birthday Spacings: Sum(O-E)^2/E= 6.562, p= 0.234 RESULTS OF GCD FOR dh-ranFile-2015-11-18_22:31 Euclid's algorithm: p-value, steps to gcd: 0.785829 p-value, dist. of gcd's: 0.241051 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-18_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.999 0.404 0.755 0.606 0.327 0.909 0.658 0.244 Bits 8 to 15---> 0.733 0.991 0.756 0.908 0.480 0.727 0.655 0.080 Bits 16 to 23---> 0.229 0.715 0.627 0.545 0.060 0.452 0.265 0.189 Bits 24 to 31---> 0.592 0.393 0.980 0.821 0.653 0.235 0.211 0.175 KS test for the above 32 p values: 0.538 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-18_22:31, p-values for 5 runs: 0.5626, 0.7588, 0.9021, 0.9144, 0.5804 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-18_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5200 5134.0 0.848 1.997 r= 30 23069 23103.0 0.050 2.047 r= 31 11504 11551.5 0.196 2.242 chi-square = 2.242 with df = 3; p-value = 0.476 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-18_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5175 5134.0 0.327 0.359 r= 31 23254 23103.0 0.986 1.345 r= 32 11357 11551.5 3.276 4.621 chi-square = 4.621 with df = 3; p-value = 0.798 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-18_22:31 b-rank test for bits 1 to 8, p=0.71283 b-rank test for bits 2 to 9, p=0.96281 b-rank test for bits 3 to 10, p=0.06908 b-rank test for bits 4 to 11, p=0.30002 b-rank test for bits 5 to 12, p=0.78643 b-rank test for bits 6 to 13, p=0.72221 b-rank test for bits 7 to 14, p=0.47478 b-rank test for bits 8 to 15, p=0.14863 b-rank test for bits 9 to 16, p=0.78198 b-rank test for bits 10 to 17, p=0.14798 b-rank test for bits 11 to 18, p=0.03329 b-rank test for bits 12 to 19, p=0.46688 b-rank test for bits 13 to 20, p=0.84946 b-rank test for bits 14 to 21, p=0.20883 b-rank test for bits 15 to 22, p=0.10290 b-rank test for bits 16 to 23, p=0.88986 b-rank test for bits 17 to 24, p=0.43895 b-rank test for bits 18 to 25, p=0.08114 b-rank test for bits 19 to 26, p=0.80048 b-rank test for bits 20 to 27, p=0.49150 b-rank test for bits 21 to 28, p=0.77821 b-rank test for bits 22 to 29, p=0.45250 b-rank test for bits 23 to 30, p=0.23858 b-rank test for bits 24 to 31, p=0.81078 b-rank test for bits 25 to 32, p=0.29375 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 = 0.830863 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-18_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 142292 0.89 0.814363 2 141668 -0.56 0.286426 3 142032 0.29 0.612795 4 141507 -0.94 0.173603 5 142498 1.38 0.915496 6 141536 -0.87 0.191532 7 141776 -0.31 0.377703 8 141710 -0.47 0.320706 9 142132 0.52 0.698558 10 142117 0.49 0.686236 11 141618 -0.68 0.248038 12 141772 -0.32 0.374157 13 141804 -0.25 0.402803 14 142351 1.03 0.848950 15 142278 0.86 0.805485 16 141682 -0.53 0.297659 17 142229 0.75 0.772436 18 143286 3.22 0.999351 19 141842 -0.16 0.437499 20 142811 2.11 0.982428 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-18_22:31 Bits used No. missing words z-score p-value 23 to 32 141811 -0.3391 0.367279 22 to 31 141868 -0.1425 0.443336 21 to 30 141781 -0.4425 0.329058 20 to 29 141241 -2.3046 0.010595 19 to 28 142058 0.5127 0.695904 18 to 27 141978 0.2368 0.593591 17 to 26 142033 0.4264 0.665109 16 to 25 141748 -0.5563 0.288999 15 to 24 141744 -0.5701 0.284304 14 to 23 141863 -0.1598 0.436536 13 to 22 141962 0.1816 0.572060 12 to 21 141830 -0.2736 0.392215 11 to 20 141908 -0.0046 0.498170 10 to 19 141792 -0.4046 0.342891 9 to 18 142011 0.3506 0.637051 8 to 17 141825 -0.2908 0.385605 7 to 16 141314 -2.0529 0.020043 6 to 15 141798 -0.3839 0.350528 5 to 14 142418 1.7540 0.960288 4 to 13 142179 0.9299 0.823788 3 to 12 141997 0.3023 0.618792 2 to 11 141879 -0.1046 0.458352 1 to 10 141744 -0.5701 0.284304 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-18_22:31 Bits used No. missing words z-score p-value 28 to 32 142103 0.6565 0.744252 27 to 31 141981 0.2429 0.595978 26 to 30 141786 -0.4181 0.337949 25 to 29 141564 -1.1706 0.120878 24 to 28 141952 0.1446 0.557504 23 to 27 141919 0.0328 0.513075 22 to 26 141680 -0.7774 0.218464 21 to 25 142332 1.4328 0.924040 20 to 24 142424 1.7446 0.959477 19 to 23 142107 0.6701 0.748593 18 to 22 142257 1.1785 0.880710 17 to 21 142377 1.5853 0.943553 16 to 20 141634 -0.9333 0.175327 15 to 19 141863 -0.1571 0.437602 14 to 18 141375 -1.8113 0.035048 13 to 17 141873 -0.1232 0.450993 12 to 16 141330 -1.9638 0.024775 11 to 15 142079 0.5752 0.717406 10 to 14 141966 0.1921 0.576169 9 to 13 141427 -1.6350 0.051023 8 to 12 142037 0.4328 0.667413 7 to 11 141919 0.0328 0.513075 6 to 10 142182 0.9243 0.822336 5 to 9 141861 -0.1638 0.434932 4 to 8 142257 1.1785 0.880710 3 to 7 141990 0.2735 0.607749 2 to 6 142492 1.9752 0.975875 1 to 5 141302 -2.0587 0.019759 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-18_22:31 Bits used No. missing words z-score p-value 31 to 32 141963 0.1583 0.562897 30 to 31 141204 -2.0806 0.018734 29 to 30 142637 2.1465 0.984084 28 to 29 141954 0.1318 0.552417 27 to 28 141610 -0.8830 0.188624 26 to 27 141714 -0.5762 0.282242 25 to 26 142073 0.4828 0.685382 24 to 25 141607 -0.8918 0.186242 23 to 24 142149 0.7070 0.760214 22 to 23 141722 -0.5526 0.290270 21 to 22 142034 0.3678 0.643473 20 to 21 142189 0.8250 0.795310 19 to 20 142080 0.5035 0.692677 18 to 19 142309 1.1790 0.880794 17 to 18 142448 1.5890 0.943969 16 to 17 141722 -0.5526 0.290270 15 to 16 141785 -0.3668 0.356901 14 to 15 142066 0.4622 0.678014 13 to 14 142252 1.0108 0.843950 12 to 13 141536 -1.1013 0.135390 11 to 12 142007 0.2881 0.613370 10 to 11 141823 -0.2547 0.399493 9 to 10 142088 0.5271 0.700921 8 to 9 141673 -0.6971 0.242858 7 to 8 141543 -1.0806 0.139933 6 to 7 141671 -0.7030 0.241016 5 to 6 141503 -1.1986 0.115339 4 to 5 142040 0.3855 0.650051 3 to 4 141854 -0.1632 0.435174 2 to 3 142158 0.7335 0.768385 1 to 2 141504 -1.1957 0.115914 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-18_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2566.23 0.937 0.825534 Test results for specific bytes for dh-ranFile-2015-11-18_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2540.06 0.567 0.714507 2 to 9 2466.58 -0.473 0.318258 3 to 10 2454.33 -0.646 0.259159 4 to 11 2470.29 -0.420 0.337201 5 to 12 2492.91 -0.100 0.460074 6 to 13 2490.42 -0.135 0.446121 7 to 14 2485.27 -0.208 0.417468 8 to 15 2560.77 0.859 0.804951 9 to 16 2474.39 -0.362 0.358632 10 to 17 2412.44 -1.238 0.107797 11 to 18 2442.26 -0.817 0.207092 12 to 19 2498.13 -0.026 0.489475 13 to 20 2436.45 -0.899 0.184408 14 to 21 2512.30 0.174 0.569064 15 to 22 2405.88 -1.331 0.091587 16 to 23 2472.00 -0.396 0.346079 17 to 24 2541.34 0.585 0.720627 18 to 25 2456.16 -0.620 0.267611 19 to 26 2429.83 -0.992 0.160521 20 to 27 2554.48 0.770 0.779467 21 to 28 2522.65 0.320 0.625640 22 to 29 2591.62 1.296 0.902451 23 to 30 2488.81 -0.158 0.437104 24 to 31 2424.99 -1.061 0.144385 25 to 32 2453.01 -0.664 0.253186 CDPARK for dh-ranFile-2015-11-18_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 3502 -0.9589 0.168804 3556 1.5068 0.934075 3494 -1.3242 0.092718 3512 -0.5023 0.307734 3511 -0.5479 0.291865 3544 0.9589 0.831196 3519 -0.1826 0.427537 3539 0.7306 0.767486 3553 1.3699 0.914635 3511 -0.5479 0.291865 Square side=100, avg. no. parked=3524.10 sample std.=20.93 p-value of the KSTEST for those 10 p-values: 0.808082 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-18_22:31 0.4489,0.9827,0.1413,0.5803,0.7287,0.9848,0.3593,0.8295,0.3111,0.5414, The KS test for those 10 p-values: 0.380566 The 3DSPHERES test for dh-ranFile-2015-11-18_22:31 sample no r^3 equiv. uni. 1 36.966 0.708351 2 64.474 0.883416 3 0.594 0.019590 4 8.362 0.243254 5 4.529 0.140114 6 43.228 0.763294 7 4.402 0.136479 8 62.040 0.873563 9 5.798 0.175750 10 25.620 0.574286 11 23.049 0.536206 12 27.429 0.599203 13 0.375 0.012411 14 1.707 0.055324 15 34.865 0.687191 16 0.436 0.014438 17 0.144 0.004786 18 42.660 0.758766 19 45.823 0.782908 20 59.948 0.864432 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.061889 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-18_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.5 -2.0 -0.3 -2.2 -1.4 -1.3 -0.0 -0.9 0.1 1.7 0.1 -1.4 -2.0 -0.3 -0.4 0.4 1.1 0.7 1.1 -0.3 1.1 1.9 0.7 -0.9 -1.3 -2.0 0.5 0.5 -1.6 -0.3 -0.2 0.4 -0.4 0.5 1.9 -0.7 -0.7 0.9 1.0 0.1 0.0 -1.1 Chi-square with 42 degrees of freedom:50.626108 z-score=0.941186, p-value=0.830254 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-18_22:31 Test no p-value 1 0.960027 2 0.125723 3 0.368961 4 0.128639 5 0.463982 6 0.311716 7 0.001478 8 0.073280 9 0.006197 10 0.267204 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.005827 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-18_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 66551 0.20 66903 0.84 3 25000.00 24993 0.00 24755 2.40 4 6666.67 6768 1.54 6706 0.23 5 1388.89 1405 0.19 1353 0.93 6 238.10 248 0.41 251 0.70 7 34.72 31 0.40 27 1.72 8 4.96 3 0.77 4 0.19 p=0.25800 p=0.67915 Number of rngs required: 687542, p-value: 0.159 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-18_22:31 No. of wins: Observed Expected 99106 98585.9 z-score= 2.326, pvalue=0.99000 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66716 66666.7 0.037 0.037 2 37443 37654.3 1.186 1.222 3 27032 26954.7 0.221 1.444 4 19454 19313.5 1.023 2.467 5 13813 13851.4 0.107 2.573 6 9970 9943.5 0.070 2.644 7 7091 7145.0 0.409 3.052 8 5143 5139.1 0.003 3.055 9 3697 3699.9 0.002 3.057 10 2693 2666.3 0.267 3.325 11 1928 1923.3 0.011 3.336 12 1366 1388.7 0.372 3.708 13 975 1003.7 0.822 4.530 14 739 726.1 0.228 4.758 15 552 525.8 1.302 6.060 16 361 381.2 1.065 7.125 17 291 276.5 0.756 7.881 18 186 200.8 1.095 8.976 19 152 146.0 0.248 9.224 20 95 106.2 1.184 10.408 21 303 287.1 0.879 11.287 Chisq= 11.29 for 20 degrees of freedom, p= 0.06157 SUMMARY of craptest p-value for no. of wins: 0.990001 p-value for throws/game: 0.061567 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-18_22:31 No. of wins: Observed Expected 98602 98585.9 z-score= 0.072, pvalue=0.52878 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66413 66666.7 0.965 0.965 2 37608 37654.3 0.057 1.022 3 26941 26954.7 0.007 1.029 4 19526 19313.5 2.339 3.368 5 13704 13851.4 1.569 4.937 6 10079 9943.5 1.845 6.782 7 7184 7145.0 0.213 6.995 8 5156 5139.1 0.056 7.051 9 3758 3699.9 0.913 7.964 10 2675 2666.3 0.028 7.993 11 1897 1923.3 0.360 8.353 12 1418 1388.7 0.616 8.969 13 1015 1003.7 0.127 9.096 14 705 726.1 0.615 9.712 15 537 525.8 0.237 9.949 16 363 381.2 0.864 10.813 17 277 276.5 0.001 10.814 18 190 200.8 0.584 11.398 19 163 146.0 1.983 13.381 20 108 106.2 0.030 13.411 21 283 287.1 0.059 13.470 Chisq= 13.47 for 20 degrees of freedom, p= 0.14369 SUMMARY of craptest p-value for no. of wins: 0.528776 p-value for throws/game: 0.143690 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0048,0.0058,0.0062,0.0106,0.0124,0.0144,0.0187,0.0196,0.0198, 0.0200,0.0248,0.0333,0.0350,0.0510,0.0553,0.0602,0.0616,0.0619,0.0691, 0.0733,0.0803,0.0811,0.0916,0.0927,0.1029,0.1078,0.1153,0.1159,0.1209, 0.1257,0.1286,0.1354,0.1365,0.1399,0.1401,0.1413,0.1437,0.1444,0.1480, 0.1486,0.1592,0.1605,0.1688,0.1736,0.1751,0.1753,0.1757,0.1844,0.1862, 0.1886,0.1887,0.1915,0.2071,0.2088,0.2106,0.2185,0.2293,0.2339,0.2346, 0.2386,0.2410,0.2411,0.2429,0.2433,0.2438,0.2480,0.2503,0.2532,0.2580, 0.2592,0.2647,0.2672,0.2676,0.2822,0.2843,0.2843,0.2864,0.2890,0.2903, 0.2903,0.2919,0.2919,0.2938,0.2977,0.3000,0.3077,0.3111,0.3117,0.3183, 0.3207,0.3270,0.3291,0.3372,0.3379,0.3429,0.3461,0.3505,0.3569,0.3586, 0.3593,0.3673,0.3690,0.3742,0.3777,0.3782,0.3806,0.3856,0.3922,0.3930, 0.3995,0.4028,0.4041,0.4175,0.4210,0.4275,0.4290,0.4349,0.4352,0.4365, 0.4371,0.4375,0.4376,0.4390,0.4433,0.4461,0.4489,0.4510,0.4521,0.4525, 0.4584,0.4601,0.4640,0.4669,0.4748,0.4763,0.4803,0.4895,0.4915,0.4982, 0.5002,0.5131,0.5131,0.5288,0.5362,0.5379,0.5414,0.5450,0.5524,0.5575, 0.5626,0.5629,0.5691,0.5721,0.5743,0.5762,0.5803,0.5804,0.5922,0.5927, 0.5936,0.5960,0.5992,0.6058,0.6077,0.6128,0.6134,0.6188,0.6256,0.6266, 0.6371,0.6435,0.6501,0.6534,0.6547,0.6584,0.6651,0.6674,0.6757,0.6780, 0.6792,0.6854,0.6862,0.6872,0.6927,0.6959,0.6986,0.7009,0.7084,0.7109, 0.7128,0.7145,0.7153,0.7174,0.7206,0.7222,0.7275,0.7287,0.7330,0.7443, 0.7486,0.7550,0.7561,0.7588,0.7588,0.7602,0.7633,0.7675,0.7684,0.7724, 0.7782,0.7795,0.7820,0.7829,0.7858,0.7864,0.7953,0.7982,0.8005,0.8050, 0.8055,0.8081,0.8108,0.8144,0.8210,0.8223,0.8238,0.8255,0.8295,0.8303, 0.8309,0.8312,0.8440,0.8489,0.8495,0.8644,0.8736,0.8807,0.8807,0.8808, 0.8834,0.8899,0.9021,0.9025,0.9081,0.9089,0.9093,0.9144,0.9146,0.9155, 0.9240,0.9341,0.9395,0.9436,0.9440,0.9595,0.9600,0.9603,0.9628,0.9759, 0.9800,0.9824,0.9827,0.9841,0.9848,0.9900,0.9914,0.9994,0.9994, Overall p-value after applying KStest on 269 p-values = 0.945036 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.