RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-12_17:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 12.2252 0.213687 2 to 25 15.46 25.6365 0.918658 3 to 26 15.64 12.2023 0.212265 4 to 27 16.17 17.0796 0.551015 5 to 28 15.81 21.9159 0.812023 6 to 29 15.86 34.6819 0.993152 7 to 30 16.08 15.2397 0.421780 8 to 31 15.61 28.7934 0.963521 9 to 32 15.94 11.2257 0.155404 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.272899 Tough bday spacings test for dh-ranFile-2018-04-12_17:31: 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 12 35 68 104 90 82 54 33 12 7 3 (O-E)^2/E 0.9 0.1 0.4 0.4 0.6 0.2 0.1 0.4 0.6 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 3.816, p= 0.045 RESULTS OF GCD FOR dh-ranFile-2018-04-12_17:31 Euclid's algorithm: p-value, steps to gcd: 0.065694 p-value, dist. of gcd's: 0.948490 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-12_17:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.413 0.536 0.923 0.933 0.378 0.941 0.039 0.503 Bits 8 to 15---> 0.621 0.439 0.202 0.129 0.268 0.769 0.078 0.223 Bits 16 to 23---> 0.278 0.087 0.835 0.916 0.723 0.664 0.421 0.114 Bits 24 to 31---> 0.409 0.978 0.458 0.744 0.752 0.392 0.637 0.347 KS test for the above 32 p values: 0.014 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-12_17:31, p-values for 5 runs: 0.1456, 0.4557, 0.7494, 0.0623, 0.4020 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-12_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 196 211.4 1.124 1.124 r= 29 5129 5134.0 0.005 1.129 r= 30 23057 23103.0 0.092 1.221 r= 31 11618 11551.5 0.383 1.604 chi-square = 1.604 with df = 3; p-value = 0.341 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-12_17:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5044 5134.0 1.578 1.677 r= 31 23162 23103.0 0.150 1.828 r= 32 11578 11551.5 0.061 1.889 chi-square = 1.889 with df = 3; p-value = 0.404 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-12_17:31 b-rank test for bits 1 to 8, p=0.33050 b-rank test for bits 2 to 9, p=0.56177 b-rank test for bits 3 to 10, p=0.66262 b-rank test for bits 4 to 11, p=0.23678 b-rank test for bits 5 to 12, p=0.04799 b-rank test for bits 6 to 13, p=0.85471 b-rank test for bits 7 to 14, p=0.72710 b-rank test for bits 8 to 15, p=0.49824 b-rank test for bits 9 to 16, p=0.77697 b-rank test for bits 10 to 17, p=0.48973 b-rank test for bits 11 to 18, p=0.56116 b-rank test for bits 12 to 19, p=0.93577 b-rank test for bits 13 to 20, p=0.23344 b-rank test for bits 14 to 21, p=0.14957 b-rank test for bits 15 to 22, p=0.85225 b-rank test for bits 16 to 23, p=0.69277 b-rank test for bits 17 to 24, p=0.71988 b-rank test for bits 18 to 25, p=0.55099 b-rank test for bits 19 to 26, p=0.44523 b-rank test for bits 20 to 27, p=0.53376 b-rank test for bits 21 to 28, p=0.14489 b-rank test for bits 22 to 29, p=0.45647 b-rank test for bits 23 to 30, p=0.00856 b-rank test for bits 24 to 31, p=0.47433 b-rank test for bits 25 to 32, p=0.82069 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 = 0.732343 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-12_17:31 (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 142115 0.48 0.684577 2 141133 -1.81 0.034850 3 141430 -1.12 0.131372 4 142561 1.52 0.936070 5 141806 -0.24 0.404613 6 142151 0.56 0.713844 7 141325 -1.37 0.086086 8 142070 0.38 0.646317 9 142071 0.38 0.647186 10 141362 -1.28 0.100482 11 141845 -0.15 0.440263 12 142133 0.52 0.699371 13 141335 -1.34 0.089815 14 142519 1.42 0.922844 15 141123 -1.84 0.033089 16 141931 0.05 0.520190 17 142040 0.31 0.619933 18 143214 3.05 0.998849 19 141631 -0.65 0.257748 20 141182 -1.70 0.044625 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-12_17:31 Bits used No. missing words z-score p-value 23 to 32 142203 1.0127 0.844388 22 to 31 142031 0.4196 0.662594 21 to 30 142019 0.3782 0.647349 20 to 29 142039 0.4471 0.672612 19 to 28 141481 -1.4770 0.069838 18 to 27 141874 -0.1218 0.451518 17 to 26 141466 -1.5287 0.063166 16 to 25 141829 -0.2770 0.390890 15 to 24 141710 -0.6873 0.245933 14 to 23 142117 0.7161 0.763036 13 to 22 141632 -0.9563 0.169458 12 to 21 141819 -0.3115 0.377717 11 to 20 142045 0.4678 0.680046 10 to 19 141659 -0.8632 0.194012 9 to 18 142234 1.1196 0.868548 8 to 17 141697 -0.7322 0.232032 7 to 16 141273 -2.1942 0.014109 6 to 15 141975 0.2264 0.589574 5 to 14 141912 0.0092 0.503673 4 to 13 141594 -1.0873 0.138442 3 to 12 142327 1.4402 0.925100 2 to 11 141920 0.0368 0.514675 1 to 10 141803 -0.3667 0.356938 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-12_17:31 Bits used No. missing words z-score p-value 28 to 32 142137 0.7718 0.779873 27 to 31 142106 0.6667 0.747511 26 to 30 142031 0.4124 0.659992 25 to 29 142096 0.6328 0.736561 24 to 28 142122 0.7209 0.764519 23 to 27 142073 0.5548 0.710489 22 to 26 141839 -0.2384 0.405783 21 to 25 141762 -0.4994 0.308741 20 to 24 142367 1.5514 0.939600 19 to 23 142394 1.6429 0.949803 18 to 22 142134 0.7616 0.776849 17 to 21 141389 -1.7638 0.038880 16 to 20 141492 -1.4147 0.078581 15 to 19 142050 0.4768 0.683265 14 to 18 141807 -0.3469 0.364340 13 to 17 142175 0.9006 0.816093 12 to 16 141767 -0.4825 0.314734 11 to 15 142139 0.7785 0.781875 10 to 14 141473 -1.4791 0.069559 9 to 13 141685 -0.7604 0.223496 8 to 12 141490 -1.4215 0.077592 7 to 11 141246 -2.2486 0.012270 6 to 10 142056 0.4972 0.690471 5 to 9 142076 0.5650 0.713957 4 to 8 141802 -0.3638 0.357992 3 to 7 141518 -1.3265 0.092330 2 to 6 141729 -0.6113 0.270504 1 to 5 141924 0.0497 0.519831 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-12_17:31 Bits used No. missing words z-score p-value 31 to 32 141865 -0.1308 0.447980 30 to 31 141934 0.0728 0.529007 29 to 30 141758 -0.4464 0.327654 28 to 29 141653 -0.7561 0.224784 27 to 28 141778 -0.3874 0.349229 26 to 27 141841 -0.2016 0.420129 25 to 26 141580 -0.9715 0.165656 24 to 25 142126 0.6391 0.738636 23 to 24 141602 -0.9066 0.182315 22 to 23 142580 1.9784 0.976057 21 to 22 141920 0.0315 0.512555 20 to 21 141786 -0.3638 0.358002 19 to 20 142080 0.5035 0.692677 18 to 19 142159 0.7365 0.769284 17 to 18 142277 1.0846 0.860944 16 to 17 142578 1.9725 0.975722 15 to 16 141694 -0.6352 0.262652 14 to 15 141815 -0.2783 0.390407 13 to 14 142608 2.0610 0.980347 12 to 13 141747 -0.4788 0.316023 11 to 12 141968 0.1731 0.568701 10 to 11 142006 0.2852 0.612240 9 to 10 141778 -0.3874 0.349229 8 to 9 142197 0.8486 0.801944 7 to 8 142046 0.4032 0.656583 6 to 7 142636 2.1436 0.983966 5 to 6 141670 -0.7060 0.240098 4 to 5 141458 -1.3314 0.091536 3 to 4 142055 0.4297 0.666295 2 to 3 141875 -0.1013 0.459669 1 to 2 141782 -0.3756 0.353605 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-12_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2542.82 0.606 0.727581 Test results for specific bytes for dh-ranFile-2018-04-12_17:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2489.92 -0.143 0.443335 2 to 9 2379.59 -1.703 0.044297 3 to 10 2524.39 0.345 0.634915 4 to 11 2485.71 -0.202 0.419934 5 to 12 2601.52 1.436 0.924466 6 to 13 2517.71 0.251 0.598906 7 to 14 2463.82 -0.512 0.304468 8 to 15 2406.35 -1.324 0.092684 9 to 16 2617.95 1.668 0.952355 10 to 17 2530.67 0.434 0.667777 11 to 18 2476.68 -0.330 0.370765 12 to 19 2503.17 0.045 0.517887 13 to 20 2514.90 0.211 0.583464 14 to 21 2534.12 0.482 0.685269 15 to 22 2365.31 -1.905 0.028402 16 to 23 2618.00 1.669 0.952425 17 to 24 2428.80 -1.007 0.156980 18 to 25 2509.74 0.138 0.554806 19 to 26 2396.24 -1.467 0.071132 20 to 27 2414.04 -1.216 0.112061 21 to 28 2430.66 -0.981 0.163399 22 to 29 2413.94 -1.217 0.111786 23 to 30 2437.00 -0.891 0.186491 24 to 31 2531.66 0.448 0.672818 25 to 32 2440.51 -0.841 0.200076 CDPARK for dh-ranFile-2018-04-12_17:31: 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 3541 0.8219 0.794438 3479 -2.0091 0.022262 3519 -0.1826 0.427537 3502 -0.9589 0.168804 3510 -0.5936 0.276387 3544 0.9589 0.831196 3549 1.1872 0.882429 3555 1.4612 0.928018 3529 0.2740 0.607947 3532 0.4110 0.659449 Square side=100, avg. no. parked=3526.00 sample std.=22.48 p-value of the KSTEST for those 10 p-values: 0.789718 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-12_17:31 0.8797,0.8035,0.5041,0.8906,0.0643,0.0434,0.5391,0.7021,0.7112,0.1165, The KS test for those 10 p-values: 0.627506 The 3DSPHERES test for dh-ranFile-2018-04-12_17:31 sample no r^3 equiv. uni. 1 11.604 0.320774 2 46.940 0.790839 3 5.503 0.167603 4 11.527 0.319025 5 6.199 0.186694 6 3.859 0.120715 7 33.431 0.671875 8 2.103 0.067711 9 114.052 0.977668 10 14.717 0.387717 11 36.174 0.700543 12 11.186 0.311248 13 23.067 0.536476 14 43.094 0.762233 15 43.446 0.765005 16 85.368 0.941900 17 22.247 0.523640 18 85.133 0.941444 19 9.531 0.272170 20 52.757 0.827709 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.897606 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-12_17:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 4.3 1.1 -0.5 -0.8 -0.7 0.6 -2.0 0.4 1.2 -0.6 0.5 1.0 1.9 -1.1 1.3 1.6 -0.9 -0.6 -0.9 1.0 -2.2 -0.5 -0.1 -1.7 0.8 -0.8 -1.1 1.1 0.6 -1.0 0.6 -0.2 1.2 0.6 -0.8 2.1 -1.0 0.5 -0.7 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:65.627209 z-score=2.577940, p-value=0.988677 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-12_17:31 Test no p-value 1 0.375038 2 0.675475 3 0.133058 4 0.433155 5 0.896461 6 0.627354 7 0.123420 8 0.207481 9 0.259006 10 0.157745 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.329167 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-12_17:31: (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 66844 0.47 66717 0.04 3 25000.00 24780 1.94 24932 0.18 4 6666.67 6713 0.32 6695 0.12 5 1388.89 1358 0.69 1384 0.02 6 238.10 262 2.40 234 0.07 7 34.72 34 0.01 32 0.21 8 4.96 8 1.86 5 0.00 p=0.73868 p=0.00439 Number of rngs required: 688148, p-value: 0.385 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-12_17:31 No. of wins: Observed Expected 98548 98585.9 z-score=-0.169, pvalue=0.43277 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67005 66666.7 1.717 1.717 2 37554 37654.3 0.267 1.984 3 26994 26954.7 0.057 2.042 4 19103 19313.5 2.293 4.335 5 13865 13851.4 0.013 4.348 6 9929 9943.5 0.021 4.370 7 7093 7145.0 0.379 4.748 8 5108 5139.1 0.188 4.936 9 3772 3699.9 1.406 6.343 10 2678 2666.3 0.051 6.394 11 1872 1923.3 1.370 7.764 12 1393 1388.7 0.013 7.777 13 990 1003.7 0.187 7.964 14 749 726.1 0.720 8.684 15 551 525.8 1.204 9.888 16 361 381.2 1.065 10.954 17 264 276.5 0.569 11.522 18 199 200.8 0.017 11.539 19 140 146.0 0.245 11.784 20 112 106.2 0.315 12.099 21 268 287.1 1.272 13.372 Chisq= 13.37 for 20 degrees of freedom, p= 0.13912 SUMMARY of craptest p-value for no. of wins: 0.432770 p-value for throws/game: 0.139124 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-12_17:31 No. of wins: Observed Expected 98896 98585.9 z-score= 1.387, pvalue=0.91730 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66341 66666.7 1.591 1.591 2 37793 37654.3 0.511 2.102 3 27192 26954.7 2.089 4.190 4 19183 19313.5 0.881 5.071 5 13865 13851.4 0.013 5.085 6 10029 9943.5 0.734 5.819 7 7160 7145.0 0.031 5.851 8 5078 5139.1 0.726 6.576 9 3740 3699.9 0.435 7.012 10 2657 2666.3 0.032 7.044 11 2002 1923.3 3.218 10.262 12 1433 1388.7 1.411 11.673 13 965 1003.7 1.493 13.166 14 682 726.1 2.683 15.849 15 541 525.8 0.437 16.286 16 348 381.2 2.883 19.170 17 254 276.5 1.837 21.007 18 213 200.8 0.737 21.744 19 138 146.0 0.437 22.181 20 113 106.2 0.433 22.614 21 273 287.1 0.694 23.308 Chisq= 23.31 for 20 degrees of freedom, p= 0.72609 SUMMARY of craptest p-value for no. of wins: 0.917299 p-value for throws/game: 0.726085 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0044,0.0086,0.0123,0.0141,0.0142,0.0223,0.0284,0.0331,0.0349,0.0389, 0.0389,0.0434,0.0443,0.0446,0.0448,0.0480,0.0623,0.0632,0.0643,0.0657, 0.0677,0.0696,0.0698,0.0711,0.0776,0.0777,0.0786,0.0861,0.0873,0.0898, 0.0915,0.0923,0.0927,0.1005,0.1118,0.1121,0.1139,0.1165,0.1207,0.1234, 0.1293,0.1314,0.1331,0.1384,0.1391,0.1449,0.1456,0.1496,0.1554,0.1570, 0.1577,0.1634,0.1657,0.1676,0.1688,0.1695,0.1823,0.1865,0.1867,0.1940, 0.2001,0.2021,0.2075,0.2123,0.2137,0.2232,0.2235,0.2248,0.2320,0.2334, 0.2368,0.2401,0.2459,0.2577,0.2590,0.2627,0.2678,0.2705,0.2722,0.2729, 0.2764,0.2782,0.3045,0.3087,0.3112,0.3147,0.3160,0.3190,0.3208,0.3277, 0.3292,0.3305,0.3414,0.3471,0.3492,0.3492,0.3536,0.3569,0.3580,0.3580, 0.3643,0.3708,0.3750,0.3777,0.3782,0.3846,0.3877,0.3904,0.3909,0.3921, 0.4020,0.4041,0.4046,0.4058,0.4088,0.4132,0.4199,0.4201,0.4211,0.4218, 0.4275,0.4328,0.4332,0.4389,0.4403,0.4433,0.4452,0.4480,0.4515,0.4557, 0.4565,0.4584,0.4597,0.4743,0.4897,0.4982,0.5034,0.5037,0.5041,0.5126, 0.5147,0.5179,0.5198,0.5202,0.5236,0.5290,0.5338,0.5356,0.5365,0.5391, 0.5510,0.5510,0.5548,0.5612,0.5618,0.5687,0.5835,0.5896,0.5989,0.6079, 0.6122,0.6199,0.6209,0.6274,0.6275,0.6349,0.6370,0.6463,0.6472,0.6473, 0.6566,0.6594,0.6600,0.6626,0.6626,0.6641,0.6663,0.6678,0.6719,0.6726, 0.6728,0.6755,0.6800,0.6833,0.6846,0.6853,0.6905,0.6927,0.6928,0.6994, 0.7005,0.7021,0.7105,0.7112,0.7138,0.7140,0.7199,0.7226,0.7261,0.7271, 0.7276,0.7323,0.7366,0.7386,0.7387,0.7440,0.7475,0.7494,0.7519,0.7622, 0.7630,0.7645,0.7650,0.7688,0.7693,0.7768,0.7770,0.7799,0.7819,0.7897, 0.7908,0.7944,0.8019,0.8035,0.8120,0.8161,0.8207,0.8277,0.8312,0.8352, 0.8444,0.8523,0.8547,0.8609,0.8685,0.8797,0.8824,0.8906,0.8965,0.8976, 0.9160,0.9173,0.9187,0.9228,0.9230,0.9245,0.9251,0.9280,0.9330,0.9358, 0.9361,0.9396,0.9406,0.9414,0.9419,0.9485,0.9498,0.9524,0.9524,0.9635, 0.9757,0.9761,0.9777,0.9778,0.9803,0.9840,0.9887,0.9932,0.9988, Overall p-value after applying KStest on 269 p-values = 0.739597 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.