RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-13_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.66 17.3816 0.571184 2 to 25 16.10 16.5384 0.513962 3 to 26 15.86 23.3058 0.860442 4 to 27 15.57 16.9799 0.544274 5 to 28 15.84 6.5667 0.011504 6 to 29 15.63 16.6928 0.524638 7 to 30 15.47 32.1228 0.985472 8 to 31 15.73 18.6642 0.651854 9 to 32 15.56 22.3213 0.827324 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.262460 Tough bday spacings test for dh-ranFile-2018-04-13_14:31: 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 44 78 108 95 61 46 25 18 9 6 (O-E)^2/E 0.1 1.5 0.3 1.1 0.1 3.8 0.7 0.8 0.7 0.9 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.701, p= 0.619 RESULTS OF GCD FOR dh-ranFile-2018-04-13_14:31 Euclid's algorithm: p-value, steps to gcd: 0.125446 p-value, dist. of gcd's: 0.837623 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-13_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.960 0.737 0.163 0.375 0.744 0.579 0.737 0.373 Bits 8 to 15---> 0.888 0.333 0.729 0.010 0.326 0.426 0.833 0.146 Bits 16 to 23---> 0.899 0.071 0.589 0.546 0.576 0.907 0.197 0.794 Bits 24 to 31---> 0.115 0.842 0.623 0.633 0.687 0.570 0.163 0.399 KS test for the above 32 p values: 0.214 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-13_14:31, p-values for 5 runs: 0.5637, 0.2240, 0.2430, 0.4944, 0.0136 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-13_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 200 211.4 0.617 0.617 r= 29 5131 5134.0 0.002 0.618 r= 30 23060 23103.0 0.080 0.699 r= 31 11609 11551.5 0.286 0.985 chi-square = 0.985 with df = 3; p-value = 0.195 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-13_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 232 211.4 2.004 2.004 r= 30 5048 5134.0 1.441 3.445 r= 31 23140 23103.0 0.059 3.504 r= 32 11580 11551.5 0.070 3.574 chi-square = 3.574 with df = 3; p-value = 0.689 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-13_14:31 b-rank test for bits 1 to 8, p=0.01643 b-rank test for bits 2 to 9, p=0.46540 b-rank test for bits 3 to 10, p=0.54976 b-rank test for bits 4 to 11, p=0.39429 b-rank test for bits 5 to 12, p=0.58281 b-rank test for bits 6 to 13, p=0.65089 b-rank test for bits 7 to 14, p=0.18586 b-rank test for bits 8 to 15, p=0.09272 b-rank test for bits 9 to 16, p=0.82575 b-rank test for bits 10 to 17, p=0.44564 b-rank test for bits 11 to 18, p=0.58483 b-rank test for bits 12 to 19, p=0.67594 b-rank test for bits 13 to 20, p=0.92550 b-rank test for bits 14 to 21, p=0.02590 b-rank test for bits 15 to 22, p=0.49072 b-rank test for bits 16 to 23, p=0.72310 b-rank test for bits 17 to 24, p=0.24775 b-rank test for bits 18 to 25, p=0.05667 b-rank test for bits 19 to 26, p=0.56231 b-rank test for bits 20 to 27, p=0.92872 b-rank test for bits 21 to 28, p=0.84698 b-rank test for bits 22 to 29, p=0.48996 b-rank test for bits 23 to 30, p=0.10433 b-rank test for bits 24 to 31, p=0.44488 b-rank test for bits 25 to 32, p=0.99866 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 = 0.788624 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-13_14:31 (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 141757 -0.36 0.360954 2 141410 -1.17 0.121674 3 141865 -0.10 0.458753 4 142477 1.33 0.907635 5 142351 1.03 0.848950 6 142350 1.03 0.848402 7 141480 -1.00 0.157905 8 142078 0.39 0.653242 9 142442 1.24 0.893353 10 141853 -0.13 0.447646 11 142433 1.22 0.889435 12 141665 -0.57 0.284046 13 142009 0.23 0.592070 14 142202 0.68 0.752952 15 142663 1.76 0.960873 16 141345 -1.32 0.093663 17 142075 0.39 0.650651 18 142149 0.56 0.712252 19 142868 2.24 0.987451 20 142158 0.58 0.719381 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-13_14:31 Bits used No. missing words z-score p-value 23 to 32 141593 -1.0908 0.137682 22 to 31 141579 -1.1391 0.127337 21 to 30 141938 0.0989 0.539376 20 to 29 141414 -1.7080 0.043815 19 to 28 142038 0.4437 0.671367 18 to 27 141947 0.1299 0.551676 17 to 26 141916 0.0230 0.509175 16 to 25 142147 0.8196 0.793764 15 to 24 142053 0.4954 0.689846 14 to 23 141862 -0.1632 0.435178 13 to 22 141708 -0.6942 0.243765 12 to 21 142302 1.3540 0.912137 11 to 20 142002 0.3196 0.625346 10 to 19 142411 1.7299 0.958176 9 to 18 141813 -0.3322 0.369880 8 to 17 141392 -1.7839 0.037220 7 to 16 141942 0.1127 0.544848 6 to 15 142063 0.5299 0.701908 5 to 14 141635 -0.9460 0.172083 4 to 13 141799 -0.3804 0.351806 3 to 12 142114 0.7058 0.759831 2 to 11 141891 -0.0632 0.474801 1 to 10 141610 -1.0322 0.150996 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-13_14:31 Bits used No. missing words z-score p-value 28 to 32 142506 2.0226 0.978443 27 to 31 142555 2.1887 0.985691 26 to 30 141609 -1.0181 0.154323 25 to 29 141897 -0.0418 0.483330 24 to 28 141472 -1.4825 0.069107 23 to 27 142410 1.6972 0.955169 22 to 26 142218 1.0463 0.852298 21 to 25 141675 -0.7943 0.213499 20 to 24 141695 -0.7265 0.233753 19 to 23 141269 -2.1706 0.014980 18 to 22 142011 0.3446 0.634819 17 to 21 142089 0.6091 0.728755 16 to 20 142011 0.3446 0.634819 15 to 19 141682 -0.7706 0.220469 14 to 18 142368 1.5548 0.940005 13 to 17 141933 0.0802 0.531976 12 to 16 141767 -0.4825 0.314734 11 to 15 141559 -1.1876 0.117504 10 to 14 142047 0.4667 0.679635 9 to 13 142316 1.3785 0.915982 8 to 12 142235 1.1040 0.865196 7 to 11 141453 -1.5469 0.060946 6 to 10 141702 -0.7028 0.241086 5 to 9 141884 -0.0859 0.465787 4 to 8 141454 -1.5435 0.061356 3 to 7 142004 0.3209 0.625863 2 to 6 141964 0.1853 0.573512 1 to 5 142137 0.7718 0.779873 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-13_14:31 Bits used No. missing words z-score p-value 31 to 32 141843 -0.1957 0.422437 30 to 31 142247 0.9961 0.840394 29 to 30 141356 -1.6322 0.051314 28 to 29 142140 0.6804 0.751888 27 to 28 142417 1.4976 0.932875 26 to 27 141635 -0.8092 0.209191 25 to 26 142060 0.4445 0.671643 24 to 25 142076 0.4917 0.688517 23 to 24 141878 -0.0924 0.463183 22 to 23 141887 -0.0659 0.473741 21 to 22 141840 -0.2045 0.418976 20 to 21 142128 0.6450 0.740551 19 to 20 141600 -0.9125 0.180759 18 to 19 141958 0.1436 0.557080 17 to 18 142242 0.9813 0.836784 16 to 17 141927 0.0521 0.520785 15 to 16 141808 -0.2989 0.382505 14 to 15 141981 0.2114 0.583719 13 to 14 141984 0.2203 0.587168 12 to 13 142107 0.5831 0.720086 11 to 12 141226 -2.0157 0.021914 10 to 11 142159 0.7365 0.769284 9 to 10 141450 -1.3550 0.087716 8 to 9 141262 -1.9095 0.028097 7 to 8 141883 -0.0777 0.469045 6 to 7 141478 -1.2724 0.101623 5 to 6 141951 0.1229 0.548915 4 to 5 142168 0.7630 0.777280 3 to 4 142249 1.0020 0.841823 2 to 3 141686 -0.6588 0.255015 1 to 2 142070 0.4740 0.682233 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-13_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2496.45 -0.050 0.479999 Test results for specific bytes for dh-ranFile-2018-04-13_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2484.25 -0.223 0.411860 2 to 9 2480.67 -0.273 0.392286 3 to 10 2615.61 1.635 0.948978 4 to 11 2518.56 0.263 0.603538 5 to 12 2478.90 -0.298 0.382725 6 to 13 2415.72 -1.192 0.116647 7 to 14 2462.16 -0.535 0.296255 8 to 15 2560.64 0.858 0.804439 9 to 16 2486.79 -0.187 0.425893 10 to 17 2434.79 -0.922 0.178222 11 to 18 2544.32 0.627 0.734579 12 to 19 2486.27 -0.194 0.423000 13 to 20 2536.31 0.513 0.696185 14 to 21 2374.82 -1.770 0.038339 15 to 22 2529.71 0.420 0.662832 16 to 23 2372.55 -1.802 0.035741 17 to 24 2456.71 -0.612 0.270179 18 to 25 2611.43 1.576 0.942472 19 to 26 2492.73 -0.103 0.459053 20 to 27 2539.93 0.565 0.713864 21 to 28 2455.40 -0.631 0.264085 22 to 29 2639.15 1.968 0.975462 23 to 30 2581.40 1.151 0.875163 24 to 31 2423.69 -1.079 0.140265 25 to 32 2490.00 -0.141 0.443788 CDPARK for dh-ranFile-2018-04-13_14:31: 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 3551 1.2785 0.899470 3512 -0.5023 0.307734 3565 1.9178 0.972432 3546 1.0502 0.853193 3516 -0.3196 0.374623 3525 0.0913 0.536383 3512 -0.5023 0.307734 3519 -0.1826 0.427537 3508 -0.6849 0.246694 3550 1.2329 0.891189 Square side=100, avg. no. parked=3530.40 sample std.=19.48 p-value of the KSTEST for those 10 p-values: 0.376852 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-13_14:31 0.7154,0.1831,0.3806,0.5037,0.8854,0.5354,0.7371,0.1430,0.5310,0.4880, The KS test for those 10 p-values: 0.719210 The 3DSPHERES test for dh-ranFile-2018-04-13_14:31 sample no r^3 equiv. uni. 1 39.784 0.734495 2 26.730 0.589758 3 2.133 0.068630 4 11.692 0.322770 5 22.350 0.525263 6 55.999 0.845357 7 2.891 0.091874 8 4.117 0.128220 9 80.484 0.931628 10 11.178 0.311058 11 2.125 0.068393 12 40.243 0.738530 13 0.803 0.026428 14 77.622 0.924785 15 58.574 0.858077 16 5.506 0.167663 17 94.115 0.956595 18 50.043 0.811398 19 10.961 0.306056 20 26.287 0.583648 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.657223 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-13_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 -0.6 -1.0 0.9 -0.4 -0.6 -0.4 0.2 0.2 -0.7 0.2 1.5 -1.2 -0.2 -0.3 -1.2 1.7 -0.4 0.6 -0.3 0.9 -1.1 0.3 0.9 0.6 -1.3 -1.5 1.1 0.9 -1.8 1.0 0.8 0.9 0.8 -1.0 0.5 0.8 -0.8 -1.3 2.4 0.0 0.8 Chi-square with 42 degrees of freedom:39.258040 z-score=-0.299172, p-value=0.407989 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-13_14:31 Test no p-value 1 0.367750 2 0.835097 3 0.318808 4 0.441707 5 0.403486 6 0.337950 7 0.988406 8 0.088400 9 0.015220 10 0.307196 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.313516 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-13_14:31: (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 66542 0.23 66552 0.20 3 25000.00 25140 0.78 24978 0.02 4 6666.67 6632 0.18 6859 5.55 5 1388.89 1383 0.02 1348 1.20 6 238.10 258 1.66 223 0.96 7 34.72 39 0.53 36 0.05 8 4.96 5 0.00 3 0.77 p=0.24468 p=0.81173 Number of rngs required: 689894, p-value: 0.960 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-13_14:31 No. of wins: Observed Expected 98561 98585.9 z-score=-0.111, pvalue=0.45574 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66536 66666.7 0.256 0.256 2 37793 37654.3 0.511 0.767 3 27212 26954.7 2.455 3.222 4 19302 19313.5 0.007 3.229 5 13676 13851.4 2.222 5.451 6 9960 9943.5 0.027 5.478 7 7097 7145.0 0.323 5.801 8 5111 5139.1 0.153 5.954 9 3690 3699.9 0.026 5.980 10 2633 2666.3 0.416 6.396 11 1997 1923.3 2.822 9.218 12 1341 1388.7 1.641 10.859 13 961 1003.7 1.818 12.677 14 771 726.1 2.771 15.448 15 518 525.8 0.117 15.565 16 380 381.2 0.003 15.569 17 292 276.5 0.864 16.433 18 173 200.8 3.857 20.290 19 166 146.0 2.744 23.034 20 87 106.2 3.476 26.510 21 304 287.1 0.993 27.503 Chisq= 27.50 for 20 degrees of freedom, p= 0.87831 SUMMARY of craptest p-value for no. of wins: 0.455736 p-value for throws/game: 0.878307 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-13_14:31 No. of wins: Observed Expected 98660 98585.9 z-score= 0.332, pvalue=0.62991 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66555 66666.7 0.187 0.187 2 37667 37654.3 0.004 0.191 3 26999 26954.7 0.073 0.264 4 19192 19313.5 0.764 1.028 5 13886 13851.4 0.086 1.114 6 10039 9943.5 0.916 2.031 7 7130 7145.0 0.032 2.062 8 5116 5139.1 0.104 2.166 9 3814 3699.9 3.521 5.687 10 2728 2666.3 1.428 7.115 11 1880 1923.3 0.976 8.091 12 1317 1388.7 3.706 11.797 13 1018 1003.7 0.203 12.000 14 692 726.1 1.605 13.605 15 531 525.8 0.051 13.656 16 350 381.2 2.546 16.202 17 305 276.5 2.929 19.131 18 228 200.8 3.676 22.807 19 147 146.0 0.007 22.814 20 92 106.2 1.902 24.716 21 314 287.1 2.518 27.234 Chisq= 27.23 for 20 degrees of freedom, p= 0.87119 SUMMARY of craptest p-value for no. of wins: 0.629906 p-value for throws/game: 0.871188 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0101,0.0115,0.0136,0.0150,0.0152,0.0164,0.0219,0.0259,0.0264,0.0281, 0.0357,0.0372,0.0383,0.0438,0.0513,0.0567,0.0609,0.0614,0.0684,0.0686, 0.0691,0.0707,0.0877,0.0884,0.0919,0.0927,0.0937,0.1016,0.1043,0.1154, 0.1166,0.1175,0.1217,0.1254,0.1273,0.1282,0.1377,0.1403,0.1430,0.1459, 0.1510,0.1543,0.1579,0.1629,0.1631,0.1677,0.1721,0.1782,0.1808,0.1831, 0.1859,0.1950,0.1973,0.2092,0.2135,0.2144,0.2205,0.2240,0.2338,0.2411, 0.2430,0.2438,0.2447,0.2467,0.2477,0.2550,0.2625,0.2641,0.2702,0.2840, 0.2963,0.3061,0.3072,0.3077,0.3077,0.3111,0.3135,0.3147,0.3188,0.3228, 0.3261,0.3331,0.3379,0.3518,0.3610,0.3677,0.3699,0.3729,0.3746,0.3754, 0.3769,0.3806,0.3825,0.3827,0.3923,0.3943,0.3992,0.4035,0.4080,0.4119, 0.4190,0.4224,0.4230,0.4256,0.4259,0.4275,0.4352,0.4417,0.4438,0.4449, 0.4456,0.4476,0.4557,0.4588,0.4591,0.4632,0.4654,0.4658,0.4690,0.4737, 0.4748,0.4800,0.4833,0.4880,0.4900,0.4907,0.4944,0.5037,0.5092,0.5140, 0.5208,0.5246,0.5253,0.5310,0.5320,0.5354,0.5364,0.5394,0.5443,0.5448, 0.5463,0.5489,0.5498,0.5517,0.5571,0.5623,0.5637,0.5701,0.5712,0.5735, 0.5756,0.5786,0.5828,0.5836,0.5837,0.5848,0.5872,0.5888,0.5898,0.5921, 0.6035,0.6187,0.6227,0.6253,0.6259,0.6299,0.6333,0.6348,0.6348,0.6507, 0.6509,0.6519,0.6532,0.6572,0.6628,0.6714,0.6716,0.6759,0.6796,0.6822, 0.6874,0.6885,0.6887,0.6898,0.6962,0.7019,0.7123,0.7139,0.7154,0.7192, 0.7194,0.7201,0.7231,0.7288,0.7288,0.7345,0.7346,0.7371,0.7372,0.7374, 0.7385,0.7406,0.7443,0.7519,0.7530,0.7598,0.7693,0.7773,0.7799,0.7886, 0.7938,0.7940,0.8044,0.8114,0.8117,0.8258,0.8273,0.8326,0.8351,0.8368, 0.8376,0.8404,0.8416,0.8418,0.8454,0.8470,0.8484,0.8489,0.8523,0.8532, 0.8581,0.8604,0.8652,0.8712,0.8752,0.8783,0.8854,0.8883,0.8894,0.8912, 0.8934,0.8985,0.8995,0.9066,0.9076,0.9121,0.9160,0.9248,0.9255,0.9287, 0.9316,0.9329,0.9400,0.9425,0.9490,0.9552,0.9566,0.9582,0.9600,0.9604, 0.9609,0.9724,0.9755,0.9784,0.9855,0.9857,0.9875,0.9884,0.9987, Overall p-value after applying KStest on 269 p-values = 0.716582 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.