RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-22_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 17.5287 0.580863 2 to 25 15.71 15.8460 0.465221 3 to 26 15.37 32.3394 0.986349 4 to 27 15.56 16.0729 0.481325 5 to 28 16.04 16.7411 0.527963 6 to 29 15.82 9.6548 0.082542 7 to 30 15.86 12.4558 0.228213 8 to 31 15.78 23.5803 0.868704 9 to 32 15.39 25.7237 0.920357 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.638368 Tough bday spacings test for dh-ranFile-2016-07-22_05:31: 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 38 68 102 104 83 44 29 12 3 5 (O-E)^2/E 0.9 0.1 0.4 0.2 0.4 0.3 1.3 0.0 0.6 2.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.240, p= 0.205 RESULTS OF GCD FOR dh-ranFile-2016-07-22_05:31 Euclid's algorithm: p-value, steps to gcd: 0.045750 p-value, dist. of gcd's: 0.042442 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-22_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.932 0.115 0.879 0.754 0.930 0.972 0.531 0.657 Bits 8 to 15---> 0.631 0.586 0.527 0.824 0.473 0.124 0.317 0.016 Bits 16 to 23---> 0.633 0.003 0.951 0.451 0.637 0.170 0.317 0.766 Bits 24 to 31---> 0.553 0.258 0.338 0.277 0.120 0.553 0.476 0.238 KS test for the above 32 p values: 0.038 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-22_05:31, p-values for 5 runs: 0.9470, 0.4238, 0.3462, 0.8980, 0.9103 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-22_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5209 5134.0 1.095 1.444 r= 30 23190 23103.0 0.327 1.771 r= 31 11381 11551.5 2.517 4.288 chi-square = 4.288 with df = 3; p-value = 0.768 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-22_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5196 5134.0 0.748 1.383 r= 31 23041 23103.0 0.167 1.550 r= 32 11540 11551.5 0.011 1.561 chi-square = 1.561 with df = 3; p-value = 0.332 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-22_05:31 b-rank test for bits 1 to 8, p=0.94206 b-rank test for bits 2 to 9, p=0.96994 b-rank test for bits 3 to 10, p=0.85293 b-rank test for bits 4 to 11, p=0.62178 b-rank test for bits 5 to 12, p=0.30338 b-rank test for bits 6 to 13, p=0.28416 b-rank test for bits 7 to 14, p=0.43986 b-rank test for bits 8 to 15, p=0.76161 b-rank test for bits 9 to 16, p=0.68777 b-rank test for bits 10 to 17, p=0.84267 b-rank test for bits 11 to 18, p=0.32755 b-rank test for bits 12 to 19, p=0.27632 b-rank test for bits 13 to 20, p=0.29250 b-rank test for bits 14 to 21, p=0.23096 b-rank test for bits 15 to 22, p=0.76807 b-rank test for bits 16 to 23, p=0.76193 b-rank test for bits 17 to 24, p=0.91542 b-rank test for bits 18 to 25, p=0.99642 b-rank test for bits 19 to 26, p=0.55276 b-rank test for bits 20 to 27, p=0.62274 b-rank test for bits 21 to 28, p=0.84800 b-rank test for bits 22 to 29, p=0.93312 b-rank test for bits 23 to 30, p=0.12396 b-rank test for bits 24 to 31, p=0.21532 b-rank test for bits 25 to 32, p=0.16878 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 = 0.140162 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-22_05:31 (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 141365 -1.27 0.101722 2 142552 1.50 0.933395 3 141693 -0.51 0.306624 4 142110 0.47 0.680413 5 141809 -0.23 0.407331 6 141255 -1.53 0.063156 7 141228 -1.59 0.055704 8 141392 -1.21 0.113386 9 141375 -1.25 0.105936 10 141370 -1.26 0.103814 11 141591 -0.74 0.228510 12 142579 1.56 0.941167 13 141672 -0.55 0.289615 14 141493 -0.97 0.165343 15 141844 -0.15 0.439341 16 141724 -0.43 0.332502 17 142122 0.50 0.690368 18 141102 -1.89 0.029628 19 142232 0.75 0.774546 20 142440 1.24 0.892491 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-22_05:31 Bits used No. missing words z-score p-value 23 to 32 141751 -0.5460 0.292545 22 to 31 142124 0.7402 0.770423 21 to 30 141649 -0.8977 0.184676 20 to 29 141683 -0.7804 0.217564 19 to 28 141515 -1.3598 0.086953 18 to 27 141380 -1.8253 0.033980 17 to 26 141714 -0.6736 0.250298 16 to 25 142089 0.6196 0.732224 15 to 24 141901 -0.0287 0.488542 14 to 23 141658 -0.8667 0.193066 13 to 22 142035 0.4333 0.667618 12 to 21 141379 -1.8287 0.033720 11 to 20 142063 0.5299 0.701908 10 to 19 141757 -0.5253 0.299696 9 to 18 141770 -0.4804 0.315454 8 to 17 141497 -1.4218 0.077538 7 to 16 141762 -0.5080 0.305715 6 to 15 141553 -1.2287 0.109588 5 to 14 142112 0.6989 0.757681 4 to 13 141646 -0.9080 0.181930 3 to 12 141339 -1.9667 0.024611 2 to 11 141438 -1.6253 0.052052 1 to 10 142125 0.7437 0.771468 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-22_05:31 Bits used No. missing words z-score p-value 28 to 32 141701 -0.7062 0.240031 27 to 31 141250 -2.2350 0.012708 26 to 30 142026 0.3955 0.653760 25 to 29 141886 -0.0791 0.468483 24 to 28 142306 1.3446 0.910630 23 to 27 141657 -0.8554 0.196177 22 to 26 142420 1.7311 0.958282 21 to 25 141396 -1.7401 0.040921 20 to 24 142242 1.1277 0.870276 19 to 23 141770 -0.4723 0.318355 18 to 22 142166 0.8701 0.807868 17 to 21 141829 -0.2723 0.392694 16 to 20 142065 0.5277 0.701145 15 to 19 141897 -0.0418 0.483330 14 to 18 141728 -0.6147 0.269384 13 to 17 141896 -0.0452 0.481979 12 to 16 141682 -0.7706 0.220469 11 to 15 142061 0.5141 0.696421 10 to 14 141499 -1.3909 0.082120 9 to 13 141559 -1.1876 0.117504 8 to 12 141444 -1.5774 0.057353 7 to 11 141672 -0.8045 0.210552 6 to 10 141590 -1.0825 0.139521 5 to 9 141753 -0.5299 0.298080 4 to 8 141585 -1.0994 0.135792 3 to 7 142124 0.7277 0.766600 2 to 6 141510 -1.3537 0.087922 1 to 5 142277 1.2463 0.893680 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-22_05:31 Bits used No. missing words z-score p-value 31 to 32 141805 -0.3078 0.379133 30 to 31 141605 -0.8977 0.184665 29 to 30 142564 1.9312 0.973270 28 to 29 141377 -1.5703 0.058173 27 to 28 141675 -0.6912 0.244708 26 to 27 142463 1.6332 0.948791 25 to 26 142200 0.8574 0.804397 24 to 25 141846 -0.1868 0.425903 23 to 24 142140 0.6804 0.751888 22 to 23 142180 0.7984 0.787691 21 to 22 141423 -1.4346 0.075700 20 to 21 142061 0.4474 0.672708 19 to 20 141813 -0.2842 0.388144 18 to 19 141854 -0.1632 0.435174 17 to 18 142288 1.1170 0.868007 16 to 17 141875 -0.1013 0.459669 15 to 16 142194 0.8397 0.799471 14 to 15 141374 -1.5791 0.057151 13 to 14 142323 1.2203 0.888818 12 to 13 141184 -2.1396 0.016193 11 to 12 141386 -1.5437 0.061325 10 to 11 141821 -0.2606 0.397216 9 to 10 141092 -2.4110 0.007954 8 to 9 142150 0.7099 0.761130 7 to 8 141506 -1.1898 0.117070 6 to 7 141929 0.0580 0.523135 5 to 6 141462 -1.3196 0.093491 4 to 5 141727 -0.5378 0.295342 3 to 4 142321 1.2144 0.887696 2 to 3 141820 -0.2635 0.396079 1 to 2 142788 2.5919 0.995228 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-22_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2531.51 0.446 0.672079 Test results for specific bytes for dh-ranFile-2016-07-22_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2492.90 -0.100 0.459993 2 to 9 2533.07 0.468 0.679970 3 to 10 2460.17 -0.563 0.286624 4 to 11 2553.89 0.762 0.776989 5 to 12 2455.73 -0.626 0.265629 6 to 13 2525.43 0.360 0.640461 7 to 14 2516.85 0.238 0.594160 8 to 15 2535.08 0.496 0.690080 9 to 16 2472.55 -0.388 0.348950 10 to 17 2524.19 0.342 0.633851 11 to 18 2558.09 0.822 0.794332 12 to 19 2488.51 -0.162 0.435478 13 to 20 2544.82 0.634 0.736909 14 to 21 2471.39 -0.405 0.342892 15 to 22 2470.89 -0.412 0.340275 16 to 23 2632.41 1.872 0.969431 17 to 24 2629.98 1.838 0.966981 18 to 25 2468.27 -0.449 0.326820 19 to 26 2561.36 0.868 0.807226 20 to 27 2617.08 1.656 0.951119 21 to 28 2515.85 0.224 0.588661 22 to 29 2645.56 2.059 0.980230 23 to 30 2466.30 -0.477 0.316834 24 to 31 2502.99 0.042 0.516869 25 to 32 2516.99 0.240 0.594959 CDPARK for dh-ranFile-2016-07-22_05:31: 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 3493 -1.3699 0.085365 3491 -1.4612 0.071982 3511 -0.5479 0.291865 3475 -2.1918 0.014198 3485 -1.7352 0.041356 3510 -0.5936 0.276387 3565 1.9178 0.972432 3544 0.9589 0.831196 3523 0.0000 0.500000 3488 -1.5982 0.055002 Square side=100, avg. no. parked=3508.50 sample std.=27.04 p-value of the KSTEST for those 10 p-values: 0.016046 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-22_05:31 0.7295,0.0536,0.8896,0.1444,0.3250,0.6229,0.6106,0.0900,0.9578,0.6988, The KS test for those 10 p-values: 0.896189 The 3DSPHERES test for dh-ranFile-2016-07-22_05:31 sample no r^3 equiv. uni. 1 44.996 0.776843 2 118.968 0.981043 3 20.847 0.500876 4 11.872 0.326815 5 6.020 0.181817 6 106.922 0.971676 7 57.688 0.853824 8 114.685 0.978135 9 11.689 0.322687 10 55.513 0.842831 11 15.750 0.408442 12 37.145 0.710085 13 37.858 0.716898 14 37.430 0.712822 15 8.302 0.241750 16 20.760 0.499425 17 9.994 0.283335 18 17.222 0.436775 19 4.924 0.151364 20 12.713 0.345428 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.362798 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-22_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 0.3 -0.5 -0.6 -0.2 -1.0 -0.2 -1.5 -1.4 0.3 2.2 -0.9 -0.9 -0.7 -1.8 0.2 0.8 0.2 -0.9 -0.6 0.4 1.2 1.1 1.3 2.3 0.3 0.6 -1.6 0.7 0.2 1.2 -1.0 0.9 0.8 0.2 1.7 -0.1 1.3 -1.3 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:44.115549 z-score=0.230825, p-value=0.617752 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-22_05:31 Test no p-value 1 0.225732 2 0.141992 3 0.015838 4 0.107204 5 0.585024 6 0.606460 7 0.842197 8 0.683990 9 0.181702 10 0.261227 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.210978 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-22_05:31: (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 66497 0.43 66543 0.23 3 25000.00 25118 0.56 25133 0.71 4 6666.67 6681 0.03 6629 0.21 5 1388.89 1411 0.35 1434 1.47 6 238.10 249 0.50 214 2.44 7 34.72 36 0.05 38 0.31 8 4.96 7 0.84 8 1.86 p=0.16136 p=0.69959 Number of rngs required: 689431, p-value: 0.884 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-22_05:31 No. of wins: Observed Expected 98844 98585.9 z-score= 1.155, pvalue=0.87586 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67035 66666.7 2.035 2.035 2 37552 37654.3 0.278 2.313 3 26800 26954.7 0.888 3.201 4 19156 19313.5 1.284 4.485 5 13940 13851.4 0.566 5.052 6 9933 9943.5 0.011 5.063 7 7161 7145.0 0.036 5.098 8 5205 5139.1 0.846 5.944 9 3646 3699.9 0.784 6.728 10 2611 2666.3 1.147 7.875 11 1962 1923.3 0.778 8.653 12 1314 1388.7 4.022 12.675 13 1035 1003.7 0.975 13.650 14 749 726.1 0.720 14.370 15 531 525.8 0.051 14.421 16 364 381.2 0.772 15.192 17 289 276.5 0.561 15.754 18 199 200.8 0.017 15.771 19 154 146.0 0.440 16.211 20 91 106.2 2.180 18.390 21 273 287.1 0.694 19.084 Chisq= 19.08 for 20 degrees of freedom, p= 0.48363 SUMMARY of craptest p-value for no. of wins: 0.875864 p-value for throws/game: 0.483632 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-22_05:31 No. of wins: Observed Expected 98565 98585.9 z-score=-0.093, pvalue=0.46284 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66627 66666.7 0.024 0.024 2 37728 37654.3 0.144 0.168 3 27021 26954.7 0.163 0.331 4 19406 19313.5 0.443 0.774 5 13866 13851.4 0.015 0.789 6 9881 9943.5 0.393 1.183 7 7181 7145.0 0.181 1.364 8 5025 5139.1 2.532 3.896 9 3599 3699.9 2.750 6.646 10 2701 2666.3 0.452 7.097 11 1912 1923.3 0.067 7.164 12 1361 1388.7 0.554 7.718 13 1056 1003.7 2.724 10.442 14 707 726.1 0.505 10.946 15 501 525.8 1.173 12.119 16 361 381.2 1.065 13.185 17 301 276.5 2.164 15.348 18 219 200.8 1.644 16.992 19 171 146.0 4.287 21.279 20 109 106.2 0.073 21.352 21 267 287.1 1.409 22.761 Chisq= 22.76 for 20 degrees of freedom, p= 0.69932 SUMMARY of craptest p-value for no. of wins: 0.462836 p-value for throws/game: 0.699319 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0029,0.0080,0.0127,0.0142,0.0158,0.0160,0.0161,0.0162,0.0246,0.0296, 0.0337,0.0340,0.0375,0.0409,0.0414,0.0424,0.0458,0.0521,0.0536,0.0550, 0.0557,0.0572,0.0574,0.0582,0.0613,0.0632,0.0720,0.0757,0.0775,0.0821, 0.0825,0.0854,0.0870,0.0879,0.0900,0.0935,0.1017,0.1038,0.1059,0.1072, 0.1096,0.1134,0.1147,0.1171,0.1175,0.1201,0.1240,0.1244,0.1358,0.1395, 0.1402,0.1420,0.1444,0.1514,0.1614,0.1653,0.1688,0.1697,0.1817,0.1818, 0.1819,0.1847,0.1847,0.1931,0.1962,0.2053,0.2106,0.2110,0.2153,0.2176, 0.2205,0.2257,0.2282,0.2285,0.2310,0.2376,0.2400,0.2417,0.2447,0.2503, 0.2581,0.2612,0.2656,0.2694,0.2763,0.2764,0.2771,0.2833,0.2842,0.2866, 0.2896,0.2919,0.2925,0.2925,0.2953,0.2981,0.2997,0.3034,0.3057,0.3066, 0.3155,0.3168,0.3173,0.3174,0.3184,0.3227,0.3250,0.3268,0.3268,0.3276, 0.3318,0.3325,0.3378,0.3403,0.3429,0.3454,0.3462,0.3490,0.3628,0.3791, 0.3881,0.3927,0.3961,0.3972,0.4073,0.4084,0.4238,0.4259,0.4352,0.4355, 0.4368,0.4393,0.4399,0.4509,0.4597,0.4600,0.4628,0.4652,0.4685,0.4733, 0.4757,0.4813,0.4820,0.4833,0.4836,0.4885,0.4994,0.5000,0.5009,0.5169, 0.5231,0.5271,0.5280,0.5308,0.5528,0.5530,0.5532,0.5809,0.5850,0.5865, 0.5887,0.5942,0.5950,0.6065,0.6106,0.6178,0.6218,0.6227,0.6229,0.6308, 0.6326,0.6339,0.6371,0.6384,0.6405,0.6538,0.6573,0.6676,0.6721,0.6727, 0.6800,0.6804,0.6840,0.6878,0.6901,0.6904,0.6964,0.6988,0.6993,0.6996, 0.7011,0.7019,0.7101,0.7128,0.7169,0.7295,0.7322,0.7369,0.7519,0.7536, 0.7577,0.7611,0.7616,0.7619,0.7656,0.7666,0.7680,0.7681,0.7704,0.7715, 0.7745,0.7768,0.7770,0.7877,0.7943,0.7995,0.8044,0.8072,0.8079,0.8235, 0.8312,0.8422,0.8427,0.8428,0.8480,0.8529,0.8538,0.8680,0.8687,0.8703, 0.8759,0.8785,0.8839,0.8877,0.8888,0.8896,0.8925,0.8937,0.8962,0.8980, 0.9103,0.9106,0.9154,0.9204,0.9302,0.9316,0.9331,0.9334,0.9412,0.9421, 0.9470,0.9488,0.9506,0.9511,0.9578,0.9583,0.9670,0.9694,0.9699,0.9717, 0.9721,0.9724,0.9733,0.9781,0.9802,0.9810,0.9863,0.9952,0.9964, Overall p-value after applying KStest on 269 p-values = 0.091259 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.