RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-26_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 23.9770 0.879938 2 to 25 15.66 31.1058 0.980612 3 to 26 15.83 15.8196 0.463345 4 to 27 15.68 14.6138 0.376723 5 to 28 15.65 20.1474 0.733243 6 to 29 15.70 16.3858 0.503329 7 to 30 15.93 18.3976 0.635819 8 to 31 15.80 13.4404 0.293759 9 to 32 15.78 9.3374 0.070920 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.932132 Tough bday spacings test for dh-ranFile-2018-03-26_06:31: 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 16 41 69 105 88 80 44 29 18 3 7 (O-E)^2/E 5.1 0.5 0.2 0.5 1.0 0.0 1.3 0.0 0.7 2.0 2.1 Birthday Spacings: Sum(O-E)^2/E= 13.456, p= 0.801 RESULTS OF GCD FOR dh-ranFile-2018-03-26_06:31 Euclid's algorithm: p-value, steps to gcd: 0.076148 p-value, dist. of gcd's: 0.432756 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-26_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.636 0.800 0.475 0.256 0.246 0.405 0.512 0.571 Bits 8 to 15---> 0.445 0.785 0.064 0.104 0.721 0.464 0.070 0.105 Bits 16 to 23---> 0.596 0.329 0.849 0.506 0.905 0.794 0.808 0.693 Bits 24 to 31---> 0.836 0.525 0.730 0.484 0.798 0.408 0.865 0.768 KS test for the above 32 p values: 0.757 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-26_06:31, p-values for 5 runs: 0.1782, 0.2864, 0.3057, 0.5016, 0.3906 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-26_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 210 211.4 0.010 0.010 r= 29 5095 5134.0 0.296 0.306 r= 30 23081 23103.0 0.021 0.327 r= 31 11614 11551.5 0.338 0.665 chi-square = 0.665 with df = 3; p-value = 0.119 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-26_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 239 211.4 3.598 3.598 r= 30 5107 5134.0 0.142 3.741 r= 31 23261 23103.0 1.080 4.820 r= 32 11393 11551.5 2.175 6.996 chi-square = 6.996 with df = 3; p-value = 0.928 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-26_06:31 b-rank test for bits 1 to 8, p=0.75427 b-rank test for bits 2 to 9, p=0.94550 b-rank test for bits 3 to 10, p=0.81577 b-rank test for bits 4 to 11, p=0.23067 b-rank test for bits 5 to 12, p=0.47063 b-rank test for bits 6 to 13, p=0.40227 b-rank test for bits 7 to 14, p=0.65899 b-rank test for bits 8 to 15, p=0.96559 b-rank test for bits 9 to 16, p=0.66899 b-rank test for bits 10 to 17, p=0.73346 b-rank test for bits 11 to 18, p=0.78761 b-rank test for bits 12 to 19, p=0.96901 b-rank test for bits 13 to 20, p=0.03976 b-rank test for bits 14 to 21, p=0.40526 b-rank test for bits 15 to 22, p=0.29091 b-rank test for bits 16 to 23, p=0.79568 b-rank test for bits 17 to 24, p=0.70074 b-rank test for bits 18 to 25, p=0.13525 b-rank test for bits 19 to 26, p=0.19313 b-rank test for bits 20 to 27, p=0.70716 b-rank test for bits 21 to 28, p=0.55040 b-rank test for bits 22 to 29, p=0.03543 b-rank test for bits 23 to 30, p=0.68981 b-rank test for bits 24 to 31, p=0.66635 b-rank test for bits 25 to 32, p=0.99477 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 = 0.181998 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-26_06:31 (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 141935 0.06 0.523913 2 141917 0.02 0.507149 3 141476 -1.01 0.155661 4 141115 -1.86 0.031733 5 142764 2.00 0.977082 6 142351 1.03 0.848950 7 142337 1.00 0.841158 8 140857 -2.46 0.006972 9 142066 0.37 0.642837 10 142783 2.04 0.979389 11 141596 -0.73 0.232060 12 141641 -0.63 0.265350 13 142306 0.93 0.822985 14 141386 -1.22 0.110715 15 141884 -0.06 0.476404 16 141627 -0.66 0.254739 17 141577 -0.78 0.218735 18 141781 -0.30 0.382151 19 142491 1.36 0.912933 20 142588 1.59 0.943594 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-26_06:31 Bits used No. missing words z-score p-value 23 to 32 141655 -0.8770 0.190243 22 to 31 141904 -0.0184 0.492668 21 to 30 142007 0.3368 0.631864 20 to 29 141719 -0.6563 0.255812 19 to 28 142300 1.3471 0.911032 18 to 27 141928 0.0644 0.525666 17 to 26 142232 1.1127 0.867072 16 to 25 141981 0.2471 0.597599 15 to 24 142032 0.4230 0.663852 14 to 23 141777 -0.4563 0.324083 13 to 22 142219 1.0678 0.857201 12 to 21 141772 -0.4736 0.317910 11 to 20 142336 1.4713 0.929392 10 to 19 142105 0.6747 0.750075 9 to 18 141819 -0.3115 0.377717 8 to 17 141748 -0.5563 0.288999 7 to 16 141931 0.0747 0.529783 6 to 15 141785 -0.4287 0.334062 5 to 14 141720 -0.6529 0.256923 4 to 13 141877 -0.1115 0.455617 3 to 12 141838 -0.2460 0.402855 2 to 11 141782 -0.4391 0.330306 1 to 10 142451 1.8678 0.969107 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-26_06:31 Bits used No. missing words z-score p-value 28 to 32 142072 0.5514 0.709328 27 to 31 141903 -0.0215 0.491440 26 to 30 141366 -1.8418 0.032752 25 to 29 142190 0.9514 0.829305 24 to 28 141899 -0.0350 0.486033 23 to 27 141227 -2.3130 0.010362 22 to 26 141948 0.1311 0.552146 21 to 25 142248 1.1480 0.874523 20 to 24 141883 -0.0893 0.464440 19 to 23 141504 -1.3740 0.084721 18 to 22 142023 0.3853 0.650001 17 to 21 142409 1.6938 0.954848 16 to 20 141911 0.0057 0.502258 15 to 19 141559 -1.1876 0.117504 14 to 18 142005 0.3243 0.627147 13 to 17 141882 -0.0926 0.463093 12 to 16 141982 0.2463 0.597290 11 to 15 141672 -0.8045 0.210552 10 to 14 141568 -1.1571 0.123626 9 to 13 142330 1.4260 0.923066 8 to 12 141303 -2.0554 0.019922 7 to 11 142314 1.3718 0.914931 6 to 10 142116 0.7006 0.758216 5 to 9 141743 -0.5638 0.286435 4 to 8 141655 -0.8621 0.194306 3 to 7 141847 -0.2113 0.416331 2 to 6 142021 0.3785 0.647486 1 to 5 141908 -0.0045 0.498201 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-26_06:31 Bits used No. missing words z-score p-value 31 to 32 142082 0.5094 0.694747 30 to 31 141859 -0.1485 0.440988 29 to 30 142314 1.1937 0.883706 28 to 29 141631 -0.8210 0.205814 27 to 28 142398 1.4415 0.925279 26 to 27 141842 -0.1986 0.421283 25 to 26 141618 -0.8594 0.195065 24 to 25 142174 0.7807 0.782522 23 to 24 142126 0.6391 0.738636 22 to 23 142134 0.6627 0.746253 21 to 22 142525 1.8161 0.965325 20 to 21 142144 0.6922 0.755607 19 to 20 141668 -0.7119 0.238267 18 to 19 142022 0.3324 0.630191 17 to 18 141579 -0.9744 0.164923 16 to 17 142042 0.3914 0.652233 15 to 16 141325 -1.7237 0.042382 14 to 15 141603 -0.9036 0.183096 13 to 14 141451 -1.3520 0.088187 12 to 13 142111 0.5949 0.724044 11 to 12 141809 -0.2960 0.383631 10 to 11 141736 -0.5113 0.304571 9 to 10 141879 -0.0895 0.464355 8 to 9 142161 0.7424 0.771074 7 to 8 141651 -0.7620 0.223019 6 to 7 141693 -0.6381 0.261691 5 to 6 141516 -1.1603 0.122970 4 to 5 141618 -0.8594 0.195065 3 to 4 142007 0.2881 0.613370 2 to 3 141617 -0.8623 0.194253 1 to 2 141861 -0.1426 0.443316 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-26_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2559.28 0.838 0.799097 Test results for specific bytes for dh-ranFile-2018-03-26_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2532.08 0.454 0.674949 2 to 9 2295.33 -2.894 0.001899 3 to 10 2532.20 0.455 0.675557 4 to 11 2468.02 -0.452 0.325560 5 to 12 2410.06 -1.272 0.101693 6 to 13 2483.75 -0.230 0.409142 7 to 14 2420.07 -1.130 0.129173 8 to 15 2430.11 -0.988 0.161488 9 to 16 2429.07 -1.003 0.157908 10 to 17 2418.97 -1.146 0.125913 11 to 18 2490.31 -0.137 0.445505 12 to 19 2584.86 1.200 0.884948 13 to 20 2506.16 0.087 0.534735 14 to 21 2440.86 -0.836 0.201492 15 to 22 2480.77 -0.272 0.392835 16 to 23 2350.01 -2.121 0.016956 17 to 24 2434.49 -0.926 0.177109 18 to 25 2492.11 -0.112 0.455567 19 to 26 2423.25 -1.085 0.138875 20 to 27 2502.82 0.040 0.515883 21 to 28 2642.34 2.013 0.977945 22 to 29 2458.69 -0.584 0.279544 23 to 30 2399.43 -1.422 0.077478 24 to 31 2473.23 -0.379 0.352516 25 to 32 2622.09 1.727 0.957877 CDPARK for dh-ranFile-2018-03-26_06:31: 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 3556 1.5068 0.934075 3516 -0.3196 0.374623 3491 -1.4612 0.071982 3539 0.7306 0.767486 3537 0.6393 0.738676 3532 0.4110 0.659449 3541 0.8219 0.794438 3489 -1.5525 0.060270 3532 0.4110 0.659449 3503 -0.9132 0.180558 Square side=100, avg. no. parked=3523.60 sample std.=21.57 p-value of the KSTEST for those 10 p-values: 0.765857 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-26_06:31 0.7788,0.5797,0.9348,0.5500,0.5686,0.0870,0.7136,0.0068,0.0971,0.9158, The KS test for those 10 p-values: 0.539183 The 3DSPHERES test for dh-ranFile-2018-03-26_06:31 sample no r^3 equiv. uni. 1 63.984 0.881496 2 64.033 0.881689 3 18.644 0.462837 4 76.174 0.921066 5 7.233 0.214226 6 6.932 0.206300 7 9.675 0.275667 8 12.379 0.338100 9 13.303 0.358162 10 8.521 0.247266 11 13.086 0.353506 12 13.749 0.367652 13 15.385 0.401211 14 40.254 0.738629 15 110.639 0.974977 16 6.320 0.189969 17 37.710 0.715489 18 65.987 0.889150 19 0.150 0.004987 20 0.603 0.019902 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.500801 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-26_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -0.4 -0.5 -0.5 -0.4 0.7 -0.6 0.2 0.8 -1.2 0.8 0.1 -0.3 1.3 2.0 -3.2 0.3 -0.8 -0.3 0.4 -0.1 1.4 0.8 -1.6 0.9 -0.4 0.8 0.1 -1.7 -0.4 -0.9 0.8 -0.6 0.6 -0.1 0.5 -1.0 -0.4 -0.7 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:38.270991 z-score=-0.406868, p-value=0.364595 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-26_06:31 Test no p-value 1 0.651487 2 0.299634 3 0.132461 4 0.116194 5 0.562110 6 0.229194 7 0.769951 8 0.861507 9 0.775555 10 0.314497 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.898211 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-26_06:31: (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 66728 0.06 66707 0.02 3 25000.00 24977 0.02 24868 0.70 4 6666.67 6623 0.29 6795 2.47 5 1388.89 1395 0.03 1361 0.56 6 238.10 237 0.01 231 0.21 7 34.72 36 0.05 33 0.09 8 4.96 3 0.77 4 0.19 p=0.02398 p=0.35498 Number of rngs required: 687417, p-value: 0.126 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-26_06:31 No. of wins: Observed Expected 98830 98585.9 z-score= 1.092, pvalue=0.86257 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66508 66666.7 0.378 0.378 2 37891 37654.3 1.488 1.865 3 27112 26954.7 0.918 2.783 4 19214 19313.5 0.512 3.295 5 13815 13851.4 0.096 3.391 6 9992 9943.5 0.236 3.627 7 7056 7145.0 1.109 4.736 8 5113 5139.1 0.132 4.869 9 3640 3699.9 0.969 5.837 10 2683 2666.3 0.105 5.942 11 1941 1923.3 0.162 6.104 12 1391 1388.7 0.004 6.108 13 1019 1003.7 0.233 6.341 14 761 726.1 1.673 8.014 15 497 525.8 1.581 9.595 16 378 381.2 0.026 9.621 17 256 276.5 1.526 11.147 18 219 200.8 1.644 12.791 19 134 146.0 0.984 13.775 20 109 106.2 0.073 13.848 21 271 287.1 0.904 14.752 Chisq= 14.75 for 20 degrees of freedom, p= 0.20959 SUMMARY of craptest p-value for no. of wins: 0.862571 p-value for throws/game: 0.209587 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-26_06:31 No. of wins: Observed Expected 98613 98585.9 z-score= 0.121, pvalue=0.54831 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66503 66666.7 0.402 0.402 2 37616 37654.3 0.039 0.441 3 27055 26954.7 0.373 0.814 4 19350 19313.5 0.069 0.883 5 13858 13851.4 0.003 0.886 6 9939 9943.5 0.002 0.888 7 7151 7145.0 0.005 0.893 8 5132 5139.1 0.010 0.903 9 3751 3699.9 0.707 1.610 10 2750 2666.3 2.628 4.237 11 1904 1923.3 0.194 4.431 12 1365 1388.7 0.406 4.837 13 1015 1003.7 0.127 4.964 14 673 726.1 3.889 8.853 15 491 525.8 2.308 11.161 16 373 381.2 0.174 11.335 17 324 276.5 8.145 19.481 18 201 200.8 0.000 19.481 19 151 146.0 0.172 19.653 20 112 106.2 0.315 19.968 21 286 287.1 0.004 19.972 Chisq= 19.97 for 20 degrees of freedom, p= 0.54034 SUMMARY of craptest p-value for no. of wins: 0.548310 p-value for throws/game: 0.540344 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0019,0.0050,0.0068,0.0070,0.0104,0.0170,0.0199,0.0199,0.0240,0.0317, 0.0328,0.0354,0.0398,0.0424,0.0603,0.0639,0.0699,0.0709,0.0720,0.0761, 0.0775,0.0847,0.0870,0.0882,0.0971,0.1017,0.1040,0.1054,0.1107,0.1162, 0.1175,0.1186,0.1230,0.1236,0.1259,0.1261,0.1292,0.1325,0.1353,0.1389, 0.1557,0.1579,0.1615,0.1649,0.1771,0.1782,0.1806,0.1820,0.1831,0.1900, 0.1902,0.1931,0.1943,0.1943,0.1951,0.1951,0.2015,0.2058,0.2063,0.2096, 0.2106,0.2142,0.2187,0.2230,0.2292,0.2307,0.2321,0.2383,0.2462,0.2473, 0.2547,0.2558,0.2562,0.2569,0.2617,0.2653,0.2757,0.2795,0.2864,0.2864, 0.2890,0.2909,0.2938,0.2996,0.3046,0.3057,0.3145,0.3179,0.3241,0.3256, 0.3294,0.3303,0.3341,0.3381,0.3525,0.3535,0.3550,0.3582,0.3646,0.3677, 0.3746,0.3767,0.3777,0.3822,0.3836,0.3906,0.3928,0.4012,0.4023,0.4029, 0.4052,0.4053,0.4082,0.4091,0.4163,0.4213,0.4328,0.4410,0.4433,0.4452, 0.4455,0.4556,0.4556,0.4628,0.4631,0.4633,0.4644,0.4644,0.4644,0.4706, 0.4746,0.4764,0.4842,0.4860,0.4914,0.4927,0.4982,0.5008,0.5016,0.5023, 0.5033,0.5060,0.5071,0.5118,0.5159,0.5239,0.5249,0.5257,0.5298,0.5347, 0.5392,0.5403,0.5483,0.5500,0.5504,0.5521,0.5621,0.5686,0.5709,0.5797, 0.5956,0.5973,0.5976,0.6134,0.6271,0.6302,0.6319,0.6358,0.6364,0.6428, 0.6475,0.6500,0.6515,0.6522,0.6590,0.6594,0.6594,0.6639,0.6663,0.6690, 0.6749,0.6756,0.6898,0.6926,0.6947,0.7007,0.7072,0.7093,0.7136,0.7155, 0.7213,0.7240,0.7302,0.7332,0.7335,0.7386,0.7386,0.7387,0.7463,0.7501, 0.7543,0.7556,0.7573,0.7582,0.7659,0.7675,0.7676,0.7700,0.7711,0.7756, 0.7788,0.7825,0.7855,0.7876,0.7935,0.7944,0.7957,0.7977,0.7991,0.8001, 0.8007,0.8077,0.8158,0.8230,0.8293,0.8362,0.8412,0.8486,0.8489,0.8572, 0.8615,0.8626,0.8649,0.8671,0.8745,0.8799,0.8815,0.8817,0.8837,0.8849, 0.8891,0.8982,0.9050,0.9110,0.9129,0.9149,0.9158,0.9211,0.9231,0.9253, 0.9280,0.9294,0.9321,0.9341,0.9348,0.9436,0.9455,0.9548,0.9579,0.9653, 0.9656,0.9690,0.9691,0.9750,0.9771,0.9779,0.9794,0.9806,0.9948, Overall p-value after applying KStest on 269 p-values = 0.994751 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.