RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 26.6004 0.935806 2 to 25 15.88 18.6842 0.653046 3 to 26 15.93 11.1345 0.150514 4 to 27 15.98 25.5431 0.916804 5 to 28 15.78 8.8260 0.054438 6 to 29 15.78 22.8079 0.844390 7 to 30 15.81 10.9391 0.140289 8 to 31 15.89 21.0716 0.776896 9 to 32 16.02 13.1997 0.277285 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.593189 Tough bday spacings test for dh-ranFile-2018-06-15_10:31: 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 9 35 59 85 95 97 61 28 20 7 4 (O-E)^2/E 0.0 0.1 2.8 1.6 0.1 4.5 1.5 0.1 1.8 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 12.528, p= 0.749 RESULTS OF GCD FOR dh-ranFile-2018-06-15_10:31 Euclid's algorithm: p-value, steps to gcd: 0.511141 p-value, dist. of gcd's: 0.324327 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.629 0.736 0.706 0.621 0.298 0.087 0.882 0.127 Bits 8 to 15---> 0.653 0.615 0.074 0.540 0.854 0.200 0.815 0.933 Bits 16 to 23---> 0.504 0.088 0.125 0.694 0.961 0.571 0.904 0.860 Bits 24 to 31---> 0.322 0.435 0.530 0.440 0.244 0.136 0.711 0.665 KS test for the above 32 p values: 0.271 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_10:31, p-values for 5 runs: 0.0153, 0.4729, 0.8859, 0.5630, 0.3597 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 232 211.4 2.004 2.004 r= 29 5092 5134.0 0.344 2.347 r= 30 23179 23103.0 0.250 2.597 r= 31 11497 11551.5 0.257 2.855 chi-square = 2.855 with df = 3; p-value = 0.585 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 200 211.4 0.617 0.617 r= 30 5125 5134.0 0.016 0.632 r= 31 23185 23103.0 0.291 0.923 r= 32 11490 11551.5 0.328 1.251 chi-square = 1.251 with df = 3; p-value = 0.259 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_10:31 b-rank test for bits 1 to 8, p=0.35794 b-rank test for bits 2 to 9, p=0.75758 b-rank test for bits 3 to 10, p=0.95412 b-rank test for bits 4 to 11, p=0.67947 b-rank test for bits 5 to 12, p=0.01487 b-rank test for bits 6 to 13, p=0.17049 b-rank test for bits 7 to 14, p=0.52054 b-rank test for bits 8 to 15, p=0.56159 b-rank test for bits 9 to 16, p=0.18948 b-rank test for bits 10 to 17, p=0.27605 b-rank test for bits 11 to 18, p=0.09024 b-rank test for bits 12 to 19, p=0.45058 b-rank test for bits 13 to 20, p=0.89793 b-rank test for bits 14 to 21, p=0.95393 b-rank test for bits 15 to 22, p=0.20998 b-rank test for bits 16 to 23, p=0.19165 b-rank test for bits 17 to 24, p=0.56487 b-rank test for bits 18 to 25, p=0.10126 b-rank test for bits 19 to 26, p=0.44429 b-rank test for bits 20 to 27, p=0.24198 b-rank test for bits 21 to 28, p=0.56338 b-rank test for bits 22 to 29, p=0.31928 b-rank test for bits 23 to 30, p=0.65257 b-rank test for bits 24 to 31, p=0.58994 b-rank test for bits 25 to 32, p=0.63235 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 = 0.664903 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_10:31 (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 141653 -0.60 0.274619 2 143083 2.74 0.996949 3 142340 1.01 0.842850 4 142061 0.35 0.638469 5 141871 -0.09 0.464320 6 141494 -0.97 0.165924 7 141772 -0.32 0.374157 8 141949 0.09 0.536924 9 141552 -0.83 0.201892 10 141774 -0.32 0.375929 11 142593 1.60 0.944907 12 142290 0.89 0.813110 13 141817 -0.22 0.414601 14 142360 1.05 0.853822 15 142415 1.18 0.881292 16 141783 -0.30 0.383935 17 141673 -0.55 0.290415 18 141582 -0.76 0.222198 19 142063 0.36 0.640218 20 141735 -0.41 0.341889 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-15_10:31 Bits used No. missing words z-score p-value 23 to 32 142339 1.4816 0.930779 22 to 31 141829 -0.2770 0.390890 21 to 30 141880 -0.1011 0.459721 20 to 29 142199 0.9989 0.841069 19 to 28 141702 -0.7149 0.237326 18 to 27 141948 0.1333 0.553040 17 to 26 142257 1.1989 0.884709 16 to 25 142024 0.3954 0.653731 15 to 24 141660 -0.8598 0.194961 14 to 23 142096 0.6437 0.740112 13 to 22 141824 -0.2942 0.384287 12 to 21 142713 2.7713 0.997208 11 to 20 141635 -0.9460 0.172083 10 to 19 141847 -0.2149 0.414911 9 to 18 141830 -0.2736 0.392215 8 to 17 142168 0.8920 0.813794 7 to 16 141898 -0.0391 0.484418 6 to 15 140851 -3.6494 0.000131 5 to 14 141854 -0.1908 0.424344 4 to 13 141642 -0.9218 0.178309 3 to 12 141978 0.2368 0.593591 2 to 11 141493 -1.4356 0.075555 1 to 10 141591 -1.0977 0.136170 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-15_10:31 Bits used No. missing words z-score p-value 28 to 32 142554 2.1853 0.985567 27 to 31 142306 1.3446 0.910630 26 to 30 141854 -0.1876 0.425611 25 to 29 142009 0.3379 0.632267 24 to 28 142106 0.6667 0.747511 23 to 27 142302 1.3311 0.908419 22 to 26 141375 -1.8113 0.035048 21 to 25 142310 1.3582 0.912800 20 to 24 141693 -0.7333 0.231681 19 to 23 142220 1.0531 0.853857 18 to 22 141556 -1.1977 0.115511 17 to 21 141876 -0.1130 0.455022 16 to 20 142296 1.3107 0.905028 15 to 19 142234 1.1006 0.864459 14 to 18 141856 -0.1808 0.428270 13 to 17 141626 -0.9604 0.168417 12 to 16 142057 0.5006 0.691665 11 to 15 141796 -0.3842 0.350426 10 to 14 141786 -0.4181 0.337949 9 to 13 141653 -0.8689 0.192447 8 to 12 142081 0.5819 0.719694 7 to 11 141923 0.0463 0.518480 6 to 10 142179 0.9141 0.819677 5 to 9 141628 -0.9537 0.170128 4 to 8 141954 0.1514 0.560179 3 to 7 141976 0.2260 0.589399 2 to 6 142112 0.6870 0.753964 1 to 5 141999 0.3040 0.619423 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-15_10:31 Bits used No. missing words z-score p-value 31 to 32 141563 -1.0216 0.153480 30 to 31 141458 -1.3314 0.091536 29 to 30 142059 0.4415 0.670576 28 to 29 142064 0.4563 0.675896 27 to 28 141508 -1.1839 0.118233 26 to 27 141951 0.1229 0.548915 25 to 26 141649 -0.7679 0.221263 24 to 25 142116 0.6096 0.728952 23 to 24 141879 -0.0895 0.464355 22 to 23 141865 -0.1308 0.447980 21 to 22 141887 -0.0659 0.473741 20 to 21 141963 0.1583 0.562897 19 to 20 142740 2.4504 0.992864 18 to 19 142345 1.2852 0.900632 17 to 18 141354 -1.6381 0.050696 16 to 17 142598 2.0315 0.978897 15 to 16 141177 -2.1603 0.015376 14 to 15 141931 0.0639 0.525484 13 to 14 141609 -0.8859 0.187828 12 to 13 142508 1.7660 0.961301 11 to 12 142036 0.3737 0.645671 10 to 11 141506 -1.1898 0.117070 9 to 10 141795 -0.3373 0.367962 8 to 9 142105 0.5772 0.718097 7 to 8 142163 0.7483 0.772857 6 to 7 141844 -0.1927 0.423592 5 to 6 142262 1.0403 0.850905 4 to 5 142158 0.7335 0.768385 3 to 4 141703 -0.6086 0.271381 2 to 3 141254 -1.9331 0.026610 1 to 2 142107 0.5831 0.720086 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2505.97 0.084 0.533621 Test results for specific bytes for dh-ranFile-2018-06-15_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2459.28 -0.576 0.282348 2 to 9 2549.50 0.700 0.758044 3 to 10 2607.81 1.525 0.936337 4 to 11 2412.71 -1.234 0.108519 5 to 12 2434.64 -0.924 0.177642 6 to 13 2466.91 -0.468 0.319892 7 to 14 2432.19 -0.959 0.168789 8 to 15 2632.72 1.877 0.969741 9 to 16 2496.43 -0.050 0.479880 10 to 17 2556.60 0.800 0.788288 11 to 18 2470.29 -0.420 0.337183 12 to 19 2456.52 -0.615 0.269307 13 to 20 2444.52 -0.785 0.216351 14 to 21 2583.86 1.186 0.882181 15 to 22 2527.52 0.389 0.651427 16 to 23 2439.94 -0.849 0.197817 17 to 24 2514.55 0.206 0.581519 18 to 25 2574.64 1.056 0.854426 19 to 26 2475.33 -0.349 0.363597 20 to 27 2408.03 -1.301 0.096689 21 to 28 2499.61 -0.006 0.497799 22 to 29 2501.52 0.021 0.508569 23 to 30 2546.08 0.652 0.742706 24 to 31 2375.44 -1.762 0.039068 25 to 32 2601.42 1.434 0.924259 CDPARK for dh-ranFile-2018-06-15_10:31: 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 3514 -0.4110 0.340551 3503 -0.9132 0.180558 3510 -0.5936 0.276387 3543 0.9132 0.819442 3520 -0.1370 0.445521 3502 -0.9589 0.168804 3556 1.5068 0.934075 3517 -0.2740 0.392053 3536 0.5936 0.723613 3557 1.5525 0.939730 Square side=100, avg. no. parked=3525.80 sample std.=19.68 p-value of the KSTEST for those 10 p-values: 0.827658 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_10:31 0.5789,0.3502,0.1913,0.5319,0.3765,0.4527,0.6254,0.6514,0.0633,0.8635, The KS test for those 10 p-values: 0.732245 The 3DSPHERES test for dh-ranFile-2018-06-15_10:31 sample no r^3 equiv. uni. 1 38.517 0.723041 2 2.048 0.065982 3 8.044 0.235186 4 31.673 0.652078 5 12.211 0.334379 6 76.768 0.922614 7 48.185 0.799342 8 56.000 0.845360 9 13.060 0.352949 10 21.163 0.506112 11 0.227 0.007529 12 24.716 0.561264 13 7.469 0.220395 14 37.875 0.717050 15 28.380 0.611704 16 1.804 0.058353 17 14.358 0.380350 18 14.324 0.379642 19 1.055 0.034569 20 42.179 0.754873 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.687194 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 1.8 -1.1 1.0 -0.4 0.1 0.2 -0.3 1.2 -1.7 1.3 -0.2 0.7 0.3 0.7 -1.8 -0.6 -0.4 -0.5 -1.1 0.9 1.0 0.9 -0.1 -0.8 0.4 -0.5 0.4 2.1 -1.0 0.3 -0.4 -0.5 -0.1 1.3 2.1 -0.1 -0.8 1.0 -0.6 1.0 -0.1 Chi-square with 42 degrees of freedom:38.583135 z-score=-0.372811, p-value=0.378241 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-15_10:31 Test no p-value 1 0.547069 2 0.162322 3 0.318456 4 0.517194 5 0.052089 6 0.001483 7 0.937287 8 0.146566 9 0.570397 10 0.126350 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.078098 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_10:31: (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 66757 0.12 66502 0.41 3 25000.00 24845 0.96 25202 1.63 4 6666.67 6694 0.11 6588 0.93 5 1388.89 1438 1.74 1447 2.43 6 238.10 235 0.04 227 0.52 7 34.72 26 2.19 28 1.30 8 4.96 4 0.19 5 0.00 p=0.49999 p=0.69871 Number of rngs required: 687505, p-value: 0.149 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_10:31 No. of wins: Observed Expected 98798 98585.9 z-score= 0.949, pvalue=0.82864 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66757 66666.7 0.122 0.122 2 37423 37654.3 1.421 1.543 3 26980 26954.7 0.024 1.567 4 19358 19313.5 0.103 1.670 5 13755 13851.4 0.671 2.341 6 10085 9943.5 2.012 4.353 7 7147 7145.0 0.001 4.354 8 5232 5139.1 1.680 6.034 9 3684 3699.9 0.068 6.102 10 2653 2666.3 0.066 6.169 11 1850 1923.3 2.796 8.964 12 1413 1388.7 0.424 9.388 13 986 1003.7 0.313 9.701 14 736 726.1 0.134 9.835 15 583 525.8 6.214 16.049 16 350 381.2 2.546 18.595 17 292 276.5 0.864 19.459 18 206 200.8 0.133 19.592 19 142 146.0 0.109 19.701 20 98 106.2 0.635 20.337 21 270 287.1 1.020 21.357 Chisq= 21.36 for 20 degrees of freedom, p= 0.62359 SUMMARY of craptest p-value for no. of wins: 0.828644 p-value for throws/game: 0.623589 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_10:31 No. of wins: Observed Expected 98127 98585.9 z-score=-2.052, pvalue=0.02007 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66480 66666.7 0.523 0.523 2 37896 37654.3 1.551 2.074 3 26831 26954.7 0.568 2.642 4 19379 19313.5 0.222 2.864 5 13772 13851.4 0.455 3.320 6 9903 9943.5 0.165 3.485 7 7256 7145.0 1.724 5.209 8 5109 5139.1 0.176 5.384 9 3734 3699.9 0.315 5.699 10 2725 2666.3 1.292 6.992 11 1901 1923.3 0.259 7.251 12 1361 1388.7 0.554 7.805 13 1014 1003.7 0.105 7.911 14 734 726.1 0.085 7.996 15 507 525.8 0.675 8.670 16 365 381.2 0.684 9.355 17 293 276.5 0.980 10.335 18 194 200.8 0.232 10.567 19 113 146.0 7.453 18.019 20 114 106.2 0.571 18.590 21 319 287.1 3.541 22.131 Chisq= 22.13 for 20 degrees of freedom, p= 0.66656 SUMMARY of craptest p-value for no. of wins: 0.020071 p-value for throws/game: 0.666564 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0015,0.0075,0.0149,0.0153,0.0154,0.0201,0.0266,0.0346,0.0350, 0.0391,0.0507,0.0521,0.0544,0.0584,0.0633,0.0660,0.0740,0.0756,0.0781, 0.0873,0.0878,0.0902,0.0915,0.0967,0.1013,0.1085,0.1155,0.1171,0.1182, 0.1253,0.1264,0.1273,0.1362,0.1363,0.1403,0.1466,0.1489,0.1505,0.1535, 0.1623,0.1659,0.1684,0.1688,0.1688,0.1701,0.1705,0.1721,0.1776,0.1783, 0.1806,0.1878,0.1895,0.1913,0.1916,0.1924,0.1950,0.1978,0.1996,0.2019, 0.2100,0.2164,0.2204,0.2213,0.2222,0.2317,0.2352,0.2373,0.2420,0.2437, 0.2592,0.2693,0.2712,0.2714,0.2746,0.2761,0.2764,0.2773,0.2823,0.2904, 0.2977,0.3185,0.3193,0.3199,0.3218,0.3243,0.3344,0.3372,0.3379,0.3406, 0.3419,0.3502,0.3504,0.3529,0.3579,0.3597,0.3636,0.3680,0.3742,0.3759, 0.3765,0.3782,0.3796,0.3804,0.3839,0.3843,0.3909,0.3921,0.3922,0.4146, 0.4149,0.4236,0.4243,0.4256,0.4283,0.4348,0.4398,0.4443,0.4455,0.4480, 0.4506,0.4527,0.4550,0.4597,0.4643,0.4644,0.4729,0.4737,0.4799,0.4844, 0.4978,0.5000,0.5038,0.5061,0.5086,0.5111,0.5172,0.5185,0.5205,0.5255, 0.5302,0.5319,0.5336,0.5369,0.5399,0.5471,0.5489,0.5530,0.5602,0.5613, 0.5616,0.5629,0.5630,0.5634,0.5649,0.5704,0.5708,0.5789,0.5815,0.5854, 0.5894,0.5899,0.5932,0.5936,0.6117,0.6153,0.6194,0.6215,0.6236,0.6254, 0.6286,0.6323,0.6323,0.6385,0.6402,0.6457,0.6514,0.6514,0.6521,0.6526, 0.6530,0.6533,0.6537,0.6649,0.6654,0.6666,0.6706,0.6759,0.6795,0.6872, 0.6917,0.6945,0.6987,0.7059,0.7108,0.7171,0.7181,0.7197,0.7201,0.7230, 0.7236,0.7290,0.7322,0.7358,0.7401,0.7427,0.7475,0.7488,0.7540,0.7549, 0.7576,0.7580,0.7684,0.7729,0.7769,0.7883,0.7993,0.8131,0.8138,0.8151, 0.8194,0.8197,0.8277,0.8286,0.8411,0.8428,0.8444,0.8454,0.8509,0.8538, 0.8539,0.8542,0.8544,0.8595,0.8635,0.8645,0.8813,0.8817,0.8822,0.8847, 0.8859,0.8979,0.9006,0.9044,0.9050,0.9084,0.9106,0.9128,0.9168,0.9226, 0.9243,0.9308,0.9325,0.9341,0.9358,0.9363,0.9373,0.9397,0.9449,0.9539, 0.9541,0.9613,0.9615,0.9697,0.9789,0.9856,0.9929,0.9969,0.9972, Overall p-value after applying KStest on 269 p-values = 0.983473 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.