RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-13_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 16.07 11.8597 0.191442 2 to 25 15.78 7.4238 0.022632 3 to 26 15.92 20.2416 0.737941 4 to 27 15.54 25.8071 0.921953 5 to 28 15.73 21.9316 0.812635 6 to 29 15.55 27.1773 0.944481 7 to 30 15.70 16.0916 0.482651 8 to 31 15.92 22.4912 0.833441 9 to 32 16.15 12.6423 0.240215 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.478450 Tough bday spacings test for dh-ranFile-2018-04-13_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 15 34 68 95 94 79 61 23 22 7 2 (O-E)^2/E 3.7 0.2 0.4 0.1 0.1 0.0 1.5 1.5 3.4 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 12.050, p= 0.718 RESULTS OF GCD FOR dh-ranFile-2018-04-13_06:31 Euclid's algorithm: p-value, steps to gcd: 0.896963 p-value, dist. of gcd's: 0.776726 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-13_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.231 0.860 0.844 0.597 0.703 0.752 0.131 0.799 Bits 8 to 15---> 0.182 0.226 0.167 0.866 0.597 0.471 0.708 0.998 Bits 16 to 23---> 0.587 0.216 0.623 0.519 0.670 0.737 0.963 0.031 Bits 24 to 31---> 0.994 0.841 0.303 0.057 0.759 0.704 0.640 0.130 KS test for the above 32 p values: 0.746 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-13_06:31, p-values for 5 runs: 0.8814, 0.3328, 0.0932, 0.4436, 0.9402 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-13_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5276 5134.0 3.927 4.656 r= 30 22905 23103.0 1.698 6.354 r= 31 11620 11551.5 0.406 6.760 chi-square = 6.760 with df = 3; p-value = 0.920 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-13_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5024 5134.0 2.357 2.496 r= 31 23263 23103.0 1.107 3.604 r= 32 11507 11551.5 0.172 3.775 chi-square = 3.775 with df = 3; p-value = 0.713 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-13_06:31 b-rank test for bits 1 to 8, p=0.81298 b-rank test for bits 2 to 9, p=0.85876 b-rank test for bits 3 to 10, p=0.39537 b-rank test for bits 4 to 11, p=0.52696 b-rank test for bits 5 to 12, p=0.99738 b-rank test for bits 6 to 13, p=0.81059 b-rank test for bits 7 to 14, p=0.98041 b-rank test for bits 8 to 15, p=0.76228 b-rank test for bits 9 to 16, p=0.90107 b-rank test for bits 10 to 17, p=0.70210 b-rank test for bits 11 to 18, p=0.07578 b-rank test for bits 12 to 19, p=0.06644 b-rank test for bits 13 to 20, p=0.54949 b-rank test for bits 14 to 21, p=0.62774 b-rank test for bits 15 to 22, p=0.78788 b-rank test for bits 16 to 23, p=0.25905 b-rank test for bits 17 to 24, p=0.63079 b-rank test for bits 18 to 25, p=0.58583 b-rank test for bits 19 to 26, p=0.95039 b-rank test for bits 20 to 27, p=0.71368 b-rank test for bits 21 to 28, p=0.79762 b-rank test for bits 22 to 29, p=0.37618 b-rank test for bits 23 to 30, p=0.38118 b-rank test for bits 24 to 31, p=0.15996 b-rank test for bits 25 to 32, p=0.46461 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 = 0.103963 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-13_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 142178 0.63 0.734911 2 142266 0.83 0.797674 3 141506 -0.94 0.173004 4 141754 -0.36 0.358332 5 142674 1.79 0.963000 6 141980 0.17 0.565574 7 142152 0.57 0.714638 8 141916 0.02 0.506217 9 142315 0.95 0.828391 10 141559 -0.82 0.206528 11 141183 -1.70 0.044845 12 141954 0.10 0.541562 13 141773 -0.32 0.375042 14 141872 -0.09 0.465249 15 142094 0.43 0.666937 16 142368 1.07 0.858063 17 142033 0.29 0.613690 18 141771 -0.32 0.373272 19 141710 -0.47 0.320706 20 141590 -0.75 0.227804 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-13_06:31 Bits used No. missing words z-score p-value 23 to 32 142312 1.3885 0.917510 22 to 31 142400 1.6920 0.954674 21 to 30 141932 0.0782 0.531155 20 to 29 141755 -0.5322 0.297303 19 to 28 141675 -0.8080 0.209535 18 to 27 141726 -0.6322 0.263637 17 to 26 141869 -0.1391 0.444698 16 to 25 142485 1.9851 0.976432 15 to 24 141548 -1.2460 0.106389 14 to 23 142452 1.8713 0.969347 13 to 22 142332 1.4575 0.927508 12 to 21 142058 0.5127 0.695904 11 to 20 142132 0.7678 0.778705 10 to 19 141495 -1.4287 0.076542 9 to 18 141753 -0.5391 0.294920 8 to 17 141610 -1.0322 0.150996 7 to 16 141709 -0.6908 0.244848 6 to 15 142391 1.6609 0.951636 5 to 14 141494 -1.4322 0.076047 4 to 13 141927 0.0609 0.524293 3 to 12 142057 0.5092 0.694696 2 to 11 141675 -0.8080 0.209535 1 to 10 142037 0.4402 0.670119 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-13_06:31 Bits used No. missing words z-score p-value 28 to 32 141954 0.1514 0.560179 27 to 31 142103 0.6565 0.744252 26 to 30 141007 -3.0587 0.001111 25 to 29 141760 -0.5062 0.306357 24 to 28 141804 -0.3571 0.360527 23 to 27 142423 1.7413 0.959181 22 to 26 142231 1.0904 0.862233 21 to 25 141490 -1.4215 0.077592 20 to 24 142341 1.4633 0.928306 19 to 23 141975 0.2226 0.588081 18 to 22 141585 -1.0994 0.135792 17 to 21 141770 -0.4723 0.318355 16 to 20 141822 -0.2960 0.383602 15 to 19 141891 -0.0621 0.475227 14 to 18 142355 1.5107 0.934573 13 to 17 142162 0.8565 0.804142 12 to 16 142191 0.9548 0.830164 11 to 15 141652 -0.8723 0.191521 10 to 14 142259 1.1853 0.882055 9 to 13 141871 -0.1299 0.448310 8 to 12 141459 -1.5265 0.063437 7 to 11 142480 1.9345 0.973473 6 to 10 141668 -0.8181 0.206659 5 to 9 141505 -1.3706 0.085248 4 to 8 141952 0.1446 0.557504 3 to 7 141899 -0.0350 0.486033 2 to 6 141676 -0.7909 0.214487 1 to 5 141834 -0.2554 0.399224 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-13_06:31 Bits used No. missing words z-score p-value 31 to 32 142300 1.1524 0.875426 30 to 31 142406 1.4651 0.928554 29 to 30 141851 -0.1721 0.431693 28 to 29 141892 -0.0511 0.479615 27 to 28 141835 -0.2193 0.413223 26 to 27 142283 1.1023 0.864828 25 to 26 142047 0.4061 0.657668 24 to 25 142052 0.4209 0.663070 23 to 24 141821 -0.2606 0.397216 22 to 23 141969 0.1760 0.569860 21 to 22 141964 0.1613 0.564059 20 to 21 141924 0.0433 0.517259 19 to 20 141253 -1.9361 0.026429 18 to 19 141487 -1.2458 0.106417 17 to 18 141298 -1.8033 0.035668 16 to 17 142294 1.1347 0.871754 15 to 16 141782 -0.3756 0.353605 14 to 15 141437 -1.3933 0.081764 13 to 14 141620 -0.8535 0.196696 12 to 13 142102 0.5683 0.715101 11 to 12 142510 1.7719 0.961793 10 to 11 141363 -1.6116 0.053525 9 to 10 141325 -1.7237 0.042382 8 to 9 142425 1.5212 0.935889 7 to 8 141616 -0.8653 0.193443 6 to 7 141990 0.2380 0.594046 5 to 6 142100 0.5624 0.713095 4 to 5 141885 -0.0718 0.471393 3 to 4 141380 -1.5614 0.059209 2 to 3 142003 0.2763 0.608846 1 to 2 141218 -2.0393 0.020709 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-13_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2423.33 -1.084 0.139136 Test results for specific bytes for dh-ranFile-2018-04-13_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2461.26 -0.548 0.291879 2 to 9 2616.17 1.643 0.949802 3 to 10 2591.61 1.296 0.902442 4 to 11 2474.93 -0.355 0.361481 5 to 12 2452.43 -0.673 0.250560 6 to 13 2489.31 -0.151 0.439921 7 to 14 2494.92 -0.072 0.471387 8 to 15 2554.10 0.765 0.777871 9 to 16 2454.25 -0.647 0.258811 10 to 17 2491.10 -0.126 0.449898 11 to 18 2562.69 0.887 0.812349 12 to 19 2364.74 -1.913 0.027884 13 to 20 2556.59 0.800 0.788222 14 to 21 2405.14 -1.341 0.089882 15 to 22 2386.59 -1.604 0.054378 16 to 23 2452.52 -0.672 0.250940 17 to 24 2549.71 0.703 0.758976 18 to 25 2510.06 0.142 0.556565 19 to 26 2437.89 -0.878 0.189876 20 to 27 2637.23 1.941 0.973858 21 to 28 2445.05 -0.777 0.218566 22 to 29 2461.27 -0.548 0.291931 23 to 30 2492.10 -0.112 0.455515 24 to 31 2423.08 -1.088 0.138353 25 to 32 2522.57 0.319 0.625218 CDPARK for dh-ranFile-2018-04-13_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 3515 -0.3653 0.357445 3541 0.8219 0.794438 3534 0.5023 0.692266 3467 -2.5571 0.005278 3510 -0.5936 0.276387 3572 2.2374 0.987371 3532 0.4110 0.659449 3518 -0.2283 0.409702 3495 -1.2785 0.100530 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3519.20 sample std.=26.81 p-value of the KSTEST for those 10 p-values: 0.766237 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-13_06:31 0.9792,0.4114,0.0886,0.8708,0.0657,0.8738,0.9104,0.5789,0.2276,0.4862, The KS test for those 10 p-values: 0.606059 The 3DSPHERES test for dh-ranFile-2018-04-13_06:31 sample no r^3 equiv. uni. 1 23.833 0.548163 2 19.370 0.475682 3 60.162 0.865395 4 28.194 0.609299 5 8.670 0.250988 6 97.455 0.961168 7 11.890 0.327219 8 102.656 0.967349 9 5.380 0.164164 10 17.067 0.433847 11 30.440 0.637473 12 7.263 0.215019 13 58.701 0.858678 14 5.898 0.178470 15 39.943 0.735897 16 132.007 0.987725 17 28.123 0.608365 18 8.650 0.250486 19 15.496 0.403422 20 117.865 0.980334 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.236347 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-13_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 0.1 0.0 -1.0 -0.7 -0.2 1.7 -0.0 -0.6 -0.2 -0.5 0.8 -0.1 -1.0 -0.3 0.4 1.1 1.2 -0.3 0.7 -0.3 -0.2 0.9 -1.2 0.3 -2.4 0.6 -1.4 -0.2 0.1 0.8 -0.9 -0.5 -0.6 -1.0 -0.2 0.2 2.5 -0.7 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:34.152803 z-score=-0.856199, p-value=0.199839 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-13_06:31 Test no p-value 1 0.375706 2 0.217074 3 0.069418 4 0.046761 5 0.695203 6 0.005060 7 0.006038 8 0.843766 9 0.052150 10 0.065931 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000462 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-13_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 66704 0.02 66675 0.00 3 25000.00 25098 0.38 24996 0.00 4 6666.67 6598 0.71 6603 0.61 5 1388.89 1337 1.94 1429 1.16 6 238.10 228 0.43 257 1.50 7 34.72 32 0.21 33 0.09 8 4.96 2 1.77 6 0.22 p=0.51353 p=0.26569 Number of rngs required: 689182, p-value: 0.816 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-13_06:31 No. of wins: Observed Expected 98455 98585.9 z-score=-0.585, pvalue=0.27918 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66585 66666.7 0.100 0.100 2 37889 37654.3 1.463 1.563 3 26843 26954.7 0.463 2.026 4 19254 19313.5 0.183 2.209 5 13790 13851.4 0.272 2.481 6 10012 9943.5 0.471 2.953 7 7106 7145.0 0.213 3.166 8 5200 5139.1 0.722 3.888 9 3700 3699.9 0.000 3.888 10 2682 2666.3 0.092 3.981 11 1991 1923.3 2.381 6.361 12 1307 1388.7 4.811 11.173 13 1011 1003.7 0.053 11.226 14 690 726.1 1.799 13.024 15 529 525.8 0.019 13.043 16 381 381.2 0.000 13.043 17 260 276.5 0.989 14.033 18 232 200.8 4.838 18.870 19 142 146.0 0.109 18.979 20 110 106.2 0.135 19.114 21 286 287.1 0.004 19.118 Chisq= 19.12 for 20 degrees of freedom, p= 0.48585 SUMMARY of craptest p-value for no. of wins: 0.279181 p-value for throws/game: 0.485852 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-13_06:31 No. of wins: Observed Expected 98458 98585.9 z-score=-0.572, pvalue=0.28371 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66852 66666.7 0.515 0.515 2 37723 37654.3 0.125 0.640 3 26720 26954.7 2.044 2.685 4 19271 19313.5 0.093 2.778 5 13906 13851.4 0.215 2.993 6 9871 9943.5 0.529 3.522 7 7144 7145.0 0.000 3.522 8 5219 5139.1 1.243 4.766 9 3717 3699.9 0.079 4.845 10 2563 2666.3 4.002 8.847 11 2012 1923.3 4.088 12.935 12 1405 1388.7 0.190 13.125 13 979 1003.7 0.609 13.734 14 744 726.1 0.439 14.173 15 548 525.8 0.934 15.107 16 389 381.2 0.162 15.269 17 268 276.5 0.264 15.533 18 183 200.8 1.583 17.116 19 132 146.0 1.340 18.455 20 88 106.2 3.124 21.579 21 266 287.1 1.553 23.132 Chisq= 23.13 for 20 degrees of freedom, p= 0.71762 SUMMARY of craptest p-value for no. of wins: 0.283709 p-value for throws/game: 0.717624 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0011,0.0051,0.0053,0.0060,0.0207,0.0226,0.0264,0.0279,0.0311, 0.0357,0.0424,0.0448,0.0468,0.0522,0.0535,0.0544,0.0575,0.0592,0.0634, 0.0657,0.0659,0.0664,0.0694,0.0758,0.0760,0.0765,0.0776,0.0818,0.0852, 0.0886,0.0899,0.0932,0.1005,0.1040,0.1064,0.1064,0.1301,0.1314,0.1358, 0.1384,0.1391,0.1510,0.1600,0.1642,0.1668,0.1730,0.1785,0.1821,0.1899, 0.1914,0.1915,0.1934,0.1967,0.1998,0.2065,0.2067,0.2095,0.2095,0.2145, 0.2150,0.2157,0.2171,0.2186,0.2256,0.2276,0.2278,0.2309,0.2363,0.2402, 0.2448,0.2467,0.2505,0.2506,0.2509,0.2510,0.2588,0.2591,0.2636,0.2657, 0.2764,0.2792,0.2837,0.2919,0.2919,0.2949,0.2973,0.3026,0.3064,0.3184, 0.3207,0.3272,0.3328,0.3536,0.3574,0.3583,0.3605,0.3615,0.3733,0.3750, 0.3757,0.3762,0.3812,0.3836,0.3954,0.3972,0.3992,0.4034,0.4097,0.4114, 0.4132,0.4317,0.4338,0.4399,0.4436,0.4447,0.4483,0.4499,0.4555,0.4646, 0.4652,0.4706,0.4714,0.4714,0.4752,0.4757,0.4785,0.4796,0.4827,0.4859, 0.4860,0.4862,0.5062,0.5135,0.5173,0.5194,0.5243,0.5270,0.5312,0.5416, 0.5482,0.5495,0.5566,0.5575,0.5602,0.5641,0.5656,0.5699,0.5789,0.5858, 0.5869,0.5881,0.5940,0.5972,0.5973,0.6061,0.6084,0.6088,0.6093,0.6137, 0.6235,0.6252,0.6277,0.6308,0.6375,0.6400,0.6577,0.6594,0.6631,0.6669, 0.6701,0.6701,0.6923,0.6947,0.6952,0.6959,0.7021,0.7027,0.7038,0.7085, 0.7131,0.7132,0.7137,0.7146,0.7151,0.7176,0.7183,0.7349,0.7359,0.7366, 0.7379,0.7443,0.7461,0.7518,0.7590,0.7592,0.7623,0.7662,0.7767,0.7779, 0.7787,0.7879,0.7882,0.7944,0.7976,0.7977,0.7994,0.8041,0.8106,0.8123, 0.8126,0.8130,0.8163,0.8284,0.8302,0.8334,0.8411,0.8438,0.8444,0.8581, 0.8587,0.8588,0.8599,0.8622,0.8648,0.8654,0.8657,0.8708,0.8718,0.8738, 0.8754,0.8814,0.8821,0.8970,0.9011,0.9024,0.9104,0.9175,0.9200,0.9220, 0.9275,0.9283,0.9286,0.9346,0.9359,0.9402,0.9445,0.9498,0.9504,0.9516, 0.9547,0.9592,0.9612,0.9618,0.9629,0.9630,0.9673,0.9693,0.9735,0.9739, 0.9764,0.9792,0.9803,0.9804,0.9874,0.9877,0.9938,0.9974,0.9982, Overall p-value after applying KStest on 269 p-values = 0.326550 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.