RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.71 17.1022 0.552536 2 to 25 15.82 25.6707 0.919327 3 to 26 15.61 20.9305 0.770586 4 to 27 15.40 42.7919 0.999485 5 to 28 15.60 18.6657 0.651946 6 to 29 15.63 24.2219 0.886471 7 to 30 15.68 11.2643 0.157501 8 to 31 15.75 22.5009 0.833784 9 to 32 15.82 12.3891 0.223975 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.079065 Tough bday spacings test for dh-ranFile-2018-07-08_23:31: 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 35 74 99 102 72 54 27 9 9 7 (O-E)^2/E 0.9 0.1 0.0 0.0 0.2 0.5 0.1 0.3 2.3 0.9 2.1 Birthday Spacings: Sum(O-E)^2/E= 7.284, p= 0.302 RESULTS OF GCD FOR dh-ranFile-2018-07-08_23:31 Euclid's algorithm: p-value, steps to gcd: 0.919069 p-value, dist. of gcd's: 0.017128 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.264 0.897 0.923 0.053 0.946 0.519 0.455 0.067 Bits 8 to 15---> 0.937 0.477 0.123 0.974 0.537 0.507 0.026 0.837 Bits 16 to 23---> 0.110 0.144 0.669 0.009 0.184 0.916 0.440 0.220 Bits 24 to 31---> 0.986 0.678 0.273 0.686 0.999 0.083 0.896 0.544 KS test for the above 32 p values: 0.803 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_23:31, p-values for 5 runs: 0.7589, 0.3795, 0.2207, 0.7644, 0.6127 Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 222 211.4 0.530 0.530 r= 29 5165 5134.0 0.187 0.717 r= 30 22990 23103.0 0.553 1.270 r= 31 11623 11551.5 0.442 1.712 chi-square = 1.712 with df = 3; p-value = 0.366 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5147 5134.0 0.033 1.637 r= 31 23185 23103.0 0.291 1.928 r= 32 11475 11551.5 0.507 2.435 chi-square = 2.435 with df = 3; p-value = 0.513 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_23:31 b-rank test for bits 1 to 8, p=0.24350 b-rank test for bits 2 to 9, p=0.23951 b-rank test for bits 3 to 10, p=0.27936 b-rank test for bits 4 to 11, p=0.98576 b-rank test for bits 5 to 12, p=0.90381 b-rank test for bits 6 to 13, p=0.39058 b-rank test for bits 7 to 14, p=0.27217 b-rank test for bits 8 to 15, p=0.75621 b-rank test for bits 9 to 16, p=0.04511 b-rank test for bits 10 to 17, p=0.84294 b-rank test for bits 11 to 18, p=0.17235 b-rank test for bits 12 to 19, p=0.62778 b-rank test for bits 13 to 20, p=0.89842 b-rank test for bits 14 to 21, p=0.24249 b-rank test for bits 15 to 22, p=0.04686 b-rank test for bits 16 to 23, p=0.18249 b-rank test for bits 17 to 24, p=0.90297 b-rank test for bits 18 to 25, p=0.09103 b-rank test for bits 19 to 26, p=0.75738 b-rank test for bits 20 to 27, p=0.91268 b-rank test for bits 21 to 28, p=0.76482 b-rank test for bits 22 to 29, p=0.05204 b-rank test for bits 23 to 30, p=0.53229 b-rank test for bits 24 to 31, p=0.89067 b-rank test for bits 25 to 32, p=0.60481 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 = 0.472475 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_23:31 (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 141793 -0.27 0.392888 2 141447 -1.08 0.140024 3 141809 -0.23 0.407331 4 141372 -1.26 0.104659 5 141668 -0.56 0.286426 6 142311 0.94 0.826001 7 142060 0.35 0.637593 8 142190 0.66 0.744014 9 142126 0.51 0.693655 10 142655 1.74 0.959265 11 141494 -0.97 0.165924 12 141340 -1.33 0.091725 13 142152 0.57 0.714638 14 141243 -1.56 0.059754 15 142417 1.19 0.882217 16 141633 -0.65 0.259259 17 141832 -0.18 0.428310 18 142334 0.99 0.839455 19 141933 0.06 0.522052 20 141977 0.16 0.562814 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-07-08_23:31 Bits used No. missing words z-score p-value 23 to 32 141789 -0.4149 0.339096 22 to 31 142019 0.3782 0.647349 21 to 30 142115 0.7092 0.760902 20 to 29 141622 -0.9908 0.160893 19 to 28 141860 -0.1701 0.432464 18 to 27 141320 -2.0322 0.021068 17 to 26 141318 -2.0391 0.020722 16 to 25 141718 -0.6598 0.254704 15 to 24 141550 -1.2391 0.107660 14 to 23 141858 -0.1770 0.429754 13 to 22 142061 0.5230 0.699513 12 to 21 142291 1.3161 0.905930 11 to 20 141586 -1.1149 0.132440 10 to 19 142171 0.9023 0.816554 9 to 18 141940 0.1058 0.542113 8 to 17 141744 -0.5701 0.284304 7 to 16 142084 0.6023 0.726516 6 to 15 142334 1.4644 0.928455 5 to 14 142425 1.7782 0.962312 4 to 13 141814 -0.3287 0.371182 3 to 12 142173 0.9092 0.818380 2 to 11 141839 -0.2425 0.404190 1 to 10 141733 -0.6080 0.271582 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-07-08_23:31 Bits used No. missing words z-score p-value 28 to 32 141450 -1.5571 0.059729 27 to 31 142027 0.3989 0.655010 26 to 30 141411 -1.6893 0.045585 25 to 29 141789 -0.4079 0.341674 24 to 28 142139 0.7785 0.781875 23 to 27 142030 0.4091 0.658749 22 to 26 141785 -0.4215 0.336711 21 to 25 141818 -0.3096 0.378435 20 to 24 141168 -2.5130 0.005986 19 to 23 141663 -0.8350 0.201854 18 to 22 141480 -1.4554 0.072785 17 to 21 141513 -1.3435 0.089556 16 to 20 141565 -1.1672 0.121561 15 to 19 142304 1.3379 0.909530 14 to 18 141542 -1.2452 0.106532 13 to 17 141136 -2.6215 0.004378 12 to 16 141663 -0.8350 0.201854 11 to 15 142198 0.9785 0.836097 10 to 14 141748 -0.5469 0.292230 9 to 13 141783 -0.4282 0.334239 8 to 12 142324 1.4057 0.920088 7 to 11 141940 0.1040 0.541402 6 to 10 141569 -1.1537 0.124320 5 to 9 142066 0.5311 0.702320 4 to 8 141695 -0.7265 0.233753 3 to 7 141682 -0.7706 0.220469 2 to 6 142035 0.4260 0.664946 1 to 5 142282 1.2633 0.896757 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-07-08_23:31 Bits used No. missing words z-score p-value 31 to 32 141470 -1.2960 0.097495 30 to 31 141770 -0.4110 0.340535 29 to 30 141962 0.1554 0.561735 28 to 29 141653 -0.7561 0.224784 27 to 28 141840 -0.2045 0.418976 26 to 27 141369 -1.5939 0.055480 25 to 26 141654 -0.7532 0.225669 24 to 25 141982 0.2144 0.584869 23 to 24 141586 -0.9538 0.170099 22 to 23 142502 1.7483 0.959793 21 to 22 141665 -0.7207 0.235536 20 to 21 141950 0.1200 0.547747 19 to 20 142088 0.5271 0.700921 18 to 19 141014 -2.6411 0.004132 17 to 18 142196 0.8456 0.801122 16 to 17 141913 0.0108 0.504319 15 to 16 141558 -1.0364 0.150014 14 to 15 141439 -1.3874 0.082659 13 to 14 141764 -0.4287 0.334070 12 to 13 141229 -2.0069 0.022382 11 to 12 142319 1.2085 0.886566 10 to 11 141507 -1.1868 0.117650 9 to 10 141739 -0.5024 0.307676 8 to 9 141663 -0.7266 0.233724 7 to 8 141679 -0.6794 0.248430 6 to 7 142113 0.6008 0.726012 5 to 6 142088 0.5271 0.700921 4 to 5 141542 -1.0836 0.139278 3 to 4 141659 -0.7384 0.230125 2 to 3 141518 -1.1544 0.124175 1 to 2 141780 -0.3815 0.351415 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2538.49 0.544 0.706896 Test results for specific bytes for dh-ranFile-2018-07-08_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2498.38 -0.023 0.490833 2 to 9 2539.54 0.559 0.711959 3 to 10 2401.05 -1.399 0.080857 4 to 11 2458.38 -0.589 0.278083 5 to 12 2531.26 0.442 0.670783 6 to 13 2518.92 0.268 0.605473 7 to 14 2484.99 -0.212 0.415969 8 to 15 2462.01 -0.537 0.295528 9 to 16 2397.08 -1.455 0.072770 10 to 17 2455.28 -0.632 0.263551 11 to 18 2556.29 0.796 0.786994 12 to 19 2410.91 -1.260 0.103844 13 to 20 2515.49 0.219 0.586694 14 to 21 2515.24 0.215 0.585307 15 to 22 2531.96 0.452 0.674384 16 to 23 2424.93 -1.062 0.144211 17 to 24 2417.98 -1.160 0.123041 18 to 25 2408.65 -1.292 0.098190 19 to 26 2573.03 1.033 0.849160 20 to 27 2457.28 -0.604 0.272885 21 to 28 2485.79 -0.201 0.420339 22 to 29 2447.46 -0.743 0.228729 23 to 30 2557.49 0.813 0.791896 24 to 31 2543.37 0.613 0.730155 25 to 32 2473.41 -0.376 0.353469 CDPARK for dh-ranFile-2018-07-08_23:31: 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 3548 1.1416 0.873180 3515 -0.3653 0.357445 3537 0.6393 0.738676 3512 -0.5023 0.307734 3546 1.0502 0.853193 3558 1.5982 0.944998 3522 -0.0457 0.481790 3506 -0.7763 0.218799 3515 -0.3653 0.357445 3499 -1.0959 0.136563 Square side=100, avg. no. parked=3525.80 sample std.=19.00 p-value of the KSTEST for those 10 p-values: 0.872780 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_23:31 0.6085,0.1904,0.8147,0.2547,0.7432,0.9104,0.4127,0.6023,0.3558,0.8177, The KS test for those 10 p-values: 0.661132 The 3DSPHERES test for dh-ranFile-2018-07-08_23:31 sample no r^3 equiv. uni. 1 0.133 0.004428 2 22.144 0.521997 3 28.296 0.610624 4 11.575 0.320124 5 69.127 0.900166 6 12.557 0.342008 7 37.392 0.712464 8 62.472 0.875369 9 12.818 0.347713 10 67.933 0.896110 11 10.473 0.294688 12 60.574 0.867227 13 24.538 0.558657 14 40.878 0.744006 15 17.345 0.439074 16 81.468 0.933834 17 3.502 0.110168 18 14.668 0.386724 19 16.463 0.422338 20 32.235 0.658536 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.598078 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.9 0.8 -0.3 -0.2 1.6 -1.8 1.1 -0.5 0.5 -0.9 -0.4 0.5 0.3 1.1 -2.0 0.6 0.5 -0.7 0.2 -1.1 0.3 0.1 2.2 -0.3 0.2 -0.1 0.1 -0.7 -0.3 1.0 -0.1 -1.5 -0.6 -0.2 0.4 1.0 -0.4 0.5 -1.3 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:33.249179 z-score=-0.954793, p-value=0.169438 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-07-08_23:31 Test no p-value 1 0.070699 2 0.094036 3 0.059483 4 0.484793 5 0.610713 6 0.030884 7 0.000938 8 0.361096 9 0.580154 10 0.636256 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.011611 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_23:31: (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 66867 0.60 66733 0.07 3 25000.00 24739 2.72 24954 0.08 4 6666.67 6688 0.07 6700 0.17 5 1388.89 1405 0.19 1360 0.60 6 238.10 251 0.70 212 2.86 7 34.72 38 0.31 32 0.21 8 4.96 11 7.36 8 1.86 p=0.93682 p=0.56032 Number of rngs required: 687801, p-value: 0.244 RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_23:31 No. of wins: Observed Expected 99020 98585.9 z-score= 1.942, pvalue=0.97392 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66834 66666.7 0.420 0.420 2 37547 37654.3 0.306 0.726 3 27060 26954.7 0.411 1.137 4 19305 19313.5 0.004 1.141 5 13796 13851.4 0.222 1.362 6 10070 9943.5 1.608 2.971 7 7154 7145.0 0.011 2.982 8 5159 5139.1 0.077 3.059 9 3711 3699.9 0.034 3.093 10 2595 2666.3 1.907 4.999 11 1842 1923.3 3.439 8.438 12 1325 1388.7 2.926 11.364 13 949 1003.7 2.983 14.346 14 726 726.1 0.000 14.347 15 500 525.8 1.269 15.616 16 404 381.2 1.370 16.986 17 280 276.5 0.043 17.029 18 187 200.8 0.952 17.981 19 162 146.0 1.757 19.738 20 111 106.2 0.216 19.954 21 283 287.1 0.059 20.013 Chisq= 20.01 for 20 degrees of freedom, p= 0.54288 SUMMARY of craptest p-value for no. of wins: 0.973915 p-value for throws/game: 0.542877 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_23:31 No. of wins: Observed Expected 98911 98585.9 z-score= 1.454, pvalue=0.92706 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66896 66666.7 0.789 0.789 2 37491 37654.3 0.708 1.497 3 27059 26954.7 0.403 1.901 4 19225 19313.5 0.405 2.306 5 13852 13851.4 0.000 2.306 6 9879 9943.5 0.419 2.725 7 7146 7145.0 0.000 2.725 8 4985 5139.1 4.619 7.344 9 3739 3699.9 0.414 7.758 10 2748 2666.3 2.504 10.262 11 1962 1923.3 0.778 11.039 12 1338 1388.7 1.854 12.893 13 988 1003.7 0.246 13.139 14 699 726.1 1.014 14.154 15 577 525.8 4.978 19.132 16 372 381.2 0.220 19.352 17 269 276.5 0.206 19.557 18 212 200.8 0.621 20.178 19 143 146.0 0.061 20.239 20 114 106.2 0.571 20.810 21 306 287.1 1.242 22.052 Chisq= 22.05 for 20 degrees of freedom, p= 0.66232 SUMMARY of craptest p-value for no. of wins: 0.927058 p-value for throws/game: 0.662315 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0041,0.0044,0.0044,0.0060,0.0091,0.0116,0.0171,0.0207,0.0211, 0.0224,0.0260,0.0309,0.0451,0.0456,0.0469,0.0520,0.0527,0.0555,0.0595, 0.0597,0.0598,0.0666,0.0707,0.0728,0.0728,0.0791,0.0809,0.0827,0.0828, 0.0896,0.0910,0.0917,0.0940,0.0975,0.0982,0.1038,0.1047,0.1065,0.1077, 0.1099,0.1102,0.1177,0.1216,0.1227,0.1230,0.1242,0.1243,0.1324,0.1366, 0.1393,0.1400,0.1436,0.1442,0.1500,0.1575,0.1609,0.1659,0.1694,0.1701, 0.1723,0.1825,0.1837,0.1904,0.2019,0.2019,0.2188,0.2201,0.2205,0.2207, 0.2240,0.2248,0.2257,0.2287,0.2301,0.2337,0.2338,0.2355,0.2395,0.2425, 0.2435,0.2435,0.2484,0.2547,0.2547,0.2593,0.2636,0.2641,0.2716,0.2722, 0.2729,0.2733,0.2781,0.2794,0.2843,0.2864,0.2922,0.2947,0.2955,0.3017, 0.3077,0.3077,0.3201,0.3341,0.3342,0.3367,0.3391,0.3405,0.3417,0.3420, 0.3477,0.3514,0.3535,0.3558,0.3574,0.3574,0.3611,0.3658,0.3712,0.3784, 0.3795,0.3867,0.3906,0.3929,0.4042,0.4073,0.4127,0.4160,0.4190,0.4203, 0.4223,0.4283,0.4298,0.4325,0.4391,0.4397,0.4549,0.4725,0.4773,0.4818, 0.4848,0.4908,0.5043,0.5074,0.5129,0.5194,0.5220,0.5221,0.5323,0.5367, 0.5414,0.5421,0.5429,0.5441,0.5477,0.5525,0.5587,0.5603,0.5617,0.5628, 0.5802,0.5849,0.5853,0.5867,0.5981,0.6023,0.6048,0.6055,0.6085,0.6106, 0.6107,0.6127,0.6278,0.6363,0.6376,0.6473,0.6519,0.6550,0.6585,0.6587, 0.6611,0.6623,0.6649,0.6688,0.6708,0.6744,0.6780,0.6855,0.6937,0.6995, 0.7009,0.7009,0.7023,0.7069,0.7120,0.7125,0.7146,0.7260,0.7265,0.7302, 0.7387,0.7432,0.7440,0.7440,0.7562,0.7574,0.7589,0.7609,0.7644,0.7648, 0.7706,0.7819,0.7870,0.7919,0.8011,0.8028,0.8147,0.8166,0.8177,0.8184, 0.8260,0.8338,0.8361,0.8374,0.8395,0.8429,0.8492,0.8532,0.8672,0.8728, 0.8732,0.8754,0.8822,0.8865,0.8866,0.8907,0.8956,0.8961,0.8968,0.8972, 0.8984,0.9002,0.9030,0.9038,0.9059,0.9095,0.9104,0.9127,0.9158,0.9191, 0.9193,0.9201,0.9227,0.9271,0.9285,0.9338,0.9368,0.9374,0.9450,0.9455, 0.9593,0.9598,0.9623,0.9737,0.9739,0.9856,0.9858,0.9985,0.9995, Overall p-value after applying KStest on 269 p-values = 0.083607 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.