RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-03_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 15.97 25.8013 0.921843 2 to 25 15.77 19.0044 0.671718 3 to 26 15.79 14.7298 0.385063 4 to 27 15.58 17.4370 0.574842 5 to 28 15.71 21.0873 0.777592 6 to 29 16.11 17.4536 0.575931 7 to 30 16.02 20.8765 0.768137 8 to 31 15.64 12.2453 0.214937 9 to 32 15.83 11.0583 0.146484 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.798524 Tough bday spacings test for dh-ranFile-2016-12-03_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 11 39 76 86 95 80 51 42 13 2 5 (O-E)^2/E 0.4 0.2 0.1 1.4 0.1 0.0 0.0 5.0 0.2 3.2 0.2 Birthday Spacings: Sum(O-E)^2/E= 10.862, p= 0.632 RESULTS OF GCD FOR dh-ranFile-2016-12-03_05:31 Euclid's algorithm: p-value, steps to gcd: 0.208273 p-value, dist. of gcd's: 0.400703 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-03_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.756 0.353 0.904 0.342 0.724 0.721 0.768 0.387 Bits 8 to 15---> 0.823 0.585 0.411 0.293 0.442 0.787 0.237 0.388 Bits 16 to 23---> 0.658 0.711 0.494 0.423 0.564 0.644 0.180 0.886 Bits 24 to 31---> 0.488 0.355 0.319 0.714 0.475 0.322 0.997 0.309 KS test for the above 32 p values: 0.888 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-03_05:31, p-values for 5 runs: 0.7993, 0.5114, 0.2397, 0.6006, 0.6869 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-03_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5246 5134.0 2.443 2.715 r= 30 23097 23103.0 0.002 2.716 r= 31 11438 11551.5 1.116 3.832 chi-square = 3.832 with df = 3; p-value = 0.720 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-03_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5168 5134.0 0.225 0.860 r= 31 23179 23103.0 0.250 1.109 r= 32 11430 11551.5 1.278 2.388 chi-square = 2.388 with df = 3; p-value = 0.504 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-03_05:31 b-rank test for bits 1 to 8, p=0.88245 b-rank test for bits 2 to 9, p=0.46886 b-rank test for bits 3 to 10, p=0.75621 b-rank test for bits 4 to 11, p=0.90703 b-rank test for bits 5 to 12, p=0.60421 b-rank test for bits 6 to 13, p=0.68619 b-rank test for bits 7 to 14, p=0.63268 b-rank test for bits 8 to 15, p=0.57324 b-rank test for bits 9 to 16, p=0.88256 b-rank test for bits 10 to 17, p=0.13832 b-rank test for bits 11 to 18, p=0.51009 b-rank test for bits 12 to 19, p=0.18202 b-rank test for bits 13 to 20, p=0.91431 b-rank test for bits 14 to 21, p=0.14191 b-rank test for bits 15 to 22, p=0.85824 b-rank test for bits 16 to 23, p=0.67034 b-rank test for bits 17 to 24, p=0.16864 b-rank test for bits 18 to 25, p=0.88246 b-rank test for bits 19 to 26, p=0.51910 b-rank test for bits 20 to 27, p=0.15254 b-rank test for bits 21 to 28, p=0.68885 b-rank test for bits 22 to 29, p=0.88679 b-rank test for bits 23 to 30, p=0.98526 b-rank test for bits 24 to 31, p=0.58097 b-rank test for bits 25 to 32, p=0.50662 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 = 0.071907 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-03_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 141744 -0.39 0.349643 2 141894 -0.04 0.485714 3 142531 1.45 0.926819 4 142043 0.31 0.622599 5 142018 0.25 0.600214 6 141487 -0.99 0.161882 7 141481 -1.00 0.158469 8 142380 1.10 0.864268 9 141950 0.10 0.537852 10 141473 -1.02 0.153992 11 142001 0.21 0.584798 12 141703 -0.48 0.314875 13 142033 0.29 0.613690 14 142166 0.60 0.725646 15 142216 0.72 0.763164 16 142131 0.52 0.697743 17 142307 0.93 0.823591 18 141371 -1.26 0.104236 19 141851 -0.14 0.445798 20 141540 -0.86 0.194091 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-03_05:31 Bits used No. missing words z-score p-value 23 to 32 142476 1.9540 0.974651 22 to 31 142003 0.3230 0.626652 21 to 30 141502 -1.4046 0.080072 20 to 29 141935 0.0885 0.535267 19 to 28 141703 -0.7115 0.238393 18 to 27 142052 0.4920 0.688628 17 to 26 141684 -0.7770 0.218579 16 to 25 142135 0.7782 0.781766 15 to 24 142108 0.6851 0.753350 14 to 23 141882 -0.0942 0.462459 13 to 22 141766 -0.4942 0.310568 12 to 21 142441 1.8333 0.966624 11 to 20 142289 1.3092 0.904768 10 to 19 141487 -1.4563 0.072653 9 to 18 141766 -0.4942 0.310568 8 to 17 141770 -0.4804 0.315454 7 to 16 141726 -0.6322 0.263637 6 to 15 142350 1.5196 0.935688 5 to 14 142136 0.7816 0.782781 4 to 13 142218 1.0644 0.856422 3 to 12 142094 0.6368 0.737870 2 to 11 141892 -0.0598 0.476174 1 to 10 141421 -1.6839 0.046101 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-03_05:31 Bits used No. missing words z-score p-value 28 to 32 142705 2.6972 0.996504 27 to 31 142248 1.1480 0.874523 26 to 30 141939 0.1006 0.540057 25 to 29 141256 -2.2147 0.013391 24 to 28 141872 -0.1265 0.449651 23 to 27 141952 0.1446 0.557504 22 to 26 142047 0.4667 0.679635 21 to 25 142721 2.7514 0.997033 20 to 24 141970 0.2057 0.581472 19 to 23 141963 0.1819 0.572182 18 to 22 141741 -0.5706 0.284132 17 to 21 142131 0.7514 0.773801 16 to 20 141721 -0.6384 0.261605 15 to 19 142055 0.4938 0.689275 14 to 18 141959 0.1684 0.566855 13 to 17 141576 -1.1299 0.129252 12 to 16 141884 -0.0859 0.465787 11 to 15 141360 -1.8621 0.031292 10 to 14 141676 -0.7909 0.214487 9 to 13 142047 0.4667 0.679635 8 to 12 142036 0.4294 0.666180 7 to 11 141906 -0.0113 0.495497 6 to 10 141886 -0.0791 0.468483 5 to 9 142046 0.4633 0.678421 4 to 8 141399 -1.7299 0.041821 3 to 7 141722 -0.6350 0.262709 2 to 6 141737 -0.5842 0.279553 1 to 5 141817 -0.3130 0.377147 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-03_05:31 Bits used No. missing words z-score p-value 31 to 32 141927 0.0521 0.520785 30 to 31 141828 -0.2399 0.405199 29 to 30 141624 -0.8417 0.199983 28 to 29 141508 -1.1839 0.118233 27 to 28 141475 -1.2812 0.100060 26 to 27 142069 0.4710 0.681181 25 to 26 141850 -0.1750 0.430534 24 to 25 141813 -0.2842 0.388144 23 to 24 141735 -0.5142 0.303539 22 to 23 142360 1.3294 0.908144 21 to 22 142178 0.7925 0.785976 20 to 21 142048 0.4091 0.658751 19 to 20 141106 -2.3697 0.008901 18 to 19 141964 0.1613 0.564059 17 to 18 141735 -0.5142 0.303539 16 to 17 142431 1.5388 0.938080 15 to 16 142310 1.1819 0.881381 14 to 15 142097 0.5536 0.710073 13 to 14 142013 0.3058 0.620126 12 to 13 141778 -0.3874 0.349229 11 to 12 141903 -0.0187 0.492551 10 to 11 142168 0.7630 0.777280 9 to 10 141894 -0.0452 0.481966 8 to 9 141917 0.0226 0.509025 7 to 8 142062 0.4504 0.673772 6 to 7 141095 -2.4022 0.008149 5 to 6 142236 0.9636 0.832384 4 to 5 142104 0.5742 0.717100 3 to 4 141806 -0.3048 0.380256 2 to 3 142445 1.5801 0.942963 1 to 2 141948 0.1141 0.545409 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-03_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2534.81 0.492 0.688751 Test results for specific bytes for dh-ranFile-2016-12-03_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2435.27 -0.915 0.179986 2 to 9 2441.99 -0.820 0.205984 3 to 10 2397.13 -1.455 0.072869 4 to 11 2533.07 0.468 0.679997 5 to 12 2525.44 0.360 0.640505 6 to 13 2545.11 0.638 0.738240 7 to 14 2501.18 0.017 0.506680 8 to 15 2390.10 -1.554 0.060058 9 to 16 2495.00 -0.071 0.471835 10 to 17 2621.14 1.713 0.956654 11 to 18 2529.22 0.413 0.660297 12 to 19 2399.91 -1.416 0.078458 13 to 20 2458.56 -0.586 0.278898 14 to 21 2345.66 -2.183 0.014530 15 to 22 2435.16 -0.917 0.179595 16 to 23 2543.18 0.611 0.729300 17 to 24 2547.79 0.676 0.750414 18 to 25 2499.30 -0.010 0.496033 19 to 26 2554.87 0.776 0.781119 20 to 27 2424.04 -1.074 0.141350 21 to 28 2561.71 0.873 0.808590 22 to 29 2460.12 -0.564 0.286370 23 to 30 2541.29 0.584 0.720377 24 to 31 2414.45 -1.210 0.113166 25 to 32 2463.19 -0.521 0.301317 CDPARK for dh-ranFile-2016-12-03_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 3526 0.1370 0.554479 3523 0.0000 0.500000 3538 0.6849 0.753306 3534 0.5023 0.692266 3530 0.3196 0.625377 3541 0.8219 0.794438 3537 0.6393 0.738676 3511 -0.5479 0.291865 3491 -1.4612 0.071982 3543 0.9132 0.819442 Square side=100, avg. no. parked=3527.40 sample std.=15.16 p-value of the KSTEST for those 10 p-values: 0.330860 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-03_05:31 0.6386,0.1374,0.4673,0.0005,0.6504,0.9040,0.6276,0.9239,0.0838,0.1427, The KS test for those 10 p-values: 0.377551 The 3DSPHERES test for dh-ranFile-2016-12-03_05:31 sample no r^3 equiv. uni. 1 17.622 0.444227 2 6.080 0.183444 3 2.047 0.065951 4 4.158 0.129437 5 17.734 0.446301 6 79.341 0.928974 7 9.514 0.271757 8 27.111 0.594928 9 22.713 0.530979 10 71.117 0.906571 11 2.110 0.067910 12 22.679 0.530443 13 11.293 0.313702 14 83.569 0.938311 15 2.320 0.074423 16 32.720 0.664009 17 13.217 0.356335 18 25.060 0.566269 19 36.280 0.701602 20 27.109 0.594903 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.798513 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-03_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 -0.4 -0.8 -0.8 0.5 -0.8 -0.1 -1.2 0.5 -2.0 -0.1 0.9 1.6 -0.1 -2.4 1.8 -1.2 1.2 1.5 -2.5 0.8 -0.5 -0.0 1.9 0.2 0.8 0.2 -2.0 0.3 0.1 -0.3 -0.9 1.4 -0.5 1.3 -0.9 1.8 -1.2 0.4 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:56.512644 z-score=1.583459, p-value=0.933420 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-03_05:31 Test no p-value 1 0.125498 2 0.354279 3 0.188081 4 0.550370 5 0.559582 6 0.039400 7 0.928983 8 0.545382 9 0.256459 10 0.285273 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.335713 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-03_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 66784 0.21 66491 0.46 3 25000.00 24905 0.36 25102 0.42 4 6666.67 6617 0.37 6767 1.51 5 1388.89 1424 0.89 1360 0.60 6 238.10 234 0.07 238 0.00 7 34.72 29 0.94 37 0.15 8 4.96 6 0.22 4 0.19 p=0.19821 p=0.23297 Number of rngs required: 689865, p-value: 0.957 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-03_05:31 No. of wins: Observed Expected 98637 98585.9 z-score= 0.229, pvalue=0.59046 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66701 66666.7 0.018 0.018 2 37540 37654.3 0.347 0.365 3 26727 26954.7 1.924 2.289 4 19343 19313.5 0.045 2.334 5 14189 13851.4 8.227 10.561 6 9921 9943.5 0.051 10.612 7 7167 7145.0 0.068 10.680 8 5075 5139.1 0.799 11.479 9 3602 3699.9 2.589 14.067 10 2676 2666.3 0.035 14.103 11 1963 1923.3 0.818 14.921 12 1393 1388.7 0.013 14.934 13 1034 1003.7 0.914 15.848 14 720 726.1 0.052 15.900 15 566 525.8 3.068 18.968 16 392 381.2 0.309 19.276 17 268 276.5 0.264 19.540 18 200 200.8 0.003 19.544 19 142 146.0 0.109 19.652 20 103 106.2 0.097 19.750 21 278 287.1 0.289 20.039 Chisq= 20.04 for 20 degrees of freedom, p= 0.54450 SUMMARY of craptest p-value for no. of wins: 0.590462 p-value for throws/game: 0.544503 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-03_05:31 No. of wins: Observed Expected 98562 98585.9 z-score=-0.107, pvalue=0.45751 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66862 66666.7 0.572 0.572 2 37678 37654.3 0.015 0.587 3 26818 26954.7 0.694 1.281 4 19187 19313.5 0.828 2.109 5 13809 13851.4 0.130 2.239 6 9944 9943.5 0.000 2.239 7 7303 7145.0 3.493 5.732 8 5155 5139.1 0.049 5.781 9 3766 3699.9 1.182 6.963 10 2630 2666.3 0.494 7.457 11 1921 1923.3 0.003 7.460 12 1317 1388.7 3.706 11.166 13 1003 1003.7 0.001 11.167 14 719 726.1 0.070 11.237 15 507 525.8 0.675 11.911 16 379 381.2 0.012 11.924 17 282 276.5 0.108 12.031 18 187 200.8 0.952 12.984 19 123 146.0 3.619 16.603 20 118 106.2 1.308 17.910 21 292 287.1 0.083 17.993 Chisq= 17.99 for 20 degrees of freedom, p= 0.41215 SUMMARY of craptest p-value for no. of wins: 0.457510 p-value for throws/game: 0.412149 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0081,0.0089,0.0134,0.0145,0.0313,0.0394,0.0418,0.0461,0.0601, 0.0660,0.0679,0.0719,0.0720,0.0727,0.0729,0.0744,0.0785,0.0801,0.0838, 0.1001,0.1042,0.1132,0.1182,0.1255,0.1293,0.1294,0.1374,0.1383,0.1414, 0.1419,0.1427,0.1465,0.1525,0.1540,0.1585,0.1619,0.1686,0.1796,0.1799, 0.1800,0.1820,0.1834,0.1881,0.1941,0.1982,0.2000,0.2060,0.2083,0.2145, 0.2149,0.2186,0.2330,0.2370,0.2384,0.2397,0.2565,0.2616,0.2627,0.2636, 0.2718,0.2789,0.2796,0.2841,0.2853,0.2864,0.2919,0.2925,0.3013,0.3035, 0.3035,0.3092,0.3106,0.3106,0.3137,0.3149,0.3155,0.3188,0.3218,0.3309, 0.3357,0.3422,0.3492,0.3496,0.3535,0.3543,0.3547,0.3563,0.3771,0.3776, 0.3803,0.3851,0.3875,0.3881,0.3883,0.4007,0.4052,0.4106,0.4121,0.4228, 0.4305,0.4422,0.4442,0.4458,0.4463,0.4497,0.4575,0.4625,0.4658,0.4673, 0.4685,0.4689,0.4718,0.4747,0.4762,0.4820,0.4857,0.4882,0.4926,0.4944, 0.4955,0.4960,0.5000,0.5041,0.5066,0.5067,0.5090,0.5101,0.5114,0.5191, 0.5208,0.5304,0.5310,0.5353,0.5379,0.5401,0.5445,0.5454,0.5454,0.5504, 0.5545,0.5575,0.5596,0.5636,0.5641,0.5663,0.5669,0.5722,0.5732,0.5748, 0.5759,0.5810,0.5815,0.5848,0.5849,0.5905,0.5949,0.5949,0.6002,0.6006, 0.6042,0.6137,0.6201,0.6226,0.6254,0.6267,0.6276,0.6316,0.6327,0.6386, 0.6405,0.6440,0.6504,0.6581,0.6588,0.6603,0.6640,0.6662,0.6703,0.6717, 0.6738,0.6784,0.6796,0.6796,0.6800,0.6812,0.6862,0.6869,0.6886,0.6888, 0.6888,0.6893,0.6923,0.6977,0.7016,0.7101,0.7110,0.7143,0.7171,0.7198, 0.7204,0.7209,0.7242,0.7256,0.7293,0.7379,0.7382,0.7387,0.7504,0.7533, 0.7533,0.7556,0.7562,0.7632,0.7681,0.7682,0.7738,0.7773,0.7776,0.7811, 0.7818,0.7828,0.7860,0.7872,0.7944,0.7985,0.7985,0.7993,0.8086,0.8194, 0.8229,0.8236,0.8324,0.8564,0.8582,0.8643,0.8745,0.8814,0.8825,0.8825, 0.8826,0.8864,0.8868,0.8877,0.9038,0.9040,0.9048,0.9066,0.9070,0.9081, 0.9143,0.9218,0.9239,0.9268,0.9290,0.9290,0.9334,0.9357,0.9381,0.9383, 0.9430,0.9567,0.9568,0.9666,0.9747,0.9853,0.9965,0.9969,0.9970, Overall p-value after applying KStest on 269 p-values = 0.163030 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.