RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-10_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 15.81 17.7209 0.593348 2 to 25 15.94 20.8370 0.766335 3 to 26 15.44 17.9330 0.606922 4 to 27 15.79 11.3260 0.160877 5 to 28 15.88 19.5170 0.700323 6 to 29 15.94 9.7422 0.085929 7 to 30 15.63 19.9557 0.723497 8 to 31 15.50 18.3917 0.635460 9 to 32 15.46 25.8881 0.923477 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.450214 Tough bday spacings test for dh-ranFile-2016-08-10_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 13 38 78 87 91 76 76 26 10 5 0 (O-E)^2/E 1.6 0.1 0.3 1.2 0.5 0.1 11.0 0.5 1.6 0.4 4.1 Birthday Spacings: Sum(O-E)^2/E= 21.162, p= 0.980 RESULTS OF GCD FOR dh-ranFile-2016-08-10_06:31 Euclid's algorithm: p-value, steps to gcd: 0.887781 p-value, dist. of gcd's: 0.497153 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-10_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.513 0.422 0.657 0.057 0.110 0.837 0.688 0.519 Bits 8 to 15---> 0.891 0.612 0.120 0.144 0.197 0.650 0.682 0.182 Bits 16 to 23---> 0.315 0.393 0.128 0.035 0.255 0.515 0.557 0.638 Bits 24 to 31---> 0.116 0.043 0.727 0.938 0.480 0.064 0.539 0.390 KS test for the above 32 p values: 0.851 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-10_06:31, p-values for 5 runs: 0.9672, 0.7212, 0.8280, 0.7073, 0.5902 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-10_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 237 211.4 3.095 3.095 r= 29 5210 5134.0 1.125 4.220 r= 30 23007 23103.0 0.399 4.620 r= 31 11546 11551.5 0.003 4.622 chi-square = 4.622 with df = 3; p-value = 0.798 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-10_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 189 211.4 2.377 2.377 r= 30 5040 5134.0 1.721 4.099 r= 31 23192 23103.0 0.342 4.441 r= 32 11579 11551.5 0.065 4.506 chi-square = 4.506 with df = 3; p-value = 0.788 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-10_06:31 b-rank test for bits 1 to 8, p=0.93814 b-rank test for bits 2 to 9, p=0.00581 b-rank test for bits 3 to 10, p=0.11681 b-rank test for bits 4 to 11, p=0.53787 b-rank test for bits 5 to 12, p=0.73237 b-rank test for bits 6 to 13, p=0.21016 b-rank test for bits 7 to 14, p=0.50622 b-rank test for bits 8 to 15, p=0.17524 b-rank test for bits 9 to 16, p=0.25033 b-rank test for bits 10 to 17, p=0.26479 b-rank test for bits 11 to 18, p=0.94080 b-rank test for bits 12 to 19, p=0.23191 b-rank test for bits 13 to 20, p=0.15716 b-rank test for bits 14 to 21, p=0.05553 b-rank test for bits 15 to 22, p=0.85388 b-rank test for bits 16 to 23, p=0.21386 b-rank test for bits 17 to 24, p=0.00600 b-rank test for bits 18 to 25, p=0.14858 b-rank test for bits 19 to 26, p=0.46122 b-rank test for bits 20 to 27, p=0.75418 b-rank test for bits 21 to 28, p=0.59321 b-rank test for bits 22 to 29, p=0.34593 b-rank test for bits 23 to 30, p=0.54557 b-rank test for bits 24 to 31, p=0.82504 b-rank test for bits 25 to 32, p=0.14419 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 = 0.096658 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-10_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 141939 0.07 0.527634 2 142764 2.00 0.977082 3 141492 -0.98 0.164763 4 141708 -0.47 0.319036 5 141913 0.01 0.503421 6 141123 -1.84 0.033089 7 141334 -1.34 0.089437 8 141336 -1.34 0.090195 9 141334 -1.34 0.089437 10 142174 0.62 0.731840 11 142757 1.98 0.976178 12 142180 0.63 0.736439 13 142093 0.43 0.666088 14 141784 -0.29 0.384827 15 141814 -0.22 0.411871 16 141772 -0.32 0.374157 17 141607 -0.71 0.239976 18 142092 0.43 0.665237 19 141239 -1.57 0.058652 20 141331 -1.35 0.088310 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-10_06:31 Bits used No. missing words z-score p-value 23 to 32 141885 -0.0839 0.466569 22 to 31 141889 -0.0701 0.472056 21 to 30 142049 0.4816 0.684962 20 to 29 142381 1.6264 0.948073 19 to 28 142197 0.9920 0.839393 18 to 27 141620 -0.9977 0.159215 17 to 26 141726 -0.6322 0.263637 16 to 25 141328 -2.0046 0.022504 15 to 24 141450 -1.5839 0.056609 14 to 23 141410 -1.7218 0.042550 13 to 22 141735 -0.6011 0.273874 12 to 21 142235 1.1230 0.869281 11 to 20 142003 0.3230 0.626652 10 to 19 141730 -0.6184 0.268163 9 to 18 141635 -0.9460 0.172083 8 to 17 141822 -0.3011 0.381655 7 to 16 141741 -0.5804 0.280806 6 to 15 142159 0.8609 0.805362 5 to 14 142260 1.2092 0.886708 4 to 13 141928 0.0644 0.525666 3 to 12 142293 1.3230 0.907082 2 to 11 142327 1.4402 0.925100 1 to 10 141705 -0.7046 0.240534 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-10_06:31 Bits used No. missing words z-score p-value 28 to 32 142121 0.7175 0.763475 27 to 31 142094 0.6260 0.734343 26 to 30 142048 0.4701 0.680847 25 to 29 142096 0.6328 0.736561 24 to 28 142383 1.6057 0.945826 23 to 27 141321 -1.9943 0.023058 22 to 26 142180 0.9175 0.820566 21 to 25 142003 0.3175 0.624578 20 to 24 141829 -0.2723 0.392694 19 to 23 142053 0.4870 0.686877 18 to 22 142084 0.5921 0.723109 17 to 21 141971 0.2091 0.582796 16 to 20 141640 -0.9130 0.180626 15 to 19 141808 -0.3435 0.365614 14 to 18 141466 -1.5028 0.066444 13 to 17 142325 1.4091 0.920590 12 to 16 141616 -0.9943 0.160029 11 to 15 141690 -0.7435 0.228592 10 to 14 141641 -0.9096 0.181519 9 to 13 142380 1.5955 0.944699 8 to 12 142314 1.3718 0.914931 7 to 11 142003 0.3175 0.624578 6 to 10 141847 -0.2113 0.416331 5 to 9 142149 0.8124 0.791731 4 to 8 141995 0.2904 0.614248 3 to 7 142113 0.6904 0.755031 2 to 6 142001 0.3107 0.622003 1 to 5 142014 0.3548 0.638635 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-10_06:31 Bits used No. missing words z-score p-value 31 to 32 141875 -0.1013 0.459669 30 to 31 142264 1.0462 0.852271 29 to 30 141438 -1.3904 0.082211 28 to 29 141774 -0.3992 0.344872 27 to 28 141920 0.0315 0.512555 26 to 27 141977 0.1996 0.579110 25 to 26 141578 -0.9774 0.164192 24 to 25 141711 -0.5850 0.279259 23 to 24 142617 2.0875 0.981580 22 to 23 141237 -1.9833 0.023668 21 to 22 141559 -1.0334 0.150703 20 to 21 142137 0.6716 0.749079 19 to 20 141657 -0.7443 0.228337 18 to 19 141870 -0.1160 0.453819 17 to 18 142719 2.3884 0.991539 16 to 17 141740 -0.4995 0.308714 15 to 16 142234 0.9577 0.830900 14 to 15 142201 0.8604 0.805211 13 to 14 141279 -1.8594 0.031487 12 to 13 141444 -1.3727 0.084930 11 to 12 141560 -1.0305 0.151394 10 to 11 141815 -0.2783 0.390407 9 to 10 141443 -1.3756 0.084472 8 to 9 142174 0.7807 0.782522 7 to 8 142088 0.5271 0.700921 6 to 7 141943 0.0993 0.539559 5 to 6 141567 -1.0098 0.156290 4 to 5 142312 1.1878 0.882547 3 to 4 142019 0.3235 0.626846 2 to 3 141291 -1.8240 0.034077 1 to 2 142753 2.4887 0.993589 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-10_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2585.29 1.206 0.886126 Test results for specific bytes for dh-ranFile-2016-08-10_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2666.78 2.359 0.990830 2 to 9 2490.23 -0.138 0.445081 3 to 10 2407.20 -1.312 0.094705 4 to 11 2590.40 1.278 0.899462 5 to 12 2271.01 -3.238 0.000601 6 to 13 2484.17 -0.224 0.411456 7 to 14 2543.53 0.616 0.730925 8 to 15 2595.71 1.354 0.912054 9 to 16 2470.85 -0.412 0.340095 10 to 17 2496.85 -0.044 0.482257 11 to 18 2420.80 -1.120 0.131341 12 to 19 2533.39 0.472 0.681587 13 to 20 2473.93 -0.369 0.356173 14 to 21 2523.61 0.334 0.630794 15 to 22 2537.54 0.531 0.702236 16 to 23 2555.45 0.784 0.783549 17 to 24 2513.59 0.192 0.576200 18 to 25 2555.84 0.790 0.785148 19 to 26 2422.69 -1.093 0.137125 20 to 27 2446.10 -0.762 0.222949 21 to 28 2714.53 3.034 0.998793 22 to 29 2548.01 0.679 0.751409 23 to 30 2470.54 -0.417 0.338461 24 to 31 2643.67 2.032 0.978910 25 to 32 2461.74 -0.541 0.294205 CDPARK for dh-ranFile-2016-08-10_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 3482 -1.8721 0.030593 3491 -1.4612 0.071982 3532 0.4110 0.659449 3489 -1.5525 0.060270 3531 0.3653 0.642555 3532 0.4110 0.659449 3509 -0.6393 0.261324 3523 0.0000 0.500000 3533 0.4566 0.676028 3531 0.3653 0.642555 Square side=100, avg. no. parked=3515.30 sample std.=19.63 p-value of the KSTEST for those 10 p-values: 0.245155 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-10_06:31 0.0559,0.5118,0.9306,0.4519,0.1924,0.8959,0.6767,0.5986,0.0182,0.7828, The KS test for those 10 p-values: 0.890473 The 3DSPHERES test for dh-ranFile-2016-08-10_06:31 sample no r^3 equiv. uni. 1 6.072 0.183242 2 32.840 0.665349 3 0.173 0.005755 4 30.468 0.637809 5 7.372 0.217873 6 5.680 0.172494 7 31.558 0.650733 8 42.715 0.759210 9 16.494 0.422941 10 19.496 0.477876 11 20.497 0.495024 12 20.393 0.493273 13 1.101 0.036050 14 1.174 0.038389 15 110.961 0.975244 16 5.432 0.165611 17 52.607 0.826847 18 98.020 0.961892 19 49.286 0.806574 20 18.344 0.457442 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.760185 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-10_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 1.3 -2.3 1.6 -0.1 -0.2 -0.6 -2.2 1.3 2.1 -1.1 0.2 0.9 0.8 0.5 -1.0 -2.3 0.4 0.4 0.8 -1.6 0.0 0.5 1.3 1.5 -0.5 -1.1 -0.1 0.2 0.8 0.6 -1.3 -2.2 -1.2 -0.1 0.2 -2.1 -0.1 -0.8 1.0 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:55.125901 z-score=1.432153, p-value=0.915662 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-10_06:31 Test no p-value 1 0.115848 2 0.052097 3 0.167502 4 0.000263 5 0.446985 6 0.828211 7 0.543731 8 0.324689 9 0.950868 10 0.522232 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.222505 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-10_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 66666 0.00 66712 0.03 3 25000.00 25080 0.26 24983 0.01 4 6666.67 6568 1.46 6628 0.22 5 1388.89 1391 0.00 1405 0.19 6 238.10 260 2.02 231 0.21 7 34.72 32 0.21 29 0.94 8 4.96 2 1.77 11 7.36 p=0.54406 p=0.82430 Number of rngs required: 687242, p-value: 0.088 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-10_06:31 No. of wins: Observed Expected 98558 98585.9 z-score=-0.125, pvalue=0.45042 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66705 66666.7 0.022 0.022 2 37511 37654.3 0.546 0.568 3 26684 26954.7 2.719 3.287 4 19378 19313.5 0.216 3.502 5 13945 13851.4 0.632 4.135 6 10019 9943.5 0.573 4.707 7 7198 7145.0 0.393 5.100 8 5146 5139.1 0.009 5.109 9 3682 3699.9 0.086 5.196 10 2672 2666.3 0.012 5.208 11 1936 1923.3 0.083 5.291 12 1397 1388.7 0.049 5.340 13 1029 1003.7 0.637 5.977 14 707 726.1 0.505 6.482 15 517 525.8 0.148 6.630 16 410 381.2 2.184 8.814 17 313 276.5 4.807 13.621 18 199 200.8 0.017 13.638 19 130 146.0 1.750 15.388 20 127 106.2 4.067 19.455 21 295 287.1 0.217 19.672 Chisq= 19.67 for 20 degrees of freedom, p= 0.52139 SUMMARY of craptest p-value for no. of wins: 0.450420 p-value for throws/game: 0.521387 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-10_06:31 No. of wins: Observed Expected 98903 98585.9 z-score= 1.418, pvalue=0.92197 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66895 66666.7 0.782 0.782 2 37384 37654.3 1.941 2.723 3 26980 26954.7 0.024 2.746 4 19240 19313.5 0.279 3.026 5 13960 13851.4 0.851 3.877 6 10036 9943.5 0.860 4.737 7 7057 7145.0 1.084 5.821 8 5161 5139.1 0.094 5.915 9 3766 3699.9 1.182 7.097 10 2594 2666.3 1.960 9.057 11 1866 1923.3 1.709 10.766 12 1362 1388.7 0.515 11.281 13 1012 1003.7 0.068 11.349 14 702 726.1 0.803 12.152 15 556 525.8 1.730 13.882 16 369 381.2 0.387 14.270 17 283 276.5 0.151 14.420 18 227 200.8 3.410 17.831 19 151 146.0 0.172 18.003 20 99 106.2 0.490 18.493 21 300 287.1 0.578 19.071 Chisq= 19.07 for 20 degrees of freedom, p= 0.48281 SUMMARY of craptest p-value for no. of wins: 0.921969 p-value for throws/game: 0.482814 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0006,0.0058,0.0058,0.0060,0.0182,0.0225,0.0231,0.0237,0.0306, 0.0315,0.0331,0.0341,0.0350,0.0360,0.0384,0.0426,0.0427,0.0521,0.0555, 0.0559,0.0566,0.0567,0.0587,0.0603,0.0637,0.0664,0.0720,0.0822,0.0845, 0.0849,0.0859,0.0881,0.0883,0.0894,0.0894,0.0902,0.0947,0.0967,0.1101, 0.1158,0.1159,0.1168,0.1196,0.1277,0.1313,0.1371,0.1439,0.1442,0.1486, 0.1507,0.1514,0.1563,0.1572,0.1592,0.1600,0.1609,0.1642,0.1648,0.1656, 0.1675,0.1721,0.1725,0.1752,0.1806,0.1815,0.1822,0.1832,0.1924,0.1972, 0.2102,0.2139,0.2179,0.2225,0.2229,0.2283,0.2286,0.2319,0.2400,0.2405, 0.2452,0.2503,0.2555,0.2613,0.2636,0.2648,0.2682,0.2739,0.2793,0.2808, 0.2942,0.3087,0.3152,0.3190,0.3247,0.3385,0.3401,0.3449,0.3459,0.3562, 0.3656,0.3742,0.3817,0.3848,0.3903,0.3904,0.3927,0.3935,0.4115,0.4119, 0.4163,0.4221,0.4229,0.4451,0.4470,0.4502,0.4504,0.4519,0.4538,0.4574, 0.4597,0.4612,0.4666,0.4721,0.4779,0.4804,0.4823,0.4828,0.4933,0.4950, 0.4972,0.5000,0.5034,0.5062,0.5118,0.5125,0.5126,0.5146,0.5187,0.5214, 0.5222,0.5257,0.5276,0.5379,0.5391,0.5396,0.5437,0.5441,0.5456,0.5572, 0.5762,0.5791,0.5828,0.5902,0.5932,0.5933,0.5986,0.6069,0.6117,0.6142, 0.6220,0.6246,0.6246,0.6267,0.6268,0.6308,0.6355,0.6378,0.6382,0.6386, 0.6426,0.6426,0.6496,0.6507,0.6569,0.6594,0.6594,0.6652,0.6653,0.6661, 0.6760,0.6767,0.6808,0.6816,0.6824,0.6850,0.6869,0.6882,0.7003,0.7009, 0.7022,0.7073,0.7212,0.7231,0.7235,0.7265,0.7309,0.7318,0.7324,0.7343, 0.7364,0.7366,0.7491,0.7514,0.7542,0.7550,0.7592,0.7602,0.7635,0.7663, 0.7825,0.7828,0.7835,0.7851,0.7883,0.7917,0.7983,0.8052,0.8054,0.8066, 0.8206,0.8243,0.8250,0.8268,0.8280,0.8282,0.8309,0.8373,0.8394,0.8514, 0.8523,0.8539,0.8693,0.8825,0.8861,0.8867,0.8878,0.8905,0.8913,0.8959, 0.8995,0.9071,0.9121,0.9149,0.9157,0.9206,0.9220,0.9235,0.9251,0.9306, 0.9381,0.9384,0.9408,0.9447,0.9458,0.9481,0.9509,0.9619,0.9672,0.9752, 0.9762,0.9771,0.9789,0.9800,0.9816,0.9908,0.9915,0.9936,0.9988, Overall p-value after applying KStest on 269 p-values = 0.237345 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.