RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-10_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.38 27.0382 0.942490 2 to 25 15.50 23.4900 0.866031 3 to 26 15.69 13.7529 0.315492 4 to 27 15.98 25.3264 0.912362 5 to 28 15.52 18.9679 0.669623 6 to 29 15.80 18.8182 0.660936 7 to 30 15.59 25.2885 0.911565 8 to 31 16.09 14.3724 0.359412 9 to 32 16.06 25.7840 0.921513 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.016494 Tough bday spacings test for dh-ranFile-2016-01-10_21:31: 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 36 64 109 97 75 52 33 16 9 0 (O-E)^2/E 0.0 0.0 1.2 1.3 0.0 0.1 0.0 0.4 0.1 0.9 4.1 Birthday Spacings: Sum(O-E)^2/E= 7.987, p= 0.370 RESULTS OF GCD FOR dh-ranFile-2016-01-10_21:31 Euclid's algorithm: p-value, steps to gcd: 0.745113 p-value, dist. of gcd's: 0.429625 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-10_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.838 0.632 0.449 0.086 0.361 0.406 0.326 0.984 Bits 8 to 15---> 0.777 0.533 0.098 0.164 0.491 0.033 0.164 0.973 Bits 16 to 23---> 0.634 0.541 0.345 0.794 0.180 0.874 0.436 0.735 Bits 24 to 31---> 0.390 0.200 0.111 0.258 0.814 0.183 0.715 0.685 KS test for the above 32 p values: 0.070 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-10_21:31, p-values for 5 runs: 0.5191, 0.7358, 0.5750, 0.7922, 0.1639 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-10_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5187 5134.0 0.547 1.060 r= 30 23029 23103.0 0.237 1.298 r= 31 11583 11551.5 0.086 1.383 chi-square = 1.383 with df = 3; p-value = 0.291 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-10_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 235 211.4 2.630 2.630 r= 30 5186 5134.0 0.526 3.157 r= 31 22996 23103.0 0.496 3.653 r= 32 11583 11551.5 0.086 3.739 chi-square = 3.739 with df = 3; p-value = 0.709 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-10_21:31 b-rank test for bits 1 to 8, p=0.72310 b-rank test for bits 2 to 9, p=0.95272 b-rank test for bits 3 to 10, p=0.05733 b-rank test for bits 4 to 11, p=0.03543 b-rank test for bits 5 to 12, p=0.77923 b-rank test for bits 6 to 13, p=0.96332 b-rank test for bits 7 to 14, p=0.69958 b-rank test for bits 8 to 15, p=0.50937 b-rank test for bits 9 to 16, p=0.78728 b-rank test for bits 10 to 17, p=0.24350 b-rank test for bits 11 to 18, p=0.97022 b-rank test for bits 12 to 19, p=0.34474 b-rank test for bits 13 to 20, p=0.62816 b-rank test for bits 14 to 21, p=0.76463 b-rank test for bits 15 to 22, p=0.21431 b-rank test for bits 16 to 23, p=0.67038 b-rank test for bits 17 to 24, p=0.49486 b-rank test for bits 18 to 25, p=0.12929 b-rank test for bits 19 to 26, p=0.74631 b-rank test for bits 20 to 27, p=0.15373 b-rank test for bits 21 to 28, p=0.54197 b-rank test for bits 22 to 29, p=0.40143 b-rank test for bits 23 to 30, p=0.59711 b-rank test for bits 24 to 31, p=0.02242 b-rank test for bits 25 to 32, p=0.30583 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 = 0.949849 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-10_21:31 (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 142096 0.44 0.668634 2 142688 1.82 0.965569 3 142696 1.84 0.966970 4 141412 -1.16 0.122621 5 141985 0.18 0.570167 6 142046 0.32 0.625259 7 141613 -0.69 0.244356 8 141594 -0.74 0.230637 9 141547 -0.85 0.198619 10 141451 -1.07 0.142115 11 142240 0.77 0.780119 12 142602 1.62 0.947210 13 141936 0.06 0.524843 14 141912 0.01 0.502489 15 142395 1.13 0.871759 16 142021 0.26 0.602920 17 142642 1.71 0.956537 18 142096 0.44 0.668634 19 140918 -2.32 0.010274 20 142300 0.91 0.819321 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-10_21:31 Bits used No. missing words z-score p-value 23 to 32 142017 0.3713 0.644784 22 to 31 141716 -0.6667 0.252496 21 to 30 141854 -0.1908 0.424344 20 to 29 142167 0.8885 0.812869 19 to 28 141780 -0.4460 0.327811 18 to 27 141838 -0.2460 0.402855 17 to 26 141819 -0.3115 0.377717 16 to 25 141238 -2.3149 0.010308 15 to 24 141018 -3.0736 0.001058 14 to 23 141604 -1.0529 0.146202 13 to 22 141777 -0.4563 0.324083 12 to 21 142093 0.6333 0.736746 11 to 20 141485 -1.4632 0.071705 10 to 19 142151 0.8333 0.797675 9 to 18 142113 0.7023 0.758757 8 to 17 141359 -1.8977 0.028868 7 to 16 141531 -1.3046 0.096017 6 to 15 142075 0.5713 0.716094 5 to 14 141779 -0.4494 0.326567 4 to 13 141539 -1.2770 0.100801 3 to 12 141619 -1.0011 0.158380 2 to 11 141796 -0.3908 0.347975 1 to 10 141616 -1.0115 0.155893 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-10_21:31 Bits used No. missing words z-score p-value 28 to 32 142231 1.0904 0.862233 27 to 31 141992 0.2802 0.610352 26 to 30 142215 1.0362 0.849938 25 to 29 141872 -0.1265 0.449651 24 to 28 141966 0.1921 0.576169 23 to 27 142097 0.6362 0.737667 22 to 26 141708 -0.6825 0.247470 21 to 25 142120 0.7141 0.762428 20 to 24 142305 1.3413 0.910081 19 to 23 142037 0.4328 0.667413 18 to 22 142003 0.3175 0.624578 17 to 21 141493 -1.4113 0.079080 16 to 20 141658 -0.8520 0.197116 15 to 19 141979 0.2362 0.593349 14 to 18 142053 0.4870 0.686877 13 to 17 141611 -1.0113 0.155939 12 to 16 141914 0.0158 0.506315 11 to 15 141616 -0.9943 0.160029 10 to 14 141879 -0.1028 0.459056 9 to 13 142292 1.2972 0.902717 8 to 12 141520 -1.3198 0.093457 7 to 11 141759 -0.5096 0.305168 6 to 10 142525 2.0870 0.981557 5 to 9 142122 0.7209 0.764519 4 to 8 142238 1.1141 0.867390 3 to 7 141859 -0.1706 0.432265 2 to 6 141762 -0.4994 0.308741 1 to 5 141329 -1.9672 0.024579 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-10_21:31 Bits used No. missing words z-score p-value 31 to 32 141787 -0.3609 0.359104 30 to 31 141236 -1.9862 0.023504 29 to 30 142171 0.7719 0.779910 28 to 29 141781 -0.3786 0.352509 27 to 28 141407 -1.4818 0.069197 26 to 27 142159 0.7365 0.769284 25 to 26 141762 -0.4346 0.331926 24 to 25 142028 0.3501 0.636853 23 to 24 141765 -0.4258 0.335144 22 to 23 141721 -0.5555 0.289261 21 to 22 142003 0.2763 0.608846 20 to 21 141635 -0.8092 0.209191 19 to 20 142155 0.7247 0.765679 18 to 19 141581 -0.9685 0.166391 17 to 18 141747 -0.4788 0.316023 16 to 17 142311 1.1849 0.881965 15 to 16 142337 1.2616 0.896447 14 to 15 142644 2.1672 0.984889 13 to 14 141951 0.1229 0.548915 12 to 13 142026 0.3442 0.634637 11 to 12 141864 -0.1337 0.446813 10 to 11 142088 0.5271 0.700921 9 to 10 142071 0.4769 0.683284 8 to 9 141755 -0.4553 0.324464 7 to 8 142083 0.5123 0.695780 6 to 7 141337 -1.6883 0.045678 5 to 6 141846 -0.1868 0.425903 4 to 5 141889 -0.0600 0.476090 3 to 4 142030 0.3560 0.639064 2 to 3 142035 0.3707 0.644573 1 to 2 142291 1.1259 0.869890 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-10_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2417.75 -1.163 0.122369 Test results for specific bytes for dh-ranFile-2016-01-10_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2402.76 -1.375 0.084537 2 to 9 2451.68 -0.683 0.247174 3 to 10 2491.06 -0.126 0.449714 4 to 11 2540.20 0.569 0.715166 5 to 12 2479.45 -0.291 0.385690 6 to 13 2395.08 -1.484 0.068940 7 to 14 2442.20 -0.817 0.206852 8 to 15 2464.43 -0.503 0.307468 9 to 16 2489.97 -0.142 0.443598 10 to 17 2282.07 -3.082 0.001028 11 to 18 2553.28 0.754 0.774444 12 to 19 2407.91 -1.302 0.096388 13 to 20 2403.93 -1.359 0.087135 14 to 21 2359.38 -1.989 0.023371 15 to 22 2519.04 0.269 0.606162 16 to 23 2366.01 -1.895 0.029050 17 to 24 2333.36 -2.357 0.009221 18 to 25 2526.06 0.369 0.643773 19 to 26 2428.27 -1.014 0.155190 20 to 27 2534.11 0.482 0.685227 21 to 28 2445.79 -0.767 0.221641 22 to 29 2552.73 0.746 0.772072 23 to 30 2707.56 2.935 0.998334 24 to 31 2431.15 -0.974 0.165121 25 to 32 2637.16 1.940 0.973790 CDPARK for dh-ranFile-2016-01-10_21:31: 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 3539 0.7306 0.767486 3540 0.7763 0.781201 3492 -1.4155 0.078457 3513 -0.4566 0.323972 3526 0.1370 0.554479 3557 1.5525 0.939730 3539 0.7306 0.767486 3500 -1.0502 0.146807 3512 -0.5023 0.307734 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3522.40 sample std.=19.91 p-value of the KSTEST for those 10 p-values: 0.954922 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-10_21:31 0.2162,0.8167,0.6557,0.3287,0.4829,0.5958,0.3426,0.1315,0.0915,0.5144, The KS test for those 10 p-values: 0.551520 The 3DSPHERES test for dh-ranFile-2016-01-10_21:31 sample no r^3 equiv. uni. 1 12.602 0.342991 2 51.116 0.818022 3 2.182 0.070150 4 75.530 0.919352 5 37.106 0.709705 6 12.503 0.340820 7 11.488 0.318136 8 2.358 0.075592 9 33.748 0.675327 10 23.563 0.544085 11 68.501 0.898060 12 5.809 0.176037 13 19.559 0.478973 14 25.251 0.569026 15 5.456 0.166294 16 67.183 0.893481 17 1.454 0.047317 18 8.085 0.236226 19 26.747 0.589983 20 1.485 0.048306 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.634234 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-10_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.5 -0.1 -0.4 -1.2 -0.5 0.4 0.1 -2.2 0.0 1.6 1.0 -2.7 0.4 0.4 -0.7 1.3 -0.1 1.3 1.4 -1.3 1.3 -1.2 0.4 -1.7 -0.6 -1.2 -1.1 1.0 0.4 0.5 -1.1 0.3 0.4 0.6 -0.3 1.0 0.5 0.1 0.4 2.4 -1.0 -0.1 Chi-square with 42 degrees of freedom:48.358012 z-score=0.693716, p-value=0.768360 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-10_21:31 Test no p-value 1 0.315708 2 0.097442 3 0.013252 4 0.117842 5 0.496628 6 0.615539 7 0.481835 8 0.643094 9 0.077261 10 0.485414 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.087153 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-10_21:31: (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 66554 0.19 66867 0.60 3 25000.00 25171 1.17 24898 0.42 4 6666.67 6610 0.48 6624 0.27 5 1388.89 1397 0.05 1317 3.72 6 238.10 235 0.04 252 0.81 7 34.72 31 0.40 34 0.01 8 4.96 1 3.16 7 0.84 p=0.51728 p=0.64838 Number of rngs required: 687397, p-value: 0.121 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-10_21:31 No. of wins: Observed Expected 98673 98585.9 z-score= 0.390, pvalue=0.65164 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66408 66666.7 1.004 1.004 2 37785 37654.3 0.454 1.457 3 26813 26954.7 0.745 2.202 4 19156 19313.5 1.284 3.486 5 14031 13851.4 2.328 5.814 6 9966 9943.5 0.051 5.865 7 7258 7145.0 1.786 7.651 8 5166 5139.1 0.141 7.793 9 3717 3699.9 0.079 7.872 10 2752 2666.3 2.755 10.627 11 1910 1923.3 0.092 10.719 12 1385 1388.7 0.010 10.729 13 1032 1003.7 0.797 11.526 14 692 726.1 1.605 13.131 15 500 525.8 1.269 14.401 16 395 381.2 0.503 14.904 17 275 276.5 0.009 14.912 18 198 200.8 0.040 14.952 19 173 146.0 4.999 19.952 20 101 106.2 0.256 20.208 21 287 287.1 0.000 20.208 Chisq= 20.21 for 20 degrees of freedom, p= 0.55501 SUMMARY of craptest p-value for no. of wins: 0.651638 p-value for throws/game: 0.555009 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-10_21:31 No. of wins: Observed Expected 98461 98585.9 z-score=-0.558, pvalue=0.28827 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66398 66666.7 1.083 1.083 2 37968 37654.3 2.613 3.696 3 27016 26954.7 0.139 3.835 4 19112 19313.5 2.101 5.937 5 13890 13851.4 0.107 6.044 6 9960 9943.5 0.027 6.071 7 7261 7145.0 1.882 7.954 8 5035 5139.1 2.108 10.061 9 3785 3699.9 1.959 12.020 10 2659 2666.3 0.020 12.040 11 1921 1923.3 0.003 12.043 12 1351 1388.7 1.026 13.069 13 1007 1003.7 0.011 13.079 14 698 726.1 1.091 14.170 15 499 525.8 1.370 15.540 16 396 381.2 0.579 16.118 17 288 276.5 0.475 16.593 18 230 200.8 4.237 20.830 19 155 146.0 0.557 21.387 20 108 106.2 0.030 21.417 21 263 287.1 2.025 23.442 Chisq= 23.44 for 20 degrees of freedom, p= 0.73238 SUMMARY of craptest p-value for no. of wins: 0.288272 p-value for throws/game: 0.732383 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0010,0.0011,0.0092,0.0103,0.0103,0.0133,0.0165,0.0224,0.0234,0.0235, 0.0246,0.0289,0.0291,0.0327,0.0354,0.0457,0.0473,0.0483,0.0573,0.0689, 0.0692,0.0698,0.0701,0.0717,0.0756,0.0773,0.0785,0.0791,0.0845,0.0859, 0.0871,0.0872,0.0915,0.0935,0.0960,0.0964,0.0974,0.0982,0.1008,0.1106, 0.1178,0.1213,0.1224,0.1226,0.1293,0.1315,0.1421,0.1462,0.1468,0.1537, 0.1552,0.1559,0.1559,0.1584,0.1600,0.1637,0.1639,0.1640,0.1651,0.1663, 0.1664,0.1760,0.1804,0.1828,0.1971,0.1986,0.1998,0.2069,0.2092,0.2143, 0.2162,0.2188,0.2216,0.2306,0.2362,0.2435,0.2444,0.2472,0.2475,0.2525, 0.2578,0.2883,0.2893,0.2906,0.3052,0.3058,0.3075,0.3077,0.3087,0.3155, 0.3157,0.3160,0.3181,0.3240,0.3241,0.3245,0.3261,0.3266,0.3278,0.3287, 0.3319,0.3351,0.3408,0.3426,0.3430,0.3447,0.3455,0.3480,0.3525,0.3591, 0.3594,0.3612,0.3699,0.3777,0.3857,0.3897,0.4014,0.4029,0.4063,0.4243, 0.4259,0.4296,0.4323,0.4356,0.4436,0.4468,0.4494,0.4497,0.4497,0.4591, 0.4761,0.4790,0.4818,0.4829,0.4854,0.4915,0.4949,0.4966,0.5025,0.5063, 0.5094,0.5144,0.5173,0.5191,0.5248,0.5326,0.5410,0.5420,0.5441,0.5489, 0.5515,0.5545,0.5550,0.5690,0.5702,0.5750,0.5762,0.5900,0.5933,0.5958, 0.5971,0.6029,0.6062,0.6088,0.6104,0.6155,0.6246,0.6253,0.6282,0.6320, 0.6336,0.6342,0.6346,0.6369,0.6391,0.6431,0.6438,0.6446,0.6448,0.6484, 0.6516,0.6557,0.6609,0.6674,0.6686,0.6686,0.6696,0.6704,0.6753,0.6833, 0.6852,0.6852,0.6869,0.6958,0.6996,0.7009,0.7089,0.7097,0.7152,0.7152, 0.7161,0.7231,0.7324,0.7349,0.7358,0.7367,0.7377,0.7451,0.7463,0.7588, 0.7624,0.7645,0.7646,0.7657,0.7675,0.7675,0.7684,0.7693,0.7721,0.7744, 0.7768,0.7792,0.7799,0.7801,0.7812,0.7873,0.7922,0.7943,0.7977,0.8129, 0.8140,0.8167,0.8180,0.8193,0.8381,0.8499,0.8622,0.8660,0.8674,0.8699, 0.8718,0.8740,0.8820,0.8935,0.8964,0.8981,0.9027,0.9101,0.9116,0.9124, 0.9194,0.9215,0.9397,0.9425,0.9472,0.9498,0.9527,0.9549,0.9565,0.9633, 0.9656,0.9670,0.9702,0.9733,0.9738,0.9816,0.9835,0.9849,0.9983, Overall p-value after applying KStest on 269 p-values = 0.194483 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.