RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-09_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 17.1041 0.552663 2 to 25 15.87 25.8178 0.922156 3 to 26 15.60 23.5551 0.867964 4 to 27 15.86 13.6890 0.311017 5 to 28 15.61 25.3513 0.912882 6 to 29 16.02 12.4286 0.226484 7 to 30 15.85 15.1752 0.417139 8 to 31 15.75 29.4709 0.969577 9 to 32 15.68 24.7144 0.898712 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.058169 Tough bday spacings test for dh-ranFile-2016-02-09_13:31: 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 7 38 88 85 108 66 58 32 7 9 2 (O-E)^2/E 0.5 0.1 3.0 1.6 1.1 1.9 0.7 0.2 4.2 0.9 1.0 Birthday Spacings: Sum(O-E)^2/E= 15.070, p= 0.870 RESULTS OF GCD FOR dh-ranFile-2016-02-09_13:31 Euclid's algorithm: p-value, steps to gcd: 0.697692 p-value, dist. of gcd's: 0.743806 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-09_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.023 0.237 0.951 0.791 0.733 0.008 0.110 0.552 Bits 8 to 15---> 0.346 0.058 0.123 0.949 0.120 0.171 0.644 0.710 Bits 16 to 23---> 0.881 0.316 0.633 0.412 0.811 0.221 0.550 0.408 Bits 24 to 31---> 0.203 0.618 0.884 0.772 0.411 0.468 0.512 0.820 KS test for the above 32 p values: 0.013 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-09_13:31, p-values for 5 runs: 0.5040, 0.6415, 0.0113, 0.4753, 0.6228 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-09_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5162 5134.0 0.153 0.413 r= 30 23137 23103.0 0.050 0.463 r= 31 11497 11551.5 0.257 0.720 chi-square = 0.720 with df = 3; p-value = 0.132 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-09_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 230 211.4 1.633 1.633 r= 30 5107 5134.0 0.142 1.775 r= 31 23103 23103.0 0.000 1.775 r= 32 11560 11551.5 0.006 1.782 chi-square = 1.782 with df = 3; p-value = 0.381 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-09_13:31 b-rank test for bits 1 to 8, p=0.96595 b-rank test for bits 2 to 9, p=0.43421 b-rank test for bits 3 to 10, p=0.16279 b-rank test for bits 4 to 11, p=0.86077 b-rank test for bits 5 to 12, p=0.95765 b-rank test for bits 6 to 13, p=0.89549 b-rank test for bits 7 to 14, p=0.20353 b-rank test for bits 8 to 15, p=0.09645 b-rank test for bits 9 to 16, p=0.27903 b-rank test for bits 10 to 17, p=0.23762 b-rank test for bits 11 to 18, p=0.83458 b-rank test for bits 12 to 19, p=0.21246 b-rank test for bits 13 to 20, p=0.50902 b-rank test for bits 14 to 21, p=0.36764 b-rank test for bits 15 to 22, p=0.30661 b-rank test for bits 16 to 23, p=0.35173 b-rank test for bits 17 to 24, p=0.20472 b-rank test for bits 18 to 25, p=0.72959 b-rank test for bits 19 to 26, p=0.54449 b-rank test for bits 20 to 27, p=0.66436 b-rank test for bits 21 to 28, p=0.61382 b-rank test for bits 22 to 29, p=0.59400 b-rank test for bits 23 to 30, p=0.72126 b-rank test for bits 24 to 31, p=0.89685 b-rank test for bits 25 to 32, p=0.58049 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 = 0.811847 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-09_13:31 (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 141649 -0.61 0.271512 2 142051 0.33 0.629680 3 141993 0.20 0.577496 4 142166 0.60 0.725646 5 142083 0.41 0.657545 6 142140 0.54 0.705039 7 142416 1.18 0.881756 8 142420 1.19 0.883596 9 141940 0.07 0.528563 10 142260 0.82 0.793699 11 141748 -0.38 0.353109 12 142207 0.70 0.756626 13 142349 1.03 0.847852 14 141986 0.18 0.571084 15 141984 0.17 0.569249 16 142386 1.11 0.867299 17 142052 0.33 0.630562 18 141688 -0.52 0.302534 19 140875 -2.42 0.007832 20 142147 0.56 0.710657 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-09_13:31 Bits used No. missing words z-score p-value 23 to 32 141970 0.2092 0.582857 22 to 31 142196 0.9885 0.838550 21 to 30 142001 0.3161 0.624038 20 to 29 141306 -2.0804 0.018742 19 to 28 141686 -0.7701 0.220619 18 to 27 141690 -0.7563 0.224732 17 to 26 141865 -0.1529 0.439254 16 to 25 141378 -1.8322 0.033463 15 to 24 142067 0.5437 0.706673 14 to 23 141936 0.0920 0.536637 13 to 22 142507 2.0609 0.980345 12 to 21 141718 -0.6598 0.254704 11 to 20 141933 0.0816 0.532526 10 to 19 141940 0.1058 0.542113 9 to 18 142071 0.5575 0.711401 8 to 17 141951 0.1437 0.557127 7 to 16 141750 -0.5494 0.291361 6 to 15 142138 0.7885 0.784803 5 to 14 141619 -1.0011 0.158380 4 to 13 141787 -0.4218 0.336575 3 to 12 141934 0.0851 0.533897 2 to 11 141817 -0.3184 0.375099 1 to 10 141783 -0.4356 0.331556 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-09_13:31 Bits used No. missing words z-score p-value 28 to 32 142051 0.4802 0.684471 27 to 31 142027 0.3989 0.655010 26 to 30 141910 0.0023 0.500906 25 to 29 142089 0.6091 0.728755 24 to 28 141740 -0.5740 0.282984 23 to 27 141955 0.1548 0.561516 22 to 26 141579 -1.1198 0.131407 21 to 25 142225 1.0701 0.857706 20 to 24 141698 -0.7164 0.236881 19 to 23 141744 -0.5604 0.287589 18 to 22 141873 -0.1232 0.450993 17 to 21 141896 -0.0452 0.481979 16 to 20 141961 0.1752 0.569520 15 to 19 141381 -1.7909 0.036651 14 to 18 141992 0.2802 0.610352 13 to 17 142060 0.5107 0.695236 12 to 16 141813 -0.3265 0.372007 11 to 15 141984 0.2531 0.599912 10 to 14 141818 -0.3096 0.378435 9 to 13 142159 0.8463 0.801318 8 to 12 141827 -0.2791 0.390090 7 to 11 142489 1.9650 0.975292 6 to 10 141846 -0.2147 0.415009 5 to 9 142012 0.3480 0.636093 4 to 8 141784 -0.4248 0.335474 3 to 7 141584 -1.1028 0.135054 2 to 6 141721 -0.6384 0.261605 1 to 5 142195 0.9684 0.833571 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-09_13:31 Bits used No. missing words z-score p-value 31 to 32 142271 1.0669 0.856985 30 to 31 141576 -0.9833 0.162736 29 to 30 141981 0.2114 0.583719 28 to 29 141754 -0.4582 0.323404 27 to 28 141969 0.1760 0.569860 26 to 27 141559 -1.0334 0.150703 25 to 26 141751 -0.4671 0.320232 24 to 25 141674 -0.6942 0.243782 23 to 24 142011 0.2999 0.617878 22 to 23 141993 0.2468 0.597474 21 to 22 142729 2.4179 0.992195 20 to 21 141522 -1.1426 0.126609 19 to 20 142274 1.0757 0.858974 18 to 19 141918 0.0256 0.510202 17 to 18 141799 -0.3255 0.372418 16 to 17 141861 -0.1426 0.443316 15 to 16 141937 0.0816 0.532527 14 to 15 141283 -1.8476 0.032331 13 to 14 142608 2.0610 0.980347 12 to 13 141689 -0.6499 0.257865 11 to 12 141323 -1.7296 0.041852 10 to 11 141498 -1.2134 0.112496 9 to 10 141936 0.0787 0.531354 8 to 9 141923 0.0403 0.516083 7 to 8 142172 0.7748 0.780782 6 to 7 142664 2.2262 0.986998 5 to 6 141684 -0.6647 0.253124 4 to 5 141811 -0.2901 0.385886 3 to 4 141825 -0.2488 0.401773 2 to 3 141909 -0.0010 0.499612 1 to 2 141789 -0.3550 0.361311 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-09_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2547.67 0.674 0.749912 Test results for specific bytes for dh-ranFile-2016-02-09_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2457.65 -0.599 0.274634 2 to 9 2608.23 1.531 0.937069 3 to 10 2431.32 -0.971 0.165710 4 to 11 2458.16 -0.592 0.277043 5 to 12 2417.43 -1.168 0.121470 6 to 13 2510.69 0.151 0.560100 7 to 14 2502.65 0.038 0.514962 8 to 15 2438.43 -0.871 0.191939 9 to 16 2396.45 -1.464 0.071549 10 to 17 2498.82 -0.017 0.493332 11 to 18 2481.21 -0.266 0.395247 12 to 19 2547.66 0.674 0.749842 13 to 20 2506.27 0.089 0.535318 14 to 21 2638.83 1.963 0.975201 15 to 22 2570.46 0.996 0.840485 16 to 23 2504.29 0.061 0.524187 17 to 24 2491.41 -0.122 0.451630 18 to 25 2433.01 -0.947 0.171728 19 to 26 2600.50 1.421 0.922375 20 to 27 2446.16 -0.761 0.223216 21 to 28 2473.38 -0.377 0.353263 22 to 29 2600.29 1.418 0.921953 23 to 30 2717.03 3.069 0.998927 24 to 31 2509.45 0.134 0.553149 25 to 32 2538.99 0.551 0.709327 CDPARK for dh-ranFile-2016-02-09_13:31: 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 3525 0.0913 0.536383 3531 0.3653 0.642555 3467 -2.5571 0.005278 3533 0.4566 0.676028 3530 0.3196 0.625377 3528 0.2283 0.590298 3538 0.6849 0.753306 3505 -0.8219 0.205562 3555 1.4612 0.928018 3533 0.4566 0.676028 Square side=100, avg. no. parked=3524.50 sample std.=22.42 p-value of the KSTEST for those 10 p-values: 0.325267 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-09_13:31 0.9075,0.0398,0.6346,0.2686,0.5332,0.3024,0.5303,0.6664,0.9943,0.4638, The KS test for those 10 p-values: 0.796069 The 3DSPHERES test for dh-ranFile-2016-02-09_13:31 sample no r^3 equiv. uni. 1 7.864 0.230579 2 65.993 0.889171 3 22.701 0.530795 4 61.796 0.872531 5 14.403 0.381275 6 108.764 0.973363 7 59.347 0.861687 8 8.657 0.250655 9 24.046 0.551360 10 43.483 0.765298 11 25.318 0.569982 12 2.793 0.088894 13 0.138 0.004599 14 21.472 0.511159 15 11.854 0.326413 16 58.317 0.856857 17 0.257 0.008516 18 9.280 0.266062 19 34.878 0.687323 20 49.203 0.806036 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.706699 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-09_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 -0.7 -1.6 -1.1 -0.6 0.0 1.3 0.7 0.2 -0.6 1.1 -0.4 0.4 0.9 -0.8 -1.3 -0.8 -0.1 1.3 1.3 0.8 -0.3 -0.8 -0.8 -1.7 -0.1 0.9 0.6 -1.0 -0.7 0.7 0.5 -0.5 0.1 2.0 -0.1 1.9 1.5 0.5 1.0 0.1 -1.0 1.8 Chi-square with 42 degrees of freedom:43.701531 z-score=0.185652, p-value=0.600941 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-09_13:31 Test no p-value 1 0.145152 2 0.484996 3 0.005397 4 0.190607 5 0.494300 6 0.674658 7 0.052017 8 0.609536 9 0.116653 10 0.632206 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.092897 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-09_13:31: (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 66513 0.35 66644 0.01 3 25000.00 25171 1.17 24940 0.14 4 6666.67 6642 0.09 6692 0.10 5 1388.89 1381 0.04 1442 2.03 6 238.10 255 1.20 244 0.15 7 34.72 34 0.01 37 0.15 8 4.96 3 0.77 0 4.96 p=0.27604 p=0.72581 Number of rngs required: 688286, p-value: 0.446 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-09_13:31 No. of wins: Observed Expected 98665 98585.9 z-score= 0.354, pvalue=0.63832 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66430 66666.7 0.840 0.840 2 37841 37654.3 0.925 1.766 3 26996 26954.7 0.063 1.829 4 19460 19313.5 1.112 2.941 5 13800 13851.4 0.191 3.132 6 9857 9943.5 0.753 3.885 7 7053 7145.0 1.185 5.070 8 5145 5139.1 0.007 5.077 9 3796 3699.9 2.498 7.575 10 2680 2666.3 0.070 7.645 11 1966 1923.3 0.947 8.592 12 1391 1388.7 0.004 8.596 13 964 1003.7 1.571 10.167 14 714 726.1 0.203 10.370 15 528 525.8 0.009 10.379 16 364 381.2 0.772 11.151 17 246 276.5 3.373 14.523 18 203 200.8 0.023 14.547 19 143 146.0 0.061 14.608 20 109 106.2 0.073 14.681 21 314 287.1 2.518 17.198 Chisq= 17.20 for 20 degrees of freedom, p= 0.35994 SUMMARY of craptest p-value for no. of wins: 0.638318 p-value for throws/game: 0.359945 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-09_13:31 No. of wins: Observed Expected 98655 98585.9 z-score= 0.309, pvalue=0.62143 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66483 66666.7 0.506 0.506 2 37822 37654.3 0.747 1.253 3 26869 26954.7 0.273 1.525 4 19392 19313.5 0.319 1.845 5 13700 13851.4 1.655 3.500 6 10046 9943.5 1.056 4.556 7 7187 7145.0 0.247 4.802 8 5104 5139.1 0.239 5.042 9 3696 3699.9 0.004 5.046 10 2628 2666.3 0.550 5.596 11 1992 1923.3 2.452 8.048 12 1418 1388.7 0.616 8.664 13 997 1003.7 0.045 8.709 14 734 726.1 0.085 8.794 15 523 525.8 0.015 8.809 16 405 381.2 1.492 10.302 17 293 276.5 0.980 11.281 18 189 200.8 0.697 11.978 19 147 146.0 0.007 11.985 20 91 106.2 2.180 14.165 21 284 287.1 0.034 14.199 Chisq= 14.20 for 20 degrees of freedom, p= 0.17972 SUMMARY of craptest p-value for no. of wins: 0.621431 p-value for throws/game: 0.179722 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0046,0.0053,0.0054,0.0077,0.0078,0.0085,0.0113,0.0128,0.0187,0.0231, 0.0323,0.0335,0.0367,0.0398,0.0419,0.0520,0.0581,0.0582,0.0715,0.0889, 0.0929,0.0965,0.1103,0.1125,0.1167,0.1200,0.1215,0.1225,0.1266,0.1314, 0.1315,0.1351,0.1452,0.1507,0.1584,0.1627,0.1628,0.1657,0.1710,0.1717, 0.1797,0.1906,0.1919,0.2027,0.2035,0.2047,0.2056,0.2125,0.2206,0.2207, 0.2232,0.2247,0.2265,0.2306,0.2369,0.2371,0.2376,0.2438,0.2507,0.2531, 0.2547,0.2579,0.2616,0.2661,0.2686,0.2715,0.2746,0.2760,0.2770,0.2790, 0.2830,0.2876,0.2914,0.3024,0.3025,0.3066,0.3110,0.3159,0.3202,0.3234, 0.3253,0.3264,0.3316,0.3355,0.3366,0.3464,0.3517,0.3531,0.3533,0.3599, 0.3613,0.3676,0.3720,0.3724,0.3751,0.3784,0.3810,0.3813,0.3859,0.3901, 0.3952,0.4018,0.4085,0.4113,0.4121,0.4150,0.4171,0.4342,0.4393,0.4433, 0.4465,0.4510,0.4516,0.4638,0.4676,0.4753,0.4820,0.4850,0.4933,0.4943, 0.4996,0.5009,0.5040,0.5090,0.5102,0.5112,0.5116,0.5150,0.5161,0.5242, 0.5286,0.5303,0.5308,0.5314,0.5325,0.5325,0.5332,0.5339,0.5353,0.5364, 0.5366,0.5421,0.5445,0.5503,0.5514,0.5518,0.5527,0.5531,0.5571,0.5601, 0.5615,0.5692,0.5695,0.5699,0.5700,0.5711,0.5775,0.5805,0.5829,0.5837, 0.5903,0.5940,0.5975,0.5999,0.6009,0.6095,0.6104,0.6138,0.6178,0.6179, 0.6214,0.6228,0.6240,0.6254,0.6297,0.6306,0.6322,0.6334,0.6346,0.6361, 0.6383,0.6415,0.6426,0.6445,0.6550,0.6575,0.6644,0.6664,0.6747,0.6760, 0.6760,0.6845,0.6873,0.6952,0.6977,0.7050,0.7067,0.7067,0.7093,0.7103, 0.7107,0.7114,0.7213,0.7256,0.7258,0.7288,0.7296,0.7329,0.7438,0.7498, 0.7499,0.7533,0.7566,0.7653,0.7720,0.7808,0.7848,0.7908,0.7937,0.7961, 0.8013,0.8060,0.8114,0.8118,0.8196,0.8336,0.8346,0.8386,0.8405,0.8479, 0.8569,0.8570,0.8577,0.8590,0.8608,0.8617,0.8673,0.8680,0.8705,0.8725, 0.8807,0.8818,0.8836,0.8841,0.8892,0.8955,0.8968,0.8987,0.9075,0.9129, 0.9220,0.9222,0.9224,0.9280,0.9371,0.9489,0.9509,0.9576,0.9659,0.9696, 0.9734,0.9752,0.9753,0.9803,0.9803,0.9870,0.9922,0.9943,0.9989, Overall p-value after applying KStest on 269 p-values = 0.366298 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.