RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-29_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.90 12.3597 0.222119 2 to 25 15.57 20.3745 0.744475 3 to 26 15.43 26.7341 0.937915 4 to 27 15.44 28.3477 0.958964 5 to 28 15.72 24.0708 0.882475 6 to 29 15.73 32.8104 0.988089 7 to 30 15.50 20.7971 0.764504 8 to 31 15.92 23.9741 0.879860 9 to 32 15.62 16.9342 0.541168 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.004434 Tough bday spacings test for dh-ranFile-2016-10-29_12:31: 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 29 84 103 88 76 60 30 14 8 1 (O-E)^2/E 0.5 1.6 1.6 0.3 1.0 0.1 1.2 0.0 0.1 0.3 2.3 Birthday Spacings: Sum(O-E)^2/E= 8.835, p= 0.452 RESULTS OF GCD FOR dh-ranFile-2016-10-29_12:31 Euclid's algorithm: p-value, steps to gcd: 0.456764 p-value, dist. of gcd's: 0.936047 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-29_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.536 0.363 0.230 0.866 0.680 0.431 0.584 0.968 Bits 8 to 15---> 0.088 0.410 0.781 0.607 0.186 0.564 0.649 0.467 Bits 16 to 23---> 0.099 0.381 0.187 0.922 0.903 0.247 0.311 0.041 Bits 24 to 31---> 0.126 0.143 0.802 0.197 0.290 0.690 0.575 0.307 KS test for the above 32 p values: 0.336 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-29_12:31, p-values for 5 runs: 0.1763, 0.7995, 0.6172, 0.4739, 0.0027 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-29_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 185 211.4 3.301 3.301 r= 29 5133 5134.0 0.000 3.301 r= 30 23165 23103.0 0.166 3.467 r= 31 11517 11551.5 0.103 3.571 chi-square = 3.571 with df = 3; p-value = 0.688 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-29_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5074 5134.0 0.701 1.050 r= 31 23247 23103.0 0.897 1.947 r= 32 11459 11551.5 0.741 2.688 chi-square = 2.688 with df = 3; p-value = 0.558 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-29_12:31 b-rank test for bits 1 to 8, p=0.30286 b-rank test for bits 2 to 9, p=0.17315 b-rank test for bits 3 to 10, p=0.92756 b-rank test for bits 4 to 11, p=0.38789 b-rank test for bits 5 to 12, p=0.18290 b-rank test for bits 6 to 13, p=0.70380 b-rank test for bits 7 to 14, p=0.13779 b-rank test for bits 8 to 15, p=0.99829 b-rank test for bits 9 to 16, p=0.91280 b-rank test for bits 10 to 17, p=0.67910 b-rank test for bits 11 to 18, p=0.54938 b-rank test for bits 12 to 19, p=0.23514 b-rank test for bits 13 to 20, p=0.31916 b-rank test for bits 14 to 21, p=0.70681 b-rank test for bits 15 to 22, p=0.92663 b-rank test for bits 16 to 23, p=0.33313 b-rank test for bits 17 to 24, p=0.75508 b-rank test for bits 18 to 25, p=0.62697 b-rank test for bits 19 to 26, p=0.95438 b-rank test for bits 20 to 27, p=0.24793 b-rank test for bits 21 to 28, p=0.60772 b-rank test for bits 22 to 29, p=0.79322 b-rank test for bits 23 to 30, p=0.84200 b-rank test for bits 24 to 31, p=0.12715 b-rank test for bits 25 to 32, p=0.76868 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 = 0.318243 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-29_12:31 (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 142009 0.23 0.592070 2 141136 -1.81 0.035393 3 141551 -0.84 0.201235 4 141623 -0.67 0.251749 5 142438 1.24 0.891624 6 142154 0.57 0.716223 7 141248 -1.55 0.061153 8 142457 1.28 0.899658 9 141594 -0.74 0.230637 10 141700 -0.49 0.312389 11 142371 1.08 0.859632 12 142101 0.45 0.672861 13 141937 0.06 0.525774 14 141638 -0.63 0.263057 15 141770 -0.33 0.372387 16 142261 0.82 0.794364 17 142485 1.35 0.910691 18 141702 -0.48 0.314045 19 142048 0.32 0.627029 20 141716 -0.45 0.325741 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-29_12:31 Bits used No. missing words z-score p-value 23 to 32 141710 -0.6873 0.245933 22 to 31 142096 0.6437 0.740112 21 to 30 142522 2.1127 0.982685 20 to 29 141956 0.1609 0.563926 19 to 28 141941 0.1092 0.543481 18 to 27 141801 -0.3736 0.354369 17 to 26 141995 0.2954 0.616161 16 to 25 141732 -0.6115 0.270440 15 to 24 141847 -0.2149 0.414911 14 to 23 142651 2.5575 0.994728 13 to 22 142013 0.3575 0.639635 12 to 21 141880 -0.1011 0.459721 11 to 20 141863 -0.1598 0.436536 10 to 19 142215 1.0540 0.854066 9 to 18 141202 -2.4391 0.007363 8 to 17 141521 -1.3391 0.090274 7 to 16 141791 -0.4080 0.341624 6 to 15 141791 -0.4080 0.341624 5 to 14 141731 -0.6149 0.269300 4 to 13 141681 -0.7873 0.215540 3 to 12 142010 0.3471 0.635756 2 to 11 142243 1.1506 0.875049 1 to 10 141318 -2.0391 0.020722 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-29_12:31 Bits used No. missing words z-score p-value 28 to 32 142117 0.7040 0.759273 27 to 31 142088 0.6057 0.727630 26 to 30 141799 -0.3740 0.354202 25 to 29 141835 -0.2520 0.400534 24 to 28 141935 0.0870 0.534671 23 to 27 142074 0.5582 0.711647 22 to 26 141955 0.1548 0.561516 21 to 25 142261 1.1921 0.883389 20 to 24 141585 -1.0994 0.135792 19 to 23 141566 -1.1638 0.122246 18 to 22 141658 -0.8520 0.197116 17 to 21 141504 -1.3740 0.084721 16 to 20 142131 0.7514 0.773801 15 to 19 141785 -0.4215 0.336711 14 to 18 142241 1.1243 0.869558 13 to 17 141611 -1.0113 0.155939 12 to 16 141768 -0.4791 0.315939 11 to 15 141910 0.0023 0.500906 10 to 14 141850 -0.2011 0.420303 9 to 13 142089 0.6091 0.728755 8 to 12 141947 0.1277 0.550805 7 to 11 141508 -1.3604 0.086845 6 to 10 142465 1.8836 0.970192 5 to 9 141909 -0.0011 0.499554 4 to 8 141948 0.1311 0.552146 3 to 7 142063 0.5209 0.698787 2 to 6 141711 -0.6723 0.250695 1 to 5 142059 0.5074 0.694048 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-29_12:31 Bits used No. missing words z-score p-value 31 to 32 142108 0.5860 0.721078 30 to 31 141774 -0.3992 0.344872 29 to 30 141879 -0.0895 0.464355 28 to 29 142150 0.7099 0.761130 27 to 28 141833 -0.2252 0.410927 26 to 27 141794 -0.3402 0.366851 25 to 26 142061 0.4474 0.672708 24 to 25 141734 -0.5172 0.302509 23 to 24 141786 -0.3638 0.358002 22 to 23 142263 1.0433 0.851589 21 to 22 141632 -0.8181 0.206655 20 to 21 141500 -1.2075 0.113627 19 to 20 141946 0.1082 0.543070 18 to 19 142102 0.5683 0.715101 17 to 18 142126 0.6391 0.738636 16 to 17 141688 -0.6529 0.256913 15 to 16 141631 -0.8210 0.205814 14 to 15 142463 1.6332 0.948791 13 to 14 141965 0.1642 0.565220 12 to 13 142113 0.6008 0.726012 11 to 12 142015 0.3117 0.622370 10 to 11 141990 0.2380 0.594046 9 to 10 142183 0.8073 0.790249 8 to 9 142013 0.3058 0.620126 7 to 8 141984 0.2203 0.587168 6 to 7 141390 -1.5319 0.062768 5 to 6 142017 0.3176 0.624610 4 to 5 141811 -0.2901 0.385886 3 to 4 142078 0.4976 0.690600 2 to 3 141893 -0.0482 0.480790 1 to 2 142063 0.4533 0.674835 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-29_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2382.27 -1.665 0.047966 Test results for specific bytes for dh-ranFile-2016-10-29_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2519.47 0.275 0.608454 2 to 9 2555.47 0.784 0.783596 3 to 10 2527.51 0.389 0.651394 4 to 11 2459.96 -0.566 0.285629 5 to 12 2536.69 0.519 0.698059 6 to 13 2470.82 -0.413 0.339933 7 to 14 2581.33 1.150 0.874962 8 to 15 2356.24 -2.033 0.021021 9 to 16 2511.03 0.156 0.561968 10 to 17 2520.75 0.293 0.615407 11 to 18 2575.11 1.062 0.855941 12 to 19 2507.60 0.107 0.542781 13 to 20 2535.41 0.501 0.691730 14 to 21 2595.75 1.354 0.912149 15 to 22 2454.35 -0.646 0.259290 16 to 23 2439.32 -0.858 0.195417 17 to 24 2515.50 0.219 0.586770 18 to 25 2451.74 -0.683 0.247439 19 to 26 2570.42 0.996 0.840332 20 to 27 2524.30 0.344 0.634461 21 to 28 2628.27 1.814 0.965164 22 to 29 2509.16 0.130 0.551540 23 to 30 2462.38 -0.532 0.297354 24 to 31 2486.25 -0.194 0.422901 25 to 32 2553.50 0.757 0.775377 CDPARK for dh-ranFile-2016-10-29_12:31: 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 3550 1.2329 0.891189 3488 -1.5982 0.055002 3543 0.9132 0.819442 3524 0.0457 0.518210 3533 0.4566 0.676028 3502 -0.9589 0.168804 3533 0.4566 0.676028 3485 -1.7352 0.041356 3516 -0.3196 0.374623 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3517.60 sample std.=21.54 p-value of the KSTEST for those 10 p-values: 0.706915 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-29_12:31 0.1694,0.4169,0.8280,0.0329,0.6983,0.3650,0.4778,0.1965,0.2924,0.3874, The KS test for those 10 p-values: 0.332852 The 3DSPHERES test for dh-ranFile-2016-10-29_12:31 sample no r^3 equiv. uni. 1 32.211 0.658258 2 14.519 0.383661 3 207.654 0.999014 4 87.192 0.945328 5 9.887 0.280776 6 79.350 0.928995 7 98.743 0.962800 8 6.185 0.186295 9 101.250 0.965782 10 2.992 0.094923 11 3.430 0.108052 12 20.669 0.497907 13 34.557 0.683969 14 2.932 0.093103 15 41.482 0.749110 16 11.672 0.322310 17 23.409 0.541738 18 73.708 0.914303 19 14.728 0.387943 20 1.180 0.038557 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.264163 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-29_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.7 -2.0 0.0 1.1 1.1 -0.6 -2.0 -0.5 1.1 -0.2 1.0 0.1 -0.8 1.0 -0.1 1.9 0.4 -1.3 0.2 -1.2 -1.2 0.4 -0.2 0.4 0.0 -0.5 -0.9 0.2 -0.3 1.4 -0.9 0.6 0.1 -0.1 -0.5 -1.4 0.2 -1.2 0.4 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:33.680025 z-score=-0.907784, p-value=0.183613 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-29_12:31 Test no p-value 1 0.730531 2 0.007637 3 0.597378 4 0.379855 5 0.923967 6 0.001511 7 0.041576 8 0.316860 9 0.000000 10 0.374892 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002097 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-29_12:31: (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 66509 0.37 66365 1.37 3 25000.00 25157 0.99 25170 1.16 4 6666.67 6602 0.63 6768 1.54 5 1388.89 1470 4.74 1433 1.40 6 238.10 224 0.83 222 1.09 7 34.72 32 0.21 33 0.09 8 4.96 5 0.00 8 1.86 p=0.74462 p=0.79620 Number of rngs required: 689218, p-value: 0.827 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-29_12:31 No. of wins: Observed Expected 98312 98585.9 z-score=-1.225, pvalue=0.11031 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66614 66666.7 0.042 0.042 2 37562 37654.3 0.226 0.268 3 27085 26954.7 0.630 0.898 4 19557 19313.5 3.071 3.968 5 13742 13851.4 0.864 4.833 6 9935 9943.5 0.007 4.840 7 7158 7145.0 0.024 4.864 8 5106 5139.1 0.213 5.077 9 3713 3699.9 0.047 5.123 10 2605 2666.3 1.409 6.532 11 1904 1923.3 0.194 6.727 12 1319 1388.7 3.502 10.229 13 1031 1003.7 0.742 10.971 14 721 726.1 0.036 11.007 15 540 525.8 0.382 11.389 16 425 381.2 5.045 16.433 17 265 276.5 0.482 16.915 18 168 200.8 5.367 22.281 19 140 146.0 0.245 22.527 20 121 106.2 2.058 24.585 21 289 287.1 0.012 24.597 Chisq= 24.60 for 20 degrees of freedom, p= 0.78272 SUMMARY of craptest p-value for no. of wins: 0.110315 p-value for throws/game: 0.782720 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-29_12:31 No. of wins: Observed Expected 98566 98585.9 z-score=-0.089, pvalue=0.46461 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66573 66666.7 0.132 0.132 2 37713 37654.3 0.091 0.223 3 26830 26954.7 0.577 0.800 4 19678 19313.5 6.881 7.681 5 13989 13851.4 1.367 9.047 6 9772 9943.5 2.959 12.007 7 7103 7145.0 0.247 12.254 8 5140 5139.1 0.000 12.254 9 3658 3699.9 0.474 12.728 10 2705 2666.3 0.562 13.290 11 1936 1923.3 0.083 13.373 12 1350 1388.7 1.081 14.454 13 1000 1003.7 0.014 14.468 14 694 726.1 1.423 15.890 15 462 525.8 7.750 23.640 16 382 381.2 0.002 23.642 17 281 276.5 0.072 23.714 18 186 200.8 1.095 24.809 19 134 146.0 0.984 25.793 20 137 106.2 8.922 34.715 21 277 287.1 0.356 35.071 Chisq= 35.07 for 20 degrees of freedom, p= 0.98027 SUMMARY of craptest p-value for no. of wins: 0.464613 p-value for throws/game: 0.980272 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0015,0.0021,0.0027,0.0044,0.0074,0.0076,0.0207,0.0210,0.0329, 0.0354,0.0386,0.0408,0.0414,0.0416,0.0480,0.0550,0.0612,0.0628,0.0847, 0.0868,0.0883,0.0903,0.0931,0.0949,0.0988,0.1081,0.1103,0.1136,0.1222, 0.1256,0.1272,0.1358,0.1378,0.1426,0.1559,0.1688,0.1688,0.1694,0.1731, 0.1763,0.1829,0.1836,0.1860,0.1863,0.1875,0.1954,0.1965,0.1969,0.1971, 0.2012,0.2058,0.2067,0.2155,0.2221,0.2302,0.2306,0.2351,0.2459,0.2468, 0.2474,0.2479,0.2507,0.2517,0.2569,0.2593,0.2631,0.2642,0.2693,0.2704, 0.2808,0.2856,0.2899,0.2924,0.2974,0.3025,0.3029,0.3075,0.3110,0.3124, 0.3140,0.3159,0.3169,0.3182,0.3192,0.3223,0.3257,0.3329,0.3331,0.3362, 0.3367,0.3399,0.3416,0.3416,0.3449,0.3542,0.3544,0.3580,0.3628,0.3650, 0.3669,0.3724,0.3746,0.3749,0.3799,0.3810,0.3837,0.3859,0.3874,0.3879, 0.3879,0.4005,0.4096,0.4109,0.4149,0.4169,0.4203,0.4229,0.4311,0.4365, 0.4522,0.4568,0.4597,0.4644,0.4646,0.4670,0.4739,0.4778,0.4808,0.4979, 0.4996,0.5009,0.5182,0.5258,0.5347,0.5363,0.5412,0.5417,0.5428,0.5431, 0.5435,0.5494,0.5508,0.5515,0.5521,0.5577,0.5615,0.5620,0.5639,0.5640, 0.5652,0.5752,0.5843,0.5868,0.5872,0.5921,0.5940,0.5974,0.6069,0.6077, 0.6085,0.6154,0.6162,0.6172,0.6201,0.6224,0.6246,0.6270,0.6270,0.6345, 0.6358,0.6396,0.6492,0.6514,0.6583,0.6727,0.6729,0.6748,0.6760,0.6760, 0.6791,0.6800,0.6840,0.6883,0.6899,0.6906,0.6917,0.6940,0.6981,0.6983, 0.6988,0.7038,0.7068,0.7069,0.7116,0.7151,0.7162,0.7211,0.7260,0.7276, 0.7288,0.7305,0.7386,0.7401,0.7445,0.7446,0.7491,0.7551,0.7593,0.7611, 0.7645,0.7687,0.7738,0.7754,0.7810,0.7827,0.7836,0.7902,0.7932,0.7944, 0.7962,0.7995,0.8024,0.8194,0.8273,0.8280,0.8403,0.8420,0.8516,0.8541, 0.8559,0.8596,0.8659,0.8696,0.8750,0.8750,0.8799,0.8825,0.8834,0.8912, 0.8916,0.8997,0.9025,0.9107,0.9121,0.9128,0.9143,0.9219,0.9240,0.9266, 0.9276,0.9290,0.9360,0.9379,0.9453,0.9488,0.9544,0.9590,0.9628,0.9652, 0.9658,0.9676,0.9702,0.9803,0.9827,0.9881,0.9947,0.9983,0.9990, Overall p-value after applying KStest on 269 p-values = 0.813095 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.