RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-16_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.96 15.7746 0.460130 2 to 25 15.80 19.9971 0.725624 3 to 26 15.64 11.0923 0.148276 4 to 27 15.67 19.8843 0.719810 5 to 28 15.97 21.7709 0.806309 6 to 29 15.34 26.8734 0.940049 7 to 30 15.94 13.4070 0.291457 8 to 31 15.91 16.5957 0.517933 9 to 32 15.84 13.9109 0.326599 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.899518 Tough bday spacings test for dh-ranFile-2015-12-16_07:31: 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 39 88 95 96 81 43 30 13 4 2 (O-E)^2/E 0.0 0.2 3.0 0.1 0.0 0.1 1.6 0.0 0.2 1.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 7.241, p= 0.297 RESULTS OF GCD FOR dh-ranFile-2015-12-16_07:31 Euclid's algorithm: p-value, steps to gcd: 0.523926 p-value, dist. of gcd's: 0.200227 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-16_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.102 0.423 0.126 0.323 0.525 0.011 0.067 0.714 Bits 8 to 15---> 0.785 0.447 0.019 0.189 0.777 0.105 0.426 0.145 Bits 16 to 23---> 0.414 0.819 0.523 0.210 0.925 0.978 0.574 0.168 Bits 24 to 31---> 0.708 0.940 0.621 0.911 0.606 0.631 0.959 0.574 KS test for the above 32 p values: 0.074 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-16_07:31, p-values for 5 runs: 0.3712, 0.2263, 0.7801, 0.2070, 0.7024 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-16_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5087 5134.0 0.430 1.893 r= 30 23021 23103.0 0.291 2.184 r= 31 11663 11551.5 1.076 3.260 chi-square = 3.260 with df = 3; p-value = 0.647 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-16_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5098 5134.0 0.253 0.766 r= 31 23244 23103.0 0.860 1.626 r= 32 11457 11551.5 0.773 2.399 chi-square = 2.399 with df = 3; p-value = 0.506 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-16_07:31 b-rank test for bits 1 to 8, p=0.09061 b-rank test for bits 2 to 9, p=0.46433 b-rank test for bits 3 to 10, p=0.04914 b-rank test for bits 4 to 11, p=0.38563 b-rank test for bits 5 to 12, p=0.56958 b-rank test for bits 6 to 13, p=0.65633 b-rank test for bits 7 to 14, p=0.63818 b-rank test for bits 8 to 15, p=0.03268 b-rank test for bits 9 to 16, p=0.84489 b-rank test for bits 10 to 17, p=0.84979 b-rank test for bits 11 to 18, p=0.84993 b-rank test for bits 12 to 19, p=0.26399 b-rank test for bits 13 to 20, p=0.51422 b-rank test for bits 14 to 21, p=0.71040 b-rank test for bits 15 to 22, p=0.50472 b-rank test for bits 16 to 23, p=0.40533 b-rank test for bits 17 to 24, p=0.47402 b-rank test for bits 18 to 25, p=0.18607 b-rank test for bits 19 to 26, p=0.39142 b-rank test for bits 20 to 27, p=0.10958 b-rank test for bits 21 to 28, p=0.31784 b-rank test for bits 22 to 29, p=0.69435 b-rank test for bits 23 to 30, p=0.41052 b-rank test for bits 24 to 31, p=0.23973 b-rank test for bits 25 to 32, p=0.92773 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 = 0.732990 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-16_07:31 (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 141911 0.00 0.501557 2 141338 -1.33 0.090957 3 142242 0.78 0.781499 4 141524 -0.90 0.183979 5 141720 -0.44 0.329114 6 141620 -0.68 0.249519 7 141080 -1.94 0.026331 8 141742 -0.39 0.347914 9 141593 -0.74 0.229927 10 142143 0.55 0.707453 11 142090 0.42 0.663534 12 142335 0.99 0.840024 13 142762 1.99 0.976827 14 142032 0.29 0.612795 15 142478 1.33 0.908021 16 141808 -0.24 0.406425 17 142003 0.22 0.586619 18 141398 -1.19 0.116103 19 141891 -0.04 0.482920 20 142193 0.66 0.746264 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-16_07:31 Bits used No. missing words z-score p-value 23 to 32 142138 0.7885 0.784803 22 to 31 141811 -0.3391 0.367279 21 to 30 142177 0.9230 0.821996 20 to 29 142633 2.4954 0.993709 19 to 28 142536 2.1609 0.984650 18 to 27 141920 0.0368 0.514675 17 to 26 141489 -1.4494 0.073611 16 to 25 141860 -0.1701 0.432464 15 to 24 141840 -0.2391 0.405526 14 to 23 141920 0.0368 0.514675 13 to 22 141969 0.2058 0.581510 12 to 21 141706 -0.7011 0.241609 11 to 20 141798 -0.3839 0.350528 10 to 19 141957 0.1644 0.565284 9 to 18 142021 0.3851 0.649907 8 to 17 141651 -0.8908 0.186520 7 to 16 142392 1.6644 0.951982 6 to 15 141631 -0.9598 0.168588 5 to 14 142001 0.3161 0.624038 4 to 13 142209 1.0333 0.849279 3 to 12 142036 0.4368 0.668869 2 to 11 141947 0.1299 0.551676 1 to 10 141876 -0.1149 0.454250 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-16_07:31 Bits used No. missing words z-score p-value 28 to 32 142129 0.7446 0.771757 27 to 31 141930 0.0701 0.527930 26 to 30 141693 -0.7333 0.231681 25 to 29 141996 0.2938 0.615543 24 to 28 141880 -0.0994 0.460401 23 to 27 141639 -0.9164 0.179736 22 to 26 141851 -0.1977 0.421629 21 to 25 142000 0.3074 0.620714 20 to 24 142028 0.4023 0.656258 19 to 23 141596 -1.0621 0.144087 18 to 22 141853 -0.1909 0.424283 17 to 21 142162 0.8565 0.804142 16 to 20 141705 -0.6926 0.244267 15 to 19 141961 0.1752 0.569520 14 to 18 141759 -0.5096 0.305168 13 to 17 141643 -0.9028 0.183312 12 to 16 142037 0.4328 0.667413 11 to 15 141812 -0.3299 0.370726 10 to 14 141955 0.1548 0.561516 9 to 13 141319 -2.0011 0.022690 8 to 12 142021 0.3785 0.647486 7 to 11 141799 -0.3740 0.354202 6 to 10 141799 -0.3740 0.354202 5 to 9 142252 1.1616 0.877300 4 to 8 142054 0.4904 0.688077 3 to 7 142199 0.9819 0.836933 2 to 6 142187 0.9413 0.826713 1 to 5 141415 -1.6757 0.046899 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-16_07:31 Bits used No. missing words z-score p-value 31 to 32 142434 1.5477 0.939153 30 to 31 141812 -0.2871 0.387014 29 to 30 142122 0.6273 0.734784 28 to 29 142059 0.4415 0.670576 27 to 28 142158 0.7335 0.768385 26 to 27 141144 -2.2576 0.011985 25 to 26 142565 1.9341 0.973451 24 to 25 142122 0.6273 0.734784 23 to 24 141875 -0.1013 0.459669 22 to 23 141805 -0.3078 0.379133 21 to 22 141926 0.0492 0.519610 20 to 21 141134 -2.2871 0.011095 19 to 20 142076 0.4917 0.688517 18 to 19 142120 0.6214 0.732847 17 to 18 141618 -0.8594 0.195065 16 to 17 141790 -0.3520 0.362417 15 to 16 142045 0.4002 0.655498 14 to 15 141154 -2.2281 0.012937 13 to 14 141755 -0.4553 0.324464 12 to 13 141901 -0.0246 0.490198 11 to 12 141819 -0.2665 0.394942 10 to 11 141817 -0.2724 0.392673 9 to 10 141715 -0.5732 0.283240 8 to 9 141684 -0.6647 0.253124 7 to 8 142481 1.6863 0.954135 6 to 7 142030 0.3560 0.639064 5 to 6 141899 -0.0305 0.487845 4 to 5 141214 -2.0511 0.020128 3 to 4 141799 -0.3255 0.372418 2 to 3 141667 -0.7148 0.237355 1 to 2 141443 -1.3756 0.084472 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-16_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2534.63 0.490 0.687842 Test results for specific bytes for dh-ranFile-2015-12-16_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2495.70 -0.061 0.475773 2 to 9 2475.52 -0.346 0.364591 3 to 10 2474.12 -0.366 0.357197 4 to 11 2417.02 -1.173 0.120303 5 to 12 2454.13 -0.649 0.258283 6 to 13 2471.55 -0.402 0.343693 7 to 14 2641.05 1.995 0.976968 8 to 15 2416.76 -1.177 0.119561 9 to 16 2405.16 -1.341 0.089923 10 to 17 2515.45 0.218 0.586468 11 to 18 2383.67 -1.645 0.049963 12 to 19 2603.40 1.462 0.928166 13 to 20 2599.01 1.400 0.919276 14 to 21 2447.30 -0.745 0.228043 15 to 22 2539.42 0.557 0.711380 16 to 23 2467.56 -0.459 0.323213 17 to 24 2562.65 0.886 0.812180 18 to 25 2576.52 1.082 0.860403 19 to 26 2467.00 -0.467 0.320350 20 to 27 2599.41 1.406 0.920119 21 to 28 2515.09 0.213 0.584469 22 to 29 2441.71 -0.824 0.204882 23 to 30 2431.25 -0.972 0.165442 24 to 31 2515.04 0.213 0.584233 25 to 32 2485.03 -0.212 0.416142 CDPARK for dh-ranFile-2015-12-16_07:31: 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 3531 0.3653 0.642555 3522 -0.0457 0.481790 3547 1.0959 0.863437 3521 -0.0913 0.463617 3565 1.9178 0.972432 3511 -0.5479 0.291865 3523 0.0000 0.500000 3521 -0.0913 0.463617 3544 0.9589 0.831196 3535 0.5479 0.708135 Square side=100, avg. no. parked=3532.00 sample std.=15.27 p-value of the KSTEST for those 10 p-values: 0.236104 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-16_07:31 0.0549,0.2552,0.6088,0.9111,0.4372,0.8531,0.5881,0.7717,0.4223,0.7658, The KS test for those 10 p-values: 0.759757 The 3DSPHERES test for dh-ranFile-2015-12-16_07:31 sample no r^3 equiv. uni. 1 60.645 0.867545 2 112.472 0.976460 3 43.410 0.764723 4 14.974 0.392952 5 3.585 0.112628 6 5.465 0.166535 7 22.723 0.531137 8 3.055 0.096816 9 48.200 0.799444 10 12.420 0.339009 11 18.698 0.463819 12 74.068 0.915326 13 5.353 0.163417 14 54.813 0.839120 15 8.935 0.257567 16 7.566 0.222923 17 49.757 0.809590 18 0.518 0.017130 19 8.556 0.248142 20 61.642 0.871874 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.705942 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-16_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 -0.6 0.8 0.7 -0.7 0.6 1.1 -1.3 0.4 -0.8 1.0 -0.2 1.4 -0.0 0.7 0.0 -0.5 -0.9 0.9 -1.0 0.4 0.4 -1.5 -1.8 -0.4 0.7 -2.2 2.0 2.4 0.5 0.6 -0.2 0.4 0.9 -0.1 -2.6 -1.7 -1.6 -0.1 0.9 0.0 -1.1 Chi-square with 42 degrees of freedom:49.999384 z-score=0.872804, p-value=0.814492 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-16_07:31 Test no p-value 1 0.294435 2 0.888318 3 0.258794 4 0.038091 5 0.090381 6 0.197807 7 0.729221 8 0.008482 9 0.846458 10 0.246101 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.106289 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-16_07:31: (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 66660 0.00 66991 1.58 3 25000.00 24870 0.68 24859 0.80 4 6666.67 6750 1.04 6543 2.29 5 1388.89 1445 2.27 1361 0.56 6 238.10 238 0.00 198 6.75 7 34.72 33 0.09 41 1.14 8 4.96 3 0.77 6 0.22 p=0.43613 p=0.96196 Number of rngs required: 689478, p-value: 0.894 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-16_07:31 No. of wins: Observed Expected 98889 98585.9 z-score= 1.356, pvalue=0.91242 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66873 66666.7 0.639 0.639 2 37808 37654.3 0.627 1.266 3 26585 26954.7 5.072 6.337 4 19313 19313.5 0.000 6.337 5 13794 13851.4 0.238 6.575 6 9806 9943.5 1.903 8.478 7 7255 7145.0 1.693 10.171 8 5083 5139.1 0.612 10.782 9 3715 3699.9 0.062 10.844 10 2634 2666.3 0.391 11.236 11 1969 1923.3 1.084 12.320 12 1373 1388.7 0.178 12.498 13 1069 1003.7 4.246 16.745 14 798 726.1 7.111 23.856 15 524 525.8 0.006 23.862 16 379 381.2 0.012 23.875 17 273 276.5 0.045 23.920 18 212 200.8 0.621 24.541 19 137 146.0 0.553 25.094 20 122 106.2 2.346 27.440 21 278 287.1 0.289 27.729 Chisq= 27.73 for 20 degrees of freedom, p= 0.88403 SUMMARY of craptest p-value for no. of wins: 0.912423 p-value for throws/game: 0.884035 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-16_07:31 No. of wins: Observed Expected 98126 98585.9 z-score=-2.057, pvalue=0.01985 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66164 66666.7 3.790 3.790 2 37866 37654.3 1.190 4.980 3 26875 26954.7 0.236 5.216 4 19528 19313.5 2.383 7.599 5 14003 13851.4 1.659 9.258 6 9875 9943.5 0.472 9.730 7 7212 7145.0 0.628 10.358 8 5141 5139.1 0.001 10.359 9 3707 3699.9 0.014 10.373 10 2631 2666.3 0.467 10.840 11 1958 1923.3 0.625 11.465 12 1390 1388.7 0.001 11.466 13 1030 1003.7 0.688 12.154 14 772 726.1 2.896 15.051 15 518 525.8 0.117 15.167 16 365 381.2 0.684 15.852 17 272 276.5 0.075 15.926 18 191 200.8 0.481 16.407 19 137 146.0 0.553 16.960 20 92 106.2 1.902 18.863 21 273 287.1 0.694 19.557 Chisq= 19.56 for 20 degrees of freedom, p= 0.51405 SUMMARY of craptest p-value for no. of wins: 0.019855 p-value for throws/game: 0.514046 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0085,0.0107,0.0111,0.0120,0.0129,0.0171,0.0194,0.0199,0.0201,0.0227, 0.0263,0.0327,0.0381,0.0469,0.0491,0.0500,0.0549,0.0674,0.0736,0.0736, 0.0845,0.0899,0.0904,0.0906,0.0910,0.0968,0.1022,0.1054,0.1063,0.1096, 0.1126,0.1161,0.1196,0.1203,0.1265,0.1441,0.1449,0.1483,0.1634,0.1654, 0.1665,0.1675,0.1686,0.1797,0.1833,0.1840,0.1861,0.1865,0.1895,0.1951, 0.1978,0.2002,0.2049,0.2070,0.2096,0.2229,0.2263,0.2280,0.2299,0.2317, 0.2361,0.2374,0.2397,0.2416,0.2443,0.2461,0.2481,0.2495,0.2531,0.2552, 0.2576,0.2583,0.2588,0.2640,0.2832,0.2915,0.2919,0.2944,0.2974,0.3052, 0.3178,0.3204,0.3228,0.3232,0.3245,0.3266,0.3291,0.3390,0.3437,0.3479, 0.3505,0.3542,0.3542,0.3572,0.3624,0.3646,0.3673,0.3707,0.3712,0.3724, 0.3791,0.3856,0.3870,0.3914,0.3927,0.3930,0.3949,0.4053,0.4055,0.4064, 0.4105,0.4137,0.4161,0.4216,0.4223,0.4232,0.4243,0.4261,0.4325,0.4361, 0.4372,0.4466,0.4542,0.4597,0.4601,0.4604,0.4636,0.4636,0.4638,0.4643, 0.4740,0.4758,0.4818,0.4829,0.4878,0.4902,0.5000,0.5016,0.5047,0.5062, 0.5140,0.5142,0.5147,0.5147,0.5179,0.5196,0.5229,0.5239,0.5247,0.5279, 0.5311,0.5517,0.5615,0.5653,0.5695,0.5696,0.5743,0.5744,0.5815,0.5842, 0.5845,0.5865,0.5866,0.5881,0.6061,0.6088,0.6128,0.6155,0.6207,0.6207, 0.6240,0.6306,0.6382,0.6391,0.6426,0.6467,0.6475,0.6499,0.6555,0.6563, 0.6563,0.6635,0.6674,0.6689,0.6706,0.6878,0.6881,0.6885,0.6944,0.7024, 0.7059,0.7075,0.7081,0.7084,0.7104,0.7114,0.7144,0.7198,0.7256,0.7292, 0.7328,0.7330,0.7348,0.7348,0.7463,0.7598,0.7647,0.7658,0.7684,0.7717, 0.7718,0.7772,0.7801,0.7815,0.7848,0.7853,0.7994,0.8041,0.8063,0.8096, 0.8122,0.8145,0.8191,0.8220,0.8267,0.8312,0.8369,0.8391,0.8400,0.8449, 0.8465,0.8493,0.8498,0.8499,0.8531,0.8604,0.8634,0.8675,0.8719,0.8773, 0.8840,0.8883,0.8944,0.8995,0.9080,0.9109,0.9111,0.9124,0.9153,0.9193, 0.9201,0.9255,0.9277,0.9282,0.9392,0.9396,0.9400,0.9520,0.9541,0.9586, 0.9620,0.9724,0.9735,0.9765,0.9768,0.9770,0.9776,0.9846,0.9937, Overall p-value after applying KStest on 269 p-values = 0.973444 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.