RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-25_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.64 24.0577 0.882125 2 to 25 15.88 15.5538 0.444347 3 to 26 15.77 17.1349 0.554735 4 to 27 15.80 18.4821 0.640943 5 to 28 15.65 18.8205 0.661067 6 to 29 15.63 37.1850 0.996824 7 to 30 15.51 20.2588 0.738791 8 to 31 15.79 14.6768 0.381252 9 to 32 15.77 15.0417 0.407522 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.176694 Tough bday spacings test for dh-ranFile-2015-06-25_08:31: 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 10 41 66 93 103 77 51 31 13 11 4 (O-E)^2/E 0.1 0.5 0.7 0.2 0.3 0.0 0.0 0.1 0.2 2.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.069, p= 0.113 RESULTS OF GCD FOR dh-ranFile-2015-06-25_08:31 Euclid's algorithm: p-value, steps to gcd: 0.953461 p-value, dist. of gcd's: 0.270827 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-25_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.342 0.422 0.055 0.440 0.775 0.886 0.612 0.620 Bits 8 to 15---> 0.835 0.146 0.801 0.228 0.838 0.252 0.733 0.615 Bits 16 to 23---> 0.933 0.904 0.050 0.271 0.010 0.378 0.385 0.228 Bits 24 to 31---> 0.347 0.660 0.064 0.431 0.155 0.085 0.047 0.408 KS test for the above 32 p values: 0.670 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-25_08:31, p-values for 5 runs: 0.2156, 0.4941, 0.5489, 0.1091, 0.5926 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-25_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 4960 5134.0 5.898 6.647 r= 30 23256 23103.0 1.013 7.659 r= 31 11560 11551.5 0.006 7.665 chi-square = 7.665 with df = 3; p-value = 0.947 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-25_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 197 211.4 0.983 0.983 r= 30 5174 5134.0 0.311 1.295 r= 31 23143 23103.0 0.069 1.364 r= 32 11486 11551.5 0.372 1.736 chi-square = 1.736 with df = 3; p-value = 0.371 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-25_08:31 b-rank test for bits 1 to 8, p=0.32724 b-rank test for bits 2 to 9, p=0.90076 b-rank test for bits 3 to 10, p=0.97167 b-rank test for bits 4 to 11, p=0.27168 b-rank test for bits 5 to 12, p=0.33371 b-rank test for bits 6 to 13, p=0.51745 b-rank test for bits 7 to 14, p=0.92408 b-rank test for bits 8 to 15, p=0.24775 b-rank test for bits 9 to 16, p=0.91108 b-rank test for bits 10 to 17, p=0.71261 b-rank test for bits 11 to 18, p=0.91281 b-rank test for bits 12 to 19, p=0.43804 b-rank test for bits 13 to 20, p=0.00938 b-rank test for bits 14 to 21, p=0.94628 b-rank test for bits 15 to 22, p=0.70841 b-rank test for bits 16 to 23, p=0.50095 b-rank test for bits 17 to 24, p=0.92910 b-rank test for bits 18 to 25, p=0.13557 b-rank test for bits 19 to 26, p=0.78170 b-rank test for bits 20 to 27, p=0.11925 b-rank test for bits 21 to 28, p=0.07854 b-rank test for bits 22 to 29, p=0.91662 b-rank test for bits 23 to 30, p=0.99335 b-rank test for bits 24 to 31, p=0.99017 b-rank test for bits 25 to 32, p=0.79363 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 = 0.013342 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-25_08:31 (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 141980 0.17 0.565574 2 141767 -0.33 0.369738 3 142204 0.69 0.754425 4 142402 1.15 0.875154 5 142001 0.21 0.584798 6 141652 -0.60 0.273841 7 141367 -1.27 0.102555 8 142233 0.76 0.775247 9 141382 -1.23 0.108960 10 141745 -0.38 0.350508 11 142645 1.72 0.957180 12 141797 -0.26 0.396486 13 142181 0.63 0.737202 14 141883 -0.06 0.475473 15 142175 0.62 0.732610 16 142131 0.52 0.697743 17 142361 1.06 0.854357 18 142007 0.23 0.590255 19 142425 1.20 0.885867 20 141480 -1.00 0.157905 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-25_08:31 Bits used No. missing words z-score p-value 23 to 32 141887 -0.0770 0.469312 22 to 31 142467 1.9230 0.972760 21 to 30 141886 -0.0804 0.467940 20 to 29 141508 -1.3839 0.083195 19 to 28 141808 -0.3494 0.363389 18 to 27 142266 1.2299 0.890632 17 to 26 141825 -0.2908 0.385605 16 to 25 141599 -1.0701 0.142286 15 to 24 141884 -0.0873 0.465199 14 to 23 142044 0.4644 0.678812 13 to 22 141889 -0.0701 0.472056 12 to 21 141284 -2.1563 0.015530 11 to 20 141891 -0.0632 0.474801 10 to 19 141400 -1.7563 0.039518 9 to 18 142019 0.3782 0.647349 8 to 17 142164 0.8782 0.810075 7 to 16 141739 -0.5873 0.278486 6 to 15 141745 -0.5667 0.285474 5 to 14 141896 -0.0460 0.481669 4 to 13 141971 0.2127 0.584202 3 to 12 141775 -0.4632 0.321608 2 to 11 141758 -0.5218 0.300895 1 to 10 141788 -0.4184 0.337835 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-25_08:31 Bits used No. missing words z-score p-value 28 to 32 142569 2.2362 0.987330 27 to 31 142504 2.0158 0.978091 26 to 30 141917 0.0260 0.510371 25 to 29 142198 0.9785 0.836097 24 to 28 142352 1.5006 0.933267 23 to 27 142024 0.3887 0.651255 22 to 26 142076 0.5650 0.713957 21 to 25 142016 0.3616 0.641172 20 to 24 141756 -0.5198 0.301615 19 to 23 142010 0.3413 0.633544 18 to 22 142537 2.1277 0.983319 17 to 21 142407 1.6870 0.954200 16 to 20 141672 -0.8045 0.210552 15 to 19 141787 -0.4147 0.339189 14 to 18 142114 0.6938 0.756095 13 to 17 141670 -0.8113 0.208600 12 to 16 142011 0.3446 0.634819 11 to 15 141754 -0.5265 0.299256 10 to 14 141918 0.0294 0.511723 9 to 13 141836 -0.2486 0.401844 8 to 12 141857 -0.1774 0.429601 7 to 11 142028 0.4023 0.656258 6 to 10 141919 0.0328 0.513075 5 to 9 141490 -1.4215 0.077592 4 to 8 142532 2.1107 0.982603 3 to 7 142386 1.6158 0.946935 2 to 6 142145 0.7989 0.787820 1 to 5 142006 0.3277 0.628429 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-25_08:31 Bits used No. missing words z-score p-value 31 to 32 141048 -2.5408 0.005530 30 to 31 141872 -0.1101 0.456158 29 to 30 141537 -1.0983 0.136033 28 to 29 141851 -0.1721 0.431693 27 to 28 142598 2.0315 0.978897 26 to 27 141824 -0.2517 0.400632 25 to 26 142390 1.4179 0.921891 24 to 25 141837 -0.2134 0.415522 23 to 24 141725 -0.5437 0.293308 22 to 23 142401 1.4504 0.926520 21 to 22 141610 -0.8830 0.188624 20 to 21 141635 -0.8092 0.209191 19 to 20 142073 0.4828 0.685382 18 to 19 141859 -0.1485 0.440988 17 to 18 142092 0.5388 0.705005 16 to 17 141182 -2.1455 0.015956 15 to 16 141684 -0.6647 0.253124 14 to 15 142329 1.2380 0.892135 13 to 14 142110 0.5919 0.723057 12 to 13 142374 1.3707 0.914767 11 to 12 141986 0.2262 0.589464 10 to 11 142178 0.7925 0.785976 9 to 10 141588 -0.9479 0.171596 8 to 9 142114 0.6037 0.726994 7 to 8 141868 -0.1219 0.451482 6 to 7 141717 -0.5673 0.285240 5 to 6 142564 1.9312 0.973270 4 to 5 141749 -0.4729 0.318125 3 to 4 141725 -0.5437 0.293308 2 to 3 142460 1.6244 0.947854 1 to 2 141415 -1.4582 0.072393 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-25_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2514.39 0.203 0.580606 Test results for specific bytes for dh-ranFile-2015-06-25_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2370.93 -1.825 0.033979 2 to 9 2428.91 -1.005 0.157347 3 to 10 2468.82 -0.441 0.329604 4 to 11 2441.04 -0.834 0.202195 5 to 12 2454.16 -0.648 0.258423 6 to 13 2407.71 -1.305 0.095916 7 to 14 2592.14 1.303 0.903732 8 to 15 2540.31 0.570 0.715702 9 to 16 2579.76 1.128 0.870346 10 to 17 2467.28 -0.463 0.321783 11 to 18 2747.14 3.495 0.999763 12 to 19 2473.01 -0.382 0.351340 13 to 20 2450.38 -0.702 0.241428 14 to 21 2508.66 0.122 0.548712 15 to 22 2518.93 0.268 0.605529 16 to 23 2338.97 -2.277 0.011382 17 to 24 2531.77 0.449 0.673367 18 to 25 2508.86 0.125 0.549869 19 to 26 2509.25 0.131 0.552066 20 to 27 2369.34 -1.848 0.032318 21 to 28 2457.94 -0.595 0.275999 22 to 29 2414.05 -1.216 0.112073 23 to 30 2460.72 -0.556 0.289265 24 to 31 2451.80 -0.682 0.247743 25 to 32 2450.58 -0.699 0.242302 CDPARK for dh-ranFile-2015-06-25_08:31: 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 3521 -0.0913 0.463617 3523 0.0000 0.500000 3525 0.0913 0.536383 3557 1.5525 0.939730 3542 0.8676 0.807188 3528 0.2283 0.590298 3511 -0.5479 0.291865 3522 -0.0457 0.481790 3539 0.7306 0.767486 3533 0.4566 0.676028 Square side=100, avg. no. parked=3530.10 sample std.=12.44 p-value of the KSTEST for those 10 p-values: 0.240116 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-25_08:31 0.0953,0.3161,0.4531,0.9707,0.0272,0.6252,0.8997,0.4841,0.4973,0.5541, The KS test for those 10 p-values: 0.897931 The 3DSPHERES test for dh-ranFile-2015-06-25_08:31 sample no r^3 equiv. uni. 1 61.506 0.871292 2 1.965 0.063397 3 8.842 0.255261 4 69.116 0.900127 5 3.446 0.108513 6 29.634 0.627608 7 37.076 0.709417 8 10.489 0.295052 9 172.226 0.996788 10 24.561 0.558994 11 9.009 0.259393 12 16.538 0.423772 13 14.773 0.388855 14 55.034 0.840303 15 25.154 0.567634 16 51.425 0.819887 17 37.748 0.715855 18 84.931 0.941048 19 10.962 0.306077 20 17.309 0.438395 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.696717 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-25_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -1.6 -0.4 -0.3 -0.2 -0.2 1.1 -0.5 0.3 0.2 1.1 1.2 -0.9 -0.2 -1.7 1.5 0.2 -1.2 2.5 -0.2 -0.1 -1.1 -2.3 0.8 0.6 0.8 -2.4 0.7 0.0 0.1 0.4 -1.1 -0.8 -0.6 1.5 1.2 1.5 -0.4 1.0 -0.6 0.0 1.8 Chi-square with 42 degrees of freedom:48.898885 z-score=0.752730, p-value=0.784342 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-25_08:31 Test no p-value 1 0.009918 2 0.094973 3 0.432160 4 0.177017 5 0.012070 6 0.679052 7 0.580779 8 0.678991 9 0.386226 10 0.384584 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.082783 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-25_08:31: (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 66673 0.00 66514 0.35 3 25000.00 25035 0.05 25084 0.28 4 6666.67 6685 0.05 6746 0.94 5 1388.89 1331 2.41 1381 0.04 6 238.10 242 0.06 237 0.01 7 34.72 29 0.94 30 0.64 8 4.96 4 0.19 7 0.84 p=0.28349 p=0.20462 Number of rngs required: 688019, p-value: 0.329 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-25_08:31 No. of wins: Observed Expected 98722 98585.9 z-score= 0.609, pvalue=0.72871 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66645 66666.7 0.007 0.007 2 37579 37654.3 0.151 0.158 3 27166 26954.7 1.656 1.814 4 19261 19313.5 0.143 1.956 5 13821 13851.4 0.067 2.023 6 9928 9943.5 0.024 2.047 7 7176 7145.0 0.134 2.181 8 5031 5139.1 2.273 4.454 9 3781 3699.9 1.779 6.233 10 2622 2666.3 0.736 6.969 11 1906 1923.3 0.156 7.125 12 1394 1388.7 0.020 7.145 13 1008 1003.7 0.018 7.164 14 747 726.1 0.599 7.763 15 513 525.8 0.313 8.076 16 375 381.2 0.099 8.176 17 240 276.5 4.828 13.004 18 191 200.8 0.481 13.485 19 179 146.0 7.467 20.951 20 114 106.2 0.571 21.522 21 323 287.1 4.485 26.007 Chisq= 26.01 for 20 degrees of freedom, p= 0.83443 SUMMARY of craptest p-value for no. of wins: 0.728706 p-value for throws/game: 0.834430 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-25_08:31 No. of wins: Observed Expected 98265 98585.9 z-score=-1.435, pvalue=0.07563 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66655 66666.7 0.002 0.002 2 37917 37654.3 1.832 1.835 3 27058 26954.7 0.396 2.230 4 19092 19313.5 2.539 4.770 5 13769 13851.4 0.490 5.260 6 9823 9943.5 1.461 6.721 7 7116 7145.0 0.118 6.839 8 5040 5139.1 1.910 8.749 9 3774 3699.9 1.485 10.235 10 2721 2666.3 1.122 11.357 11 1906 1923.3 0.156 11.513 12 1462 1388.7 3.865 15.378 13 1008 1003.7 0.018 15.396 14 736 726.1 0.134 15.530 15 518 525.8 0.117 15.647 16 392 381.2 0.309 15.955 17 284 276.5 0.201 16.157 18 187 200.8 0.952 17.109 19 139 146.0 0.334 17.443 20 103 106.2 0.097 17.541 21 300 287.1 0.578 18.119 Chisq= 18.12 for 20 degrees of freedom, p= 0.42043 SUMMARY of craptest p-value for no. of wins: 0.075634 p-value for throws/game: 0.420426 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0055,0.0094,0.0095,0.0099,0.0114,0.0121,0.0133,0.0155,0.0160,0.0272, 0.0323,0.0340,0.0395,0.0469,0.0505,0.0553,0.0634,0.0639,0.0724,0.0756, 0.0776,0.0785,0.0828,0.0832,0.0851,0.0950,0.0953,0.0959,0.1026,0.1085, 0.1090,0.1091,0.1121,0.1135,0.1193,0.1356,0.1360,0.1423,0.1464,0.1549, 0.1573,0.1579,0.1716,0.1767,0.1770,0.1886,0.2022,0.2046,0.2086,0.2092, 0.2106,0.2156,0.2275,0.2280,0.2401,0.2414,0.2423,0.2477,0.2477,0.2517, 0.2531,0.2553,0.2584,0.2594,0.2706,0.2708,0.2717,0.2738,0.2760,0.2785, 0.2835,0.2852,0.2855,0.2893,0.2919,0.2933,0.2933,0.2951,0.2993,0.3009, 0.3016,0.3061,0.3161,0.3181,0.3216,0.3218,0.3272,0.3291,0.3296,0.3337, 0.3378,0.3392,0.3417,0.3466,0.3505,0.3513,0.3634,0.3697,0.3709,0.3782, 0.3813,0.3846,0.3850,0.3856,0.3862,0.3889,0.3965,0.4006,0.4018,0.4075, 0.4077,0.4155,0.4204,0.4216,0.4238,0.4296,0.4309,0.4317,0.4322,0.4380, 0.4384,0.4400,0.4410,0.4443,0.4515,0.4531,0.4562,0.4636,0.4652,0.4679, 0.4693,0.4721,0.4748,0.4755,0.4817,0.4818,0.4841,0.4941,0.4973,0.5000, 0.5009,0.5104,0.5117,0.5131,0.5174,0.5364,0.5487,0.5489,0.5499,0.5521, 0.5541,0.5547,0.5590,0.5656,0.5676,0.5806,0.5808,0.5842,0.5848,0.5895, 0.5903,0.5903,0.5926,0.6055,0.6123,0.6150,0.6200,0.6252,0.6276,0.6284, 0.6335,0.6348,0.6409,0.6412,0.6473,0.6513,0.6563,0.6596,0.6611,0.6696, 0.6734,0.6760,0.6788,0.6790,0.6791,0.6854,0.6967,0.6977,0.7050,0.7084, 0.7094,0.7126,0.7140,0.7157,0.7159,0.7231,0.7270,0.7287,0.7326,0.7328, 0.7372,0.7388,0.7544,0.7561,0.7675,0.7748,0.7752,0.7817,0.7843,0.7860, 0.7878,0.7936,0.8009,0.8072,0.8101,0.8199,0.8344,0.8354,0.8361,0.8377, 0.8403,0.8544,0.8703,0.8713,0.8752,0.8821,0.8859,0.8861,0.8906,0.8921, 0.8979,0.8997,0.9001,0.9008,0.9037,0.9044,0.9111,0.9128,0.9148,0.9166, 0.9219,0.9241,0.9265,0.9291,0.9331,0.9333,0.9397,0.9410,0.9463,0.9465, 0.9469,0.9479,0.9535,0.9542,0.9572,0.9707,0.9717,0.9728,0.9733,0.9781, 0.9789,0.9826,0.9833,0.9873,0.9902,0.9933,0.9968,0.9968,0.9998, Overall p-value after applying KStest on 269 p-values = 0.579480 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.