RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-12_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 15.6081 0.448235 2 to 25 15.86 16.6950 0.524791 3 to 26 15.79 11.4568 0.168143 4 to 27 15.57 19.2917 0.687952 5 to 28 15.47 24.5217 0.894062 6 to 29 15.92 22.5662 0.836088 7 to 30 15.90 11.8967 0.193646 8 to 31 15.78 23.7416 0.873371 9 to 32 15.59 11.5539 0.173632 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.837153 Tough bday spacings test for dh-ranFile-2016-03-12_18:31: 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 6 41 78 89 96 86 44 32 18 9 1 (O-E)^2/E 1.1 0.5 0.3 0.8 0.0 0.8 1.3 0.2 0.7 0.9 2.3 Birthday Spacings: Sum(O-E)^2/E= 8.755, p= 0.445 RESULTS OF GCD FOR dh-ranFile-2016-03-12_18:31 Euclid's algorithm: p-value, steps to gcd: 0.459573 p-value, dist. of gcd's: 0.874601 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-12_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.559 0.986 0.647 0.914 0.780 0.923 0.552 0.390 Bits 8 to 15---> 0.999 0.543 0.736 0.155 0.985 0.731 0.529 0.951 Bits 16 to 23---> 0.283 0.430 0.341 0.819 0.553 0.756 0.664 0.144 Bits 24 to 31---> 0.803 0.874 0.363 0.202 0.901 0.675 0.500 0.370 KS test for the above 32 p values: 0.982 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-12_18:31, p-values for 5 runs: 0.6846, 0.2485, 0.5579, 0.7040, 0.8923 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-12_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5089 5134.0 0.395 0.829 r= 30 23223 23103.0 0.623 1.452 r= 31 11467 11551.5 0.618 2.070 chi-square = 2.070 with df = 3; p-value = 0.442 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-12_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 231 211.4 1.814 1.814 r= 30 5154 5134.0 0.078 1.892 r= 31 22980 23103.0 0.655 2.547 r= 32 11635 11551.5 0.603 3.150 chi-square = 3.150 with df = 3; p-value = 0.631 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-12_18:31 b-rank test for bits 1 to 8, p=0.95543 b-rank test for bits 2 to 9, p=0.78889 b-rank test for bits 3 to 10, p=0.08876 b-rank test for bits 4 to 11, p=0.08894 b-rank test for bits 5 to 12, p=0.97534 b-rank test for bits 6 to 13, p=0.00733 b-rank test for bits 7 to 14, p=0.39954 b-rank test for bits 8 to 15, p=0.48724 b-rank test for bits 9 to 16, p=0.09005 b-rank test for bits 10 to 17, p=0.72012 b-rank test for bits 11 to 18, p=0.27117 b-rank test for bits 12 to 19, p=0.31814 b-rank test for bits 13 to 20, p=0.43574 b-rank test for bits 14 to 21, p=0.23424 b-rank test for bits 15 to 22, p=0.60081 b-rank test for bits 16 to 23, p=0.36931 b-rank test for bits 17 to 24, p=0.98414 b-rank test for bits 18 to 25, p=0.63078 b-rank test for bits 19 to 26, p=0.82488 b-rank test for bits 20 to 27, p=0.00339 b-rank test for bits 21 to 28, p=0.39314 b-rank test for bits 22 to 29, p=0.32275 b-rank test for bits 23 to 30, p=0.42694 b-rank test for bits 24 to 31, p=0.43743 b-rank test for bits 25 to 32, p=0.11006 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 = 0.291453 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-12_18:31 (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 142198 0.67 0.749991 2 142406 1.16 0.877066 3 142389 1.12 0.868797 4 142195 0.67 0.747759 5 142242 0.78 0.781499 6 142337 1.00 0.841158 7 142015 0.25 0.597504 8 142253 0.80 0.789003 9 142482 1.34 0.909554 10 142553 1.50 0.933697 11 142028 0.28 0.609212 12 142214 0.71 0.761720 13 142029 0.28 0.610109 14 142271 0.85 0.800951 15 142507 1.40 0.918707 16 141942 0.08 0.530422 17 141896 -0.03 0.487577 18 141838 -0.17 0.433819 19 142479 1.33 0.908406 20 141883 -0.06 0.475473 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-12_18:31 Bits used No. missing words z-score p-value 23 to 32 141842 -0.2322 0.408202 22 to 31 142124 0.7402 0.770423 21 to 30 141811 -0.3391 0.367279 20 to 29 141951 0.1437 0.557127 19 to 28 142329 1.4471 0.926071 18 to 27 142021 0.3851 0.649907 17 to 26 141730 -0.6184 0.268163 16 to 25 141561 -1.2011 0.114849 15 to 24 141911 0.0058 0.502297 14 to 23 142013 0.3575 0.639635 13 to 22 141687 -0.7667 0.221643 12 to 21 141836 -0.2529 0.400187 11 to 20 142258 1.2023 0.885378 10 to 19 142039 0.4471 0.672612 9 to 18 142258 1.2023 0.885378 8 to 17 141794 -0.3977 0.345430 7 to 16 142156 0.8506 0.802500 6 to 15 142421 1.7644 0.961166 5 to 14 141860 -0.1701 0.432464 4 to 13 141298 -2.1080 0.017514 3 to 12 142214 1.0506 0.853276 2 to 11 141314 -2.0529 0.020043 1 to 10 141707 -0.6977 0.242686 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-12_18:31 Bits used No. missing words z-score p-value 28 to 32 141727 -0.6181 0.268265 27 to 31 141662 -0.8384 0.200901 26 to 30 141989 0.2701 0.606446 25 to 29 141772 -0.4655 0.320778 24 to 28 141788 -0.4113 0.340431 23 to 27 142068 0.5379 0.704665 22 to 26 142405 1.6802 0.953544 21 to 25 142188 0.9446 0.827580 20 to 24 142082 0.5853 0.720834 19 to 23 141661 -0.8418 0.199951 18 to 22 141604 -1.0350 0.150331 17 to 21 141609 -1.0181 0.154323 16 to 20 142023 0.3853 0.650001 15 to 19 142060 0.5107 0.695236 14 to 18 141933 0.0802 0.531976 13 to 17 141781 -0.4350 0.331775 12 to 16 142834 3.1345 0.999139 11 to 15 141813 -0.3265 0.372007 10 to 14 141975 0.2226 0.588081 9 to 13 142410 1.6972 0.955169 8 to 12 142391 1.6328 0.948742 7 to 11 142017 0.3650 0.642438 6 to 10 141667 -0.8215 0.205693 5 to 9 142358 1.5209 0.935859 4 to 8 141964 0.1853 0.573512 3 to 7 141775 -0.4554 0.324427 2 to 6 141766 -0.4859 0.313532 1 to 5 141862 -0.1604 0.436267 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-12_18:31 Bits used No. missing words z-score p-value 31 to 32 141645 -0.7797 0.217774 30 to 31 142030 0.3560 0.639064 29 to 30 142296 1.1406 0.872986 28 to 29 142235 0.9607 0.831643 27 to 28 142871 2.8368 0.997721 26 to 27 141496 -1.2193 0.111372 25 to 26 141931 0.0639 0.525484 24 to 25 142183 0.8073 0.790249 23 to 24 141656 -0.7473 0.227445 22 to 23 142110 0.5919 0.723057 21 to 22 141628 -0.8299 0.203303 20 to 21 141891 -0.0541 0.478439 19 to 20 142309 1.1790 0.880794 18 to 19 141560 -1.0305 0.151394 17 to 18 142202 0.8633 0.806023 16 to 17 141528 -1.1249 0.130323 15 to 16 142069 0.4710 0.681181 14 to 15 142267 1.0551 0.854304 13 to 14 142400 1.4474 0.926108 12 to 13 141814 -0.2812 0.389275 11 to 12 142065 0.4592 0.676956 10 to 11 141580 -0.9715 0.165656 9 to 10 142059 0.4415 0.670576 8 to 9 141664 -0.7237 0.234629 7 to 8 141661 -0.7325 0.231921 6 to 7 141764 -0.4287 0.334070 5 to 6 141926 0.0492 0.519610 4 to 5 141475 -1.2812 0.100060 3 to 4 142284 1.1052 0.865468 2 to 3 141982 0.2144 0.584869 1 to 2 141395 -1.5172 0.064608 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-12_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2603.96 1.470 0.929241 Test results for specific bytes for dh-ranFile-2016-03-12_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2552.88 0.748 0.772706 2 to 9 2494.48 -0.078 0.468883 3 to 10 2512.08 0.171 0.567799 4 to 11 2492.86 -0.101 0.459789 5 to 12 2754.49 3.599 0.999840 6 to 13 2507.18 0.102 0.540446 7 to 14 2341.50 -2.242 0.012496 8 to 15 2595.09 1.345 0.910647 9 to 16 2479.53 -0.290 0.386095 10 to 17 2581.86 1.158 0.876507 11 to 18 2515.67 0.222 0.587672 12 to 19 2498.44 -0.022 0.491212 13 to 20 2457.61 -0.599 0.274435 14 to 21 2460.34 -0.561 0.287434 15 to 22 2511.96 0.169 0.567170 16 to 23 2425.80 -1.049 0.147003 17 to 24 2590.10 1.274 0.898710 18 to 25 2474.70 -0.358 0.360230 19 to 26 2519.99 0.283 0.611306 20 to 27 2522.29 0.315 0.623684 21 to 28 2506.16 0.087 0.534718 22 to 29 2479.51 -0.290 0.386005 23 to 30 2398.86 -1.430 0.076313 24 to 31 2520.81 0.294 0.615748 25 to 32 2388.16 -1.582 0.056865 CDPARK for dh-ranFile-2016-03-12_18:31: 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 3517 -0.2740 0.392053 3529 0.2740 0.607947 3516 -0.3196 0.374623 3491 -1.4612 0.071982 3512 -0.5023 0.307734 3505 -0.8219 0.205562 3522 -0.0457 0.481790 3508 -0.6849 0.246694 3485 -1.7352 0.041356 3552 1.3242 0.907282 Square side=100, avg. no. parked=3513.70 sample std.=17.99 p-value of the KSTEST for those 10 p-values: 0.230186 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-12_18:31 0.8255,0.0969,0.4848,0.8391,0.5571,0.8245,0.6890,0.2253,0.7680,0.6292, The KS test for those 10 p-values: 0.360605 The 3DSPHERES test for dh-ranFile-2016-03-12_18:31 sample no r^3 equiv. uni. 1 52.568 0.826620 2 39.384 0.730938 3 17.966 0.450561 4 38.185 0.719962 5 6.467 0.193913 6 13.004 0.351746 7 0.534 0.017639 8 11.343 0.314845 9 18.129 0.453544 10 36.103 0.699835 11 26.191 0.582315 12 5.505 0.167658 13 32.592 0.662569 14 49.123 0.805519 15 6.297 0.189348 16 1.983 0.063955 17 8.380 0.243701 18 6.295 0.189284 19 51.384 0.819642 20 52.759 0.827722 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.690231 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-12_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 0.6 -1.1 0.0 0.6 -1.1 -0.4 0.5 -1.3 0.1 -0.8 1.9 -1.0 -0.3 -0.1 -0.4 -0.3 -0.9 1.7 0.7 0.8 -0.0 -1.8 2.3 -0.4 -0.2 -0.3 2.1 -1.1 -0.7 -0.7 -0.2 0.3 -0.1 0.1 0.3 -1.0 -1.6 1.0 0.1 2.0 0.8 Chi-square with 42 degrees of freedom:42.821030 z-score=0.089582, p-value=0.564232 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-12_18:31 Test no p-value 1 0.037448 2 0.151690 3 0.351028 4 0.191720 5 0.099968 6 0.040691 7 0.713471 8 0.560763 9 0.619488 10 0.418389 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.071646 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-12_18:31: (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 66679 0.00 66960 1.29 3 25000.00 24922 0.24 24624 5.66 4 6666.67 6670 0.00 6729 0.58 5 1388.89 1424 0.89 1414 0.45 6 238.10 259 1.84 242 0.06 7 34.72 38 0.31 25 2.72 8 4.96 7 0.84 5 0.00 p=0.33945 p=0.90418 Number of rngs required: 687760, p-value: 0.229 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-12_18:31 No. of wins: Observed Expected 98591 98585.9 z-score= 0.023, pvalue=0.50917 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66952 66666.7 1.221 1.221 2 37570 37654.3 0.189 1.410 3 27054 26954.7 0.366 1.776 4 19289 19313.5 0.031 1.807 5 13800 13851.4 0.191 1.997 6 9812 9943.5 1.740 3.738 7 7124 7145.0 0.062 3.800 8 5244 5139.1 2.142 5.942 9 3700 3699.9 0.000 5.942 10 2653 2666.3 0.066 6.008 11 1909 1923.3 0.107 6.115 12 1318 1388.7 3.603 9.718 13 948 1003.7 3.093 12.811 14 703 726.1 0.737 13.549 15 519 525.8 0.089 13.637 16 363 381.2 0.864 14.502 17 248 276.5 2.945 17.447 18 243 200.8 8.855 26.302 19 142 146.0 0.109 26.411 20 100 106.2 0.364 26.774 21 309 287.1 1.668 28.443 Chisq= 28.44 for 20 degrees of freedom, p= 0.90067 SUMMARY of craptest p-value for no. of wins: 0.509173 p-value for throws/game: 0.900672 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-12_18:31 No. of wins: Observed Expected 98541 98585.9 z-score=-0.201, pvalue=0.42049 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66888 66666.7 0.735 0.735 2 37777 37654.3 0.400 1.135 3 26931 26954.7 0.021 1.155 4 19260 19313.5 0.148 1.303 5 13843 13851.4 0.005 1.309 6 9825 9943.5 1.413 2.722 7 7089 7145.0 0.439 3.161 8 4975 5139.1 5.238 8.399 9 3675 3699.9 0.167 8.566 10 2656 2666.3 0.040 8.606 11 2015 1923.3 4.369 12.975 12 1441 1388.7 1.967 14.942 13 992 1003.7 0.137 15.079 14 727 726.1 0.001 15.080 15 551 525.8 1.204 16.284 16 338 381.2 4.885 21.169 17 254 276.5 1.837 23.006 18 223 200.8 2.447 25.454 19 144 146.0 0.027 25.481 20 117 106.2 1.095 26.576 21 279 287.1 0.229 26.805 Chisq= 26.80 for 20 degrees of freedom, p= 0.85916 SUMMARY of craptest p-value for no. of wins: 0.420492 p-value for throws/game: 0.859160 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0034,0.0073,0.0125,0.0175,0.0176,0.0200,0.0374,0.0407,0.0414,0.0569, 0.0640,0.0646,0.0716,0.0720,0.0763,0.0888,0.0889,0.0900,0.0969,0.1000, 0.1001,0.1101,0.1114,0.1148,0.1303,0.1441,0.1470,0.1503,0.1514,0.1517, 0.1543,0.1552,0.1657,0.1677,0.1681,0.1736,0.1893,0.1893,0.1917,0.1936, 0.1939,0.2000,0.2009,0.2017,0.2033,0.2056,0.2057,0.2178,0.2216,0.2253, 0.2274,0.2288,0.2302,0.2319,0.2342,0.2346,0.2427,0.2437,0.2467,0.2485, 0.2682,0.2683,0.2712,0.2744,0.2828,0.2874,0.2915,0.3077,0.3135,0.3148, 0.3181,0.3208,0.3227,0.3244,0.3318,0.3341,0.3395,0.3404,0.3411,0.3454, 0.3510,0.3517,0.3602,0.3606,0.3631,0.3673,0.3693,0.3704,0.3720,0.3746, 0.3860,0.3861,0.3893,0.3898,0.3921,0.3931,0.3995,0.4002,0.4082,0.4184, 0.4205,0.4269,0.4300,0.4325,0.4338,0.4357,0.4363,0.4374,0.4420,0.4445, 0.4482,0.4506,0.4535,0.4596,0.4598,0.4689,0.4755,0.4784,0.4818,0.4848, 0.4872,0.4876,0.4912,0.5005,0.5023,0.5092,0.5196,0.5248,0.5255,0.5290, 0.5304,0.5320,0.5347,0.5404,0.5435,0.5525,0.5532,0.5571,0.5571,0.5579, 0.5593,0.5608,0.5642,0.5672,0.5678,0.5735,0.5823,0.5849,0.5877,0.5881, 0.5975,0.6008,0.6064,0.6079,0.6092,0.6101,0.6113,0.6157,0.6195,0.6237, 0.6292,0.6308,0.6310,0.6391,0.6396,0.6424,0.6473,0.6499,0.6500,0.6626, 0.6644,0.6706,0.6726,0.6751,0.6770,0.6812,0.6846,0.6880,0.6890,0.6902, 0.6952,0.6998,0.7040,0.7047,0.7135,0.7200,0.7201,0.7208,0.7231,0.7309, 0.7311,0.7363,0.7478,0.7500,0.7558,0.7617,0.7680,0.7704,0.7727,0.7803, 0.7815,0.7889,0.7890,0.7902,0.8010,0.8025,0.8025,0.8055,0.8060,0.8189, 0.8196,0.8245,0.8249,0.8255,0.8266,0.8276,0.8277,0.8316,0.8361,0.8372, 0.8391,0.8412,0.8533,0.8543,0.8592,0.8655,0.8688,0.8730,0.8734,0.8741, 0.8746,0.8765,0.8771,0.8808,0.8854,0.8854,0.8923,0.8941,0.8987,0.9007, 0.9008,0.9042,0.9073,0.9084,0.9096,0.9106,0.9136,0.9187,0.9227,0.9261, 0.9261,0.9292,0.9337,0.9359,0.9487,0.9507,0.9535,0.9552,0.9554,0.9612, 0.9753,0.9820,0.9841,0.9850,0.9860,0.9977,0.9989,0.9991,0.9998, Overall p-value after applying KStest on 269 p-values = 0.110799 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.