RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-24_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.51 19.9342 0.722393 2 to 25 15.65 17.6426 0.588286 3 to 26 15.87 18.1070 0.617881 4 to 27 15.74 13.4283 0.292925 5 to 28 15.98 11.4757 0.169207 6 to 29 15.94 18.3583 0.633418 7 to 30 15.53 26.9535 0.941246 8 to 31 15.59 20.2675 0.739221 9 to 32 15.53 27.6171 0.950383 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.277367 Tough bday spacings test for dh-ranFile-2016-02-24_21:31: 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 11 48 68 83 102 69 56 36 15 7 5 (O-E)^2/E 0.4 3.5 0.4 2.2 0.2 1.1 0.3 1.3 0.0 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.579, p= 0.522 RESULTS OF GCD FOR dh-ranFile-2016-02-24_21:31 Euclid's algorithm: p-value, steps to gcd: 0.696839 p-value, dist. of gcd's: 0.724429 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-24_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.548 0.934 0.292 0.343 0.261 0.455 0.904 0.174 Bits 8 to 15---> 0.610 0.118 0.889 0.196 0.254 0.766 0.936 0.524 Bits 16 to 23---> 0.359 0.942 0.265 0.116 0.155 0.315 0.535 0.990 Bits 24 to 31---> 0.272 0.348 0.830 0.431 0.844 0.887 0.806 0.761 KS test for the above 32 p values: 0.573 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-24_21:31, p-values for 5 runs: 0.3916, 0.5811, 0.8376, 0.9415, 0.3899 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-24_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5085 5134.0 0.468 0.981 r= 30 23359 23103.0 2.836 3.817 r= 31 11355 11551.5 3.343 7.160 chi-square = 7.160 with df = 3; p-value = 0.933 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-24_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5054 5134.0 1.247 2.395 r= 31 23105 23103.0 0.000 2.396 r= 32 11614 11551.5 0.338 2.733 chi-square = 2.733 with df = 3; p-value = 0.565 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-24_21:31 b-rank test for bits 1 to 8, p=0.15263 b-rank test for bits 2 to 9, p=0.71579 b-rank test for bits 3 to 10, p=0.25252 b-rank test for bits 4 to 11, p=0.31734 b-rank test for bits 5 to 12, p=0.09767 b-rank test for bits 6 to 13, p=0.24252 b-rank test for bits 7 to 14, p=0.91536 b-rank test for bits 8 to 15, p=0.40018 b-rank test for bits 9 to 16, p=0.65634 b-rank test for bits 10 to 17, p=0.83217 b-rank test for bits 11 to 18, p=0.16964 b-rank test for bits 12 to 19, p=0.49600 b-rank test for bits 13 to 20, p=0.59803 b-rank test for bits 14 to 21, p=0.03015 b-rank test for bits 15 to 22, p=0.21033 b-rank test for bits 16 to 23, p=0.57034 b-rank test for bits 17 to 24, p=0.67142 b-rank test for bits 18 to 25, p=0.10674 b-rank test for bits 19 to 26, p=0.59502 b-rank test for bits 20 to 27, p=0.40941 b-rank test for bits 21 to 28, p=0.46172 b-rank test for bits 22 to 29, p=0.34017 b-rank test for bits 23 to 30, p=0.93741 b-rank test for bits 24 to 31, p=0.92867 b-rank test for bits 25 to 32, p=0.06159 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 = 0.684111 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-24_21:31 (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 141468 -1.03 0.151236 3 142011 0.24 0.593884 4 142111 0.47 0.681248 5 141189 -1.68 0.046186 6 141885 -0.06 0.477334 7 141437 -1.10 0.134889 8 141686 -0.52 0.300905 9 141230 -1.59 0.056231 10 141714 -0.46 0.324059 11 142662 1.76 0.960675 12 141428 -1.12 0.130379 13 141405 -1.18 0.119330 14 141069 -1.96 0.024801 15 141808 -0.24 0.406425 16 141744 -0.39 0.349643 17 141520 -0.91 0.181504 18 142063 0.36 0.640218 19 142797 2.07 0.980960 20 141833 -0.18 0.429228 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-24_21:31 Bits used No. missing words z-score p-value 23 to 32 142408 1.7196 0.957243 22 to 31 142273 1.2540 0.895085 21 to 30 142121 0.7299 0.767273 20 to 29 142195 0.9851 0.837705 19 to 28 141777 -0.4563 0.324083 18 to 27 141864 -0.1563 0.437894 17 to 26 142014 0.3609 0.640925 16 to 25 142357 1.5437 0.938668 15 to 24 141864 -0.1563 0.437894 14 to 23 142106 0.6782 0.751169 13 to 22 141667 -0.8356 0.201684 12 to 21 141665 -0.8425 0.199749 11 to 20 142009 0.3437 0.634460 10 to 19 142173 0.9092 0.818380 9 to 18 142094 0.6368 0.737870 8 to 17 142075 0.5713 0.716094 7 to 16 141516 -1.3563 0.087500 6 to 15 141656 -0.8736 0.191181 5 to 14 141998 0.3058 0.620106 4 to 13 141556 -1.2184 0.111540 3 to 12 141666 -0.8391 0.200715 2 to 11 141395 -1.7736 0.038069 1 to 10 141671 -0.8218 0.205588 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-24_21:31 Bits used No. missing words z-score p-value 28 to 32 141811 -0.3333 0.369446 27 to 31 142084 0.5921 0.723109 26 to 30 141908 -0.0045 0.498201 25 to 29 142279 1.2531 0.894919 24 to 28 141813 -0.3265 0.372007 23 to 27 142035 0.4260 0.664946 22 to 26 142195 0.9684 0.833571 21 to 25 141518 -1.3265 0.092330 20 to 24 142022 0.3819 0.648744 19 to 23 141678 -0.7842 0.216470 18 to 22 141861 -0.1638 0.434932 17 to 21 142313 1.3684 0.914402 16 to 20 140979 -3.1537 0.000806 15 to 19 141311 -2.0282 0.021268 14 to 18 141744 -0.5604 0.287589 13 to 17 141904 -0.0181 0.492792 12 to 16 141901 -0.0282 0.488737 11 to 15 142080 0.5785 0.718551 10 to 14 142200 0.9853 0.837767 9 to 13 141704 -0.6960 0.243204 8 to 12 141671 -0.8079 0.209575 7 to 11 141955 0.1548 0.561516 6 to 10 141883 -0.0893 0.464440 5 to 9 141909 -0.0011 0.499554 4 to 8 141708 -0.6825 0.247470 3 to 7 142015 0.3582 0.639905 2 to 6 142145 0.7989 0.787820 1 to 5 141397 -1.7367 0.041219 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-24_21:31 Bits used No. missing words z-score p-value 31 to 32 141522 -1.1426 0.126609 30 to 31 141910 0.0020 0.500789 29 to 30 142340 1.2704 0.898031 28 to 29 142002 0.2734 0.607713 27 to 28 142061 0.4474 0.672708 26 to 27 141452 -1.3491 0.088660 25 to 26 141733 -0.5201 0.301480 24 to 25 141706 -0.5998 0.274322 23 to 24 142097 0.5536 0.710073 22 to 23 141715 -0.5732 0.283240 21 to 22 142141 0.6834 0.752821 20 to 21 141900 -0.0275 0.489022 19 to 20 141913 0.0108 0.504319 18 to 19 141629 -0.8269 0.204138 17 to 18 141628 -0.8299 0.203303 16 to 17 141836 -0.2163 0.414372 15 to 16 141649 -0.7679 0.221263 14 to 15 142438 1.5595 0.940561 13 to 14 141530 -1.1190 0.131577 12 to 13 142023 0.3353 0.631304 11 to 12 141585 -0.9567 0.169353 10 to 11 142159 0.7365 0.769284 9 to 10 141766 -0.4228 0.336220 8 to 9 142129 0.6480 0.741506 7 to 8 142204 0.8692 0.807640 6 to 7 142357 1.3206 0.906676 5 to 6 141730 -0.5290 0.298404 4 to 5 141856 -0.1573 0.437498 3 to 4 142438 1.5595 0.940561 2 to 3 141517 -1.1573 0.123572 1 to 2 142010 0.2970 0.616752 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-24_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2430.81 -0.978 0.163923 Test results for specific bytes for dh-ranFile-2016-02-24_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2539.56 0.559 0.712067 2 to 9 2434.31 -0.929 0.176449 3 to 10 2586.19 1.219 0.888557 4 to 11 2544.04 0.623 0.733306 5 to 12 2363.60 -1.929 0.026865 6 to 13 2519.77 0.280 0.610086 7 to 14 2434.18 -0.931 0.175980 8 to 15 2524.87 0.352 0.637474 9 to 16 2484.46 -0.220 0.413033 10 to 17 2537.17 0.526 0.700447 11 to 18 2460.25 -0.562 0.287002 12 to 19 2604.00 1.471 0.929324 13 to 20 2532.08 0.454 0.674948 14 to 21 2553.93 0.763 0.777177 15 to 22 2471.91 -0.397 0.345581 16 to 23 2472.32 -0.392 0.347707 17 to 24 2547.02 0.665 0.746958 18 to 25 2517.39 0.246 0.597140 19 to 26 2471.63 -0.401 0.344148 20 to 27 2578.95 1.117 0.867908 21 to 28 2376.43 -1.748 0.040268 22 to 29 2339.12 -2.275 0.011448 23 to 30 2478.04 -0.311 0.378051 24 to 31 2459.98 -0.566 0.285717 25 to 32 2527.37 0.387 0.650640 CDPARK for dh-ranFile-2016-02-24_21:31: 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 3515 -0.3653 0.357445 3536 0.5936 0.723613 3531 0.3653 0.642555 3487 -1.6438 0.050105 3527 0.1826 0.572463 3549 1.1872 0.882429 3554 1.4155 0.921543 3519 -0.1826 0.427537 3532 0.4110 0.659449 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3527.10 sample std.=17.83 p-value of the KSTEST for those 10 p-values: 0.643905 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-24_21:31 0.6943,0.5979,0.8325,0.6080,0.0849,0.1204,0.1012,0.3403,0.3991,0.7662, The KS test for those 10 p-values: 0.787193 The 3DSPHERES test for dh-ranFile-2016-02-24_21:31 sample no r^3 equiv. uni. 1 3.951 0.123406 2 2.026 0.065317 3 0.138 0.004581 4 16.898 0.430647 5 24.137 0.552712 6 33.215 0.669506 7 6.153 0.185440 8 15.603 0.405533 9 27.213 0.596304 10 0.093 0.003105 11 93.821 0.956166 12 0.573 0.018924 13 35.782 0.696608 14 52.994 0.829062 15 17.391 0.439925 16 48.846 0.803718 17 89.201 0.948869 18 25.433 0.571635 19 13.975 0.372392 20 26.629 0.588374 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.324808 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-24_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.3 -1.4 0.1 -1.6 -0.2 -1.7 -0.3 0.7 1.1 -0.0 1.5 1.1 0.6 0.1 -0.5 -1.0 0.2 -0.7 0.9 -0.4 -0.9 0.7 -0.4 -1.5 0.5 -0.4 -0.7 -0.6 0.2 1.0 1.0 -2.6 1.3 0.2 -1.4 -0.1 0.9 -0.7 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:35.748342 z-score=-0.682112, p-value=0.259310 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-24_21:31 Test no p-value 1 0.937318 2 0.732921 3 0.545677 4 0.409398 5 0.982621 6 0.045430 7 0.271495 8 0.353642 9 0.970176 10 0.002925 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.295346 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-24_21:31: (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 66666 0.00 66404 1.03 3 25000.00 24941 0.14 25181 1.31 4 6666.67 6692 0.10 6719 0.41 5 1388.89 1425 0.94 1423 0.84 6 238.10 224 0.83 232 0.16 7 34.72 49 5.87 33 0.09 8 4.96 2 1.77 7 0.84 p=0.85974 p=0.41377 Number of rngs required: 688952, p-value: 0.737 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-24_21:31 No. of wins: Observed Expected 98651 98585.9 z-score= 0.291, pvalue=0.61461 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66483 66666.7 0.506 0.506 2 37899 37654.3 1.590 2.096 3 27083 26954.7 0.610 2.706 4 19264 19313.5 0.127 2.833 5 13877 13851.4 0.047 2.880 6 9823 9943.5 1.461 4.342 7 7165 7145.0 0.056 4.397 8 5122 5139.1 0.057 4.454 9 3749 3699.9 0.653 5.107 10 2613 2666.3 1.065 6.172 11 1937 1923.3 0.097 6.269 12 1350 1388.7 1.081 7.350 13 979 1003.7 0.609 7.958 14 743 726.1 0.391 8.350 15 505 525.8 0.826 9.175 16 399 381.2 0.836 10.011 17 282 276.5 0.108 10.119 18 194 200.8 0.232 10.351 19 156 146.0 0.687 11.039 20 83 106.2 5.074 16.113 21 294 287.1 0.165 16.278 Chisq= 16.28 for 20 degrees of freedom, p= 0.30076 SUMMARY of craptest p-value for no. of wins: 0.614608 p-value for throws/game: 0.300757 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-24_21:31 No. of wins: Observed Expected 98586 98585.9 z-score= 0.001, pvalue=0.50025 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66542 66666.7 0.233 0.233 2 37956 37654.3 2.417 2.650 3 27309 26954.7 4.656 7.306 4 19115 19313.5 2.039 9.346 5 13815 13851.4 0.096 9.441 6 9822 9943.5 1.486 10.927 7 7220 7145.0 0.787 11.714 8 4977 5139.1 5.111 16.825 9 3584 3699.9 3.628 20.454 10 2697 2666.3 0.354 20.807 11 1952 1923.3 0.427 21.234 12 1369 1388.7 0.281 21.515 13 995 1003.7 0.076 21.591 14 710 726.1 0.359 21.950 15 529 525.8 0.019 21.969 16 418 381.2 3.563 25.531 17 284 276.5 0.201 25.732 18 191 200.8 0.481 26.214 19 128 146.0 2.216 28.429 20 110 106.2 0.135 28.564 21 277 287.1 0.356 28.920 Chisq= 28.92 for 20 degrees of freedom, p= 0.91066 SUMMARY of craptest p-value for no. of wins: 0.500252 p-value for throws/game: 0.910658 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0029,0.0031,0.0046,0.0114,0.0189,0.0213,0.0248,0.0269,0.0302, 0.0381,0.0403,0.0412,0.0454,0.0462,0.0501,0.0562,0.0616,0.0653,0.0849, 0.0875,0.0887,0.0923,0.0977,0.1012,0.1067,0.1115,0.1159,0.1183,0.1193, 0.1204,0.1234,0.1236,0.1266,0.1304,0.1316,0.1349,0.1512,0.1526,0.1548, 0.1639,0.1692,0.1694,0.1696,0.1741,0.1760,0.1764,0.1815,0.1854,0.1912, 0.1960,0.1997,0.2007,0.2017,0.2033,0.2041,0.2056,0.2096,0.2103,0.2165, 0.2213,0.2425,0.2432,0.2475,0.2525,0.2543,0.2593,0.2609,0.2648,0.2715, 0.2723,0.2743,0.2774,0.2832,0.2857,0.2870,0.2876,0.2917,0.2929,0.2953, 0.2984,0.3008,0.3009,0.3015,0.3151,0.3173,0.3241,0.3241,0.3248,0.3362, 0.3402,0.3403,0.3426,0.3441,0.3456,0.3475,0.3477,0.3496,0.3536,0.3574, 0.3586,0.3694,0.3720,0.3724,0.3781,0.3899,0.3916,0.3991,0.4002,0.4055, 0.4064,0.4094,0.4094,0.4130,0.4138,0.4144,0.4275,0.4292,0.4306,0.4314, 0.4349,0.4375,0.4379,0.4379,0.4399,0.4546,0.4617,0.4636,0.4644,0.4773, 0.4887,0.4890,0.4928,0.4960,0.4982,0.4996,0.5003,0.5008,0.5043,0.5218, 0.5241,0.5348,0.5457,0.5481,0.5527,0.5615,0.5654,0.5656,0.5703,0.5716, 0.5725,0.5734,0.5811,0.5883,0.5884,0.5939,0.5950,0.5963,0.5971,0.5979, 0.5980,0.6077,0.6080,0.6101,0.6104,0.6146,0.6168,0.6179,0.6201,0.6313, 0.6334,0.6345,0.6375,0.6399,0.6402,0.6409,0.6426,0.6439,0.6487,0.6506, 0.6563,0.6594,0.6649,0.6695,0.6714,0.6727,0.6749,0.6812,0.6841,0.6943, 0.6966,0.6968,0.7004,0.7101,0.7121,0.7158,0.7161,0.7186,0.7224,0.7231, 0.7236,0.7244,0.7329,0.7333,0.7368,0.7379,0.7392,0.7415,0.7470,0.7512, 0.7528,0.7608,0.7657,0.7662,0.7673,0.7693,0.7772,0.7872,0.7878,0.8037, 0.8063,0.8076,0.8184,0.8291,0.8298,0.8322,0.8325,0.8336,0.8376,0.8377, 0.8378,0.8437,0.8597,0.8679,0.8824,0.8874,0.8886,0.8888,0.8949,0.8951, 0.8980,0.9040,0.9067,0.9107,0.9144,0.9154,0.9215,0.9287,0.9293,0.9330, 0.9335,0.9359,0.9373,0.9374,0.9387,0.9406,0.9406,0.9412,0.9415,0.9420, 0.9489,0.9504,0.9562,0.9572,0.9607,0.9702,0.9810,0.9826,0.9901, Overall p-value after applying KStest on 269 p-values = 0.883131 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.