RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-07_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.11 6.3956 0.009891 2 to 25 15.55 23.5596 0.868097 3 to 26 15.84 22.3666 0.828971 4 to 27 15.59 15.8699 0.466928 5 to 28 16.02 20.7230 0.761076 6 to 29 15.71 20.2974 0.740701 7 to 30 15.91 21.0842 0.777455 8 to 31 15.64 21.2800 0.785985 9 to 32 15.89 21.1718 0.781300 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.036789 Tough bday spacings test for dh-ranFile-2016-01-07_16:31: 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 41 66 100 102 70 51 37 12 8 6 (O-E)^2/E 0.5 0.5 0.7 0.1 0.2 0.8 0.0 1.8 0.6 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 6.392, p= 0.219 RESULTS OF GCD FOR dh-ranFile-2016-01-07_16:31 Euclid's algorithm: p-value, steps to gcd: 0.896415 p-value, dist. of gcd's: 0.858303 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-07_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.789 0.040 0.850 0.311 0.965 0.931 0.855 0.446 Bits 8 to 15---> 0.514 0.359 0.512 0.017 0.166 0.807 0.332 0.306 Bits 16 to 23---> 0.649 0.917 0.124 0.402 0.177 0.085 0.314 0.344 Bits 24 to 31---> 0.419 0.816 0.308 0.719 0.190 0.010 0.020 0.195 KS test for the above 32 p values: 0.768 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-07_16:31, p-values for 5 runs: 0.6543, 0.5356, 0.0709, 0.2511, 0.8664 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-07_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5221 5134.0 1.474 1.566 r= 30 22966 23103.0 0.813 2.379 r= 31 11606 11551.5 0.257 2.636 chi-square = 2.636 with df = 3; p-value = 0.549 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-07_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5161 5134.0 0.142 0.143 r= 31 23109 23103.0 0.002 0.145 r= 32 11518 11551.5 0.097 0.242 chi-square = 0.242 with df = 3; p-value = 0.030 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-07_16:31 b-rank test for bits 1 to 8, p=0.65253 b-rank test for bits 2 to 9, p=0.36544 b-rank test for bits 3 to 10, p=0.52495 b-rank test for bits 4 to 11, p=0.31365 b-rank test for bits 5 to 12, p=0.89735 b-rank test for bits 6 to 13, p=0.56830 b-rank test for bits 7 to 14, p=0.43171 b-rank test for bits 8 to 15, p=0.05281 b-rank test for bits 9 to 16, p=0.97285 b-rank test for bits 10 to 17, p=0.68364 b-rank test for bits 11 to 18, p=0.18156 b-rank test for bits 12 to 19, p=0.77012 b-rank test for bits 13 to 20, p=0.71880 b-rank test for bits 14 to 21, p=0.27989 b-rank test for bits 15 to 22, p=0.57873 b-rank test for bits 16 to 23, p=0.42756 b-rank test for bits 17 to 24, p=0.55165 b-rank test for bits 18 to 25, p=0.08333 b-rank test for bits 19 to 26, p=0.70181 b-rank test for bits 20 to 27, p=0.22760 b-rank test for bits 21 to 28, p=0.07323 b-rank test for bits 22 to 29, p=0.55488 b-rank test for bits 23 to 30, p=0.71584 b-rank test for bits 24 to 31, p=0.47695 b-rank test for bits 25 to 32, p=0.57629 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 = 0.614315 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-07_16:31 (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 142177 0.63 0.734145 2 142063 0.36 0.640218 3 142030 0.28 0.611005 4 141275 -1.48 0.069160 5 141951 0.10 0.538780 6 141714 -0.46 0.324059 7 141490 -0.98 0.163607 8 141830 -0.19 0.426477 9 141871 -0.09 0.464320 10 142145 0.55 0.709057 11 141997 0.20 0.581150 12 141737 -0.40 0.343607 13 141649 -0.61 0.271512 14 141633 -0.65 0.259259 15 141738 -0.40 0.344466 16 141208 -1.64 0.050646 17 140737 -2.74 0.003080 18 142524 1.44 0.924519 19 142178 0.63 0.734911 20 141838 -0.17 0.433819 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-07_16:31 Bits used No. missing words z-score p-value 23 to 32 142025 0.3989 0.655003 22 to 31 141632 -0.9563 0.169458 21 to 30 142002 0.3196 0.625346 20 to 29 141960 0.1747 0.569352 19 to 28 142034 0.4299 0.666365 18 to 27 142254 1.1885 0.882685 17 to 26 142706 2.7471 0.996994 16 to 25 142101 0.6609 0.745672 15 to 24 141467 -1.5253 0.063595 14 to 23 141716 -0.6667 0.252496 13 to 22 141788 -0.4184 0.337835 12 to 21 142129 0.7575 0.775620 11 to 20 141702 -0.7149 0.237326 10 to 19 142220 1.0713 0.857977 9 to 18 141829 -0.2770 0.390890 8 to 17 141386 -1.8046 0.035570 7 to 16 142126 0.7471 0.772510 6 to 15 141678 -0.7977 0.212525 5 to 14 141618 -1.0046 0.157548 4 to 13 141601 -1.0632 0.143844 3 to 12 141515 -1.3598 0.086953 2 to 11 141565 -1.1873 0.117546 1 to 10 141357 -1.9046 0.028417 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-07_16:31 Bits used No. missing words z-score p-value 28 to 32 142126 0.7345 0.768670 27 to 31 142450 1.8328 0.966582 26 to 30 142522 2.0768 0.981092 25 to 29 142422 1.7379 0.958883 24 to 28 141363 -1.8520 0.032015 23 to 27 141615 -0.9977 0.159205 22 to 26 141467 -1.4994 0.066882 21 to 25 141954 0.1514 0.560179 20 to 24 142295 1.3074 0.904454 19 to 23 142177 0.9074 0.817891 18 to 22 141514 -1.3401 0.090106 17 to 21 142094 0.6260 0.734343 16 to 20 141925 0.0531 0.521181 15 to 19 141112 -2.7028 0.003438 14 to 18 142025 0.3921 0.652509 13 to 17 141528 -1.2926 0.098067 12 to 16 142021 0.3785 0.647486 11 to 15 141550 -1.2181 0.111599 10 to 14 141810 -0.3367 0.368167 9 to 13 141337 -1.9401 0.026184 8 to 12 141702 -0.7028 0.241086 7 to 11 141939 0.1006 0.540057 6 to 10 142281 1.2599 0.896147 5 to 9 142350 1.4938 0.932386 4 to 8 142014 0.3548 0.638635 3 to 7 142154 0.8294 0.796558 2 to 6 141586 -1.0960 0.136532 1 to 5 142398 1.6565 0.951191 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-07_16:31 Bits used No. missing words z-score p-value 31 to 32 141553 -1.0511 0.146602 30 to 31 141715 -0.5732 0.283240 29 to 30 141818 -0.2694 0.393807 28 to 29 141611 -0.8800 0.189422 27 to 28 142030 0.3560 0.639064 26 to 27 141611 -0.8800 0.189422 25 to 26 141593 -0.9331 0.175377 24 to 25 141681 -0.6735 0.250302 23 to 24 141689 -0.6499 0.257865 22 to 23 141833 -0.2252 0.410927 21 to 22 142532 1.8368 0.966879 20 to 21 141538 -1.0954 0.136678 19 to 20 142168 0.7630 0.777280 18 to 19 142612 2.0728 0.980903 17 to 18 141776 -0.3933 0.347048 16 to 17 141832 -0.2281 0.409780 15 to 16 142249 1.0020 0.841823 14 to 15 141712 -0.5821 0.280252 13 to 14 141776 -0.3933 0.347048 12 to 13 141514 -1.1662 0.121774 11 to 12 141661 -0.7325 0.231921 10 to 11 141819 -0.2665 0.394942 9 to 10 141566 -1.0128 0.155584 8 to 9 141760 -0.4405 0.329787 7 to 8 141542 -1.0836 0.139278 6 to 7 142050 0.4150 0.660913 5 to 6 141700 -0.6175 0.268455 4 to 5 141496 -1.2193 0.111372 3 to 4 142121 0.6244 0.733816 2 to 3 142008 0.2911 0.614498 1 to 2 142246 0.9931 0.839676 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-07_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2543.82 0.620 0.732255 Test results for specific bytes for dh-ranFile-2016-01-07_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2521.41 0.303 0.618977 2 to 9 2428.46 -1.012 0.155822 3 to 10 2476.10 -0.338 0.367682 4 to 11 2654.84 2.190 0.985730 5 to 12 2466.49 -0.474 0.317791 6 to 13 2544.58 0.630 0.735809 7 to 14 2553.70 0.759 0.776210 8 to 15 2478.08 -0.310 0.378306 9 to 16 2493.04 -0.098 0.460803 10 to 17 2543.82 0.620 0.732262 11 to 18 2421.21 -1.114 0.132575 12 to 19 2522.91 0.324 0.627006 13 to 20 2470.98 -0.410 0.340760 14 to 21 2505.36 0.076 0.530231 15 to 22 2530.03 0.425 0.664489 16 to 23 2337.54 -2.297 0.010796 17 to 24 2503.39 0.048 0.519120 18 to 25 2605.97 1.499 0.933020 19 to 26 2501.07 0.015 0.506052 20 to 27 2430.59 -0.982 0.163152 21 to 28 2412.44 -1.238 0.107801 22 to 29 2574.83 1.058 0.855029 23 to 30 2546.75 0.661 0.745759 24 to 31 2506.18 0.087 0.534823 25 to 32 2575.03 1.061 0.855659 CDPARK for dh-ranFile-2016-01-07_16:31: 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 3512 -0.5023 0.307734 3568 2.0548 0.980051 3531 0.3653 0.642555 3513 -0.4566 0.323972 3530 0.3196 0.625377 3509 -0.6393 0.261324 3503 -0.9132 0.180558 3523 0.0000 0.500000 3564 1.8721 0.969407 3532 0.4110 0.659449 Square side=100, avg. no. parked=3528.50 sample std.=21.01 p-value of the KSTEST for those 10 p-values: 0.576446 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-07_16:31 0.0711,0.8634,0.1236,0.6205,0.9637,0.5581,0.1908,0.8354,0.5100,0.5544, The KS test for those 10 p-values: 0.925298 The 3DSPHERES test for dh-ranFile-2016-01-07_16:31 sample no r^3 equiv. uni. 1 37.637 0.714798 2 12.319 0.336777 3 0.378 0.012520 4 72.627 0.911157 5 73.769 0.914478 6 24.230 0.554110 7 5.026 0.154249 8 73.720 0.914336 9 7.173 0.212664 10 54.186 0.835721 11 53.802 0.833604 12 11.538 0.319272 13 33.233 0.669707 14 48.528 0.801625 15 8.272 0.240985 16 23.428 0.542016 17 43.860 0.768231 18 5.936 0.179514 19 71.063 0.906404 20 8.571 0.248518 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.448943 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-07_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 -0.8 1.5 0.7 -0.7 0.2 1.6 -1.7 -0.3 -1.1 1.2 0.5 -0.2 -0.1 0.3 0.7 0.0 -1.1 1.3 1.2 -1.3 -0.2 -0.8 0.9 -0.5 -1.2 -0.8 -0.4 1.4 -0.4 -0.4 -0.0 -0.4 0.2 0.6 1.0 -0.7 1.3 -0.7 0.9 -1.0 0.8 Chi-square with 42 degrees of freedom:33.180242 z-score=-0.962314, p-value=0.167226 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-07_16:31 Test no p-value 1 0.231140 2 0.495782 3 0.002779 4 0.788813 5 0.000333 6 0.204780 7 0.508534 8 0.440694 9 0.052262 10 0.932567 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.043892 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-07_16:31: (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 66577 0.12 67093 2.73 3 25000.00 25083 0.28 24741 2.68 4 6666.67 6703 0.20 6607 0.53 5 1388.89 1371 0.23 1300 5.69 6 238.10 224 0.83 227 0.52 7 34.72 34 0.01 29 0.94 8 4.96 7 0.84 2 1.77 p=0.13299 p=0.97861 Number of rngs required: 687546, p-value: 0.160 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-07_16:31 No. of wins: Observed Expected 98236 98585.9 z-score=-1.565, pvalue=0.05882 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66450 66666.7 0.704 0.704 2 37749 37654.3 0.238 0.942 3 26794 26954.7 0.958 1.901 4 19320 19313.5 0.002 1.903 5 14117 13851.4 5.092 6.995 6 9988 9943.5 0.199 7.194 7 7095 7145.0 0.350 7.544 8 5100 5139.1 0.297 7.841 9 3797 3699.9 2.550 10.391 10 2700 2666.3 0.426 10.817 11 1987 1923.3 2.108 12.925 12 1331 1388.7 2.401 15.326 13 1038 1003.7 1.171 16.497 14 741 726.1 0.304 16.801 15 465 525.8 7.038 23.839 16 347 381.2 3.060 26.899 17 267 276.5 0.329 27.228 18 187 200.8 0.952 28.181 19 166 146.0 2.744 30.925 20 110 106.2 0.135 31.060 21 251 287.1 4.543 35.602 Chisq= 35.60 for 20 degrees of freedom, p= 0.98288 SUMMARY of craptest p-value for no. of wins: 0.058818 p-value for throws/game: 0.982878 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-07_16:31 No. of wins: Observed Expected 98453 98585.9 z-score=-0.594, pvalue=0.27618 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66671 66666.7 0.000 0.000 2 37545 37654.3 0.317 0.318 3 26959 26954.7 0.001 0.318 4 19472 19313.5 1.301 1.620 5 13831 13851.4 0.030 1.650 6 9855 9943.5 0.788 2.438 7 7041 7145.0 1.515 3.953 8 5110 5139.1 0.164 4.117 9 3780 3699.9 1.736 5.853 10 2655 2666.3 0.048 5.901 11 1922 1923.3 0.001 5.902 12 1421 1388.7 0.749 6.651 13 1013 1003.7 0.086 6.737 14 752 726.1 0.921 7.658 15 535 525.8 0.160 7.818 16 385 381.2 0.039 7.856 17 282 276.5 0.108 7.964 18 206 200.8 0.133 8.097 19 156 146.0 0.687 8.785 20 116 106.2 0.901 9.686 21 293 287.1 0.121 9.807 Chisq= 9.81 for 20 degrees of freedom, p= 0.02845 SUMMARY of craptest p-value for no. of wins: 0.276182 p-value for throws/game: 0.028455 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0028,0.0031,0.0034,0.0099,0.0101,0.0108,0.0125,0.0170,0.0196, 0.0262,0.0284,0.0285,0.0295,0.0320,0.0356,0.0368,0.0401,0.0439,0.0506, 0.0523,0.0528,0.0588,0.0636,0.0669,0.0692,0.0709,0.0711,0.0732,0.0833, 0.0853,0.0870,0.0901,0.0981,0.1078,0.1114,0.1116,0.1175,0.1218,0.1235, 0.1236,0.1326,0.1330,0.1365,0.1367,0.1393,0.1438,0.1466,0.1542,0.1556, 0.1558,0.1575,0.1592,0.1604,0.1632,0.1636,0.1661,0.1672,0.1695,0.1754, 0.1769,0.1795,0.1806,0.1816,0.1894,0.1894,0.1902,0.1908,0.1952,0.2048, 0.2125,0.2127,0.2187,0.2276,0.2311,0.2319,0.2373,0.2410,0.2411,0.2485, 0.2503,0.2511,0.2525,0.2579,0.2593,0.2613,0.2685,0.2715,0.2762,0.2799, 0.2803,0.2832,0.3059,0.3076,0.3077,0.3113,0.3135,0.3136,0.3178,0.3193, 0.3240,0.3241,0.3298,0.3320,0.3368,0.3378,0.3408,0.3436,0.3436,0.3445, 0.3470,0.3470,0.3586,0.3654,0.3677,0.3682,0.3783,0.3909,0.3938,0.3949, 0.4017,0.4098,0.4109,0.4186,0.4265,0.4276,0.4317,0.4338,0.4407,0.4458, 0.4489,0.4608,0.4643,0.4669,0.4770,0.4958,0.5000,0.5061,0.5085,0.5100, 0.5124,0.5139,0.5191,0.5212,0.5249,0.5302,0.5348,0.5356,0.5388,0.5401, 0.5420,0.5488,0.5517,0.5541,0.5544,0.5549,0.5581,0.5602,0.5683,0.5694, 0.5763,0.5764,0.5787,0.5812,0.6110,0.6143,0.6145,0.6190,0.6205,0.6253, 0.6254,0.6270,0.6386,0.6391,0.6402,0.6426,0.6475,0.6490,0.6525,0.6525, 0.6543,0.6550,0.6594,0.6609,0.6645,0.6664,0.6697,0.6836,0.7018,0.7091, 0.7148,0.7158,0.7188,0.7191,0.7323,0.7323,0.7338,0.7341,0.7343,0.7349, 0.7358,0.7407,0.7457,0.7458,0.7611,0.7678,0.7682,0.7687,0.7701,0.7725, 0.7756,0.7762,0.7773,0.7775,0.7813,0.7860,0.7888,0.7891,0.7966,0.8016, 0.8072,0.8156,0.8179,0.8290,0.8336,0.8354,0.8357,0.8397,0.8418,0.8501, 0.8550,0.8551,0.8557,0.8580,0.8583,0.8634,0.8664,0.8681,0.8827,0.8961, 0.8964,0.8973,0.9045,0.9064,0.9112,0.9143,0.9145,0.9171,0.9245,0.9253, 0.9312,0.9324,0.9326,0.9330,0.9512,0.9589,0.9637,0.9647,0.9666,0.9669, 0.9694,0.9728,0.9786,0.9801,0.9809,0.9811,0.9829,0.9857,0.9970, Overall p-value after applying KStest on 269 p-values = 0.164632 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.