RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-29_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.46 26.9698 0.941488 2 to 25 15.69 12.2280 0.213864 3 to 26 15.85 18.4708 0.640264 4 to 27 15.62 12.0595 0.203478 5 to 28 15.50 24.3373 0.889444 6 to 29 15.56 16.9371 0.541366 7 to 30 15.84 19.0796 0.676015 8 to 31 15.58 19.7985 0.715336 9 to 32 15.67 15.6476 0.451059 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.625151 Tough bday spacings test for dh-ranFile-2016-02-29_03:31: 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 34 72 90 90 95 52 30 20 8 2 (O-E)^2/E 0.5 0.2 0.0 0.6 0.6 3.6 0.0 0.0 1.8 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.662, p= 0.436 RESULTS OF GCD FOR dh-ranFile-2016-02-29_03:31 Euclid's algorithm: p-value, steps to gcd: 0.819283 p-value, dist. of gcd's: 0.514161 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-29_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.345 0.184 0.151 0.345 0.004 0.189 0.854 0.359 Bits 8 to 15---> 0.730 0.737 0.565 0.481 0.156 0.661 0.779 0.210 Bits 16 to 23---> 0.623 0.350 0.834 0.488 0.790 0.502 0.511 0.379 Bits 24 to 31---> 0.083 0.648 0.553 0.178 0.012 0.503 0.170 0.345 KS test for the above 32 p values: 0.835 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-29_03:31, p-values for 5 runs: 0.6910, 0.6991, 0.4540, 0.6554, 0.5667 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-29_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5103 5134.0 0.187 0.622 r= 30 23278 23103.0 1.325 1.946 r= 31 11398 11551.5 2.040 3.987 chi-square = 3.987 with df = 3; p-value = 0.737 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-29_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5199 5134.0 0.823 1.336 r= 31 23122 23103.0 0.016 1.352 r= 32 11478 11551.5 0.468 1.820 chi-square = 1.820 with df = 3; p-value = 0.389 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-29_03:31 b-rank test for bits 1 to 8, p=0.50198 b-rank test for bits 2 to 9, p=0.41622 b-rank test for bits 3 to 10, p=0.45947 b-rank test for bits 4 to 11, p=0.65842 b-rank test for bits 5 to 12, p=0.39798 b-rank test for bits 6 to 13, p=0.81358 b-rank test for bits 7 to 14, p=0.16608 b-rank test for bits 8 to 15, p=0.60608 b-rank test for bits 9 to 16, p=0.94704 b-rank test for bits 10 to 17, p=0.84721 b-rank test for bits 11 to 18, p=0.98054 b-rank test for bits 12 to 19, p=0.72982 b-rank test for bits 13 to 20, p=0.81620 b-rank test for bits 14 to 21, p=0.01824 b-rank test for bits 15 to 22, p=0.64795 b-rank test for bits 16 to 23, p=0.99813 b-rank test for bits 17 to 24, p=0.17745 b-rank test for bits 18 to 25, p=0.83040 b-rank test for bits 19 to 26, p=0.92006 b-rank test for bits 20 to 27, p=0.50850 b-rank test for bits 21 to 28, p=0.37857 b-rank test for bits 22 to 29, p=0.06391 b-rank test for bits 23 to 30, p=0.73028 b-rank test for bits 24 to 31, p=0.89217 b-rank test for bits 25 to 32, p=0.17698 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 = 0.196112 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-29_03:31 (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 141661 -0.58 0.280886 2 142674 1.79 0.963000 3 141895 -0.03 0.486645 4 142558 1.52 0.935188 5 141231 -1.58 0.056496 6 142046 0.32 0.625259 7 141900 -0.02 0.491304 8 141112 -1.86 0.031237 9 141068 -1.97 0.024665 10 141775 -0.31 0.376816 11 141777 -0.31 0.378591 12 142560 1.52 0.935777 13 142276 0.86 0.804196 14 141641 -0.63 0.265350 15 142030 0.28 0.611005 16 142419 1.19 0.883137 17 141684 -0.53 0.299280 18 141952 0.10 0.539707 19 141673 -0.55 0.290415 20 142099 0.44 0.671173 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-29_03:31 Bits used No. missing words z-score p-value 23 to 32 142135 0.7782 0.781766 22 to 31 142253 1.1851 0.882005 21 to 30 141981 0.2471 0.597599 20 to 29 142233 1.1161 0.867811 19 to 28 141983 0.2540 0.600266 18 to 27 141774 -0.4667 0.320373 17 to 26 142018 0.3747 0.646067 16 to 25 141992 0.2851 0.612204 15 to 24 141594 -1.0873 0.138442 14 to 23 141267 -2.2149 0.013382 13 to 22 142151 0.8333 0.797675 12 to 21 142296 1.3333 0.908791 11 to 20 141786 -0.4253 0.335318 10 to 19 141758 -0.5218 0.300895 9 to 18 141980 0.2437 0.596264 8 to 17 142050 0.4851 0.686186 7 to 16 141709 -0.6908 0.244848 6 to 15 141504 -1.3977 0.081103 5 to 14 142055 0.5023 0.692275 4 to 13 142192 0.9747 0.835151 3 to 12 142109 0.6885 0.754436 2 to 11 141836 -0.2529 0.400187 1 to 10 141849 -0.2080 0.417601 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-29_03:31 Bits used No. missing words z-score p-value 28 to 32 142155 0.8328 0.797516 27 to 31 141808 -0.3435 0.365614 26 to 30 142265 1.2057 0.886026 25 to 29 141809 -0.3401 0.366890 24 to 28 141687 -0.7537 0.225526 23 to 27 141818 -0.3096 0.378435 22 to 26 141618 -0.9876 0.161684 21 to 25 141678 -0.7842 0.216470 20 to 24 141829 -0.2723 0.392694 19 to 23 141801 -0.3672 0.356727 18 to 22 141567 -1.1604 0.122935 17 to 21 142117 0.7040 0.759273 16 to 20 141823 -0.2926 0.384897 15 to 19 141945 0.1209 0.548121 14 to 18 141964 0.1853 0.573512 13 to 17 141676 -0.7909 0.214487 12 to 16 141967 0.1955 0.577496 11 to 15 141719 -0.6452 0.259403 10 to 14 141544 -1.2384 0.107783 9 to 13 141930 0.0701 0.527930 8 to 12 141949 0.1345 0.553486 7 to 11 141828 -0.2757 0.391391 6 to 10 141875 -0.1164 0.453679 5 to 9 141853 -0.1909 0.424283 4 to 8 142187 0.9413 0.826713 3 to 7 141969 0.2023 0.580148 2 to 6 142447 1.8226 0.965819 1 to 5 141607 -1.0248 0.152718 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-29_03:31 Bits used No. missing words z-score p-value 31 to 32 142045 0.4002 0.655498 30 to 31 142405 1.4622 0.928150 29 to 30 142072 0.4799 0.684334 28 to 29 142179 0.7955 0.786835 27 to 28 142028 0.3501 0.636853 26 to 27 141853 -0.1662 0.434014 25 to 26 142259 1.0315 0.848841 24 to 25 141857 -0.1544 0.438661 23 to 24 141762 -0.4346 0.331926 22 to 23 141709 -0.5909 0.277279 21 to 22 142379 1.3855 0.917044 20 to 21 141524 -1.1367 0.127839 19 to 20 141792 -0.3461 0.364632 18 to 19 141680 -0.6765 0.249365 17 to 18 141730 -0.5290 0.298404 16 to 17 141877 -0.0954 0.462011 15 to 16 142112 0.5978 0.725029 14 to 15 141583 -0.9626 0.167868 13 to 14 142081 0.5064 0.693713 12 to 13 142502 1.7483 0.959793 11 to 12 142258 1.0285 0.848149 10 to 11 141166 -2.1927 0.014164 9 to 10 141581 -0.9685 0.166391 8 to 9 141757 -0.4494 0.326589 7 to 8 142003 0.2763 0.608846 6 to 7 141672 -0.7001 0.241936 5 to 6 141763 -0.4317 0.332997 4 to 5 142105 0.5772 0.718097 3 to 4 141843 -0.1957 0.422437 2 to 3 142497 1.7335 0.958500 1 to 2 142021 0.3294 0.629077 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-29_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2506.20 0.088 0.534921 Test results for specific bytes for dh-ranFile-2016-02-29_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2640.66 1.989 0.976659 2 to 9 2463.87 -0.511 0.304701 3 to 10 2432.35 -0.957 0.169367 4 to 11 2694.36 2.749 0.997009 5 to 12 2448.63 -0.726 0.233775 6 to 13 2473.17 -0.379 0.352208 7 to 14 2556.35 0.797 0.787230 8 to 15 2565.31 0.924 0.822177 9 to 16 2633.79 1.892 0.970761 10 to 17 2465.31 -0.491 0.311835 11 to 18 2548.18 0.681 0.752192 12 to 19 2442.94 -0.807 0.209862 13 to 20 2431.77 -0.965 0.167281 14 to 21 2396.26 -1.467 0.071168 15 to 22 2471.85 -0.398 0.345274 16 to 23 2449.69 -0.711 0.238407 17 to 24 2421.51 -1.110 0.133481 18 to 25 2537.53 0.531 0.702224 19 to 26 2466.52 -0.474 0.317919 20 to 27 2403.54 -1.364 0.086270 21 to 28 2412.03 -1.244 0.106735 22 to 29 2546.89 0.663 0.746381 23 to 30 2532.61 0.461 0.677678 24 to 31 2455.01 -0.636 0.262293 25 to 32 2611.53 1.577 0.942626 CDPARK for dh-ranFile-2016-02-29_03:31: 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 3555 1.4612 0.928018 3539 0.7306 0.767486 3503 -0.9132 0.180558 3539 0.7306 0.767486 3523 0.0000 0.500000 3487 -1.6438 0.050105 3494 -1.3242 0.092718 3580 2.6027 0.995376 3508 -0.6849 0.246694 3554 1.4155 0.921543 Square side=100, avg. no. parked=3528.20 sample std.=28.70 p-value of the KSTEST for those 10 p-values: 0.361436 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-29_03:31 0.7048,0.1085,0.8996,0.9143,0.9482,0.8226,0.3597,0.3650,0.2941,0.0942, The KS test for those 10 p-values: 0.589706 The 3DSPHERES test for dh-ranFile-2016-02-29_03:31 sample no r^3 equiv. uni. 1 0.373 0.012351 2 0.876 0.028771 3 43.953 0.768941 4 45.804 0.782774 5 69.239 0.900537 6 36.721 0.705954 7 7.377 0.218006 8 90.695 0.951353 9 20.839 0.500736 10 21.116 0.505328 11 22.948 0.534631 12 19.924 0.485276 13 3.916 0.122361 14 29.110 0.621047 15 34.233 0.680535 16 1.829 0.059160 17 25.181 0.568020 18 2.292 0.073562 19 39.597 0.732838 20 19.863 0.484233 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.585615 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-29_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.5 -0.1 0.3 -0.3 0.2 0.1 -0.3 1.0 -0.1 -0.6 0.6 -1.0 0.7 2.2 -0.4 -1.0 0.7 1.1 -0.4 0.7 -1.2 -1.6 -1.0 -0.8 1.0 1.2 -1.6 0.2 -0.4 0.6 -2.1 -0.2 1.0 -0.4 0.1 -0.7 -1.0 0.5 0.4 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:35.193162 z-score=-0.742687, p-value=0.237849 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-29_03:31 Test no p-value 1 0.130389 2 0.068192 3 0.259679 4 0.009218 5 0.642492 6 0.532465 7 0.653606 8 0.006864 9 0.791432 10 0.125880 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.030062 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-29_03:31: (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 66523 0.31 66681 0.00 3 25000.00 25023 0.02 24936 0.16 4 6666.67 6772 1.66 6668 0.00 5 1388.89 1409 0.29 1431 1.28 6 238.10 228 0.43 241 0.04 7 34.72 41 1.14 38 0.31 8 4.96 3 0.77 4 0.19 p=0.40722 p=0.07802 Number of rngs required: 688621, p-value: 0.599 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-29_03:31 No. of wins: Observed Expected 98254 98585.9 z-score=-1.484, pvalue=0.06887 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66757 66666.7 0.122 0.122 2 37482 37654.3 0.789 0.911 3 26932 26954.7 0.019 0.930 4 19312 19313.5 0.000 0.930 5 14014 13851.4 1.908 2.839 6 9878 9943.5 0.432 3.271 7 7127 7145.0 0.045 3.316 8 5029 5139.1 2.358 5.674 9 3737 3699.9 0.373 6.046 10 2665 2666.3 0.001 6.047 11 1967 1923.3 0.992 7.039 12 1338 1388.7 1.854 8.893 13 1018 1003.7 0.203 9.096 14 728 726.1 0.005 9.101 15 607 525.8 12.528 21.628 16 404 381.2 1.370 22.998 17 281 276.5 0.072 23.070 18 218 200.8 1.468 24.538 19 145 146.0 0.007 24.545 20 92 106.2 1.902 26.447 21 269 287.1 1.143 27.590 Chisq= 27.59 for 20 degrees of freedom, p= 0.88054 SUMMARY of craptest p-value for no. of wins: 0.068869 p-value for throws/game: 0.880537 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-29_03:31 No. of wins: Observed Expected 98544 98585.9 z-score=-0.187, pvalue=0.42575 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66701 66666.7 0.018 0.018 2 37790 37654.3 0.489 0.507 3 27107 26954.7 0.860 1.367 4 19380 19313.5 0.229 1.596 5 13702 13851.4 1.612 3.208 6 9753 9943.5 3.651 6.859 7 7129 7145.0 0.036 6.895 8 5203 5139.1 0.795 7.690 9 3684 3699.9 0.068 7.758 10 2678 2666.3 0.051 7.810 11 1933 1923.3 0.049 7.858 12 1384 1388.7 0.016 7.874 13 949 1003.7 2.983 10.857 14 725 726.1 0.002 10.859 15 517 525.8 0.148 11.007 16 361 381.2 1.065 12.073 17 253 276.5 2.004 14.076 18 184 200.8 1.410 15.487 19 149 146.0 0.062 15.549 20 126 106.2 3.685 19.234 21 292 287.1 0.083 19.318 Chisq= 19.32 for 20 degrees of freedom, p= 0.49872 SUMMARY of craptest p-value for no. of wins: 0.425746 p-value for throws/game: 0.498722 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0043,0.0069,0.0092,0.0118,0.0124,0.0134,0.0142,0.0182,0.0247,0.0288, 0.0301,0.0312,0.0501,0.0565,0.0592,0.0639,0.0682,0.0689,0.0712,0.0736, 0.0780,0.0811,0.0833,0.0863,0.0927,0.0942,0.1067,0.1078,0.1085,0.1224, 0.1229,0.1259,0.1278,0.1304,0.1335,0.1384,0.1511,0.1527,0.1564,0.1617, 0.1661,0.1664,0.1673,0.1679,0.1694,0.1699,0.1770,0.1774,0.1777,0.1806, 0.1835,0.1888,0.1961,0.2035,0.2097,0.2099,0.2139,0.2145,0.2165,0.2180, 0.2255,0.2338,0.2378,0.2384,0.2419,0.2448,0.2467,0.2494,0.2594,0.2597, 0.2623,0.2653,0.2773,0.2809,0.2904,0.2941,0.2984,0.2993,0.3009,0.3047, 0.3118,0.3179,0.3204,0.3266,0.3319,0.3330,0.3353,0.3446,0.3449,0.3449, 0.3453,0.3501,0.3522,0.3567,0.3586,0.3597,0.3614,0.3646,0.3650,0.3656, 0.3669,0.3768,0.3784,0.3786,0.3786,0.3790,0.3849,0.3893,0.3914,0.3927, 0.3980,0.4002,0.4072,0.4162,0.4176,0.4224,0.4243,0.4257,0.4340,0.4355, 0.4387,0.4511,0.4537,0.4540,0.4595,0.4620,0.4807,0.4842,0.4853,0.4866, 0.4878,0.4913,0.4987,0.5000,0.5007,0.5017,0.5020,0.5026,0.5053,0.5085, 0.5112,0.5142,0.5279,0.5325,0.5346,0.5349,0.5397,0.5414,0.5481,0.5534, 0.5535,0.5647,0.5667,0.5680,0.5735,0.5775,0.5801,0.5856,0.5897,0.5963, 0.5976,0.5990,0.6003,0.6061,0.6088,0.6110,0.6122,0.6210,0.6228,0.6252, 0.6253,0.6291,0.6369,0.6403,0.6425,0.6461,0.6479,0.6481,0.6536,0.6554, 0.6555,0.6584,0.6613,0.6712,0.6760,0.6777,0.6805,0.6843,0.6862,0.6910, 0.6923,0.6937,0.6991,0.7022,0.7048,0.7060,0.7153,0.7181,0.7250,0.7298, 0.7299,0.7303,0.7328,0.7367,0.7371,0.7464,0.7522,0.7544,0.7593,0.7675, 0.7675,0.7689,0.7786,0.7818,0.7828,0.7868,0.7872,0.7903,0.7914,0.7975, 0.7977,0.8042,0.8136,0.8162,0.8193,0.8222,0.8226,0.8267,0.8304,0.8337, 0.8345,0.8352,0.8472,0.8481,0.8488,0.8545,0.8678,0.8805,0.8820,0.8831, 0.8860,0.8894,0.8922,0.8996,0.9005,0.9088,0.9143,0.9170,0.9201,0.9215, 0.9280,0.9282,0.9352,0.9358,0.9415,0.9426,0.9470,0.9482,0.9514,0.9585, 0.9598,0.9630,0.9658,0.9708,0.9767,0.9805,0.9954,0.9970,0.9981, Overall p-value after applying KStest on 269 p-values = 0.983156 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.