RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-08_13:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.88 27.3416 0.946755 2 to 25 15.93 16.1911 0.489666 3 to 26 15.88 16.3188 0.498645 4 to 27 15.81 13.1962 0.277043 5 to 28 15.76 13.3808 0.289659 6 to 29 15.63 17.8994 0.604785 7 to 30 15.69 20.3867 0.745069 8 to 31 15.71 19.4803 0.698328 9 to 32 15.50 22.4061 0.830399 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.474634 Tough bday spacings test for dh-ranFile-2016-05-08_13:31: 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 5 31 85 107 90 77 48 40 11 3 3 (O-E)^2/E 1.9 0.9 1.9 0.9 0.6 0.0 0.3 3.5 1.0 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 13.251, p= 0.790 RESULTS OF GCD FOR dh-ranFile-2016-05-08_13:31 Euclid's algorithm: p-value, steps to gcd: 0.801106 p-value, dist. of gcd's: 0.563246 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-08_13:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.135 0.214 0.568 0.477 0.581 0.225 0.422 0.576 Bits 8 to 15---> 0.937 0.942 0.947 0.305 0.949 0.024 0.984 0.580 Bits 16 to 23---> 0.927 0.967 0.451 0.166 0.326 0.881 0.980 0.137 Bits 24 to 31---> 0.143 0.306 0.052 0.500 0.026 0.664 0.863 0.044 KS test for the above 32 p values: 0.818 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-08_13:31, p-values for 5 runs: 0.9331, 0.1676, 0.0080, 0.6227, 0.7476 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-08_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5170 5134.0 0.252 0.352 r= 30 23237 23103.0 0.777 1.128 r= 31 11377 11551.5 2.637 3.765 chi-square = 3.765 with df = 3; p-value = 0.712 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-08_13:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 223 211.4 0.634 0.634 r= 30 5221 5134.0 1.474 2.108 r= 31 22931 23103.0 1.281 3.390 r= 32 11625 11551.5 0.467 3.857 chi-square = 3.857 with df = 3; p-value = 0.723 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-08_13:31 b-rank test for bits 1 to 8, p=0.05533 b-rank test for bits 2 to 9, p=0.38889 b-rank test for bits 3 to 10, p=0.84315 b-rank test for bits 4 to 11, p=0.05061 b-rank test for bits 5 to 12, p=0.07646 b-rank test for bits 6 to 13, p=0.16949 b-rank test for bits 7 to 14, p=0.74098 b-rank test for bits 8 to 15, p=0.05452 b-rank test for bits 9 to 16, p=0.27966 b-rank test for bits 10 to 17, p=0.74637 b-rank test for bits 11 to 18, p=0.24999 b-rank test for bits 12 to 19, p=0.94977 b-rank test for bits 13 to 20, p=0.52205 b-rank test for bits 14 to 21, p=0.03044 b-rank test for bits 15 to 22, p=0.41021 b-rank test for bits 16 to 23, p=0.00244 b-rank test for bits 17 to 24, p=0.33453 b-rank test for bits 18 to 25, p=0.54048 b-rank test for bits 19 to 26, p=0.02755 b-rank test for bits 20 to 27, p=0.20446 b-rank test for bits 21 to 28, p=0.05431 b-rank test for bits 22 to 29, p=0.96513 b-rank test for bits 23 to 30, p=0.25945 b-rank test for bits 24 to 31, p=0.54340 b-rank test for bits 25 to 32, p=0.00297 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 = 0.001676 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-08_13:31 (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 141001 -2.12 0.016908 2 141348 -1.31 0.094841 3 141300 -1.42 0.077271 4 141549 -0.84 0.199924 5 141238 -1.57 0.058379 6 142204 0.69 0.754425 7 141071 -1.96 0.025073 8 141958 0.11 0.545268 9 141871 -0.09 0.464320 10 141789 -0.28 0.389300 11 142658 1.75 0.959874 12 141634 -0.64 0.260017 13 141430 -1.12 0.131372 14 141374 -1.25 0.105509 15 141719 -0.44 0.328270 16 141608 -0.70 0.240703 17 142101 0.45 0.672861 18 142281 0.87 0.807409 19 141718 -0.45 0.327426 20 140889 -2.38 0.008564 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-08_13:31 Bits used No. missing words z-score p-value 23 to 32 142276 1.2644 0.896953 22 to 31 141889 -0.0701 0.472056 21 to 30 141658 -0.8667 0.193066 20 to 29 141959 0.1713 0.567997 19 to 28 142334 1.4644 0.928455 18 to 27 142200 1.0023 0.841903 17 to 26 142070 0.5540 0.710222 16 to 25 141503 -1.4011 0.080586 15 to 24 141597 -1.0770 0.140740 14 to 23 141776 -0.4598 0.322845 13 to 22 141703 -0.7115 0.238393 12 to 21 141513 -1.3667 0.085867 11 to 20 141667 -0.8356 0.201684 10 to 19 141922 0.0437 0.517424 9 to 18 141672 -0.8184 0.206570 8 to 17 142202 1.0092 0.843562 7 to 16 141927 0.0609 0.524293 6 to 15 141829 -0.2770 0.390890 5 to 14 141326 -2.0115 0.022137 4 to 13 141900 -0.0322 0.487167 3 to 12 142080 0.5885 0.721907 2 to 11 141721 -0.6494 0.258036 1 to 10 141154 -2.6046 0.004599 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-08_13:31 Bits used No. missing words z-score p-value 28 to 32 142079 0.5752 0.717406 27 to 31 141861 -0.1638 0.434932 26 to 30 142180 0.9175 0.820566 25 to 29 142158 0.8429 0.800372 24 to 28 141284 -2.1198 0.017013 23 to 27 141520 -1.3198 0.093457 22 to 26 142022 0.3819 0.648744 21 to 25 142235 1.1040 0.865196 20 to 24 141645 -0.8960 0.185117 19 to 23 141760 -0.5062 0.306357 18 to 22 141830 -0.2689 0.393998 17 to 21 142522 2.0768 0.981092 16 to 20 141512 -1.3469 0.089009 15 to 19 142154 0.8294 0.796558 14 to 18 141785 -0.4215 0.336711 13 to 17 141879 -0.1028 0.459056 12 to 16 142298 1.3175 0.906169 11 to 15 141466 -1.5028 0.066444 10 to 14 141860 -0.1672 0.433598 9 to 13 141736 -0.5876 0.278414 8 to 12 142286 1.2768 0.899172 7 to 11 141524 -1.3062 0.095742 6 to 10 141747 -0.5503 0.291067 5 to 9 141719 -0.6452 0.259403 4 to 8 141992 0.2802 0.610352 3 to 7 142084 0.5921 0.723109 2 to 6 141930 0.0701 0.527930 1 to 5 141559 -1.1876 0.117504 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-08_13:31 Bits used No. missing words z-score p-value 31 to 32 142692 2.3088 0.989522 30 to 31 142048 0.4091 0.658751 29 to 30 142432 1.5418 0.938439 28 to 29 142430 1.5359 0.937719 27 to 28 142435 1.5506 0.939507 26 to 27 142431 1.5388 0.938080 25 to 26 141852 -0.1691 0.432853 24 to 25 141838 -0.2104 0.416673 23 to 24 141468 -1.3019 0.096482 22 to 23 141835 -0.2193 0.413223 21 to 22 141738 -0.5054 0.306640 20 to 21 141540 -1.0895 0.137974 19 to 20 142476 1.6716 0.952698 18 to 19 142193 0.8368 0.798643 17 to 18 141508 -1.1839 0.118233 16 to 17 141863 -0.1367 0.445647 15 to 16 141653 -0.7561 0.224784 14 to 15 142501 1.7453 0.959537 13 to 14 141864 -0.1337 0.446813 12 to 13 142330 1.2409 0.892681 11 to 12 141669 -0.7089 0.239182 10 to 11 141658 -0.7414 0.229230 9 to 10 142153 0.7188 0.763865 8 to 9 142090 0.5329 0.702966 7 to 8 142145 0.6952 0.756532 6 to 7 141483 -1.2576 0.104266 5 to 6 142345 1.2852 0.900632 4 to 5 141849 -0.1780 0.429375 3 to 4 141579 -0.9744 0.164923 2 to 3 141668 -0.7119 0.238267 1 to 2 142297 1.1436 0.873599 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-08_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2517.65 0.250 0.598566 Test results for specific bytes for dh-ranFile-2016-05-08_13:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2477.70 -0.315 0.376224 2 to 9 2553.51 0.757 0.775385 3 to 10 2475.52 -0.346 0.364620 4 to 11 2400.18 -1.412 0.079021 5 to 12 2525.26 0.357 0.639531 6 to 13 2489.64 -0.147 0.441746 7 to 14 2405.72 -1.333 0.091204 8 to 15 2534.66 0.490 0.687995 9 to 16 2507.12 0.101 0.540106 10 to 17 2578.53 1.111 0.866634 11 to 18 2527.50 0.389 0.651348 12 to 19 2607.71 1.523 0.936160 13 to 20 2440.00 -0.849 0.198069 14 to 21 2344.85 -2.194 0.014111 15 to 22 2508.52 0.121 0.547960 16 to 23 2407.50 -1.308 0.095408 17 to 24 2404.61 -1.349 0.088668 18 to 25 2490.65 -0.132 0.447374 19 to 26 2436.70 -0.895 0.185345 20 to 27 2600.99 1.428 0.923378 21 to 28 2573.77 1.043 0.851597 22 to 29 2517.16 0.243 0.595853 23 to 30 2393.84 -1.501 0.066627 24 to 31 2645.81 2.062 0.980396 25 to 32 2522.05 0.312 0.622405 CDPARK for dh-ranFile-2016-05-08_13:31: 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 3573 2.2831 0.988788 3538 0.6849 0.753306 3537 0.6393 0.738676 3507 -0.7306 0.232514 3529 0.2740 0.607947 3533 0.4566 0.676028 3531 0.3653 0.642555 3498 -1.1416 0.126820 3536 0.5936 0.723613 3511 -0.5479 0.291865 Square side=100, avg. no. parked=3529.30 sample std.=19.79 p-value of the KSTEST for those 10 p-values: 0.450579 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-08_13:31 0.2589,0.3138,0.1043,0.7646,0.2178,0.3015,0.3606,0.3935,0.7144,0.3569, The KS test for those 10 p-values: 0.150229 The 3DSPHERES test for dh-ranFile-2016-05-08_13:31 sample no r^3 equiv. uni. 1 0.694 0.022860 2 12.510 0.340969 3 17.939 0.450074 4 25.044 0.566040 5 69.491 0.901370 6 31.676 0.652106 7 18.983 0.468880 8 18.240 0.455557 9 35.255 0.691234 10 33.439 0.671968 11 0.352 0.011663 12 6.519 0.195311 13 2.040 0.065753 14 49.628 0.808767 15 20.040 0.487271 16 101.314 0.965855 17 9.930 0.281797 18 82.837 0.936785 19 0.354 0.011738 20 6.137 0.185005 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.504732 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-08_13:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.1 0.8 -2.2 -2.4 0.1 1.3 -0.2 -0.8 -0.6 -1.4 1.5 0.2 -0.7 0.5 -0.1 -0.3 0.0 -1.2 1.9 2.3 0.2 -3.0 -0.8 -0.7 -0.3 1.6 -0.4 0.5 0.7 1.2 -0.9 -0.8 2.1 1.6 0.1 1.0 -0.7 -0.4 0.4 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:59.725853 z-score=1.934049, p-value=0.962835 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-08_13:31 Test no p-value 1 0.561489 2 0.040424 3 0.676569 4 0.112621 5 0.100250 6 0.682561 7 0.507354 8 0.146009 9 0.043159 10 0.048458 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.013601 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-08_13:31: (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 66589 0.09 66802 0.27 3 25000.00 24953 0.09 24948 0.11 4 6666.67 6780 1.93 6594 0.79 5 1388.89 1390 0.00 1377 0.10 6 238.10 251 0.70 234 0.07 7 34.72 32 0.21 38 0.31 8 4.96 4 0.19 6 0.22 p=0.21724 p=0.06919 Number of rngs required: 688214, p-value: 0.414 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-08_13:31 No. of wins: Observed Expected 98266 98585.9 z-score=-1.431, pvalue=0.07627 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66390 66666.7 1.148 1.148 2 37379 37654.3 2.013 3.161 3 26847 26954.7 0.431 3.592 4 19421 19313.5 0.599 4.191 5 14050 13851.4 2.847 7.038 6 10077 9943.5 1.791 8.829 7 7209 7145.0 0.573 9.402 8 5180 5139.1 0.326 9.727 9 3740 3699.9 0.435 10.163 10 2685 2666.3 0.131 10.294 11 1974 1923.3 1.335 11.629 12 1390 1388.7 0.001 11.630 13 1019 1003.7 0.233 11.863 14 700 726.1 0.941 12.804 15 519 525.8 0.089 12.893 16 410 381.2 2.184 15.076 17 271 276.5 0.111 15.187 18 201 200.8 0.000 15.188 19 141 146.0 0.170 15.358 20 126 106.2 3.685 19.043 21 271 287.1 0.904 19.947 Chisq= 19.95 for 20 degrees of freedom, p= 0.53878 SUMMARY of craptest p-value for no. of wins: 0.076273 p-value for throws/game: 0.538778 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-08_13:31 No. of wins: Observed Expected 98534 98585.9 z-score=-0.232, pvalue=0.40829 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66542 66666.7 0.233 0.233 2 37857 37654.3 1.091 1.324 3 26844 26954.7 0.455 1.779 4 19226 19313.5 0.396 2.175 5 13818 13851.4 0.081 2.256 6 10072 9943.5 1.659 3.915 7 7223 7145.0 0.851 4.766 8 5106 5139.1 0.213 4.979 9 3592 3699.9 3.145 8.124 10 2709 2666.3 0.684 8.808 11 1920 1923.3 0.006 8.813 12 1420 1388.7 0.704 9.517 13 972 1003.7 1.002 10.519 14 749 726.1 0.720 11.239 15 551 525.8 1.204 12.443 16 382 381.2 0.002 12.445 17 265 276.5 0.482 12.926 18 202 200.8 0.007 12.933 19 141 146.0 0.170 13.103 20 116 106.2 0.901 14.005 21 293 287.1 0.121 14.125 Chisq= 14.13 for 20 degrees of freedom, p= 0.17592 SUMMARY of craptest p-value for no. of wins: 0.408292 p-value for throws/game: 0.175918 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0024,0.0030,0.0046,0.0080,0.0086,0.0117,0.0117,0.0136,0.0141, 0.0169,0.0170,0.0221,0.0229,0.0241,0.0251,0.0260,0.0276,0.0304,0.0404, 0.0432,0.0445,0.0485,0.0506,0.0517,0.0543,0.0545,0.0553,0.0584,0.0658, 0.0664,0.0666,0.0692,0.0763,0.0765,0.0773,0.0790,0.0806,0.0859,0.0887, 0.0890,0.0912,0.0935,0.0948,0.0954,0.0957,0.0965,0.1002,0.1043,0.1043, 0.1055,0.1126,0.1175,0.1182,0.1268,0.1314,0.1346,0.1367,0.1380,0.1407, 0.1433,0.1460,0.1502,0.1649,0.1658,0.1676,0.1695,0.1759,0.1850,0.1851, 0.1853,0.1931,0.1953,0.1981,0.1999,0.2017,0.2045,0.2066,0.2135,0.2172, 0.2178,0.2245,0.2248,0.2292,0.2325,0.2383,0.2384,0.2392,0.2407,0.2500, 0.2580,0.2589,0.2594,0.2595,0.2600,0.2770,0.2784,0.2797,0.2818,0.2897, 0.2911,0.2919,0.3015,0.3048,0.3059,0.3064,0.3066,0.3138,0.3228,0.3262, 0.3274,0.3283,0.3345,0.3367,0.3410,0.3569,0.3606,0.3646,0.3762,0.3889, 0.3893,0.3909,0.3935,0.3940,0.4083,0.4102,0.4132,0.4139,0.4167,0.4220, 0.4294,0.4329,0.4336,0.4349,0.4417,0.4456,0.4468,0.4474,0.4501,0.4506, 0.4512,0.4556,0.4591,0.4643,0.4689,0.4721,0.4746,0.4766,0.4872,0.4873, 0.4897,0.4986,0.4997,0.5047,0.5074,0.5174,0.5220,0.5243,0.5279,0.5388, 0.5401,0.5405,0.5434,0.5453,0.5480,0.5615,0.5632,0.5660,0.5678,0.5680, 0.5762,0.5802,0.5814,0.5959,0.5986,0.6048,0.6079,0.6104,0.6224,0.6227, 0.6395,0.6426,0.6487,0.6513,0.6521,0.6588,0.6639,0.6720,0.6729,0.6760, 0.6766,0.6826,0.6880,0.6912,0.6983,0.7030,0.7102,0.7120,0.7144,0.7174, 0.7219,0.7227,0.7231,0.7236,0.7387,0.7410,0.7451,0.7464,0.7476,0.7533, 0.7544,0.7565,0.7639,0.7646,0.7754,0.7900,0.7966,0.7986,0.8004,0.8011, 0.8074,0.8088,0.8182,0.8206,0.8304,0.8419,0.8431,0.8436,0.8516,0.8626, 0.8652,0.8666,0.8736,0.8813,0.8927,0.8970,0.8992,0.9006,0.9014,0.9062, 0.9234,0.9270,0.9285,0.9331,0.9362,0.9368,0.9368,0.9377,0.9381,0.9384, 0.9395,0.9416,0.9466,0.9468,0.9487,0.9498,0.9527,0.9595,0.9599,0.9628, 0.9651,0.9659,0.9667,0.9796,0.9804,0.9811,0.9840,0.9888,0.9895, Overall p-value after applying KStest on 269 p-values = 0.002505 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.