RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-01_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 9.1183 0.063522 2 to 25 15.78 9.6237 0.081354 3 to 26 15.79 17.1200 0.553732 4 to 27 15.51 22.1960 0.822701 5 to 28 15.79 16.6894 0.524408 6 to 29 15.73 30.0576 0.974067 7 to 30 15.51 19.6568 0.707839 8 to 31 15.79 12.9590 0.261075 9 to 32 15.72 12.4783 0.229651 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.941736 Tough bday spacings test for dh-ranFile-2015-07-01_08:31: 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 39 80 97 105 81 36 27 16 5 3 (O-E)^2/E 0.4 0.2 0.6 0.0 0.5 0.1 5.0 0.3 0.1 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.790, p= 0.351 RESULTS OF GCD FOR dh-ranFile-2015-07-01_08:31 Euclid's algorithm: p-value, steps to gcd: 0.259216 p-value, dist. of gcd's: 0.197298 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-01_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.971 0.046 0.467 0.176 0.678 0.584 0.946 0.036 Bits 8 to 15---> 0.812 0.143 0.485 0.670 0.493 0.392 0.486 0.258 Bits 16 to 23---> 0.502 0.122 0.890 0.955 0.545 0.768 0.391 0.301 Bits 24 to 31---> 0.767 0.006 0.383 0.028 0.813 0.565 0.862 0.197 KS test for the above 32 p values: 0.045 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-01_08:31, p-values for 5 runs: 0.0944, 0.2186, 0.2840, 0.1911, 0.3984 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-01_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5184 5134.0 0.487 0.514 r= 30 23128 23103.0 0.027 0.541 r= 31 11479 11551.5 0.455 0.997 chi-square = 0.997 with df = 3; p-value = 0.198 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-01_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5240 5134.0 2.188 2.287 r= 31 23133 23103.0 0.039 2.326 r= 32 11411 11551.5 1.709 4.036 chi-square = 4.036 with df = 3; p-value = 0.742 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-01_08:31 b-rank test for bits 1 to 8, p=0.60043 b-rank test for bits 2 to 9, p=0.81035 b-rank test for bits 3 to 10, p=0.51003 b-rank test for bits 4 to 11, p=0.44534 b-rank test for bits 5 to 12, p=0.89141 b-rank test for bits 6 to 13, p=0.41575 b-rank test for bits 7 to 14, p=0.28733 b-rank test for bits 8 to 15, p=0.35397 b-rank test for bits 9 to 16, p=0.68756 b-rank test for bits 10 to 17, p=0.34451 b-rank test for bits 11 to 18, p=0.14767 b-rank test for bits 12 to 19, p=0.05061 b-rank test for bits 13 to 20, p=0.65960 b-rank test for bits 14 to 21, p=0.65312 b-rank test for bits 15 to 22, p=0.03912 b-rank test for bits 16 to 23, p=0.79364 b-rank test for bits 17 to 24, p=0.96365 b-rank test for bits 18 to 25, p=0.01228 b-rank test for bits 19 to 26, p=0.32850 b-rank test for bits 20 to 27, p=0.27383 b-rank test for bits 21 to 28, p=0.89800 b-rank test for bits 22 to 29, p=0.75445 b-rank test for bits 23 to 30, p=0.64801 b-rank test for bits 24 to 31, p=0.77475 b-rank test for bits 25 to 32, p=0.56594 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 = 0.917539 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-01_08:31 (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 142333 0.99 0.838884 2 141370 -1.26 0.103814 3 141530 -0.89 0.187732 4 142408 1.17 0.878014 5 142590 1.59 0.944122 6 141667 -0.57 0.285632 7 142726 1.91 0.971811 8 141915 0.01 0.505285 9 142634 1.69 0.954787 10 141886 -0.05 0.478265 11 142265 0.83 0.797015 12 142428 1.21 0.887214 13 142585 1.58 0.942794 14 142268 0.84 0.798989 15 141995 0.20 0.579324 16 142332 0.99 0.838313 17 142280 0.87 0.806769 18 142752 1.97 0.975515 19 141683 -0.53 0.298469 20 142158 0.58 0.719381 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-01_08:31 Bits used No. missing words z-score p-value 23 to 32 142126 0.7471 0.772510 22 to 31 142170 0.8989 0.815637 21 to 30 142211 1.0402 0.850886 20 to 29 142198 0.9954 0.840233 19 to 28 142818 3.1333 0.999136 18 to 27 142308 1.3747 0.915392 17 to 26 142094 0.6368 0.737870 16 to 25 142246 1.1609 0.877165 15 to 24 141806 -0.3563 0.360804 14 to 23 141693 -0.7460 0.227844 13 to 22 142004 0.3264 0.627957 12 to 21 141847 -0.2149 0.414911 11 to 20 141751 -0.5460 0.292545 10 to 19 142027 0.4058 0.657540 9 to 18 141882 -0.0942 0.462459 8 to 17 141945 0.1230 0.548947 7 to 16 141760 -0.5149 0.303301 6 to 15 141827 -0.2839 0.388245 5 to 14 141741 -0.5804 0.280806 4 to 13 141903 -0.0218 0.491293 3 to 12 142218 1.0644 0.856422 2 to 11 142672 2.6299 0.995729 1 to 10 141801 -0.3736 0.354369 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-01_08:31 Bits used No. missing words z-score p-value 28 to 32 142419 1.7277 0.957979 27 to 31 142309 1.3548 0.912262 26 to 30 141673 -0.8011 0.211532 25 to 29 141445 -1.5740 0.057744 24 to 28 141883 -0.0893 0.464440 23 to 27 141384 -1.7808 0.037474 22 to 26 141423 -1.6486 0.049617 21 to 25 142077 0.5684 0.715109 20 to 24 141635 -0.9299 0.176203 19 to 23 142516 2.0565 0.980133 18 to 22 141991 0.2768 0.609051 17 to 21 141983 0.2497 0.598602 16 to 20 142096 0.6328 0.736561 15 to 19 141794 -0.3909 0.347917 14 to 18 141933 0.0802 0.531976 13 to 17 142435 1.7819 0.962620 12 to 16 142014 0.3548 0.638635 11 to 15 141772 -0.4655 0.320778 10 to 14 142219 1.0497 0.853079 9 to 13 141794 -0.3909 0.347917 8 to 12 141408 -1.6994 0.044620 7 to 11 141554 -1.2045 0.114197 6 to 10 141814 -0.3232 0.373290 5 to 9 141895 -0.0486 0.480629 4 to 8 141636 -0.9265 0.177082 3 to 7 141850 -0.2011 0.420303 2 to 6 141886 -0.0791 0.468483 1 to 5 141469 -1.4926 0.067765 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-01_08:31 Bits used No. missing words z-score p-value 31 to 32 141916 0.0197 0.507849 30 to 31 141990 0.2380 0.594046 29 to 30 141503 -1.1986 0.115339 28 to 29 142198 0.8515 0.802764 27 to 28 142173 0.7778 0.781653 26 to 27 142098 0.5565 0.711082 25 to 26 142215 0.9017 0.816387 24 to 25 141954 0.1318 0.552417 23 to 24 142130 0.6509 0.742459 22 to 23 141567 -1.0098 0.156290 21 to 22 141704 -0.6057 0.272359 20 to 21 142047 0.4061 0.657668 19 to 20 141600 -0.9125 0.180759 18 to 19 141865 -0.1308 0.447980 17 to 18 141550 -1.0600 0.144579 16 to 17 141809 -0.2960 0.383631 15 to 16 141559 -1.0334 0.150703 14 to 15 141692 -0.6411 0.260732 13 to 14 142466 1.6421 0.949715 12 to 13 142125 0.6362 0.737675 11 to 12 141618 -0.8594 0.195065 10 to 11 141162 -2.2045 0.013744 9 to 10 141827 -0.2429 0.404056 8 to 9 141709 -0.5909 0.277279 7 to 8 141667 -0.7148 0.237355 6 to 7 142025 0.3412 0.633527 5 to 6 142140 0.6804 0.751888 4 to 5 141890 -0.0570 0.477264 3 to 4 141804 -0.3107 0.378011 2 to 3 141571 -0.9980 0.159134 1 to 2 141396 -1.5142 0.064982 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-01_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2395.91 -1.472 0.070499 Test results for specific bytes for dh-ranFile-2015-07-01_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2613.32 1.603 0.945482 2 to 9 2554.07 0.765 0.777776 3 to 10 2482.69 -0.245 0.403285 4 to 11 2454.32 -0.646 0.259126 5 to 12 2627.20 1.799 0.963978 6 to 13 2534.34 0.486 0.686393 7 to 14 2558.75 0.831 0.796963 8 to 15 2579.14 1.119 0.868459 9 to 16 2484.41 -0.221 0.412733 10 to 17 2589.67 1.268 0.897636 11 to 18 2487.06 -0.183 0.427372 12 to 19 2527.76 0.393 0.652707 13 to 20 2395.00 -1.485 0.068773 14 to 21 2570.25 0.994 0.839773 15 to 22 2547.31 0.669 0.748253 16 to 23 2466.61 -0.472 0.318409 17 to 24 2523.69 0.335 0.631203 18 to 25 2541.79 0.591 0.722758 19 to 26 2398.68 -1.433 0.075953 20 to 27 2465.39 -0.490 0.312243 21 to 28 2467.80 -0.455 0.324410 22 to 29 2484.59 -0.218 0.413743 23 to 30 2461.69 -0.542 0.293964 24 to 31 2457.68 -0.598 0.274776 25 to 32 2600.77 1.425 0.922941 CDPARK for dh-ranFile-2015-07-01_08:31: 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 3519 -0.1826 0.427537 3491 -1.4612 0.071982 3525 0.0913 0.536383 3524 0.0457 0.518210 3483 -1.8265 0.033889 3526 0.1370 0.554479 3527 0.1826 0.572463 3537 0.6393 0.738676 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3515.30 sample std.=16.09 p-value of the KSTEST for those 10 p-values: 0.328578 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-01_08:31 0.0184,0.1117,0.0045,0.5568,0.4127,0.8128,0.9758,0.5745,0.2050,0.6408, The KS test for those 10 p-values: 0.362333 The 3DSPHERES test for dh-ranFile-2015-07-01_08:31 sample no r^3 equiv. uni. 1 12.603 0.343024 2 42.941 0.761018 3 34.251 0.680723 4 47.333 0.793562 5 46.248 0.785961 6 4.457 0.138054 7 22.885 0.533663 8 24.084 0.551925 9 3.836 0.120042 10 10.711 0.300255 11 5.963 0.180255 12 17.505 0.442067 13 40.860 0.743855 14 0.037 0.001240 15 47.771 0.796557 16 65.929 0.888936 17 23.831 0.548132 18 26.011 0.579806 19 60.788 0.868174 20 8.232 0.239974 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.747570 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-01_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 0.1 0.3 -0.9 0.2 -0.1 -0.0 -0.6 -0.5 -0.4 -0.8 -0.6 -1.6 0.3 0.1 -0.1 0.1 0.8 -0.1 1.8 2.4 0.6 0.0 -1.9 -1.1 0.4 0.0 -0.6 0.1 -0.6 -0.3 -0.0 -0.2 -1.3 0.4 0.7 1.1 -0.4 0.4 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:28.537689 z-score=-1.468859, p-value=0.056047 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-01_08:31 Test no p-value 1 0.010482 2 0.527434 3 0.225366 4 0.039074 5 0.155856 6 0.346660 7 0.553208 8 0.165218 9 0.959399 10 0.076467 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.035143 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-01_08:31: (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 66870 0.62 66814 0.33 3 25000.00 24865 0.73 24944 0.13 4 6666.67 6621 0.31 6601 0.65 5 1388.89 1398 0.06 1381 0.04 6 238.10 214 2.44 227 0.52 7 34.72 29 0.94 27 1.72 8 4.96 2 1.77 5 0.00 p=0.66687 p=0.23970 Number of rngs required: 687736, p-value: 0.220 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-01_08:31 No. of wins: Observed Expected 98392 98585.9 z-score=-0.867, pvalue=0.19296 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66811 66666.7 0.312 0.312 2 37786 37654.3 0.460 0.773 3 26949 26954.7 0.001 0.774 4 19300 19313.5 0.009 0.784 5 13772 13851.4 0.455 1.239 6 9830 9943.5 1.297 2.535 7 7134 7145.0 0.017 2.552 8 5194 5139.1 0.587 3.140 9 3715 3699.9 0.062 3.201 10 2613 2666.3 1.065 4.267 11 1900 1923.3 0.283 4.550 12 1436 1388.7 1.608 6.158 13 1023 1003.7 0.371 6.529 14 706 726.1 0.559 7.087 15 515 525.8 0.223 7.311 16 341 381.2 4.229 11.540 17 266 276.5 0.402 11.942 18 182 200.8 1.765 13.707 19 137 146.0 0.553 14.260 20 105 106.2 0.014 14.274 21 285 287.1 0.016 14.290 Chisq= 14.29 for 20 degrees of freedom, p= 0.18449 SUMMARY of craptest p-value for no. of wins: 0.192958 p-value for throws/game: 0.184487 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-01_08:31 No. of wins: Observed Expected 98902 98585.9 z-score= 1.414, pvalue=0.92131 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67026 66666.7 1.937 1.937 2 37398 37654.3 1.745 3.682 3 26903 26954.7 0.099 3.781 4 19328 19313.5 0.011 3.792 5 13663 13851.4 2.563 6.355 6 9815 9943.5 1.662 8.017 7 7282 7145.0 2.626 10.643 8 5120 5139.1 0.071 10.713 9 3833 3699.9 4.791 15.504 10 2623 2666.3 0.703 16.207 11 1952 1923.3 0.427 16.634 12 1396 1388.7 0.038 16.672 13 1022 1003.7 0.333 17.006 14 706 726.1 0.559 17.564 15 546 525.8 0.773 18.337 16 383 381.2 0.009 18.346 17 296 276.5 1.369 19.716 18 205 200.8 0.087 19.802 19 134 146.0 0.984 20.786 20 94 106.2 1.405 22.191 21 275 287.1 0.511 22.702 Chisq= 22.70 for 20 degrees of freedom, p= 0.69635 SUMMARY of craptest p-value for no. of wins: 0.921314 p-value for throws/game: 0.696348 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0045,0.0056,0.0105,0.0123,0.0137,0.0184,0.0283,0.0339,0.0351, 0.0363,0.0375,0.0391,0.0391,0.0446,0.0448,0.0463,0.0496,0.0506,0.0560, 0.0577,0.0635,0.0650,0.0678,0.0688,0.0705,0.0720,0.0760,0.0765,0.0814, 0.0944,0.1038,0.1117,0.1142,0.1153,0.1200,0.1223,0.1381,0.1427,0.1446, 0.1477,0.1507,0.1559,0.1563,0.1591,0.1652,0.1762,0.1764,0.1771,0.1803, 0.1808,0.1845,0.1877,0.1911,0.1930,0.1951,0.1969,0.1973,0.1979,0.2050, 0.2115,0.2186,0.2205,0.2254,0.2278,0.2297,0.2374,0.2397,0.2400,0.2576, 0.2591,0.2592,0.2607,0.2611,0.2613,0.2724,0.2738,0.2748,0.2773,0.2808, 0.2840,0.2856,0.2873,0.2925,0.2940,0.2985,0.3003,0.3009,0.3033,0.3077, 0.3122,0.3184,0.3208,0.3244,0.3285,0.3286,0.3430,0.3445,0.3467,0.3479, 0.3479,0.3506,0.3540,0.3544,0.3608,0.3623,0.3733,0.3780,0.3832,0.3836, 0.3882,0.3913,0.3919,0.3984,0.4033,0.4041,0.4127,0.4127,0.4137,0.4149, 0.4158,0.4203,0.4274,0.4275,0.4421,0.4453,0.4480,0.4625,0.4644,0.4666, 0.4685,0.4773,0.4783,0.4806,0.4850,0.4860,0.4913,0.4929,0.5025,0.5053, 0.5078,0.5100,0.5182,0.5244,0.5274,0.5320,0.5337,0.5364,0.5455,0.5481, 0.5489,0.5519,0.5524,0.5532,0.5537,0.5545,0.5568,0.5651,0.5659,0.5725, 0.5745,0.5793,0.5798,0.5839,0.5940,0.5986,0.6004,0.6091,0.6280,0.6312, 0.6335,0.6386,0.6408,0.6480,0.6527,0.6531,0.6575,0.6577,0.6596,0.6669, 0.6701,0.6777,0.6807,0.6864,0.6876,0.6963,0.7078,0.7111,0.7151,0.7194, 0.7228,0.7366,0.7377,0.7379,0.7387,0.7424,0.7425,0.7439,0.7476,0.7483, 0.7519,0.7545,0.7610,0.7674,0.7681,0.7725,0.7748,0.7778,0.7817,0.7860, 0.7936,0.7936,0.7966,0.7970,0.7970,0.7990,0.8028,0.8068,0.8104,0.8124, 0.8128,0.8134,0.8156,0.8164,0.8227,0.8383,0.8389,0.8398,0.8402,0.8509, 0.8531,0.8564,0.8615,0.8682,0.8685,0.8772,0.8780,0.8872,0.8889,0.8897, 0.8914,0.8976,0.8980,0.9123,0.9154,0.9175,0.9213,0.9229,0.9417,0.9428, 0.9441,0.9455,0.9463,0.9497,0.9548,0.9550,0.9580,0.9594,0.9626,0.9636, 0.9640,0.9713,0.9718,0.9741,0.9755,0.9758,0.9801,0.9957,0.9991, Overall p-value after applying KStest on 269 p-values = 0.860258 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.