RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-05_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.55 27.3179 0.946432 2 to 25 15.56 36.7234 0.996332 3 to 26 15.59 24.4702 0.892787 4 to 27 15.97 19.0015 0.671553 5 to 28 16.15 17.0001 0.545640 6 to 29 15.99 16.5024 0.511459 7 to 30 15.69 20.1622 0.733982 8 to 31 15.77 13.7117 0.312608 9 to 32 15.76 21.2712 0.785605 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.042429 Tough bday spacings test for dh-ranFile-2015-10-05_07:31: 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 12 34 76 103 112 74 43 27 12 4 3 (O-E)^2/E 0.9 0.2 0.1 0.3 2.1 0.2 1.6 0.3 0.6 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.500, p= 0.322 RESULTS OF GCD FOR dh-ranFile-2015-10-05_07:31 Euclid's algorithm: p-value, steps to gcd: 0.151144 p-value, dist. of gcd's: 0.661466 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-05_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.296 0.285 0.665 0.190 0.743 0.871 0.238 0.837 Bits 8 to 15---> 0.680 0.362 0.030 0.303 0.311 0.504 0.500 0.198 Bits 16 to 23---> 0.232 0.036 0.354 0.717 0.744 0.218 0.193 0.946 Bits 24 to 31---> 0.732 0.684 0.076 0.423 0.676 0.054 0.078 0.649 KS test for the above 32 p values: 0.751 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-05_07:31, p-values for 5 runs: 0.3285, 0.2831, 0.8020, 0.8308, 0.5117 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-05_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 202 211.4 0.420 0.420 r= 29 5081 5134.0 0.547 0.967 r= 30 23220 23103.0 0.592 1.559 r= 31 11497 11551.5 0.257 1.816 chi-square = 1.816 with df = 3; p-value = 0.389 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-05_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 219 211.4 0.272 0.272 r= 30 5109 5134.0 0.122 0.394 r= 31 23129 23103.0 0.029 0.423 r= 32 11543 11551.5 0.006 0.429 chi-square = 0.429 with df = 3; p-value = 0.066 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-05_07:31 b-rank test for bits 1 to 8, p=0.52711 b-rank test for bits 2 to 9, p=0.06802 b-rank test for bits 3 to 10, p=0.28754 b-rank test for bits 4 to 11, p=0.16311 b-rank test for bits 5 to 12, p=0.53118 b-rank test for bits 6 to 13, p=0.93378 b-rank test for bits 7 to 14, p=0.89543 b-rank test for bits 8 to 15, p=0.73170 b-rank test for bits 9 to 16, p=0.80712 b-rank test for bits 10 to 17, p=0.93894 b-rank test for bits 11 to 18, p=0.16419 b-rank test for bits 12 to 19, p=0.25841 b-rank test for bits 13 to 20, p=0.87335 b-rank test for bits 14 to 21, p=0.46702 b-rank test for bits 15 to 22, p=0.32219 b-rank test for bits 16 to 23, p=0.51492 b-rank test for bits 17 to 24, p=0.33446 b-rank test for bits 18 to 25, p=0.02627 b-rank test for bits 19 to 26, p=0.26419 b-rank test for bits 20 to 27, p=0.89731 b-rank test for bits 21 to 28, p=0.66044 b-rank test for bits 22 to 29, p=0.58662 b-rank test for bits 23 to 30, p=0.23908 b-rank test for bits 24 to 31, p=0.47395 b-rank test for bits 25 to 32, p=0.43690 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 = 0.954445 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-05_07:31 (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 141809 -0.23 0.407331 2 141454 -1.06 0.143697 3 142360 1.05 0.853822 4 143186 2.98 0.998572 5 142280 0.87 0.806769 6 142770 2.01 0.977833 7 141609 -0.70 0.241431 8 141779 -0.30 0.380370 9 141789 -0.28 0.389300 10 141809 -0.23 0.407331 11 142467 1.30 0.903707 12 141946 0.09 0.534139 13 142962 2.46 0.993044 14 141363 -1.28 0.100894 15 141283 -1.46 0.071681 16 141689 -0.51 0.303350 17 142076 0.39 0.651516 18 142341 1.01 0.843411 19 141148 -1.78 0.037636 20 142570 1.54 0.938660 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-05_07:31 Bits used No. missing words z-score p-value 23 to 32 141464 -1.5356 0.062316 22 to 31 141593 -1.0908 0.137682 21 to 30 141312 -2.0598 0.019711 20 to 29 141741 -0.5804 0.280806 19 to 28 141889 -0.0701 0.472056 18 to 27 141671 -0.8218 0.205588 17 to 26 141672 -0.8184 0.206570 16 to 25 141475 -1.4977 0.067107 15 to 24 141390 -1.7908 0.036663 14 to 23 141902 -0.0253 0.489918 13 to 22 141952 0.1471 0.558488 12 to 21 141957 0.1644 0.565284 11 to 20 141713 -0.6770 0.249203 10 to 19 141799 -0.3804 0.351806 9 to 18 142052 0.4920 0.688628 8 to 17 142064 0.5333 0.703103 7 to 16 142005 0.3299 0.629261 6 to 15 141863 -0.1598 0.436536 5 to 14 141786 -0.4253 0.335318 4 to 13 141985 0.2609 0.602927 3 to 12 142012 0.3540 0.638344 2 to 11 141790 -0.4115 0.340359 1 to 10 141723 -0.6425 0.260269 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-05_07:31 Bits used No. missing words z-score p-value 28 to 32 141992 0.2802 0.610352 27 to 31 141258 -2.2079 0.013626 26 to 30 141834 -0.2554 0.399224 25 to 29 141540 -1.2520 0.105291 24 to 28 141641 -0.9096 0.181519 23 to 27 141828 -0.2757 0.391391 22 to 26 141928 0.0633 0.525232 21 to 25 142016 0.3616 0.641172 20 to 24 141816 -0.3164 0.375860 19 to 23 141772 -0.4655 0.320778 18 to 22 142310 1.3582 0.912800 17 to 21 142076 0.5650 0.713957 16 to 20 142028 0.4023 0.656258 15 to 19 141527 -1.2960 0.097482 14 to 18 141595 -1.0655 0.143319 13 to 17 141807 -0.3469 0.364340 12 to 16 141802 -0.3638 0.357992 11 to 15 141349 -1.8994 0.028754 10 to 14 142022 0.3819 0.648744 9 to 13 142071 0.5480 0.708166 8 to 12 142312 1.3650 0.913871 7 to 11 142027 0.3989 0.655010 6 to 10 141955 0.1548 0.561516 5 to 9 141600 -1.0486 0.147187 4 to 8 141912 0.0091 0.503611 3 to 7 142000 0.3074 0.620714 2 to 6 141897 -0.0418 0.483330 1 to 5 142255 1.1718 0.879354 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-05_07:31 Bits used No. missing words z-score p-value 31 to 32 142054 0.4268 0.665221 30 to 31 141989 0.2350 0.592901 29 to 30 141674 -0.6942 0.243782 28 to 29 141680 -0.6765 0.249365 27 to 28 141986 0.2262 0.589464 26 to 27 142110 0.5919 0.723057 25 to 26 141684 -0.6647 0.253124 24 to 25 141526 -1.1308 0.129077 23 to 24 141972 0.1849 0.573333 22 to 23 141732 -0.5231 0.300453 21 to 22 141887 -0.0659 0.473741 20 to 21 142199 0.8545 0.803582 19 to 20 142071 0.4769 0.683284 18 to 19 141485 -1.2517 0.105338 17 to 18 142192 0.8338 0.797813 16 to 17 142098 0.5565 0.711082 15 to 16 141892 -0.0511 0.479615 14 to 15 141717 -0.5673 0.285240 13 to 14 141788 -0.3579 0.360207 12 to 13 142341 1.2734 0.898555 11 to 12 141974 0.1908 0.575646 10 to 11 142255 1.0197 0.846059 9 to 10 141743 -0.4906 0.311837 8 to 9 141699 -0.6204 0.267483 7 to 8 141791 -0.3491 0.363524 6 to 7 142231 0.9489 0.828659 5 to 6 142118 0.6155 0.730903 4 to 5 142451 1.5978 0.944961 3 to 4 141541 -1.0865 0.138625 2 to 3 142435 1.5506 0.939507 1 to 2 141755 -0.4553 0.324464 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-05_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2581.20 1.148 0.874597 Test results for specific bytes for dh-ranFile-2015-10-05_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2330.29 -2.400 0.008197 2 to 9 2585.40 1.208 0.886430 3 to 10 2486.08 -0.197 0.421980 4 to 11 2431.72 -0.966 0.167123 5 to 12 2555.25 0.781 0.782704 6 to 13 2623.15 1.742 0.959205 7 to 14 2629.48 1.831 0.966463 8 to 15 2461.79 -0.540 0.294489 9 to 16 2544.03 0.623 0.733251 10 to 17 2605.40 1.491 0.931968 11 to 18 2517.99 0.254 0.600415 12 to 19 2371.83 -1.813 0.034950 13 to 20 2501.06 0.015 0.505971 14 to 21 2533.01 0.467 0.679689 15 to 22 2488.24 -0.166 0.433969 16 to 23 2617.48 1.661 0.951692 17 to 24 2394.29 -1.495 0.067457 18 to 25 2511.75 0.166 0.565974 19 to 26 2571.20 1.007 0.843026 20 to 27 2522.88 0.324 0.626867 21 to 28 2501.26 0.018 0.507090 22 to 29 2458.25 -0.590 0.277456 23 to 30 2547.34 0.670 0.748415 24 to 31 2441.15 -0.832 0.202633 25 to 32 2433.47 -0.941 0.173394 CDPARK for dh-ranFile-2015-10-05_07:31: 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 3513 -0.4566 0.323972 3494 -1.3242 0.092718 3526 0.1370 0.554479 3515 -0.3653 0.357445 3519 -0.1826 0.427537 3545 1.0046 0.842447 3519 -0.1826 0.427537 3504 -0.8676 0.192812 3533 0.4566 0.676028 3534 0.5023 0.692266 Square side=100, avg. no. parked=3520.20 sample std.=14.26 p-value of the KSTEST for those 10 p-values: 0.732100 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-05_07:31 0.1146,0.9837,0.8123,0.9410,0.0186,0.6255,0.8237,0.3850,0.4309,0.0716, The KS test for those 10 p-values: 0.566619 The 3DSPHERES test for dh-ranFile-2015-10-05_07:31 sample no r^3 equiv. uni. 1 12.865 0.348739 2 19.445 0.477004 3 58.889 0.859561 4 9.012 0.259485 5 88.717 0.948037 6 33.787 0.675752 7 9.215 0.264468 8 8.401 0.244244 9 29.766 0.629235 10 50.477 0.814106 11 31.678 0.652135 12 53.165 0.830038 13 22.312 0.524662 14 10.914 0.304969 15 33.884 0.676790 16 36.883 0.707544 17 31.706 0.652459 18 45.674 0.781827 19 13.864 0.370071 20 83.412 0.937987 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.146564 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-05_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 0.1 1.4 0.1 1.3 -0.1 -0.3 0.8 -0.7 -0.6 0.9 2.7 -0.6 -0.1 -0.1 -1.3 1.2 -0.0 -0.5 -0.5 -0.3 0.4 0.3 0.2 0.4 -1.3 -1.0 -0.7 -0.7 0.2 -0.7 -0.0 -0.4 -0.4 -0.3 1.0 -1.0 0.5 -0.1 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:27.679911 z-score=-1.562450, p-value=0.043487 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-05_07:31 Test no p-value 1 0.001806 2 0.172299 3 0.002472 4 0.215245 5 0.833376 6 0.003892 7 0.318883 8 0.071892 9 0.159434 10 0.310178 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000141 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-05_07:31: (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 66808 0.30 66729 0.06 3 25000.00 24978 0.02 25065 0.17 4 6666.67 6567 1.49 6540 2.41 5 1388.89 1392 0.01 1395 0.03 6 238.10 214 2.44 236 0.02 7 34.72 35 0.00 34 0.01 8 4.96 5 0.00 0 4.96 p=0.35807 p=0.73546 Number of rngs required: 687691, p-value: 0.205 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-05_07:31 No. of wins: Observed Expected 98480 98585.9 z-score=-0.473, pvalue=0.31794 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66817 66666.7 0.339 0.339 2 37740 37654.3 0.195 0.534 3 26710 26954.7 2.222 2.756 4 19270 19313.5 0.098 2.854 5 13866 13851.4 0.015 2.869 6 9953 9943.5 0.009 2.878 7 7139 7145.0 0.005 2.883 8 5115 5139.1 0.113 2.996 9 3749 3699.9 0.653 3.648 10 2691 2666.3 0.229 3.877 11 1915 1923.3 0.036 3.913 12 1331 1388.7 2.401 6.314 13 1013 1003.7 0.086 6.400 14 763 726.1 1.871 8.271 15 532 525.8 0.072 8.343 16 369 381.2 0.387 8.731 17 299 276.5 1.824 10.555 18 195 200.8 0.169 10.724 19 157 146.0 0.831 11.555 20 95 106.2 1.184 12.740 21 281 287.1 0.130 12.870 Chisq= 12.87 for 20 degrees of freedom, p= 0.11710 SUMMARY of craptest p-value for no. of wins: 0.317942 p-value for throws/game: 0.117097 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-05_07:31 No. of wins: Observed Expected 98623 98585.9 z-score= 0.166, pvalue=0.56597 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66846 66666.7 0.482 0.482 2 37440 37654.3 1.220 1.702 3 27003 26954.7 0.086 1.789 4 19318 19313.5 0.001 1.790 5 13919 13851.4 0.330 2.119 6 10063 9943.5 1.435 3.555 7 7029 7145.0 1.884 5.439 8 5162 5139.1 0.102 5.541 9 3619 3699.9 1.767 7.308 10 2649 2666.3 0.112 7.421 11 1942 1923.3 0.181 7.602 12 1368 1388.7 0.310 7.912 13 1009 1003.7 0.028 7.939 14 724 726.1 0.006 7.946 15 516 525.8 0.184 8.130 16 381 381.2 0.000 8.130 17 287 276.5 0.396 8.525 18 172 200.8 4.139 12.664 19 125 146.0 3.016 15.680 20 117 106.2 1.095 16.776 21 311 287.1 1.987 18.763 Chisq= 18.76 for 20 degrees of freedom, p= 0.46270 SUMMARY of craptest p-value for no. of wins: 0.565968 p-value for throws/game: 0.462704 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0018,0.0025,0.0039,0.0082,0.0136,0.0186,0.0197,0.0263,0.0288, 0.0296,0.0349,0.0362,0.0367,0.0376,0.0424,0.0435,0.0543,0.0623,0.0659, 0.0671,0.0675,0.0680,0.0716,0.0717,0.0719,0.0755,0.0780,0.0927,0.0975, 0.1009,0.1053,0.1053,0.1146,0.1171,0.1291,0.1377,0.1386,0.1433,0.1437, 0.1466,0.1472,0.1511,0.1594,0.1631,0.1642,0.1671,0.1723,0.1734,0.1815, 0.1900,0.1927,0.1928,0.1985,0.2026,0.2052,0.2056,0.2066,0.2152,0.2183, 0.2320,0.2381,0.2391,0.2414,0.2438,0.2442,0.2492,0.2494,0.2531,0.2584, 0.2595,0.2603,0.2642,0.2645,0.2675,0.2775,0.2808,0.2831,0.2851,0.2852, 0.2875,0.2945,0.2962,0.3005,0.3033,0.3034,0.3050,0.3102,0.3107,0.3118, 0.3126,0.3179,0.3189,0.3208,0.3222,0.3225,0.3240,0.3245,0.3285,0.3345, 0.3353,0.3404,0.3487,0.3518,0.3539,0.3574,0.3580,0.3581,0.3602,0.3623, 0.3635,0.3643,0.3701,0.3759,0.3804,0.3850,0.3886,0.3893,0.3914,0.3992, 0.4073,0.4073,0.4220,0.4233,0.4275,0.4275,0.4309,0.4340,0.4365,0.4369, 0.4627,0.4670,0.4721,0.4737,0.4740,0.4770,0.4796,0.4833,0.4899,0.4997, 0.5036,0.5036,0.5060,0.5071,0.5115,0.5117,0.5149,0.5247,0.5252,0.5271, 0.5312,0.5341,0.5456,0.5545,0.5585,0.5615,0.5653,0.5660,0.5660,0.5666, 0.5733,0.5756,0.5866,0.5895,0.5929,0.6004,0.6029,0.6104,0.6207,0.6255, 0.6269,0.6292,0.6293,0.6383,0.6412,0.6487,0.6487,0.6515,0.6521,0.6525, 0.6550,0.6563,0.6604,0.6615,0.6652,0.6652,0.6716,0.6758,0.6760,0.6764, 0.6768,0.6797,0.6801,0.6833,0.6836,0.6886,0.6923,0.7031,0.7075,0.7082, 0.7111,0.7140,0.7170,0.7231,0.7309,0.7316,0.7317,0.7321,0.7333,0.7340, 0.7355,0.7433,0.7436,0.7484,0.7512,0.7818,0.7827,0.7856,0.7978,0.8020, 0.8036,0.8068,0.8071,0.8123,0.8141,0.8237,0.8287,0.8300,0.8308,0.8334, 0.8373,0.8424,0.8430,0.8434,0.8461,0.8538,0.8596,0.8714,0.8734,0.8746, 0.8794,0.8864,0.8928,0.8954,0.8973,0.8986,0.9037,0.9128,0.9139,0.9320, 0.9338,0.9380,0.9387,0.9389,0.9395,0.9410,0.9450,0.9459,0.9464,0.9480, 0.9517,0.9544,0.9592,0.9665,0.9778,0.9837,0.9930,0.9963,0.9986, Overall p-value after applying KStest on 269 p-values = 0.456765 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.