RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-20_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 15.9487 0.472522 2 to 25 15.60 21.8999 0.811401 3 to 26 15.57 18.4619 0.639720 4 to 27 15.69 19.8657 0.718846 5 to 28 15.74 18.8024 0.660011 6 to 29 15.97 13.6975 0.311611 7 to 30 15.94 8.5199 0.045869 8 to 31 15.77 19.2137 0.683596 9 to 32 15.59 24.2879 0.888178 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.491501 Tough bday spacings test for dh-ranFile-2015-07-20_09:31: 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 39 76 99 112 73 47 28 9 8 2 (O-E)^2/E 0.5 0.2 0.1 0.0 2.1 0.3 0.5 0.1 2.3 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 7.489, p= 0.321 RESULTS OF GCD FOR dh-ranFile-2015-07-20_09:31 Euclid's algorithm: p-value, steps to gcd: 0.094298 p-value, dist. of gcd's: 0.265698 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-20_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.241 0.039 0.694 0.621 0.297 0.652 0.617 0.911 Bits 8 to 15---> 0.145 0.490 0.579 0.519 0.525 0.296 0.864 0.495 Bits 16 to 23---> 0.787 0.267 0.613 0.127 0.436 0.275 0.263 0.677 Bits 24 to 31---> 0.626 0.241 0.620 0.542 0.393 0.668 0.884 0.764 KS test for the above 32 p values: 0.720 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-20_09:31, p-values for 5 runs: 0.7876, 0.1919, 0.0806, 0.6607, 0.2171 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-20_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5091 5134.0 0.360 0.709 r= 30 23116 23103.0 0.007 0.716 r= 31 11573 11551.5 0.040 0.756 chi-square = 0.756 with df = 3; p-value = 0.140 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-20_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5189 5134.0 0.589 1.102 r= 31 23024 23103.0 0.270 1.373 r= 32 11586 11551.5 0.103 1.476 chi-square = 1.476 with df = 3; p-value = 0.312 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-20_09:31 b-rank test for bits 1 to 8, p=0.55034 b-rank test for bits 2 to 9, p=0.01912 b-rank test for bits 3 to 10, p=0.07394 b-rank test for bits 4 to 11, p=0.57804 b-rank test for bits 5 to 12, p=0.36491 b-rank test for bits 6 to 13, p=0.93642 b-rank test for bits 7 to 14, p=0.79004 b-rank test for bits 8 to 15, p=0.14104 b-rank test for bits 9 to 16, p=0.08476 b-rank test for bits 10 to 17, p=0.61259 b-rank test for bits 11 to 18, p=0.31300 b-rank test for bits 12 to 19, p=0.51435 b-rank test for bits 13 to 20, p=0.46700 b-rank test for bits 14 to 21, p=0.72281 b-rank test for bits 15 to 22, p=0.31519 b-rank test for bits 16 to 23, p=0.75265 b-rank test for bits 17 to 24, p=0.45786 b-rank test for bits 18 to 25, p=0.30899 b-rank test for bits 19 to 26, p=0.65683 b-rank test for bits 20 to 27, p=0.57652 b-rank test for bits 21 to 28, p=0.25156 b-rank test for bits 22 to 29, p=0.82033 b-rank test for bits 23 to 30, p=0.23197 b-rank test for bits 24 to 31, p=0.09818 b-rank test for bits 25 to 32, p=0.39142 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 = 0.476689 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-20_09:31 (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 141783 -0.30 0.383935 2 142267 0.84 0.798332 3 141768 -0.33 0.370621 4 141062 -1.98 0.023866 5 141167 -1.73 0.041422 6 141783 -0.30 0.383935 7 142136 0.53 0.701806 8 142205 0.69 0.755160 9 141359 -1.29 0.099253 10 141462 -1.05 0.147974 11 140684 -2.86 0.002099 12 142392 1.13 0.870284 13 141625 -0.66 0.253242 14 142178 0.63 0.734911 15 141592 -0.74 0.229218 16 142597 1.61 0.945941 17 142834 2.16 0.984631 18 142240 0.77 0.780119 19 141810 -0.23 0.408238 20 142257 0.81 0.791694 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-20_09:31 Bits used No. missing words z-score p-value 23 to 32 141689 -0.7598 0.223699 22 to 31 142044 0.4644 0.678812 21 to 30 141960 0.1747 0.569352 20 to 29 142296 1.3333 0.908791 19 to 28 141939 0.1023 0.540745 18 to 27 142032 0.4230 0.663852 17 to 26 141584 -1.1218 0.130968 16 to 25 141929 0.0678 0.527039 15 to 24 141357 -1.9046 0.028417 14 to 23 141631 -0.9598 0.168588 13 to 22 142132 0.7678 0.778705 12 to 21 141997 0.3023 0.618792 11 to 20 141797 -0.3873 0.349251 10 to 19 141614 -1.0184 0.154249 9 to 18 141263 -2.2287 0.012916 8 to 17 141683 -0.7804 0.217564 7 to 16 141536 -1.2873 0.098987 6 to 15 141759 -0.5184 0.302097 5 to 14 141646 -0.9080 0.181930 4 to 13 141657 -0.8701 0.192122 3 to 12 141324 -2.0184 0.021776 2 to 11 141790 -0.4115 0.340359 1 to 10 141777 -0.4563 0.324083 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-20_09:31 Bits used No. missing words z-score p-value 28 to 32 141728 -0.6147 0.269384 27 to 31 141347 -1.9062 0.028312 26 to 30 142142 0.7887 0.784860 25 to 29 142585 2.2904 0.989001 24 to 28 141919 0.0328 0.513075 23 to 27 142092 0.6192 0.732114 22 to 26 142238 1.1141 0.867390 21 to 25 142035 0.4260 0.664946 20 to 24 141743 -0.5638 0.286435 19 to 23 141510 -1.3537 0.087922 18 to 22 141837 -0.2452 0.403156 17 to 21 141874 -0.1198 0.452336 16 to 20 141453 -1.5469 0.060946 15 to 19 142383 1.6057 0.945826 14 to 18 142299 1.3209 0.906735 13 to 17 142118 0.7074 0.760327 12 to 16 141606 -1.0282 0.151919 11 to 15 141536 -1.2655 0.102842 10 to 14 141959 0.1684 0.566855 9 to 13 141627 -0.9571 0.169271 8 to 12 141943 0.1141 0.545435 7 to 11 141683 -0.7672 0.221475 6 to 10 141879 -0.1028 0.459056 5 to 9 141975 0.2226 0.588081 4 to 8 141873 -0.1232 0.450993 3 to 7 142069 0.5413 0.705834 2 to 6 141852 -0.1943 0.422955 1 to 5 141375 -1.8113 0.035048 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-20_09:31 Bits used No. missing words z-score p-value 31 to 32 142311 1.1849 0.881965 30 to 31 142026 0.3442 0.634637 29 to 30 142253 1.0138 0.844655 28 to 29 142454 1.6067 0.945939 27 to 28 141802 -0.3166 0.375771 26 to 27 141742 -0.4936 0.310795 25 to 26 141798 -0.3284 0.371302 24 to 25 142056 0.4327 0.667367 23 to 24 142240 0.9754 0.835326 22 to 23 142379 1.3855 0.917044 21 to 22 141596 -0.9243 0.177671 20 to 21 141591 -0.9390 0.173859 19 to 20 142117 0.6126 0.729928 18 to 19 142027 0.3471 0.635745 17 to 18 141932 0.0669 0.526659 16 to 17 141823 -0.2547 0.399493 15 to 16 142881 2.8663 0.997923 14 to 15 142136 0.6686 0.748138 13 to 14 142241 0.9784 0.836056 12 to 13 141513 -1.1691 0.121179 11 to 12 141679 -0.6794 0.248430 10 to 11 142036 0.3737 0.645671 9 to 10 141841 -0.2016 0.420129 8 to 9 142421 1.5094 0.934395 7 to 8 141651 -0.7620 0.223019 6 to 7 141800 -0.3225 0.373534 5 to 6 141147 -2.2488 0.012264 4 to 5 142089 0.5300 0.701944 3 to 4 142942 3.0462 0.998841 2 to 3 141471 -1.2930 0.098004 1 to 2 142146 0.6981 0.757456 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-20_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2498.91 -0.015 0.493825 Test results for specific bytes for dh-ranFile-2015-07-20_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2536.12 0.511 0.695267 2 to 9 2543.40 0.614 0.730306 3 to 10 2559.52 0.842 0.800045 4 to 11 2679.34 2.536 0.994397 5 to 12 2573.00 1.032 0.849063 6 to 13 2585.46 1.209 0.886587 7 to 14 2480.35 -0.278 0.390571 8 to 15 2562.29 0.881 0.810807 9 to 16 2473.99 -0.368 0.356476 10 to 17 2496.83 -0.045 0.482136 11 to 18 2544.36 0.627 0.734790 12 to 19 2522.02 0.311 0.622252 13 to 20 2516.20 0.229 0.590617 14 to 21 2668.25 2.379 0.991329 15 to 22 2409.91 -1.274 0.101328 16 to 23 2574.19 1.049 0.852950 17 to 24 2485.74 -0.202 0.420109 18 to 25 2539.20 0.554 0.710318 19 to 26 2604.30 1.475 0.929895 20 to 27 2524.10 0.341 0.633399 21 to 28 2504.74 0.067 0.526736 22 to 29 2575.69 1.070 0.857773 23 to 30 2676.50 2.496 0.993721 24 to 31 2473.70 -0.372 0.354979 25 to 32 2441.45 -0.828 0.203845 CDPARK for dh-ranFile-2015-07-20_09:31: 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 3516 -0.3196 0.374623 3496 -1.2329 0.108811 3548 1.1416 0.873180 3535 0.5479 0.708135 3532 0.4110 0.659449 3539 0.7306 0.767486 3516 -0.3196 0.374623 3505 -0.8219 0.205562 3523 0.0000 0.500000 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3522.90 sample std.=15.08 p-value of the KSTEST for those 10 p-values: 0.901785 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-20_09:31 0.9747,0.4948,0.7194,0.3317,0.2982,0.8730,0.9890,0.1692,0.9687,0.4900, The KS test for those 10 p-values: 0.099482 The 3DSPHERES test for dh-ranFile-2015-07-20_09:31 sample no r^3 equiv. uni. 1 8.220 0.239658 2 19.132 0.471509 3 1.434 0.046676 4 28.351 0.611333 5 13.943 0.371720 6 16.550 0.424013 7 37.219 0.710801 8 7.794 0.228803 9 20.449 0.494204 10 49.113 0.805455 11 36.507 0.703854 12 23.121 0.537303 13 6.281 0.188900 14 12.871 0.348869 15 5.779 0.175210 16 2.797 0.089006 17 22.803 0.532374 18 36.079 0.699598 19 3.716 0.116514 20 4.031 0.125730 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.142697 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-20_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 0.3 -0.3 -0.7 1.9 0.8 -0.7 -0.8 0.5 1.3 -0.5 -0.2 -0.3 0.2 -0.5 -0.7 0.1 0.9 -1.5 1.0 -0.8 -0.2 0.9 0.7 0.1 0.3 0.6 -0.5 -1.2 -0.3 0.6 3.4 -0.4 -3.1 -1.4 0.0 1.5 2.5 0.4 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:53.022214 z-score=1.202622, p-value=0.881481 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-20_09:31 Test no p-value 1 0.540737 2 0.647424 3 0.677112 4 0.155784 5 0.042182 6 0.809573 7 0.304957 8 0.643783 9 0.278293 10 0.170147 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.636624 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-20_09:31: (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 66486 0.49 66400 1.07 3 25000.00 25123 0.61 25266 2.83 4 6666.67 6700 0.17 6639 0.11 5 1388.89 1391 0.00 1405 0.19 6 238.10 245 0.20 246 0.26 7 34.72 47 4.34 37 0.15 8 4.96 7 0.84 6 0.22 p=0.64529 p=0.43406 Number of rngs required: 689135, p-value: 0.801 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-20_09:31 No. of wins: Observed Expected 98604 98585.9 z-score= 0.081, pvalue=0.53233 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66490 66666.7 0.468 0.468 2 37803 37654.3 0.587 1.055 3 26815 26954.7 0.724 1.780 4 19395 19313.5 0.344 2.124 5 13737 13851.4 0.945 3.069 6 9961 9943.5 0.031 3.100 7 7111 7145.0 0.162 3.262 8 5197 5139.1 0.653 3.915 9 3695 3699.9 0.006 3.921 10 2676 2666.3 0.035 3.956 11 1937 1923.3 0.097 4.054 12 1467 1388.7 4.410 8.464 13 1042 1003.7 1.460 9.924 14 757 726.1 1.311 11.235 15 535 525.8 0.160 11.395 16 351 381.2 2.385 13.780 17 287 276.5 0.396 14.176 18 197 200.8 0.073 14.249 19 145 146.0 0.007 14.256 20 105 106.2 0.014 14.269 21 297 287.1 0.340 14.610 Chisq= 14.61 for 20 degrees of freedom, p= 0.20172 SUMMARY of craptest p-value for no. of wins: 0.532334 p-value for throws/game: 0.201721 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-20_09:31 No. of wins: Observed Expected 98674 98585.9 z-score= 0.394, pvalue=0.65329 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66594 66666.7 0.079 0.079 2 37771 37654.3 0.362 0.441 3 27034 26954.7 0.233 0.674 4 19310 19313.5 0.001 0.674 5 13837 13851.4 0.015 0.689 6 9868 9943.5 0.574 1.263 7 7290 7145.0 2.942 4.205 8 5107 5139.1 0.200 4.405 9 3674 3699.9 0.181 4.586 10 2629 2666.3 0.522 5.108 11 1910 1923.3 0.092 5.200 12 1386 1388.7 0.005 5.205 13 1030 1003.7 0.688 5.894 14 724 726.1 0.006 5.900 15 477 525.8 4.536 10.436 16 369 381.2 0.387 10.823 17 240 276.5 4.828 15.651 18 203 200.8 0.023 15.674 19 153 146.0 0.337 16.012 20 117 106.2 1.095 17.107 21 277 287.1 0.356 17.463 Chisq= 17.46 for 20 degrees of freedom, p= 0.37726 SUMMARY of craptest p-value for no. of wins: 0.653291 p-value for throws/game: 0.377258 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0021,0.0123,0.0129,0.0191,0.0218,0.0239,0.0283,0.0284,0.0350,0.0386, 0.0414,0.0422,0.0459,0.0467,0.0609,0.0739,0.0806,0.0848,0.0879,0.0890, 0.0943,0.0980,0.0982,0.0990,0.0993,0.0995,0.1013,0.1028,0.1088,0.1165, 0.1212,0.1257,0.1268,0.1310,0.1400,0.1410,0.1427,0.1450,0.1480,0.1519, 0.1542,0.1558,0.1686,0.1692,0.1693,0.1701,0.1739,0.1752,0.1777,0.1819, 0.1889,0.1919,0.1921,0.2017,0.2038,0.2056,0.2171,0.2176,0.2215,0.2230, 0.2237,0.2288,0.2292,0.2320,0.2397,0.2406,0.2408,0.2484,0.2516,0.2532, 0.2633,0.2657,0.2674,0.2694,0.2753,0.2783,0.2864,0.2955,0.2972,0.2982, 0.3021,0.3050,0.3090,0.3108,0.3116,0.3121,0.3130,0.3152,0.3214,0.3241, 0.3317,0.3404,0.3489,0.3493,0.3550,0.3565,0.3649,0.3706,0.3713,0.3717, 0.3735,0.3746,0.3746,0.3758,0.3773,0.3839,0.3839,0.3906,0.3914,0.3929, 0.3995,0.4032,0.4082,0.4201,0.4201,0.4230,0.4240,0.4275,0.4341,0.4361, 0.4510,0.4523,0.4579,0.4591,0.4670,0.4715,0.4725,0.4767,0.4821,0.4899, 0.4900,0.4915,0.4938,0.4942,0.4947,0.4948,0.5000,0.5131,0.5144,0.5187, 0.5248,0.5267,0.5267,0.5270,0.5323,0.5324,0.5373,0.5407,0.5407,0.5419, 0.5454,0.5503,0.5669,0.5694,0.5765,0.5780,0.5794,0.5881,0.5906,0.6113, 0.6126,0.6129,0.6168,0.6188,0.6196,0.6215,0.6223,0.6263,0.6334,0.6346, 0.6357,0.6366,0.6397,0.6438,0.6453,0.6457,0.6474,0.6524,0.6533,0.6568, 0.6594,0.6600,0.6607,0.6639,0.6649,0.6674,0.6681,0.6771,0.6774,0.6788, 0.6836,0.6942,0.6953,0.6996,0.7018,0.7019,0.7039,0.7058,0.7081,0.7103, 0.7108,0.7188,0.7194,0.7198,0.7228,0.7299,0.7303,0.7321,0.7348,0.7349, 0.7481,0.7527,0.7552,0.7575,0.7603,0.7641,0.7675,0.7787,0.7801,0.7849, 0.7870,0.7876,0.7900,0.7917,0.7983,0.8000,0.8013,0.8055,0.8096,0.8108, 0.8114,0.8203,0.8353,0.8361,0.8447,0.8491,0.8529,0.8578,0.8644,0.8674, 0.8703,0.8730,0.8732,0.8815,0.8820,0.8843,0.8866,0.8882,0.9018,0.9067, 0.9088,0.9109,0.9170,0.9299,0.9344,0.9364,0.9458,0.9459,0.9459,0.9687, 0.9747,0.9846,0.9890,0.9890,0.9913,0.9937,0.9944,0.9979,0.9988, Overall p-value after applying KStest on 269 p-values = 0.648486 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.