RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-17_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.59 25.6287 0.918504 2 to 25 15.90 16.7418 0.528013 3 to 26 15.97 28.4413 0.959961 4 to 27 15.77 22.0432 0.816938 5 to 28 15.86 8.8492 0.055126 6 to 29 15.90 18.8263 0.661405 7 to 30 15.79 14.6418 0.378738 8 to 31 15.65 15.4647 0.437951 9 to 32 15.70 20.4440 0.747847 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.465410 Tough bday spacings test for dh-ranFile-2016-02-17_16:31: 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 6 47 72 115 84 70 50 35 12 6 3 (O-E)^2/E 1.1 2.9 0.0 3.1 1.9 0.8 0.1 0.9 0.6 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 11.781, p= 0.700 RESULTS OF GCD FOR dh-ranFile-2016-02-17_16:31 Euclid's algorithm: p-value, steps to gcd: 0.054239 p-value, dist. of gcd's: 0.894092 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-17_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.172 0.614 0.807 0.537 0.443 0.509 0.809 0.566 Bits 8 to 15---> 0.484 0.759 0.678 0.534 0.928 0.851 0.305 0.620 Bits 16 to 23---> 0.122 0.876 0.967 0.577 0.943 0.981 0.271 0.766 Bits 24 to 31---> 0.599 0.544 0.848 0.165 0.699 0.726 0.415 0.129 KS test for the above 32 p values: 0.934 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-17_16:31, p-values for 5 runs: 0.5718, 0.6457, 0.3520, 0.7254, 0.0937 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-17_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5072 5134.0 0.749 1.478 r= 30 23348 23103.0 2.597 4.076 r= 31 11381 11551.5 2.517 6.593 chi-square = 6.593 with df = 3; p-value = 0.914 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-17_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5237 5134.0 2.066 2.205 r= 31 22987 23103.0 0.583 2.788 r= 32 11570 11551.5 0.030 2.817 chi-square = 2.817 with df = 3; p-value = 0.579 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-17_16:31 b-rank test for bits 1 to 8, p=0.10658 b-rank test for bits 2 to 9, p=0.92395 b-rank test for bits 3 to 10, p=0.83318 b-rank test for bits 4 to 11, p=0.13080 b-rank test for bits 5 to 12, p=0.62778 b-rank test for bits 6 to 13, p=0.73998 b-rank test for bits 7 to 14, p=0.97266 b-rank test for bits 8 to 15, p=0.95145 b-rank test for bits 9 to 16, p=0.71720 b-rank test for bits 10 to 17, p=0.40777 b-rank test for bits 11 to 18, p=0.41596 b-rank test for bits 12 to 19, p=0.27329 b-rank test for bits 13 to 20, p=0.54878 b-rank test for bits 14 to 21, p=0.07892 b-rank test for bits 15 to 22, p=0.04223 b-rank test for bits 16 to 23, p=0.71815 b-rank test for bits 17 to 24, p=0.33431 b-rank test for bits 18 to 25, p=0.89472 b-rank test for bits 19 to 26, p=0.97374 b-rank test for bits 20 to 27, p=0.11506 b-rank test for bits 21 to 28, p=0.45647 b-rank test for bits 22 to 29, p=0.05196 b-rank test for bits 23 to 30, p=0.34342 b-rank test for bits 24 to 31, p=0.90589 b-rank test for bits 25 to 32, p=0.25116 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 = 0.621098 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-17_16:31 (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 141077 -1.94 0.025906 2 142098 0.44 0.670328 3 142643 1.71 0.956752 4 141083 -1.93 0.026761 5 141410 -1.17 0.121674 6 141929 0.05 0.518328 7 141880 -0.07 0.472683 8 141346 -1.32 0.094055 9 141557 -0.82 0.205197 10 141238 -1.57 0.058379 11 141812 -0.23 0.410054 12 142110 0.47 0.680413 13 141608 -0.70 0.240703 14 140677 -2.88 0.001993 15 141887 -0.05 0.479196 16 141833 -0.18 0.429228 17 141876 -0.08 0.468964 18 141897 -0.03 0.488509 19 142750 1.96 0.975246 20 142096 0.44 0.668634 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-17_16:31 Bits used No. missing words z-score p-value 23 to 32 141894 -0.0529 0.478921 22 to 31 141888 -0.0736 0.470684 21 to 30 141806 -0.3563 0.360804 20 to 29 141933 0.0816 0.532526 19 to 28 141815 -0.3253 0.372486 18 to 27 141782 -0.4391 0.330306 17 to 26 141959 0.1713 0.567997 16 to 25 141953 0.1506 0.559849 15 to 24 142361 1.5575 0.940322 14 to 23 141739 -0.5873 0.278486 13 to 22 141810 -0.3425 0.365981 12 to 21 141895 -0.0494 0.480295 11 to 20 141879 -0.1046 0.458352 10 to 19 141978 0.2368 0.593591 9 to 18 141683 -0.7804 0.217564 8 to 17 141494 -1.4322 0.076047 7 to 16 141826 -0.2873 0.386924 6 to 15 141152 -2.6115 0.004508 5 to 14 141473 -1.5046 0.066215 4 to 13 142141 0.7989 0.787815 3 to 12 141753 -0.5391 0.294920 2 to 11 142098 0.6506 0.742343 1 to 10 142301 1.3506 0.911586 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-17_16:31 Bits used No. missing words z-score p-value 28 to 32 141991 0.2768 0.609051 27 to 31 142255 1.1718 0.879354 26 to 30 141592 -1.0757 0.141032 25 to 29 141922 0.0429 0.517129 24 to 28 141561 -1.1808 0.118845 23 to 27 142323 1.4023 0.919583 22 to 26 142282 1.2633 0.896757 21 to 25 142098 0.6396 0.738770 20 to 24 141885 -0.0825 0.467135 19 to 23 141765 -0.4893 0.312331 18 to 22 141837 -0.2452 0.403156 17 to 21 141098 -2.7503 0.002977 16 to 20 142438 1.7921 0.963442 15 to 19 141966 0.1921 0.576169 14 to 18 142096 0.6328 0.736561 13 to 17 141948 0.1311 0.552146 12 to 16 142076 0.5650 0.713957 11 to 15 142059 0.5074 0.694048 10 to 14 141800 -0.3706 0.355464 9 to 13 142139 0.7785 0.781875 8 to 12 142603 2.3514 0.990649 7 to 11 142297 1.3141 0.905600 6 to 10 141675 -0.7943 0.213499 5 to 9 141674 -0.7977 0.212514 4 to 8 141268 -2.1740 0.014853 3 to 7 141799 -0.3740 0.354202 2 to 6 141829 -0.2723 0.392694 1 to 5 142328 1.4192 0.922083 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-17_16:31 Bits used No. missing words z-score p-value 31 to 32 141555 -1.0452 0.147960 30 to 31 141523 -1.1396 0.127223 29 to 30 141995 0.2527 0.599755 28 to 29 141413 -1.4641 0.071583 27 to 28 141897 -0.0364 0.485493 26 to 27 141539 -1.0924 0.137325 25 to 26 142151 0.7129 0.762043 24 to 25 141932 0.0669 0.526659 23 to 24 141509 -1.1809 0.118818 22 to 23 141919 0.0285 0.511378 21 to 22 141907 -0.0069 0.497258 20 to 21 142202 0.8633 0.806023 19 to 20 141935 0.0757 0.530180 18 to 19 141939 0.0875 0.534872 17 to 18 141855 -0.1603 0.436336 16 to 17 142200 0.8574 0.804397 15 to 16 141652 -0.7591 0.223901 14 to 15 141952 0.1259 0.550083 13 to 14 141811 -0.2901 0.385886 12 to 13 142069 0.4710 0.681181 11 to 12 141313 -1.7591 0.039282 10 to 11 141817 -0.2724 0.392673 9 to 10 141849 -0.1780 0.429375 8 to 9 141696 -0.6293 0.264579 7 to 8 141742 -0.4936 0.310795 6 to 7 141386 -1.5437 0.061325 5 to 6 142020 0.3265 0.627962 4 to 5 142007 0.2881 0.613370 3 to 4 142098 0.5565 0.711082 2 to 3 141513 -1.1691 0.121179 1 to 2 141942 0.0964 0.538387 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-17_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2409.61 -1.278 0.100566 Test results for specific bytes for dh-ranFile-2016-02-17_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2464.99 -0.495 0.310263 2 to 9 2635.32 1.914 0.972174 3 to 10 2453.90 -0.652 0.257194 4 to 11 2536.92 0.522 0.699188 5 to 12 2575.47 1.067 0.857098 6 to 13 2460.98 -0.552 0.290541 7 to 14 2453.28 -0.661 0.254383 8 to 15 2601.88 1.441 0.925170 9 to 16 2499.28 -0.010 0.495931 10 to 17 2435.55 -0.912 0.181016 11 to 18 2609.88 1.554 0.939896 12 to 19 2437.31 -0.887 0.187662 13 to 20 2504.27 0.060 0.524065 14 to 21 2566.59 0.942 0.826828 15 to 22 2466.88 -0.468 0.319754 16 to 23 2500.79 0.011 0.504468 17 to 24 2442.59 -0.812 0.208422 18 to 25 2523.57 0.333 0.630544 19 to 26 2457.87 -0.596 0.275649 20 to 27 2394.59 -1.491 0.068009 21 to 28 2507.59 0.107 0.542713 22 to 29 2477.82 -0.314 0.376900 23 to 30 2436.02 -0.905 0.182801 24 to 31 2592.20 1.304 0.903856 25 to 32 2527.91 0.395 0.653471 CDPARK for dh-ranFile-2016-02-17_16:31: 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 3559 1.6438 0.949895 3532 0.4110 0.659449 3519 -0.1826 0.427537 3554 1.4155 0.921543 3527 0.1826 0.572463 3538 0.6849 0.753306 3518 -0.2283 0.409702 3493 -1.3699 0.085365 3498 -1.1416 0.126820 3533 0.4566 0.676028 Square side=100, avg. no. parked=3527.10 sample std.=20.19 p-value of the KSTEST for those 10 p-values: 0.839936 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-17_16:31 0.9729,0.6643,0.5117,0.4758,0.1571,0.2260,0.5058,0.2949,0.7430,0.1870, The KS test for those 10 p-values: 0.826114 The 3DSPHERES test for dh-ranFile-2016-02-17_16:31 sample no r^3 equiv. uni. 1 88.266 0.947250 2 18.741 0.464585 3 5.484 0.167078 4 34.914 0.687700 5 4.813 0.148218 6 30.475 0.637903 7 19.901 0.484886 8 2.223 0.071434 9 11.405 0.316252 10 4.052 0.126339 11 12.976 0.351130 12 21.375 0.509576 13 60.836 0.868383 14 59.461 0.862213 15 1.404 0.045724 16 14.766 0.388716 17 0.035 0.001157 18 12.060 0.331018 19 50.208 0.812430 20 40.634 0.741912 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.673458 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-17_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 1.5 0.5 0.2 -0.1 1.3 0.2 -1.4 0.2 -0.7 0.1 -1.2 -0.5 -1.0 -0.6 -0.2 0.3 1.2 0.8 1.0 -1.2 1.7 0.3 0.5 0.5 -0.6 -0.2 -0.0 -0.1 -0.1 -0.2 -0.0 0.0 0.1 -0.7 0.0 -0.4 -2.0 -1.3 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:25.959822 z-score=-1.750127, p-value=0.024659 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-17_16:31 Test no p-value 1 0.132990 2 0.113636 3 0.436626 4 0.576652 5 0.120108 6 0.018245 7 0.115305 8 0.786863 9 0.348411 10 0.704626 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.088414 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-17_16:31: (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 66781 0.20 66544 0.23 3 25000.00 24877 0.61 25125 0.62 4 6666.67 6641 0.10 6651 0.04 5 1388.89 1397 0.05 1412 0.38 6 238.10 264 2.82 223 0.96 7 34.72 36 0.05 39 0.53 8 4.96 3 0.77 5 0.00 p=0.40231 p=0.16134 Number of rngs required: 688012, p-value: 0.326 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-17_16:31 No. of wins: Observed Expected 98576 98585.9 z-score=-0.044, pvalue=0.48241 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66350 66666.7 1.504 1.504 2 37528 37654.3 0.424 1.928 3 27131 26954.7 1.153 3.081 4 19568 19313.5 3.355 6.435 5 13892 13851.4 0.119 6.554 6 9861 9943.5 0.685 7.239 7 7242 7145.0 1.316 8.556 8 5072 5139.1 0.875 9.431 9 3683 3699.9 0.077 9.508 10 2667 2666.3 0.000 9.508 11 1915 1923.3 0.036 9.544 12 1327 1388.7 2.745 12.289 13 1025 1003.7 0.451 12.740 14 751 726.1 0.851 13.591 15 534 525.8 0.127 13.718 16 408 381.2 1.891 15.609 17 270 276.5 0.155 15.764 18 199 200.8 0.017 15.781 19 162 146.0 1.757 17.538 20 113 106.2 0.433 17.971 21 302 287.1 0.772 18.743 Chisq= 18.74 for 20 degrees of freedom, p= 0.46141 SUMMARY of craptest p-value for no. of wins: 0.482415 p-value for throws/game: 0.461413 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-17_16:31 No. of wins: Observed Expected 98696 98585.9 z-score= 0.493, pvalue=0.68886 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66848 66666.7 0.493 0.493 2 37546 37654.3 0.312 0.805 3 26754 26954.7 1.495 2.300 4 19352 19313.5 0.077 2.377 5 13999 13851.4 1.572 3.949 6 9981 9943.5 0.141 4.090 7 7169 7145.0 0.080 4.171 8 5120 5139.1 0.071 4.241 9 3677 3699.9 0.141 4.383 10 2624 2666.3 0.671 5.054 11 1955 1923.3 0.522 5.575 12 1319 1388.7 3.502 9.077 13 1025 1003.7 0.451 9.529 14 728 726.1 0.005 9.534 15 518 525.8 0.117 9.650 16 367 381.2 0.525 10.176 17 282 276.5 0.108 10.283 18 208 200.8 0.256 10.539 19 142 146.0 0.109 10.648 20 100 106.2 0.364 11.012 21 286 287.1 0.004 11.016 Chisq= 11.02 for 20 degrees of freedom, p= 0.05420 SUMMARY of craptest p-value for no. of wins: 0.688858 p-value for throws/game: 0.054198 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0012,0.0020,0.0030,0.0045,0.0149,0.0182,0.0247,0.0259,0.0268,0.0393, 0.0422,0.0457,0.0520,0.0542,0.0542,0.0551,0.0584,0.0613,0.0662,0.0680, 0.0714,0.0716,0.0760,0.0789,0.0854,0.0884,0.0937,0.0941,0.1006,0.1066, 0.1136,0.1151,0.1153,0.1188,0.1188,0.1201,0.1212,0.1216,0.1217,0.1263, 0.1268,0.1272,0.1291,0.1308,0.1330,0.1373,0.1410,0.1480,0.1482,0.1571, 0.1613,0.1650,0.1671,0.1722,0.1810,0.1828,0.1870,0.1877,0.2052,0.2084, 0.2125,0.2135,0.2176,0.2239,0.2260,0.2407,0.2512,0.2544,0.2572,0.2646, 0.2712,0.2733,0.2756,0.2785,0.2905,0.2949,0.2949,0.3048,0.3103,0.3108, 0.3123,0.3163,0.3198,0.3262,0.3303,0.3310,0.3343,0.3434,0.3484,0.3511, 0.3520,0.3542,0.3555,0.3608,0.3660,0.3725,0.3769,0.3787,0.3859,0.3869, 0.3887,0.3927,0.3927,0.4023,0.4032,0.4078,0.4097,0.4101,0.4155,0.4160, 0.4275,0.4292,0.4294,0.4363,0.4366,0.4380,0.4433,0.4565,0.4584,0.4614, 0.4646,0.4654,0.4671,0.4690,0.4707,0.4727,0.4758,0.4789,0.4792,0.4803, 0.4824,0.4838,0.4849,0.4855,0.4885,0.4959,0.4973,0.5045,0.5058,0.5095, 0.5096,0.5114,0.5117,0.5171,0.5183,0.5241,0.5267,0.5280,0.5302,0.5325, 0.5342,0.5349,0.5369,0.5384,0.5427,0.5438,0.5488,0.5501,0.5521,0.5598, 0.5661,0.5680,0.5718,0.5725,0.5762,0.5767,0.5769,0.5793,0.5936,0.5988, 0.5998,0.6091,0.6134,0.6142,0.6200,0.6211,0.6278,0.6280,0.6305,0.6379, 0.6457,0.6535,0.6594,0.6614,0.6643,0.6686,0.6703,0.6735,0.6760,0.6781, 0.6804,0.6812,0.6877,0.6889,0.6940,0.6988,0.6992,0.7000,0.7046,0.7111, 0.7140,0.7172,0.7181,0.7254,0.7257,0.7366,0.7388,0.7400,0.7419,0.7423, 0.7430,0.7478,0.7533,0.7591,0.7620,0.7660,0.7819,0.7869,0.7878,0.8044, 0.8060,0.8073,0.8088,0.8124,0.8169,0.8261,0.8268,0.8332,0.8399,0.8478, 0.8513,0.8571,0.8622,0.8684,0.8762,0.8794,0.8941,0.8947,0.8968,0.9039, 0.9056,0.9059,0.9116,0.9139,0.9185,0.9196,0.9215,0.9221,0.9240,0.9252, 0.9285,0.9339,0.9399,0.9403,0.9434,0.9473,0.9499,0.9514,0.9568,0.9600, 0.9634,0.9672,0.9722,0.9727,0.9729,0.9737,0.9752,0.9807,0.9906, Overall p-value after applying KStest on 269 p-values = 0.622118 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.