RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-31_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.65 20.9364 0.770851 2 to 25 15.65 26.7041 0.937447 3 to 26 15.66 17.8815 0.603647 4 to 27 15.78 21.3880 0.790584 5 to 28 15.91 18.2910 0.629290 6 to 29 15.90 11.1341 0.150493 7 to 30 15.67 13.2028 0.277495 8 to 31 15.34 26.3457 0.931612 9 to 32 15.57 24.9845 0.904943 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.117130 Tough bday spacings test for dh-ranFile-2016-03-31_03:31: 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 44 64 92 100 83 52 29 17 4 3 (O-E)^2/E 0.9 1.5 1.2 0.3 0.1 0.3 0.0 0.0 0.3 1.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 5.857, p= 0.173 RESULTS OF GCD FOR dh-ranFile-2016-03-31_03:31 Euclid's algorithm: p-value, steps to gcd: 0.252240 p-value, dist. of gcd's: 0.420889 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-31_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.021 0.736 0.707 0.803 0.491 0.392 0.801 0.110 Bits 8 to 15---> 0.236 0.051 0.576 0.710 0.344 0.348 0.659 0.109 Bits 16 to 23---> 0.264 0.830 0.147 0.596 0.225 0.914 0.439 0.542 Bits 24 to 31---> 0.384 0.790 0.751 0.184 0.089 0.422 0.424 0.103 KS test for the above 32 p values: 0.588 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-31_03:31, p-values for 5 runs: 0.6760, 0.3119, 0.9093, 0.2822, 0.8738 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-31_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 194 211.4 1.435 1.435 r= 29 5079 5134.0 0.589 2.024 r= 30 23076 23103.0 0.032 2.056 r= 31 11651 11551.5 0.857 2.913 chi-square = 2.913 with df = 3; p-value = 0.595 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-31_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 186 211.4 3.056 3.056 r= 30 5074 5134.0 0.701 3.757 r= 31 23111 23103.0 0.003 3.760 r= 32 11629 11551.5 0.520 4.280 chi-square = 4.280 with df = 3; p-value = 0.767 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-31_03:31 b-rank test for bits 1 to 8, p=0.45529 b-rank test for bits 2 to 9, p=0.21381 b-rank test for bits 3 to 10, p=0.74335 b-rank test for bits 4 to 11, p=0.26259 b-rank test for bits 5 to 12, p=0.47712 b-rank test for bits 6 to 13, p=0.63729 b-rank test for bits 7 to 14, p=0.88677 b-rank test for bits 8 to 15, p=0.92691 b-rank test for bits 9 to 16, p=0.50364 b-rank test for bits 10 to 17, p=0.08840 b-rank test for bits 11 to 18, p=0.00316 b-rank test for bits 12 to 19, p=0.50950 b-rank test for bits 13 to 20, p=0.42066 b-rank test for bits 14 to 21, p=0.90449 b-rank test for bits 15 to 22, p=0.83520 b-rank test for bits 16 to 23, p=0.70443 b-rank test for bits 17 to 24, p=0.39109 b-rank test for bits 18 to 25, p=0.74076 b-rank test for bits 19 to 26, p=0.65477 b-rank test for bits 20 to 27, p=0.45488 b-rank test for bits 21 to 28, p=0.21995 b-rank test for bits 22 to 29, p=0.81698 b-rank test for bits 23 to 30, p=0.73572 b-rank test for bits 24 to 31, p=0.15916 b-rank test for bits 25 to 32, p=0.97474 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 = 0.682583 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-31_03:31 (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 142087 0.42 0.660972 2 142403 1.15 0.875634 3 142244 0.78 0.782875 4 142071 0.38 0.647186 5 142014 0.24 0.596600 6 142146 0.55 0.709857 7 142373 1.08 0.860672 8 141534 -0.88 0.190260 9 141799 -0.26 0.398288 10 141715 -0.45 0.324899 11 142340 1.01 0.842850 12 142015 0.25 0.597504 13 141973 0.15 0.559129 14 142075 0.39 0.650651 15 142414 1.18 0.880828 16 141565 -0.80 0.210551 17 142643 1.71 0.956752 18 141488 -0.98 0.162456 19 142125 0.50 0.692835 20 141806 -0.24 0.404613 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-31_03:31 Bits used No. missing words z-score p-value 23 to 32 141863 -0.1598 0.436536 22 to 31 142217 1.0609 0.855639 21 to 30 142552 2.2161 0.986658 20 to 29 141501 -1.4080 0.079560 19 to 28 142006 0.3333 0.630563 18 to 27 142313 1.3920 0.918034 17 to 26 142163 0.8747 0.809138 16 to 25 141679 -0.7942 0.213528 15 to 24 142088 0.6161 0.731087 14 to 23 141913 0.0127 0.505049 13 to 22 141480 -1.4804 0.069377 12 to 21 141371 -1.8563 0.031705 11 to 20 142449 1.8609 0.968623 10 to 19 142072 0.5609 0.712578 9 to 18 141570 -1.1701 0.120980 8 to 17 141816 -0.3218 0.373792 7 to 16 142086 0.6092 0.728806 6 to 15 142263 1.2196 0.888683 5 to 14 142422 1.7678 0.961455 4 to 13 142088 0.6161 0.731087 3 to 12 141744 -0.5701 0.284304 2 to 11 141663 -0.8494 0.197826 1 to 10 141656 -0.8736 0.191181 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-31_03:31 Bits used No. missing words z-score p-value 28 to 32 142103 0.6565 0.744252 27 to 31 141206 -2.3842 0.008559 26 to 30 141817 -0.3130 0.377147 25 to 29 142164 0.8633 0.806011 24 to 28 141993 0.2836 0.611652 23 to 27 142445 1.8158 0.965302 22 to 26 142130 0.7480 0.772780 21 to 25 142981 3.6328 0.999860 20 to 24 141768 -0.4791 0.315939 19 to 23 141578 -1.1232 0.130686 18 to 22 142160 0.8497 0.802262 17 to 21 142239 1.1175 0.868115 16 to 20 141936 0.0904 0.536018 15 to 19 142119 0.7107 0.761379 14 to 18 141998 0.3006 0.618131 13 to 17 141739 -0.5774 0.281838 12 to 16 142332 1.4328 0.924040 11 to 15 141447 -1.5672 0.058532 10 to 14 141481 -1.4520 0.073256 9 to 13 141997 0.2972 0.616838 8 to 12 141787 -0.4147 0.339189 7 to 11 141929 0.0667 0.526581 6 to 10 141748 -0.5469 0.292230 5 to 9 142009 0.3379 0.632267 4 to 8 141736 -0.5876 0.278414 3 to 7 141784 -0.4248 0.335474 2 to 6 141377 -1.8045 0.035576 1 to 5 141746 -0.5537 0.289905 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-31_03:31 Bits used No. missing words z-score p-value 31 to 32 141544 -1.0777 0.140591 30 to 31 142921 2.9843 0.998579 29 to 30 141629 -0.8269 0.204138 28 to 29 141802 -0.3166 0.375771 27 to 28 142248 0.9990 0.841109 26 to 27 141853 -0.1662 0.434014 25 to 26 141567 -1.0098 0.156290 24 to 25 141894 -0.0452 0.481966 23 to 24 141606 -0.8948 0.185453 22 to 23 142018 0.3206 0.625728 21 to 22 142142 0.6863 0.753751 20 to 21 141368 -1.5968 0.055150 19 to 20 142021 0.3294 0.629077 18 to 19 141915 0.0167 0.506672 17 to 18 141553 -1.0511 0.146602 16 to 17 142256 1.0226 0.846758 15 to 16 142003 0.2763 0.608846 14 to 15 141849 -0.1780 0.429375 13 to 14 141487 -1.2458 0.106417 12 to 13 141887 -0.0659 0.473741 11 to 12 141729 -0.5319 0.297381 10 to 11 142191 0.8309 0.796981 9 to 10 142211 0.8899 0.813235 8 to 9 142114 0.6037 0.726994 7 to 8 142621 2.0993 0.982106 6 to 7 141431 -1.4110 0.079122 5 to 6 141493 -1.2281 0.109702 4 to 5 141642 -0.7886 0.215178 3 to 4 142122 0.6273 0.734784 2 to 3 140933 -2.8800 0.001988 1 to 2 141964 0.1613 0.564059 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-31_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2571.09 1.005 0.842641 Test results for specific bytes for dh-ranFile-2016-03-31_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2533.70 0.477 0.683162 2 to 9 2462.06 -0.537 0.295783 3 to 10 2511.61 0.164 0.565201 4 to 11 2540.10 0.567 0.714663 5 to 12 2494.55 -0.077 0.469272 6 to 13 2481.12 -0.267 0.394752 7 to 14 2469.71 -0.428 0.334195 8 to 15 2538.52 0.545 0.707047 9 to 16 2611.48 1.577 0.942557 10 to 17 2556.03 0.792 0.785922 11 to 18 2497.03 -0.042 0.483261 12 to 19 2461.41 -0.546 0.292604 13 to 20 2646.13 2.067 0.980611 14 to 21 2367.57 -1.873 0.030545 15 to 22 2610.44 1.562 0.940837 16 to 23 2547.23 0.668 0.747932 17 to 24 2479.68 -0.287 0.386937 18 to 25 2593.13 1.317 0.906086 19 to 26 2406.94 -1.316 0.094086 20 to 27 2512.70 0.180 0.571274 21 to 28 2438.88 -0.864 0.193696 22 to 29 2488.21 -0.167 0.433798 23 to 30 2489.68 -0.146 0.441960 24 to 31 2479.98 -0.283 0.388555 25 to 32 2589.81 1.270 0.897964 CDPARK for dh-ranFile-2016-03-31_03:31: 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 3536 0.5936 0.723613 3528 0.2283 0.590298 3544 0.9589 0.831196 3552 1.3242 0.907282 3505 -0.8219 0.205562 3550 1.2329 0.891189 3534 0.5023 0.692266 3504 -0.8676 0.192812 3537 0.6393 0.738676 3494 -1.3242 0.092718 Square side=100, avg. no. parked=3528.40 sample std.=19.38 p-value of the KSTEST for those 10 p-values: 0.432842 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-31_03:31 0.6147,0.3843,0.0232,0.9359,0.6658,0.3638,0.1149,0.5177,0.2825,0.0382, The KS test for those 10 p-values: 0.391155 The 3DSPHERES test for dh-ranFile-2016-03-31_03:31 sample no r^3 equiv. uni. 1 45.837 0.783007 2 7.753 0.227738 3 40.799 0.743332 4 7.999 0.234047 5 10.011 0.283737 6 25.528 0.572984 7 63.385 0.879104 8 7.473 0.220508 9 10.614 0.297975 10 0.747 0.024594 11 23.287 0.539868 12 9.880 0.280588 13 27.976 0.606448 14 25.008 0.565513 15 8.736 0.252635 16 31.569 0.650870 17 14.316 0.379482 18 1.907 0.061574 19 4.428 0.137232 20 23.793 0.547567 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.236173 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-31_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 -0.4 -1.4 1.4 -1.7 0.2 1.7 0.0 -0.3 0.3 -0.5 0.9 -0.5 1.0 1.4 -0.2 -0.1 -1.2 -0.7 -0.6 -0.4 0.2 0.4 0.2 -0.9 0.6 0.8 0.1 -0.4 -0.6 1.0 -1.5 0.0 -0.9 -0.3 -0.7 0.2 -1.2 -0.1 1.6 -1.0 0.8 Chi-square with 42 degrees of freedom:31.497954 z-score=-1.145867, p-value=0.118237 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-31_03:31 Test no p-value 1 0.048334 2 0.468449 3 0.187314 4 0.308491 5 0.238603 6 0.053050 7 0.461656 8 0.209406 9 0.206336 10 0.240964 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.005533 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-31_03:31: (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 66463 0.62 66687 0.01 3 25000.00 25092 0.34 24975 0.03 4 6666.67 6786 2.14 6707 0.24 5 1388.89 1364 0.45 1370 0.26 6 238.10 254 1.06 222 1.09 7 34.72 35 0.00 34 0.01 8 4.96 5 0.00 4 0.19 p=0.40500 p=0.06459 Number of rngs required: 688105, p-value: 0.366 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-31_03:31 No. of wins: Observed Expected 98704 98585.9 z-score= 0.528, pvalue=0.70139 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66697 66666.7 0.014 0.014 2 37765 37654.3 0.325 0.339 3 26978 26954.7 0.020 0.359 4 19372 19313.5 0.177 0.537 5 13747 13851.4 0.787 1.324 6 9873 9943.5 0.500 1.824 7 7167 7145.0 0.068 1.892 8 5088 5139.1 0.508 2.399 9 3669 3699.9 0.257 2.657 10 2679 2666.3 0.061 2.717 11 1904 1923.3 0.194 2.912 12 1404 1388.7 0.168 3.079 13 955 1003.7 2.364 5.444 14 727 726.1 0.001 5.445 15 567 525.8 3.222 8.667 16 381 381.2 0.000 8.667 17 295 276.5 1.232 9.900 18 181 200.8 1.958 11.858 19 161 146.0 1.544 13.402 20 112 106.2 0.315 13.717 21 278 287.1 0.289 14.006 Chisq= 14.01 for 20 degrees of freedom, p= 0.16983 SUMMARY of craptest p-value for no. of wins: 0.701388 p-value for throws/game: 0.169830 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-31_03:31 No. of wins: Observed Expected 98693 98585.9 z-score= 0.479, pvalue=0.68410 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66628 66666.7 0.022 0.022 2 37410 37654.3 1.585 1.608 3 26973 26954.7 0.012 1.620 4 19490 19313.5 1.614 3.234 5 13764 13851.4 0.552 3.785 6 9946 9943.5 0.001 3.786 7 7107 7145.0 0.202 3.988 8 5185 5139.1 0.410 4.399 9 3750 3699.9 0.679 5.078 10 2671 2666.3 0.008 5.087 11 1933 1923.3 0.049 5.135 12 1436 1388.7 1.608 6.743 13 1030 1003.7 0.688 7.432 14 733 726.1 0.065 7.497 15 564 525.8 2.770 10.266 16 356 381.2 1.660 11.926 17 285 276.5 0.259 12.185 18 195 200.8 0.169 12.354 19 140 146.0 0.245 12.599 20 125 106.2 3.322 15.922 21 279 287.1 0.229 16.151 Chisq= 16.15 for 20 degrees of freedom, p= 0.29279 SUMMARY of craptest p-value for no. of wins: 0.684101 p-value for throws/game: 0.292786 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0020,0.0032,0.0055,0.0086,0.0212,0.0232,0.0246,0.0305,0.0317,0.0356, 0.0382,0.0483,0.0510,0.0531,0.0552,0.0585,0.0616,0.0646,0.0694,0.0733, 0.0791,0.0796,0.0884,0.0886,0.0927,0.0941,0.1026,0.1064,0.1085,0.1097, 0.1097,0.1149,0.1171,0.1182,0.1210,0.1307,0.1372,0.1406,0.1466,0.1470, 0.1505,0.1563,0.1592,0.1625,0.1698,0.1728,0.1837,0.1855,0.1873,0.1903, 0.1912,0.1928,0.1937,0.1978,0.2041,0.2056,0.2063,0.2094,0.2106,0.2135, 0.2138,0.2152,0.2200,0.2205,0.2254,0.2277,0.2340,0.2357,0.2362,0.2386, 0.2410,0.2522,0.2526,0.2626,0.2640,0.2775,0.2784,0.2806,0.2818,0.2822, 0.2825,0.2837,0.2843,0.2899,0.2922,0.2926,0.2928,0.2958,0.2974,0.2980, 0.3085,0.3119,0.3159,0.3249,0.3342,0.3355,0.3392,0.3435,0.3485,0.3638, 0.3658,0.3738,0.3758,0.3771,0.3795,0.3838,0.3843,0.3869,0.3886,0.3911, 0.3912,0.3916,0.3948,0.3983,0.4046,0.4050,0.4207,0.4209,0.4221,0.4239, 0.4294,0.4328,0.4338,0.4340,0.4365,0.4385,0.4420,0.4549,0.4553,0.4617, 0.4684,0.4693,0.4737,0.4771,0.4820,0.4833,0.4910,0.5036,0.5050,0.5067, 0.5095,0.5177,0.5266,0.5360,0.5399,0.5416,0.5476,0.5591,0.5641,0.5652, 0.5655,0.5713,0.5730,0.5760,0.5878,0.5903,0.5947,0.5960,0.5966,0.5975, 0.6036,0.6064,0.6088,0.6117,0.6147,0.6168,0.6181,0.6257,0.6291,0.6293, 0.6306,0.6323,0.6373,0.6472,0.6507,0.6509,0.6548,0.6595,0.6610,0.6658, 0.6760,0.6826,0.6832,0.6841,0.6923,0.6928,0.7014,0.7044,0.7070,0.7071, 0.7099,0.7102,0.7126,0.7147,0.7236,0.7270,0.7288,0.7311,0.7311,0.7348, 0.7357,0.7365,0.7387,0.7408,0.7433,0.7434,0.7443,0.7479,0.7513,0.7538, 0.7614,0.7672,0.7709,0.7728,0.7829,0.7830,0.7859,0.7902,0.7906,0.7970, 0.8013,0.8023,0.8032,0.8060,0.8091,0.8132,0.8170,0.8296,0.8312,0.8352, 0.8411,0.8426,0.8428,0.8468,0.8556,0.8607,0.8681,0.8738,0.8756,0.8791, 0.8808,0.8868,0.8887,0.8912,0.8980,0.9045,0.9049,0.9061,0.9073,0.9093, 0.9139,0.9180,0.9240,0.9269,0.9316,0.9359,0.9374,0.9408,0.9426,0.9568, 0.9615,0.9653,0.9686,0.9747,0.9806,0.9821,0.9867,0.9986,0.9999, Overall p-value after applying KStest on 269 p-values = 0.910766 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.