RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-24_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.64 19.3843 0.693073 2 to 25 15.69 24.3726 0.890339 3 to 26 15.65 16.9826 0.544457 4 to 27 15.80 18.9158 0.666614 5 to 28 16.14 13.0321 0.265967 6 to 29 15.85 20.9044 0.769405 7 to 30 15.64 10.8310 0.134788 8 to 31 15.88 27.2337 0.945272 9 to 32 15.93 7.9542 0.032483 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.855941 Tough bday spacings test for dh-ranFile-2016-09-24_12:31: 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 14 42 64 102 105 76 50 26 9 6 6 (O-E)^2/E 2.6 0.8 1.2 0.2 0.5 0.1 0.1 0.5 2.3 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 9.182, p= 0.485 RESULTS OF GCD FOR dh-ranFile-2016-09-24_12:31 Euclid's algorithm: p-value, steps to gcd: 0.873764 p-value, dist. of gcd's: 0.550073 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-24_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.678 0.736 0.926 0.593 0.082 0.772 0.592 0.396 Bits 8 to 15---> 0.473 0.324 0.323 0.736 0.174 0.579 0.518 0.857 Bits 16 to 23---> 0.580 0.452 0.641 0.245 0.059 0.712 0.919 0.269 Bits 24 to 31---> 0.518 0.120 0.100 0.702 0.635 0.654 0.514 0.858 KS test for the above 32 p values: 0.545 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-24_12:31, p-values for 5 runs: 0.3494, 0.4265, 0.4989, 0.6496, 0.1628 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-24_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 232 211.4 2.004 2.004 r= 29 5069 5134.0 0.823 2.827 r= 30 23260 23103.0 1.066 3.893 r= 31 11439 11551.5 1.096 4.989 chi-square = 4.989 with df = 3; p-value = 0.827 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-24_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5244 5134.0 2.356 2.692 r= 31 23122 23103.0 0.016 2.707 r= 32 11431 11551.5 1.257 3.965 chi-square = 3.965 with df = 3; p-value = 0.735 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-24_12:31 b-rank test for bits 1 to 8, p=0.88930 b-rank test for bits 2 to 9, p=0.60488 b-rank test for bits 3 to 10, p=0.72108 b-rank test for bits 4 to 11, p=0.70999 b-rank test for bits 5 to 12, p=0.77359 b-rank test for bits 6 to 13, p=0.61647 b-rank test for bits 7 to 14, p=0.19886 b-rank test for bits 8 to 15, p=0.02494 b-rank test for bits 9 to 16, p=0.00615 b-rank test for bits 10 to 17, p=0.59183 b-rank test for bits 11 to 18, p=0.19775 b-rank test for bits 12 to 19, p=0.96310 b-rank test for bits 13 to 20, p=0.25044 b-rank test for bits 14 to 21, p=0.82162 b-rank test for bits 15 to 22, p=0.76981 b-rank test for bits 16 to 23, p=0.49676 b-rank test for bits 17 to 24, p=0.94384 b-rank test for bits 18 to 25, p=0.27600 b-rank test for bits 19 to 26, p=0.64427 b-rank test for bits 20 to 27, p=0.75392 b-rank test for bits 21 to 28, p=0.57190 b-rank test for bits 22 to 29, p=0.53084 b-rank test for bits 23 to 30, p=0.23637 b-rank test for bits 24 to 31, p=0.09399 b-rank test for bits 25 to 32, p=0.88975 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 = 0.593441 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-24_12:31 (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 142172 0.61 0.730298 2 141545 -0.85 0.197319 3 142187 0.65 0.741754 4 142421 1.20 0.884052 5 142153 0.57 0.715431 6 141858 -0.12 0.452269 7 141758 -0.35 0.361829 8 142041 0.31 0.620822 9 141426 -1.13 0.129391 10 141920 0.02 0.509945 11 141761 -0.35 0.364459 12 142403 1.15 0.875634 13 142265 0.83 0.797015 14 141184 -1.69 0.045067 15 142335 0.99 0.840024 16 141814 -0.22 0.411871 17 141648 -0.61 0.270738 18 142169 0.61 0.727977 19 141219 -1.61 0.053381 20 141954 0.10 0.541562 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-24_12:31 Bits used No. missing words z-score p-value 23 to 32 141962 0.1816 0.572060 22 to 31 141649 -0.8977 0.184676 21 to 30 141843 -0.2287 0.409542 20 to 29 142226 1.0920 0.862576 19 to 28 141488 -1.4529 0.073131 18 to 27 141615 -1.0149 0.155069 17 to 26 141824 -0.2942 0.384287 16 to 25 141866 -0.1494 0.440614 15 to 24 141670 -0.8253 0.204608 14 to 23 141892 -0.0598 0.476174 13 to 22 141975 0.2264 0.589574 12 to 21 142060 0.5196 0.698312 11 to 20 142013 0.3575 0.639635 10 to 19 141342 -1.9563 0.025214 9 to 18 141829 -0.2770 0.390890 8 to 17 141726 -0.6322 0.263637 7 to 16 141653 -0.8839 0.188376 6 to 15 141528 -1.3149 0.094267 5 to 14 141598 -1.0736 0.141512 4 to 13 141622 -0.9908 0.160893 3 to 12 141601 -1.0632 0.143844 2 to 11 141953 0.1506 0.559849 1 to 10 141912 0.0092 0.503673 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-24_12:31 Bits used No. missing words z-score p-value 28 to 32 141879 -0.1028 0.459056 27 to 31 141986 0.2599 0.602529 26 to 30 141692 -0.7367 0.230649 25 to 29 142308 1.3514 0.911720 24 to 28 141928 0.0633 0.525232 23 to 27 141763 -0.4960 0.309935 22 to 26 142222 1.0599 0.855405 21 to 25 142152 0.8226 0.794635 20 to 24 141567 -1.1604 0.122935 19 to 23 142294 1.3040 0.903877 18 to 22 141786 -0.4181 0.337949 17 to 21 142271 1.2260 0.889901 16 to 20 141959 0.1684 0.566855 15 to 19 142128 0.7413 0.770730 14 to 18 142486 1.9548 0.974697 13 to 17 141811 -0.3333 0.369446 12 to 16 141800 -0.3706 0.355464 11 to 15 142129 0.7446 0.771757 10 to 14 141132 -2.6350 0.004207 9 to 13 141691 -0.7401 0.229619 8 to 12 142472 1.9074 0.971763 7 to 11 141907 -0.0079 0.496849 6 to 10 141521 -1.3164 0.094024 5 to 9 141955 0.1548 0.561516 4 to 8 141656 -0.8587 0.195240 3 to 7 142091 0.6158 0.730997 2 to 6 142134 0.7616 0.776849 1 to 5 141543 -1.2418 0.107156 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-24_12:31 Bits used No. missing words z-score p-value 31 to 32 142047 0.4061 0.657668 30 to 31 142090 0.5329 0.702966 29 to 30 141566 -1.0128 0.155584 28 to 29 142249 1.0020 0.841823 27 to 28 141821 -0.2606 0.397216 26 to 27 142439 1.5624 0.940909 25 to 26 142046 0.4032 0.656583 24 to 25 141840 -0.2045 0.418976 23 to 24 142076 0.4917 0.688517 22 to 23 142088 0.5271 0.700921 21 to 22 141824 -0.2517 0.400632 20 to 21 142040 0.3855 0.650051 19 to 20 141948 0.1141 0.545409 18 to 19 141281 -1.8535 0.031907 17 to 18 141755 -0.4553 0.324464 16 to 17 141714 -0.5762 0.282242 15 to 16 141744 -0.4877 0.312882 14 to 15 141924 0.0433 0.517259 13 to 14 141854 -0.1632 0.435174 12 to 13 141374 -1.5791 0.057151 11 to 12 141610 -0.8830 0.188624 10 to 11 142142 0.6863 0.753751 9 to 10 141603 -0.9036 0.183096 8 to 9 141738 -0.5054 0.306640 7 to 8 141494 -1.2252 0.110257 6 to 7 141832 -0.2281 0.409780 5 to 6 142586 1.9961 0.977037 4 to 5 142180 0.7984 0.787691 3 to 4 141478 -1.2724 0.101623 2 to 3 141938 0.0846 0.533699 1 to 2 141767 -0.4199 0.337297 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-24_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2395.57 -1.477 0.069851 Test results for specific bytes for dh-ranFile-2016-09-24_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2458.82 -0.582 0.280141 2 to 9 2449.07 -0.720 0.235670 3 to 10 2519.72 0.279 0.609813 4 to 11 2553.42 0.755 0.775003 5 to 12 2535.86 0.507 0.693972 6 to 13 2551.39 0.727 0.766331 7 to 14 2509.30 0.132 0.552321 8 to 15 2363.97 -1.924 0.027197 9 to 16 2459.43 -0.574 0.283069 10 to 17 2531.29 0.442 0.670914 11 to 18 2499.23 -0.011 0.495661 12 to 19 2641.66 2.003 0.977435 13 to 20 2569.53 0.983 0.837279 14 to 21 2477.24 -0.322 0.373785 15 to 22 2518.56 0.262 0.603526 16 to 23 2549.17 0.695 0.756573 17 to 24 2519.46 0.275 0.608423 18 to 25 2546.93 0.664 0.746560 19 to 26 2471.76 -0.399 0.344808 20 to 27 2487.49 -0.177 0.429780 21 to 28 2410.45 -1.266 0.102670 22 to 29 2424.85 -1.063 0.143925 23 to 30 2478.85 -0.299 0.382422 24 to 31 2397.33 -1.452 0.073246 25 to 32 2490.69 -0.132 0.447598 CDPARK for dh-ranFile-2016-09-24_12:31: 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 3511 -0.5479 0.291865 3528 0.2283 0.590298 3556 1.5068 0.934075 3561 1.7352 0.958644 3511 -0.5479 0.291865 3521 -0.0913 0.463617 3517 -0.2740 0.392053 3527 0.1826 0.572463 3507 -0.7306 0.232514 3499 -1.0959 0.136563 Square side=100, avg. no. parked=3523.80 sample std.=19.31 p-value of the KSTEST for those 10 p-values: 0.753567 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-24_12:31 0.3748,0.3166,0.7849,0.2294,0.0369,0.4575,0.8573,0.6977,0.5299,0.6057, The KS test for those 10 p-values: 0.948595 The 3DSPHERES test for dh-ranFile-2016-09-24_12:31 sample no r^3 equiv. uni. 1 10.829 0.302990 2 171.526 0.996712 3 5.172 0.158361 4 12.109 0.332107 5 82.986 0.937098 6 4.707 0.145212 7 30.623 0.639686 8 44.105 0.770112 9 24.511 0.558262 10 3.174 0.100410 11 10.116 0.286233 12 18.845 0.466432 13 60.566 0.867193 14 1.436 0.046736 15 12.102 0.331950 16 33.260 0.670002 17 4.230 0.131507 18 10.543 0.296316 19 16.830 0.429360 20 36.117 0.699981 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.762528 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-24_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.5 -0.8 0.6 0.1 -0.3 2.1 -0.3 1.4 1.7 0.4 1.7 1.1 -1.6 -0.1 -0.0 -1.0 -0.5 -1.4 1.6 -0.7 -0.4 -0.4 -0.5 -0.2 2.3 0.7 -0.1 -0.8 -0.5 -1.4 -0.2 -0.3 0.1 0.3 -0.8 -0.9 -0.4 0.5 -0.1 -1.3 0.0 -0.1 Chi-square with 42 degrees of freedom:37.375812 z-score=-0.504540, p-value=0.326053 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-24_12:31 Test no p-value 1 0.246548 2 0.902369 3 0.203602 4 0.051351 5 0.290004 6 0.257465 7 0.977757 8 0.051083 9 0.643259 10 0.292217 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.203357 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-24_12:31: (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 66382 1.22 66790 0.23 3 25000.00 25245 2.40 24914 0.30 4 6666.67 6649 0.05 6622 0.30 5 1388.89 1466 4.28 1376 0.12 6 238.10 218 1.70 261 2.20 7 34.72 32 0.21 29 0.94 8 4.96 7 0.84 7 0.84 p=0.90165 p=0.44689 Number of rngs required: 687691, p-value: 0.205 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-24_12:31 No. of wins: Observed Expected 98211 98585.9 z-score=-1.677, pvalue=0.04681 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66237 66666.7 2.769 2.769 2 37574 37654.3 0.171 2.941 3 26838 26954.7 0.506 3.446 4 19508 19313.5 1.960 5.406 5 14096 13851.4 4.319 9.724 6 10018 9943.5 0.558 10.282 7 7127 7145.0 0.045 10.327 8 5139 5139.1 0.000 10.327 9 3721 3699.9 0.121 10.448 10 2615 2666.3 0.987 11.435 11 1952 1923.3 0.427 11.862 12 1416 1388.7 0.535 12.397 13 1071 1003.7 4.511 16.908 14 750 726.1 0.784 17.692 15 529 525.8 0.019 17.711 16 384 381.2 0.021 17.732 17 283 276.5 0.151 17.883 18 208 200.8 0.256 18.139 19 128 146.0 2.216 20.355 20 138 106.2 9.512 29.866 21 268 287.1 1.272 31.139 Chisq= 31.14 for 20 degrees of freedom, p= 0.94661 SUMMARY of craptest p-value for no. of wins: 0.046812 p-value for throws/game: 0.946614 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-24_12:31 No. of wins: Observed Expected 98891 98585.9 z-score= 1.365, pvalue=0.91384 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67057 66666.7 2.285 2.285 2 37582 37654.3 0.139 2.424 3 26759 26954.7 1.421 3.846 4 19157 19313.5 1.268 5.113 5 13840 13851.4 0.009 5.123 6 10078 9943.5 1.818 6.941 7 7025 7145.0 2.016 8.957 8 5168 5139.1 0.163 9.120 9 3680 3699.9 0.107 9.226 10 2606 2666.3 1.364 10.590 11 1962 1923.3 0.778 11.368 12 1314 1388.7 4.022 15.390 13 1036 1003.7 1.038 16.428 14 736 726.1 0.134 16.562 15 544 525.8 0.627 17.190 16 381 381.2 0.000 17.190 17 289 276.5 0.561 17.751 18 205 200.8 0.087 17.838 19 141 146.0 0.170 18.008 20 129 106.2 4.888 22.896 21 311 287.1 1.987 24.883 Chisq= 24.88 for 20 degrees of freedom, p= 0.79405 SUMMARY of craptest p-value for no. of wins: 0.913837 p-value for throws/game: 0.794052 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0042,0.0061,0.0249,0.0252,0.0272,0.0319,0.0325,0.0369,0.0451,0.0467, 0.0468,0.0511,0.0514,0.0534,0.0572,0.0585,0.0699,0.0731,0.0732,0.0816, 0.0940,0.0940,0.0943,0.0996,0.1004,0.1016,0.1027,0.1072,0.1103,0.1205, 0.1229,0.1294,0.1315,0.1348,0.1366,0.1415,0.1438,0.1439,0.1452,0.1551, 0.1556,0.1584,0.1609,0.1628,0.1743,0.1831,0.1847,0.1884,0.1886,0.1952, 0.1973,0.1977,0.1989,0.2034,0.2036,0.2046,0.2052,0.2294,0.2296,0.2306, 0.2325,0.2357,0.2364,0.2451,0.2465,0.2504,0.2575,0.2636,0.2660,0.2690, 0.2707,0.2760,0.2801,0.2822,0.2831,0.2862,0.2900,0.2919,0.2919,0.2922, 0.2963,0.3030,0.3066,0.3099,0.3129,0.3166,0.3234,0.3236,0.3245,0.3261, 0.3320,0.3321,0.3373,0.3379,0.3448,0.3494,0.3555,0.3618,0.3645,0.3694, 0.3738,0.3748,0.3824,0.3843,0.3909,0.3921,0.3960,0.3972,0.4006,0.4095, 0.4098,0.4119,0.4190,0.4265,0.4294,0.4298,0.4352,0.4406,0.4469,0.4476, 0.4517,0.4523,0.4575,0.4591,0.4636,0.4664,0.4733,0.4762,0.4850,0.4957, 0.4968,0.4968,0.4989,0.5037,0.5099,0.5141,0.5173,0.5178,0.5178,0.5252, 0.5299,0.5308,0.5337,0.5416,0.5445,0.5453,0.5454,0.5501,0.5523,0.5583, 0.5598,0.5615,0.5669,0.5719,0.5721,0.5725,0.5788,0.5801,0.5896,0.5903, 0.5918,0.5921,0.5927,0.5934,0.6025,0.6035,0.6049,0.6057,0.6084,0.6098, 0.6165,0.6208,0.6346,0.6396,0.6397,0.6411,0.6433,0.6443,0.6496,0.6501, 0.6538,0.6566,0.6577,0.6666,0.6700,0.6709,0.6783,0.6885,0.6931,0.6940, 0.6977,0.6983,0.7000,0.7009,0.7021,0.7030,0.7100,0.7116,0.7154,0.7211, 0.7280,0.7303,0.7310,0.7347,0.7359,0.7359,0.7418,0.7466,0.7536,0.7538, 0.7539,0.7566,0.7625,0.7663,0.7694,0.7698,0.7701,0.7707,0.7718,0.7724, 0.7736,0.7750,0.7768,0.7849,0.7877,0.7941,0.7946,0.7970,0.8216,0.8274, 0.8373,0.8400,0.8418,0.8554,0.8559,0.8571,0.8573,0.8584,0.8626,0.8672, 0.8738,0.8756,0.8841,0.8893,0.8897,0.8899,0.8903,0.9016,0.9024,0.9039, 0.9117,0.9138,0.9193,0.9264,0.9341,0.9371,0.9409,0.9438,0.9453,0.9466, 0.9486,0.9586,0.9631,0.9718,0.9747,0.9770,0.9774,0.9778,0.9967, Overall p-value after applying KStest on 269 p-values = 0.695646 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.