RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-11_20:31 (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 23.0500 0.852371 2 to 25 15.80 12.9567 0.260922 3 to 26 15.57 12.2501 0.215237 4 to 27 15.43 35.2847 0.994293 5 to 28 15.61 26.9340 0.940957 6 to 29 15.92 17.9588 0.608556 7 to 30 15.77 10.1742 0.103853 8 to 31 15.70 31.7922 0.984032 9 to 32 15.68 18.6660 0.651965 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.103075 Tough bday spacings test for dh-ranFile-2015-08-11_20:31: 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 10 26 84 105 96 74 48 26 17 10 4 (O-E)^2/E 0.1 3.1 1.6 0.5 0.0 0.2 0.3 0.5 0.3 1.7 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.366, p= 0.407 RESULTS OF GCD FOR dh-ranFile-2015-08-11_20:31 Euclid's algorithm: p-value, steps to gcd: 0.174596 p-value, dist. of gcd's: 0.723615 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-11_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.158 0.173 0.974 0.677 0.438 0.870 0.149 0.905 Bits 8 to 15---> 0.267 0.073 0.588 0.585 0.849 0.212 0.191 0.304 Bits 16 to 23---> 0.315 0.087 0.121 0.468 0.422 0.225 0.867 0.948 Bits 24 to 31---> 0.182 0.858 0.075 0.303 0.814 0.234 0.587 0.842 KS test for the above 32 p values: 0.649 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-11_20:31, p-values for 5 runs: 0.2603, 0.3615, 0.4003, 0.2012, 0.2957 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-11_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 199 211.4 0.729 0.729 r= 29 5125 5134.0 0.016 0.745 r= 30 23016 23103.0 0.328 1.073 r= 31 11660 11551.5 1.019 2.092 chi-square = 2.092 with df = 3; p-value = 0.446 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-11_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 179 211.4 4.971 4.971 r= 30 5019 5134.0 2.576 7.547 r= 31 23266 23103.0 1.149 8.697 r= 32 11536 11551.5 0.021 8.717 chi-square = 8.717 with df = 3; p-value = 0.967 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-11_20:31 b-rank test for bits 1 to 8, p=0.07543 b-rank test for bits 2 to 9, p=0.55041 b-rank test for bits 3 to 10, p=0.44099 b-rank test for bits 4 to 11, p=0.01077 b-rank test for bits 5 to 12, p=0.12949 b-rank test for bits 6 to 13, p=0.36441 b-rank test for bits 7 to 14, p=0.76316 b-rank test for bits 8 to 15, p=0.48133 b-rank test for bits 9 to 16, p=0.28623 b-rank test for bits 10 to 17, p=0.71069 b-rank test for bits 11 to 18, p=0.29917 b-rank test for bits 12 to 19, p=0.26972 b-rank test for bits 13 to 20, p=0.97573 b-rank test for bits 14 to 21, p=0.92177 b-rank test for bits 15 to 22, p=0.03577 b-rank test for bits 16 to 23, p=0.84133 b-rank test for bits 17 to 24, p=0.03000 b-rank test for bits 18 to 25, p=0.43751 b-rank test for bits 19 to 26, p=0.24554 b-rank test for bits 20 to 27, p=0.77033 b-rank test for bits 21 to 28, p=0.51417 b-rank test for bits 22 to 29, p=0.76567 b-rank test for bits 23 to 30, p=0.03847 b-rank test for bits 24 to 31, p=0.00504 b-rank test for bits 25 to 32, p=0.55959 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 = 0.144093 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-11_20:31 (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 142676 1.79 0.963376 2 142350 1.03 0.848402 3 141992 0.19 0.576581 4 141661 -0.58 0.280886 5 142517 1.42 0.922166 6 141472 -1.02 0.153438 7 141603 -0.72 0.237081 8 141628 -0.66 0.255490 9 142115 0.48 0.684577 10 141523 -0.90 0.183358 11 142082 0.40 0.656686 12 141446 -1.08 0.139505 13 141170 -1.73 0.042047 14 141296 -1.43 0.075927 15 141329 -1.36 0.087564 16 142178 0.63 0.734911 17 142152 0.57 0.714638 18 141750 -0.37 0.354847 19 142846 2.19 0.985683 20 142272 0.85 0.801603 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-11_20:31 Bits used No. missing words z-score p-value 23 to 32 142184 0.9471 0.828216 22 to 31 142035 0.4333 0.667618 21 to 30 142094 0.6368 0.737870 20 to 29 141885 -0.0839 0.466569 19 to 28 142134 0.7747 0.780749 18 to 27 141646 -0.9080 0.181930 17 to 26 142238 1.1333 0.871465 16 to 25 142385 1.6402 0.949523 15 to 24 141446 -1.5977 0.055056 14 to 23 141693 -0.7460 0.227844 13 to 22 142240 1.1402 0.872907 12 to 21 141559 -1.2080 0.113517 11 to 20 141880 -0.1011 0.459721 10 to 19 141906 -0.0115 0.495419 9 to 18 141718 -0.6598 0.254704 8 to 17 141798 -0.3839 0.350528 7 to 16 142238 1.1333 0.871465 6 to 15 141939 0.1023 0.540745 5 to 14 141968 0.2023 0.580163 4 to 13 141833 -0.2632 0.396196 3 to 12 141913 0.0127 0.505049 2 to 11 142396 1.6782 0.953343 1 to 10 142197 0.9920 0.839393 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-11_20:31 Bits used No. missing words z-score p-value 28 to 32 141723 -0.6316 0.263815 27 to 31 141742 -0.5672 0.285282 26 to 30 142420 1.7311 0.958282 25 to 29 142001 0.3107 0.622003 24 to 28 141518 -1.3265 0.092330 23 to 27 141639 -0.9164 0.179736 22 to 26 141739 -0.5774 0.281838 21 to 25 142261 1.1921 0.883389 20 to 24 142070 0.5446 0.707001 19 to 23 142260 1.1887 0.882723 18 to 22 141792 -0.3977 0.345415 17 to 21 141361 -1.8587 0.031532 16 to 20 141799 -0.3740 0.354202 15 to 19 141845 -0.2181 0.413688 14 to 18 141773 -0.4621 0.321992 13 to 17 141944 0.1175 0.546778 12 to 16 141825 -0.2859 0.387491 11 to 15 141923 0.0463 0.518480 10 to 14 141464 -1.5096 0.065574 9 to 13 141895 -0.0486 0.480629 8 to 12 141660 -0.8452 0.199003 7 to 11 142152 0.8226 0.794635 6 to 10 142316 1.3785 0.915982 5 to 9 142351 1.4972 0.932828 4 to 8 141933 0.0802 0.531976 3 to 7 141412 -1.6859 0.045911 2 to 6 141763 -0.4960 0.309935 1 to 5 142021 0.3785 0.647486 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-11_20:31 Bits used No. missing words z-score p-value 31 to 32 142198 0.8515 0.802764 30 to 31 142181 0.8014 0.788546 29 to 30 142385 1.4032 0.919715 28 to 29 142215 0.9017 0.816387 27 to 28 141858 -0.1514 0.439824 26 to 27 141502 -1.2016 0.114766 25 to 26 141279 -1.8594 0.031487 24 to 25 142298 1.1465 0.874210 23 to 24 141946 0.1082 0.543070 22 to 23 141782 -0.3756 0.353605 21 to 22 141956 0.1377 0.554749 20 to 21 142430 1.5359 0.937719 19 to 20 141539 -1.0924 0.137325 18 to 19 142240 0.9754 0.835326 17 to 18 142272 1.0698 0.857651 16 to 17 142209 0.8840 0.811647 15 to 16 142322 1.2173 0.888258 14 to 15 142220 0.9164 0.820280 13 to 14 142163 0.7483 0.772857 12 to 13 141988 0.2321 0.591756 11 to 12 141465 -1.3107 0.094978 10 to 11 142044 0.3973 0.654411 9 to 10 142065 0.4592 0.676956 8 to 9 142422 1.5123 0.934771 7 to 8 141686 -0.6588 0.255015 6 to 7 141763 -0.4317 0.332997 5 to 6 141916 0.0197 0.507849 4 to 5 141562 -1.0246 0.152783 3 to 4 141714 -0.5762 0.282242 2 to 3 141789 -0.3550 0.361311 1 to 2 141894 -0.0452 0.481966 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-11_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2525.55 0.361 0.641096 Test results for specific bytes for dh-ranFile-2015-08-11_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2415.29 -1.198 0.115458 2 to 9 2518.67 0.264 0.604103 3 to 10 2432.18 -0.959 0.168738 4 to 11 2528.38 0.401 0.655896 5 to 12 2491.06 -0.126 0.449701 6 to 13 2589.19 1.261 0.896418 7 to 14 2532.75 0.463 0.678381 8 to 15 2653.22 2.167 0.984878 9 to 16 2484.55 -0.219 0.413516 10 to 17 2580.16 1.134 0.871531 11 to 18 2448.40 -0.730 0.232758 12 to 19 2668.85 2.388 0.991529 13 to 20 2515.88 0.225 0.588842 14 to 21 2559.17 0.837 0.798626 15 to 22 2370.70 -1.829 0.033733 16 to 23 2499.62 -0.005 0.497877 17 to 24 2543.58 0.616 0.731176 18 to 25 2567.09 0.949 0.828624 19 to 26 2519.86 0.281 0.610584 20 to 27 2650.83 2.133 0.983538 21 to 28 2542.00 0.594 0.723741 22 to 29 2505.15 0.073 0.529034 23 to 30 2534.08 0.482 0.685076 24 to 31 2395.41 -1.479 0.069551 25 to 32 2494.81 -0.073 0.470740 CDPARK for dh-ranFile-2015-08-11_20:31: 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 3494 -1.3242 0.092718 3563 1.8265 0.966111 3538 0.6849 0.753306 3506 -0.7763 0.218799 3528 0.2283 0.590298 3530 0.3196 0.625377 3499 -1.0959 0.136563 3525 0.0913 0.536383 3527 0.1826 0.572463 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3521.60 sample std.=19.73 p-value of the KSTEST for those 10 p-values: 0.868911 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-11_20:31 0.6248,0.0568,0.9406,0.8983,0.3310,0.2262,0.2367,0.6832,0.7748,0.4533, The KS test for those 10 p-values: 0.996139 The 3DSPHERES test for dh-ranFile-2015-08-11_20:31 sample no r^3 equiv. uni. 1 6.139 0.185041 2 2.400 0.076877 3 2.283 0.073266 4 10.748 0.301112 5 43.899 0.768528 6 15.549 0.404467 7 19.410 0.476388 8 4.785 0.147424 9 1.622 0.052639 10 49.071 0.805185 11 40.034 0.736706 12 5.884 0.178084 13 2.156 0.069345 14 25.199 0.568278 15 23.419 0.541889 16 73.596 0.913982 17 1.749 0.056620 18 11.648 0.321772 19 53.875 0.834010 20 17.575 0.443356 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.148482 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-11_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 2.6 -0.4 -1.0 3.3 -1.4 -1.1 -1.3 -0.7 -0.3 -0.3 0.5 -0.9 1.0 1.0 -0.2 -0.2 -0.8 -0.9 -2.0 0.3 0.7 2.4 2.1 -1.9 1.3 0.2 -1.3 0.6 0.3 1.3 -0.3 1.0 0.3 -0.9 0.2 -0.9 -1.7 0.9 -0.7 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:62.180923 z-score=2.201919, p-value=0.976928 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-11_20:31 Test no p-value 1 0.008195 2 0.872966 3 0.991823 4 0.077471 5 0.141455 6 0.002331 7 0.327211 8 0.511874 9 0.104469 10 0.528288 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.036490 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-11_20:31: (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 66606 0.06 66586 0.10 3 25000.00 25071 0.20 25080 0.26 4 6666.67 6657 0.01 6670 0.00 5 1388.89 1375 0.14 1392 0.01 6 238.10 245 0.20 238 0.00 7 34.72 37 0.15 29 0.94 8 4.96 8 1.86 4 0.19 p=0.14554 p=0.03987 Number of rngs required: 689031, p-value: 0.766 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-11_20:31 No. of wins: Observed Expected 98866 98585.9 z-score= 1.253, pvalue=0.89489 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66507 66666.7 0.382 0.382 2 37855 37654.3 1.070 1.452 3 26823 26954.7 0.644 2.096 4 19219 19313.5 0.462 2.558 5 13954 13851.4 0.760 3.317 6 9962 9943.5 0.034 3.352 7 7192 7145.0 0.309 3.661 8 5215 5139.1 1.122 4.782 9 3724 3699.9 0.157 4.940 10 2672 2666.3 0.012 4.952 11 1890 1923.3 0.578 5.529 12 1392 1388.7 0.008 5.537 13 989 1003.7 0.216 5.753 14 751 726.1 0.851 6.604 15 511 525.8 0.419 7.023 16 336 381.2 5.348 12.371 17 288 276.5 0.475 12.846 18 204 200.8 0.050 12.896 19 138 146.0 0.437 13.333 20 95 106.2 1.184 14.517 21 283 287.1 0.059 14.576 Chisq= 14.58 for 20 degrees of freedom, p= 0.19986 SUMMARY of craptest p-value for no. of wins: 0.894889 p-value for throws/game: 0.199859 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-11_20:31 No. of wins: Observed Expected 98679 98585.9 z-score= 0.417, pvalue=0.66151 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66719 66666.7 0.041 0.041 2 37435 37654.3 1.277 1.319 3 27126 26954.7 1.088 2.407 4 19433 19313.5 0.740 3.147 5 13704 13851.4 1.569 4.716 6 9806 9943.5 1.903 6.618 7 7255 7145.0 1.693 8.311 8 5140 5139.1 0.000 8.311 9 3712 3699.9 0.040 8.351 10 2703 2666.3 0.505 8.856 11 1924 1923.3 0.000 8.856 12 1448 1388.7 2.529 11.385 13 963 1003.7 1.652 13.037 14 692 726.1 1.605 14.642 15 530 525.8 0.033 14.675 16 390 381.2 0.205 14.880 17 293 276.5 0.980 15.860 18 183 200.8 1.583 17.443 19 143 146.0 0.061 17.504 20 111 106.2 0.216 17.719 21 290 287.1 0.029 17.748 Chisq= 17.75 for 20 degrees of freedom, p= 0.39603 SUMMARY of craptest p-value for no. of wins: 0.661508 p-value for throws/game: 0.396027 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0050,0.0082,0.0108,0.0300,0.0315,0.0315,0.0337,0.0358,0.0365, 0.0385,0.0399,0.0420,0.0459,0.0526,0.0551,0.0566,0.0568,0.0656,0.0693, 0.0696,0.0732,0.0733,0.0752,0.0754,0.0759,0.0769,0.0775,0.0875,0.0876, 0.0923,0.0927,0.0950,0.1031,0.1039,0.1045,0.1135,0.1148,0.1155,0.1207, 0.1295,0.1366,0.1373,0.1395,0.1415,0.1441,0.1455,0.1474,0.1485,0.1490, 0.1528,0.1534,0.1577,0.1687,0.1730,0.1746,0.1781,0.1797,0.1819,0.1820, 0.1834,0.1850,0.1911,0.1990,0.1999,0.2012,0.2125,0.2152,0.2188,0.2188, 0.2253,0.2262,0.2278,0.2328,0.2341,0.2367,0.2371,0.2455,0.2547,0.2550, 0.2555,0.2603,0.2609,0.2638,0.2674,0.2697,0.2809,0.2818,0.2822,0.2853, 0.2862,0.2957,0.2992,0.3011,0.3033,0.3037,0.3099,0.3149,0.3218,0.3220, 0.3272,0.3310,0.3330,0.3454,0.3505,0.3536,0.3542,0.3548,0.3613,0.3615, 0.3644,0.3875,0.3960,0.3962,0.4003,0.4045,0.4069,0.4135,0.4137,0.4223, 0.4375,0.4376,0.4398,0.4410,0.4434,0.4464,0.4497,0.4533,0.4597,0.4666, 0.4679,0.4707,0.4764,0.4806,0.4813,0.4820,0.4954,0.4979,0.5050,0.5078, 0.5119,0.5142,0.5185,0.5283,0.5290,0.5320,0.5364,0.5407,0.5419,0.5431, 0.5468,0.5504,0.5547,0.5596,0.5683,0.5725,0.5766,0.5802,0.5854,0.5875, 0.5884,0.5888,0.5903,0.5918,0.6041,0.6086,0.6106,0.6220,0.6248,0.6254, 0.6411,0.6475,0.6492,0.6520,0.6544,0.6559,0.6567,0.6615,0.6676,0.6768, 0.6770,0.6784,0.6832,0.6846,0.6851,0.7070,0.7107,0.7146,0.7236,0.7237, 0.7312,0.7349,0.7367,0.7379,0.7533,0.7632,0.7657,0.7658,0.7685,0.7703, 0.7729,0.7748,0.7807,0.7885,0.7946,0.7986,0.8016,0.8028,0.8052,0.8116, 0.8135,0.8164,0.8203,0.8282,0.8286,0.8340,0.8353,0.8394,0.8413,0.8425, 0.8484,0.8487,0.8524,0.8577,0.8579,0.8669,0.8689,0.8699,0.8715,0.8715, 0.8715,0.8729,0.8730,0.8742,0.8827,0.8834,0.8883,0.8949,0.8964,0.8983, 0.9050,0.9140,0.9160,0.9197,0.9218,0.9222,0.9328,0.9348,0.9377,0.9406, 0.9410,0.9483,0.9495,0.9533,0.9583,0.9634,0.9661,0.9667,0.9745,0.9757, 0.9769,0.9835,0.9840,0.9849,0.9857,0.9915,0.9918,0.9943,0.9961, Overall p-value after applying KStest on 269 p-values = 0.307278 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.