RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-06_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 15.37 29.1474 0.966809 2 to 25 15.73 11.9114 0.194530 3 to 26 15.69 15.3897 0.432569 4 to 27 15.81 14.5943 0.375323 5 to 28 15.65 20.5831 0.754504 6 to 29 15.71 18.8985 0.665608 7 to 30 15.57 34.7678 0.993327 8 to 31 15.65 19.6802 0.709088 9 to 32 15.79 24.1611 0.884876 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.119307 Tough bday spacings test for dh-ranFile-2017-02-06_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 8 34 78 93 115 73 55 27 14 3 0 (O-E)^2/E 0.1 0.2 0.3 0.2 3.1 0.3 0.2 0.3 0.1 2.0 4.1 Birthday Spacings: Sum(O-E)^2/E= 10.789, p= 0.626 RESULTS OF GCD FOR dh-ranFile-2017-02-06_09:31 Euclid's algorithm: p-value, steps to gcd: 0.687234 p-value, dist. of gcd's: 0.424933 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-06_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.184 0.914 0.390 0.736 0.694 0.616 0.912 0.575 Bits 8 to 15---> 0.561 0.377 0.226 0.394 0.367 0.849 0.954 0.982 Bits 16 to 23---> 0.254 0.693 0.107 0.204 0.138 0.724 0.871 0.726 Bits 24 to 31---> 0.783 0.751 0.325 0.010 0.185 0.123 0.457 0.752 KS test for the above 32 p values: 0.108 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-06_09:31, p-values for 5 runs: 0.9451, 0.8651, 0.1934, 0.1888, 0.7283 Rank test for binary matrices (31x31) for dh-ranFile-2017-02-06_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 5140 5134.0 0.007 1.282 r= 30 23142 23103.0 0.066 1.348 r= 31 11523 11551.5 0.070 1.418 chi-square = 1.418 with df = 3; p-value = 0.299 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-02-06_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 225 211.4 0.873 0.873 r= 30 5130 5134.0 0.003 0.876 r= 31 23231 23103.0 0.709 1.584 r= 32 11414 11551.5 1.637 3.222 chi-square = 3.222 with df = 3; p-value = 0.641 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-02-06_09:31 b-rank test for bits 1 to 8, p=0.48008 b-rank test for bits 2 to 9, p=0.11424 b-rank test for bits 3 to 10, p=0.61231 b-rank test for bits 4 to 11, p=0.70255 b-rank test for bits 5 to 12, p=0.81761 b-rank test for bits 6 to 13, p=0.29595 b-rank test for bits 7 to 14, p=0.97136 b-rank test for bits 8 to 15, p=0.42115 b-rank test for bits 9 to 16, p=0.90988 b-rank test for bits 10 to 17, p=0.36913 b-rank test for bits 11 to 18, p=0.33116 b-rank test for bits 12 to 19, p=0.31548 b-rank test for bits 13 to 20, p=0.96327 b-rank test for bits 14 to 21, p=0.42934 b-rank test for bits 15 to 22, p=0.29401 b-rank test for bits 16 to 23, p=0.33686 b-rank test for bits 17 to 24, p=0.50943 b-rank test for bits 18 to 25, p=0.15942 b-rank test for bits 19 to 26, p=0.23080 b-rank test for bits 20 to 27, p=0.06465 b-rank test for bits 21 to 28, p=0.13462 b-rank test for bits 22 to 29, p=0.12487 b-rank test for bits 23 to 30, p=0.01651 b-rank test for bits 24 to 31, p=0.37214 b-rank test for bits 25 to 32, p=0.98080 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 = 0.280822 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-06_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 142144 0.55 0.708255 2 141806 -0.24 0.404613 3 142613 1.64 0.949921 4 141861 -0.11 0.455047 5 141452 -1.07 0.142641 6 141824 -0.20 0.420987 7 141767 -0.33 0.369738 8 141675 -0.55 0.292018 9 142063 0.36 0.640218 10 142548 1.49 0.932179 11 141481 -1.00 0.158469 12 141618 -0.68 0.248038 13 141857 -0.12 0.451344 14 141667 -0.57 0.285632 15 142376 1.09 0.862221 16 141558 -0.82 0.205862 17 141881 -0.07 0.473613 18 142575 1.56 0.940063 19 141198 -1.66 0.048258 20 141231 -1.58 0.056496 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-02-06_09:31 Bits used No. missing words z-score p-value 23 to 32 142198 0.9954 0.840233 22 to 31 141720 -0.6529 0.256923 21 to 30 141551 -1.2356 0.108300 20 to 29 142062 0.5264 0.700712 19 to 28 142108 0.6851 0.753350 18 to 27 142364 1.5678 0.941539 17 to 26 141835 -0.2563 0.398856 16 to 25 141779 -0.4494 0.326567 15 to 24 141902 -0.0253 0.489918 14 to 23 142188 0.9609 0.831707 13 to 22 141938 0.0989 0.539376 12 to 21 142204 1.0161 0.845210 11 to 20 142249 1.1713 0.879256 10 to 19 141934 0.0851 0.533897 9 to 18 141790 -0.4115 0.340359 8 to 17 142040 0.4506 0.673856 7 to 16 141998 0.3058 0.620106 6 to 15 141763 -0.5046 0.306925 5 to 14 142043 0.4609 0.677576 4 to 13 142416 1.7471 0.959693 3 to 12 142030 0.4161 0.661333 2 to 11 141904 -0.0184 0.492668 1 to 10 142160 0.8644 0.806310 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-02-06_09:31 Bits used No. missing words z-score p-value 28 to 32 141504 -1.3740 0.084721 27 to 31 141308 -2.0384 0.020755 26 to 30 141797 -0.3808 0.351683 25 to 29 142172 0.8904 0.813376 24 to 28 141531 -1.2825 0.099838 23 to 27 141896 -0.0452 0.481979 22 to 26 141890 -0.0655 0.473878 21 to 25 142106 0.6667 0.747511 20 to 24 141973 0.2158 0.585440 19 to 23 141792 -0.3977 0.345415 18 to 22 141943 0.1141 0.545435 17 to 21 141686 -0.7571 0.224510 16 to 20 141994 0.2870 0.612950 15 to 19 141870 -0.1333 0.446969 14 to 18 141748 -0.5469 0.292230 13 to 17 142068 0.5379 0.704665 12 to 16 141529 -1.2893 0.098655 11 to 15 141864 -0.1537 0.438939 10 to 14 142061 0.5141 0.696421 9 to 13 142056 0.4972 0.690471 8 to 12 142792 2.9921 0.998615 7 to 11 142170 0.8836 0.811551 6 to 10 141625 -0.9638 0.167565 5 to 9 141797 -0.3808 0.351683 4 to 8 141866 -0.1469 0.441613 3 to 7 141757 -0.5164 0.302797 2 to 6 142026 0.3955 0.653760 1 to 5 141796 -0.3842 0.350426 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-02-06_09:31 Bits used No. missing words z-score p-value 31 to 32 141666 -0.7178 0.236444 30 to 31 142132 0.6568 0.744359 29 to 30 141980 0.2085 0.582568 28 to 29 141558 -1.0364 0.150014 27 to 28 141469 -1.2989 0.096988 26 to 27 142318 1.2055 0.885998 25 to 26 141910 0.0020 0.500789 24 to 25 141649 -0.7679 0.221263 23 to 24 142220 0.9164 0.820280 22 to 23 141608 -0.8889 0.187034 21 to 22 141675 -0.6912 0.244708 20 to 21 141882 -0.0806 0.467872 19 to 20 142475 1.6686 0.952406 18 to 19 141870 -0.1160 0.453819 17 to 18 142445 1.5801 0.942963 16 to 17 141488 -1.2429 0.106959 15 to 16 142153 0.7188 0.763865 14 to 15 141812 -0.2871 0.387014 13 to 14 141221 -2.0305 0.021154 12 to 13 141451 -1.3520 0.088187 11 to 12 141690 -0.6470 0.258819 10 to 11 141634 -0.8122 0.208343 9 to 10 142061 0.4474 0.672708 8 to 9 141307 -1.7768 0.037802 7 to 8 141839 -0.2075 0.417824 6 to 7 141723 -0.5496 0.291281 5 to 6 142181 0.8014 0.788546 4 to 5 141564 -1.0187 0.154179 3 to 4 141936 0.0787 0.531354 2 to 3 142056 0.4327 0.667367 1 to 2 142035 0.3707 0.644573 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-06_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2496.80 -0.045 0.481951 Test results for specific bytes for dh-ranFile-2017-02-06_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2484.94 -0.213 0.415653 2 to 9 2467.24 -0.463 0.321563 3 to 10 2550.97 0.721 0.764491 4 to 11 2644.60 2.045 0.979570 5 to 12 2355.47 -2.044 0.020476 6 to 13 2580.54 1.139 0.872642 7 to 14 2557.35 0.811 0.791342 8 to 15 2512.25 0.173 0.568743 9 to 16 2467.67 -0.457 0.323768 10 to 17 2347.80 -2.152 0.015684 11 to 18 2426.88 -1.034 0.150538 12 to 19 2561.70 0.873 0.808533 13 to 20 2572.97 1.032 0.848943 14 to 21 2472.52 -0.389 0.348777 15 to 22 2458.24 -0.591 0.277398 16 to 23 2603.10 1.458 0.927588 17 to 24 2468.65 -0.443 0.328741 18 to 25 2569.45 0.982 0.836977 19 to 26 2588.31 1.249 0.894141 20 to 27 2497.38 -0.037 0.485221 21 to 28 2556.78 0.803 0.789022 22 to 29 2545.66 0.646 0.740779 23 to 30 2533.08 0.468 0.680048 24 to 31 2433.79 -0.936 0.174535 25 to 32 2547.69 0.674 0.749973 CDPARK for dh-ranFile-2017-02-06_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 3477 -2.1005 0.017844 3528 0.2283 0.590298 3537 0.6393 0.738676 3527 0.1826 0.572463 3513 -0.4566 0.323972 3547 1.0959 0.863437 3486 -1.6895 0.045562 3498 -1.1416 0.126820 3519 -0.1826 0.427537 3528 0.2283 0.590298 Square side=100, avg. no. parked=3516.00 sample std.=21.39 p-value of the KSTEST for those 10 p-values: 0.579508 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-06_09:31 0.5815,0.0719,0.5593,0.8070,0.1622,0.5115,0.9129,0.0709,0.8225,0.8587, The KS test for those 10 p-values: 0.694325 The 3DSPHERES test for dh-ranFile-2017-02-06_09:31 sample no r^3 equiv. uni. 1 3.729 0.116894 2 40.082 0.737125 3 49.799 0.809857 4 19.551 0.478837 5 17.519 0.442314 6 127.289 0.985635 7 43.732 0.767241 8 62.414 0.875126 9 27.389 0.598669 10 21.186 0.506489 11 86.565 0.944173 12 8.159 0.238132 13 20.128 0.488761 14 4.139 0.128865 15 4.590 0.141870 16 161.656 0.995431 17 5.415 0.165139 18 82.622 0.936331 19 15.885 0.411107 20 8.821 0.254748 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.430601 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-06_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 2.0 -0.4 0.0 -0.1 0.8 -0.1 0.6 1.2 0.9 -0.6 1.0 0.2 1.3 0.0 -1.2 1.8 -3.0 0.5 -1.6 -1.1 -1.1 0.0 0.8 1.0 0.2 1.1 -1.0 0.7 0.2 1.0 -0.1 1.3 -0.2 0.6 1.4 -1.0 -1.2 -0.7 0.1 3.0 0.8 Chi-square with 42 degrees of freedom:52.826853 z-score=1.181307, p-value=0.877818 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-02-06_09:31 Test no p-value 1 0.181136 2 0.623034 3 0.762918 4 0.130210 5 0.013888 6 0.597544 7 0.911736 8 0.013089 9 0.226311 10 0.214461 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.121493 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-06_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 66750 0.10 66839 0.45 3 25000.00 24815 1.37 24923 0.24 4 6666.67 6754 1.14 6609 0.50 5 1388.89 1400 0.09 1378 0.09 6 238.10 235 0.04 214 2.44 7 34.72 41 1.14 32 0.21 8 4.96 4 0.19 4 0.19 p=0.33252 p=0.33742 Number of rngs required: 687506, p-value: 0.149 RESULTS OF CRAPS TEST for dh-ranFile-2017-02-06_09:31 No. of wins: Observed Expected 98669 98585.9 z-score= 0.372, pvalue=0.64500 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66231 66666.7 2.847 2.847 2 37687 37654.3 0.028 2.875 3 27180 26954.7 1.883 4.758 4 19399 19313.5 0.379 5.137 5 13871 13851.4 0.028 5.165 6 9759 9943.5 3.425 8.590 7 7201 7145.0 0.439 9.028 8 5170 5139.1 0.186 9.214 9 3729 3699.9 0.229 9.444 10 2719 2666.3 1.042 10.485 11 1929 1923.3 0.017 10.502 12 1417 1388.7 0.575 11.077 13 954 1003.7 2.462 13.540 14 728 726.1 0.005 13.544 15 585 525.8 6.657 20.201 16 416 381.2 3.186 23.387 17 276 276.5 0.001 23.389 18 197 200.8 0.073 23.462 19 143 146.0 0.061 23.523 20 109 106.2 0.073 23.596 21 300 287.1 0.578 24.174 Chisq= 24.17 for 20 degrees of freedom, p= 0.76512 SUMMARY of craptest p-value for no. of wins: 0.645000 p-value for throws/game: 0.765123 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-06_09:31 No. of wins: Observed Expected 99008 98585.9 z-score= 1.888, pvalue=0.97049 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67070 66666.7 2.440 2.440 2 37484 37654.3 0.770 3.211 3 26879 26954.7 0.213 3.423 4 19069 19313.5 3.094 6.518 5 13986 13851.4 1.308 7.825 6 9701 9943.5 5.916 13.741 7 7094 7145.0 0.364 14.106 8 5236 5139.1 1.828 15.934 9 3766 3699.9 1.182 17.116 10 2689 2666.3 0.193 17.309 11 2022 1923.3 5.062 22.371 12 1364 1388.7 0.441 22.812 13 1015 1003.7 0.127 22.939 14 716 726.1 0.142 23.081 15 520 525.8 0.065 23.145 16 398 381.2 0.745 23.890 17 268 276.5 0.264 24.154 18 187 200.8 0.952 25.106 19 147 146.0 0.007 25.113 20 120 106.2 1.789 26.902 21 269 287.1 1.143 28.045 Chisq= 28.05 for 20 degrees of freedom, p= 0.89167 SUMMARY of craptest p-value for no. of wins: 0.970491 p-value for throws/game: 0.891667 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0101,0.0131,0.0139,0.0157,0.0165,0.0178,0.0205,0.0208,0.0212,0.0378, 0.0456,0.0483,0.0565,0.0646,0.0709,0.0719,0.0847,0.0882,0.0970,0.0987, 0.0998,0.1070,0.1070,0.1080,0.1083,0.1142,0.1169,0.1193,0.1215,0.1225, 0.1249,0.1268,0.1289,0.1302,0.1346,0.1381,0.1419,0.1426,0.1492,0.1500, 0.1505,0.1542,0.1585,0.1594,0.1622,0.1651,0.1676,0.1745,0.1811,0.1844, 0.1845,0.1870,0.1888,0.1934,0.1945,0.2040,0.2059,0.2083,0.2145,0.2213, 0.2245,0.2261,0.2263,0.2308,0.2364,0.2381,0.2447,0.2480,0.2543,0.2547, 0.2569,0.2588,0.2774,0.2808,0.2856,0.2913,0.2920,0.2922,0.2940,0.2959, 0.2987,0.3028,0.3069,0.3155,0.3216,0.3238,0.3240,0.3253,0.3266,0.3287, 0.3312,0.3325,0.3369,0.3374,0.3404,0.3454,0.3488,0.3504,0.3517,0.3517, 0.3672,0.3691,0.3697,0.3721,0.3753,0.3770,0.3870,0.3897,0.3938,0.3989, 0.4046,0.4111,0.4157,0.4178,0.4210,0.4211,0.4249,0.4275,0.4293,0.4306, 0.4326,0.4389,0.4416,0.4423,0.4470,0.4513,0.4538,0.4550,0.4567,0.4679, 0.4736,0.4739,0.4788,0.4801,0.4820,0.4820,0.4852,0.4888,0.4899,0.4927, 0.5008,0.5065,0.5094,0.5115,0.5314,0.5339,0.5394,0.5454,0.5593,0.5612, 0.5687,0.5725,0.5753,0.5795,0.5815,0.5826,0.5854,0.5903,0.5903,0.5975, 0.5987,0.6123,0.6130,0.6160,0.6201,0.6230,0.6258,0.6402,0.6413,0.6446, 0.6450,0.6538,0.6613,0.6656,0.6674,0.6727,0.6739,0.6776,0.6800,0.6872, 0.6905,0.6929,0.6936,0.6943,0.6964,0.7007,0.7025,0.7047,0.7083,0.7091, 0.7243,0.7258,0.7283,0.7358,0.7371,0.7387,0.7408,0.7444,0.7475,0.7500, 0.7514,0.7518,0.7533,0.7545,0.7629,0.7639,0.7645,0.7651,0.7672,0.7832, 0.7885,0.7890,0.7913,0.8063,0.8070,0.8085,0.8099,0.8116,0.8134,0.8176, 0.8203,0.8225,0.8317,0.8370,0.8402,0.8452,0.8489,0.8489,0.8587,0.8622, 0.8634,0.8651,0.8708,0.8726,0.8751,0.8778,0.8793,0.8849,0.8860,0.8917, 0.8941,0.9099,0.9117,0.9119,0.9129,0.9144,0.9276,0.9322,0.9363,0.9401, 0.9415,0.9430,0.9442,0.9451,0.9499,0.9524,0.9541,0.9597,0.9633,0.9668, 0.9705,0.9714,0.9796,0.9808,0.9817,0.9856,0.9933,0.9954,0.9986, Overall p-value after applying KStest on 269 p-values = 0.973266 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.