RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-17_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.38 33.9334 0.991436 2 to 25 15.67 14.2750 0.352452 3 to 26 15.70 15.8056 0.462347 4 to 27 15.63 15.7611 0.459169 5 to 28 15.65 13.7363 0.314328 6 to 29 15.63 16.1863 0.489328 7 to 30 15.87 14.8693 0.395106 8 to 31 15.85 19.8463 0.717835 9 to 32 15.48 21.3596 0.789383 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.390002 Tough bday spacings test for dh-ranFile-2017-01-17_11:31: 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 54 63 96 86 85 49 36 11 5 9 (O-E)^2/E 1.1 8.2 1.4 0.0 1.4 0.6 0.2 1.3 1.0 0.4 6.0 Birthday Spacings: Sum(O-E)^2/E= 21.673, p= 0.983 RESULTS OF GCD FOR dh-ranFile-2017-01-17_11:31 Euclid's algorithm: p-value, steps to gcd: 0.526157 p-value, dist. of gcd's: 0.227973 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-17_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.618 0.352 0.510 0.115 0.942 0.120 0.345 0.376 Bits 8 to 15---> 0.649 0.470 0.542 0.755 0.801 0.842 0.414 0.205 Bits 16 to 23---> 0.179 0.305 0.205 0.457 0.951 0.372 0.298 0.083 Bits 24 to 31---> 0.866 0.049 0.114 0.338 0.913 0.952 0.936 0.262 KS test for the above 32 p values: 0.332 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-17_11:31, p-values for 5 runs: 0.4485, 0.5552, 0.4481, 0.8023, 0.2860 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-17_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 236 211.4 2.858 2.858 r= 29 5027 5134.0 2.230 5.089 r= 30 23057 23103.0 0.092 5.180 r= 31 11680 11551.5 1.429 6.609 chi-square = 6.609 with df = 3; p-value = 0.915 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-17_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 189 211.4 2.377 2.377 r= 30 5158 5134.0 0.112 2.489 r= 31 23273 23103.0 1.250 3.739 r= 32 11380 11551.5 2.547 6.286 chi-square = 6.286 with df = 3; p-value = 0.902 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-17_11:31 b-rank test for bits 1 to 8, p=0.27198 b-rank test for bits 2 to 9, p=0.04688 b-rank test for bits 3 to 10, p=0.32344 b-rank test for bits 4 to 11, p=0.36402 b-rank test for bits 5 to 12, p=0.83623 b-rank test for bits 6 to 13, p=0.28094 b-rank test for bits 7 to 14, p=0.42175 b-rank test for bits 8 to 15, p=0.31335 b-rank test for bits 9 to 16, p=0.89276 b-rank test for bits 10 to 17, p=0.73996 b-rank test for bits 11 to 18, p=0.81717 b-rank test for bits 12 to 19, p=0.10521 b-rank test for bits 13 to 20, p=0.45258 b-rank test for bits 14 to 21, p=0.10339 b-rank test for bits 15 to 22, p=0.16711 b-rank test for bits 16 to 23, p=0.38298 b-rank test for bits 17 to 24, p=0.94297 b-rank test for bits 18 to 25, p=0.63275 b-rank test for bits 19 to 26, p=0.92154 b-rank test for bits 20 to 27, p=0.52537 b-rank test for bits 21 to 28, p=0.18763 b-rank test for bits 22 to 29, p=0.99243 b-rank test for bits 23 to 30, p=0.51857 b-rank test for bits 24 to 31, p=0.22961 b-rank test for bits 25 to 32, p=0.89919 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 = 0.844952 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-17_11:31 (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 141990 0.19 0.574750 2 142009 0.23 0.592070 3 142431 1.22 0.888550 4 141780 -0.30 0.381260 5 142001 0.21 0.584798 6 141868 -0.10 0.461536 7 141523 -0.90 0.183358 8 141166 -1.74 0.041215 9 142301 0.92 0.819935 10 142161 0.59 0.721739 11 142226 0.74 0.770315 12 141887 -0.05 0.479196 13 141920 0.02 0.509945 14 141850 -0.14 0.444875 15 143242 3.11 0.999076 16 142385 1.11 0.866797 17 141787 -0.29 0.387509 18 142699 1.85 0.967483 19 141477 -1.01 0.156220 20 141944 0.08 0.532281 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-17_11:31 Bits used No. missing words z-score p-value 23 to 32 141762 -0.5080 0.305715 22 to 31 141441 -1.6149 0.053163 21 to 30 141920 0.0368 0.514675 20 to 29 141955 0.1575 0.562568 19 to 28 142180 0.9333 0.824679 18 to 27 142049 0.4816 0.684962 17 to 26 141873 -0.1253 0.450153 16 to 25 141526 -1.3218 0.093113 15 to 24 141829 -0.2770 0.390890 14 to 23 142244 1.1540 0.875757 13 to 22 142013 0.3575 0.639635 12 to 21 142241 1.1437 0.873624 11 to 20 141913 0.0127 0.505049 10 to 19 141942 0.1127 0.544848 9 to 18 142347 1.5092 0.934377 8 to 17 142313 1.3920 0.918034 7 to 16 141901 -0.0287 0.488542 6 to 15 141532 -1.3011 0.096606 5 to 14 142003 0.3230 0.626652 4 to 13 142444 1.8437 0.967386 3 to 12 142192 0.9747 0.835151 2 to 11 142113 0.7023 0.758757 1 to 10 141841 -0.2356 0.406864 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-17_11:31 Bits used No. missing words z-score p-value 28 to 32 141469 -1.4926 0.067765 27 to 31 142068 0.5379 0.704665 26 to 30 141562 -1.1774 0.119520 25 to 29 142471 1.9040 0.971543 24 to 28 141577 -1.1265 0.129968 23 to 27 141724 -0.6282 0.264924 22 to 26 142179 0.9141 0.819677 21 to 25 142255 1.1718 0.879354 20 to 24 141948 0.1311 0.552146 19 to 23 141918 0.0294 0.511723 18 to 22 142115 0.6972 0.757157 17 to 21 141368 -1.8350 0.033252 16 to 20 142016 0.3616 0.641172 15 to 19 142474 1.9141 0.972199 14 to 18 141987 0.2633 0.603836 13 to 17 141582 -1.1096 0.133587 12 to 16 142126 0.7345 0.768670 11 to 15 141863 -0.1571 0.437602 10 to 14 141823 -0.2926 0.384897 9 to 13 141351 -1.8926 0.029203 8 to 12 141825 -0.2859 0.387491 7 to 11 142035 0.4260 0.664946 6 to 10 142042 0.4497 0.673547 5 to 9 141330 -1.9638 0.024775 4 to 8 141802 -0.3638 0.357992 3 to 7 142110 0.6802 0.751823 2 to 6 141881 -0.0960 0.461747 1 to 5 141654 -0.8655 0.193375 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-17_11:31 Bits used No. missing words z-score p-value 31 to 32 141882 -0.0806 0.467872 30 to 31 142105 0.5772 0.718097 29 to 30 141918 0.0256 0.510202 28 to 29 141976 0.1967 0.577956 27 to 28 141935 0.0757 0.530180 26 to 27 141783 -0.3727 0.354703 25 to 26 141855 -0.1603 0.436336 24 to 25 141436 -1.3963 0.081319 23 to 24 141794 -0.3402 0.366851 22 to 23 142660 2.2144 0.986598 21 to 22 142114 0.6037 0.726994 20 to 21 141383 -1.5526 0.060260 19 to 20 142218 0.9105 0.818729 18 to 19 141906 -0.0098 0.496081 17 to 18 141920 0.0315 0.512555 16 to 17 141657 -0.7443 0.228337 15 to 16 141671 -0.7030 0.241016 14 to 15 142101 0.5654 0.714099 13 to 14 142255 1.0197 0.846059 12 to 13 141975 0.1937 0.576801 11 to 12 142036 0.3737 0.645671 10 to 11 141381 -1.5585 0.059558 9 to 10 142094 0.5447 0.707037 8 to 9 141780 -0.3815 0.351415 7 to 8 141957 0.1406 0.555915 6 to 7 142045 0.4002 0.655498 5 to 6 142076 0.4917 0.688517 4 to 5 141593 -0.9331 0.175377 3 to 4 142188 0.8220 0.794472 2 to 3 141654 -0.7532 0.225669 1 to 2 141471 -1.2930 0.098004 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-17_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2428.27 -1.014 0.155208 Test results for specific bytes for dh-ranFile-2017-01-17_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2423.70 -1.079 0.140299 2 to 9 2597.31 1.376 0.915625 3 to 10 2519.58 0.277 0.609068 4 to 11 2582.96 1.173 0.879662 5 to 12 2542.76 0.605 0.727333 6 to 13 2517.41 0.246 0.597237 7 to 14 2596.39 1.363 0.913588 8 to 15 2476.92 -0.326 0.372061 9 to 16 2543.44 0.614 0.730520 10 to 17 2502.81 0.040 0.515844 11 to 18 2443.71 -0.796 0.212993 12 to 19 2446.61 -0.755 0.225102 13 to 20 2473.77 -0.371 0.355321 14 to 21 2593.65 1.324 0.907317 15 to 22 2472.42 -0.390 0.348235 16 to 23 2459.15 -0.578 0.281718 17 to 24 2469.20 -0.436 0.331586 18 to 25 2590.68 1.282 0.900141 19 to 26 2517.89 0.253 0.599852 20 to 27 2514.89 0.211 0.583377 21 to 28 2539.06 0.552 0.709651 22 to 29 2464.15 -0.507 0.306097 23 to 30 2543.51 0.615 0.730818 24 to 31 2358.09 -2.007 0.022381 25 to 32 2565.95 0.933 0.824509 CDPARK for dh-ranFile-2017-01-17_11:31: 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 3519 -0.1826 0.427537 3517 -0.2740 0.392053 3511 -0.5479 0.291865 3524 0.0457 0.518210 3488 -1.5982 0.055002 3527 0.1826 0.572463 3539 0.7306 0.767486 3503 -0.9132 0.180558 3499 -1.0959 0.136563 3585 2.8311 0.997680 Square side=100, avg. no. parked=3521.20 sample std.=25.46 p-value of the KSTEST for those 10 p-values: 0.590957 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-17_11:31 0.6267,0.3772,0.9447,0.0168,0.7992,0.7812,0.4130,0.9385,0.1329,0.3640, The KS test for those 10 p-values: 0.829383 The 3DSPHERES test for dh-ranFile-2017-01-17_11:31 sample no r^3 equiv. uni. 1 7.870 0.230735 2 37.960 0.717856 3 12.908 0.349670 4 22.656 0.530081 5 16.829 0.429343 6 70.485 0.904584 7 9.439 0.269946 8 33.309 0.670542 9 0.210 0.006987 10 33.055 0.667742 11 96.324 0.959676 12 19.985 0.486325 13 106.875 0.971632 14 14.658 0.386513 15 25.280 0.569433 16 10.242 0.289237 17 10.749 0.301143 18 26.617 0.588203 19 10.532 0.296071 20 12.973 0.351066 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.548954 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-17_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 1.8 -0.1 0.8 0.9 -0.4 2.2 0.0 0.5 -0.3 0.5 1.8 -1.0 1.2 -0.9 -0.2 0.2 0.3 -0.1 0.5 -0.3 -0.5 0.5 0.7 -1.2 -1.2 -0.0 -1.3 0.3 -2.5 -0.9 0.1 -0.3 0.5 -0.1 -0.8 -0.5 0.2 0.9 1.0 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:36.996512 z-score=-0.545925, p-value=0.310060 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-17_11:31 Test no p-value 1 0.800444 2 0.090612 3 0.226954 4 0.073689 5 0.061448 6 0.151262 7 0.201220 8 0.662075 9 0.385949 10 0.025782 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.010680 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-17_11:31: (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 66626 0.02 66377 1.26 3 25000.00 25004 0.00 25221 1.95 4 6666.67 6699 0.16 6736 0.72 5 1388.89 1399 0.07 1413 0.42 6 238.10 226 0.61 215 2.24 7 34.72 38 0.31 30 0.64 8 4.96 7 0.84 7 0.84 p=0.08207 p=0.76718 Number of rngs required: 688703, p-value: 0.635 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-17_11:31 No. of wins: Observed Expected 98808 98585.9 z-score= 0.994, pvalue=0.83978 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66676 66666.7 0.001 0.001 2 37784 37654.3 0.447 0.448 3 26796 26954.7 0.935 1.383 4 19399 19313.5 0.379 1.762 5 13652 13851.4 2.871 4.633 6 10057 9943.5 1.295 5.927 7 7202 7145.0 0.454 6.381 8 5043 5139.1 1.796 8.177 9 3674 3699.9 0.181 8.358 10 2678 2666.3 0.051 8.410 11 1939 1923.3 0.128 8.537 12 1451 1388.7 2.791 11.329 13 1003 1003.7 0.001 11.329 14 748 726.1 0.658 11.987 15 528 525.8 0.009 11.996 16 383 381.2 0.009 12.005 17 277 276.5 0.001 12.006 18 181 200.8 1.958 13.964 19 164 146.0 2.223 16.187 20 97 106.2 0.800 16.987 21 268 287.1 1.272 18.259 Chisq= 18.26 for 20 degrees of freedom, p= 0.42965 SUMMARY of craptest p-value for no. of wins: 0.839778 p-value for throws/game: 0.429648 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-17_11:31 No. of wins: Observed Expected 98504 98585.9 z-score=-0.366, pvalue=0.35714 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66532 66666.7 0.272 0.272 2 37815 37654.3 0.686 0.958 3 26841 26954.7 0.480 1.438 4 19301 19313.5 0.008 1.446 5 13946 13851.4 0.646 2.091 6 10045 9943.5 1.035 3.127 7 7154 7145.0 0.011 3.138 8 5034 5139.1 2.148 5.286 9 3683 3699.9 0.077 5.363 10 2657 2666.3 0.032 5.395 11 1894 1923.3 0.447 5.843 12 1401 1388.7 0.108 5.951 13 997 1003.7 0.045 5.996 14 782 726.1 4.297 10.293 15 562 525.8 2.487 12.780 16 379 381.2 0.012 12.792 17 263 276.5 0.663 13.455 18 184 200.8 1.410 14.865 19 142 146.0 0.109 14.974 20 92 106.2 1.902 16.877 21 296 287.1 0.275 17.152 Chisq= 17.15 for 20 degrees of freedom, p= 0.35690 SUMMARY of craptest p-value for no. of wins: 0.357138 p-value for throws/game: 0.356900 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0070,0.0107,0.0168,0.0224,0.0248,0.0258,0.0292,0.0333,0.0412,0.0469, 0.0495,0.0532,0.0550,0.0596,0.0603,0.0614,0.0678,0.0737,0.0813,0.0821, 0.0831,0.0906,0.0931,0.0966,0.0980,0.1034,0.1052,0.1144,0.1147,0.1195, 0.1195,0.1300,0.1329,0.1336,0.1366,0.1403,0.1513,0.1552,0.1562,0.1671, 0.1754,0.1788,0.1806,0.1834,0.1876,0.1934,0.2012,0.2048,0.2053,0.2130, 0.2251,0.2257,0.2270,0.2280,0.2283,0.2296,0.2307,0.2410,0.2623,0.2649, 0.2699,0.2720,0.2809,0.2817,0.2860,0.2892,0.2919,0.2961,0.2983,0.3011, 0.3046,0.3057,0.3061,0.3101,0.3133,0.3143,0.3234,0.3316,0.3322,0.3382, 0.3447,0.3482,0.3497,0.3511,0.3514,0.3523,0.3525,0.3547,0.3553,0.3569, 0.3571,0.3580,0.3640,0.3640,0.3669,0.3721,0.3723,0.3761,0.3772,0.3813, 0.3830,0.3849,0.3859,0.3865,0.3875,0.3875,0.3900,0.3909,0.3921,0.3951, 0.4069,0.4130,0.4137,0.4218,0.4275,0.4293,0.4296,0.4363,0.4376,0.4449, 0.4481,0.4485,0.4502,0.4526,0.4567,0.4592,0.4615,0.4617,0.4623,0.4679, 0.4696,0.4792,0.4863,0.4885,0.4893,0.4961,0.5050,0.5099,0.5100,0.5102, 0.5117,0.5126,0.5147,0.5158,0.5182,0.5186,0.5254,0.5262,0.5301,0.5302, 0.5323,0.5417,0.5448,0.5490,0.5521,0.5552,0.5559,0.5626,0.5694,0.5725, 0.5748,0.5768,0.5780,0.5834,0.5848,0.5882,0.5910,0.5921,0.5972,0.5999, 0.6038,0.6091,0.6179,0.6267,0.6267,0.6328,0.6351,0.6396,0.6412,0.6457, 0.6495,0.6555,0.6621,0.6649,0.6677,0.6705,0.6735,0.6850,0.6885,0.7047, 0.7070,0.7097,0.7141,0.7178,0.7179,0.7181,0.7217,0.7270,0.7273,0.7305, 0.7308,0.7400,0.7518,0.7553,0.7572,0.7588,0.7672,0.7675,0.7687,0.7703, 0.7812,0.7894,0.7945,0.7992,0.8004,0.8014,0.8023,0.8172,0.8187,0.8197, 0.8199,0.8245,0.8247,0.8294,0.8352,0.8362,0.8398,0.8418,0.8450,0.8461, 0.8660,0.8668,0.8736,0.8758,0.8794,0.8797,0.8886,0.8928,0.8992,0.9001, 0.9015,0.9046,0.9073,0.9127,0.9136,0.9146,0.9156,0.9180,0.9215,0.9344, 0.9362,0.9385,0.9425,0.9430,0.9447,0.9510,0.9522,0.9597,0.9674,0.9675, 0.9715,0.9716,0.9722,0.9831,0.9866,0.9914,0.9924,0.9977,0.9991, Overall p-value after applying KStest on 269 p-values = 0.686606 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.