RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-25_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 15.78 18.6924 0.653529 2 to 25 15.55 30.8265 0.979035 3 to 26 15.71 17.7708 0.596566 4 to 27 15.71 13.1417 0.273347 5 to 28 15.75 9.0766 0.062173 6 to 29 15.46 17.1398 0.555068 7 to 30 15.62 14.4448 0.364594 8 to 31 15.63 18.5982 0.647925 9 to 32 15.90 15.4034 0.433549 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.819426 Tough bday spacings test for dh-ranFile-2016-05-25_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 7 39 71 92 101 75 64 30 12 7 2 (O-E)^2/E 0.5 0.2 0.1 0.3 0.1 0.1 2.7 0.0 0.6 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 5.654, p= 0.157 RESULTS OF GCD FOR dh-ranFile-2016-05-25_12:31 Euclid's algorithm: p-value, steps to gcd: 0.549553 p-value, dist. of gcd's: 0.501309 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-25_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.187 0.625 0.743 0.183 0.121 0.539 0.748 0.313 Bits 8 to 15---> 0.190 0.872 0.130 0.655 0.762 0.870 0.522 0.397 Bits 16 to 23---> 0.653 0.662 0.576 0.557 0.231 0.953 0.642 0.841 Bits 24 to 31---> 0.554 0.940 0.717 0.813 0.786 0.567 0.955 0.757 KS test for the above 32 p values: 0.937 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-25_12:31, p-values for 5 runs: 0.0317, 0.6995, 0.3458, 0.0944, 0.3118 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-25_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 217 211.4 0.147 0.147 r= 29 5175 5134.0 0.327 0.475 r= 30 23150 23103.0 0.095 0.570 r= 31 11458 11551.5 0.757 1.327 chi-square = 1.327 with df = 3; p-value = 0.277 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-25_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5251 5134.0 2.666 3.790 r= 31 23097 23103.0 0.002 3.792 r= 32 11456 11551.5 0.790 4.582 chi-square = 4.582 with df = 3; p-value = 0.795 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-25_12:31 b-rank test for bits 1 to 8, p=0.59950 b-rank test for bits 2 to 9, p=0.75622 b-rank test for bits 3 to 10, p=0.96120 b-rank test for bits 4 to 11, p=0.86672 b-rank test for bits 5 to 12, p=0.25136 b-rank test for bits 6 to 13, p=0.69913 b-rank test for bits 7 to 14, p=0.37968 b-rank test for bits 8 to 15, p=0.72861 b-rank test for bits 9 to 16, p=0.29910 b-rank test for bits 10 to 17, p=0.05022 b-rank test for bits 11 to 18, p=0.20434 b-rank test for bits 12 to 19, p=0.40996 b-rank test for bits 13 to 20, p=0.52126 b-rank test for bits 14 to 21, p=0.60151 b-rank test for bits 15 to 22, p=0.23080 b-rank test for bits 16 to 23, p=0.21550 b-rank test for bits 17 to 24, p=0.39122 b-rank test for bits 18 to 25, p=0.03682 b-rank test for bits 19 to 26, p=0.29197 b-rank test for bits 20 to 27, p=0.67120 b-rank test for bits 21 to 28, p=0.92261 b-rank test for bits 22 to 29, p=0.37395 b-rank test for bits 23 to 30, p=0.68527 b-rank test for bits 24 to 31, p=0.61085 b-rank test for bits 25 to 32, p=0.66656 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 = 0.831592 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-25_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 142113 0.48 0.682915 2 141958 0.11 0.545268 3 141999 0.21 0.582975 4 142031 0.28 0.611900 5 141848 -0.14 0.443029 6 141401 -1.19 0.117478 7 141339 -1.33 0.091340 8 141912 0.01 0.502489 9 141902 -0.02 0.493168 10 141396 -1.20 0.115192 11 142220 0.73 0.766039 12 141800 -0.26 0.399190 13 141771 -0.32 0.373272 14 141789 -0.28 0.389300 15 142087 0.42 0.660972 16 141853 -0.13 0.447646 17 141653 -0.60 0.274619 18 141554 -0.83 0.203210 19 141994 0.20 0.578410 20 141640 -0.63 0.264584 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-25_12:31 Bits used No. missing words z-score p-value 23 to 32 142246 1.1609 0.877165 22 to 31 142009 0.3437 0.634460 21 to 30 142238 1.1333 0.871465 20 to 29 141862 -0.1632 0.435178 19 to 28 142041 0.4540 0.675098 18 to 27 142189 0.9644 0.832572 17 to 26 142112 0.6989 0.757681 16 to 25 141429 -1.6563 0.048830 15 to 24 142278 1.2713 0.898185 14 to 23 141845 -0.2218 0.412224 13 to 22 141553 -1.2287 0.109588 12 to 21 141594 -1.0873 0.138442 11 to 20 141565 -1.1873 0.117546 10 to 19 141854 -0.1908 0.424344 9 to 18 141784 -0.4322 0.332808 8 to 17 141857 -0.1804 0.428400 7 to 16 142330 1.4506 0.926552 6 to 15 141892 -0.0598 0.476174 5 to 14 141636 -0.9425 0.172964 4 to 13 141958 0.1678 0.566641 3 to 12 141985 0.2609 0.602927 2 to 11 141886 -0.0804 0.467940 1 to 10 141801 -0.3736 0.354369 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-25_12:31 Bits used No. missing words z-score p-value 28 to 32 141748 -0.5469 0.292230 27 to 31 141955 0.1548 0.561516 26 to 30 142172 0.8904 0.813376 25 to 29 141879 -0.1028 0.459056 24 to 28 141661 -0.8418 0.199951 23 to 27 141613 -1.0045 0.157567 22 to 26 141578 -1.1232 0.130686 21 to 25 142023 0.3853 0.650001 20 to 24 141859 -0.1706 0.432265 19 to 23 141914 0.0158 0.506315 18 to 22 141815 -0.3198 0.374574 17 to 21 142008 0.3345 0.630989 16 to 20 141704 -0.6960 0.243204 15 to 19 141979 0.2362 0.593349 14 to 18 141947 0.1277 0.550805 13 to 17 141685 -0.7604 0.223496 12 to 16 142223 1.0633 0.856174 11 to 15 141935 0.0870 0.534671 10 to 14 141829 -0.2723 0.392694 9 to 13 141889 -0.0689 0.472529 8 to 12 142366 1.5480 0.939193 7 to 11 141687 -0.7537 0.225526 6 to 10 142269 1.2192 0.888620 5 to 9 141648 -0.8859 0.187845 4 to 8 142102 0.6531 0.743160 3 to 7 141849 -0.2045 0.418978 2 to 6 141738 -0.5808 0.280695 1 to 5 141394 -1.7469 0.040329 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-25_12:31 Bits used No. missing words z-score p-value 31 to 32 142052 0.4209 0.663070 30 to 31 142154 0.7217 0.764773 29 to 30 141732 -0.5231 0.300453 28 to 29 141645 -0.7797 0.217774 27 to 28 141606 -0.8948 0.185453 26 to 27 142009 0.2940 0.615626 25 to 26 142530 1.8309 0.966441 24 to 25 141595 -0.9272 0.176904 23 to 24 141655 -0.7502 0.226556 22 to 23 142364 1.3412 0.910074 21 to 22 141270 -1.8859 0.029652 20 to 21 141887 -0.0659 0.473741 19 to 20 142177 0.7896 0.785116 18 to 19 142230 0.9459 0.827908 17 to 18 142144 0.6922 0.755607 16 to 17 141118 -2.3343 0.009790 15 to 16 141809 -0.2960 0.383631 14 to 15 142121 0.6244 0.733816 13 to 14 141682 -0.6706 0.251241 12 to 13 141810 -0.2930 0.384758 11 to 12 141556 -1.0423 0.148643 10 to 11 141841 -0.2016 0.420129 9 to 10 141946 0.1082 0.543070 8 to 9 141416 -1.4553 0.072800 7 to 8 141984 0.2203 0.587168 6 to 7 141640 -0.7945 0.213457 5 to 6 141721 -0.5555 0.289261 4 to 5 142181 0.8014 0.788546 3 to 4 141418 -1.4494 0.073620 2 to 3 141698 -0.6234 0.266513 1 to 2 141757 -0.4494 0.326589 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-25_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2502.32 0.033 0.513102 Test results for specific bytes for dh-ranFile-2016-05-25_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2608.05 1.528 0.936755 2 to 9 2487.14 -0.182 0.427824 3 to 10 2509.50 0.134 0.553449 4 to 11 2543.55 0.616 0.730999 5 to 12 2612.12 1.586 0.943579 6 to 13 2482.08 -0.253 0.399947 7 to 14 2561.30 0.867 0.807022 8 to 15 2471.76 -0.399 0.344793 9 to 16 2553.78 0.761 0.776552 10 to 17 2449.93 -0.708 0.239436 11 to 18 2544.38 0.628 0.734855 12 to 19 2591.50 1.294 0.902171 13 to 20 2426.46 -1.040 0.149183 14 to 21 2413.10 -1.229 0.109552 15 to 22 2434.51 -0.926 0.177176 16 to 23 2533.09 0.468 0.680088 17 to 24 2588.00 1.244 0.893338 18 to 25 2497.76 -0.032 0.487379 19 to 26 2560.28 0.853 0.803041 20 to 27 2549.29 0.697 0.757108 21 to 28 2607.80 1.525 0.936314 22 to 29 2558.25 0.824 0.794981 23 to 30 2464.40 -0.504 0.307298 24 to 31 2586.27 1.220 0.888779 25 to 32 2546.17 0.653 0.743086 CDPARK for dh-ranFile-2016-05-25_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 3529 0.2740 0.607947 3538 0.6849 0.753306 3523 0.0000 0.500000 3549 1.1872 0.882429 3540 0.7763 0.781201 3549 1.1872 0.882429 3516 -0.3196 0.374623 3513 -0.4566 0.323972 3529 0.2740 0.607947 3521 -0.0913 0.463617 Square side=100, avg. no. parked=3530.70 sample std.=12.24 p-value of the KSTEST for those 10 p-values: 0.230021 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-25_12:31 0.0145,0.6731,0.5173,0.7683,0.6578,0.0060,0.4495,0.1392,0.1002,0.0170, The KS test for those 10 p-values: 0.022395 The 3DSPHERES test for dh-ranFile-2016-05-25_12:31 sample no r^3 equiv. uni. 1 25.752 0.576163 2 33.360 0.671094 3 20.216 0.490271 4 15.546 0.404407 5 9.753 0.277556 6 18.672 0.463345 7 44.467 0.772867 8 19.430 0.476739 9 45.812 0.782828 10 61.558 0.871513 11 31.665 0.651979 12 29.460 0.625440 13 25.565 0.573515 14 63.630 0.880090 15 52.681 0.827270 16 29.440 0.625191 17 1.432 0.046625 18 5.756 0.174591 19 16.699 0.426856 20 2.839 0.090293 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.501010 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-25_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 -1.1 -0.7 1.0 0.0 1.9 0.6 -0.9 -0.6 1.8 0.8 1.0 -1.1 0.8 0.3 0.1 -0.2 -0.5 -1.7 -0.3 -1.1 0.2 -0.5 1.4 0.1 1.9 -0.7 -0.1 -0.1 -1.0 2.3 -2.9 -0.5 -0.8 0.4 0.0 2.1 -1.6 0.4 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:49.727772 z-score=0.843169, p-value=0.807345 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-25_12:31 Test no p-value 1 0.482812 2 0.132698 3 0.000133 4 0.228269 5 0.798033 6 0.297303 7 0.030838 8 0.500082 9 0.079265 10 0.346039 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.018888 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-25_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 66515 0.35 66661 0.00 3 25000.00 25122 0.60 24956 0.08 4 6666.67 6722 0.46 6663 0.00 5 1388.89 1341 1.65 1462 3.85 6 238.10 247 0.33 227 0.52 7 34.72 43 1.97 27 1.72 8 4.96 9 3.29 3 0.77 p=0.80571 p=0.67324 Number of rngs required: 687755, p-value: 0.227 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-25_12:31 No. of wins: Observed Expected 98503 98585.9 z-score=-0.371, pvalue=0.35547 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67004 66666.7 1.707 1.707 2 37583 37654.3 0.135 1.842 3 26765 26954.7 1.336 3.178 4 19403 19313.5 0.415 3.593 5 13830 13851.4 0.033 3.626 6 10002 9943.5 0.344 3.969 7 7094 7145.0 0.364 4.334 8 5096 5139.1 0.361 4.695 9 3667 3699.9 0.292 4.987 10 2677 2666.3 0.043 5.030 11 1876 1923.3 1.165 6.194 12 1344 1388.7 1.441 7.636 13 976 1003.7 0.765 8.401 14 753 726.1 0.994 9.395 15 517 525.8 0.148 9.543 16 410 381.2 2.184 11.727 17 293 276.5 0.980 12.706 18 189 200.8 0.697 13.403 19 140 146.0 0.245 13.649 20 95 106.2 1.184 14.833 21 286 287.1 0.004 14.837 Chisq= 14.84 for 20 degrees of freedom, p= 0.21435 SUMMARY of craptest p-value for no. of wins: 0.355471 p-value for throws/game: 0.214348 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-25_12:31 No. of wins: Observed Expected 98695 98585.9 z-score= 0.488, pvalue=0.68728 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66690 66666.7 0.008 0.008 2 37562 37654.3 0.226 0.235 3 27003 26954.7 0.086 0.321 4 19334 19313.5 0.022 0.343 5 13870 13851.4 0.025 0.368 6 9991 9943.5 0.226 0.594 7 7050 7145.0 1.264 1.858 8 5053 5139.1 1.442 3.300 9 3700 3699.9 0.000 3.300 10 2682 2666.3 0.092 3.392 11 1995 1923.3 2.671 6.063 12 1392 1388.7 0.008 6.070 13 987 1003.7 0.278 6.349 14 754 726.1 1.069 7.418 15 561 525.8 2.352 9.769 16 416 381.2 3.186 12.956 17 246 276.5 3.373 16.328 18 190 200.8 0.584 16.912 19 142 146.0 0.109 17.021 20 99 106.2 0.490 17.511 21 283 287.1 0.059 17.570 Chisq= 17.57 for 20 degrees of freedom, p= 0.38429 SUMMARY of craptest p-value for no. of wins: 0.687276 p-value for throws/game: 0.384290 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0060,0.0098,0.0145,0.0170,0.0189,0.0224,0.0297,0.0308,0.0317, 0.0368,0.0403,0.0466,0.0488,0.0502,0.0622,0.0728,0.0736,0.0793,0.0903, 0.0913,0.0944,0.1002,0.1096,0.1096,0.1152,0.1175,0.1175,0.1208,0.1298, 0.1307,0.1327,0.1384,0.1392,0.1486,0.1492,0.1565,0.1576,0.1730,0.1746, 0.1769,0.1772,0.1827,0.1855,0.1866,0.1878,0.1900,0.2000,0.2032,0.2043, 0.2135,0.2143,0.2155,0.2178,0.2235,0.2255,0.2266,0.2271,0.2283,0.2300, 0.2308,0.2312,0.2394,0.2432,0.2512,0.2514,0.2646,0.2665,0.2733,0.2746, 0.2773,0.2776,0.2807,0.2893,0.2920,0.2922,0.2973,0.2991,0.3005,0.3073, 0.3118,0.3131,0.3240,0.3266,0.3328,0.3448,0.3458,0.3460,0.3544,0.3555, 0.3646,0.3733,0.3739,0.3746,0.3746,0.3797,0.3836,0.3843,0.3848,0.3893, 0.3912,0.3927,0.3972,0.3992,0.3999,0.4044,0.4100,0.4122,0.4190,0.4201, 0.4243,0.4269,0.4278,0.4284,0.4323,0.4335,0.4352,0.4430,0.4476,0.4495, 0.4591,0.4633,0.4636,0.4679,0.4725,0.4737,0.4762,0.4767,0.4828,0.4874, 0.4903,0.4932,0.5000,0.5001,0.5010,0.5013,0.5025,0.5063,0.5131,0.5173, 0.5213,0.5221,0.5347,0.5390,0.5431,0.5453,0.5496,0.5508,0.5534,0.5545, 0.5551,0.5567,0.5615,0.5666,0.5673,0.5735,0.5762,0.5765,0.5784,0.5830, 0.5872,0.5933,0.5966,0.5995,0.6015,0.6029,0.6079,0.6079,0.6108,0.6119, 0.6156,0.6252,0.6254,0.6254,0.6310,0.6345,0.6422,0.6479,0.6500,0.6520, 0.6532,0.6535,0.6551,0.6578,0.6610,0.6617,0.6631,0.6666,0.6711,0.6712, 0.6731,0.6732,0.6751,0.6801,0.6829,0.6853,0.6873,0.6991,0.6995,0.7166, 0.7286,0.7310,0.7338,0.7349,0.7431,0.7432,0.7433,0.7481,0.7533,0.7556, 0.7562,0.7565,0.7571,0.7577,0.7619,0.7648,0.7660,0.7683,0.7729,0.7766, 0.7812,0.7828,0.7851,0.7863,0.7885,0.7949,0.7950,0.7980,0.8030,0.8057, 0.8070,0.8073,0.8128,0.8134,0.8194,0.8273,0.8279,0.8316,0.8326,0.8414, 0.8562,0.8667,0.8702,0.8715,0.8715,0.8723,0.8772,0.8801,0.8824,0.8824, 0.8886,0.8888,0.8933,0.8982,0.9022,0.9101,0.9226,0.9266,0.9363,0.9365, 0.9368,0.9392,0.9396,0.9436,0.9531,0.9551,0.9612,0.9664,0.9790, Overall p-value after applying KStest on 269 p-values = 0.208554 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.