RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-04_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.63 12.7794 0.249177 2 to 25 15.77 17.8640 0.602533 3 to 26 15.83 14.7781 0.388542 4 to 27 16.05 20.1194 0.731833 5 to 28 16.07 18.2422 0.626281 6 to 29 15.68 27.8604 0.953404 7 to 30 15.67 16.6670 0.522858 8 to 31 15.94 13.1606 0.274627 9 to 32 15.45 32.2230 0.985884 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.441729 Tough bday spacings test for dh-ranFile-2016-04-04_03:31: 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 35 64 85 104 77 70 30 15 12 2 (O-E)^2/E 1.1 0.1 1.2 1.6 0.4 0.0 6.2 0.0 0.0 4.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 15.991, p= 0.900 RESULTS OF GCD FOR dh-ranFile-2016-04-04_03:31 Euclid's algorithm: p-value, steps to gcd: 0.854019 p-value, dist. of gcd's: 0.838945 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-04_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.395 0.804 0.816 0.656 0.351 0.898 0.715 0.779 Bits 8 to 15---> 0.330 0.116 0.310 0.673 0.378 0.078 0.125 0.218 Bits 16 to 23---> 0.608 0.168 0.737 0.757 0.933 0.305 0.282 0.835 Bits 24 to 31---> 0.163 0.619 0.334 0.846 0.585 0.686 0.432 0.683 KS test for the above 32 p values: 0.407 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-04_03:31, p-values for 5 runs: 0.3740, 0.6727, 0.4375, 0.3115, 0.8770 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-04_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5185 5134.0 0.506 0.518 r= 30 23002 23103.0 0.442 0.960 r= 31 11600 11551.5 0.203 1.164 chi-square = 1.164 with df = 3; p-value = 0.238 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-04_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 204 211.4 0.260 0.260 r= 30 5119 5134.0 0.044 0.304 r= 31 23172 23103.0 0.206 0.510 r= 32 11505 11551.5 0.187 0.697 chi-square = 0.697 with df = 3; p-value = 0.126 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-04_03:31 b-rank test for bits 1 to 8, p=0.45852 b-rank test for bits 2 to 9, p=0.36714 b-rank test for bits 3 to 10, p=0.91502 b-rank test for bits 4 to 11, p=0.49042 b-rank test for bits 5 to 12, p=0.27858 b-rank test for bits 6 to 13, p=0.44087 b-rank test for bits 7 to 14, p=0.74212 b-rank test for bits 8 to 15, p=0.58598 b-rank test for bits 9 to 16, p=0.59246 b-rank test for bits 10 to 17, p=0.82422 b-rank test for bits 11 to 18, p=0.85296 b-rank test for bits 12 to 19, p=0.60777 b-rank test for bits 13 to 20, p=0.31512 b-rank test for bits 14 to 21, p=0.57190 b-rank test for bits 15 to 22, p=0.73386 b-rank test for bits 16 to 23, p=0.07370 b-rank test for bits 17 to 24, p=0.13804 b-rank test for bits 18 to 25, p=0.89920 b-rank test for bits 19 to 26, p=0.55096 b-rank test for bits 20 to 27, p=0.73033 b-rank test for bits 21 to 28, p=0.55588 b-rank test for bits 22 to 29, p=0.52308 b-rank test for bits 23 to 30, p=0.06159 b-rank test for bits 24 to 31, p=0.21760 b-rank test for bits 25 to 32, p=0.45540 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 = 0.536727 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-04_03:31 (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 142078 0.39 0.653242 2 141584 -0.76 0.223592 3 140974 -2.19 0.014432 4 142014 0.24 0.596600 5 142130 0.52 0.696928 6 141886 -0.05 0.478265 7 141613 -0.69 0.244356 8 141199 -1.66 0.048492 9 142214 0.71 0.761720 10 141413 -1.16 0.123096 11 141558 -0.82 0.205862 12 141992 0.19 0.576581 13 142015 0.25 0.597504 14 141752 -0.37 0.356588 15 141673 -0.55 0.290415 16 141405 -1.18 0.119330 17 141818 -0.21 0.415512 18 141652 -0.60 0.273841 19 142742 1.95 0.974142 20 142294 0.90 0.815610 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-04_03:31 Bits used No. missing words z-score p-value 23 to 32 141961 0.1782 0.570706 22 to 31 142036 0.4368 0.668869 21 to 30 141903 -0.0218 0.491293 20 to 29 142184 0.9471 0.828216 19 to 28 141820 -0.3080 0.379028 18 to 27 142142 0.8023 0.788813 17 to 26 142306 1.3678 0.914317 16 to 25 142190 0.9678 0.833435 15 to 24 141652 -0.8873 0.187447 14 to 23 141481 -1.4770 0.069838 13 to 22 141847 -0.2149 0.414911 12 to 21 141174 -2.5356 0.005612 11 to 20 141910 0.0023 0.500922 10 to 19 141717 -0.6632 0.253599 9 to 18 142289 1.3092 0.904768 8 to 17 141599 -1.0701 0.142286 7 to 16 142023 0.3920 0.652458 6 to 15 141692 -0.7494 0.226804 5 to 14 142159 0.8609 0.805362 4 to 13 142104 0.6713 0.748978 3 to 12 142064 0.5333 0.703103 2 to 11 141926 0.0575 0.522920 1 to 10 141844 -0.2253 0.410882 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-04_03:31 Bits used No. missing words z-score p-value 28 to 32 142085 0.5955 0.724243 27 to 31 142050 0.4768 0.683265 26 to 30 142246 1.1413 0.873118 25 to 29 141371 -1.8248 0.034012 24 to 28 141252 -2.2282 0.012932 23 to 27 142161 0.8531 0.803203 22 to 26 141949 0.1345 0.553486 21 to 25 141804 -0.3571 0.360527 20 to 24 141343 -1.9198 0.027444 19 to 23 141932 0.0768 0.530628 18 to 22 142128 0.7413 0.770730 17 to 21 141994 0.2870 0.612950 16 to 20 141697 -0.7198 0.235836 15 to 19 141605 -1.0316 0.151123 14 to 18 142094 0.6260 0.734343 13 to 17 142005 0.3243 0.627147 12 to 16 142294 1.3040 0.903877 11 to 15 142139 0.7785 0.781875 10 to 14 142006 0.3277 0.628429 9 to 13 141780 -0.4384 0.330546 8 to 12 141802 -0.3638 0.357992 7 to 11 141811 -0.3333 0.369446 6 to 10 141950 0.1379 0.554826 5 to 9 141510 -1.3537 0.087922 4 to 8 142022 0.3819 0.648744 3 to 7 142051 0.4802 0.684471 2 to 6 142115 0.6972 0.757157 1 to 5 141935 0.0870 0.534671 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-04_03:31 Bits used No. missing words z-score p-value 31 to 32 142195 0.8427 0.800298 30 to 31 141900 -0.0275 0.489022 29 to 30 141802 -0.3166 0.375771 28 to 29 141988 0.2321 0.591756 27 to 28 142138 0.6745 0.750017 26 to 27 141609 -0.8859 0.187828 25 to 26 141762 -0.4346 0.331926 24 to 25 141093 -2.4081 0.008019 23 to 24 141604 -0.9007 0.183880 22 to 23 141872 -0.1101 0.456158 21 to 22 141927 0.0521 0.520785 20 to 21 141915 0.0167 0.506672 19 to 20 142189 0.8250 0.795310 18 to 19 141800 -0.3225 0.373534 17 to 18 142295 1.1377 0.872371 16 to 17 142087 0.5241 0.699896 15 to 16 142577 1.9695 0.975554 14 to 15 141639 -0.7974 0.212600 13 to 14 141746 -0.4818 0.314974 12 to 13 141837 -0.2134 0.415522 11 to 12 141936 0.0787 0.531354 10 to 11 141951 0.1229 0.548915 9 to 10 141916 0.0197 0.507849 8 to 9 142093 0.5418 0.706022 7 to 8 141904 -0.0157 0.493728 6 to 7 141904 -0.0157 0.493728 5 to 6 142100 0.5624 0.713095 4 to 5 142104 0.5742 0.717100 3 to 4 142187 0.8191 0.793631 2 to 3 141453 -1.3461 0.089134 1 to 2 142070 0.4740 0.682233 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-04_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2555.01 0.778 0.781685 Test results for specific bytes for dh-ranFile-2016-04-04_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2462.42 -0.532 0.297532 2 to 9 2513.63 0.193 0.576417 3 to 10 2491.92 -0.114 0.454533 4 to 11 2402.67 -1.376 0.084349 5 to 12 2632.51 1.874 0.969532 6 to 13 2320.30 -2.541 0.005521 7 to 14 2532.90 0.465 0.679142 8 to 15 2445.42 -0.772 0.220080 9 to 16 2487.66 -0.175 0.430721 10 to 17 2469.06 -0.438 0.330874 11 to 18 2567.80 0.959 0.831194 12 to 19 2494.98 -0.071 0.471697 13 to 20 2383.29 -1.651 0.049416 14 to 21 2587.82 1.242 0.892874 15 to 22 2430.37 -0.985 0.162389 16 to 23 2499.34 -0.009 0.496264 17 to 24 2524.47 0.346 0.635368 18 to 25 2560.22 0.852 0.802787 19 to 26 2410.21 -1.270 0.102065 20 to 27 2452.24 -0.675 0.249686 21 to 28 2555.04 0.778 0.781843 22 to 29 2392.33 -1.523 0.063920 23 to 30 2585.96 1.216 0.887953 24 to 31 2548.80 0.690 0.754942 25 to 32 2434.21 -0.930 0.176095 CDPARK for dh-ranFile-2016-04-04_03:31: 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 3513 -0.4566 0.323972 3566 1.9635 0.975204 3555 1.4612 0.928018 3551 1.2785 0.899470 3482 -1.8721 0.030593 3488 -1.5982 0.055002 3530 0.3196 0.625377 3548 1.1416 0.873180 3534 0.5023 0.692266 3525 0.0913 0.536383 Square side=100, avg. no. parked=3529.20 sample std.=26.60 p-value of the KSTEST for those 10 p-values: 0.270874 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-04_03:31 0.6207,0.6525,0.6736,0.9047,0.5967,0.4662,0.7575,0.0476,0.7071,0.6009, The KS test for those 10 p-values: 0.168290 The 3DSPHERES test for dh-ranFile-2016-04-04_03:31 sample no r^3 equiv. uni. 1 1.865 0.060263 2 59.186 0.860940 3 67.704 0.895314 4 29.723 0.628712 5 15.407 0.401648 6 44.763 0.775100 7 20.586 0.496508 8 17.164 0.435676 9 56.000 0.845359 10 44.948 0.776482 11 28.922 0.618666 12 18.806 0.465741 13 24.019 0.550963 14 26.518 0.586849 15 29.315 0.623619 16 36.639 0.705155 17 39.182 0.729120 18 30.047 0.632700 19 99.297 0.963480 20 27.892 0.605347 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.028866 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-04_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -0.8 2.4 -1.7 0.7 -0.0 0.9 -1.5 -0.9 0.0 -1.6 -0.1 -1.5 1.8 1.1 -1.2 0.9 -1.3 1.1 1.1 1.3 -1.2 -1.0 0.5 -0.2 -0.8 0.6 -0.5 0.6 1.7 1.4 -0.7 2.0 0.2 -0.8 -0.7 -0.1 0.5 -0.7 0.1 2.0 -0.1 Chi-square with 42 degrees of freedom:51.094637 z-score=0.992306, p-value=0.841382 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-04_03:31 Test no p-value 1 0.963125 2 0.179499 3 0.135994 4 0.037523 5 0.042348 6 0.406361 7 0.083503 8 0.122347 9 0.288648 10 0.354555 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.007158 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-04_03:31: (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 66748 0.10 66575 0.13 3 25000.00 24879 0.59 25144 0.83 4 6666.67 6664 0.00 6642 0.09 5 1388.89 1418 0.61 1372 0.21 6 238.10 253 0.93 229 0.35 7 34.72 32 0.21 33 0.09 8 4.96 5 0.00 4 0.19 p=0.12515 p=0.06880 Number of rngs required: 687591, p-value: 0.174 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-04_03:31 No. of wins: Observed Expected 98248 98585.9 z-score=-1.511, pvalue=0.06538 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66627 66666.7 0.024 0.024 2 37636 37654.3 0.009 0.033 3 27186 26954.7 1.984 2.017 4 19187 19313.5 0.828 2.845 5 14032 13851.4 2.354 5.199 6 9754 9943.5 3.613 8.812 7 6992 7145.0 3.277 12.089 8 5176 5139.1 0.265 12.355 9 3709 3699.9 0.023 12.377 10 2756 2666.3 3.018 15.395 11 1931 1923.3 0.031 15.426 12 1383 1388.7 0.024 15.450 13 1011 1003.7 0.053 15.502 14 702 726.1 0.803 16.305 15 533 525.8 0.098 16.403 16 372 381.2 0.220 16.622 17 302 276.5 2.344 18.966 18 192 200.8 0.388 19.355 19 124 146.0 3.311 22.665 20 111 106.2 0.216 22.881 21 284 287.1 0.034 22.915 Chisq= 22.91 for 20 degrees of freedom, p= 0.70699 SUMMARY of craptest p-value for no. of wins: 0.065381 p-value for throws/game: 0.706995 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-04_03:31 No. of wins: Observed Expected 98737 98585.9 z-score= 0.676, pvalue=0.75048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66448 66666.7 0.717 0.717 2 38024 37654.3 3.629 4.347 3 27135 26954.7 1.206 5.552 4 19310 19313.5 0.001 5.553 5 13664 13851.4 2.536 8.089 6 10027 9943.5 0.700 8.789 7 6985 7145.0 3.584 12.373 8 5082 5139.1 0.634 13.007 9 3706 3699.9 0.010 13.017 10 2663 2666.3 0.004 13.021 11 1946 1923.3 0.267 13.289 12 1330 1388.7 2.485 15.773 13 1012 1003.7 0.068 15.842 14 751 726.1 0.851 16.693 15 520 525.8 0.065 16.757 16 389 381.2 0.162 16.919 17 255 276.5 1.678 18.597 18 216 200.8 1.146 19.743 19 152 146.0 0.248 19.991 20 100 106.2 0.364 20.354 21 285 287.1 0.016 20.370 Chisq= 20.37 for 20 degrees of freedom, p= 0.56498 SUMMARY of craptest p-value for no. of wins: 0.750477 p-value for throws/game: 0.564977 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0055,0.0056,0.0072,0.0080,0.0129,0.0144,0.0274,0.0289,0.0306,0.0340, 0.0375,0.0423,0.0476,0.0485,0.0494,0.0550,0.0603,0.0616,0.0639,0.0654, 0.0688,0.0698,0.0737,0.0776,0.0835,0.0843,0.0879,0.0891,0.1021,0.1164, 0.1193,0.1223,0.1231,0.1251,0.1252,0.1262,0.1360,0.1380,0.1423,0.1511, 0.1624,0.1628,0.1677,0.1683,0.1736,0.1761,0.1795,0.1839,0.1874,0.1878, 0.2059,0.2126,0.2176,0.2180,0.2201,0.2236,0.2268,0.2358,0.2383,0.2444, 0.2492,0.2497,0.2536,0.2709,0.2738,0.2746,0.2786,0.2817,0.2886,0.2904, 0.2975,0.3048,0.3096,0.3115,0.3150,0.3151,0.3240,0.3301,0.3305,0.3309, 0.3319,0.3335,0.3505,0.3546,0.3566,0.3580,0.3605,0.3671,0.3694,0.3735, 0.3740,0.3758,0.3783,0.3790,0.3885,0.3950,0.4016,0.4064,0.4072,0.4109, 0.4149,0.4155,0.4155,0.4307,0.4322,0.4357,0.4375,0.4409,0.4417,0.4545, 0.4554,0.4562,0.4585,0.4657,0.4662,0.4717,0.4783,0.4890,0.4904,0.4913, 0.4937,0.4937,0.4963,0.4965,0.5009,0.5067,0.5078,0.5208,0.5229,0.5229, 0.5231,0.5306,0.5314,0.5347,0.5364,0.5367,0.5489,0.5510,0.5510,0.5535, 0.5548,0.5559,0.5650,0.5707,0.5719,0.5764,0.5766,0.5854,0.5860,0.5868, 0.5918,0.5925,0.5966,0.5967,0.5975,0.6009,0.6025,0.6053,0.6078,0.6085, 0.6130,0.6187,0.6188,0.6207,0.6236,0.6254,0.6263,0.6271,0.6284,0.6287, 0.6327,0.6354,0.6487,0.6525,0.6525,0.6532,0.6560,0.6689,0.6727,0.6729, 0.6736,0.6791,0.6822,0.6833,0.6833,0.6845,0.6860,0.6923,0.6969,0.6999, 0.7031,0.7052,0.7060,0.7070,0.7071,0.7131,0.7153,0.7171,0.7242,0.7291, 0.7303,0.7318,0.7339,0.7343,0.7366,0.7421,0.7490,0.7500,0.7505,0.7549, 0.7567,0.7572,0.7575,0.7617,0.7707,0.7751,0.7765,0.7788,0.7817,0.7818, 0.7819,0.7888,0.7936,0.7953,0.8003,0.8028,0.8032,0.8037,0.8054,0.8156, 0.8158,0.8242,0.8282,0.8312,0.8334,0.8351,0.8389,0.8414,0.8454,0.8464, 0.8530,0.8540,0.8609,0.8724,0.8731,0.8732,0.8770,0.8880,0.8929,0.8953, 0.8980,0.8992,0.8995,0.9001,0.9039,0.9047,0.9048,0.9143,0.9150,0.9280, 0.9327,0.9534,0.9631,0.9635,0.9695,0.9741,0.9752,0.9756,0.9859, Overall p-value after applying KStest on 269 p-values = 0.186348 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.