RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-20_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.48 19.4410 0.696187 2 to 25 15.49 25.8316 0.922417 3 to 26 15.70 16.9065 0.539281 4 to 27 15.75 19.9405 0.722717 5 to 28 15.48 27.6798 0.951178 6 to 29 15.54 19.1687 0.681062 7 to 30 15.65 19.0342 0.673425 8 to 31 15.85 14.6578 0.379883 9 to 32 15.78 12.0315 0.201775 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.215168 Tough bday spacings test for dh-ranFile-2016-12-20_05:31: 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 48 74 103 83 76 59 22 17 4 6 (O-E)^2/E 0.1 3.5 0.0 0.3 2.2 0.1 0.9 2.0 0.3 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 11.435, p= 0.675 RESULTS OF GCD FOR dh-ranFile-2016-12-20_05:31 Euclid's algorithm: p-value, steps to gcd: 0.589843 p-value, dist. of gcd's: 0.831039 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-20_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.013 0.457 0.792 0.203 0.416 0.606 0.046 0.912 Bits 8 to 15---> 0.496 0.279 0.224 0.489 0.516 0.278 0.574 0.138 Bits 16 to 23---> 0.969 0.444 0.434 0.704 0.546 0.780 0.419 0.397 Bits 24 to 31---> 0.670 0.631 0.645 0.658 0.033 0.571 0.123 0.841 KS test for the above 32 p values: 0.448 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-20_05:31, p-values for 5 runs: 0.3911, 0.8858, 0.9519, 0.0005, 0.1343 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-20_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 215 211.4 0.061 0.061 r= 29 5270 5134.0 3.602 3.663 r= 30 22931 23103.0 1.281 4.944 r= 31 11584 11551.5 0.091 5.035 chi-square = 5.035 with df = 3; p-value = 0.831 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-20_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5159 5134.0 0.122 0.851 r= 31 23179 23103.0 0.250 1.101 r= 32 11463 11551.5 0.678 1.779 chi-square = 1.779 with df = 3; p-value = 0.381 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-20_05:31 b-rank test for bits 1 to 8, p=0.66761 b-rank test for bits 2 to 9, p=0.69385 b-rank test for bits 3 to 10, p=0.11743 b-rank test for bits 4 to 11, p=0.89202 b-rank test for bits 5 to 12, p=0.89984 b-rank test for bits 6 to 13, p=0.18092 b-rank test for bits 7 to 14, p=0.16296 b-rank test for bits 8 to 15, p=0.74795 b-rank test for bits 9 to 16, p=0.13774 b-rank test for bits 10 to 17, p=0.93194 b-rank test for bits 11 to 18, p=0.74567 b-rank test for bits 12 to 19, p=0.00365 b-rank test for bits 13 to 20, p=0.05323 b-rank test for bits 14 to 21, p=0.86897 b-rank test for bits 15 to 22, p=0.70205 b-rank test for bits 16 to 23, p=0.58459 b-rank test for bits 17 to 24, p=0.68447 b-rank test for bits 18 to 25, p=0.24617 b-rank test for bits 19 to 26, p=0.89135 b-rank test for bits 20 to 27, p=0.91538 b-rank test for bits 21 to 28, p=0.80977 b-rank test for bits 22 to 29, p=0.97383 b-rank test for bits 23 to 30, p=0.00542 b-rank test for bits 24 to 31, p=0.86501 b-rank test for bits 25 to 32, p=0.16109 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 = 0.067689 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-20_05:31 (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 142794 2.07 0.980632 2 141499 -0.96 0.168851 3 141593 -0.74 0.229927 4 141961 0.12 0.548045 5 141969 0.14 0.555439 6 142154 0.57 0.716223 7 141655 -0.59 0.276180 8 141360 -1.28 0.099662 9 141987 0.18 0.572001 10 141908 -0.00 0.498760 11 140917 -2.32 0.010210 12 142087 0.42 0.660972 13 142174 0.62 0.731840 14 141584 -0.76 0.223592 15 142324 0.97 0.833691 16 142436 1.23 0.890752 17 141987 0.18 0.572001 18 141745 -0.38 0.350508 19 142385 1.11 0.866797 20 142172 0.61 0.730298 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-20_05:31 Bits used No. missing words z-score p-value 23 to 32 142442 1.8368 0.966880 22 to 31 141698 -0.7287 0.233085 21 to 30 141764 -0.5011 0.308137 20 to 29 141980 0.2437 0.596264 19 to 28 142171 0.9023 0.816554 18 to 27 141675 -0.8080 0.209535 17 to 26 141598 -1.0736 0.141512 16 to 25 141244 -2.2942 0.010888 15 to 24 141705 -0.7046 0.240534 14 to 23 141887 -0.0770 0.469312 13 to 22 142041 0.4540 0.675098 12 to 21 141839 -0.2425 0.404190 11 to 20 141796 -0.3908 0.347975 10 to 19 142061 0.5230 0.699513 9 to 18 142044 0.4644 0.678812 8 to 17 142138 0.7885 0.784803 7 to 16 142083 0.5989 0.725368 6 to 15 141924 0.0506 0.520172 5 to 14 141958 0.1678 0.566641 4 to 13 142105 0.6747 0.750075 3 to 12 142030 0.4161 0.661333 2 to 11 141803 -0.3667 0.356938 1 to 10 141538 -1.2804 0.100194 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-20_05:31 Bits used No. missing words z-score p-value 28 to 32 141906 -0.0113 0.495497 27 to 31 141435 -1.6079 0.053929 26 to 30 142175 0.9006 0.816093 25 to 29 142263 1.1989 0.884713 24 to 28 142068 0.5379 0.704665 23 to 27 142278 1.2497 0.894301 22 to 26 141319 -2.0011 0.022690 21 to 25 141964 0.1853 0.573512 20 to 24 142021 0.3785 0.647486 19 to 23 141987 0.2633 0.603836 18 to 22 142275 1.2396 0.892431 17 to 21 142329 1.4226 0.922575 16 to 20 141373 -1.8181 0.034527 15 to 19 141751 -0.5367 0.295733 14 to 18 141527 -1.2960 0.097482 13 to 17 142220 1.0531 0.853857 12 to 16 142803 3.0294 0.998775 11 to 15 142638 2.4701 0.993246 10 to 14 141988 0.2667 0.605141 9 to 13 142111 0.6836 0.752895 8 to 12 141997 0.2972 0.616838 7 to 11 141888 -0.0723 0.471180 6 to 10 142073 0.5548 0.710489 5 to 9 141649 -0.8825 0.188760 4 to 8 141666 -0.8248 0.204729 3 to 7 141866 -0.1469 0.441613 2 to 6 141948 0.1311 0.552146 1 to 5 141610 -1.0147 0.155130 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-20_05:31 Bits used No. missing words z-score p-value 31 to 32 141772 -0.4051 0.342701 30 to 31 142001 0.2704 0.606579 29 to 30 141973 0.1878 0.574490 28 to 29 141644 -0.7827 0.216906 27 to 28 141363 -1.6116 0.053525 26 to 27 141635 -0.8092 0.209191 25 to 26 141835 -0.2193 0.413223 24 to 25 142136 0.6686 0.748138 23 to 24 142290 1.1229 0.869264 22 to 23 141695 -0.6322 0.263614 21 to 22 141756 -0.4523 0.325526 20 to 21 142394 1.4297 0.923599 19 to 20 141593 -0.9331 0.175377 18 to 19 142052 0.4209 0.663070 17 to 18 141584 -0.9597 0.168609 16 to 17 142154 0.7217 0.764773 15 to 16 141821 -0.2606 0.397216 14 to 15 142022 0.3324 0.630191 13 to 14 141715 -0.5732 0.283240 12 to 13 141730 -0.5290 0.298404 11 to 12 141849 -0.1780 0.429375 10 to 11 141902 -0.0216 0.491375 9 to 10 142097 0.5536 0.710073 8 to 9 141925 0.0462 0.518434 7 to 8 142110 0.5919 0.723057 6 to 7 142125 0.6362 0.737675 5 to 6 141980 0.2085 0.582568 4 to 5 141884 -0.0747 0.470219 3 to 4 142280 1.0934 0.862896 2 to 3 141332 -1.7030 0.044280 1 to 2 142351 1.3029 0.903689 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-20_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2347.50 -2.157 0.015516 Test results for specific bytes for dh-ranFile-2016-12-20_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2441.27 -0.831 0.203098 2 to 9 2445.56 -0.770 0.220689 3 to 10 2600.06 1.415 0.921471 4 to 11 2395.88 -1.472 0.070447 5 to 12 2446.93 -0.751 0.226458 6 to 13 2515.99 0.226 0.589478 7 to 14 2547.53 0.672 0.749280 8 to 15 2515.11 0.214 0.584593 9 to 16 2484.19 -0.224 0.411550 10 to 17 2463.65 -0.514 0.303604 11 to 18 2471.53 -0.403 0.343637 12 to 19 2501.16 0.016 0.506535 13 to 20 2327.01 -2.446 0.007215 14 to 21 2592.02 1.301 0.903438 15 to 22 2524.89 0.352 0.637600 16 to 23 2502.64 0.037 0.514911 17 to 24 2393.43 -1.507 0.065882 18 to 25 2480.16 -0.281 0.389519 19 to 26 2361.02 -1.966 0.024678 20 to 27 2501.16 0.016 0.506558 21 to 28 2511.72 0.166 0.565849 22 to 29 2578.64 1.112 0.866975 23 to 30 2500.04 0.001 0.500245 24 to 31 2425.48 -1.054 0.145967 25 to 32 2434.89 -0.921 0.178588 CDPARK for dh-ranFile-2016-12-20_05:31: 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 3550 1.2329 0.891189 3531 0.3653 0.642555 3510 -0.5936 0.276387 3530 0.3196 0.625377 3484 -1.7808 0.037471 3545 1.0046 0.842447 3563 1.8265 0.966111 3490 -1.5068 0.065925 3522 -0.0457 0.481790 3543 0.9132 0.819442 Square side=100, avg. no. parked=3526.80 sample std.=24.42 p-value of the KSTEST for those 10 p-values: 0.606376 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-20_05:31 0.6770,0.8383,0.1581,0.7994,0.2404,0.7325,0.4195,0.3245,0.2224,0.1241, The KS test for those 10 p-values: 0.762762 The 3DSPHERES test for dh-ranFile-2016-12-20_05:31 sample no r^3 equiv. uni. 1 41.972 0.753174 2 27.514 0.600339 3 14.316 0.379488 4 9.281 0.266089 5 118.727 0.980890 6 24.062 0.551593 7 39.532 0.732262 8 12.272 0.335723 9 4.882 0.150196 10 6.592 0.197275 11 12.719 0.345546 12 1.962 0.063318 13 37.831 0.716639 14 66.287 0.890252 15 54.807 0.839088 16 7.096 0.210646 17 32.625 0.662941 18 11.299 0.313835 19 1.209 0.039493 20 48.624 0.802261 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.993576 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-20_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 -1.6 -1.9 -1.4 -0.1 0.9 0.6 0.3 -1.4 -0.1 0.8 -0.0 -0.5 1.9 0.8 -1.0 -0.3 -1.4 -0.4 -0.8 0.3 -0.4 1.7 0.5 0.4 1.4 -0.3 -1.8 0.9 0.3 -1.3 -1.1 1.6 -0.8 1.1 -0.7 -0.1 -0.4 0.4 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:39.607168 z-score=-0.261079, p-value=0.423464 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-20_05:31 Test no p-value 1 0.602602 2 0.076108 3 0.013635 4 0.141432 5 0.772345 6 0.243539 7 0.020903 8 0.282812 9 0.220068 10 0.001360 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001607 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-20_05:31: (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 66569 0.14 66505 0.39 3 25000.00 25133 0.71 25160 1.02 4 6666.67 6636 0.14 6754 1.14 5 1388.89 1398 0.06 1320 3.42 6 238.10 221 1.23 224 0.83 7 34.72 35 0.00 29 0.94 8 4.96 7 0.84 7 0.84 p=0.20639 p=0.80220 Number of rngs required: 689133, p-value: 0.801 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-20_05:31 No. of wins: Observed Expected 98813 98585.9 z-score= 1.016, pvalue=0.84516 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66441 66666.7 0.764 0.764 2 38033 37654.3 3.808 4.572 3 26877 26954.7 0.224 4.796 4 19276 19313.5 0.073 4.869 5 13782 13851.4 0.348 5.217 6 9905 9943.5 0.149 5.366 7 7164 7145.0 0.050 5.417 8 5151 5139.1 0.028 5.444 9 3675 3699.9 0.167 5.611 10 2677 2666.3 0.043 5.654 11 1888 1923.3 0.649 6.303 12 1427 1388.7 1.054 7.357 13 1040 1003.7 1.312 8.669 14 757 726.1 1.311 9.981 15 538 525.8 0.281 10.262 16 353 381.2 2.079 12.341 17 267 276.5 0.329 12.670 18 213 200.8 0.737 13.408 19 134 146.0 0.984 14.392 20 106 106.2 0.000 14.392 21 296 287.1 0.275 14.667 Chisq= 14.67 for 20 degrees of freedom, p= 0.20487 SUMMARY of craptest p-value for no. of wins: 0.845164 p-value for throws/game: 0.204865 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-20_05:31 No. of wins: Observed Expected 98712 98585.9 z-score= 0.564, pvalue=0.71368 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66519 66666.7 0.327 0.327 2 37690 37654.3 0.034 0.361 3 26823 26954.7 0.644 1.005 4 19344 19313.5 0.048 1.053 5 14098 13851.4 4.390 5.443 6 10085 9943.5 2.012 7.455 7 7260 7145.0 1.850 9.305 8 5001 5139.1 3.710 13.015 9 3640 3699.9 0.969 13.983 10 2614 2666.3 1.026 15.009 11 1898 1923.3 0.334 15.343 12 1363 1388.7 0.477 15.820 13 1014 1003.7 0.105 15.925 14 727 726.1 0.001 15.926 15 552 525.8 1.302 17.228 16 381 381.2 0.000 17.228 17 289 276.5 0.561 17.789 18 178 200.8 2.595 20.385 19 158 146.0 0.989 21.374 20 109 106.2 0.073 21.447 21 257 287.1 3.159 24.605 Chisq= 24.61 for 20 degrees of freedom, p= 0.78305 SUMMARY of craptest p-value for no. of wins: 0.713683 p-value for throws/game: 0.783047 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0014,0.0016,0.0037,0.0054,0.0072,0.0102,0.0109,0.0132,0.0136, 0.0155,0.0209,0.0227,0.0247,0.0332,0.0345,0.0375,0.0395,0.0443,0.0465, 0.0532,0.0535,0.0539,0.0633,0.0659,0.0659,0.0677,0.0704,0.0761,0.0975, 0.0997,0.1002,0.1174,0.1231,0.1241,0.1343,0.1377,0.1381,0.1414,0.1415, 0.1460,0.1502,0.1551,0.1581,0.1611,0.1630,0.1686,0.1689,0.1754,0.1786, 0.1809,0.1888,0.1973,0.2018,0.2031,0.2033,0.2047,0.2049,0.2064,0.2092, 0.2095,0.2106,0.2152,0.2169,0.2201,0.2207,0.2224,0.2236,0.2236,0.2265, 0.2299,0.2331,0.2404,0.2405,0.2435,0.2462,0.2636,0.2661,0.2762,0.2764, 0.2784,0.2786,0.2828,0.2832,0.2957,0.2984,0.3036,0.3081,0.3138,0.3245, 0.3255,0.3357,0.3427,0.3436,0.3455,0.3480,0.3505,0.3569,0.3795,0.3799, 0.3805,0.3895,0.3911,0.3972,0.3974,0.4042,0.4115,0.4132,0.4163,0.4187, 0.4195,0.4235,0.4294,0.4337,0.4416,0.4437,0.4483,0.4574,0.4693,0.4702, 0.4712,0.4818,0.4892,0.4914,0.4955,0.4965,0.4988,0.5002,0.5065,0.5066, 0.5149,0.5155,0.5184,0.5202,0.5393,0.5456,0.5480,0.5516,0.5521,0.5554, 0.5658,0.5666,0.5706,0.5720,0.5720,0.5735,0.5742,0.5745,0.5826,0.5846, 0.5846,0.5895,0.5898,0.5963,0.6003,0.6026,0.6038,0.6051,0.6055,0.6064, 0.6066,0.6168,0.6254,0.6302,0.6314,0.6376,0.6426,0.6455,0.6475,0.6580, 0.6610,0.6613,0.6629,0.6631,0.6676,0.6699,0.6734,0.6751,0.6753,0.6770, 0.6788,0.6811,0.6845,0.6939,0.6962,0.6995,0.7020,0.7037,0.7047,0.7101, 0.7105,0.7137,0.7162,0.7166,0.7227,0.7231,0.7254,0.7303,0.7318,0.7323, 0.7325,0.7377,0.7457,0.7479,0.7481,0.7493,0.7501,0.7529,0.7532,0.7628, 0.7648,0.7723,0.7802,0.7830,0.7848,0.7920,0.7994,0.8007,0.8022,0.8023, 0.8098,0.8161,0.8166,0.8194,0.8308,0.8310,0.8337,0.8383,0.8391,0.8412, 0.8424,0.8452,0.8539,0.8629,0.8650,0.8668,0.8670,0.8690,0.8693,0.8847, 0.8858,0.8903,0.8908,0.8912,0.8914,0.8920,0.8924,0.8943,0.8998,0.9034, 0.9037,0.9121,0.9154,0.9215,0.9224,0.9226,0.9236,0.9319,0.9512,0.9519, 0.9661,0.9669,0.9692,0.9738,0.9806,0.9809,0.9932,0.9936,0.9988, Overall p-value after applying KStest on 269 p-values = 0.409549 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.