RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-06_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.72 19.9243 0.721879 2 to 25 15.67 15.0100 0.405236 3 to 26 15.78 24.5431 0.894586 4 to 27 16.09 12.8353 0.252858 5 to 28 15.81 22.3183 0.827215 6 to 29 15.75 11.2562 0.157060 7 to 30 15.42 28.0060 0.955132 8 to 31 15.70 13.7107 0.312537 9 to 32 15.97 11.4615 0.168406 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.838540 Tough bday spacings test for dh-ranFile-2016-04-06_04:31: 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 10 32 71 98 104 71 67 26 11 7 3 (O-E)^2/E 0.1 0.6 0.1 0.0 0.4 0.7 4.3 0.5 1.0 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 7.852, p= 0.357 RESULTS OF GCD FOR dh-ranFile-2016-04-06_04:31 Euclid's algorithm: p-value, steps to gcd: 0.268507 p-value, dist. of gcd's: 0.110014 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-06_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.664 0.748 0.826 0.948 0.086 0.976 0.144 0.345 Bits 8 to 15---> 0.342 0.777 0.094 0.246 0.435 0.868 0.111 0.301 Bits 16 to 23---> 0.940 0.300 0.146 0.019 0.883 0.775 0.460 0.418 Bits 24 to 31---> 0.062 0.131 0.964 0.325 0.817 0.771 0.374 0.131 KS test for the above 32 p values: 0.542 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-06_04:31, p-values for 5 runs: 0.9295, 0.3997, 0.4082, 0.4311, 0.6398 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-06_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 191 211.4 1.972 1.972 r= 29 5123 5134.0 0.024 1.996 r= 30 22953 23103.0 0.975 2.970 r= 31 11733 11551.5 2.851 5.821 chi-square = 5.821 with df = 3; p-value = 0.879 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-06_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5156 5134.0 0.094 0.824 r= 31 23210 23103.0 0.495 1.319 r= 32 11435 11551.5 1.175 2.494 chi-square = 2.494 with df = 3; p-value = 0.524 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-06_04:31 b-rank test for bits 1 to 8, p=0.06825 b-rank test for bits 2 to 9, p=0.18095 b-rank test for bits 3 to 10, p=0.09567 b-rank test for bits 4 to 11, p=0.69702 b-rank test for bits 5 to 12, p=0.08987 b-rank test for bits 6 to 13, p=0.79515 b-rank test for bits 7 to 14, p=0.51893 b-rank test for bits 8 to 15, p=0.39608 b-rank test for bits 9 to 16, p=0.59610 b-rank test for bits 10 to 17, p=0.38803 b-rank test for bits 11 to 18, p=0.62358 b-rank test for bits 12 to 19, p=0.67854 b-rank test for bits 13 to 20, p=0.24096 b-rank test for bits 14 to 21, p=0.54309 b-rank test for bits 15 to 22, p=0.62788 b-rank test for bits 16 to 23, p=0.56417 b-rank test for bits 17 to 24, p=0.42194 b-rank test for bits 18 to 25, p=0.17192 b-rank test for bits 19 to 26, p=0.30676 b-rank test for bits 20 to 27, p=0.31787 b-rank test for bits 21 to 28, p=0.03620 b-rank test for bits 22 to 29, p=0.43305 b-rank test for bits 23 to 30, p=0.93013 b-rank test for bits 24 to 31, p=0.81587 b-rank test for bits 25 to 32, p=0.23324 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 = 0.348282 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-06_04:31 (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 141450 -1.07 0.141591 2 141733 -0.41 0.340175 3 141453 -1.07 0.143169 4 142415 1.18 0.881292 5 141881 -0.07 0.473613 6 141197 -1.66 0.048024 7 141393 -1.21 0.113836 8 141892 -0.04 0.483851 9 141374 -1.25 0.105509 10 141448 -1.08 0.140545 11 142495 1.37 0.914405 12 142283 0.87 0.808685 13 141555 -0.83 0.203871 14 141417 -1.15 0.125009 15 142225 0.74 0.769605 16 142555 1.51 0.934296 17 142035 0.29 0.615476 18 142155 0.57 0.717015 19 141614 -0.69 0.245090 20 141186 -1.69 0.045512 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-06_04:31 Bits used No. missing words z-score p-value 23 to 32 142309 1.3782 0.915925 22 to 31 141735 -0.6011 0.273874 21 to 30 141878 -0.1080 0.456984 20 to 29 141557 -1.2149 0.112196 19 to 28 141720 -0.6529 0.256923 18 to 27 141684 -0.7770 0.218579 17 to 26 141218 -2.3839 0.008565 16 to 25 141668 -0.8322 0.202656 15 to 24 141578 -1.1425 0.126620 14 to 23 141265 -2.2218 0.013147 13 to 22 141454 -1.5701 0.058196 12 to 21 142081 0.5920 0.723063 11 to 20 142590 2.3471 0.990541 10 to 19 142228 1.0989 0.864086 9 to 18 142169 0.8954 0.814717 8 to 17 141698 -0.7287 0.233085 7 to 16 142059 0.5161 0.697109 6 to 15 141976 0.2299 0.590914 5 to 14 142299 1.3437 0.910476 4 to 13 141849 -0.2080 0.417601 3 to 12 141784 -0.4322 0.332808 2 to 11 141792 -0.4046 0.342891 1 to 10 142416 1.7471 0.959693 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-06_04:31 Bits used No. missing words z-score p-value 28 to 32 141672 -0.8045 0.210552 27 to 31 141773 -0.4621 0.321992 26 to 30 141334 -1.9503 0.025572 25 to 29 141945 0.1209 0.548121 24 to 28 141776 -0.4520 0.325647 23 to 27 141284 -2.1198 0.017013 22 to 26 141860 -0.1672 0.433598 21 to 25 142008 0.3345 0.630989 20 to 24 142005 0.3243 0.627147 19 to 23 141825 -0.2859 0.387491 18 to 22 141873 -0.1232 0.450993 17 to 21 141914 0.0158 0.506315 16 to 20 141815 -0.3198 0.374574 15 to 19 142119 0.7107 0.761379 14 to 18 141580 -1.1164 0.132131 13 to 17 142200 0.9853 0.837767 12 to 16 142575 2.2565 0.987981 11 to 15 141891 -0.0621 0.475227 10 to 14 141833 -0.2587 0.397916 9 to 13 142065 0.5277 0.701145 8 to 12 141985 0.2565 0.601221 7 to 11 141777 -0.4486 0.326869 6 to 10 142040 0.4429 0.671099 5 to 9 142170 0.8836 0.811551 4 to 8 141438 -1.5977 0.055052 3 to 7 142540 2.1379 0.983736 2 to 6 141641 -0.9096 0.181519 1 to 5 141866 -0.1469 0.441613 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-06_04:31 Bits used No. missing words z-score p-value 31 to 32 142460 1.6244 0.947854 30 to 31 141919 0.0285 0.511378 29 to 30 141919 0.0285 0.511378 28 to 29 142233 0.9548 0.830155 27 to 28 141736 -0.5113 0.304571 26 to 27 141820 -0.2635 0.396079 25 to 26 142292 1.1288 0.870513 24 to 25 141999 0.2645 0.604308 23 to 24 141395 -1.5172 0.064608 22 to 23 142247 0.9961 0.840394 21 to 22 141630 -0.8240 0.204975 20 to 21 141910 0.0020 0.500789 19 to 20 142232 0.9518 0.829408 18 to 19 142125 0.6362 0.737675 17 to 18 142024 0.3383 0.632416 16 to 17 142035 0.3707 0.644573 15 to 16 141751 -0.4671 0.320232 14 to 15 141359 -1.6234 0.052253 13 to 14 141448 -1.3609 0.086780 12 to 13 142215 0.9017 0.816387 11 to 12 142556 1.9076 0.971777 10 to 11 141891 -0.0541 0.478439 9 to 10 141800 -0.3225 0.373534 8 to 9 142482 1.6893 0.954418 7 to 8 142195 0.8427 0.800298 6 to 7 142032 0.3619 0.641271 5 to 6 141636 -0.8063 0.210040 4 to 5 142280 1.0934 0.862896 3 to 4 141795 -0.3373 0.367962 2 to 3 142261 1.0374 0.850219 1 to 2 142116 0.6096 0.728952 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-06_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2499.87 -0.002 0.499294 Test results for specific bytes for dh-ranFile-2016-04-06_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2470.70 -0.414 0.339282 2 to 9 2431.16 -0.974 0.165139 3 to 10 2453.19 -0.662 0.253982 4 to 11 2544.32 0.627 0.734587 5 to 12 2546.33 0.655 0.743836 6 to 13 2488.89 -0.157 0.437557 7 to 14 2533.36 0.472 0.681445 8 to 15 2469.21 -0.435 0.331602 9 to 16 2512.69 0.179 0.571220 10 to 17 2445.99 -0.764 0.222490 11 to 18 2464.40 -0.504 0.307306 12 to 19 2468.27 -0.449 0.326819 13 to 20 2496.21 -0.054 0.478640 14 to 21 2472.88 -0.384 0.350659 15 to 22 2458.44 -0.588 0.278349 16 to 23 2562.48 0.884 0.811552 17 to 24 2532.47 0.459 0.676934 18 to 25 2499.15 -0.012 0.495191 19 to 26 2368.24 -1.863 0.031203 20 to 27 2577.24 1.092 0.862654 21 to 28 2507.04 0.099 0.539629 22 to 29 2573.07 1.033 0.849293 23 to 30 2401.37 -1.395 0.081527 24 to 31 2456.98 -0.608 0.271449 25 to 32 2428.45 -1.012 0.155791 CDPARK for dh-ranFile-2016-04-06_04:31: 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 3500 -1.0502 0.146807 3541 0.8219 0.794438 3533 0.4566 0.676028 3527 0.1826 0.572463 3514 -0.4110 0.340551 3501 -1.0046 0.157553 3497 -1.1872 0.117571 3542 0.8676 0.807188 3510 -0.5936 0.276387 3527 0.1826 0.572463 Square side=100, avg. no. parked=3519.20 sample std.=16.16 p-value of the KSTEST for those 10 p-values: 0.733487 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-06_04:31 0.7036,0.0563,0.8675,0.6017,0.5766,0.2067,0.2820,0.4705,0.3869,0.2186, The KS test for those 10 p-values: 0.767153 The 3DSPHERES test for dh-ranFile-2016-04-06_04:31 sample no r^3 equiv. uni. 1 51.356 0.819472 2 2.042 0.065814 3 24.470 0.557650 4 5.269 0.161069 5 48.187 0.799360 6 87.202 0.945346 7 16.289 0.418984 8 70.662 0.905145 9 18.389 0.458264 10 5.360 0.163624 11 5.028 0.154302 12 134.645 0.988759 13 65.503 0.887346 14 23.888 0.548994 15 7.478 0.220618 16 44.014 0.769417 17 67.207 0.893567 18 37.943 0.717691 19 53.134 0.829861 20 40.829 0.743584 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.136554 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-06_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 3.8 -0.6 1.5 -0.7 -0.6 0.6 0.7 0.8 -1.6 2.0 -0.7 1.8 -0.4 -1.3 -1.2 -0.3 0.7 -2.0 -0.4 0.5 -0.6 1.4 -1.5 0.7 1.5 1.4 0.9 2.0 1.2 -0.3 -1.1 -1.4 -0.5 0.1 -1.6 -0.5 2.1 -0.8 1.5 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:68.960247 z-score=2.941604, p-value=0.994556 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-06_04:31 Test no p-value 1 0.102741 2 0.033288 3 0.033714 4 0.009194 5 0.072171 6 0.012470 7 0.037828 8 0.273306 9 0.576295 10 0.054249 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000001 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-06_04:31: (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 66658 0.00 66695 0.01 3 25000.00 25033 0.04 25010 0.00 4 6666.67 6644 0.08 6589 0.90 5 1388.89 1369 0.28 1432 1.34 6 238.10 253 0.93 223 0.96 7 34.72 37 0.15 44 2.48 8 4.96 5 0.00 6 0.22 p=0.03982 p=0.56716 Number of rngs required: 688418, p-value: 0.507 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-06_04:31 No. of wins: Observed Expected 98895 98585.9 z-score= 1.383, pvalue=0.91662 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66656 66666.7 0.002 0.002 2 37678 37654.3 0.015 0.017 3 26848 26954.7 0.423 0.439 4 19232 19313.5 0.344 0.783 5 13957 13851.4 0.805 1.588 6 9937 9943.5 0.004 1.592 7 7116 7145.0 0.118 1.710 8 5179 5139.1 0.310 2.020 9 3724 3699.9 0.157 2.177 10 2722 2666.3 1.164 3.341 11 1956 1923.3 0.555 3.896 12 1352 1388.7 0.972 4.868 13 1001 1003.7 0.007 4.875 14 712 726.1 0.275 5.151 15 534 525.8 0.127 5.278 16 386 381.2 0.062 5.339 17 268 276.5 0.264 5.603 18 203 200.8 0.023 5.626 19 148 146.0 0.028 5.654 20 112 106.2 0.315 5.969 21 279 287.1 0.229 6.199 Chisq= 6.20 for 20 degrees of freedom, p= 0.00140 SUMMARY of craptest p-value for no. of wins: 0.916616 p-value for throws/game: 0.001399 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-06_04:31 No. of wins: Observed Expected 98618 98585.9 z-score= 0.144, pvalue=0.55715 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67032 66666.7 2.002 2.002 2 37616 37654.3 0.039 2.041 3 26824 26954.7 0.634 2.675 4 19065 19313.5 3.196 5.871 5 13668 13851.4 2.429 8.300 6 10090 9943.5 2.157 10.457 7 7107 7145.0 0.202 10.660 8 5102 5139.1 0.267 10.927 9 3819 3699.9 3.836 14.763 10 2692 2666.3 0.248 15.011 11 1891 1923.3 0.543 15.555 12 1420 1388.7 0.704 16.258 13 1000 1003.7 0.014 16.272 14 771 726.1 2.771 19.043 15 521 525.8 0.044 19.088 16 407 381.2 1.753 20.841 17 277 276.5 0.001 20.842 18 210 200.8 0.419 21.260 19 128 146.0 2.216 23.476 20 84 106.2 4.646 28.122 21 276 287.1 0.430 28.552 Chisq= 28.55 for 20 degrees of freedom, p= 0.90305 SUMMARY of craptest p-value for no. of wins: 0.557153 p-value for throws/game: 0.903048 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0014,0.0086,0.0092,0.0125,0.0131,0.0170,0.0189,0.0256,0.0312, 0.0333,0.0337,0.0362,0.0378,0.0398,0.0455,0.0480,0.0523,0.0542,0.0551, 0.0563,0.0582,0.0620,0.0646,0.0658,0.0682,0.0722,0.0815,0.0864,0.0868, 0.0899,0.0935,0.0957,0.1027,0.1055,0.1100,0.1107,0.1122,0.1138,0.1176, 0.1250,0.1266,0.1306,0.1309,0.1321,0.1366,0.1405,0.1416,0.1432,0.1441, 0.1459,0.1468,0.1543,0.1558,0.1571,0.1576,0.1611,0.1636,0.1651,0.1684, 0.1719,0.1809,0.1815,0.2027,0.2039,0.2050,0.2067,0.2100,0.2106,0.2186, 0.2186,0.2206,0.2225,0.2331,0.2332,0.2410,0.2451,0.2460,0.2529,0.2540, 0.2569,0.2685,0.2714,0.2733,0.2739,0.2764,0.2783,0.2820,0.3001,0.3012, 0.3046,0.3068,0.3073,0.3125,0.3179,0.3202,0.3220,0.3250,0.3256,0.3268, 0.3269,0.3316,0.3328,0.3393,0.3402,0.3406,0.3423,0.3429,0.3446,0.3483, 0.3507,0.3567,0.3680,0.3735,0.3742,0.3746,0.3869,0.3875,0.3880,0.3961, 0.3961,0.3979,0.3997,0.4052,0.4082,0.4176,0.4183,0.4190,0.4219,0.4311, 0.4330,0.4336,0.4346,0.4376,0.4416,0.4510,0.4570,0.4583,0.4599,0.4705, 0.4736,0.4752,0.4784,0.4786,0.4839,0.4952,0.4993,0.5008,0.5063,0.5069, 0.5114,0.5114,0.5189,0.5236,0.5396,0.5424,0.5431,0.5481,0.5490,0.5572, 0.5576,0.5642,0.5672,0.5712,0.5725,0.5725,0.5763,0.5766,0.5909,0.5961, 0.6012,0.6017,0.6043,0.6155,0.6236,0.6271,0.6279,0.6310,0.6324,0.6398, 0.6413,0.6446,0.6639,0.6711,0.6760,0.6769,0.6785,0.6814,0.6970,0.6971, 0.7011,0.7036,0.7170,0.7177,0.7219,0.7231,0.7290,0.7335,0.7346,0.7377, 0.7436,0.7438,0.7479,0.7614,0.7672,0.7694,0.7696,0.7712,0.7748,0.7766, 0.7944,0.7951,0.7994,0.8003,0.8072,0.8087,0.8116,0.8116,0.8147,0.8159, 0.8164,0.8170,0.8195,0.8263,0.8272,0.8294,0.8299,0.8302,0.8378,0.8385, 0.8404,0.8493,0.8502,0.8627,0.8629,0.8641,0.8675,0.8680,0.8705,0.8794, 0.8813,0.8831,0.8873,0.8936,0.8946,0.9030,0.9051,0.9105,0.9144,0.9159, 0.9166,0.9295,0.9301,0.9343,0.9400,0.9453,0.9479,0.9483,0.9544,0.9551, 0.9597,0.9639,0.9718,0.9764,0.9837,0.9880,0.9888,0.9905,0.9946, Overall p-value after applying KStest on 269 p-values = 0.151552 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.