RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-03_07:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 16.4339 0.506688 2 to 25 15.63 20.6792 0.759029 3 to 26 15.96 15.1487 0.415230 4 to 27 16.23 21.9394 0.812940 5 to 28 15.78 17.8771 0.603369 6 to 29 15.95 7.0655 0.017315 7 to 30 15.96 13.5349 0.300295 8 to 31 15.90 11.3939 0.164633 9 to 32 15.88 15.7655 0.459483 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.811778 Tough bday spacings test for dh-ranFile-2016-07-03_07:31: 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 11 37 78 99 106 69 43 30 18 5 4 (O-E)^2/E 0.4 0.0 0.3 0.0 0.7 1.1 1.6 0.0 0.7 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 5.115, p= 0.117 RESULTS OF GCD FOR dh-ranFile-2016-07-03_07:31 Euclid's algorithm: p-value, steps to gcd: 0.234368 p-value, dist. of gcd's: 0.941600 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-03_07:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.333 0.924 0.313 0.287 0.444 1.000 0.153 0.949 Bits 8 to 15---> 0.884 0.869 0.433 0.222 0.942 0.044 0.851 0.765 Bits 16 to 23---> 0.614 0.386 0.922 0.766 0.651 0.392 0.510 0.635 Bits 24 to 31---> 0.713 0.331 0.539 0.660 0.926 0.496 0.779 0.748 KS test for the above 32 p values: 0.954 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-03_07:31, p-values for 5 runs: 0.8846, 0.6677, 0.8632, 0.4472, 0.8203 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-03_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5059 5134.0 1.096 1.188 r= 30 23232 23103.0 0.720 1.908 r= 31 11502 11551.5 0.212 2.120 chi-square = 2.120 with df = 3; p-value = 0.452 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-03_07:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 181 211.4 4.376 4.376 r= 30 5118 5134.0 0.050 4.426 r= 31 23269 23103.0 1.192 5.618 r= 32 11432 11551.5 1.237 6.855 chi-square = 6.855 with df = 3; p-value = 0.923 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-03_07:31 b-rank test for bits 1 to 8, p=0.76625 b-rank test for bits 2 to 9, p=0.07182 b-rank test for bits 3 to 10, p=0.73117 b-rank test for bits 4 to 11, p=0.27718 b-rank test for bits 5 to 12, p=0.00729 b-rank test for bits 6 to 13, p=0.64572 b-rank test for bits 7 to 14, p=0.58791 b-rank test for bits 8 to 15, p=0.65734 b-rank test for bits 9 to 16, p=0.59488 b-rank test for bits 10 to 17, p=0.53118 b-rank test for bits 11 to 18, p=0.21638 b-rank test for bits 12 to 19, p=0.34858 b-rank test for bits 13 to 20, p=0.66454 b-rank test for bits 14 to 21, p=0.89672 b-rank test for bits 15 to 22, p=0.77712 b-rank test for bits 16 to 23, p=0.30611 b-rank test for bits 17 to 24, p=0.31500 b-rank test for bits 18 to 25, p=0.82590 b-rank test for bits 19 to 26, p=0.53981 b-rank test for bits 20 to 27, p=0.48138 b-rank test for bits 21 to 28, p=0.95193 b-rank test for bits 22 to 29, p=0.86440 b-rank test for bits 23 to 30, p=0.77649 b-rank test for bits 24 to 31, p=0.71500 b-rank test for bits 25 to 32, p=0.41434 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 = 0.361514 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-03_07:31 (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 141451 -1.07 0.142115 2 141896 -0.03 0.487577 3 141695 -0.50 0.308266 4 142001 0.21 0.584798 5 141869 -0.09 0.462464 6 142071 0.38 0.647186 7 142477 1.33 0.907635 8 141790 -0.28 0.390196 9 142214 0.71 0.761720 10 141454 -1.06 0.143697 11 142386 1.11 0.867299 12 141828 -0.19 0.424645 13 141991 0.19 0.575666 14 141750 -0.37 0.354847 15 142290 0.89 0.813110 16 141856 -0.12 0.450419 17 142583 1.57 0.942256 18 141858 -0.12 0.452269 19 141752 -0.37 0.356588 20 141791 -0.28 0.391093 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-03_07:31 Bits used No. missing words z-score p-value 23 to 32 142128 0.7540 0.774586 22 to 31 141648 -0.9011 0.183758 21 to 30 141703 -0.7115 0.238393 20 to 29 141240 -2.3080 0.010499 19 to 28 141955 0.1575 0.562568 18 to 27 141941 0.1092 0.543481 17 to 26 141824 -0.2942 0.384287 16 to 25 141933 0.0816 0.532526 15 to 24 141893 -0.0563 0.477547 14 to 23 141552 -1.2322 0.108942 13 to 22 141899 -0.0356 0.485792 12 to 21 141767 -0.4908 0.311786 11 to 20 141423 -1.6770 0.046771 10 to 19 142196 0.9885 0.838550 9 to 18 142236 1.1264 0.870012 8 to 17 141221 -2.3736 0.008809 7 to 16 141714 -0.6736 0.250298 6 to 15 141935 0.0885 0.535267 5 to 14 142064 0.5333 0.703103 4 to 13 142051 0.4885 0.687408 3 to 12 142200 1.0023 0.841903 2 to 11 142032 0.4230 0.663852 1 to 10 142164 0.8782 0.810075 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-03_07:31 Bits used No. missing words z-score p-value 28 to 32 141906 -0.0113 0.495497 27 to 31 141823 -0.2926 0.384897 26 to 30 142134 0.7616 0.776849 25 to 29 141741 -0.5706 0.284132 24 to 28 141920 0.0362 0.514426 23 to 27 142416 1.7175 0.957058 22 to 26 141730 -0.6079 0.271628 21 to 25 142303 1.3345 0.908976 20 to 24 141736 -0.5876 0.278414 19 to 23 141847 -0.2113 0.416331 18 to 22 141523 -1.3096 0.095167 17 to 21 141658 -0.8520 0.197116 16 to 20 142194 0.9650 0.832723 15 to 19 141579 -1.1198 0.131407 14 to 18 141888 -0.0723 0.471180 13 to 17 142113 0.6904 0.755031 12 to 16 142250 1.1548 0.875917 11 to 15 142023 0.3853 0.650001 10 to 14 142288 1.2836 0.900364 9 to 13 141890 -0.0655 0.473878 8 to 12 141893 -0.0554 0.477928 7 to 11 142387 1.6192 0.947300 6 to 10 141697 -0.7198 0.235836 5 to 9 141543 -1.2418 0.107156 4 to 8 141811 -0.3333 0.369446 3 to 7 142327 1.4158 0.921587 2 to 6 141562 -1.1774 0.119520 1 to 5 141719 -0.6452 0.259403 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-03_07:31 Bits used No. missing words z-score p-value 31 to 32 142564 1.9312 0.973270 30 to 31 142230 0.9459 0.827908 29 to 30 141662 -0.7296 0.232821 28 to 29 141836 -0.2163 0.414372 27 to 28 141955 0.1347 0.553583 26 to 27 141970 0.1790 0.571018 25 to 26 142352 1.3058 0.904192 24 to 25 142617 2.0875 0.981580 23 to 24 142127 0.6421 0.739594 22 to 23 141879 -0.0895 0.464355 21 to 22 142190 0.8279 0.796146 20 to 21 141530 -1.1190 0.131577 19 to 20 142305 1.1672 0.878429 18 to 19 142194 0.8397 0.799471 17 to 18 142432 1.5418 0.938439 16 to 17 141316 -1.7502 0.040039 15 to 16 142125 0.6362 0.737675 14 to 15 141984 0.2203 0.587168 13 to 14 142593 2.0167 0.978138 12 to 13 141920 0.0315 0.512555 11 to 12 142251 1.0079 0.843243 10 to 11 142196 0.8456 0.801122 9 to 10 142277 1.0846 0.860944 8 to 9 142597 2.0285 0.978747 7 to 8 141484 -1.2547 0.104801 6 to 7 142176 0.7866 0.784253 5 to 6 141930 0.0610 0.524310 4 to 5 141750 -0.4700 0.319178 3 to 4 141629 -0.8269 0.204138 2 to 3 142198 0.8515 0.802764 1 to 2 141523 -1.1396 0.127223 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-03_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2466.54 -0.473 0.318056 Test results for specific bytes for dh-ranFile-2016-07-03_07:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2401.51 -1.393 0.081831 2 to 9 2532.01 0.453 0.674615 3 to 10 2479.05 -0.296 0.383528 4 to 11 2495.42 -0.065 0.474201 5 to 12 2460.24 -0.562 0.286967 6 to 13 2544.21 0.625 0.734093 7 to 14 2487.02 -0.184 0.427167 8 to 15 2388.50 -1.577 0.057419 9 to 16 2613.59 1.606 0.945910 10 to 17 2569.84 0.988 0.838346 11 to 18 2645.42 2.056 0.980133 12 to 19 2658.80 2.246 0.987639 13 to 20 2536.22 0.512 0.695778 14 to 21 2491.88 -0.115 0.454265 15 to 22 2622.09 1.727 0.957885 16 to 23 2677.38 2.509 0.993939 17 to 24 2468.38 -0.447 0.327371 18 to 25 2428.62 -1.010 0.156359 19 to 26 2492.35 -0.108 0.456915 20 to 27 2447.15 -0.747 0.227417 21 to 28 2487.72 -0.174 0.431044 22 to 29 2496.73 -0.046 0.481567 23 to 30 2529.40 0.416 0.661225 24 to 31 2410.72 -1.263 0.103369 25 to 32 2475.15 -0.351 0.362655 CDPARK for dh-ranFile-2016-07-03_07:31: 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 3542 0.8676 0.807188 3530 0.3196 0.625377 3521 -0.0913 0.463617 3524 0.0457 0.518210 3513 -0.4566 0.323972 3547 1.0959 0.863437 3493 -1.3699 0.085365 3521 -0.0913 0.463617 3546 1.0502 0.853193 3528 0.2283 0.590298 Square side=100, avg. no. parked=3526.50 sample std.=15.58 p-value of the KSTEST for those 10 p-values: 0.620801 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-03_07:31 0.0768,0.6758,0.0010,0.0307,0.0241,0.8384,0.1101,0.2905,0.1655,0.7115, The KS test for those 10 p-values: 0.006498 The 3DSPHERES test for dh-ranFile-2016-07-03_07:31 sample no r^3 equiv. uni. 1 1.963 0.063326 2 10.926 0.305248 3 11.315 0.314197 4 15.766 0.408763 5 18.723 0.464251 6 25.062 0.566304 7 41.121 0.746069 8 58.352 0.857022 9 63.569 0.879845 10 11.193 0.311405 11 50.751 0.815796 12 45.063 0.777336 13 6.153 0.185445 14 3.806 0.119137 15 3.503 0.110211 16 2.350 0.075340 17 12.100 0.331903 18 26.064 0.580551 19 0.650 0.021446 20 13.251 0.357058 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.311482 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-03_07:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 -0.8 -0.5 1.3 0.0 1.7 0.9 0.6 0.2 -1.2 -1.4 1.6 -1.3 0.0 0.5 0.5 -0.8 0.9 1.5 -0.7 -0.9 -1.0 0.0 0.3 1.1 -0.1 -2.1 1.2 -0.7 1.2 -0.6 -0.3 1.1 -1.2 -1.0 -0.7 -0.4 -1.6 -0.1 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:38.852759 z-score=-0.343392, p-value=0.390091 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-03_07:31 Test no p-value 1 0.394433 2 0.066409 3 0.045406 4 0.207754 5 0.184122 6 0.040295 7 0.030134 8 0.914378 9 0.175759 10 0.445733 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.004063 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-03_07:31: (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 66896 0.79 66720 0.04 3 25000.00 24800 1.60 24880 0.58 4 6666.67 6665 0.00 6718 0.40 5 1388.89 1368 0.31 1409 0.29 6 238.10 233 0.11 241 0.04 7 34.72 30 0.64 26 2.19 8 4.96 7 0.84 5 0.00 p=0.36294 p=0.26014 Number of rngs required: 689695, p-value: 0.934 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-03_07:31 No. of wins: Observed Expected 98477 98585.9 z-score=-0.487, pvalue=0.31317 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66746 66666.7 0.094 0.094 2 37743 37654.3 0.209 0.303 3 26684 26954.7 2.719 3.022 4 19463 19313.5 1.158 4.180 5 13783 13851.4 0.338 4.518 6 9874 9943.5 0.486 5.005 7 7204 7145.0 0.487 5.491 8 5146 5139.1 0.009 5.501 9 3735 3699.9 0.334 5.834 10 2660 2666.3 0.015 5.849 11 1890 1923.3 0.578 6.427 12 1438 1388.7 1.747 8.174 13 999 1003.7 0.022 8.196 14 717 726.1 0.115 8.311 15 506 525.8 0.748 9.060 16 396 381.2 0.579 9.638 17 280 276.5 0.043 9.681 18 204 200.8 0.050 9.731 19 149 146.0 0.062 9.794 20 94 106.2 1.405 11.199 21 289 287.1 0.012 11.211 Chisq= 11.21 for 20 degrees of freedom, p= 0.05943 SUMMARY of craptest p-value for no. of wins: 0.313172 p-value for throws/game: 0.059432 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-03_07:31 No. of wins: Observed Expected 98452 98585.9 z-score=-0.599, pvalue=0.27469 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66464 66666.7 0.616 0.616 2 37715 37654.3 0.098 0.714 3 27097 26954.7 0.751 1.465 4 19472 19313.5 1.301 2.766 5 13652 13851.4 2.871 5.637 6 10020 9943.5 0.588 6.225 7 7124 7145.0 0.062 6.287 8 5107 5139.1 0.200 6.487 9 3750 3699.9 0.679 7.167 10 2669 2666.3 0.003 7.169 11 1945 1923.3 0.244 7.413 12 1373 1388.7 0.178 7.592 13 1041 1003.7 1.385 8.977 14 676 726.1 3.462 12.439 15 477 525.8 4.536 16.975 16 381 381.2 0.000 16.975 17 284 276.5 0.201 17.176 18 202 200.8 0.007 17.183 19 146 146.0 0.000 17.183 20 97 106.2 0.800 17.982 21 308 287.1 1.519 19.502 Chisq= 19.50 for 20 degrees of freedom, p= 0.51053 SUMMARY of craptest p-value for no. of wins: 0.274689 p-value for throws/game: 0.510533 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0010,0.0041,0.0065,0.0073,0.0088,0.0105,0.0173,0.0214,0.0241,0.0301, 0.0307,0.0400,0.0403,0.0445,0.0454,0.0468,0.0574,0.0594,0.0633,0.0664, 0.0718,0.0753,0.0768,0.0818,0.0854,0.0952,0.1034,0.1048,0.1072,0.1089, 0.1101,0.1102,0.1166,0.1191,0.1195,0.1272,0.1314,0.1316,0.1421,0.1437, 0.1531,0.1564,0.1646,0.1655,0.1758,0.1838,0.1841,0.1854,0.1971,0.2041, 0.2078,0.2164,0.2221,0.2274,0.2328,0.2344,0.2358,0.2384,0.2503,0.2594, 0.2601,0.2716,0.2747,0.2772,0.2784,0.2841,0.2870,0.2871,0.2905,0.3003, 0.3052,0.3061,0.3083,0.3114,0.3115,0.3118,0.3126,0.3132,0.3142,0.3150, 0.3181,0.3192,0.3240,0.3274,0.3308,0.3319,0.3330,0.3486,0.3548,0.3566, 0.3571,0.3615,0.3627,0.3629,0.3694,0.3835,0.3843,0.3849,0.3862,0.3901, 0.3902,0.3911,0.3920,0.3944,0.4088,0.4143,0.4144,0.4152,0.4163,0.4246, 0.4272,0.4310,0.4333,0.4442,0.4457,0.4472,0.4504,0.4522,0.4523,0.4543, 0.4569,0.4595,0.4625,0.4636,0.4636,0.4643,0.4644,0.4712,0.4739,0.4742, 0.4775,0.4779,0.4814,0.4816,0.4858,0.4876,0.4955,0.4960,0.5067,0.5099, 0.5105,0.5126,0.5144,0.5182,0.5243,0.5312,0.5325,0.5353,0.5389,0.5398, 0.5435,0.5536,0.5626,0.5663,0.5710,0.5757,0.5806,0.5848,0.5872,0.5879, 0.5903,0.5949,0.6034,0.6139,0.6208,0.6254,0.6354,0.6457,0.6472,0.6500, 0.6507,0.6573,0.6598,0.6612,0.6639,0.6645,0.6677,0.6746,0.6758,0.6874, 0.6958,0.7031,0.7115,0.7130,0.7150,0.7312,0.7341,0.7377,0.7396,0.7461, 0.7481,0.7550,0.7590,0.7617,0.7651,0.7663,0.7665,0.7746,0.7765,0.7768, 0.7771,0.7773,0.7786,0.7843,0.7961,0.7995,0.8011,0.8028,0.8072,0.8101, 0.8118,0.8129,0.8131,0.8158,0.8203,0.8259,0.8279,0.8327,0.8383,0.8384, 0.8386,0.8419,0.8432,0.8508,0.8532,0.8570,0.8609,0.8632,0.8634,0.8644, 0.8673,0.8685,0.8700,0.8759,0.8784,0.8798,0.8837,0.8846,0.8967,0.9004, 0.9042,0.9076,0.9090,0.9144,0.9216,0.9222,0.9233,0.9240,0.9258,0.9344, 0.9384,0.9416,0.9423,0.9424,0.9459,0.9473,0.9494,0.9519,0.9536,0.9571, 0.9579,0.9733,0.9781,0.9787,0.9801,0.9816,0.9876,0.9939,0.9999, Overall p-value after applying KStest on 269 p-values = 0.618077 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.