RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-26_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 25.4488 0.914895 2 to 25 15.49 30.9120 0.979530 3 to 26 15.87 18.1572 0.621011 4 to 27 15.79 15.2918 0.425525 5 to 28 15.70 30.0162 0.973771 6 to 29 16.00 17.2460 0.562176 7 to 30 15.78 9.8666 0.090888 8 to 31 15.65 13.4087 0.291576 9 to 32 15.82 7.4522 0.023098 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.407542 Tough bday spacings test for dh-ranFile-2016-05-26_16:31: 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 39 82 86 96 81 51 30 16 4 4 (O-E)^2/E 0.4 0.2 1.0 1.4 0.0 0.1 0.0 0.0 0.1 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 4.240, p= 0.064 RESULTS OF GCD FOR dh-ranFile-2016-05-26_16:31 Euclid's algorithm: p-value, steps to gcd: 0.283871 p-value, dist. of gcd's: 0.564167 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-26_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.927 0.186 0.216 0.124 0.690 0.725 0.990 0.625 Bits 8 to 15---> 0.390 0.670 0.155 0.369 0.221 0.190 0.178 0.260 Bits 16 to 23---> 0.277 0.564 0.809 0.701 0.107 0.433 0.891 0.968 Bits 24 to 31---> 0.177 0.678 0.004 0.598 0.174 0.949 0.440 0.431 KS test for the above 32 p values: 0.382 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-26_16:31, p-values for 5 runs: 0.0628, 0.2052, 0.6468, 0.4283, 0.5839 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-26_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5169 5134.0 0.238 0.266 r= 30 23117 23103.0 0.008 0.275 r= 31 11505 11551.5 0.187 0.462 chi-square = 0.462 with df = 3; p-value = 0.073 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-26_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 201 211.4 0.513 0.513 r= 30 5154 5134.0 0.078 0.591 r= 31 23119 23103.0 0.011 0.602 r= 32 11526 11551.5 0.056 0.659 chi-square = 0.659 with df = 3; p-value = 0.117 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-26_16:31 b-rank test for bits 1 to 8, p=0.95951 b-rank test for bits 2 to 9, p=0.56201 b-rank test for bits 3 to 10, p=0.37724 b-rank test for bits 4 to 11, p=0.42442 b-rank test for bits 5 to 12, p=0.40294 b-rank test for bits 6 to 13, p=0.39164 b-rank test for bits 7 to 14, p=0.69550 b-rank test for bits 8 to 15, p=0.72781 b-rank test for bits 9 to 16, p=0.35809 b-rank test for bits 10 to 17, p=0.42132 b-rank test for bits 11 to 18, p=0.91548 b-rank test for bits 12 to 19, p=0.86606 b-rank test for bits 13 to 20, p=0.10787 b-rank test for bits 14 to 21, p=0.23391 b-rank test for bits 15 to 22, p=0.12218 b-rank test for bits 16 to 23, p=0.25320 b-rank test for bits 17 to 24, p=0.94056 b-rank test for bits 18 to 25, p=0.19868 b-rank test for bits 19 to 26, p=0.33948 b-rank test for bits 20 to 27, p=0.28517 b-rank test for bits 21 to 28, p=0.40237 b-rank test for bits 22 to 29, p=0.99220 b-rank test for bits 23 to 30, p=0.30591 b-rank test for bits 24 to 31, p=0.15188 b-rank test for bits 25 to 32, p=0.71678 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 = 0.463494 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-26_16:31 (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 141917 0.02 0.507149 2 142013 0.24 0.595695 3 141759 -0.35 0.362705 4 142024 0.27 0.605620 5 141900 -0.02 0.491304 6 142661 1.76 0.960476 7 141761 -0.35 0.364459 8 142312 0.94 0.826601 9 141887 -0.05 0.479196 10 142139 0.54 0.704232 11 142530 1.45 0.926494 12 142110 0.47 0.680413 13 141564 -0.81 0.209878 14 142104 0.45 0.675387 15 141409 -1.17 0.121203 16 142276 0.86 0.804196 17 142233 0.76 0.775247 18 142051 0.33 0.629680 19 142455 1.27 0.898833 20 142074 0.38 0.649786 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-26_16:31 Bits used No. missing words z-score p-value 23 to 32 141674 -0.8115 0.208544 22 to 31 141909 -0.0011 0.499546 21 to 30 141854 -0.1908 0.424344 20 to 29 142285 1.2954 0.902411 19 to 28 141644 -0.9149 0.180114 18 to 27 141956 0.1609 0.563926 17 to 26 141723 -0.6425 0.260269 16 to 25 142319 1.4127 0.921121 15 to 24 142064 0.5333 0.703103 14 to 23 141799 -0.3804 0.351806 13 to 22 142399 1.6885 0.954344 12 to 21 142035 0.4333 0.667618 11 to 20 141932 0.0782 0.531155 10 to 19 141960 0.1747 0.569352 9 to 18 142207 1.0264 0.847660 8 to 17 141644 -0.9149 0.180114 7 to 16 141690 -0.7563 0.224732 6 to 15 142658 2.5816 0.995083 5 to 14 141854 -0.1908 0.424344 4 to 13 141474 -1.5011 0.066660 3 to 12 142296 1.3333 0.908791 2 to 11 142131 0.7644 0.777679 1 to 10 141853 -0.1942 0.422994 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-26_16:31 Bits used No. missing words z-score p-value 28 to 32 141720 -0.6418 0.260503 27 to 31 142105 0.6633 0.746427 26 to 30 142608 2.3684 0.991067 25 to 29 141757 -0.5164 0.302797 24 to 28 141632 -0.9401 0.173583 23 to 27 142079 0.5752 0.717406 22 to 26 141594 -1.0689 0.142554 21 to 25 142016 0.3616 0.641172 20 to 24 141577 -1.1265 0.129968 19 to 23 141174 -2.4926 0.006340 18 to 22 142197 0.9752 0.835258 17 to 21 142062 0.5175 0.697605 16 to 20 141635 -0.9299 0.176203 15 to 19 141741 -0.5706 0.284132 14 to 18 142016 0.3616 0.641172 13 to 17 142040 0.4429 0.671099 12 to 16 142112 0.6870 0.753964 11 to 15 141793 -0.3943 0.346665 10 to 14 141267 -2.1774 0.014726 9 to 13 141844 -0.2215 0.412368 8 to 12 141783 -0.4282 0.334239 7 to 11 142136 0.7684 0.778867 6 to 10 141825 -0.2859 0.387491 5 to 9 141507 -1.3638 0.086310 4 to 8 141790 -0.4045 0.342919 3 to 7 141888 -0.0723 0.471180 2 to 6 141950 0.1379 0.554826 1 to 5 141926 0.0565 0.522532 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-26_16:31 Bits used No. missing words z-score p-value 31 to 32 141916 0.0197 0.507849 30 to 31 141220 -2.0334 0.021005 29 to 30 142357 1.3206 0.906676 28 to 29 141232 -1.9980 0.022857 27 to 28 142477 1.6745 0.952988 26 to 27 142294 1.1347 0.871754 25 to 26 141927 0.0521 0.520785 24 to 25 141675 -0.6912 0.244708 23 to 24 141826 -0.2458 0.402914 22 to 23 142547 1.8810 0.970016 21 to 22 141746 -0.4818 0.314974 20 to 21 141761 -0.4376 0.330856 19 to 20 141657 -0.7443 0.228337 18 to 19 141785 -0.3668 0.356901 17 to 18 142028 0.3501 0.636853 16 to 17 142072 0.4799 0.684334 15 to 16 141565 -1.0157 0.154881 14 to 15 141604 -0.9007 0.183880 13 to 14 141873 -0.1072 0.457328 12 to 13 141539 -1.0924 0.137325 11 to 12 142349 1.2970 0.902678 10 to 11 141951 0.1229 0.548915 9 to 10 141889 -0.0600 0.476090 8 to 9 142199 0.8545 0.803582 7 to 8 141604 -0.9007 0.183880 6 to 7 141757 -0.4494 0.326589 5 to 6 141448 -1.3609 0.086780 4 to 5 141845 -0.1898 0.424747 3 to 4 141886 -0.0688 0.472566 2 to 3 141970 0.1790 0.571018 1 to 2 141866 -0.1278 0.449147 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-26_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2408.11 -1.300 0.096877 Test results for specific bytes for dh-ranFile-2016-05-26_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2453.04 -0.664 0.253322 2 to 9 2561.84 0.874 0.809075 3 to 10 2571.73 1.014 0.844792 4 to 11 2607.56 1.521 0.935880 5 to 12 2401.65 -1.391 0.082140 6 to 13 2440.85 -0.836 0.201438 7 to 14 2477.55 -0.318 0.375422 8 to 15 2358.49 -2.001 0.022683 9 to 16 2568.18 0.964 0.832527 10 to 17 2529.47 0.417 0.661567 11 to 18 2491.31 -0.123 0.451091 12 to 19 2502.95 0.042 0.516645 13 to 20 2482.19 -0.252 0.400584 14 to 21 2441.87 -0.822 0.205521 15 to 22 2490.70 -0.132 0.447682 16 to 23 2539.84 0.563 0.713443 17 to 24 2466.55 -0.473 0.318112 18 to 25 2566.70 0.943 0.827218 19 to 26 2645.18 2.053 0.979968 20 to 27 2571.50 1.011 0.844018 21 to 28 2650.54 2.129 0.983372 22 to 29 2549.30 0.697 0.757162 23 to 30 2560.17 0.851 0.802608 24 to 31 2519.93 0.282 0.610949 25 to 32 2483.55 -0.233 0.408015 CDPARK for dh-ranFile-2016-05-26_16:31: 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 3560 1.6895 0.954438 3517 -0.2740 0.392053 3549 1.1872 0.882429 3551 1.2785 0.899470 3551 1.2785 0.899470 3530 0.3196 0.625377 3526 0.1370 0.554479 3508 -0.6849 0.246694 3470 -2.4201 0.007758 3514 -0.4110 0.340551 Square side=100, avg. no. parked=3527.60 sample std.=25.71 p-value of the KSTEST for those 10 p-values: 0.400078 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-26_16:31 0.5475,0.5974,0.7756,0.1034,0.0179,0.0212,0.6996,0.2859,0.2605,0.1066, The KS test for those 10 p-values: 0.088367 The 3DSPHERES test for dh-ranFile-2016-05-26_16:31 sample no r^3 equiv. uni. 1 4.255 0.132241 2 59.308 0.861506 3 6.083 0.183541 4 95.816 0.958987 5 22.850 0.533106 6 33.319 0.670653 7 32.726 0.664072 8 73.775 0.914495 9 14.252 0.378153 10 11.728 0.323567 11 1.055 0.034559 12 15.428 0.402067 13 6.212 0.187041 14 34.684 0.685299 15 36.741 0.706152 16 60.555 0.867144 17 2.067 0.066585 18 4.721 0.145602 19 3.484 0.109634 20 16.834 0.429430 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.835627 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-26_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.2 -0.4 1.6 1.5 -1.5 -0.8 -0.5 1.2 -0.5 1.4 -1.9 -0.8 -0.5 0.9 0.6 -1.3 1.8 0.5 -1.0 0.4 0.9 -0.9 -0.9 0.5 0.5 0.1 1.0 -1.7 -0.5 1.1 0.0 -0.5 -0.4 -0.9 0.6 0.0 1.1 -0.8 0.4 -0.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:39.548282 z-score=-0.267504, p-value=0.420852 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-26_16:31 Test no p-value 1 0.527630 2 0.798661 3 0.623579 4 0.703616 5 0.772158 6 0.455283 7 0.508176 8 0.000350 9 0.080472 10 0.998917 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.275685 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-26_16:31: (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 66910 0.89 66649 0.00 3 25000.00 24748 2.54 25075 0.23 4 6666.67 6726 0.53 6660 0.01 5 1388.89 1342 1.58 1363 0.48 6 238.10 228 0.43 217 1.87 7 34.72 42 1.53 30 0.64 8 4.96 3 0.77 5 0.00 p=0.78091 p=0.22052 Number of rngs required: 686950, p-value: 0.044 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-26_16:31 No. of wins: Observed Expected 98419 98585.9 z-score=-0.746, pvalue=0.22775 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66857 66666.7 0.543 0.543 2 37544 37654.3 0.323 0.867 3 27104 26954.7 0.827 1.693 4 19080 19313.5 2.822 4.515 5 13957 13851.4 0.805 5.320 6 10034 9943.5 0.823 6.143 7 7182 7145.0 0.191 6.334 8 5089 5139.1 0.488 6.822 9 3629 3699.9 1.357 8.179 10 2653 2666.3 0.066 8.246 11 1876 1923.3 1.165 9.410 12 1415 1388.7 0.497 9.907 13 984 1003.7 0.387 10.294 14 663 726.1 5.490 15.785 15 506 525.8 0.748 16.533 16 361 381.2 1.065 17.598 17 303 276.5 2.532 20.130 18 189 200.8 0.697 20.827 19 137 146.0 0.553 21.380 20 126 106.2 3.685 25.065 21 311 287.1 1.987 27.052 Chisq= 27.05 for 20 degrees of freedom, p= 0.86620 SUMMARY of craptest p-value for no. of wins: 0.227746 p-value for throws/game: 0.866200 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-26_16:31 No. of wins: Observed Expected 98417 98585.9 z-score=-0.755, pvalue=0.22505 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66794 66666.7 0.243 0.243 2 37582 37654.3 0.139 0.382 3 26952 26954.7 0.000 0.382 4 19218 19313.5 0.472 0.854 5 13729 13851.4 1.082 1.936 6 9955 9943.5 0.013 1.949 7 7083 7145.0 0.538 2.488 8 5198 5139.1 0.676 3.164 9 3773 3699.9 1.446 4.609 10 2702 2666.3 0.478 5.087 11 1937 1923.3 0.097 5.184 12 1319 1388.7 3.502 8.687 13 1023 1003.7 0.371 9.057 14 757 726.1 1.311 10.369 15 522 525.8 0.028 10.397 16 363 381.2 0.864 11.261 17 321 276.5 7.148 18.409 18 202 200.8 0.007 18.416 19 160 146.0 1.346 19.762 20 104 106.2 0.046 19.808 21 306 287.1 1.242 21.050 Chisq= 21.05 for 20 degrees of freedom, p= 0.60581 SUMMARY of craptest p-value for no. of wins: 0.225054 p-value for throws/game: 0.605808 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0040,0.0063,0.0078,0.0147,0.0179,0.0210,0.0212,0.0227,0.0229, 0.0231,0.0346,0.0442,0.0628,0.0641,0.0666,0.0667,0.0728,0.0805,0.0821, 0.0863,0.0868,0.0884,0.0909,0.0969,0.1034,0.1066,0.1073,0.1079,0.1096, 0.1171,0.1212,0.1222,0.1237,0.1300,0.1322,0.1373,0.1426,0.1456,0.1519, 0.1549,0.1552,0.1736,0.1740,0.1762,0.1768,0.1782,0.1801,0.1801,0.1835, 0.1839,0.1839,0.1855,0.1870,0.1899,0.1987,0.2014,0.2052,0.2055,0.2085, 0.2099,0.2161,0.2205,0.2206,0.2247,0.2251,0.2277,0.2283,0.2339,0.2447, 0.2467,0.2532,0.2533,0.2599,0.2603,0.2605,0.2605,0.2757,0.2768,0.2839, 0.2841,0.2852,0.2859,0.2916,0.3028,0.3059,0.3150,0.3181,0.3236,0.3266, 0.3309,0.3342,0.3395,0.3406,0.3429,0.3467,0.3518,0.3569,0.3581,0.3627, 0.3645,0.3691,0.3754,0.3772,0.3782,0.3817,0.3875,0.3904,0.3916,0.3921, 0.4001,0.4006,0.4021,0.4024,0.4029,0.4029,0.4075,0.4080,0.4124,0.4209, 0.4213,0.4230,0.4243,0.4243,0.4244,0.4247,0.4255,0.4283,0.4294,0.4315, 0.4330,0.4403,0.4477,0.4491,0.4511,0.4553,0.4573,0.4635,0.4712,0.4726, 0.4761,0.4792,0.4913,0.4995,0.5071,0.5078,0.5082,0.5166,0.5208,0.5225, 0.5276,0.5312,0.5331,0.5475,0.5489,0.5545,0.5548,0.5620,0.5622,0.5636, 0.5639,0.5642,0.5694,0.5710,0.5839,0.5957,0.5974,0.5983,0.6056,0.6058, 0.6109,0.6210,0.6236,0.6247,0.6254,0.6297,0.6369,0.6412,0.6412,0.6468, 0.6498,0.6616,0.6641,0.6676,0.6699,0.6707,0.6711,0.6754,0.6780,0.6804, 0.6843,0.6853,0.6900,0.6955,0.6976,0.6996,0.7007,0.7031,0.7036,0.7042, 0.7062,0.7134,0.7168,0.7174,0.7246,0.7278,0.7464,0.7540,0.7572,0.7722, 0.7752,0.7756,0.7777,0.7789,0.7809,0.7987,0.8026,0.8036,0.8042,0.8088, 0.8091,0.8266,0.8272,0.8325,0.8353,0.8356,0.8440,0.8448,0.8477,0.8615, 0.8661,0.8662,0.8671,0.8718,0.8824,0.8914,0.8988,0.8995,0.8995,0.9024, 0.9027,0.9067,0.9088,0.9145,0.9149,0.9155,0.9211,0.9265,0.9268,0.9359, 0.9406,0.9494,0.9530,0.9543,0.9544,0.9590,0.9595,0.9605,0.9678,0.9700, 0.9738,0.9795,0.9800,0.9834,0.9903,0.9911,0.9922,0.9951,0.9989, Overall p-value after applying KStest on 269 p-values = 0.661467 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.