RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-10_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.57 15.5063 0.440939 2 to 25 15.84 12.6254 0.239123 3 to 26 16.04 18.3070 0.630277 4 to 27 16.02 15.9894 0.475415 5 to 28 16.05 15.1732 0.416992 6 to 29 15.96 8.3345 0.041139 7 to 30 16.12 20.1699 0.734370 8 to 31 16.06 14.3085 0.354843 9 to 32 16.03 17.8566 0.602057 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.479568 Tough bday spacings test for dh-ranFile-2015-09-10_00:31: 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 23 65 97 87 79 69 35 21 9 4 (O-E)^2/E 0.4 5.1 0.9 0.0 1.2 0.0 5.5 0.9 2.5 0.9 0.0 Birthday Spacings: Sum(O-E)^2/E= 17.332, p= 0.933 RESULTS OF GCD FOR dh-ranFile-2015-09-10_00:31 Euclid's algorithm: p-value, steps to gcd: 0.548013 p-value, dist. of gcd's: 0.443741 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-10_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.148 0.040 0.108 0.075 0.232 0.653 0.831 0.830 Bits 8 to 15---> 0.070 0.470 0.446 0.820 0.508 0.135 0.586 0.867 Bits 16 to 23---> 0.961 0.794 0.989 0.876 0.948 0.576 0.998 0.437 Bits 24 to 31---> 0.707 0.849 0.414 0.734 0.943 0.059 0.844 0.143 KS test for the above 32 p values: 0.888 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-10_00:31, p-values for 5 runs: 0.2549, 0.4565, 0.4443, 0.4807, 0.8983 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-10_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 190 211.4 2.170 2.170 r= 29 5205 5134.0 0.982 3.151 r= 30 23113 23103.0 0.004 3.156 r= 31 11492 11551.5 0.307 3.462 chi-square = 3.462 with df = 3; p-value = 0.674 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-10_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 240 211.4 3.864 3.864 r= 30 5266 5134.0 3.393 7.257 r= 31 23017 23103.0 0.320 7.578 r= 32 11477 11551.5 0.481 8.059 chi-square = 8.059 with df = 3; p-value = 0.955 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-10_00:31 b-rank test for bits 1 to 8, p=0.74477 b-rank test for bits 2 to 9, p=0.83051 b-rank test for bits 3 to 10, p=0.77779 b-rank test for bits 4 to 11, p=0.42891 b-rank test for bits 5 to 12, p=0.14785 b-rank test for bits 6 to 13, p=0.26153 b-rank test for bits 7 to 14, p=0.21016 b-rank test for bits 8 to 15, p=0.49187 b-rank test for bits 9 to 16, p=0.28338 b-rank test for bits 10 to 17, p=0.21997 b-rank test for bits 11 to 18, p=0.08500 b-rank test for bits 12 to 19, p=0.18553 b-rank test for bits 13 to 20, p=0.60567 b-rank test for bits 14 to 21, p=0.14125 b-rank test for bits 15 to 22, p=0.22075 b-rank test for bits 16 to 23, p=0.74276 b-rank test for bits 17 to 24, p=0.33760 b-rank test for bits 18 to 25, p=0.07185 b-rank test for bits 19 to 26, p=0.61662 b-rank test for bits 20 to 27, p=0.17129 b-rank test for bits 21 to 28, p=0.05326 b-rank test for bits 22 to 29, p=0.87665 b-rank test for bits 23 to 30, p=0.18332 b-rank test for bits 24 to 31, p=0.73248 b-rank test for bits 25 to 32, p=0.67334 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 = 0.105483 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-10_00:31 (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 141832 -0.18 0.428310 2 142001 0.21 0.584798 3 142036 0.30 0.616369 4 142205 0.69 0.755160 5 142285 0.88 0.809956 6 141861 -0.11 0.455047 7 141988 0.18 0.572918 8 140666 -2.90 0.001836 9 143062 2.69 0.996461 10 142141 0.54 0.705844 11 141917 0.02 0.507149 12 142013 0.24 0.595695 13 142292 0.89 0.814363 14 142296 0.90 0.816852 15 141847 -0.15 0.442106 16 141783 -0.30 0.383935 17 141372 -1.26 0.104659 18 141924 0.03 0.513671 19 142058 0.35 0.635840 20 141745 -0.38 0.350508 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-10_00:31 Bits used No. missing words z-score p-value 23 to 32 142018 0.3747 0.646067 22 to 31 141602 -1.0598 0.144627 21 to 30 141080 -2.8598 0.002120 20 to 29 142139 0.7920 0.785810 19 to 28 142606 2.4023 0.991854 18 to 27 141641 -0.9253 0.177411 17 to 26 141458 -1.5563 0.059817 16 to 25 141487 -1.4563 0.072653 15 to 24 142026 0.4023 0.656272 14 to 23 142401 1.6954 0.955002 13 to 22 141557 -1.2149 0.112196 12 to 21 141543 -1.2632 0.103257 11 to 20 141953 0.1506 0.559849 10 to 19 141896 -0.0460 0.481669 9 to 18 142107 0.6816 0.752261 8 to 17 142358 1.5471 0.939085 7 to 16 141853 -0.1942 0.422994 6 to 15 141897 -0.0425 0.483043 5 to 14 141435 -1.6356 0.050960 4 to 13 141828 -0.2804 0.389567 3 to 12 141659 -0.8632 0.194012 2 to 11 142141 0.7989 0.787815 1 to 10 142011 0.3506 0.637051 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-10_00:31 Bits used No. missing words z-score p-value 28 to 32 142322 1.3989 0.919076 27 to 31 142181 0.9209 0.821453 26 to 30 141993 0.2836 0.611652 25 to 29 141457 -1.5333 0.062598 24 to 28 141490 -1.4215 0.077592 23 to 27 141595 -1.0655 0.143319 22 to 26 142378 1.5887 0.943937 21 to 25 141647 -0.8893 0.186933 20 to 24 142198 0.9785 0.836097 19 to 23 141570 -1.1503 0.125016 18 to 22 141904 -0.0181 0.492792 17 to 21 141919 0.0328 0.513075 16 to 20 141683 -0.7672 0.221475 15 to 19 141325 -1.9808 0.023808 14 to 18 141329 -1.9672 0.024579 13 to 17 141585 -1.0994 0.135792 12 to 16 141711 -0.6723 0.250695 11 to 15 142006 0.3277 0.628429 10 to 14 141702 -0.7028 0.241086 9 to 13 141708 -0.6825 0.247470 8 to 12 141880 -0.0994 0.460401 7 to 11 142107 0.6701 0.748593 6 to 10 141362 -1.8554 0.031773 5 to 9 141811 -0.3333 0.369446 4 to 8 142313 1.3684 0.914402 3 to 7 141736 -0.5876 0.278414 2 to 6 141665 -0.8282 0.203768 1 to 5 142076 0.5650 0.713957 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-10_00:31 Bits used No. missing words z-score p-value 31 to 32 141924 0.0433 0.517259 30 to 31 141765 -0.4258 0.335144 29 to 30 141967 0.1701 0.567541 28 to 29 142221 0.9194 0.821052 27 to 28 142475 1.6686 0.952406 26 to 27 142102 0.5683 0.715101 25 to 26 141541 -1.0865 0.138625 24 to 25 141946 0.1082 0.543070 23 to 24 142235 0.9607 0.831643 22 to 23 142368 1.3530 0.911974 21 to 22 142045 0.4002 0.655498 20 to 21 141755 -0.4553 0.324464 19 to 20 142020 0.3265 0.627962 18 to 19 141685 -0.6617 0.254069 17 to 18 142296 1.1406 0.872986 16 to 17 141951 0.1229 0.548915 15 to 16 141493 -1.2281 0.109702 14 to 15 142056 0.4327 0.667367 13 to 14 142055 0.4297 0.666295 12 to 13 141746 -0.4818 0.314974 11 to 12 142290 1.1229 0.869264 10 to 11 141879 -0.0895 0.464355 9 to 10 142130 0.6509 0.742459 8 to 9 141929 0.0580 0.523135 7 to 8 141913 0.0108 0.504319 6 to 7 142028 0.3501 0.636853 5 to 6 142038 0.3796 0.647863 4 to 5 142478 1.6775 0.953277 3 to 4 142281 1.0964 0.863542 2 to 3 141511 -1.1750 0.119994 1 to 2 141846 -0.1868 0.425903 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-10_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2586.86 1.228 0.890362 Test results for specific bytes for dh-ranFile-2015-09-10_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2532.29 0.457 0.676055 2 to 9 2594.68 1.339 0.909705 3 to 10 2466.24 -0.477 0.316540 4 to 11 2475.45 -0.347 0.364230 5 to 12 2530.05 0.425 0.664574 6 to 13 2565.64 0.928 0.823373 7 to 14 2426.04 -1.046 0.147804 8 to 15 2618.95 1.682 0.953733 9 to 16 2458.61 -0.585 0.279182 10 to 17 2509.28 0.131 0.552234 11 to 18 2578.15 1.105 0.865462 12 to 19 2441.18 -0.832 0.202762 13 to 20 2502.01 0.028 0.511314 14 to 21 2494.81 -0.073 0.470754 15 to 22 2492.72 -0.103 0.458992 16 to 23 2352.36 -2.088 0.018404 17 to 24 2550.31 0.711 0.761609 18 to 25 2473.21 -0.379 0.352385 19 to 26 2684.14 2.604 0.995395 20 to 27 2573.67 1.042 0.851261 21 to 28 2470.22 -0.421 0.336826 22 to 29 2513.20 0.187 0.574060 23 to 30 2331.42 -2.384 0.008562 24 to 31 2602.83 1.454 0.927067 25 to 32 2414.68 -1.207 0.113800 CDPARK for dh-ranFile-2015-09-10_00:31: 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 3495 -1.2785 0.100530 3521 -0.0913 0.463617 3544 0.9589 0.831196 3498 -1.1416 0.126820 3476 -2.1461 0.015932 3559 1.6438 0.949895 3536 0.5936 0.723613 3521 -0.0913 0.463617 3541 0.8219 0.794438 3555 1.4612 0.928018 Square side=100, avg. no. parked=3524.60 sample std.=26.18 p-value of the KSTEST for those 10 p-values: 0.580340 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-10_00:31 0.2568,0.1679,0.1800,0.9752,0.7205,0.5382,0.7574,0.9205,0.3233,0.3107, The KS test for those 10 p-values: 0.858471 The 3DSPHERES test for dh-ranFile-2015-09-10_00:31 sample no r^3 equiv. uni. 1 26.724 0.589674 2 9.738 0.277195 3 22.731 0.531255 4 8.645 0.250360 5 105.028 0.969830 6 108.502 0.973130 7 18.961 0.468494 8 2.554 0.081605 9 3.391 0.106877 10 10.949 0.305786 11 3.244 0.102493 12 2.902 0.092188 13 8.335 0.242585 14 29.245 0.622741 15 11.565 0.319892 16 19.384 0.475937 17 6.140 0.185075 18 40.007 0.736466 19 27.092 0.594676 20 4.805 0.148005 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.162253 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-10_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.6 -2.3 -1.0 1.4 0.7 -0.2 0.2 -0.4 1.5 -1.2 1.5 0.4 0.8 0.8 -1.5 0.3 -0.5 0.8 0.2 -1.3 -0.3 0.4 0.0 -0.1 -0.2 -0.1 -1.3 -0.8 0.3 -0.3 1.6 -0.1 -1.4 -1.0 -1.2 1.0 -1.0 -0.4 -0.7 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:39.733216 z-score=-0.247326, p-value=0.429059 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-10_00:31 Test no p-value 1 0.042233 2 0.397877 3 0.442844 4 0.022268 5 0.014142 6 0.253392 7 0.565481 8 0.812226 9 0.229191 10 0.359538 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.044915 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-10_00:31: (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 66821 0.36 66391 1.14 3 25000.00 24917 0.28 25256 2.62 4 6666.67 6617 0.37 6706 0.23 5 1388.89 1380 0.06 1368 0.31 6 238.10 219 1.53 245 0.20 7 34.72 41 1.14 29 0.94 8 4.96 4 0.19 4 0.19 p=0.31154 p=0.53482 Number of rngs required: 688952, p-value: 0.737 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-10_00:31 No. of wins: Observed Expected 98965 98585.9 z-score= 1.696, pvalue=0.95503 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66401 66666.7 1.059 1.059 2 37689 37654.3 0.032 1.091 3 27047 26954.7 0.316 1.406 4 19272 19313.5 0.089 1.495 5 13848 13851.4 0.001 1.496 6 9928 9943.5 0.024 1.521 7 7182 7145.0 0.191 1.712 8 5222 5139.1 1.338 3.050 9 3772 3699.9 1.406 4.457 10 2695 2666.3 0.309 4.766 11 2054 1923.3 8.878 13.643 12 1349 1388.7 1.137 14.780 13 934 1003.7 4.842 19.623 14 752 726.1 0.921 20.544 15 534 525.8 0.127 20.670 16 349 381.2 2.712 23.382 17 260 276.5 0.989 24.372 18 190 200.8 0.584 24.956 19 156 146.0 0.687 25.643 20 101 106.2 0.256 25.899 21 265 287.1 1.703 27.602 Chisq= 27.60 for 20 degrees of freedom, p= 0.88084 SUMMARY of craptest p-value for no. of wins: 0.955033 p-value for throws/game: 0.880839 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-10_00:31 No. of wins: Observed Expected 98491 98585.9 z-score=-0.424, pvalue=0.33569 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66633 66666.7 0.017 0.017 2 37795 37654.3 0.526 0.543 3 26873 26954.7 0.248 0.790 4 19292 19313.5 0.024 0.814 5 13816 13851.4 0.091 0.905 6 9747 9943.5 3.885 4.790 7 7120 7145.0 0.088 4.877 8 5251 5139.1 2.438 7.315 9 3839 3699.9 5.232 12.547 10 2616 2666.3 0.949 13.496 11 1858 1923.3 2.219 15.715 12 1438 1388.7 1.747 17.462 13 999 1003.7 0.022 17.485 14 742 726.1 0.346 17.831 15 558 525.8 1.967 19.798 16 421 381.2 4.166 23.965 17 257 276.5 1.381 25.345 18 215 200.8 1.000 26.345 19 128 146.0 2.216 28.561 20 93 106.2 1.644 30.205 21 309 287.1 1.668 31.873 Chisq= 31.87 for 20 degrees of freedom, p= 0.95533 SUMMARY of craptest p-value for no. of wins: 0.335687 p-value for throws/game: 0.955331 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0021,0.0086,0.0141,0.0159,0.0184,0.0223,0.0238,0.0246,0.0318, 0.0403,0.0411,0.0422,0.0449,0.0510,0.0533,0.0592,0.0598,0.0626,0.0703, 0.0719,0.0727,0.0754,0.0776,0.0816,0.0850,0.0922,0.1005,0.1025,0.1033, 0.1047,0.1055,0.1069,0.1084,0.1097,0.1122,0.1138,0.1200,0.1250,0.1268, 0.1346,0.1358,0.1386,0.1412,0.1433,0.1435,0.1446,0.1478,0.1478,0.1479, 0.1480,0.1623,0.1679,0.1713,0.1774,0.1800,0.1833,0.1851,0.1855,0.1869, 0.1940,0.2028,0.2038,0.2102,0.2200,0.2207,0.2215,0.2292,0.2318,0.2391, 0.2411,0.2426,0.2475,0.2504,0.2507,0.2534,0.2541,0.2549,0.2568,0.2615, 0.2772,0.2784,0.2792,0.2834,0.3058,0.3107,0.3115,0.3150,0.3165,0.3199, 0.3233,0.3245,0.3351,0.3357,0.3368,0.3376,0.3505,0.3524,0.3548,0.3595, 0.3642,0.3694,0.3839,0.3896,0.3979,0.4137,0.4170,0.4230,0.4259,0.4283, 0.4289,0.4291,0.4367,0.4409,0.4421,0.4428,0.4437,0.4443,0.4461,0.4550, 0.4565,0.4590,0.4604,0.4636,0.4636,0.4644,0.4685,0.4695,0.4708,0.4754, 0.4759,0.4796,0.4807,0.4817,0.4830,0.4919,0.4928,0.5043,0.5071,0.5081, 0.5113,0.5131,0.5137,0.5173,0.5231,0.5313,0.5348,0.5382,0.5431,0.5480, 0.5489,0.5522,0.5598,0.5655,0.5675,0.5729,0.5741,0.5757,0.5803,0.5848, 0.5857,0.5897,0.5947,0.5957,0.6021,0.6057,0.6117,0.6164,0.6166,0.6227, 0.6280,0.6284,0.6303,0.6358,0.6369,0.6371,0.6461,0.6479,0.6527,0.6555, 0.6563,0.6646,0.6663,0.6674,0.6733,0.6743,0.6761,0.7058,0.7069,0.7140, 0.7151,0.7205,0.7236,0.7325,0.7338,0.7344,0.7365,0.7368,0.7425,0.7428, 0.7448,0.7486,0.7523,0.7552,0.7574,0.7616,0.7778,0.7858,0.7878,0.7935, 0.7944,0.8100,0.8122,0.8144,0.8169,0.8197,0.8211,0.8215,0.8234,0.8296, 0.8305,0.8312,0.8315,0.8316,0.8361,0.8442,0.8487,0.8513,0.8585,0.8635, 0.8655,0.8671,0.8693,0.8730,0.8764,0.8767,0.8808,0.8879,0.8904,0.8983, 0.9097,0.9120,0.9144,0.9191,0.9205,0.9271,0.9280,0.9327,0.9391,0.9432, 0.9439,0.9479,0.9499,0.9524,0.9533,0.9537,0.9550,0.9550,0.9552,0.9553, 0.9614,0.9698,0.9731,0.9752,0.9889,0.9919,0.9954,0.9965,0.9982, Overall p-value after applying KStest on 269 p-values = 0.851054 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.