RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-07_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 14.4262 0.363262 2 to 25 15.63 20.4413 0.747718 3 to 26 15.64 13.1454 0.273599 4 to 27 15.77 16.9903 0.544975 5 to 28 15.85 16.2971 0.497124 6 to 29 15.63 23.6000 0.869283 7 to 30 15.65 18.1949 0.623353 8 to 31 15.86 28.0028 0.955094 9 to 32 16.17 16.9389 0.541489 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.408666 Tough bday spacings test for dh-ranFile-2015-09-07_09:31: 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 33 90 102 82 88 49 28 11 7 2 (O-E)^2/E 0.1 0.4 3.8 0.2 2.5 1.2 0.2 0.1 1.0 0.0 1.0 Birthday Spacings: Sum(O-E)^2/E= 10.657, p= 0.615 RESULTS OF GCD FOR dh-ranFile-2015-09-07_09:31 Euclid's algorithm: p-value, steps to gcd: 0.834748 p-value, dist. of gcd's: 0.814718 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-07_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.247 0.190 0.402 0.300 0.243 0.316 0.341 0.124 Bits 8 to 15---> 0.146 0.749 0.091 0.339 0.498 0.909 0.652 0.561 Bits 16 to 23---> 0.693 0.687 0.414 0.243 0.226 0.547 0.783 0.166 Bits 24 to 31---> 0.379 0.670 0.366 0.174 0.494 0.523 0.223 0.534 KS test for the above 32 p values: 0.956 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-07_09:31, p-values for 5 runs: 0.6188, 0.2908, 0.6451, 0.2489, 0.3043 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-07_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5217 5134.0 1.341 1.602 r= 30 22986 23103.0 0.593 2.195 r= 31 11593 11551.5 0.149 2.344 chi-square = 2.344 with df = 3; p-value = 0.496 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-07_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 207 211.4 0.092 0.092 r= 30 5183 5134.0 0.467 0.560 r= 31 23070 23103.0 0.047 0.607 r= 32 11540 11551.5 0.011 0.619 chi-square = 0.619 with df = 3; p-value = 0.108 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-07_09:31 b-rank test for bits 1 to 8, p=0.55412 b-rank test for bits 2 to 9, p=0.06954 b-rank test for bits 3 to 10, p=0.47352 b-rank test for bits 4 to 11, p=0.81524 b-rank test for bits 5 to 12, p=0.09462 b-rank test for bits 6 to 13, p=0.22443 b-rank test for bits 7 to 14, p=0.78104 b-rank test for bits 8 to 15, p=0.10275 b-rank test for bits 9 to 16, p=0.06821 b-rank test for bits 10 to 17, p=0.09152 b-rank test for bits 11 to 18, p=0.10766 b-rank test for bits 12 to 19, p=0.54710 b-rank test for bits 13 to 20, p=0.95977 b-rank test for bits 14 to 21, p=0.94427 b-rank test for bits 15 to 22, p=0.96842 b-rank test for bits 16 to 23, p=0.89569 b-rank test for bits 17 to 24, p=0.21021 b-rank test for bits 18 to 25, p=0.34787 b-rank test for bits 19 to 26, p=0.81546 b-rank test for bits 20 to 27, p=0.12653 b-rank test for bits 21 to 28, p=0.81967 b-rank test for bits 22 to 29, p=0.51490 b-rank test for bits 23 to 30, p=0.54783 b-rank test for bits 24 to 31, p=0.90440 b-rank test for bits 25 to 32, p=0.94476 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 = 0.245972 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-07_09:31 (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 141836 -0.17 0.431981 2 142632 1.69 0.954341 3 142463 1.29 0.902102 4 142091 0.42 0.664386 5 141676 -0.55 0.292821 6 141840 -0.16 0.435658 7 142012 0.24 0.594790 8 142642 1.71 0.956537 9 141744 -0.39 0.349643 10 141983 0.17 0.568331 11 141847 -0.15 0.442106 12 141813 -0.23 0.410962 13 141675 -0.55 0.292018 14 141958 0.11 0.545268 15 141861 -0.11 0.455047 16 142180 0.63 0.736439 17 141571 -0.79 0.214621 18 141572 -0.79 0.215303 19 141565 -0.80 0.210551 20 142096 0.44 0.668634 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-07_09:31 Bits used No. missing words z-score p-value 23 to 32 141858 -0.1770 0.429754 22 to 31 141541 -1.2701 0.102024 21 to 30 141862 -0.1632 0.435178 20 to 29 141538 -1.2804 0.100194 19 to 28 141573 -1.1598 0.123074 18 to 27 141882 -0.0942 0.462459 17 to 26 142016 0.3678 0.643499 16 to 25 141473 -1.5046 0.066215 15 to 24 141892 -0.0598 0.476174 14 to 23 141724 -0.6391 0.261389 13 to 22 142085 0.6058 0.727663 12 to 21 142212 1.0437 0.851686 11 to 20 142206 1.0230 0.846846 10 to 19 142799 3.0678 0.998922 9 to 18 141856 -0.1839 0.427047 8 to 17 142034 0.4299 0.666365 7 to 16 142171 0.9023 0.816554 6 to 15 141903 -0.0218 0.491293 5 to 14 142313 1.3920 0.918034 4 to 13 141943 0.1161 0.546215 3 to 12 142117 0.7161 0.763036 2 to 11 142180 0.9333 0.824679 1 to 10 141705 -0.7046 0.240534 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-07_09:31 Bits used No. missing words z-score p-value 28 to 32 141818 -0.3096 0.378435 27 to 31 141665 -0.8282 0.203768 26 to 30 142435 1.7819 0.962620 25 to 29 141533 -1.2757 0.101032 24 to 28 142182 0.9243 0.822336 23 to 27 141891 -0.0621 0.475227 22 to 26 142165 0.8667 0.806941 21 to 25 141540 -1.2520 0.105291 20 to 24 141927 0.0599 0.523882 19 to 23 141662 -0.8384 0.200901 18 to 22 141893 -0.0554 0.477928 17 to 21 141969 0.2023 0.580148 16 to 20 142035 0.4260 0.664946 15 to 19 141660 -0.8452 0.199003 14 to 18 141748 -0.5469 0.292230 13 to 17 142042 0.4497 0.673547 12 to 16 142267 1.2124 0.887328 11 to 15 141713 -0.6655 0.252857 10 to 14 141477 -1.4655 0.071389 9 to 13 142070 0.5446 0.707001 8 to 12 141502 -1.3808 0.083673 7 to 11 141869 -0.1367 0.445629 6 to 10 141627 -0.9571 0.169271 5 to 9 142262 1.1955 0.884053 4 to 8 142184 0.9311 0.824095 3 to 7 141541 -1.2486 0.105910 2 to 6 142385 1.6124 0.946567 1 to 5 141586 -1.0960 0.136532 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-07_09:31 Bits used No. missing words z-score p-value 31 to 32 141920 0.0315 0.512555 30 to 31 141548 -1.0659 0.143241 29 to 30 141896 -0.0393 0.484317 28 to 29 141988 0.2321 0.591756 27 to 28 141740 -0.4995 0.308714 26 to 27 141836 -0.2163 0.414372 25 to 26 142511 1.7748 0.962038 24 to 25 141761 -0.4376 0.330856 23 to 24 141794 -0.3402 0.366851 22 to 23 141811 -0.2901 0.385886 21 to 22 142474 1.6657 0.952113 20 to 21 141726 -0.5408 0.294324 19 to 20 141827 -0.2429 0.404056 18 to 19 141919 0.0285 0.511378 17 to 18 141544 -1.0777 0.140591 16 to 17 141633 -0.8151 0.207498 15 to 16 142263 1.0433 0.851589 14 to 15 142221 0.9194 0.821052 13 to 14 141576 -0.9833 0.162736 12 to 13 141829 -0.2370 0.406343 11 to 12 141421 -1.4405 0.074863 10 to 11 141358 -1.6263 0.051938 9 to 10 142054 0.4268 0.665221 8 to 9 141828 -0.2399 0.405199 7 to 8 141754 -0.4582 0.323404 6 to 7 141853 -0.1662 0.434014 5 to 6 142651 2.1878 0.985659 4 to 5 141652 -0.7591 0.223901 3 to 4 142286 1.1111 0.866742 2 to 3 141686 -0.6588 0.255015 1 to 2 141968 0.1731 0.568701 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-07_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2453.97 -0.651 0.257518 Test results for specific bytes for dh-ranFile-2015-09-07_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2433.27 -0.944 0.172669 2 to 9 2541.96 0.593 0.723568 3 to 10 2547.53 0.672 0.749249 4 to 11 2594.16 1.332 0.908509 5 to 12 2474.32 -0.363 0.358246 6 to 13 2558.63 0.829 0.796493 7 to 14 2570.03 0.990 0.839018 8 to 15 2510.49 0.148 0.558963 9 to 16 2570.53 0.997 0.840720 10 to 17 2406.50 -1.322 0.093034 11 to 18 2592.03 1.302 0.903467 12 to 19 2469.15 -0.436 0.331318 13 to 20 2473.62 -0.373 0.354536 14 to 21 2346.87 -2.166 0.015170 15 to 22 2560.07 0.850 0.802216 16 to 23 2510.02 0.142 0.556357 17 to 24 2464.26 -0.505 0.306608 18 to 25 2440.69 -0.839 0.200790 19 to 26 2593.60 1.324 0.907193 20 to 27 2546.70 0.660 0.745505 21 to 28 2399.62 -1.420 0.077868 22 to 29 2477.27 -0.321 0.373947 23 to 30 2503.18 0.045 0.517960 24 to 31 2509.18 0.130 0.551626 25 to 32 2586.34 1.221 0.888976 CDPARK for dh-ranFile-2015-09-07_09:31: 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 3518 -0.2283 0.409702 3518 -0.2283 0.409702 3514 -0.4110 0.340551 3483 -1.8265 0.033889 3518 -0.2283 0.409702 3521 -0.0913 0.463617 3544 0.9589 0.831196 3502 -0.9589 0.168804 3550 1.2329 0.891189 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3517.00 sample std.=18.58 p-value of the KSTEST for those 10 p-values: 0.456207 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-07_09:31 0.2532,0.1615,0.0473,0.7421,0.7490,0.0480,0.5650,0.5102,0.9839,0.8531, The KS test for those 10 p-values: 0.821922 The 3DSPHERES test for dh-ranFile-2015-09-07_09:31 sample no r^3 equiv. uni. 1 18.741 0.464583 2 42.245 0.755410 3 35.429 0.693023 4 45.733 0.782257 5 27.750 0.603463 6 20.424 0.493794 7 25.943 0.578851 8 77.038 0.923305 9 13.403 0.360301 10 8.826 0.254866 11 3.762 0.117862 12 28.453 0.612646 13 18.402 0.458491 14 4.353 0.135061 15 63.951 0.881366 16 14.453 0.382303 17 78.587 0.927166 18 9.212 0.264408 19 4.042 0.126064 20 57.097 0.850913 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.858213 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-07_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.1 -0.4 -1.6 -3.0 1.0 0.6 -1.2 -1.3 1.0 -0.2 1.0 0.9 -0.4 1.0 1.6 -1.4 -0.7 0.2 -0.8 0.8 -0.5 -0.4 -0.9 0.6 -0.5 0.2 -0.4 -1.6 1.6 0.3 -0.2 1.5 -1.0 0.6 0.3 -0.1 -0.8 -0.1 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:41.314008 z-score=-0.074848, p-value=0.499067 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-07_09:31 Test no p-value 1 0.012872 2 0.186133 3 0.108129 4 0.021992 5 0.413751 6 0.008711 7 0.381037 8 0.489666 9 0.037859 10 0.547993 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000884 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-07_09:31: (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 66599 0.07 66613 0.04 3 25000.00 25014 0.01 25008 0.00 4 6666.67 6731 0.62 6720 0.43 5 1388.89 1354 0.88 1363 0.48 6 238.10 247 0.33 253 0.93 7 34.72 51 7.63 34 0.01 8 4.96 3 0.77 8 1.86 p=0.88800 p=0.29172 Number of rngs required: 688114, p-value: 0.370 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-07_09:31 No. of wins: Observed Expected 98660 98585.9 z-score= 0.332, pvalue=0.62991 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66547 66666.7 0.215 0.215 2 37658 37654.3 0.000 0.215 3 26878 26954.7 0.218 0.434 4 19452 19313.5 0.994 1.427 5 13827 13851.4 0.043 1.470 6 9965 9943.5 0.046 1.517 7 7095 7145.0 0.350 1.867 8 5198 5139.1 0.676 2.543 9 3725 3699.9 0.171 2.713 10 2666 2666.3 0.000 2.713 11 1921 1923.3 0.003 2.716 12 1422 1388.7 0.797 3.513 13 1019 1003.7 0.233 3.746 14 731 726.1 0.033 3.778 15 473 525.8 5.309 9.087 16 400 381.2 0.932 10.019 17 287 276.5 0.396 10.415 18 205 200.8 0.087 10.501 19 147 146.0 0.007 10.509 20 103 106.2 0.097 10.606 21 281 287.1 0.130 10.736 Chisq= 10.74 for 20 degrees of freedom, p= 0.04722 SUMMARY of craptest p-value for no. of wins: 0.629906 p-value for throws/game: 0.047218 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-07_09:31 No. of wins: Observed Expected 98341 98585.9 z-score=-1.095, pvalue=0.13673 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66614 66666.7 0.042 0.042 2 37632 37654.3 0.013 0.055 3 26994 26954.7 0.057 0.112 4 19533 19313.5 2.496 2.608 5 13810 13851.4 0.124 2.731 6 9956 9943.5 0.016 2.747 7 7263 7145.0 1.948 4.695 8 5020 5139.1 2.759 7.454 9 3607 3699.9 2.331 9.785 10 2695 2666.3 0.309 10.094 11 1884 1923.3 0.804 10.898 12 1415 1388.7 0.497 11.394 13 965 1003.7 1.493 12.888 14 701 726.1 0.870 13.758 15 510 525.8 0.477 14.235 16 397 381.2 0.659 14.894 17 282 276.5 0.108 15.002 18 189 200.8 0.697 15.699 19 160 146.0 1.346 17.044 20 91 106.2 2.180 19.224 21 282 287.1 0.091 19.315 Chisq= 19.32 for 20 degrees of freedom, p= 0.49856 SUMMARY of craptest p-value for no. of wins: 0.136725 p-value for throws/game: 0.498562 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0009,0.0087,0.0129,0.0152,0.0220,0.0339,0.0379,0.0472,0.0473,0.0480, 0.0519,0.0662,0.0682,0.0695,0.0714,0.0749,0.0779,0.0837,0.0912,0.0915, 0.0930,0.0946,0.1002,0.1010,0.1020,0.1027,0.1053,0.1059,0.1077,0.1078, 0.1081,0.1179,0.1231,0.1236,0.1261,0.1265,0.1351,0.1365,0.1367,0.1406, 0.1432,0.1464,0.1615,0.1627,0.1662,0.1688,0.1688,0.1693,0.1727,0.1738, 0.1861,0.1897,0.1990,0.2008,0.2009,0.2038,0.2075,0.2102,0.2106,0.2146, 0.2153,0.2232,0.2239,0.2244,0.2257,0.2405,0.2426,0.2426,0.2460,0.2467, 0.2489,0.2529,0.2532,0.2549,0.2550,0.2575,0.2614,0.2644,0.2736,0.2908, 0.2917,0.2920,0.2922,0.2928,0.2943,0.3004,0.3043,0.3066,0.3087,0.3162, 0.3234,0.3309,0.3313,0.3395,0.3406,0.3408,0.3479,0.3496,0.3545,0.3582, 0.3603,0.3633,0.3656,0.3669,0.3697,0.3739,0.3784,0.3785,0.3810,0.3823, 0.3859,0.4015,0.4041,0.4052,0.4063,0.4087,0.4097,0.4097,0.4097,0.4110, 0.4135,0.4138,0.4144,0.4270,0.4298,0.4320,0.4340,0.4352,0.4357,0.4421, 0.4456,0.4550,0.4562,0.4585,0.4625,0.4636,0.4646,0.4735,0.4752,0.4762, 0.4779,0.4843,0.4897,0.4913,0.4938,0.4943,0.4958,0.4971,0.4984,0.4986, 0.4991,0.5102,0.5114,0.5126,0.5149,0.5180,0.5227,0.5239,0.5342,0.5415, 0.5450,0.5453,0.5462,0.5471,0.5474,0.5478,0.5480,0.5516,0.5541,0.5564, 0.5590,0.5614,0.5650,0.5683,0.5687,0.5789,0.5801,0.5918,0.5948,0.6035, 0.6126,0.6151,0.6188,0.6234,0.6299,0.6435,0.6451,0.6516,0.6644,0.6649, 0.6652,0.6664,0.6686,0.6701,0.6735,0.6875,0.6930,0.6933,0.7070,0.7236, 0.7277,0.7364,0.7421,0.7455,0.7477,0.7490,0.7490,0.7492,0.7554,0.7630, 0.7810,0.7823,0.7832,0.7965,0.8022,0.8069,0.8147,0.8152,0.8155,0.8166, 0.8197,0.8211,0.8219,0.8223,0.8241,0.8247,0.8312,0.8347,0.8390,0.8407, 0.8468,0.8509,0.8516,0.8517,0.8531,0.8582,0.8667,0.8693,0.8814,0.8841, 0.8873,0.8880,0.8890,0.8912,0.8957,0.9021,0.9035,0.9044,0.9072,0.9085, 0.9093,0.9180,0.9233,0.9272,0.9443,0.9448,0.9466,0.9521,0.9543,0.9551, 0.9561,0.9565,0.9598,0.9620,0.9626,0.9684,0.9839,0.9857,0.9989, Overall p-value after applying KStest on 269 p-values = 0.238735 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.