RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-12-24_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.73 12.6853 0.243015 2 to 25 15.91 11.2885 0.158820 3 to 26 15.84 36.3370 0.995866 4 to 27 15.78 25.7892 0.921613 5 to 28 16.01 9.8726 0.091134 6 to 29 15.90 8.3583 0.041727 7 to 30 15.85 29.9103 0.973001 8 to 31 15.42 22.6500 0.839003 9 to 32 15.51 29.1577 0.966900 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.027521 Tough bday spacings test for dh-ranFile-2016-12-24_21:31: 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 14 39 78 80 106 78 51 27 12 6 9 (O-E)^2/E 2.6 0.2 0.3 3.2 0.7 0.0 0.0 0.3 0.6 0.1 6.0 Birthday Spacings: Sum(O-E)^2/E= 13.814, p= 0.818 RESULTS OF GCD FOR dh-ranFile-2016-12-24_21:31 Euclid's algorithm: p-value, steps to gcd: 0.080374 p-value, dist. of gcd's: 0.689903 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-12-24_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.079 0.109 0.653 0.385 0.338 0.518 0.684 0.531 Bits 8 to 15---> 0.119 0.443 0.887 0.566 0.606 0.934 0.503 0.614 Bits 16 to 23---> 0.276 0.647 0.906 0.558 0.974 0.740 0.518 0.203 Bits 24 to 31---> 0.124 0.925 0.017 0.081 0.836 0.214 0.637 0.000 KS test for the above 32 p values: 0.244 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-12-24_21:31, p-values for 5 runs: 0.9335, 0.5621, 0.8863, 0.5896, 0.9898 Rank test for binary matrices (31x31) for dh-ranFile-2016-12-24_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5093 5134.0 0.328 0.355 r= 30 23013 23103.0 0.351 0.706 r= 31 11685 11551.5 1.542 2.249 chi-square = 2.249 with df = 3; p-value = 0.478 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-12-24_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5147 5134.0 0.033 1.039 r= 31 23216 23103.0 0.552 1.591 r= 32 11411 11551.5 1.709 3.300 chi-square = 3.300 with df = 3; p-value = 0.652 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-12-24_21:31 b-rank test for bits 1 to 8, p=0.45899 b-rank test for bits 2 to 9, p=0.29777 b-rank test for bits 3 to 10, p=0.77029 b-rank test for bits 4 to 11, p=0.47942 b-rank test for bits 5 to 12, p=0.36482 b-rank test for bits 6 to 13, p=0.12915 b-rank test for bits 7 to 14, p=0.35982 b-rank test for bits 8 to 15, p=0.50929 b-rank test for bits 9 to 16, p=0.14498 b-rank test for bits 10 to 17, p=0.70637 b-rank test for bits 11 to 18, p=0.45047 b-rank test for bits 12 to 19, p=0.91404 b-rank test for bits 13 to 20, p=0.36521 b-rank test for bits 14 to 21, p=0.10448 b-rank test for bits 15 to 22, p=0.44432 b-rank test for bits 16 to 23, p=0.46736 b-rank test for bits 17 to 24, p=0.12422 b-rank test for bits 18 to 25, p=0.00733 b-rank test for bits 19 to 26, p=0.31013 b-rank test for bits 20 to 27, p=0.37356 b-rank test for bits 21 to 28, p=0.82622 b-rank test for bits 22 to 29, p=0.35524 b-rank test for bits 23 to 30, p=0.05243 b-rank test for bits 24 to 31, p=0.46062 b-rank test for bits 25 to 32, p=0.69759 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 = 0.098382 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-12-24_21:31 (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 142155 0.57 0.717015 2 141131 -1.82 0.034492 3 141811 -0.23 0.409146 4 141674 -0.55 0.291216 5 141243 -1.56 0.059754 6 142001 0.21 0.584798 7 141279 -1.47 0.070411 8 141007 -2.11 0.017505 9 142857 2.21 0.986592 10 141820 -0.21 0.417335 11 142834 2.16 0.984631 12 142020 0.26 0.602018 13 141933 0.06 0.522052 14 141163 -1.74 0.040600 15 142102 0.45 0.673704 16 141845 -0.15 0.440263 17 142049 0.33 0.627913 18 141446 -1.08 0.139505 19 142247 0.79 0.784929 20 142158 0.58 0.719381 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-12-24_21:31 Bits used No. missing words z-score p-value 23 to 32 142054 0.4989 0.691062 22 to 31 142006 0.3333 0.630563 21 to 30 142072 0.5609 0.712578 20 to 29 141714 -0.6736 0.250298 19 to 28 141778 -0.4529 0.325324 18 to 27 141664 -0.8460 0.198786 17 to 26 141651 -0.8908 0.186520 16 to 25 142170 0.8989 0.815637 15 to 24 141734 -0.6046 0.272727 14 to 23 141768 -0.4873 0.313007 13 to 22 141853 -0.1942 0.422994 12 to 21 142368 1.5816 0.943132 11 to 20 141957 0.1644 0.565284 10 to 19 142102 0.6644 0.746776 9 to 18 141747 -0.5598 0.287822 8 to 17 141868 -0.1425 0.443336 7 to 16 142458 1.8920 0.970752 6 to 15 141226 -2.3563 0.009229 5 to 14 142312 1.3885 0.917510 4 to 13 141874 -0.1218 0.451518 3 to 12 141974 0.2230 0.588232 2 to 11 141988 0.2713 0.606911 1 to 10 142022 0.3885 0.651183 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-12-24_21:31 Bits used No. missing words z-score p-value 28 to 32 141911 0.0057 0.502258 27 to 31 141634 -0.9333 0.175327 26 to 30 141777 -0.4486 0.326869 25 to 29 141249 -2.2384 0.012597 24 to 28 141927 0.0599 0.523882 23 to 27 142483 1.9446 0.974091 22 to 26 142210 1.0192 0.845951 21 to 25 142422 1.7379 0.958883 20 to 24 142198 0.9785 0.836097 19 to 23 141878 -0.1062 0.457711 18 to 22 141762 -0.4994 0.308741 17 to 21 142163 0.8599 0.805077 16 to 20 141895 -0.0486 0.480629 15 to 19 141578 -1.1232 0.130686 14 to 18 141681 -0.7740 0.219465 13 to 17 141247 -2.2452 0.012378 12 to 16 142038 0.4362 0.668643 11 to 15 141865 -0.1503 0.440275 10 to 14 141794 -0.3909 0.347917 9 to 13 141961 0.1752 0.569520 8 to 12 141377 -1.8045 0.035576 7 to 11 142450 1.8328 0.966582 6 to 10 141920 0.0362 0.514426 5 to 9 142779 2.9480 0.998401 4 to 8 142284 1.2701 0.897970 3 to 7 141759 -0.5096 0.305168 2 to 6 141419 -1.6621 0.048243 1 to 5 141839 -0.2384 0.405783 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-12-24_21:31 Bits used No. missing words z-score p-value 31 to 32 141692 -0.6411 0.260732 30 to 31 141795 -0.3373 0.367962 29 to 30 142018 0.3206 0.625728 28 to 29 141367 -1.5998 0.054822 27 to 28 142097 0.5536 0.710073 26 to 27 141658 -0.7414 0.229230 25 to 26 141866 -0.1278 0.449147 24 to 25 141397 -1.5113 0.065356 23 to 24 141893 -0.0482 0.480790 22 to 23 142787 2.5890 0.995187 21 to 22 142617 2.0875 0.981580 20 to 21 141562 -1.0246 0.152783 19 to 20 141766 -0.4228 0.336220 18 to 19 141815 -0.2783 0.390407 17 to 18 141996 0.2557 0.600895 16 to 17 142001 0.2704 0.606579 15 to 16 141723 -0.5496 0.291281 14 to 15 141743 -0.4906 0.311837 13 to 14 141677 -0.6853 0.246565 12 to 13 142034 0.3678 0.643473 11 to 12 141416 -1.4553 0.072800 10 to 11 142148 0.7040 0.759297 9 to 10 142166 0.7571 0.775517 8 to 9 142113 0.6008 0.726012 7 to 8 141984 0.2203 0.587168 6 to 7 141741 -0.4965 0.309754 5 to 6 141919 0.0285 0.511378 4 to 5 141771 -0.4081 0.341617 3 to 4 141711 -0.5850 0.279259 2 to 3 142578 1.9725 0.975722 1 to 2 141756 -0.4523 0.325526 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-12-24_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2433.50 -0.940 0.173493 Test results for specific bytes for dh-ranFile-2016-12-24_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2488.87 -0.157 0.437450 2 to 9 2306.80 -2.732 0.003146 3 to 10 2568.06 0.963 0.832109 4 to 11 2529.22 0.413 0.660289 5 to 12 2571.18 1.007 0.842956 6 to 13 2500.55 0.008 0.503087 7 to 14 2496.27 -0.053 0.478992 8 to 15 2443.87 -0.794 0.213650 9 to 16 2465.23 -0.492 0.311474 10 to 17 2396.42 -1.465 0.071482 11 to 18 2630.47 1.845 0.967485 12 to 19 2442.71 -0.810 0.208892 13 to 20 2413.00 -1.230 0.109271 14 to 21 2531.56 0.446 0.672309 15 to 22 2441.97 -0.821 0.205910 16 to 23 2577.00 1.089 0.861913 17 to 24 2409.03 -1.286 0.099144 18 to 25 2462.67 -0.528 0.298772 19 to 26 2550.28 0.711 0.761463 20 to 27 2489.05 -0.155 0.438495 21 to 28 2557.77 0.817 0.793045 22 to 29 2435.21 -0.916 0.179764 23 to 30 2497.71 -0.032 0.487101 24 to 31 2536.53 0.517 0.697288 25 to 32 2467.35 -0.462 0.322121 CDPARK for dh-ranFile-2016-12-24_21:31: 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 3539 0.7306 0.767486 3525 0.0913 0.536383 3520 -0.1370 0.445521 3530 0.3196 0.625377 3536 0.5936 0.723613 3481 -1.9178 0.027568 3533 0.4566 0.676028 3520 -0.1370 0.445521 3509 -0.6393 0.261324 3551 1.2785 0.899470 Square side=100, avg. no. parked=3524.40 sample std.=18.22 p-value of the KSTEST for those 10 p-values: 0.744638 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-12-24_21:31 0.4959,0.1345,0.6826,0.7326,0.5860,0.1017,0.4281,0.3693,0.0405,0.2380, The KS test for those 10 p-values: 0.339148 The 3DSPHERES test for dh-ranFile-2016-12-24_21:31 sample no r^3 equiv. uni. 1 88.515 0.947686 2 47.333 0.793563 3 39.118 0.728536 4 17.582 0.443495 5 31.223 0.646814 6 21.873 0.517658 7 12.044 0.330670 8 7.055 0.209556 9 0.655 0.021608 10 116.549 0.979451 11 27.257 0.596902 12 0.021 0.000711 13 20.509 0.495221 14 11.576 0.320142 15 12.122 0.332406 16 1.698 0.055041 17 24.245 0.554327 18 54.217 0.835892 19 64.381 0.883053 20 44.341 0.771916 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.759693 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-12-24_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.1 -0.5 -0.4 -0.4 1.5 0.8 0.6 0.4 1.6 -1.6 -0.3 0.5 -0.5 -0.2 -0.3 0.5 -0.4 0.0 -0.2 -0.7 -0.3 0.4 -0.2 0.5 0.8 0.3 0.0 -0.3 1.0 -2.4 -1.0 1.1 1.9 0.4 0.7 0.8 1.3 -0.1 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:29.277317 z-score=-1.388159, p-value=0.068764 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-12-24_21:31 Test no p-value 1 0.006783 2 0.116473 3 0.126322 4 0.087882 5 0.033785 6 0.975494 7 0.074912 8 0.364790 9 0.019458 10 0.402916 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000411 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-12-24_21:31: (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 66660 0.00 66678 0.00 3 25000.00 24933 0.18 24924 0.23 4 6666.67 6733 0.66 6637 0.13 5 1388.89 1422 0.79 1459 3.54 6 238.10 222 1.09 266 3.27 7 34.72 24 3.31 32 0.21 8 4.96 5 0.00 3 0.77 p=0.57991 p=0.77354 Number of rngs required: 687541, p-value: 0.159 RESULTS OF CRAPS TEST for dh-ranFile-2016-12-24_21:31 No. of wins: Observed Expected 98540 98585.9 z-score=-0.205, pvalue=0.41874 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66936 66666.7 1.088 1.088 2 37453 37654.3 1.076 2.164 3 26870 26954.7 0.266 2.431 4 19252 19313.5 0.196 2.626 5 13994 13851.4 1.468 4.094 6 9779 9943.5 2.723 6.817 7 7277 7145.0 2.438 9.255 8 5127 5139.1 0.028 9.283 9 3730 3699.9 0.245 9.528 10 2608 2666.3 1.275 10.803 11 1906 1923.3 0.156 10.959 12 1449 1388.7 2.615 13.574 13 974 1003.7 0.880 14.454 14 705 726.1 0.615 15.069 15 578 525.8 5.175 20.244 16 352 381.2 2.229 22.473 17 268 276.5 0.264 22.737 18 212 200.8 0.621 23.358 19 159 146.0 1.160 24.519 20 110 106.2 0.135 24.654 21 261 287.1 2.375 27.029 Chisq= 27.03 for 20 degrees of freedom, p= 0.86554 SUMMARY of craptest p-value for no. of wins: 0.418745 p-value for throws/game: 0.865545 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-12-24_21:31 No. of wins: Observed Expected 98813 98585.9 z-score= 1.016, pvalue=0.84516 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66729 66666.7 0.058 0.058 2 37143 37654.3 6.943 7.002 3 27028 26954.7 0.199 7.201 4 19632 19313.5 5.254 12.454 5 13889 13851.4 0.102 12.556 6 9950 9943.5 0.004 12.561 7 7076 7145.0 0.667 13.227 8 5041 5139.1 1.872 15.099 9 3735 3699.9 0.334 15.433 10 2683 2666.3 0.105 15.537 11 1953 1923.3 0.458 15.995 12 1403 1388.7 0.146 16.141 13 1000 1003.7 0.014 16.155 14 712 726.1 0.275 16.431 15 596 525.8 9.362 25.793 16 404 381.2 1.370 27.163 17 277 276.5 0.001 27.163 18 201 200.8 0.000 27.164 19 151 146.0 0.172 27.336 20 98 106.2 0.635 27.971 21 299 287.1 0.492 28.463 Chisq= 28.46 for 20 degrees of freedom, p= 0.90112 SUMMARY of craptest p-value for no. of wins: 0.845164 p-value for throws/game: 0.901123 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0004,0.0007,0.0031,0.0068,0.0073,0.0092,0.0124,0.0126,0.0170, 0.0175,0.0195,0.0216,0.0275,0.0276,0.0338,0.0345,0.0356,0.0405,0.0406, 0.0417,0.0482,0.0524,0.0548,0.0550,0.0598,0.0654,0.0688,0.0704,0.0715, 0.0728,0.0749,0.0794,0.0804,0.0806,0.0879,0.0911,0.0984,0.0991,0.1017, 0.1045,0.1092,0.1093,0.1165,0.1189,0.1239,0.1242,0.1263,0.1291,0.1307, 0.1345,0.1395,0.1450,0.1528,0.1588,0.1590,0.1735,0.1753,0.1798,0.1865, 0.1988,0.2035,0.2059,0.2089,0.2096,0.2136,0.2139,0.2195,0.2292,0.2380, 0.2430,0.2437,0.2466,0.2503,0.2607,0.2613,0.2727,0.2760,0.2793,0.2878, 0.2912,0.2913,0.2978,0.2988,0.3052,0.3087,0.3098,0.3101,0.3115,0.3118, 0.3130,0.3201,0.3221,0.3253,0.3255,0.3269,0.3307,0.3324,0.3362,0.3378, 0.3391,0.3416,0.3479,0.3552,0.3598,0.3648,0.3648,0.3652,0.3680,0.3693, 0.3736,0.3846,0.3904,0.4029,0.4058,0.4091,0.4173,0.4187,0.4230,0.4281, 0.4374,0.4385,0.4403,0.4403,0.4430,0.4433,0.4435,0.4443,0.4455,0.4455, 0.4491,0.4505,0.4515,0.4577,0.4590,0.4606,0.4674,0.4775,0.4790,0.4794, 0.4806,0.4808,0.4871,0.4952,0.4959,0.5023,0.5031,0.5034,0.5093,0.5114, 0.5144,0.5177,0.5177,0.5177,0.5221,0.5239,0.5311,0.5364,0.5543,0.5577, 0.5621,0.5653,0.5664,0.5695,0.5799,0.5848,0.5860,0.5872,0.5882,0.5896, 0.5969,0.6009,0.6020,0.6060,0.6066,0.6069,0.6144,0.6254,0.6257,0.6279, 0.6306,0.6365,0.6435,0.6468,0.6469,0.6512,0.6524,0.6527,0.6603,0.6686, 0.6723,0.6737,0.6760,0.6826,0.6840,0.6899,0.6911,0.6973,0.6976,0.7064, 0.7101,0.7126,0.7170,0.7194,0.7236,0.7260,0.7285,0.7326,0.7396,0.7446, 0.7468,0.7593,0.7597,0.7615,0.7675,0.7703,0.7719,0.7735,0.7755,0.7849, 0.7930,0.7936,0.8051,0.8156,0.8183,0.8262,0.8321,0.8359,0.8361,0.8365, 0.8390,0.8430,0.8452,0.8460,0.8619,0.8655,0.8831,0.8863,0.8866,0.8980, 0.8995,0.9011,0.9061,0.9140,0.9175,0.9216,0.9245,0.9335,0.9345,0.9431, 0.9477,0.9589,0.9666,0.9669,0.9675,0.9708,0.9730,0.9738,0.9741,0.9755, 0.9757,0.9795,0.9816,0.9846,0.9866,0.9898,0.9952,0.9959,0.9984, Overall p-value after applying KStest on 269 p-values = 0.084395 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.