RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-20_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.66 27.8773 0.953607 2 to 25 16.13 28.4625 0.960184 3 to 26 15.76 27.3046 0.946251 4 to 27 15.61 20.7319 0.761486 5 to 28 16.08 19.0328 0.673348 6 to 29 15.82 11.1111 0.149270 7 to 30 15.96 13.2815 0.282854 8 to 31 15.91 24.9347 0.903818 9 to 32 15.77 13.1847 0.276267 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.068618 Tough bday spacings test for dh-ranFile-2016-03-20_08:31: 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 13 31 79 102 96 70 52 32 13 5 7 (O-E)^2/E 1.6 0.9 0.4 0.2 0.0 0.8 0.0 0.2 0.2 0.4 2.1 Birthday Spacings: Sum(O-E)^2/E= 6.913, p= 0.266 RESULTS OF GCD FOR dh-ranFile-2016-03-20_08:31 Euclid's algorithm: p-value, steps to gcd: 0.052997 p-value, dist. of gcd's: 0.039150 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-20_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.224 0.673 0.785 0.795 0.157 0.827 0.242 0.178 Bits 8 to 15---> 0.796 0.487 0.312 0.501 0.896 0.534 0.110 0.948 Bits 16 to 23---> 0.430 0.847 0.885 0.037 0.506 0.235 0.379 0.087 Bits 24 to 31---> 0.005 0.913 0.320 0.791 0.371 0.008 0.951 0.284 KS test for the above 32 p values: 0.305 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-20_08:31, p-values for 5 runs: 0.9863, 0.7189, 0.5553, 0.9118, 0.8758 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-20_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 229 211.4 1.462 1.462 r= 29 5100 5134.0 0.225 1.687 r= 30 23246 23103.0 0.885 2.572 r= 31 11425 11551.5 1.386 3.958 chi-square = 3.958 with df = 3; p-value = 0.734 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-20_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5141 5134.0 0.010 0.070 r= 31 23226 23103.0 0.654 0.725 r= 32 11418 11551.5 1.543 2.268 chi-square = 2.268 with df = 3; p-value = 0.481 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-20_08:31 b-rank test for bits 1 to 8, p=0.59300 b-rank test for bits 2 to 9, p=0.30591 b-rank test for bits 3 to 10, p=0.58368 b-rank test for bits 4 to 11, p=0.50356 b-rank test for bits 5 to 12, p=0.80966 b-rank test for bits 6 to 13, p=0.35356 b-rank test for bits 7 to 14, p=0.39248 b-rank test for bits 8 to 15, p=0.12351 b-rank test for bits 9 to 16, p=0.54251 b-rank test for bits 10 to 17, p=0.12397 b-rank test for bits 11 to 18, p=0.35401 b-rank test for bits 12 to 19, p=0.15272 b-rank test for bits 13 to 20, p=0.25937 b-rank test for bits 14 to 21, p=0.28607 b-rank test for bits 15 to 22, p=0.83253 b-rank test for bits 16 to 23, p=0.76858 b-rank test for bits 17 to 24, p=0.73978 b-rank test for bits 18 to 25, p=0.96929 b-rank test for bits 19 to 26, p=0.66119 b-rank test for bits 20 to 27, p=0.50080 b-rank test for bits 21 to 28, p=0.79929 b-rank test for bits 22 to 29, p=0.55376 b-rank test for bits 23 to 30, p=0.49589 b-rank test for bits 24 to 31, p=0.56659 b-rank test for bits 25 to 32, p=0.63523 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 = 0.421307 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-20_08:31 (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 141646 -0.62 0.269193 2 141887 -0.05 0.479196 3 142127 0.51 0.694475 4 141392 -1.21 0.113386 5 141833 -0.18 0.429228 6 141980 0.17 0.565574 7 142340 1.01 0.842850 8 141780 -0.30 0.381260 9 142022 0.26 0.603820 10 141750 -0.37 0.354847 11 142573 1.55 0.939505 12 141495 -0.97 0.166507 13 141958 0.11 0.545268 14 141722 -0.44 0.330807 15 141585 -0.76 0.224291 16 141437 -1.10 0.134889 17 141386 -1.22 0.110715 18 141713 -0.46 0.323219 19 142334 0.99 0.839455 20 142360 1.05 0.853822 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-20_08:31 Bits used No. missing words z-score p-value 23 to 32 141675 -0.8080 0.209535 22 to 31 142097 0.6471 0.741229 21 to 30 141614 -1.0184 0.154249 20 to 29 141840 -0.2391 0.405526 19 to 28 141605 -1.0494 0.146994 18 to 27 142025 0.3989 0.655003 17 to 26 142179 0.9299 0.823788 16 to 25 141829 -0.2770 0.390890 15 to 24 142051 0.4885 0.687408 14 to 23 141660 -0.8598 0.194961 13 to 22 141971 0.2127 0.584202 12 to 21 141792 -0.4046 0.342891 11 to 20 142198 0.9954 0.840233 10 to 19 141479 -1.4839 0.068918 9 to 18 141793 -0.4011 0.344159 8 to 17 142072 0.5609 0.712578 7 to 16 142009 0.3437 0.634460 6 to 15 142181 0.9368 0.825568 5 to 14 141455 -1.5667 0.058598 4 to 13 141975 0.2264 0.589574 3 to 12 141477 -1.4908 0.068008 2 to 11 141674 -0.8115 0.208544 1 to 10 141480 -1.4804 0.069377 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-20_08:31 Bits used No. missing words z-score p-value 28 to 32 141720 -0.6418 0.260503 27 to 31 142232 1.0938 0.862978 26 to 30 141854 -0.1876 0.425611 25 to 29 141796 -0.3842 0.350426 24 to 28 142331 1.4294 0.923554 23 to 27 141875 -0.1164 0.453679 22 to 26 142322 1.3989 0.919076 21 to 25 142287 1.2802 0.899769 20 to 24 141719 -0.6452 0.259403 19 to 23 141976 0.2260 0.589399 18 to 22 142404 1.6768 0.953214 17 to 21 141521 -1.3164 0.094024 16 to 20 142210 1.0192 0.845951 15 to 19 141839 -0.2384 0.405783 14 to 18 141859 -0.1706 0.432265 13 to 17 142155 0.8328 0.797516 12 to 16 142339 1.4565 0.927374 11 to 15 142151 0.8192 0.793670 10 to 14 142077 0.5684 0.715109 9 to 13 141828 -0.2757 0.391391 8 to 12 141722 -0.6350 0.262709 7 to 11 141508 -1.3604 0.086845 6 to 10 142091 0.6158 0.730997 5 to 9 141985 0.2565 0.601221 4 to 8 141486 -1.4350 0.075641 3 to 7 142096 0.6328 0.736561 2 to 6 141413 -1.6825 0.046238 1 to 5 141721 -0.6384 0.261605 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-20_08:31 Bits used No. missing words z-score p-value 31 to 32 142413 1.4858 0.931328 30 to 31 142114 0.6037 0.726994 29 to 30 141373 -1.5821 0.056814 28 to 29 141540 -1.0895 0.137974 27 to 28 142328 1.2350 0.891588 26 to 27 141418 -1.4494 0.073620 25 to 26 141679 -0.6794 0.248430 24 to 25 141894 -0.0452 0.481966 23 to 24 141871 -0.1131 0.454988 22 to 23 141839 -0.2075 0.417824 21 to 22 141804 -0.3107 0.378011 20 to 21 141864 -0.1337 0.446813 19 to 20 142079 0.5005 0.691639 18 to 19 141556 -1.0423 0.148643 17 to 18 141558 -1.0364 0.150014 16 to 17 141739 -0.5024 0.307676 15 to 16 141265 -1.9007 0.028672 14 to 15 141955 0.1347 0.553583 13 to 14 141623 -0.8446 0.199158 12 to 13 141660 -0.7355 0.231022 11 to 12 142660 2.2144 0.986598 10 to 11 141170 -2.1809 0.014595 9 to 10 142123 0.6303 0.735749 8 to 9 141548 -1.0659 0.143241 7 to 8 141746 -0.4818 0.314974 6 to 7 142608 2.0610 0.980347 5 to 6 141619 -0.8564 0.195880 4 to 5 141719 -0.5614 0.287247 3 to 4 141708 -0.5939 0.276292 2 to 3 141707 -0.5968 0.275306 1 to 2 141730 -0.5290 0.298404 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-20_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2418.79 -1.148 0.125394 Test results for specific bytes for dh-ranFile-2016-03-20_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2458.97 -0.580 0.280872 2 to 9 2417.38 -1.168 0.121315 3 to 10 2481.30 -0.265 0.395692 4 to 11 2537.80 0.535 0.703521 5 to 12 2327.38 -2.441 0.007319 6 to 13 2517.47 0.247 0.597552 7 to 14 2494.24 -0.081 0.467547 8 to 15 2533.02 0.467 0.679738 9 to 16 2517.95 0.254 0.600200 10 to 17 2424.45 -1.069 0.142646 11 to 18 2579.02 1.118 0.868116 12 to 19 2466.03 -0.480 0.315447 13 to 20 2431.70 -0.966 0.167043 14 to 21 2512.60 0.178 0.570729 15 to 22 2422.17 -1.101 0.135532 16 to 23 2476.32 -0.335 0.368864 17 to 24 2462.65 -0.528 0.298695 18 to 25 2462.61 -0.529 0.298505 19 to 26 2565.46 0.926 0.822700 20 to 27 2512.33 0.174 0.569186 21 to 28 2361.89 -1.953 0.025397 22 to 29 2496.66 -0.047 0.481187 23 to 30 2487.35 -0.179 0.429029 24 to 31 2448.57 -0.727 0.233517 25 to 32 2548.78 0.690 0.754876 CDPARK for dh-ranFile-2016-03-20_08:31: 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 3538 0.6849 0.753306 3576 2.4201 0.992242 3521 -0.0913 0.463617 3449 -3.3790 0.000364 3540 0.7763 0.781201 3483 -1.8265 0.033889 3540 0.7763 0.781201 3491 -1.4612 0.071982 3517 -0.2740 0.392053 3485 -1.7352 0.041356 Square side=100, avg. no. parked=3514.00 sample std.=35.19 p-value of the KSTEST for those 10 p-values: 0.079726 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-20_08:31 0.2133,0.8694,0.8412,0.2309,0.4762,0.0869,0.9692,0.1300,0.6283,0.4702, The KS test for those 10 p-values: 0.956321 The 3DSPHERES test for dh-ranFile-2016-03-20_08:31 sample no r^3 equiv. uni. 1 5.959 0.180153 2 7.556 0.222661 3 38.558 0.723421 4 11.720 0.323403 5 0.069 0.002292 6 20.048 0.487403 7 55.401 0.842244 8 83.747 0.938676 9 0.814 0.026754 10 17.930 0.449904 11 34.365 0.681938 12 28.613 0.614718 13 41.689 0.750837 14 74.307 0.915996 15 6.144 0.185181 16 39.053 0.727948 17 43.267 0.763600 18 4.848 0.149208 19 91.646 0.952871 20 33.700 0.674810 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.671541 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-20_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -1.6 -0.7 -2.4 1.1 -0.1 -0.1 -0.1 0.0 0.5 -0.6 -0.6 -1.0 -1.6 -0.9 1.0 0.9 0.2 0.0 0.0 -0.3 -0.0 1.1 1.2 1.1 0.8 0.9 -1.3 1.0 -1.8 1.1 0.5 0.7 -0.4 0.1 -2.1 1.8 0.1 -1.3 -1.3 0.0 -1.1 Chi-square with 42 degrees of freedom:42.893733 z-score=0.097514, p-value=0.567308 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-20_08:31 Test no p-value 1 0.164593 2 0.724449 3 0.139419 4 0.541959 5 0.882425 6 0.169787 7 0.005148 8 0.357303 9 0.205076 10 0.265690 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.119150 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-20_08:31: (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 66650 0.00 66665 0.00 3 25000.00 25020 0.02 24990 0.00 4 6666.67 6636 0.14 6640 0.11 5 1388.89 1386 0.01 1444 2.19 6 238.10 276 6.03 227 0.52 7 34.72 28 1.30 30 0.64 8 4.96 3 0.77 3 0.77 p=0.78149 p=0.35451 Number of rngs required: 687645, p-value: 0.190 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-20_08:31 No. of wins: Observed Expected 98749 98585.9 z-score= 0.730, pvalue=0.76720 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66696 66666.7 0.013 0.013 2 37825 37654.3 0.774 0.787 3 26892 26954.7 0.146 0.933 4 19448 19313.5 0.937 1.870 5 13753 13851.4 0.699 2.569 6 9784 9943.5 2.560 5.129 7 7284 7145.0 2.703 7.832 8 5094 5139.1 0.395 8.227 9 3670 3699.9 0.241 8.468 10 2674 2666.3 0.022 8.491 11 1819 1923.3 5.659 14.150 12 1344 1388.7 1.441 15.591 13 1029 1003.7 0.637 16.228 14 752 726.1 0.921 17.149 15 541 525.8 0.437 17.586 16 398 381.2 0.745 18.331 17 266 276.5 0.402 18.733 18 202 200.8 0.007 18.740 19 144 146.0 0.027 18.767 20 99 106.2 0.490 19.257 21 286 287.1 0.004 19.261 Chisq= 19.26 for 20 degrees of freedom, p= 0.49509 SUMMARY of craptest p-value for no. of wins: 0.767202 p-value for throws/game: 0.495091 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-20_08:31 No. of wins: Observed Expected 98611 98585.9 z-score= 0.112, pvalue=0.54477 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66845 66666.7 0.477 0.477 2 37427 37654.3 1.372 1.849 3 27059 26954.7 0.403 2.253 4 19182 19313.5 0.895 3.148 5 13868 13851.4 0.020 3.167 6 9939 9943.5 0.002 3.169 7 7281 7145.0 2.588 5.757 8 5202 5139.1 0.771 6.528 9 3609 3699.9 2.232 8.759 10 2639 2666.3 0.279 9.039 11 1959 1923.3 0.662 9.700 12 1408 1388.7 0.267 9.967 13 1000 1003.7 0.014 9.981 14 679 726.1 3.060 13.041 15 489 525.8 2.580 15.622 16 388 381.2 0.123 15.745 17 292 276.5 0.864 16.609 18 180 200.8 2.160 18.770 19 143 146.0 0.061 18.831 20 117 106.2 1.095 19.926 21 294 287.1 0.165 20.091 Chisq= 20.09 for 20 degrees of freedom, p= 0.54775 SUMMARY of craptest p-value for no. of wins: 0.544766 p-value for throws/game: 0.547751 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0023,0.0050,0.0051,0.0073,0.0078,0.0146,0.0254,0.0268,0.0287, 0.0339,0.0367,0.0392,0.0414,0.0462,0.0530,0.0568,0.0586,0.0680,0.0686, 0.0689,0.0694,0.0720,0.0736,0.0756,0.0797,0.0865,0.0868,0.0869,0.0940, 0.1099,0.1107,0.1134,0.1191,0.1213,0.1235,0.1240,0.1254,0.1300,0.1349, 0.1355,0.1380,0.1394,0.1426,0.1432,0.1470,0.1486,0.1492,0.1493,0.1500, 0.1527,0.1542,0.1567,0.1646,0.1665,0.1670,0.1698,0.1777,0.1802,0.1852, 0.1903,0.1950,0.1959,0.1992,0.2051,0.2085,0.2095,0.2133,0.2227,0.2240, 0.2243,0.2309,0.2310,0.2335,0.2349,0.2424,0.2484,0.2594,0.2594,0.2605, 0.2616,0.2627,0.2657,0.2664,0.2692,0.2753,0.2763,0.2763,0.2809,0.2829, 0.2839,0.2861,0.2872,0.2984,0.2985,0.2987,0.3046,0.3059,0.3077,0.3115, 0.3150,0.3154,0.3195,0.3232,0.3234,0.3308,0.3429,0.3442,0.3504,0.3536, 0.3540,0.3545,0.3548,0.3573,0.3689,0.3708,0.3780,0.3791,0.3813,0.3909, 0.3914,0.3921,0.3925,0.3957,0.4055,0.4058,0.4178,0.4213,0.4256,0.4290, 0.4292,0.4298,0.4323,0.4468,0.4499,0.4537,0.4550,0.4636,0.4675,0.4702, 0.4762,0.4792,0.4812,0.4813,0.4820,0.4873,0.4874,0.4951,0.4959,0.5008, 0.5010,0.5036,0.5061,0.5344,0.5420,0.5425,0.5448,0.5453,0.5478,0.5536, 0.5538,0.5553,0.5656,0.5666,0.5673,0.5692,0.5707,0.5837,0.5842,0.5894, 0.5896,0.5930,0.5976,0.6002,0.6012,0.6038,0.6147,0.6283,0.6345,0.6352, 0.6550,0.6612,0.6715,0.6729,0.6733,0.6748,0.6797,0.6819,0.6874,0.6916, 0.6945,0.7035,0.7126,0.7151,0.7189,0.7234,0.7244,0.7270,0.7279,0.7310, 0.7339,0.7357,0.7366,0.7398,0.7412,0.7508,0.7533,0.7549,0.7615,0.7636, 0.7672,0.7686,0.7812,0.7812,0.7815,0.7851,0.7910,0.7937,0.7952,0.7958, 0.7975,0.7993,0.8097,0.8227,0.8238,0.8256,0.8273,0.8325,0.8395,0.8402, 0.8412,0.8422,0.8428,0.8460,0.8465,0.8538,0.8630,0.8681,0.8694,0.8758, 0.8824,0.8851,0.8916,0.8963,0.8998,0.9038,0.9118,0.9127,0.9160,0.9191, 0.9236,0.9274,0.9313,0.9387,0.9395,0.9463,0.9479,0.9512,0.9529,0.9532, 0.9536,0.9563,0.9602,0.9692,0.9693,0.9803,0.9863,0.9866,0.9922, Overall p-value after applying KStest on 269 p-values = 0.145050 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.