RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-09-10_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.60 15.9265 0.470947 2 to 25 15.82 31.9786 0.984860 3 to 26 15.61 17.3106 0.566475 4 to 27 15.71 21.9699 0.814121 5 to 28 15.73 16.0231 0.477799 6 to 29 15.79 13.3438 0.287114 7 to 30 15.65 12.1270 0.207611 8 to 31 15.70 21.8700 0.810231 9 to 32 15.93 15.1832 0.417709 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.664688 Tough bday spacings test for dh-ranFile-2016-09-10_22:31: 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 6 45 72 99 88 88 57 22 16 5 2 (O-E)^2/E 1.1 1.9 0.0 0.0 1.0 1.2 0.5 2.0 0.1 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 9.260, p= 0.492 RESULTS OF GCD FOR dh-ranFile-2016-09-10_22:31 Euclid's algorithm: p-value, steps to gcd: 0.744347 p-value, dist. of gcd's: 0.468762 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-09-10_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.295 0.034 0.779 0.972 0.255 0.529 0.901 0.394 Bits 8 to 15---> 0.582 0.236 0.220 0.183 0.434 0.872 0.742 0.555 Bits 16 to 23---> 0.343 0.185 0.848 0.632 0.958 0.007 0.008 0.742 Bits 24 to 31---> 0.621 0.450 0.720 0.695 0.285 0.127 0.291 0.514 KS test for the above 32 p values: 0.062 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-09-10_22:31, p-values for 5 runs: 0.8079, 0.8032, 0.8253, 0.5455, 0.8937 Rank test for binary matrices (31x31) for dh-ranFile-2016-09-10_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5162 5134.0 0.153 0.164 r= 30 23027 23103.0 0.250 0.415 r= 31 11598 11551.5 0.187 0.602 chi-square = 0.602 with df = 3; p-value = 0.104 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-09-10_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 233 211.4 2.203 2.203 r= 30 5081 5134.0 0.547 2.750 r= 31 23036 23103.0 0.195 2.945 r= 32 11650 11551.5 0.840 3.785 chi-square = 3.785 with df = 3; p-value = 0.714 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-09-10_22:31 b-rank test for bits 1 to 8, p=0.50309 b-rank test for bits 2 to 9, p=0.36268 b-rank test for bits 3 to 10, p=0.26388 b-rank test for bits 4 to 11, p=0.42644 b-rank test for bits 5 to 12, p=0.63267 b-rank test for bits 6 to 13, p=0.23820 b-rank test for bits 7 to 14, p=0.60086 b-rank test for bits 8 to 15, p=0.84256 b-rank test for bits 9 to 16, p=0.94163 b-rank test for bits 10 to 17, p=0.72954 b-rank test for bits 11 to 18, p=0.94427 b-rank test for bits 12 to 19, p=0.02809 b-rank test for bits 13 to 20, p=0.05757 b-rank test for bits 14 to 21, p=0.01178 b-rank test for bits 15 to 22, p=0.33003 b-rank test for bits 16 to 23, p=0.01052 b-rank test for bits 17 to 24, p=0.34935 b-rank test for bits 18 to 25, p=0.71881 b-rank test for bits 19 to 26, p=0.42796 b-rank test for bits 20 to 27, p=0.44810 b-rank test for bits 21 to 28, p=0.24103 b-rank test for bits 22 to 29, p=0.94244 b-rank test for bits 23 to 30, p=0.60969 b-rank test for bits 24 to 31, p=0.53658 b-rank test for bits 25 to 32, p=0.56366 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 = 0.602721 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-09-10_22:31 (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 141724 -0.43 0.332502 2 142117 0.49 0.686236 3 141440 -1.10 0.136416 4 141926 0.04 0.515534 5 142775 2.02 0.978442 6 142816 2.12 0.982929 7 141818 -0.21 0.415512 8 140985 -2.16 0.015400 9 141769 -0.33 0.371504 10 140993 -2.14 0.016139 11 142436 1.23 0.890752 12 141427 -1.13 0.129884 13 141500 -0.96 0.169441 14 141742 -0.39 0.347914 15 141146 -1.78 0.037254 16 142191 0.66 0.744765 17 141695 -0.50 0.308266 18 141581 -0.77 0.221503 19 141775 -0.31 0.376816 20 142154 0.57 0.716223 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-09-10_22:31 Bits used No. missing words z-score p-value 23 to 32 142090 0.6230 0.733358 22 to 31 142354 1.5333 0.937405 21 to 30 142155 0.8471 0.801541 20 to 29 142236 1.1264 0.870012 19 to 28 141766 -0.4942 0.310568 18 to 27 141455 -1.5667 0.058598 17 to 26 141767 -0.4908 0.311786 16 to 25 142293 1.3230 0.907082 15 to 24 142081 0.5920 0.723063 14 to 23 141623 -0.9873 0.161737 13 to 22 141933 0.0816 0.532526 12 to 21 141277 -2.1804 0.014612 11 to 20 141582 -1.1287 0.129507 10 to 19 141646 -0.9080 0.181930 9 to 18 141353 -1.9184 0.027531 8 to 17 142033 0.4264 0.665109 7 to 16 141932 0.0782 0.531155 6 to 15 141485 -1.4632 0.071705 5 to 14 141556 -1.2184 0.111540 4 to 13 141366 -1.8736 0.030496 3 to 12 142027 0.4058 0.657540 2 to 11 141594 -1.0873 0.138442 1 to 10 141911 0.0058 0.502297 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-09-10_22:31 Bits used No. missing words z-score p-value 28 to 32 141534 -1.2723 0.101632 27 to 31 141517 -1.3299 0.091770 26 to 30 141588 -1.0893 0.138021 25 to 29 141865 -0.1503 0.440275 24 to 28 141802 -0.3638 0.357992 23 to 27 142073 0.5548 0.710489 22 to 26 142110 0.6802 0.751823 21 to 25 141906 -0.0113 0.495497 20 to 24 141886 -0.0791 0.468483 19 to 23 141588 -1.0893 0.138021 18 to 22 142008 0.3345 0.630989 17 to 21 142040 0.4429 0.671099 16 to 20 141914 0.0158 0.506315 15 to 19 142042 0.4497 0.673547 14 to 18 142247 1.1446 0.873822 13 to 17 141846 -0.2147 0.415009 12 to 16 142034 0.4226 0.663710 11 to 15 141641 -0.9096 0.181519 10 to 14 141948 0.1311 0.552146 9 to 13 141719 -0.6452 0.259403 8 to 12 141349 -1.8994 0.028754 7 to 11 141565 -1.1672 0.121561 6 to 10 142442 1.8057 0.964514 5 to 9 142027 0.3989 0.655010 4 to 8 142538 2.1311 0.983459 3 to 7 141898 -0.0384 0.484682 2 to 6 141586 -1.0960 0.136532 1 to 5 141764 -0.4926 0.311132 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-09-10_22:31 Bits used No. missing words z-score p-value 31 to 32 141934 0.0728 0.529007 30 to 31 141730 -0.5290 0.298404 29 to 30 141666 -0.7178 0.236444 28 to 29 141787 -0.3609 0.359104 27 to 28 142778 2.5624 0.994803 26 to 27 141690 -0.6470 0.258819 25 to 26 141939 0.0875 0.534872 24 to 25 141995 0.2527 0.599755 23 to 24 141875 -0.1013 0.459669 22 to 23 142258 1.0285 0.848149 21 to 22 142248 0.9990 0.841109 20 to 21 141680 -0.6765 0.249365 19 to 20 141199 -2.0954 0.018069 18 to 19 142037 0.3766 0.646767 17 to 18 142112 0.5978 0.725029 16 to 17 142244 0.9872 0.838234 15 to 16 142042 0.3914 0.652233 14 to 15 141789 -0.3550 0.361311 13 to 14 141895 -0.0423 0.483141 12 to 13 141627 -0.8328 0.202470 11 to 12 142542 1.8663 0.968999 10 to 11 142523 1.8102 0.964870 9 to 10 141597 -0.9213 0.178440 8 to 9 142020 0.3265 0.627962 7 to 8 141640 -0.7945 0.213457 6 to 7 141568 -1.0069 0.156998 5 to 6 141699 -0.6204 0.267483 4 to 5 142187 0.8191 0.793631 3 to 4 141046 -2.5467 0.005437 2 to 3 141886 -0.0688 0.472566 1 to 2 141884 -0.0747 0.470219 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-09-10_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2580.13 1.133 0.871433 Test results for specific bytes for dh-ranFile-2016-09-10_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2569.81 0.987 0.838252 2 to 9 2498.85 -0.016 0.493503 3 to 10 2493.34 -0.094 0.462498 4 to 11 2477.95 -0.312 0.377574 5 to 12 2514.03 0.198 0.578650 6 to 13 2638.08 1.953 0.974572 7 to 14 2448.79 -0.724 0.234467 8 to 15 2467.76 -0.456 0.324200 9 to 16 2593.54 1.323 0.907057 10 to 17 2450.12 -0.705 0.240282 11 to 18 2467.21 -0.464 0.321426 12 to 19 2469.55 -0.431 0.333369 13 to 20 2474.79 -0.356 0.360744 14 to 21 2527.46 0.388 0.651108 15 to 22 2530.55 0.432 0.667138 16 to 23 2414.19 -1.214 0.112453 17 to 24 2435.18 -0.917 0.179656 18 to 25 2533.98 0.481 0.684570 19 to 26 2512.42 0.176 0.569741 20 to 27 2465.51 -0.488 0.312866 21 to 28 2469.57 -0.430 0.333450 22 to 29 2528.38 0.401 0.655939 23 to 30 2531.33 0.443 0.671136 24 to 31 2478.86 -0.299 0.382458 25 to 32 2548.44 0.685 0.753357 CDPARK for dh-ranFile-2016-09-10_22:31: 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 3517 -0.2740 0.392053 3553 1.3699 0.914635 3538 0.6849 0.753306 3517 -0.2740 0.392053 3526 0.1370 0.554479 3500 -1.0502 0.146807 3540 0.7763 0.781201 3543 0.9132 0.819442 3508 -0.6849 0.246694 3530 0.3196 0.625377 Square side=100, avg. no. parked=3527.20 sample std.=15.88 p-value of the KSTEST for those 10 p-values: 0.769275 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-09-10_22:31 0.9798,0.0366,0.1397,0.9280,0.0356,0.3823,0.6451,0.1863,0.7130,0.9464, The KS test for those 10 p-values: 0.325378 The 3DSPHERES test for dh-ranFile-2016-09-10_22:31 sample no r^3 equiv. uni. 1 37.615 0.714594 2 44.916 0.776241 3 15.372 0.400944 4 6.215 0.187129 5 9.054 0.260514 6 3.344 0.105478 7 50.350 0.813316 8 65.918 0.888893 9 26.097 0.581001 10 15.685 0.407162 11 10.520 0.295779 12 16.993 0.432463 13 23.513 0.543323 14 10.664 0.299147 15 24.983 0.565158 16 7.235 0.214288 17 2.181 0.070119 18 33.064 0.667836 19 42.052 0.753831 20 3.831 0.119875 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.671616 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-09-10_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.3 -1.3 -0.4 -0.5 -0.4 0.4 -0.5 -0.3 0.1 -0.6 -0.6 0.3 0.2 -1.4 0.5 0.8 0.2 -0.9 0.7 -0.4 1.2 -0.4 0.9 0.3 -1.6 3.0 -1.3 -0.9 0.8 -0.6 -0.5 -1.0 0.5 1.6 -0.5 -1.2 -0.4 1.3 0.4 0.9 1.0 0.8 Chi-square with 42 degrees of freedom:36.405755 z-score=-0.610382, p-value=0.285647 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-09-10_22:31 Test no p-value 1 0.530515 2 0.016791 3 0.834909 4 0.102735 5 0.506938 6 0.108990 7 0.002495 8 0.764102 9 0.008492 10 0.216513 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.008746 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-09-10_22:31: (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 66728 0.06 66622 0.03 3 25000.00 25103 0.42 25008 0.00 4 6666.67 6525 3.01 6764 1.42 5 1388.89 1362 0.52 1329 2.58 6 238.10 244 0.15 234 0.07 7 34.72 31 0.40 40 0.80 8 4.96 6 0.22 2 1.77 p=0.42703 p=0.64813 Number of rngs required: 688304, p-value: 0.455 RESULTS OF CRAPS TEST for dh-ranFile-2016-09-10_22:31 No. of wins: Observed Expected 98746 98585.9 z-score= 0.716, pvalue=0.76308 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66725 66666.7 0.051 0.051 2 37547 37654.3 0.306 0.357 3 26841 26954.7 0.480 0.837 4 19337 19313.5 0.029 0.865 5 13808 13851.4 0.136 1.002 6 10056 9943.5 1.272 2.273 7 7196 7145.0 0.364 2.637 8 5083 5139.1 0.612 3.249 9 3746 3699.9 0.575 3.824 10 2678 2666.3 0.051 3.876 11 1958 1923.3 0.625 4.501 12 1341 1388.7 1.641 6.142 13 1014 1003.7 0.105 6.247 14 716 726.1 0.142 6.389 15 531 525.8 0.051 6.439 16 397 381.2 0.659 7.098 17 266 276.5 0.402 7.500 18 215 200.8 1.000 8.500 19 147 146.0 0.007 8.507 20 110 106.2 0.135 8.642 21 288 287.1 0.003 8.645 Chisq= 8.64 for 20 degrees of freedom, p= 0.01333 SUMMARY of craptest p-value for no. of wins: 0.763080 p-value for throws/game: 0.013330 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-09-10_22:31 No. of wins: Observed Expected 98591 98585.9 z-score= 0.023, pvalue=0.50917 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66876 66666.7 0.657 0.657 2 37536 37654.3 0.372 1.029 3 26888 26954.7 0.165 1.194 4 19512 19313.5 2.041 3.235 5 13946 13851.4 0.646 3.881 6 9821 9943.5 1.510 5.391 7 7163 7145.0 0.045 5.436 8 5022 5139.1 2.667 8.103 9 3716 3699.9 0.070 8.174 10 2704 2666.3 0.533 8.707 11 1889 1923.3 0.613 9.320 12 1327 1388.7 2.745 12.065 13 1044 1003.7 1.617 13.681 14 703 726.1 0.737 14.419 15 520 525.8 0.065 14.484 16 364 381.2 0.772 15.255 17 254 276.5 1.837 17.092 18 199 200.8 0.017 17.109 19 135 146.0 0.827 17.936 20 96 106.2 0.982 18.918 21 285 287.1 0.016 18.934 Chisq= 18.93 for 20 degrees of freedom, p= 0.47386 SUMMARY of craptest p-value for no. of wins: 0.509173 p-value for throws/game: 0.473856 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0025,0.0054,0.0069,0.0084,0.0085,0.0087,0.0105,0.0118,0.0133,0.0146, 0.0154,0.0161,0.0168,0.0181,0.0275,0.0281,0.0288,0.0305,0.0340,0.0356, 0.0366,0.0373,0.0576,0.0586,0.0621,0.0701,0.0717,0.0918,0.1016,0.1027, 0.1040,0.1055,0.1090,0.1115,0.1125,0.1199,0.1216,0.1274,0.1295,0.1299, 0.1364,0.1365,0.1380,0.1380,0.1384,0.1397,0.1468,0.1570,0.1617,0.1694, 0.1784,0.1797,0.1815,0.1819,0.1829,0.1849,0.1863,0.1871,0.2025,0.2076, 0.2135,0.2143,0.2165,0.2200,0.2215,0.2345,0.2356,0.2364,0.2382,0.2403, 0.2410,0.2467,0.2494,0.2554,0.2588,0.2594,0.2605,0.2639,0.2675,0.2852, 0.2856,0.2871,0.2914,0.2946,0.2958,0.2984,0.2991,0.3083,0.3106,0.3111, 0.3118,0.3129,0.3214,0.3242,0.3254,0.3300,0.3325,0.3334,0.3335,0.3430, 0.3479,0.3494,0.3580,0.3591,0.3607,0.3613,0.3627,0.3715,0.3768,0.3776, 0.3823,0.3825,0.3921,0.3921,0.3939,0.4009,0.4072,0.4150,0.4155,0.4177, 0.4264,0.4270,0.4280,0.4325,0.4343,0.4403,0.4481,0.4504,0.4547,0.4597, 0.4625,0.4685,0.4688,0.4702,0.4709,0.4726,0.4739,0.4778,0.4831,0.4847, 0.4924,0.4935,0.4955,0.5023,0.5031,0.5063,0.5069,0.5092,0.5144,0.5155, 0.5290,0.5294,0.5305,0.5312,0.5325,0.5349,0.5366,0.5433,0.5455,0.5521, 0.5545,0.5547,0.5637,0.5652,0.5665,0.5697,0.5787,0.5810,0.5820,0.5998, 0.6009,0.6027,0.6097,0.6211,0.6254,0.6280,0.6310,0.6324,0.6327,0.6451, 0.6468,0.6481,0.6511,0.6522,0.6550,0.6559,0.6575,0.6637,0.6647,0.6651, 0.6671,0.6678,0.6711,0.6711,0.6716,0.6735,0.6846,0.6862,0.6947,0.7105, 0.7130,0.7143,0.7146,0.7162,0.7188,0.7204,0.7231,0.7250,0.7295,0.7334, 0.7416,0.7418,0.7443,0.7448,0.7518,0.7533,0.7534,0.7538,0.7631,0.7641, 0.7693,0.7762,0.7791,0.7812,0.7936,0.8015,0.8032,0.8079,0.8102,0.8133, 0.8141,0.8194,0.8253,0.8349,0.8382,0.8383,0.8411,0.8426,0.8477,0.8481, 0.8700,0.8714,0.8719,0.8738,0.8889,0.8908,0.8937,0.9007,0.9071,0.9071, 0.9146,0.9280,0.9374,0.9416,0.9424,0.9443,0.9464,0.9578,0.9645,0.9649, 0.9690,0.9722,0.9746,0.9784,0.9798,0.9829,0.9835,0.9849,0.9948, Overall p-value after applying KStest on 269 p-values = 0.134729 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.