RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-12_19:31 (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 11.5623 0.174112 2 to 25 15.63 17.1241 0.554009 3 to 26 15.68 23.5315 0.867265 4 to 27 15.48 26.4460 0.933290 5 to 28 15.54 17.2888 0.565026 6 to 29 15.95 7.5787 0.025254 7 to 30 15.59 16.8362 0.534487 8 to 31 16.30 16.9439 0.541828 9 to 32 15.92 14.1322 0.342280 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.893589 Tough bday spacings test for dh-ranFile-2018-04-12_19:31: 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 7 39 69 105 93 69 54 34 17 8 5 (O-E)^2/E 0.5 0.2 0.2 0.5 0.2 1.1 0.1 0.6 0.3 0.3 0.2 Birthday Spacings: Sum(O-E)^2/E= 4.228, p= 0.064 RESULTS OF GCD FOR dh-ranFile-2018-04-12_19:31 Euclid's algorithm: p-value, steps to gcd: 0.956579 p-value, dist. of gcd's: 0.285247 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-12_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.938 0.924 0.373 0.108 0.271 0.989 0.740 0.700 Bits 8 to 15---> 0.585 0.548 0.929 0.372 0.473 0.761 0.826 0.413 Bits 16 to 23---> 0.578 0.503 0.505 0.887 0.145 0.862 0.279 0.119 Bits 24 to 31---> 0.275 0.150 0.405 0.882 0.615 0.012 0.786 0.989 KS test for the above 32 p values: 0.607 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-12_19:31, p-values for 5 runs: 0.5562, 0.2723, 0.5813, 0.4719, 0.8834 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5181 5134.0 0.430 0.765 r= 30 23117 23103.0 0.008 0.774 r= 31 11499 11551.5 0.239 1.013 chi-square = 1.013 with df = 3; p-value = 0.202 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-12_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5171 5134.0 0.267 0.276 r= 31 23161 23103.0 0.145 0.421 r= 32 11458 11551.5 0.757 1.179 chi-square = 1.179 with df = 3; p-value = 0.242 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-12_19:31 b-rank test for bits 1 to 8, p=0.47684 b-rank test for bits 2 to 9, p=0.29536 b-rank test for bits 3 to 10, p=0.11154 b-rank test for bits 4 to 11, p=0.57764 b-rank test for bits 5 to 12, p=0.98140 b-rank test for bits 6 to 13, p=0.52117 b-rank test for bits 7 to 14, p=0.98299 b-rank test for bits 8 to 15, p=0.91545 b-rank test for bits 9 to 16, p=0.83764 b-rank test for bits 10 to 17, p=0.11421 b-rank test for bits 11 to 18, p=0.31884 b-rank test for bits 12 to 19, p=0.53244 b-rank test for bits 13 to 20, p=0.45250 b-rank test for bits 14 to 21, p=0.53637 b-rank test for bits 15 to 22, p=0.27332 b-rank test for bits 16 to 23, p=0.09186 b-rank test for bits 17 to 24, p=0.20998 b-rank test for bits 18 to 25, p=0.60085 b-rank test for bits 19 to 26, p=0.34869 b-rank test for bits 20 to 27, p=0.03926 b-rank test for bits 21 to 28, p=0.20484 b-rank test for bits 22 to 29, p=0.42194 b-rank test for bits 23 to 30, p=0.15275 b-rank test for bits 24 to 31, p=0.22920 b-rank test for bits 25 to 32, p=0.08668 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 = 0.151255 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-12_19:31 (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 141880 -0.07 0.472683 2 142481 1.34 0.909173 3 142535 1.46 0.928108 4 141330 -1.35 0.087936 5 141807 -0.24 0.405518 6 141748 -0.38 0.353109 7 141704 -0.48 0.315705 8 141832 -0.18 0.428310 9 141240 -1.56 0.058926 10 142158 0.58 0.719381 11 141044 -2.02 0.021599 12 142109 0.47 0.679578 13 141491 -0.98 0.164184 14 142171 0.61 0.729526 15 141599 -0.73 0.234205 16 141710 -0.47 0.320706 17 143110 2.81 0.997487 18 141741 -0.39 0.347051 19 141383 -1.23 0.109397 20 141628 -0.66 0.255490 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-12_19:31 Bits used No. missing words z-score p-value 23 to 32 141821 -0.3046 0.380341 22 to 31 142263 1.2196 0.888683 21 to 30 142094 0.6368 0.737870 20 to 29 141787 -0.4218 0.336575 19 to 28 142171 0.9023 0.816554 18 to 27 142340 1.4851 0.931237 17 to 26 141695 -0.7391 0.229933 16 to 25 141572 -1.1632 0.122373 15 to 24 141411 -1.7184 0.042864 14 to 23 141940 0.1058 0.542113 13 to 22 141835 -0.2563 0.398856 12 to 21 141581 -1.1322 0.128781 11 to 20 141493 -1.4356 0.075555 10 to 19 141741 -0.5804 0.280806 9 to 18 141801 -0.3736 0.354369 8 to 17 141844 -0.2253 0.410882 7 to 16 141827 -0.2839 0.388245 6 to 15 142090 0.6230 0.733358 5 to 14 141934 0.0851 0.533897 4 to 13 141796 -0.3908 0.347975 3 to 12 142337 1.4747 0.929857 2 to 11 141472 -1.5080 0.065773 1 to 10 141898 -0.0391 0.484418 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-12_19:31 Bits used No. missing words z-score p-value 28 to 32 141754 -0.5265 0.299256 27 to 31 142182 0.9243 0.822336 26 to 30 142192 0.9582 0.831020 25 to 29 142072 0.5514 0.709328 24 to 28 141783 -0.4282 0.334239 23 to 27 142037 0.4328 0.667413 22 to 26 142318 1.3853 0.917023 21 to 25 141622 -0.9740 0.165028 20 to 24 142126 0.7345 0.768670 19 to 23 141918 0.0294 0.511723 18 to 22 141925 0.0531 0.521181 17 to 21 141845 -0.2181 0.413688 16 to 20 142307 1.3480 0.911176 15 to 19 142231 1.0904 0.862233 14 to 18 141617 -0.9909 0.160855 13 to 17 141534 -1.2723 0.101632 12 to 16 141804 -0.3571 0.360527 11 to 15 141970 0.2057 0.581472 10 to 14 141882 -0.0926 0.463093 9 to 13 142185 0.9345 0.824970 8 to 12 141985 0.2565 0.601221 7 to 11 141809 -0.3401 0.366890 6 to 10 141546 -1.2316 0.109044 5 to 9 141592 -1.0757 0.141032 4 to 8 141858 -0.1740 0.430933 3 to 7 141482 -1.4486 0.073728 2 to 6 141948 0.1311 0.552146 1 to 5 141833 -0.2587 0.397916 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-12_19:31 Bits used No. missing words z-score p-value 31 to 32 141843 -0.1957 0.422437 30 to 31 141898 -0.0334 0.486669 29 to 30 142341 1.2734 0.898555 28 to 29 141893 -0.0482 0.480790 27 to 28 141641 -0.7915 0.214316 26 to 27 142421 1.5094 0.934395 25 to 26 142014 0.3088 0.621248 24 to 25 141612 -0.8771 0.190222 23 to 24 142190 0.8279 0.796146 22 to 23 142089 0.5300 0.701944 21 to 22 142086 0.5212 0.698869 20 to 21 141481 -1.2635 0.103203 19 to 20 141572 -0.9951 0.159850 18 to 19 141876 -0.0983 0.460840 17 to 18 142387 1.4091 0.920591 16 to 17 142176 0.7866 0.784253 15 to 16 142141 0.6834 0.752821 14 to 15 141891 -0.0541 0.478439 13 to 14 141693 -0.6381 0.261691 12 to 13 142014 0.3088 0.621248 11 to 12 142196 0.8456 0.801122 10 to 11 142602 2.0433 0.979487 9 to 10 141672 -0.7001 0.241936 8 to 9 142611 2.0698 0.980766 7 to 8 141241 -1.9715 0.024335 6 to 7 141604 -0.9007 0.183880 5 to 6 142227 0.9371 0.825641 4 to 5 142390 1.4179 0.921891 3 to 4 142436 1.5536 0.939860 2 to 3 142268 1.0580 0.854978 1 to 2 142082 0.5094 0.694747 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2492.87 -0.101 0.459831 Test results for specific bytes for dh-ranFile-2018-04-12_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2581.90 1.158 0.876619 2 to 9 2464.41 -0.503 0.307353 3 to 10 2500.32 0.005 0.501814 4 to 11 2465.65 -0.486 0.313538 5 to 12 2485.18 -0.210 0.416983 6 to 13 2605.58 1.493 0.932299 7 to 14 2541.95 0.593 0.723514 8 to 15 2475.34 -0.349 0.363622 9 to 16 2465.52 -0.488 0.312891 10 to 17 2537.23 0.526 0.700720 11 to 18 2530.58 0.432 0.667297 12 to 19 2455.32 -0.632 0.263739 13 to 20 2508.39 0.119 0.547236 14 to 21 2460.87 -0.553 0.289981 15 to 22 2487.80 -0.173 0.431505 16 to 23 2543.52 0.616 0.730892 17 to 24 2522.40 0.317 0.624322 18 to 25 2431.81 -0.964 0.167424 19 to 26 2441.09 -0.833 0.202385 20 to 27 2592.70 1.311 0.905071 21 to 28 2409.50 -1.280 0.100307 22 to 29 2502.62 0.037 0.514767 23 to 30 2424.57 -1.067 0.143051 24 to 31 2570.61 0.999 0.841006 25 to 32 2551.44 0.727 0.766524 CDPARK for dh-ranFile-2018-04-12_19:31: 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 3534 0.5023 0.692266 3513 -0.4566 0.323972 3531 0.3653 0.642555 3512 -0.5023 0.307734 3516 -0.3196 0.374623 3510 -0.5936 0.276387 3534 0.5023 0.692266 3490 -1.5068 0.065925 3539 0.7306 0.767486 3542 0.8676 0.807188 Square side=100, avg. no. parked=3522.10 sample std.=15.63 p-value of the KSTEST for those 10 p-values: 0.755294 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-12_19:31 0.5189,0.6032,0.6080,0.4930,0.5389,0.4750,0.2179,0.3472,0.7732,0.8890, The KS test for those 10 p-values: 0.359787 The 3DSPHERES test for dh-ranFile-2018-04-12_19:31 sample no r^3 equiv. uni. 1 117.948 0.980388 2 38.362 0.721609 3 10.226 0.288835 4 12.201 0.334149 5 50.087 0.811674 6 13.692 0.366448 7 70.135 0.903462 8 130.371 0.987038 9 36.318 0.701986 10 58.826 0.859261 11 4.565 0.141159 12 5.469 0.166648 13 7.002 0.208159 14 95.068 0.957952 15 17.624 0.444259 16 38.143 0.719571 17 23.623 0.544989 18 34.269 0.680914 19 24.694 0.560951 20 31.353 0.648343 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.184958 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-12_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.8 -1.1 -0.5 -1.6 -1.6 -0.5 0.0 1.2 0.3 1.4 -1.8 1.4 -1.9 -0.4 1.2 0.9 -1.6 0.6 0.4 -0.3 1.4 0.8 1.5 -1.6 -1.5 -0.3 0.6 0.1 -0.4 -2.1 -0.7 -0.5 -1.6 -0.3 -0.7 -0.4 -1.2 -0.7 0.9 1.0 -1.1 Chi-square with 42 degrees of freedom:49.577802 z-score=0.826806, p-value=0.803316 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-12_19:31 Test no p-value 1 0.693984 2 0.029045 3 0.760661 4 0.953946 5 0.079862 6 0.284067 7 0.586732 8 0.774445 9 0.225704 10 0.152963 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.786002 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-12_19:31: (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 66570 0.14 66633 0.02 3 25000.00 25176 1.24 24909 0.33 4 6666.67 6585 1.00 6775 1.76 5 1388.89 1389 0.00 1394 0.02 6 238.10 248 0.41 253 0.93 7 34.72 26 2.19 31 0.40 8 4.96 5 0.00 4 0.19 p=0.45389 p=0.27538 Number of rngs required: 688824, p-value: 0.686 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-12_19:31 No. of wins: Observed Expected 98668 98585.9 z-score= 0.367, pvalue=0.64333 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66415 66666.7 0.950 0.950 2 37942 37654.3 2.198 3.148 3 26831 26954.7 0.568 3.716 4 19306 19313.5 0.003 3.719 5 13796 13851.4 0.222 3.941 6 9947 9943.5 0.001 3.942 7 7263 7145.0 1.948 5.890 8 5062 5139.1 1.156 7.046 9 3724 3699.9 0.157 7.203 10 2736 2666.3 1.822 9.025 11 1878 1923.3 1.068 10.093 12 1397 1388.7 0.049 10.143 13 1023 1003.7 0.371 10.513 14 722 726.1 0.024 10.537 15 503 525.8 0.992 11.528 16 405 381.2 1.492 13.021 17 318 276.5 6.216 19.237 18 217 200.8 1.302 20.539 19 161 146.0 1.544 22.083 20 100 106.2 0.364 22.447 21 254 287.1 3.819 26.266 Chisq= 26.27 for 20 degrees of freedom, p= 0.84280 SUMMARY of craptest p-value for no. of wins: 0.643334 p-value for throws/game: 0.842796 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-12_19:31 No. of wins: Observed Expected 98437 98585.9 z-score=-0.666, pvalue=0.25278 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66297 66666.7 2.050 2.050 2 37728 37654.3 0.144 2.194 3 26954 26954.7 0.000 2.194 4 19272 19313.5 0.089 2.283 5 14050 13851.4 2.847 5.130 6 10058 9943.5 1.317 6.447 7 6986 7145.0 3.539 9.987 8 5187 5139.1 0.447 10.434 9 3659 3699.9 0.451 10.885 10 2715 2666.3 0.890 11.775 11 1909 1923.3 0.107 11.882 12 1441 1388.7 1.967 13.848 13 1048 1003.7 1.954 15.802 14 744 726.1 0.439 16.241 15 560 525.8 2.220 18.461 16 360 381.2 1.174 19.635 17 274 276.5 0.023 19.658 18 178 200.8 2.595 22.253 19 150 146.0 0.110 22.364 20 125 106.2 3.322 25.686 21 305 287.1 1.114 26.800 Chisq= 26.80 for 20 degrees of freedom, p= 0.85902 SUMMARY of craptest p-value for no. of wins: 0.252775 p-value for throws/game: 0.859016 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0121,0.0216,0.0243,0.0253,0.0290,0.0393,0.0429,0.0589,0.0635,0.0658, 0.0659,0.0737,0.0756,0.0799,0.0867,0.0879,0.0919,0.1003,0.1016,0.1032, 0.1084,0.1090,0.1094,0.1115,0.1142,0.1193,0.1224,0.1288,0.1410,0.1412, 0.1431,0.1451,0.1496,0.1513,0.1528,0.1530,0.1599,0.1609,0.1642,0.1650, 0.1666,0.1674,0.1741,0.1839,0.1850,0.1902,0.2018,0.2024,0.2048,0.2082, 0.2100,0.2143,0.2179,0.2257,0.2292,0.2299,0.2342,0.2419,0.2419,0.2528, 0.2555,0.2617,0.2637,0.2705,0.2723,0.2733,0.2747,0.2754,0.2764,0.2788, 0.2808,0.2841,0.2852,0.2888,0.2900,0.2954,0.2993,0.3074,0.3077,0.3129, 0.3135,0.3157,0.3188,0.3207,0.3240,0.3341,0.3342,0.3366,0.3423,0.3471, 0.3472,0.3480,0.3487,0.3531,0.3544,0.3598,0.3605,0.3636,0.3664,0.3669, 0.3717,0.3734,0.3746,0.3803,0.3882,0.3979,0.3989,0.4051,0.4055,0.4109, 0.4131,0.4137,0.4170,0.4219,0.4224,0.4283,0.4309,0.4315,0.4443,0.4525, 0.4539,0.4598,0.4608,0.4631,0.4719,0.4727,0.4730,0.4750,0.4768,0.4784, 0.4808,0.4844,0.4867,0.4930,0.5018,0.5030,0.5047,0.5117,0.5148,0.5189, 0.5212,0.5212,0.5324,0.5339,0.5345,0.5364,0.5389,0.5418,0.5421,0.5450, 0.5472,0.5485,0.5521,0.5540,0.5562,0.5610,0.5650,0.5776,0.5776,0.5813, 0.5815,0.5846,0.5867,0.6009,0.6012,0.6032,0.6072,0.6080,0.6149,0.6212, 0.6212,0.6243,0.6426,0.6433,0.6483,0.6673,0.6674,0.6796,0.6809,0.6862, 0.6923,0.6923,0.6940,0.6947,0.6989,0.6995,0.7007,0.7019,0.7020,0.7093, 0.7194,0.7196,0.7216,0.7235,0.7295,0.7309,0.7334,0.7379,0.7399,0.7528, 0.7553,0.7607,0.7610,0.7665,0.7675,0.7687,0.7732,0.7744,0.7843,0.7860, 0.7861,0.7961,0.8011,0.8033,0.8072,0.8117,0.8166,0.8223,0.8250,0.8256, 0.8263,0.8310,0.8376,0.8410,0.8428,0.8550,0.8590,0.8593,0.8619,0.8622, 0.8673,0.8766,0.8816,0.8834,0.8869,0.8887,0.8890,0.8936,0.8986,0.9035, 0.9051,0.9092,0.9112,0.9154,0.9170,0.9206,0.9219,0.9244,0.9281,0.9285, 0.9299,0.9312,0.9323,0.9333,0.9344,0.9379,0.9399,0.9539,0.9566,0.9580, 0.9795,0.9804,0.9808,0.9814,0.9830,0.9870,0.9892,0.9893,0.9975, Overall p-value after applying KStest on 269 p-values = 0.598016 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.