RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-01_12:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.65 21.6361 0.800880 2 to 25 15.62 21.4581 0.793532 3 to 26 15.80 14.5084 0.369154 4 to 27 15.78 19.8462 0.717830 5 to 28 15.79 16.7147 0.526149 6 to 29 15.99 14.7810 0.388747 7 to 30 16.22 22.4182 0.830832 8 to 31 15.95 26.5678 0.935282 9 to 32 16.16 20.5564 0.753234 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.081247 Tough bday spacings test for dh-ranFile-2016-11-01_12:31: 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 33 69 106 94 85 50 31 15 9 1 (O-E)^2/E 0.5 0.4 0.2 0.7 0.1 0.6 0.1 0.1 0.0 0.9 2.3 Birthday Spacings: Sum(O-E)^2/E= 5.872, p= 0.174 RESULTS OF GCD FOR dh-ranFile-2016-11-01_12:31 Euclid's algorithm: p-value, steps to gcd: 0.734562 p-value, dist. of gcd's: 0.105148 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-01_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.384 0.844 0.186 0.531 0.883 0.712 0.593 0.681 Bits 8 to 15---> 0.977 0.647 0.661 0.610 0.878 0.939 0.879 0.720 Bits 16 to 23---> 0.641 0.375 0.263 0.195 0.226 0.549 0.759 0.457 Bits 24 to 31---> 0.156 0.244 0.054 0.731 0.523 0.439 0.778 0.052 KS test for the above 32 p values: 0.484 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-01_12:31, p-values for 5 runs: 0.1173, 0.9717, 0.9966, 0.9988, 0.3689 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-01_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 228 211.4 1.301 1.301 r= 29 5122 5134.0 0.028 1.329 r= 30 23067 23103.0 0.056 1.385 r= 31 11583 11551.5 0.086 1.471 chi-square = 1.471 with df = 3; p-value = 0.311 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-01_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 194 211.4 1.435 1.435 r= 30 5043 5134.0 1.613 3.048 r= 31 23191 23103.0 0.335 3.383 r= 32 11572 11551.5 0.036 3.419 chi-square = 3.419 with df = 3; p-value = 0.669 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-01_12:31 b-rank test for bits 1 to 8, p=0.70404 b-rank test for bits 2 to 9, p=0.88957 b-rank test for bits 3 to 10, p=0.88459 b-rank test for bits 4 to 11, p=0.40138 b-rank test for bits 5 to 12, p=0.29170 b-rank test for bits 6 to 13, p=0.76388 b-rank test for bits 7 to 14, p=0.60831 b-rank test for bits 8 to 15, p=0.84651 b-rank test for bits 9 to 16, p=0.04926 b-rank test for bits 10 to 17, p=0.26674 b-rank test for bits 11 to 18, p=0.54344 b-rank test for bits 12 to 19, p=0.80899 b-rank test for bits 13 to 20, p=0.34154 b-rank test for bits 14 to 21, p=0.04459 b-rank test for bits 15 to 22, p=0.18212 b-rank test for bits 16 to 23, p=0.23529 b-rank test for bits 17 to 24, p=0.03712 b-rank test for bits 18 to 25, p=0.31938 b-rank test for bits 19 to 26, p=0.06992 b-rank test for bits 20 to 27, p=0.94030 b-rank test for bits 21 to 28, p=0.62412 b-rank test for bits 22 to 29, p=0.59292 b-rank test for bits 23 to 30, p=0.77803 b-rank test for bits 24 to 31, p=0.45128 b-rank test for bits 25 to 32, p=0.39578 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 = 0.956938 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-01_12:31 (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 142002 0.22 0.585708 2 142092 0.43 0.665237 3 142003 0.22 0.586619 4 142004 0.22 0.587528 5 141329 -1.36 0.087564 6 141799 -0.26 0.398288 7 141897 -0.03 0.488509 8 141993 0.20 0.577496 9 141768 -0.33 0.370621 10 141595 -0.73 0.231348 11 141386 -1.22 0.110715 12 142376 1.09 0.862221 13 141503 -0.95 0.171216 14 142326 0.97 0.834855 15 141350 -1.31 0.095633 16 141859 -0.12 0.453195 17 141391 -1.21 0.112938 18 141897 -0.03 0.488509 19 141856 -0.12 0.450419 20 142722 1.90 0.971202 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-01_12:31 Bits used No. missing words z-score p-value 23 to 32 142295 1.3299 0.908224 22 to 31 142113 0.7023 0.758757 21 to 30 141945 0.1230 0.548947 20 to 29 141910 0.0023 0.500922 19 to 28 141709 -0.6908 0.244848 18 to 27 142311 1.3851 0.916984 17 to 26 142104 0.6713 0.748978 16 to 25 142055 0.5023 0.692275 15 to 24 142025 0.3989 0.655003 14 to 23 141849 -0.2080 0.417601 13 to 22 141711 -0.6839 0.247020 12 to 21 141945 0.1230 0.548947 11 to 20 141751 -0.5460 0.292545 10 to 19 142000 0.3127 0.622729 9 to 18 141964 0.1885 0.574764 8 to 17 142036 0.4368 0.668869 7 to 16 141459 -1.5529 0.060228 6 to 15 142241 1.1437 0.873624 5 to 14 141927 0.0609 0.524293 4 to 13 142169 0.8954 0.814717 3 to 12 141870 -0.1356 0.446061 2 to 11 141605 -1.0494 0.146994 1 to 10 141674 -0.8115 0.208544 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-01_12:31 Bits used No. missing words z-score p-value 28 to 32 141595 -1.0655 0.143319 27 to 31 142152 0.8226 0.794635 26 to 30 141881 -0.0960 0.461747 25 to 29 141970 0.2057 0.581472 24 to 28 141594 -1.0689 0.142554 23 to 27 141673 -0.8011 0.211532 22 to 26 141540 -1.2520 0.105291 21 to 25 142075 0.5616 0.712803 20 to 24 142097 0.6362 0.737667 19 to 23 141405 -1.7096 0.043671 18 to 22 141894 -0.0520 0.479278 17 to 21 142045 0.4599 0.677205 16 to 20 142096 0.6328 0.736561 15 to 19 141652 -0.8723 0.191521 14 to 18 141679 -0.7808 0.217466 13 to 17 141899 -0.0350 0.486033 12 to 16 141981 0.2429 0.595978 11 to 15 142198 0.9785 0.836097 10 to 14 142133 0.7582 0.775835 9 to 13 141360 -1.8621 0.031292 8 to 12 142215 1.0362 0.849938 7 to 11 142342 1.4667 0.928768 6 to 10 142019 0.3718 0.644965 5 to 9 141721 -0.6384 0.261605 4 to 8 141901 -0.0282 0.488737 3 to 7 141581 -1.1130 0.132858 2 to 6 141916 0.0226 0.509019 1 to 5 142421 1.7345 0.958583 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-01_12:31 Bits used No. missing words z-score p-value 31 to 32 141466 -1.3078 0.095478 30 to 31 141868 -0.1219 0.451482 29 to 30 141852 -0.1691 0.432853 28 to 29 141518 -1.1544 0.124175 27 to 28 141970 0.1790 0.571018 26 to 27 142466 1.6421 0.949715 25 to 26 141996 0.2557 0.600895 24 to 25 141954 0.1318 0.552417 23 to 24 141736 -0.5113 0.304571 22 to 23 141592 -0.9361 0.174617 21 to 22 142026 0.3442 0.634637 20 to 21 142336 1.2586 0.895915 19 to 20 141876 -0.0983 0.460840 18 to 19 141894 -0.0452 0.481966 17 to 18 141778 -0.3874 0.349229 16 to 17 142086 0.5212 0.698869 15 to 16 142104 0.5742 0.717100 14 to 15 141655 -0.7502 0.226556 13 to 14 141707 -0.5968 0.275306 12 to 13 142008 0.2911 0.614498 11 to 12 142307 1.1731 0.879616 10 to 11 142203 0.8663 0.806833 9 to 10 142368 1.3530 0.911974 8 to 9 141877 -0.0954 0.462011 7 to 8 141761 -0.4376 0.330856 6 to 7 142116 0.6096 0.728952 5 to 6 141799 -0.3255 0.372418 4 to 5 141585 -0.9567 0.169353 3 to 4 141724 -0.5467 0.292294 2 to 3 142165 0.7542 0.774632 1 to 2 142227 0.9371 0.825641 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-01_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2571.38 1.009 0.843632 Test results for specific bytes for dh-ranFile-2016-11-01_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2509.88 0.140 0.555589 2 to 9 2489.21 -0.153 0.439381 3 to 10 2560.38 0.854 0.803430 4 to 11 2443.91 -0.793 0.213839 5 to 12 2455.42 -0.630 0.264209 6 to 13 2351.06 -2.106 0.017586 7 to 14 2414.08 -1.215 0.112177 8 to 15 2471.04 -0.410 0.341071 9 to 16 2461.48 -0.545 0.292953 10 to 17 2472.95 -0.382 0.351048 11 to 18 2534.05 0.482 0.684926 12 to 19 2574.56 1.054 0.854169 13 to 20 2564.11 0.907 0.817721 14 to 21 2344.16 -2.204 0.013765 15 to 22 2470.52 -0.417 0.338367 16 to 23 2536.99 0.523 0.699540 17 to 24 2428.97 -1.005 0.157558 18 to 25 2469.01 -0.438 0.330618 19 to 26 2512.44 0.176 0.569818 20 to 27 2533.12 0.468 0.680226 21 to 28 2472.90 -0.383 0.350772 22 to 29 2492.43 -0.107 0.457380 23 to 30 2511.91 0.168 0.566893 24 to 31 2501.91 0.027 0.510762 25 to 32 2634.11 1.897 0.971061 CDPARK for dh-ranFile-2016-11-01_12:31: 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 3508 -0.6849 0.246694 3527 0.1826 0.572463 3520 -0.1370 0.445521 3503 -0.9132 0.180558 3523 0.0000 0.500000 3532 0.4110 0.659449 3482 -1.8721 0.030593 3505 -0.8219 0.205562 3510 -0.5936 0.276387 3507 -0.7306 0.232514 Square side=100, avg. no. parked=3511.70 sample std.=13.73 p-value of the KSTEST for those 10 p-values: 0.092705 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-01_12:31 0.3234,0.8455,0.5972,0.3052,0.7449,0.2412,0.8159,0.8577,0.3365,0.3868, The KS test for those 10 p-values: 0.568160 The 3DSPHERES test for dh-ranFile-2016-11-01_12:31 sample no r^3 equiv. uni. 1 15.048 0.394436 2 5.450 0.166133 3 67.046 0.892992 4 4.850 0.149263 5 20.426 0.493829 6 20.201 0.490012 7 39.991 0.736326 8 26.009 0.579777 9 13.285 0.357783 10 3.954 0.123484 11 34.301 0.681261 12 4.547 0.140650 13 43.706 0.767034 14 40.143 0.737659 15 0.765 0.025192 16 17.862 0.448659 17 41.015 0.745172 18 2.899 0.092117 19 12.712 0.345410 20 36.764 0.706380 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.600237 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-01_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 0.3 1.1 1.3 -0.2 -0.2 -1.8 -1.0 -0.4 -1.1 -2.2 -0.4 1.6 0.0 0.5 0.4 0.5 1.6 -0.5 -0.4 -0.1 -0.9 0.2 0.4 0.6 1.5 -0.7 -1.7 -0.4 1.6 0.7 -0.0 -1.6 0.2 0.2 0.7 -0.1 -1.6 -0.1 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:37.232200 z-score=-0.520210, p-value=0.319971 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-01_12:31 Test no p-value 1 0.738837 2 0.941192 3 0.134735 4 0.020783 5 0.967885 6 0.701784 7 0.001135 8 0.114581 9 0.370980 10 0.517742 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.229174 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-01_12:31: (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 66716 0.04 66760 0.13 3 25000.00 24890 0.48 25028 0.03 4 6666.67 6669 0.00 6558 1.77 5 1388.89 1417 0.57 1390 0.00 6 238.10 263 2.61 229 0.35 7 34.72 37 0.15 27 1.72 8 4.96 7 0.84 7 0.84 p=0.41507 p=0.43515 Number of rngs required: 687993, p-value: 0.318 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-01_12:31 No. of wins: Observed Expected 98034 98585.9 z-score=-2.468, pvalue=0.00679 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66500 66666.7 0.417 0.417 2 37508 37654.3 0.569 0.985 3 26926 26954.7 0.031 1.016 4 19400 19313.5 0.388 1.404 5 13927 13851.4 0.412 1.816 6 10008 9943.5 0.418 2.234 7 7183 7145.0 0.202 2.436 8 5090 5139.1 0.469 2.904 9 3740 3699.9 0.435 3.340 10 2732 2666.3 1.619 4.959 11 1920 1923.3 0.006 4.964 12 1455 1388.7 3.161 8.126 13 1000 1003.7 0.014 8.140 14 731 726.1 0.033 8.172 15 511 525.8 0.419 8.591 16 382 381.2 0.002 8.593 17 264 276.5 0.569 9.161 18 178 200.8 2.595 11.756 19 148 146.0 0.028 11.784 20 106 106.2 0.000 11.785 21 291 287.1 0.053 11.837 Chisq= 11.84 for 20 degrees of freedom, p= 0.07844 SUMMARY of craptest p-value for no. of wins: 0.006789 p-value for throws/game: 0.078437 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-01_12:31 No. of wins: Observed Expected 98717 98585.9 z-score= 0.587, pvalue=0.72124 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66494 66666.7 0.447 0.447 2 37415 37654.3 1.521 1.968 3 26991 26954.7 0.049 2.017 4 19498 19313.5 1.763 3.780 5 13902 13851.4 0.185 3.965 6 9870 9943.5 0.544 4.509 7 7112 7145.0 0.153 4.662 8 5262 5139.1 2.940 7.602 9 3775 3699.9 1.526 9.128 10 2817 2666.3 8.518 17.646 11 1879 1923.3 1.022 18.667 12 1325 1388.7 2.926 21.593 13 1018 1003.7 0.203 21.796 14 687 726.1 2.110 23.906 15 541 525.8 0.437 24.343 16 405 381.2 1.492 25.836 17 284 276.5 0.201 26.037 18 203 200.8 0.023 26.060 19 149 146.0 0.062 26.123 20 101 106.2 0.256 26.379 21 272 287.1 0.796 27.174 Chisq= 27.17 for 20 degrees of freedom, p= 0.86957 SUMMARY of craptest p-value for no. of wins: 0.721244 p-value for throws/game: 0.869572 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0068,0.0138,0.0176,0.0208,0.0252,0.0306,0.0313,0.0371,0.0437, 0.0446,0.0493,0.0523,0.0536,0.0602,0.0699,0.0784,0.0812,0.0876,0.0921, 0.0927,0.0955,0.0956,0.1051,0.1053,0.1107,0.1122,0.1129,0.1146,0.1173, 0.1235,0.1242,0.1329,0.1347,0.1407,0.1426,0.1433,0.1470,0.1493,0.1562, 0.1576,0.1661,0.1694,0.1712,0.1741,0.1746,0.1806,0.1821,0.1858,0.1915, 0.1951,0.2056,0.2085,0.2115,0.2138,0.2175,0.2260,0.2266,0.2292,0.2313, 0.2325,0.2353,0.2412,0.2435,0.2448,0.2467,0.2470,0.2616,0.2634,0.2642, 0.2667,0.2753,0.2764,0.2917,0.2923,0.2925,0.2930,0.3046,0.3052,0.3109, 0.3183,0.3194,0.3200,0.3234,0.3306,0.3309,0.3365,0.3384,0.3411,0.3415, 0.3454,0.3492,0.3508,0.3510,0.3578,0.3689,0.3692,0.3706,0.3710,0.3724, 0.3746,0.3840,0.3868,0.3887,0.3944,0.3958,0.3983,0.4014,0.4151,0.4176, 0.4329,0.4352,0.4386,0.4394,0.4455,0.4461,0.4487,0.4504,0.4513,0.4515, 0.4532,0.4568,0.4574,0.4608,0.4617,0.4620,0.4793,0.4820,0.4840,0.4860, 0.4885,0.4885,0.4887,0.4900,0.4938,0.5000,0.5009,0.5090,0.5108,0.5177, 0.5229,0.5243,0.5261,0.5310,0.5434,0.5489,0.5489,0.5489,0.5524,0.5556, 0.5669,0.5682,0.5698,0.5710,0.5725,0.5748,0.5775,0.5798,0.5815,0.5857, 0.5866,0.5875,0.5926,0.5929,0.5960,0.5972,0.6002,0.6009,0.6083,0.6097, 0.6145,0.6227,0.6241,0.6346,0.6414,0.6450,0.6468,0.6550,0.6594,0.6614, 0.6652,0.6686,0.6689,0.6772,0.6802,0.6813,0.6814,0.6849,0.6923,0.6989, 0.6995,0.7018,0.7040,0.7064,0.7117,0.7128,0.7171,0.7178,0.7204,0.7212, 0.7290,0.7312,0.7346,0.7363,0.7366,0.7377,0.7377,0.7388,0.7449,0.7452, 0.7490,0.7532,0.7588,0.7590,0.7639,0.7670,0.7746,0.7758,0.7779,0.7780, 0.7935,0.7946,0.8009,0.8034,0.8068,0.8090,0.8147,0.8159,0.8177,0.8256, 0.8308,0.8349,0.8361,0.8436,0.8444,0.8455,0.8465,0.8499,0.8542,0.8577, 0.8622,0.8696,0.8736,0.8779,0.8788,0.8796,0.8831,0.8846,0.8896,0.8930, 0.8959,0.9082,0.9120,0.9170,0.9288,0.9353,0.9386,0.9403,0.9412,0.9497, 0.9569,0.9586,0.9679,0.9711,0.9712,0.9717,0.9775,0.9966,0.9988, Overall p-value after applying KStest on 269 p-values = 0.650049 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.