RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-19_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 13.7996 0.318767 2 to 25 15.39 27.6759 0.951130 3 to 26 15.95 21.4827 0.794561 4 to 27 15.88 17.2178 0.560296 5 to 28 15.55 20.3309 0.742342 6 to 29 15.88 8.6618 0.049721 7 to 30 15.83 23.7518 0.873664 8 to 31 15.46 21.8932 0.811139 9 to 32 15.69 24.3652 0.890152 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.101694 Tough bday spacings test for dh-ranFile-2016-04-19_20:31: 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 10 35 82 98 95 72 37 37 18 13 3 (O-E)^2/E 0.1 0.1 1.0 0.0 0.1 0.5 4.4 1.8 0.7 6.2 0.3 Birthday Spacings: Sum(O-E)^2/E= 14.974, p= 0.867 RESULTS OF GCD FOR dh-ranFile-2016-04-19_20:31 Euclid's algorithm: p-value, steps to gcd: 0.339774 p-value, dist. of gcd's: 0.772183 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-19_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.116 0.092 0.244 0.110 0.771 0.122 0.347 0.235 Bits 8 to 15---> 0.504 0.083 0.370 0.719 0.853 0.694 0.028 0.191 Bits 16 to 23---> 0.398 1.000 0.858 0.461 0.713 0.400 0.395 0.620 Bits 24 to 31---> 0.066 0.883 0.864 0.952 0.763 0.042 0.183 0.158 KS test for the above 32 p values: 0.730 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-19_20:31, p-values for 5 runs: 0.0574, 0.2981, 0.1676, 0.0525, 1.0000 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-19_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5028 5134.0 2.189 3.172 r= 30 23444 23103.0 5.032 8.204 r= 31 11331 11551.5 4.210 12.414 chi-square = 12.414 with df = 3; p-value = 0.994 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-19_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5080 5134.0 0.568 0.903 r= 31 23119 23103.0 0.011 0.914 r= 32 11598 11551.5 0.187 1.101 chi-square = 1.101 with df = 3; p-value = 0.223 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-19_20:31 b-rank test for bits 1 to 8, p=0.60477 b-rank test for bits 2 to 9, p=0.03650 b-rank test for bits 3 to 10, p=0.65346 b-rank test for bits 4 to 11, p=0.81790 b-rank test for bits 5 to 12, p=0.99814 b-rank test for bits 6 to 13, p=0.66258 b-rank test for bits 7 to 14, p=0.91905 b-rank test for bits 8 to 15, p=0.39434 b-rank test for bits 9 to 16, p=0.23230 b-rank test for bits 10 to 17, p=0.74598 b-rank test for bits 11 to 18, p=0.86281 b-rank test for bits 12 to 19, p=0.65349 b-rank test for bits 13 to 20, p=0.95209 b-rank test for bits 14 to 21, p=0.69482 b-rank test for bits 15 to 22, p=0.90960 b-rank test for bits 16 to 23, p=0.63952 b-rank test for bits 17 to 24, p=0.46501 b-rank test for bits 18 to 25, p=0.41146 b-rank test for bits 19 to 26, p=0.94038 b-rank test for bits 20 to 27, p=0.15459 b-rank test for bits 21 to 28, p=0.76495 b-rank test for bits 22 to 29, p=0.42579 b-rank test for bits 23 to 30, p=0.85872 b-rank test for bits 24 to 31, p=0.77548 b-rank test for bits 25 to 32, p=0.25050 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 = 0.033338 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-19_20:31 (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 142230 0.75 0.773140 2 142790 2.06 0.980188 3 141969 0.14 0.555439 4 141889 -0.05 0.481057 5 141487 -0.99 0.161882 6 141525 -0.90 0.184602 7 141834 -0.18 0.430145 8 142433 1.22 0.889435 9 141378 -1.24 0.107224 10 141952 0.10 0.539707 11 141278 -1.48 0.070097 12 141832 -0.18 0.428310 13 141435 -1.11 0.133877 14 141495 -0.97 0.166507 15 142178 0.63 0.734911 16 141713 -0.46 0.323219 17 141814 -0.22 0.411871 18 141150 -1.77 0.038020 19 141958 0.11 0.545268 20 142634 1.69 0.954787 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-19_20:31 Bits used No. missing words z-score p-value 23 to 32 141860 -0.1701 0.432464 22 to 31 141713 -0.6770 0.249203 21 to 30 141320 -2.0322 0.021068 20 to 29 142065 0.5368 0.704295 19 to 28 142428 1.7885 0.963154 18 to 27 142203 1.0127 0.844388 17 to 26 141798 -0.3839 0.350528 16 to 25 142269 1.2402 0.892557 15 to 24 141437 -1.6287 0.051686 14 to 23 141853 -0.1942 0.422994 13 to 22 141606 -1.0460 0.147789 12 to 21 141539 -1.2770 0.100801 11 to 20 142188 0.9609 0.831707 10 to 19 142153 0.8402 0.799614 9 to 18 141542 -1.2667 0.102639 8 to 17 142646 2.5402 0.994461 7 to 16 141988 0.2713 0.606911 6 to 15 141898 -0.0391 0.484418 5 to 14 142056 0.5058 0.693487 4 to 13 142023 0.3920 0.652458 3 to 12 141552 -1.2322 0.108942 2 to 11 142198 0.9954 0.840233 1 to 10 142232 1.1127 0.867072 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-19_20:31 Bits used No. missing words z-score p-value 28 to 32 141117 -2.6859 0.003617 27 to 31 142183 0.9277 0.823217 26 to 30 142129 0.7446 0.771757 25 to 29 141881 -0.0960 0.461747 24 to 28 141602 -1.0418 0.148753 23 to 27 141711 -0.6723 0.250695 22 to 26 142575 2.2565 0.987981 21 to 25 141836 -0.2486 0.401844 20 to 24 142222 1.0599 0.855405 19 to 23 141595 -1.0655 0.143319 18 to 22 142040 0.4429 0.671099 17 to 21 142094 0.6260 0.734343 16 to 20 142412 1.7040 0.955806 15 to 19 142198 0.9785 0.836097 14 to 18 142507 2.0260 0.978618 13 to 17 141995 0.2904 0.614248 12 to 16 141947 0.1277 0.550805 11 to 15 142068 0.5379 0.704665 10 to 14 141551 -1.2147 0.112244 9 to 13 142281 1.2599 0.896147 8 to 12 141880 -0.0994 0.460401 7 to 11 141923 0.0463 0.518480 6 to 10 141789 -0.4079 0.341674 5 to 9 141972 0.2124 0.584118 4 to 8 141757 -0.5164 0.302797 3 to 7 141681 -0.7740 0.219465 2 to 6 141770 -0.4723 0.318355 1 to 5 141802 -0.3638 0.357992 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-19_20:31 Bits used No. missing words z-score p-value 31 to 32 142062 0.4504 0.673772 30 to 31 141669 -0.7089 0.239182 29 to 30 141702 -0.6116 0.270404 28 to 29 141935 0.0757 0.530180 27 to 28 141779 -0.3845 0.350321 26 to 27 142093 0.5418 0.706022 25 to 26 141934 0.0728 0.529007 24 to 25 142102 0.5683 0.715101 23 to 24 142089 0.5300 0.701944 22 to 23 141587 -0.9508 0.170846 21 to 22 141519 -1.1514 0.124781 20 to 21 142202 0.8633 0.806023 19 to 20 141932 0.0669 0.526659 18 to 19 142192 0.8338 0.797813 17 to 18 141736 -0.5113 0.304571 16 to 17 142238 0.9695 0.833859 15 to 16 142012 0.3029 0.619002 14 to 15 141735 -0.5142 0.303539 13 to 14 142061 0.4474 0.672708 12 to 13 142312 1.1878 0.882547 11 to 12 141441 -1.3815 0.083562 10 to 11 142215 0.9017 0.816387 9 to 10 141967 0.1701 0.567541 8 to 9 142457 1.6155 0.946904 7 to 8 141541 -1.0865 0.138625 6 to 7 141562 -1.0246 0.152783 5 to 6 141672 -0.7001 0.241936 4 to 5 142001 0.2704 0.606579 3 to 4 142258 1.0285 0.848149 2 to 3 142123 0.6303 0.735749 1 to 2 141689 -0.6499 0.257865 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-19_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2452.94 -0.666 0.252845 Test results for specific bytes for dh-ranFile-2016-04-19_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2564.79 0.916 0.820242 2 to 9 2470.28 -0.420 0.337112 3 to 10 2490.55 -0.134 0.446827 4 to 11 2478.90 -0.298 0.382698 5 to 12 2474.78 -0.357 0.360666 6 to 13 2498.79 -0.017 0.493155 7 to 14 2539.77 0.562 0.713090 8 to 15 2449.23 -0.718 0.236358 9 to 16 2515.95 0.226 0.589206 10 to 17 2482.54 -0.247 0.402478 11 to 18 2434.09 -0.932 0.175627 12 to 19 2585.26 1.206 0.886037 13 to 20 2570.63 0.999 0.841083 14 to 21 2506.29 0.089 0.535446 15 to 22 2632.85 1.879 0.969858 16 to 23 2680.59 2.554 0.994674 17 to 24 2454.55 -0.643 0.260206 18 to 25 2357.91 -2.010 0.022241 19 to 26 2488.91 -0.157 0.437688 20 to 27 2551.02 0.722 0.764730 21 to 28 2524.20 0.342 0.633896 22 to 29 2593.50 1.322 0.906955 23 to 30 2520.29 0.287 0.612922 24 to 31 2451.67 -0.684 0.247136 25 to 32 2477.52 -0.318 0.375253 CDPARK for dh-ranFile-2016-04-19_20:31: 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 3530 0.3196 0.625377 3530 0.3196 0.625377 3540 0.7763 0.781201 3525 0.0913 0.536383 3536 0.5936 0.723613 3521 -0.0913 0.463617 3516 -0.3196 0.374623 3569 2.1005 0.982156 3500 -1.0502 0.146807 3516 -0.3196 0.374623 Square side=100, avg. no. parked=3528.30 sample std.=17.40 p-value of the KSTEST for those 10 p-values: 0.581461 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-19_20:31 0.7758,0.1827,0.5642,0.2452,0.1746,0.3740,0.0325,0.8721,0.0677,0.4580, The KS test for those 10 p-values: 0.314640 The 3DSPHERES test for dh-ranFile-2016-04-19_20:31 sample no r^3 equiv. uni. 1 36.862 0.707338 2 10.578 0.297150 3 44.491 0.773055 4 56.341 0.847107 5 19.968 0.486034 6 130.814 0.987228 7 58.052 0.855583 8 19.688 0.481216 9 63.042 0.877715 10 14.717 0.387716 11 35.849 0.697290 12 1.858 0.060057 13 42.311 0.755948 14 5.106 0.156495 15 20.659 0.497736 16 4.811 0.148167 17 119.728 0.981518 18 4.095 0.127593 19 16.464 0.422358 20 19.671 0.480916 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.659455 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-19_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 0.1 -1.3 0.4 0.5 -0.6 1.0 1.6 -0.5 1.4 -0.6 -1.9 0.5 -0.8 1.0 -0.1 0.4 0.8 -0.4 -1.6 -0.8 1.4 -0.1 -0.2 0.3 0.2 0.6 0.3 -1.8 -0.5 -0.3 1.8 0.2 -0.6 -1.2 -1.2 0.5 1.3 2.1 -1.3 1.0 -0.1 Chi-square with 42 degrees of freedom:42.846404 z-score=0.092350, p-value=0.565306 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-19_20:31 Test no p-value 1 0.029783 2 0.291472 3 0.825962 4 0.835974 5 0.097252 6 0.151806 7 0.324207 8 0.061879 9 0.445747 10 0.680099 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.243201 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-19_20:31: (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 67122 3.11 66617 0.04 3 25000.00 24607 6.18 25019 0.01 4 6666.67 6601 0.65 6642 0.09 5 1388.89 1377 0.10 1414 0.45 6 238.10 249 0.50 267 3.51 7 34.72 38 0.31 34 0.01 8 4.96 5 0.00 6 0.22 p=0.90675 p=0.36906 Number of rngs required: 686995, p-value: 0.050 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-19_20:31 No. of wins: Observed Expected 98191 98585.9 z-score=-1.766, pvalue=0.03869 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66313 66666.7 1.876 1.876 2 37693 37654.3 0.040 1.916 3 26951 26954.7 0.001 1.916 4 19461 19313.5 1.127 3.044 5 13917 13851.4 0.310 3.354 6 9996 9943.5 0.277 3.631 7 7096 7145.0 0.336 3.967 8 5075 5139.1 0.799 4.766 9 3808 3699.9 3.160 7.926 10 2708 2666.3 0.652 8.579 11 1929 1923.3 0.017 8.595 12 1383 1388.7 0.024 8.619 13 1037 1003.7 1.104 9.723 14 724 726.1 0.006 9.729 15 488 525.8 2.722 12.452 16 367 381.2 0.525 12.977 17 296 276.5 1.369 14.346 18 210 200.8 0.419 14.765 19 156 146.0 0.687 15.452 20 88 106.2 3.124 18.576 21 304 287.1 0.993 19.569 Chisq= 19.57 for 20 degrees of freedom, p= 0.51485 SUMMARY of craptest p-value for no. of wins: 0.038695 p-value for throws/game: 0.514850 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-19_20:31 No. of wins: Observed Expected 98533 98585.9 z-score=-0.236, pvalue=0.40656 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66152 66666.7 3.973 3.973 2 37819 37654.3 0.720 4.693 3 27387 26954.7 6.932 11.626 4 19184 19313.5 0.868 12.493 5 13861 13851.4 0.007 12.500 6 9897 9943.5 0.218 12.718 7 7269 7145.0 2.151 14.869 8 5109 5139.1 0.176 15.045 9 3659 3699.9 0.451 15.496 10 2728 2666.3 1.428 16.924 11 1861 1923.3 2.020 18.944 12 1448 1388.7 2.529 21.473 13 993 1003.7 0.114 21.587 14 736 726.1 0.134 21.721 15 512 525.8 0.364 22.085 16 373 381.2 0.174 22.259 17 290 276.5 0.655 22.915 18 182 200.8 1.765 24.680 19 130 146.0 1.750 26.430 20 131 106.2 5.783 32.214 21 279 287.1 0.229 32.443 Chisq= 32.44 for 20 degrees of freedom, p= 0.96120 SUMMARY of craptest p-value for no. of wins: 0.406556 p-value for throws/game: 0.961200 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0036,0.0211,0.0222,0.0278,0.0298,0.0325,0.0333,0.0365,0.0380,0.0387, 0.0423,0.0495,0.0497,0.0517,0.0525,0.0574,0.0601,0.0619,0.0655,0.0677, 0.0701,0.0832,0.0836,0.0922,0.0973,0.1008,0.1017,0.1026,0.1072,0.1089, 0.1105,0.1122,0.1158,0.1221,0.1248,0.1276,0.1339,0.1386,0.1433,0.1468, 0.1478,0.1482,0.1488,0.1518,0.1528,0.1546,0.1565,0.1582,0.1619,0.1665, 0.1676,0.1708,0.1746,0.1756,0.1826,0.1827,0.1846,0.1912,0.2195,0.2233, 0.2323,0.2348,0.2364,0.2392,0.2419,0.2432,0.2442,0.2452,0.2471,0.2492, 0.2505,0.2507,0.2528,0.2579,0.2602,0.2704,0.2915,0.2972,0.2981,0.3028, 0.3035,0.3046,0.3146,0.3184,0.3188,0.3232,0.3242,0.3371,0.3398,0.3417, 0.3470,0.3503,0.3505,0.3580,0.3607,0.3691,0.3701,0.3740,0.3746,0.3746, 0.3753,0.3827,0.3877,0.3943,0.3954,0.3982,0.4004,0.4018,0.4025,0.4066, 0.4115,0.4119,0.4224,0.4230,0.4258,0.4283,0.4301,0.4325,0.4377,0.4457, 0.4468,0.4580,0.4604,0.4613,0.4617,0.4636,0.4650,0.4809,0.4811,0.4812, 0.4844,0.4860,0.4932,0.4977,0.5036,0.5148,0.5185,0.5267,0.5290,0.5302, 0.5354,0.5364,0.5397,0.5453,0.5508,0.5554,0.5603,0.5642,0.5653,0.5675, 0.5815,0.5841,0.5892,0.6048,0.6066,0.6069,0.6129,0.6142,0.6190,0.6200, 0.6254,0.6254,0.6339,0.6395,0.6525,0.6535,0.6535,0.6595,0.6626,0.6711, 0.6727,0.6738,0.6801,0.6935,0.6941,0.6948,0.6973,0.7019,0.7043,0.7047, 0.7060,0.7073,0.7130,0.7131,0.7151,0.7187,0.7236,0.7304,0.7343,0.7349, 0.7357,0.7423,0.7460,0.7559,0.7626,0.7647,0.7650,0.7707,0.7718,0.7722, 0.7731,0.7731,0.7755,0.7758,0.7812,0.7946,0.7978,0.7996,0.8060,0.8111, 0.8164,0.8179,0.8202,0.8232,0.8260,0.8317,0.8339,0.8360,0.8361,0.8402, 0.8411,0.8444,0.8471,0.8481,0.8527,0.8554,0.8556,0.8577,0.8587,0.8628, 0.8642,0.8670,0.8671,0.8721,0.8737,0.8777,0.8825,0.8830,0.8860,0.8894, 0.8902,0.8926,0.8961,0.9068,0.9070,0.9096,0.9191,0.9404,0.9469,0.9511, 0.9517,0.9521,0.9548,0.9558,0.9612,0.9632,0.9699,0.9786,0.9802,0.9815, 0.9822,0.9872,0.9880,0.9939,0.9945,0.9947,0.9981,0.9999,1.0000, Overall p-value after applying KStest on 269 p-values = 0.492029 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.