RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-09_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.80 18.4157 0.636919 2 to 25 15.70 19.4708 0.697815 3 to 26 15.81 16.0903 0.482559 4 to 27 15.99 12.9770 0.262273 5 to 28 15.78 21.8460 0.809285 6 to 29 15.90 27.0273 0.942331 7 to 30 15.60 18.1407 0.619984 8 to 31 15.56 24.2129 0.886234 9 to 32 15.87 13.8912 0.325212 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.317723 Tough bday spacings test for dh-ranFile-2016-07-09_10:31: 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 8 30 76 95 101 89 49 22 21 5 4 (O-E)^2/E 0.1 1.2 0.1 0.1 0.1 1.5 0.2 2.0 2.5 0.4 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.263, p= 0.397 RESULTS OF GCD FOR dh-ranFile-2016-07-09_10:31 Euclid's algorithm: p-value, steps to gcd: 0.755301 p-value, dist. of gcd's: 0.465117 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-09_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.555 0.351 0.503 0.679 0.179 0.205 0.780 0.074 Bits 8 to 15---> 0.298 0.483 0.182 0.223 0.056 0.525 0.519 0.469 Bits 16 to 23---> 0.472 0.850 0.948 0.107 0.559 0.275 0.473 0.125 Bits 24 to 31---> 0.127 0.253 0.596 0.765 0.770 0.140 0.263 0.709 KS test for the above 32 p values: 0.852 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-09_10:31, p-values for 5 runs: 0.1859, 0.9039, 0.8756, 0.1842, 0.4297 Rank test for binary matrices (31x31) for dh-ranFile-2016-07-09_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 198 211.4 0.852 0.852 r= 29 5205 5134.0 0.982 1.833 r= 30 23045 23103.0 0.146 1.979 r= 31 11552 11551.5 0.000 1.979 chi-square = 1.979 with df = 3; p-value = 0.423 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-07-09_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5069 5134.0 0.823 0.855 r= 31 23118 23103.0 0.010 0.864 r= 32 11599 11551.5 0.195 1.060 chi-square = 1.060 with df = 3; p-value = 0.213 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-07-09_10:31 b-rank test for bits 1 to 8, p=0.66274 b-rank test for bits 2 to 9, p=0.93643 b-rank test for bits 3 to 10, p=0.99682 b-rank test for bits 4 to 11, p=0.95279 b-rank test for bits 5 to 12, p=0.34807 b-rank test for bits 6 to 13, p=0.03548 b-rank test for bits 7 to 14, p=0.24359 b-rank test for bits 8 to 15, p=0.04278 b-rank test for bits 9 to 16, p=0.64049 b-rank test for bits 10 to 17, p=0.38816 b-rank test for bits 11 to 18, p=0.10189 b-rank test for bits 12 to 19, p=0.30320 b-rank test for bits 13 to 20, p=0.83294 b-rank test for bits 14 to 21, p=0.10708 b-rank test for bits 15 to 22, p=0.87324 b-rank test for bits 16 to 23, p=0.85251 b-rank test for bits 17 to 24, p=0.46709 b-rank test for bits 18 to 25, p=0.68131 b-rank test for bits 19 to 26, p=0.56481 b-rank test for bits 20 to 27, p=0.34919 b-rank test for bits 21 to 28, p=0.39048 b-rank test for bits 22 to 29, p=0.43820 b-rank test for bits 23 to 30, p=0.53081 b-rank test for bits 24 to 31, p=0.79521 b-rank test for bits 25 to 32, p=0.48739 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 = 0.943388 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-09_10:31 (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 141424 -1.13 0.128408 2 142153 0.57 0.715431 3 141732 -0.41 0.339319 4 142478 1.33 0.908021 5 142154 0.57 0.716223 6 141769 -0.33 0.371504 7 142861 2.22 0.986910 8 142494 1.37 0.914039 9 142651 1.73 0.958441 10 142079 0.40 0.654104 11 141827 -0.19 0.423730 12 141520 -0.91 0.181504 13 142677 1.79 0.963563 14 141895 -0.03 0.486645 15 141760 -0.35 0.363582 16 142137 0.53 0.702616 17 142941 2.41 0.992033 18 141329 -1.36 0.087564 19 141612 -0.69 0.243623 20 142132 0.52 0.698558 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-07-09_10:31 Bits used No. missing words z-score p-value 23 to 32 142218 1.0644 0.856422 22 to 31 141954 0.1540 0.561209 21 to 30 141769 -0.4839 0.314230 20 to 29 141498 -1.4184 0.078040 19 to 28 142217 1.0609 0.855639 18 to 27 141925 0.0540 0.521546 17 to 26 141880 -0.1011 0.459721 16 to 25 141898 -0.0391 0.484418 15 to 24 142427 1.7851 0.962875 14 to 23 141872 -0.1287 0.448788 13 to 22 141965 0.1920 0.576115 12 to 21 142376 1.6092 0.946214 11 to 20 141602 -1.0598 0.144627 10 to 19 142338 1.4782 0.930319 9 to 18 142125 0.7437 0.771468 8 to 17 141987 0.2678 0.605584 7 to 16 141697 -0.7322 0.232032 6 to 15 141525 -1.3253 0.092540 5 to 14 141834 -0.2598 0.397525 4 to 13 141863 -0.1598 0.436536 3 to 12 141662 -0.8529 0.196868 2 to 11 141416 -1.7011 0.044459 1 to 10 141692 -0.7494 0.226804 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-07-09_10:31 Bits used No. missing words z-score p-value 28 to 32 141772 -0.4655 0.320778 27 to 31 142036 0.4294 0.666180 26 to 30 141948 0.1311 0.552146 25 to 29 141395 -1.7435 0.040624 24 to 28 142025 0.3921 0.652509 23 to 27 141748 -0.5469 0.292230 22 to 26 142216 1.0396 0.850728 21 to 25 141846 -0.2147 0.415009 20 to 24 141615 -0.9977 0.159205 19 to 23 141641 -0.9096 0.181519 18 to 22 141752 -0.5333 0.296905 17 to 21 141973 0.2158 0.585440 16 to 20 141639 -0.9164 0.179736 15 to 19 141619 -0.9842 0.162516 14 to 18 142065 0.5277 0.701145 13 to 17 141631 -0.9435 0.172715 12 to 16 141669 -0.8147 0.207628 11 to 15 142276 1.2429 0.893057 10 to 14 141568 -1.1571 0.123626 9 to 13 141965 0.1887 0.574841 8 to 12 142249 1.1514 0.875221 7 to 11 142257 1.1785 0.880710 6 to 10 141542 -1.2452 0.106532 5 to 9 142042 0.4497 0.673547 4 to 8 142308 1.3514 0.911720 3 to 7 142258 1.1819 0.881384 2 to 6 141752 -0.5333 0.296905 1 to 5 141735 -0.5909 0.277277 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-07-09_10:31 Bits used No. missing words z-score p-value 31 to 32 141332 -1.7030 0.044280 30 to 31 142373 1.3678 0.914306 29 to 30 141294 -1.8151 0.034752 28 to 29 141797 -0.3314 0.370187 27 to 28 142434 1.5477 0.939153 26 to 27 141844 -0.1927 0.423592 25 to 26 142179 0.7955 0.786835 24 to 25 141604 -0.9007 0.183880 23 to 24 142638 2.1495 0.984201 22 to 23 141288 -1.8328 0.033414 21 to 22 141890 -0.0570 0.477264 20 to 21 141909 -0.0010 0.499612 19 to 20 141680 -0.6765 0.249365 18 to 19 141936 0.0787 0.531354 17 to 18 142086 0.5212 0.698869 16 to 17 141513 -1.1691 0.121179 15 to 16 142066 0.4622 0.678014 14 to 15 142160 0.7394 0.770180 13 to 14 142091 0.5359 0.703986 12 to 13 142021 0.3294 0.629077 11 to 12 141481 -1.2635 0.103203 10 to 11 142184 0.8102 0.791098 9 to 10 142279 1.0905 0.862247 8 to 9 141832 -0.2281 0.409780 7 to 8 141697 -0.6263 0.265545 6 to 7 142796 2.6155 0.995546 5 to 6 141885 -0.0718 0.471393 4 to 5 141019 -2.6263 0.004315 3 to 4 141502 -1.2016 0.114766 2 to 3 141427 -1.4228 0.077397 1 to 2 141747 -0.4788 0.316023 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-09_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2481.42 -0.263 0.396351 Test results for specific bytes for dh-ranFile-2016-07-09_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2475.45 -0.347 0.364246 2 to 9 2560.82 0.860 0.805137 3 to 10 2441.18 -0.832 0.202750 4 to 11 2678.96 2.531 0.994311 5 to 12 2491.01 -0.127 0.449414 6 to 13 2540.10 0.567 0.714670 7 to 14 2550.53 0.715 0.762579 8 to 15 2434.91 -0.921 0.178654 9 to 16 2687.25 2.648 0.995954 10 to 17 2492.41 -0.107 0.457269 11 to 18 2443.85 -0.794 0.213577 12 to 19 2523.01 0.325 0.627574 13 to 20 2497.00 -0.042 0.483058 14 to 21 2510.84 0.153 0.560922 15 to 22 2458.26 -0.590 0.277511 16 to 23 2640.88 1.992 0.976830 17 to 24 2440.76 -0.838 0.201081 18 to 25 2413.13 -1.229 0.109618 19 to 26 2413.63 -1.222 0.110948 20 to 27 2533.76 0.477 0.683468 21 to 28 2587.85 1.242 0.892958 22 to 29 2442.45 -0.814 0.207854 23 to 30 2509.49 0.134 0.553376 24 to 31 2528.63 0.405 0.657231 25 to 32 2610.29 1.560 0.940585 CDPARK for dh-ranFile-2016-07-09_10:31: 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 3539 0.7306 0.767486 3548 1.1416 0.873180 3534 0.5023 0.692266 3548 1.1416 0.873180 3515 -0.3653 0.357445 3527 0.1826 0.572463 3532 0.4110 0.659449 3531 0.3653 0.642555 3559 1.6438 0.949895 3530 0.3196 0.625377 Square side=100, avg. no. parked=3536.30 sample std.=11.95 p-value of the KSTEST for those 10 p-values: 0.035339 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-09_10:31 0.5522,0.4416,0.8872,0.1819,0.1285,0.4832,0.8392,0.5779,0.5240,0.2845, The KS test for those 10 p-values: 0.829446 The 3DSPHERES test for dh-ranFile-2016-07-09_10:31 sample no r^3 equiv. uni. 1 0.731 0.024073 2 50.269 0.812813 3 25.588 0.573831 4 21.910 0.518248 5 8.515 0.247096 6 22.790 0.532178 7 19.022 0.469575 8 59.774 0.863641 9 36.379 0.702586 10 35.884 0.697642 11 1.720 0.055707 12 10.553 0.296545 13 151.595 0.993611 14 7.082 0.210284 15 20.260 0.491020 16 12.863 0.348680 17 4.105 0.127872 18 31.981 0.655624 19 16.666 0.426238 20 4.942 0.151883 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.857710 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-09_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 1.3 1.3 0.2 0.5 0.5 -0.9 0.6 1.0 0.3 -0.0 -0.2 -0.3 -0.8 1.8 -1.5 0.1 1.8 0.5 -0.6 -1.7 -0.9 0.4 1.1 -0.5 -0.7 0.3 -0.2 -0.5 0.0 0.2 0.4 -0.5 -0.3 1.7 -0.7 1.0 -0.4 0.5 1.0 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:33.145886 z-score=-0.966063, p-value=0.166130 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-07-09_10:31 Test no p-value 1 0.700691 2 0.016412 3 0.786837 4 0.734513 5 0.987256 6 0.472804 7 0.069657 8 0.624250 9 0.634598 10 0.160802 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.677259 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-09_10:31: (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 66763 0.14 66559 0.17 3 25000.00 24969 0.04 25068 0.18 4 6666.67 6672 0.00 6741 0.83 5 1388.89 1317 3.72 1375 0.14 6 238.10 238 0.00 220 1.38 7 34.72 33 0.09 29 0.94 8 4.96 7 0.84 7 0.84 p=0.43385 p=0.38841 Number of rngs required: 688550, p-value: 0.567 RESULTS OF CRAPS TEST for dh-ranFile-2016-07-09_10:31 No. of wins: Observed Expected 98718 98585.9 z-score= 0.591, pvalue=0.72274 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66435 66666.7 0.805 0.805 2 37713 37654.3 0.091 0.896 3 27067 26954.7 0.468 1.364 4 19482 19313.5 1.471 2.835 5 13966 13851.4 0.948 3.783 6 9812 9943.5 1.740 5.523 7 7172 7145.0 0.102 5.625 8 5035 5139.1 2.108 7.732 9 3695 3699.9 0.006 7.739 10 2655 2666.3 0.048 7.786 11 1984 1923.3 1.914 9.700 12 1373 1388.7 0.178 9.879 13 991 1003.7 0.161 10.040 14 691 726.1 1.701 11.740 15 502 525.8 1.080 12.821 16 423 381.2 4.595 17.416 17 261 276.5 0.873 18.289 18 201 200.8 0.000 18.289 19 154 146.0 0.440 18.729 20 118 106.2 1.308 20.037 21 270 287.1 1.020 21.057 Chisq= 21.06 for 20 degrees of freedom, p= 0.60621 SUMMARY of craptest p-value for no. of wins: 0.722744 p-value for throws/game: 0.606213 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-09_10:31 No. of wins: Observed Expected 98193 98585.9 z-score=-1.757, pvalue=0.03945 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67051 66666.7 2.216 2.216 2 37605 37654.3 0.065 2.280 3 26701 26954.7 2.388 4.669 4 19271 19313.5 0.093 4.762 5 13813 13851.4 0.107 4.869 6 9923 9943.5 0.042 4.911 7 7038 7145.0 1.603 6.514 8 5151 5139.1 0.028 6.542 9 3697 3699.9 0.002 6.544 10 2705 2666.3 0.562 7.106 11 1955 1923.3 0.522 7.627 12 1379 1388.7 0.068 7.696 13 1039 1003.7 1.240 8.936 14 743 726.1 0.391 9.328 15 505 525.8 0.826 10.153 16 374 381.2 0.134 10.287 17 274 276.5 0.023 10.311 18 221 200.8 2.026 12.336 19 148 146.0 0.028 12.364 20 132 106.2 6.260 18.624 21 275 287.1 0.511 19.135 Chisq= 19.13 for 20 degrees of freedom, p= 0.48693 SUMMARY of craptest p-value for no. of wins: 0.039451 p-value for throws/game: 0.486927 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0043,0.0164,0.0241,0.0334,0.0348,0.0353,0.0355,0.0395,0.0406,0.0428, 0.0443,0.0445,0.0557,0.0562,0.0697,0.0742,0.0774,0.0780,0.0876,0.0925, 0.1019,0.1032,0.1065,0.1071,0.1073,0.1096,0.1109,0.1148,0.1212,0.1236, 0.1254,0.1269,0.1279,0.1284,0.1285,0.1399,0.1446,0.1519,0.1592,0.1608, 0.1625,0.1661,0.1727,0.1786,0.1787,0.1797,0.1815,0.1815,0.1816,0.1819, 0.1839,0.1842,0.1859,0.1969,0.2011,0.2027,0.2053,0.2076,0.2079,0.2103, 0.2132,0.2136,0.2229,0.2268,0.2320,0.2436,0.2436,0.2471,0.2494,0.2530, 0.2623,0.2630,0.2655,0.2752,0.2773,0.2775,0.2845,0.2922,0.2965,0.2969, 0.2969,0.2985,0.3032,0.3142,0.3160,0.3177,0.3208,0.3252,0.3393,0.3481, 0.3487,0.3492,0.3507,0.3574,0.3636,0.3642,0.3702,0.3715,0.3882,0.3884, 0.3905,0.3964,0.3968,0.3975,0.4098,0.4150,0.4232,0.4236,0.4237,0.4262, 0.4297,0.4338,0.4365,0.4382,0.4416,0.4488,0.4494,0.4573,0.4597,0.4651, 0.4671,0.4686,0.4696,0.4714,0.4716,0.4728,0.4733,0.4773,0.4826,0.4831, 0.4832,0.4834,0.4844,0.4866,0.4869,0.4874,0.4910,0.4996,0.5026,0.5182, 0.5189,0.5215,0.5240,0.5247,0.5308,0.5314,0.5322,0.5521,0.5522,0.5534, 0.5553,0.5590,0.5609,0.5612,0.5648,0.5672,0.5725,0.5738,0.5748,0.5761, 0.5779,0.5854,0.5961,0.6056,0.6062,0.6200,0.6242,0.6254,0.6276,0.6291, 0.6346,0.6369,0.6405,0.6426,0.6525,0.6541,0.6556,0.6572,0.6594,0.6627, 0.6662,0.6735,0.6773,0.6780,0.6789,0.6813,0.6835,0.6923,0.6976,0.6978, 0.6986,0.6989,0.7007,0.7011,0.7026,0.7026,0.7040,0.7088,0.7147,0.7154, 0.7162,0.7227,0.7345,0.7553,0.7626,0.7648,0.7675,0.7701,0.7702,0.7715, 0.7797,0.7868,0.7868,0.7911,0.7952,0.8051,0.8093,0.8128,0.8294,0.8329, 0.8392,0.8503,0.8507,0.8517,0.8525,0.8556,0.8564,0.8577,0.8622,0.8636, 0.8732,0.8732,0.8732,0.8752,0.8756,0.8807,0.8814,0.8862,0.8872,0.8930, 0.8931,0.9039,0.9080,0.9117,0.9140,0.9143,0.9303,0.9364,0.9392,0.9406, 0.9423,0.9434,0.9462,0.9478,0.9499,0.9528,0.9584,0.9629,0.9636,0.9768, 0.9842,0.9869,0.9873,0.9920,0.9936,0.9943,0.9955,0.9960,0.9968, Overall p-value after applying KStest on 269 p-values = 0.855933 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.