RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-28_16:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.85 7.7661 0.028704 2 to 25 16.00 25.4710 0.915347 3 to 26 15.77 14.5729 0.373783 4 to 27 15.89 21.8479 0.809361 5 to 28 15.93 6.1594 0.007951 6 to 29 15.69 15.9237 0.470752 7 to 30 15.63 27.3073 0.946288 8 to 31 15.96 18.3390 0.632235 9 to 32 15.89 9.5462 0.078444 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.353029 Tough bday spacings test for dh-ranFile-2016-03-28_16:31: 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 46 83 100 93 76 51 29 9 5 2 (O-E)^2/E 1.1 2.4 1.3 0.1 0.2 0.1 0.0 0.0 2.3 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 8.932, p= 0.461 RESULTS OF GCD FOR dh-ranFile-2016-03-28_16:31 Euclid's algorithm: p-value, steps to gcd: 0.697735 p-value, dist. of gcd's: 0.271402 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-28_16:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.921 0.398 0.995 0.732 0.051 0.444 0.821 0.605 Bits 8 to 15---> 0.905 0.079 0.076 0.554 0.419 0.953 0.288 0.004 Bits 16 to 23---> 0.309 0.770 0.993 0.784 0.762 0.239 0.904 0.127 Bits 24 to 31---> 0.909 0.297 0.708 0.771 0.683 0.572 0.064 0.185 KS test for the above 32 p values: 0.638 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-28_16:31, p-values for 5 runs: 0.6042, 0.4667, 0.3860, 0.4137, 0.2744 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-28_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5260 5134.0 3.092 3.841 r= 30 23129 23103.0 0.029 3.870 r= 31 11387 11551.5 2.343 6.213 chi-square = 6.213 with df = 3; p-value = 0.898 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-28_16:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 228 211.4 1.301 1.301 r= 30 5176 5134.0 0.343 1.644 r= 31 23239 23103.0 0.800 2.444 r= 32 11357 11551.5 3.276 5.720 chi-square = 5.720 with df = 3; p-value = 0.874 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-28_16:31 b-rank test for bits 1 to 8, p=0.28999 b-rank test for bits 2 to 9, p=0.83397 b-rank test for bits 3 to 10, p=0.69410 b-rank test for bits 4 to 11, p=0.68055 b-rank test for bits 5 to 12, p=0.31916 b-rank test for bits 6 to 13, p=0.07926 b-rank test for bits 7 to 14, p=0.53519 b-rank test for bits 8 to 15, p=0.63648 b-rank test for bits 9 to 16, p=0.99273 b-rank test for bits 10 to 17, p=0.88970 b-rank test for bits 11 to 18, p=0.55314 b-rank test for bits 12 to 19, p=0.65736 b-rank test for bits 13 to 20, p=0.51524 b-rank test for bits 14 to 21, p=0.64024 b-rank test for bits 15 to 22, p=0.57739 b-rank test for bits 16 to 23, p=0.06475 b-rank test for bits 17 to 24, p=0.79217 b-rank test for bits 18 to 25, p=0.07166 b-rank test for bits 19 to 26, p=0.11508 b-rank test for bits 20 to 27, p=0.37226 b-rank test for bits 21 to 28, p=0.39479 b-rank test for bits 22 to 29, p=0.78814 b-rank test for bits 23 to 30, p=0.14293 b-rank test for bits 24 to 31, p=0.97095 b-rank test for bits 25 to 32, p=0.07907 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 = 0.870513 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-28_16:31 (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 142255 0.81 0.790351 2 141644 -0.62 0.267652 3 141801 -0.25 0.400093 4 141116 -1.85 0.031900 5 141351 -1.30 0.096030 6 141268 -1.50 0.067010 7 141536 -0.87 0.191532 8 142251 0.80 0.787650 9 141994 0.20 0.578410 10 142764 2.00 0.977082 11 142647 1.72 0.957603 12 141467 -1.03 0.150689 13 142269 0.84 0.799644 14 141984 0.17 0.569249 15 142030 0.28 0.611005 16 142041 0.31 0.620822 17 142391 1.13 0.869790 18 142139 0.54 0.704232 19 142133 0.52 0.699371 20 141918 0.02 0.508081 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-28_16:31 Bits used No. missing words z-score p-value 23 to 32 141436 -1.6322 0.051322 22 to 31 141543 -1.2632 0.103257 21 to 30 141562 -1.1977 0.115519 20 to 29 141320 -2.0322 0.021068 19 to 28 141555 -1.2218 0.110886 18 to 27 142247 1.1644 0.877865 17 to 26 142013 0.3575 0.639635 16 to 25 142044 0.4644 0.678812 15 to 24 141712 -0.6804 0.248110 14 to 23 141907 -0.0080 0.496795 13 to 22 141526 -1.3218 0.093113 12 to 21 141848 -0.2115 0.416255 11 to 20 142135 0.7782 0.781766 10 to 19 141593 -1.0908 0.137682 9 to 18 141617 -1.0080 0.156719 8 to 17 142216 1.0575 0.854854 7 to 16 142273 1.2540 0.895085 6 to 15 142238 1.1333 0.871465 5 to 14 141985 0.2609 0.602927 4 to 13 141811 -0.3391 0.367279 3 to 12 142145 0.8127 0.791792 2 to 11 141820 -0.3080 0.379028 1 to 10 141530 -1.3080 0.095431 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-28_16:31 Bits used No. missing words z-score p-value 28 to 32 141927 0.0599 0.523882 27 to 31 141964 0.1853 0.573512 26 to 30 141873 -0.1232 0.450993 25 to 29 142079 0.5752 0.717406 24 to 28 141800 -0.3706 0.355464 23 to 27 142106 0.6667 0.747511 22 to 26 141736 -0.5876 0.278414 21 to 25 141640 -0.9130 0.180626 20 to 24 142015 0.3582 0.639905 19 to 23 142105 0.6633 0.746427 18 to 22 142261 1.1921 0.883389 17 to 21 141871 -0.1299 0.448310 16 to 20 142241 1.1243 0.869558 15 to 19 141504 -1.3740 0.084721 14 to 18 142317 1.3819 0.916504 13 to 17 141854 -0.1876 0.425611 12 to 16 142148 0.8091 0.790757 11 to 15 142245 1.1379 0.872411 10 to 14 141804 -0.3571 0.360527 9 to 13 142357 1.5175 0.935433 8 to 12 142474 1.9141 0.972199 7 to 11 142048 0.4701 0.680847 6 to 10 142201 0.9887 0.838598 5 to 9 141988 0.2667 0.605141 4 to 8 141974 0.2192 0.586761 3 to 7 141995 0.2904 0.614248 2 to 6 142392 1.6362 0.949098 1 to 5 141981 0.2429 0.595978 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-28_16:31 Bits used No. missing words z-score p-value 31 to 32 142234 0.9577 0.830900 30 to 31 141483 -1.2576 0.104266 29 to 30 142181 0.8014 0.788546 28 to 29 141722 -0.5526 0.290270 27 to 28 141451 -1.3520 0.088187 26 to 27 141806 -0.3048 0.380256 25 to 26 141489 -1.2399 0.107504 24 to 25 141634 -0.8122 0.208343 23 to 24 142052 0.4209 0.663070 22 to 23 142580 1.9784 0.976057 21 to 22 141880 -0.0865 0.465527 20 to 21 141721 -0.5555 0.289261 19 to 20 141955 0.1347 0.553583 18 to 19 141552 -1.0541 0.145925 17 to 18 142019 0.3235 0.626846 16 to 17 142201 0.8604 0.805211 15 to 16 141404 -1.4906 0.068027 14 to 15 142009 0.2940 0.615626 13 to 14 142029 0.3530 0.637959 12 to 13 141919 0.0285 0.511378 11 to 12 141715 -0.5732 0.283240 10 to 11 141665 -0.7207 0.235536 9 to 10 141224 -2.0216 0.021608 8 to 9 142203 0.8663 0.806833 7 to 8 141406 -1.4847 0.068805 6 to 7 141808 -0.2989 0.382505 5 to 6 141433 -1.4051 0.079995 4 to 5 141853 -0.1662 0.434014 3 to 4 141974 0.1908 0.575646 2 to 3 141612 -0.8771 0.190222 1 to 2 142235 0.9607 0.831643 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-28_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2459.74 -0.569 0.284572 Test results for specific bytes for dh-ranFile-2016-03-28_16:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2613.73 1.608 0.946123 2 to 9 2527.12 0.383 0.649314 3 to 10 2523.60 0.334 0.630738 4 to 11 2645.89 2.063 0.980456 5 to 12 2460.04 -0.565 0.286016 6 to 13 2476.37 -0.334 0.369103 7 to 14 2558.59 0.829 0.796349 8 to 15 2408.25 -1.298 0.097216 9 to 16 2571.47 1.011 0.843920 10 to 17 2615.35 1.631 0.948584 11 to 18 2518.76 0.265 0.604613 12 to 19 2542.84 0.606 0.727687 13 to 20 2602.20 1.445 0.925820 14 to 21 2531.35 0.443 0.671257 15 to 22 2439.60 -0.854 0.196504 16 to 23 2547.28 0.669 0.748145 17 to 24 2265.53 -3.316 0.000457 18 to 25 2325.45 -2.468 0.006784 19 to 26 2407.08 -1.314 0.094407 20 to 27 2377.73 -1.729 0.041887 21 to 28 2545.59 0.645 0.740447 22 to 29 2510.49 0.148 0.558963 23 to 30 2427.74 -1.022 0.153410 24 to 31 2526.18 0.370 0.644372 25 to 32 2549.35 0.698 0.757399 CDPARK for dh-ranFile-2016-03-28_16:31: 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 3510 -0.5936 0.276387 3485 -1.7352 0.041356 3534 0.5023 0.692266 3539 0.7306 0.767486 3510 -0.5936 0.276387 3536 0.5936 0.723613 3507 -0.7306 0.232514 3529 0.2740 0.607947 3561 1.7352 0.958644 3501 -1.0046 0.157553 Square side=100, avg. no. parked=3521.20 sample std.=21.25 p-value of the KSTEST for those 10 p-values: 0.928297 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-28_16:31 0.5095,0.9791,0.3410,0.5416,0.8066,0.4816,0.9756,0.6798,0.3828,0.9735, The KS test for those 10 p-values: 0.050491 The 3DSPHERES test for dh-ranFile-2016-03-28_16:31 sample no r^3 equiv. uni. 1 4.812 0.148199 2 1.809 0.058517 3 9.283 0.266132 4 125.864 0.984936 5 33.391 0.671442 6 18.988 0.468959 7 9.345 0.267661 8 25.381 0.570888 9 7.005 0.208242 10 5.436 0.165729 11 61.965 0.873243 12 26.244 0.583059 13 27.493 0.600053 14 5.282 0.161424 15 2.025 0.065263 16 30.149 0.633946 17 49.519 0.808070 18 85.822 0.942774 19 4.223 0.131319 20 9.031 0.259937 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.498878 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-28_16:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 2.7 1.5 0.0 0.4 -0.3 1.9 -0.9 -0.7 -0.1 -0.4 0.8 0.2 -0.2 0.5 -0.9 -0.3 0.0 0.5 -0.4 0.5 1.6 0.2 -0.9 -0.7 -0.2 -1.7 -0.6 0.4 0.7 0.8 -0.4 -0.4 0.2 -0.8 1.2 -1.0 -0.8 -0.1 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:33.432223 z-score=-0.934821, p-value=0.175387 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-28_16:31 Test no p-value 1 0.538791 2 0.347714 3 0.231345 4 0.309956 5 0.030148 6 0.166546 7 0.900815 8 0.525532 9 0.272827 10 0.190294 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.147377 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-28_16:31: (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 66654 0.00 66760 0.13 3 25000.00 25069 0.19 25002 0.00 4 6666.67 6609 0.50 6509 3.73 5 1388.89 1365 0.41 1408 0.26 6 238.10 265 3.04 277 6.36 7 34.72 35 0.00 38 0.31 8 4.96 2 1.77 5 0.00 p=0.56684 p=0.90491 Number of rngs required: 688102, p-value: 0.364 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-28_16:31 No. of wins: Observed Expected 98481 98585.9 z-score=-0.469, pvalue=0.31954 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66531 66666.7 0.276 0.276 2 37741 37654.3 0.200 0.476 3 26850 26954.7 0.407 0.883 4 19525 19313.5 2.317 3.199 5 13685 13851.4 1.999 5.199 6 10012 9943.5 0.471 5.670 7 7085 7145.0 0.504 6.175 8 5148 5139.1 0.016 6.190 9 3746 3699.9 0.575 6.765 10 2719 2666.3 1.042 7.807 11 1967 1923.3 0.992 8.799 12 1364 1388.7 0.441 9.239 13 971 1003.7 1.066 10.306 14 696 726.1 1.251 11.557 15 504 525.8 0.907 12.464 16 410 381.2 2.184 14.647 17 305 276.5 2.929 17.576 18 201 200.8 0.000 17.576 19 154 146.0 0.440 18.016 20 111 106.2 0.216 18.232 21 275 287.1 0.511 18.743 Chisq= 18.74 for 20 degrees of freedom, p= 0.46143 SUMMARY of craptest p-value for no. of wins: 0.319539 p-value for throws/game: 0.461427 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-28_16:31 No. of wins: Observed Expected 98598 98585.9 z-score= 0.054, pvalue=0.52165 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66282 66666.7 2.220 2.220 2 37542 37654.3 0.335 2.555 3 27271 26954.7 3.711 6.265 4 19302 19313.5 0.007 6.272 5 13993 13851.4 1.447 7.719 6 10056 9943.5 1.272 8.991 7 7184 7145.0 0.213 9.204 8 5106 5139.1 0.213 9.417 9 3569 3699.9 4.629 14.045 10 2640 2666.3 0.259 14.305 11 1856 1923.3 2.357 16.662 12 1421 1388.7 0.749 17.411 13 1062 1003.7 3.385 20.796 14 782 726.1 4.297 25.093 15 541 525.8 0.437 25.530 16 354 381.2 1.934 27.464 17 270 276.5 0.155 27.619 18 203 200.8 0.023 27.642 19 150 146.0 0.110 27.753 20 112 106.2 0.315 28.068 21 304 287.1 0.993 29.061 Chisq= 29.06 for 20 degrees of freedom, p= 0.91343 SUMMARY of craptest p-value for no. of wins: 0.521653 p-value for throws/game: 0.913429 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0005,0.0039,0.0068,0.0080,0.0211,0.0216,0.0287,0.0301,0.0319,0.0414, 0.0419,0.0505,0.0508,0.0513,0.0585,0.0635,0.0648,0.0653,0.0670,0.0680, 0.0688,0.0717,0.0761,0.0784,0.0788,0.0791,0.0793,0.0800,0.0847,0.0882, 0.0931,0.0944,0.0954,0.0960,0.0972,0.1033,0.1043,0.1075,0.1109,0.1151, 0.1155,0.1271,0.1313,0.1377,0.1429,0.1459,0.1474,0.1482,0.1507,0.1534, 0.1567,0.1576,0.1614,0.1657,0.1665,0.1754,0.1806,0.1851,0.1902,0.1903, 0.1915,0.1965,0.2082,0.2083,0.2313,0.2325,0.2355,0.2385,0.2481,0.2599, 0.2661,0.2677,0.2677,0.2714,0.2728,0.2744,0.2764,0.2764,0.2784,0.2832, 0.2846,0.2860,0.2880,0.2893,0.2900,0.2903,0.2967,0.3091,0.3100,0.3192, 0.3195,0.3410,0.3477,0.3530,0.3555,0.3605,0.3645,0.3673,0.3691,0.3723, 0.3738,0.3790,0.3803,0.3825,0.3828,0.3860,0.3948,0.3983,0.4001,0.4137, 0.4163,0.4190,0.4256,0.4340,0.4442,0.4483,0.4510,0.4614,0.4614,0.4655, 0.4667,0.4690,0.4708,0.4816,0.4968,0.4989,0.5081,0.5095,0.5114,0.5152, 0.5217,0.5239,0.5255,0.5352,0.5388,0.5416,0.5531,0.5536,0.5540,0.5590, 0.5668,0.5692,0.5709,0.5722,0.5735,0.5756,0.5774,0.5784,0.5831,0.5868, 0.5960,0.6001,0.6029,0.6042,0.6046,0.6051,0.6052,0.6079,0.6110,0.6142, 0.6156,0.6208,0.6268,0.6307,0.6322,0.6339,0.6365,0.6376,0.6380,0.6396, 0.6399,0.6402,0.6444,0.6493,0.6574,0.6631,0.6713,0.6714,0.6788,0.6798, 0.6805,0.6808,0.6831,0.6923,0.6941,0.6977,0.6994,0.7042,0.7085,0.7174, 0.7236,0.7277,0.7315,0.7404,0.7464,0.7475,0.7481,0.7574,0.7615,0.7675, 0.7703,0.7712,0.7818,0.7836,0.7877,0.7881,0.7885,0.7904,0.7908,0.7918, 0.7922,0.7963,0.7996,0.8052,0.8066,0.8068,0.8081,0.8094,0.8209,0.8309, 0.8316,0.8340,0.8386,0.8439,0.8549,0.8696,0.8698,0.8705,0.8715,0.8724, 0.8732,0.8739,0.8779,0.8834,0.8897,0.8951,0.8983,0.9008,0.9036,0.9049, 0.9052,0.9094,0.9134,0.9153,0.9165,0.9208,0.9258,0.9283,0.9354,0.9428, 0.9461,0.9463,0.9486,0.9491,0.9534,0.9576,0.9586,0.9710,0.9722,0.9735, 0.9756,0.9761,0.9771,0.9791,0.9805,0.9849,0.9927,0.9930,0.9947, Overall p-value after applying KStest on 269 p-values = 0.562550 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.