RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-15_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.48 32.6221 0.987419 2 to 25 15.85 19.0336 0.673394 3 to 26 15.84 16.2438 0.493380 4 to 27 15.59 36.2666 0.995775 5 to 28 15.59 14.1371 0.342628 6 to 29 15.77 19.5851 0.704003 7 to 30 15.68 11.1347 0.150526 8 to 31 15.63 20.8000 0.764637 9 to 32 15.92 15.3608 0.430486 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.198479 Tough bday spacings test for dh-ranFile-2015-10-15_14:31: 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 35 86 87 109 71 57 28 12 4 5 (O-E)^2/E 1.1 0.1 2.2 1.2 1.3 0.7 0.5 0.1 0.6 1.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.883, p= 0.457 RESULTS OF GCD FOR dh-ranFile-2015-10-15_14:31 Euclid's algorithm: p-value, steps to gcd: 0.859294 p-value, dist. of gcd's: 0.764283 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-15_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.252 0.578 0.729 0.300 0.441 0.924 0.153 0.617 Bits 8 to 15---> 0.912 0.815 0.836 0.077 0.592 0.142 0.509 0.328 Bits 16 to 23---> 0.302 0.613 0.512 0.730 0.224 0.417 0.308 0.724 Bits 24 to 31---> 0.631 0.032 0.798 0.513 0.502 0.558 0.141 0.697 KS test for the above 32 p values: 0.350 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-15_14:31, p-values for 5 runs: 0.2507, 0.9764, 0.6791, 0.7086, 0.2370 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-15_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5156 5134.0 0.094 0.106 r= 30 23179 23103.0 0.250 0.356 r= 31 11452 11551.5 0.857 1.213 chi-square = 1.213 with df = 3; p-value = 0.250 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-15_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 203 211.4 0.335 0.335 r= 30 5237 5134.0 2.066 2.401 r= 31 22792 23103.0 4.188 6.589 r= 32 11768 11551.5 4.057 10.646 chi-square = 10.646 with df = 3; p-value = 0.986 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-15_14:31 b-rank test for bits 1 to 8, p=0.10601 b-rank test for bits 2 to 9, p=0.12670 b-rank test for bits 3 to 10, p=0.60848 b-rank test for bits 4 to 11, p=0.03782 b-rank test for bits 5 to 12, p=0.74618 b-rank test for bits 6 to 13, p=0.03775 b-rank test for bits 7 to 14, p=0.86394 b-rank test for bits 8 to 15, p=0.09729 b-rank test for bits 9 to 16, p=0.46913 b-rank test for bits 10 to 17, p=0.82800 b-rank test for bits 11 to 18, p=0.71690 b-rank test for bits 12 to 19, p=0.56510 b-rank test for bits 13 to 20, p=0.98590 b-rank test for bits 14 to 21, p=0.71281 b-rank test for bits 15 to 22, p=0.01547 b-rank test for bits 16 to 23, p=0.30360 b-rank test for bits 17 to 24, p=0.93330 b-rank test for bits 18 to 25, p=0.99453 b-rank test for bits 19 to 26, p=0.95646 b-rank test for bits 20 to 27, p=0.30195 b-rank test for bits 21 to 28, p=0.78424 b-rank test for bits 22 to 29, p=0.31371 b-rank test for bits 23 to 30, p=0.13441 b-rank test for bits 24 to 31, p=0.01746 b-rank test for bits 25 to 32, p=0.84124 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 = 0.182323 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-15_14:31 (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 141577 -0.78 0.218735 2 141767 -0.33 0.369738 3 141827 -0.19 0.423730 4 142432 1.22 0.888993 5 142096 0.44 0.668634 6 141653 -0.60 0.274619 7 141677 -0.54 0.293624 8 141516 -0.92 0.179049 9 141293 -1.44 0.074930 10 141227 -1.59 0.055442 11 141478 -1.01 0.156780 12 142533 1.46 0.927466 13 141413 -1.16 0.123096 14 141672 -0.55 0.289615 15 141789 -0.28 0.389300 16 141956 0.11 0.543415 17 142013 0.24 0.595695 18 141543 -0.86 0.196023 19 142039 0.30 0.619043 20 141620 -0.68 0.249519 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-15_14:31 Bits used No. missing words z-score p-value 23 to 32 142445 1.8471 0.967636 22 to 31 142665 2.6058 0.995416 21 to 30 142448 1.8575 0.968379 20 to 29 142521 2.1092 0.982537 19 to 28 141463 -1.5391 0.061894 18 to 27 142167 0.8885 0.812869 17 to 26 141899 -0.0356 0.485792 16 to 25 141857 -0.1804 0.428400 15 to 24 141930 0.0713 0.528411 14 to 23 141983 0.2540 0.600266 13 to 22 142374 1.6023 0.945457 12 to 21 142147 0.8196 0.793764 11 to 20 141667 -0.8356 0.201684 10 to 19 141880 -0.1011 0.459721 9 to 18 142021 0.3851 0.649907 8 to 17 142212 1.0437 0.851686 7 to 16 142071 0.5575 0.711401 6 to 15 141563 -1.1942 0.116192 5 to 14 141935 0.0885 0.535267 4 to 13 141894 -0.0529 0.478921 3 to 12 141746 -0.5632 0.286647 2 to 11 142037 0.4402 0.670119 1 to 10 141293 -2.1253 0.016782 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-15_14:31 Bits used No. missing words z-score p-value 28 to 32 141602 -1.0418 0.148753 27 to 31 141970 0.2057 0.581472 26 to 30 141719 -0.6452 0.259403 25 to 29 142343 1.4701 0.929228 24 to 28 141834 -0.2554 0.399224 23 to 27 142147 0.8057 0.789781 22 to 26 141714 -0.6621 0.253942 21 to 25 141700 -0.7096 0.238978 20 to 24 142288 1.2836 0.900364 19 to 23 141691 -0.7401 0.229619 18 to 22 142070 0.5446 0.707001 17 to 21 141630 -0.9469 0.171850 16 to 20 142166 0.8701 0.807868 15 to 19 142130 0.7480 0.772780 14 to 18 141877 -0.1096 0.456366 13 to 17 141263 -2.1909 0.014228 12 to 16 141530 -1.2859 0.099245 11 to 15 141632 -0.9401 0.173583 10 to 14 141757 -0.5164 0.302797 9 to 13 142397 1.6531 0.950847 8 to 12 141877 -0.1096 0.456366 7 to 11 142604 2.3548 0.990734 6 to 10 141581 -1.1130 0.132858 5 to 9 142185 0.9345 0.824970 4 to 8 141509 -1.3571 0.087383 3 to 7 141503 -1.3774 0.084196 2 to 6 142388 1.6226 0.947664 1 to 5 142065 0.5277 0.701145 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-15_14:31 Bits used No. missing words z-score p-value 31 to 32 141470 -1.2960 0.097495 30 to 31 141380 -1.5614 0.059209 29 to 30 141804 -0.3107 0.378011 28 to 29 141788 -0.3579 0.360207 27 to 28 142113 0.6008 0.726012 26 to 27 141428 -1.4199 0.077825 25 to 26 141606 -0.8948 0.185453 24 to 25 141815 -0.2783 0.390407 23 to 24 141897 -0.0364 0.485493 22 to 23 141830 -0.2340 0.407488 21 to 22 141979 0.2055 0.581416 20 to 21 141138 -2.2753 0.011444 19 to 20 141424 -1.4317 0.076122 18 to 19 142184 0.8102 0.791098 17 to 18 142018 0.3206 0.625728 16 to 17 141428 -1.4199 0.077825 15 to 16 141516 -1.1603 0.122970 14 to 15 142222 0.9223 0.821822 13 to 14 141764 -0.4287 0.334070 12 to 13 142082 0.5094 0.694747 11 to 12 141724 -0.5467 0.292294 10 to 11 142232 0.9518 0.829408 9 to 10 142230 0.9459 0.827908 8 to 9 141959 0.1465 0.558244 7 to 8 141586 -0.9538 0.170099 6 to 7 142276 1.0816 0.860290 5 to 6 142194 0.8397 0.799471 4 to 5 142075 0.4887 0.687474 3 to 4 141826 -0.2458 0.402914 2 to 3 142031 0.3589 0.640168 1 to 2 142705 2.3471 0.990540 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-15_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2575.05 1.061 0.855737 Test results for specific bytes for dh-ranFile-2015-10-15_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2553.15 0.752 0.773872 2 to 9 2451.39 -0.687 0.245895 3 to 10 2392.26 -1.524 0.063792 4 to 11 2490.94 -0.128 0.449045 5 to 12 2378.34 -1.721 0.042664 6 to 13 2467.07 -0.466 0.320739 7 to 14 2453.98 -0.651 0.257566 8 to 15 2569.85 0.988 0.838398 9 to 16 2639.74 1.976 0.975933 10 to 17 2490.65 -0.132 0.447397 11 to 18 2502.47 0.035 0.513951 12 to 19 2500.72 0.010 0.504068 13 to 20 2583.42 1.180 0.880940 14 to 21 2451.53 -0.685 0.246525 15 to 22 2387.35 -1.593 0.055566 16 to 23 2634.72 1.905 0.971628 17 to 24 2413.90 -1.218 0.111693 18 to 25 2429.57 -0.996 0.159609 19 to 26 2623.18 1.742 0.959246 20 to 27 2501.87 0.026 0.510527 21 to 28 2479.01 -0.297 0.383307 22 to 29 2555.89 0.790 0.785348 23 to 30 2539.11 0.553 0.709893 24 to 31 2582.83 1.171 0.879266 25 to 32 2613.38 1.603 0.945587 CDPARK for dh-ranFile-2015-10-15_14:31: 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 3520 -0.1370 0.445521 3486 -1.6895 0.045562 3511 -0.5479 0.291865 3512 -0.5023 0.307734 3524 0.0457 0.518210 3542 0.8676 0.807188 3509 -0.6393 0.261324 3544 0.9589 0.831196 3518 -0.2283 0.409702 3518 -0.2283 0.409702 Square side=100, avg. no. parked=3518.40 sample std.=15.75 p-value of the KSTEST for those 10 p-values: 0.486329 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-15_14:31 0.0760,0.8321,0.6203,0.4520,0.8207,0.8326,0.1394,0.8931,0.9146,0.5995, The KS test for those 10 p-values: 0.233713 The 3DSPHERES test for dh-ranFile-2015-10-15_14:31 sample no r^3 equiv. uni. 1 13.970 0.372281 2 3.125 0.098939 3 7.325 0.216644 4 9.491 0.271201 5 16.081 0.414926 6 30.129 0.633697 7 90.703 0.951366 8 13.149 0.354860 9 15.713 0.407710 10 26.013 0.579825 11 30.424 0.637280 12 66.929 0.892575 13 43.347 0.764233 14 14.061 0.374184 15 36.812 0.706847 16 38.336 0.721371 17 48.160 0.799174 18 31.337 0.648159 19 40.232 0.738432 20 34.806 0.686581 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.293106 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-15_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 -1.3 0.5 -0.3 0.7 2.0 1.0 0.1 0.1 0.6 -0.9 -1.1 0.7 0.1 0.2 1.4 0.3 0.3 0.0 0.4 -0.5 0.2 -1.6 -1.1 -0.8 1.5 -1.2 0.0 -1.5 -2.2 0.8 0.3 -0.1 -1.3 -1.0 -1.6 -1.7 -0.8 1.5 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:42.557771 z-score=0.060858, p-value=0.553034 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-15_14:31 Test no p-value 1 0.003090 2 0.929911 3 0.420667 4 0.029009 5 0.324973 6 0.000130 7 0.675845 8 0.212793 9 0.046770 10 0.147239 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002341 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-15_14:31: (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 66755 0.12 66565 0.16 3 25000.00 24961 0.06 25058 0.13 4 6666.67 6662 0.00 6680 0.03 5 1388.89 1366 0.38 1418 0.61 6 238.10 214 2.44 236 0.02 7 34.72 32 0.21 39 0.53 8 4.96 9 3.29 3 0.77 p=0.63049 p=0.10436 Number of rngs required: 688111, p-value: 0.368 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-15_14:31 No. of wins: Observed Expected 98314 98585.9 z-score=-1.216, pvalue=0.11201 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66178 66666.7 3.582 3.582 2 37888 37654.3 1.450 5.032 3 26956 26954.7 0.000 5.032 4 19361 19313.5 0.117 5.149 5 13694 13851.4 1.789 6.938 6 9957 9943.5 0.018 6.956 7 7076 7145.0 0.667 7.623 8 5243 5139.1 2.102 9.725 9 3819 3699.9 3.836 13.561 10 2671 2666.3 0.008 13.569 11 1996 1923.3 2.746 16.315 12 1370 1388.7 0.253 16.568 13 982 1003.7 0.470 17.038 14 770 726.1 2.649 19.687 15 552 525.8 1.302 20.989 16 419 381.2 3.759 24.747 17 286 276.5 0.324 25.071 18 224 200.8 2.673 27.744 19 149 146.0 0.062 27.807 20 104 106.2 0.046 27.853 21 305 287.1 1.114 28.967 Chisq= 28.97 for 20 degrees of freedom, p= 0.91159 SUMMARY of craptest p-value for no. of wins: 0.112010 p-value for throws/game: 0.911589 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-15_14:31 No. of wins: Observed Expected 98260 98585.9 z-score=-1.457, pvalue=0.07250 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66690 66666.7 0.008 0.008 2 37662 37654.3 0.002 0.010 3 27008 26954.7 0.105 0.115 4 19193 19313.5 0.751 0.866 5 13945 13851.4 0.632 1.499 6 10031 9943.5 0.769 2.268 7 7165 7145.0 0.056 2.324 8 5081 5139.1 0.656 2.980 9 3646 3699.9 0.784 3.764 10 2713 2666.3 0.818 4.582 11 1821 1923.3 5.444 10.026 12 1407 1388.7 0.240 10.267 13 973 1003.7 0.940 11.206 14 729 726.1 0.011 11.218 15 534 525.8 0.127 11.344 16 372 381.2 0.220 11.564 17 302 276.5 2.344 13.908 18 193 200.8 0.305 14.214 19 151 146.0 0.172 14.386 20 83 106.2 5.074 19.460 21 301 287.1 0.672 20.132 Chisq= 20.13 for 20 degrees of freedom, p= 0.55027 SUMMARY of craptest p-value for no. of wins: 0.072499 p-value for throws/game: 0.550270 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0023,0.0031,0.0114,0.0142,0.0155,0.0168,0.0175,0.0290,0.0318, 0.0378,0.0378,0.0427,0.0456,0.0468,0.0554,0.0556,0.0592,0.0619,0.0638, 0.0725,0.0749,0.0760,0.0761,0.0771,0.0778,0.0778,0.0842,0.0874,0.0973, 0.0975,0.0989,0.0992,0.1044,0.1060,0.1117,0.1120,0.1162,0.1230,0.1231, 0.1267,0.1329,0.1344,0.1394,0.1411,0.1425,0.1472,0.1488,0.1505,0.1534, 0.1568,0.1596,0.1701,0.1718,0.1736,0.1790,0.1823,0.1855,0.1960,0.1985, 0.2017,0.2128,0.2166,0.2187,0.2237,0.2296,0.2337,0.2370,0.2390,0.2459, 0.2465,0.2495,0.2502,0.2507,0.2523,0.2539,0.2576,0.2594,0.2613,0.2712, 0.2746,0.2866,0.2896,0.2919,0.2923,0.2931,0.2936,0.3000,0.3019,0.3022, 0.3028,0.3036,0.3077,0.3081,0.3137,0.3207,0.3250,0.3275,0.3341,0.3426, 0.3499,0.3549,0.3602,0.3684,0.3697,0.3723,0.3742,0.3780,0.3833,0.3893, 0.3904,0.3992,0.4029,0.4075,0.4077,0.4097,0.4097,0.4149,0.4165,0.4207, 0.4237,0.4284,0.4305,0.4413,0.4455,0.4474,0.4490,0.4520,0.4564,0.4564, 0.4568,0.4597,0.4691,0.4789,0.4855,0.4858,0.4863,0.4934,0.5019,0.5041, 0.5092,0.5105,0.5116,0.5132,0.5140,0.5182,0.5284,0.5353,0.5434,0.5503, 0.5530,0.5580,0.5582,0.5651,0.5776,0.5798,0.5814,0.5815,0.5915,0.5957, 0.5995,0.6003,0.6085,0.6130,0.6172,0.6190,0.6203,0.6257,0.6305,0.6314, 0.6337,0.6373,0.6402,0.6482,0.6499,0.6686,0.6701,0.6734,0.6758,0.6791, 0.6866,0.6875,0.6947,0.6974,0.7011,0.7040,0.7068,0.7070,0.7086,0.7099, 0.7114,0.7128,0.7169,0.7214,0.7243,0.7260,0.7292,0.7304,0.7384,0.7462, 0.7642,0.7643,0.7646,0.7728,0.7739,0.7842,0.7853,0.7898,0.7911,0.7938, 0.7976,0.7992,0.7995,0.8072,0.8079,0.8129,0.8150,0.8207,0.8218,0.8250, 0.8279,0.8280,0.8294,0.8312,0.8321,0.8326,0.8363,0.8384,0.8412,0.8517, 0.8557,0.8593,0.8603,0.8639,0.8793,0.8809,0.8890,0.8926,0.8931,0.9004, 0.9116,0.9116,0.9146,0.9236,0.9275,0.9292,0.9299,0.9333,0.9455,0.9456, 0.9477,0.9508,0.9514,0.9565,0.9592,0.9676,0.9684,0.9716,0.9759,0.9764, 0.9825,0.9859,0.9862,0.9874,0.9905,0.9907,0.9945,0.9954,0.9958, Overall p-value after applying KStest on 269 p-values = 0.649618 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.