RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-16_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 15.63 36.8062 0.996425 2 to 25 15.67 22.2919 0.826248 3 to 26 15.48 27.0506 0.942670 4 to 27 15.79 17.7392 0.594530 5 to 28 15.98 15.8339 0.464362 6 to 29 15.83 17.3835 0.571309 7 to 30 16.06 9.0484 0.061270 8 to 31 15.77 20.6505 0.757684 9 to 32 16.08 21.0556 0.776188 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.108281 Tough bday spacings test for dh-ranFile-2015-11-16_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 12 41 73 99 110 65 44 34 9 7 6 (O-E)^2/E 0.9 0.5 0.0 0.0 1.6 2.2 1.3 0.6 2.3 0.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 10.315, p= 0.587 RESULTS OF GCD FOR dh-ranFile-2015-11-16_12:31 Euclid's algorithm: p-value, steps to gcd: 0.698924 p-value, dist. of gcd's: 0.493329 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-16_12:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.282 0.856 0.076 0.561 0.669 0.506 0.090 0.026 Bits 8 to 15---> 0.615 0.990 0.226 0.617 0.076 0.946 0.114 0.183 Bits 16 to 23---> 0.845 0.838 0.757 0.905 0.988 0.633 0.158 0.058 Bits 24 to 31---> 0.169 0.617 0.607 0.849 0.388 0.221 0.731 0.963 KS test for the above 32 p values: 0.555 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-16_12:31, p-values for 5 runs: 0.7247, 0.4885, 0.7302, 0.5506, 0.1219 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-16_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 205 211.4 0.195 0.195 r= 29 5081 5134.0 0.547 0.742 r= 30 23131 23103.0 0.034 0.776 r= 31 11583 11551.5 0.086 0.862 chi-square = 0.862 with df = 3; p-value = 0.165 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-16_12:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5205 5134.0 0.982 1.037 r= 31 22930 23103.0 1.296 2.333 r= 32 11657 11551.5 0.963 3.296 chi-square = 3.296 with df = 3; p-value = 0.652 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-16_12:31 b-rank test for bits 1 to 8, p=0.75282 b-rank test for bits 2 to 9, p=0.69762 b-rank test for bits 3 to 10, p=0.31732 b-rank test for bits 4 to 11, p=0.04668 b-rank test for bits 5 to 12, p=0.00215 b-rank test for bits 6 to 13, p=0.78827 b-rank test for bits 7 to 14, p=0.78477 b-rank test for bits 8 to 15, p=0.85466 b-rank test for bits 9 to 16, p=0.61203 b-rank test for bits 10 to 17, p=0.03694 b-rank test for bits 11 to 18, p=0.02494 b-rank test for bits 12 to 19, p=0.71584 b-rank test for bits 13 to 20, p=0.33134 b-rank test for bits 14 to 21, p=0.31034 b-rank test for bits 15 to 22, p=0.16586 b-rank test for bits 16 to 23, p=0.86558 b-rank test for bits 17 to 24, p=0.53036 b-rank test for bits 18 to 25, p=0.47266 b-rank test for bits 19 to 26, p=0.64405 b-rank test for bits 20 to 27, p=0.80656 b-rank test for bits 21 to 28, p=0.99195 b-rank test for bits 22 to 29, p=0.11204 b-rank test for bits 23 to 30, p=0.42173 b-rank test for bits 24 to 31, p=0.03679 b-rank test for bits 25 to 32, p=0.19710 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 = 0.342177 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-16_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 141728 -0.42 0.335904 2 141472 -1.02 0.153438 3 142094 0.43 0.666937 4 141718 -0.45 0.327426 5 140336 -3.68 0.000118 6 142274 0.85 0.802902 7 141906 -0.01 0.496896 8 141712 -0.46 0.322381 9 142065 0.36 0.641965 10 141503 -0.95 0.171216 11 141996 0.20 0.580237 12 141772 -0.32 0.374157 13 141666 -0.57 0.284838 14 141869 -0.09 0.462464 15 141466 -1.04 0.150144 16 142018 0.25 0.600214 17 142191 0.66 0.744765 18 141738 -0.40 0.344466 19 141534 -0.88 0.190260 20 142441 1.24 0.892922 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-16_12:31 Bits used No. missing words z-score p-value 23 to 32 142041 0.4540 0.675098 22 to 31 142125 0.7437 0.771468 21 to 30 141987 0.2678 0.605584 20 to 29 142068 0.5471 0.707858 19 to 28 142177 0.9230 0.821996 18 to 27 141982 0.2506 0.598933 17 to 26 141603 -1.0563 0.145413 16 to 25 141843 -0.2287 0.409542 15 to 24 142361 1.5575 0.940322 14 to 23 141879 -0.1046 0.458352 13 to 22 142358 1.5471 0.939085 12 to 21 141887 -0.0770 0.469312 11 to 20 141662 -0.8529 0.196868 10 to 19 142344 1.4989 0.933045 9 to 18 142104 0.6713 0.748978 8 to 17 141633 -0.9529 0.170330 7 to 16 142275 1.2609 0.896333 6 to 15 141874 -0.1218 0.451518 5 to 14 142160 0.8644 0.806310 4 to 13 142217 1.0609 0.855639 3 to 12 141346 -1.9425 0.026037 2 to 11 141717 -0.6632 0.253599 1 to 10 142073 0.5644 0.713752 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-16_12:31 Bits used No. missing words z-score p-value 28 to 32 141859 -0.1706 0.432265 27 to 31 141976 0.2260 0.589399 26 to 30 142033 0.4192 0.662473 25 to 29 141940 0.1040 0.541402 24 to 28 141028 -2.9876 0.001406 23 to 27 142346 1.4802 0.930595 22 to 26 141523 -1.3096 0.095167 21 to 25 141901 -0.0282 0.488737 20 to 24 141436 -1.6045 0.054301 19 to 23 141846 -0.2147 0.415009 18 to 22 142019 0.3718 0.644965 17 to 21 142036 0.4294 0.666180 16 to 20 141688 -0.7503 0.226546 15 to 19 141986 0.2599 0.602529 14 to 18 141723 -0.6316 0.263815 13 to 17 141685 -0.7604 0.223496 12 to 16 141252 -2.2282 0.012932 11 to 15 141906 -0.0113 0.495497 10 to 14 141616 -0.9943 0.160029 9 to 13 141916 0.0226 0.509019 8 to 12 141852 -0.1943 0.422955 7 to 11 142746 2.8362 0.997717 6 to 10 142046 0.4633 0.678421 5 to 9 142125 0.7311 0.767636 4 to 8 142030 0.4091 0.658749 3 to 7 141783 -0.4282 0.334239 2 to 6 141697 -0.7198 0.235836 1 to 5 142308 1.3514 0.911720 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-16_12:31 Bits used No. missing words z-score p-value 31 to 32 141816 -0.2753 0.391539 30 to 31 142145 0.6952 0.756532 29 to 30 142052 0.4209 0.663070 28 to 29 141965 0.1642 0.565220 27 to 28 141908 -0.0039 0.498435 26 to 27 142017 0.3176 0.624610 25 to 26 141294 -1.8151 0.034752 24 to 25 141522 -1.1426 0.126609 23 to 24 142307 1.1731 0.879616 22 to 23 141570 -1.0010 0.158420 21 to 22 142094 0.5447 0.707037 20 to 21 142329 1.2380 0.892135 19 to 20 142041 0.3884 0.651143 18 to 19 141977 0.1996 0.579110 17 to 18 141900 -0.0275 0.489022 16 to 17 142384 1.4002 0.919274 15 to 16 142339 1.2675 0.897505 14 to 15 141663 -0.7266 0.233724 13 to 14 142499 1.7394 0.959021 12 to 13 142271 1.0669 0.856985 11 to 12 141454 -1.3432 0.089611 10 to 11 142091 0.5359 0.703986 9 to 10 141767 -0.4199 0.337297 8 to 9 141548 -1.0659 0.143241 7 to 8 141911 0.0049 0.501965 6 to 7 141441 -1.3815 0.083562 5 to 6 142177 0.7896 0.785116 4 to 5 141409 -1.4759 0.069985 3 to 4 141607 -0.8918 0.186242 2 to 3 142018 0.3206 0.625728 1 to 2 140918 -2.9243 0.001726 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-16_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2578.58 1.111 0.866777 Test results for specific bytes for dh-ranFile-2015-11-16_12:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2440.68 -0.839 0.200766 2 to 9 2456.62 -0.614 0.269759 3 to 10 2499.28 -0.010 0.495938 4 to 11 2416.37 -1.183 0.118475 5 to 12 2343.17 -2.218 0.013281 6 to 13 2477.46 -0.319 0.374963 7 to 14 2521.55 0.305 0.619747 8 to 15 2506.08 0.086 0.534255 9 to 16 2467.62 -0.458 0.323492 10 to 17 2530.95 0.438 0.669208 11 to 18 2507.13 0.101 0.540136 12 to 19 2360.13 -1.978 0.023964 13 to 20 2494.13 -0.083 0.466920 14 to 21 2499.14 -0.012 0.495154 15 to 22 2390.41 -1.550 0.060595 16 to 23 2499.92 -0.001 0.499567 17 to 24 2448.60 -0.727 0.233630 18 to 25 2430.49 -0.983 0.162810 19 to 26 2424.40 -1.069 0.142489 20 to 27 2541.86 0.592 0.723065 21 to 28 2528.75 0.407 0.657851 22 to 29 2576.34 1.080 0.859827 23 to 30 2526.32 0.372 0.645131 24 to 31 2534.91 0.494 0.689231 25 to 32 2646.47 2.071 0.980840 CDPARK for dh-ranFile-2015-11-16_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 3522 -0.0457 0.481790 3549 1.1872 0.882429 3499 -1.0959 0.136563 3462 -2.7854 0.002673 3523 0.0000 0.500000 3555 1.4612 0.928018 3538 0.6849 0.753306 3542 0.8676 0.807188 3534 0.5023 0.692266 3531 0.3653 0.642555 Square side=100, avg. no. parked=3525.50 sample std.=25.90 p-value of the KSTEST for those 10 p-values: 0.396619 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-16_12:31 0.9457,0.7844,0.4513,0.2040,0.6564,0.0782,0.4071,0.2686,0.8596,0.4802, The KS test for those 10 p-values: 0.998480 The 3DSPHERES test for dh-ranFile-2015-11-16_12:31 sample no r^3 equiv. uni. 1 41.559 0.749755 2 21.518 0.511918 3 29.736 0.628871 4 94.125 0.956609 5 3.186 0.100752 6 28.976 0.619350 7 9.850 0.279881 8 51.677 0.821394 9 48.129 0.798967 10 73.751 0.914426 11 19.905 0.484954 12 1.426 0.046420 13 6.438 0.193127 14 37.203 0.710648 15 6.203 0.186791 16 0.688 0.022681 17 19.911 0.485062 18 185.193 0.997915 19 2.636 0.084104 20 12.363 0.337746 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.898647 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-16_12:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.1 0.6 0.4 -0.6 1.2 0.3 0.8 0.4 0.7 0.2 0.1 0.3 -0.8 1.2 -0.1 0.6 -2.0 1.0 -0.9 -0.2 0.5 -0.6 -0.3 -0.9 1.1 -0.3 0.9 -0.7 -0.9 -0.3 -1.0 -0.5 -0.4 -0.3 1.0 -0.7 0.5 -1.8 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:26.429955 z-score=-1.698831, p-value=0.029032 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-16_12:31 Test no p-value 1 0.120281 2 0.034692 3 0.323324 4 0.153770 5 0.788420 6 0.860864 7 0.318483 8 0.108766 9 0.064420 10 0.292805 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.034676 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-16_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 66517 0.34 66620 0.03 3 25000.00 25126 0.64 25116 0.54 4 6666.67 6636 0.14 6648 0.05 5 1388.89 1412 0.38 1324 3.03 6 238.10 259 1.84 246 0.26 7 34.72 39 0.53 35 0.00 8 4.96 10 5.12 10 5.12 p=0.82535 p=0.82871 Number of rngs required: 688320, p-value: 0.462 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-16_12:31 No. of wins: Observed Expected 98430 98585.9 z-score=-0.697, pvalue=0.24287 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66442 66666.7 0.757 0.757 2 37759 37654.3 0.291 1.048 3 26643 26954.7 3.605 4.653 4 19481 19313.5 1.453 6.107 5 14150 13851.4 6.436 12.543 6 10115 9943.5 2.956 15.499 7 7066 7145.0 0.874 16.373 8 5015 5139.1 2.995 19.369 9 3741 3699.9 0.457 19.826 10 2596 2666.3 1.853 21.680 11 1939 1923.3 0.128 21.807 12 1350 1388.7 1.081 22.888 13 1022 1003.7 0.333 23.221 14 723 726.1 0.014 23.235 15 554 525.8 1.508 24.743 16 378 381.2 0.026 24.769 17 269 276.5 0.206 24.975 18 205 200.8 0.087 25.061 19 148 146.0 0.028 25.089 20 105 106.2 0.014 25.103 21 299 287.1 0.492 25.595 Chisq= 25.60 for 20 degrees of freedom, p= 0.82039 SUMMARY of craptest p-value for no. of wins: 0.242873 p-value for throws/game: 0.820394 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-16_12:31 No. of wins: Observed Expected 98381 98585.9 z-score=-0.916, pvalue=0.17977 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66485 66666.7 0.495 0.495 2 37671 37654.3 0.007 0.502 3 26906 26954.7 0.088 0.591 4 19547 19313.5 2.824 3.414 5 13909 13851.4 0.239 3.654 6 9779 9943.5 2.723 6.377 7 7165 7145.0 0.056 6.432 8 5089 5139.1 0.488 6.920 9 3747 3699.9 0.600 7.521 10 2711 2666.3 0.749 8.270 11 1891 1923.3 0.543 8.814 12 1450 1388.7 2.702 11.516 13 993 1003.7 0.114 11.630 14 720 726.1 0.052 11.682 15 535 525.8 0.160 11.842 16 387 381.2 0.090 11.932 17 276 276.5 0.001 11.933 18 193 200.8 0.305 12.238 19 133 146.0 1.155 13.393 20 119 106.2 1.539 14.932 21 294 287.1 0.165 15.097 Chisq= 15.10 for 20 degrees of freedom, p= 0.22917 SUMMARY of craptest p-value for no. of wins: 0.179769 p-value for throws/game: 0.229170 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0014,0.0017,0.0021,0.0027,0.0129,0.0133,0.0227,0.0240,0.0249, 0.0260,0.0261,0.0290,0.0347,0.0347,0.0348,0.0368,0.0369,0.0464,0.0467, 0.0543,0.0583,0.0606,0.0613,0.0644,0.0700,0.0760,0.0763,0.0782,0.0836, 0.0841,0.0896,0.0903,0.0952,0.1008,0.1083,0.1088,0.1120,0.1140,0.1185, 0.1203,0.1219,0.1266,0.1366,0.1425,0.1432,0.1454,0.1501,0.1534,0.1538, 0.1582,0.1584,0.1600,0.1628,0.1654,0.1659,0.1690,0.1703,0.1712,0.1798, 0.1832,0.1862,0.1868,0.1903,0.1931,0.1969,0.1971,0.2008,0.2040,0.2209, 0.2235,0.2262,0.2265,0.2292,0.2336,0.2337,0.2358,0.2429,0.2536,0.2638, 0.2686,0.2698,0.2799,0.2820,0.2848,0.2928,0.3103,0.3173,0.3185,0.3224, 0.3233,0.3235,0.3274,0.3313,0.3342,0.3359,0.3373,0.3377,0.3422,0.3445, 0.3742,0.3750,0.3883,0.3915,0.3966,0.4071,0.4095,0.4150,0.4217,0.4230, 0.4323,0.4513,0.4515,0.4584,0.4620,0.4625,0.4644,0.4669,0.4693,0.4727, 0.4802,0.4818,0.4850,0.4851,0.4885,0.4887,0.4890,0.4933,0.4952,0.4955, 0.4959,0.4969,0.4984,0.4996,0.5000,0.5020,0.5064,0.5090,0.5119,0.5304, 0.5343,0.5401,0.5414,0.5506,0.5550,0.5606,0.5652,0.5713,0.5791,0.5802, 0.5867,0.5894,0.5945,0.5989,0.6002,0.6025,0.6056,0.6066,0.6120,0.6151, 0.6175,0.6175,0.6194,0.6197,0.6246,0.6257,0.6289,0.6325,0.6420,0.6426, 0.6440,0.6450,0.6451,0.6511,0.6518,0.6564,0.6579,0.6587,0.6625,0.6631, 0.6662,0.6669,0.6692,0.6692,0.6751,0.6784,0.6892,0.6923,0.6976,0.6989, 0.7040,0.7070,0.7079,0.7106,0.7138,0.7158,0.7231,0.7247,0.7302,0.7307, 0.7448,0.7490,0.7498,0.7528,0.7533,0.7565,0.7565,0.7577,0.7676,0.7715, 0.7762,0.7844,0.7848,0.7851,0.7883,0.7884,0.7990,0.8029,0.8063,0.8066, 0.8072,0.8204,0.8214,0.8220,0.8254,0.8262,0.8287,0.8382,0.8451,0.8491, 0.8547,0.8556,0.8561,0.8570,0.8596,0.8598,0.8609,0.8656,0.8668,0.8796, 0.8824,0.8921,0.8929,0.8963,0.8975,0.8986,0.9048,0.9117,0.9144,0.9193, 0.9280,0.9306,0.9330,0.9391,0.9403,0.9427,0.9457,0.9460,0.9566,0.9590, 0.9633,0.9808,0.9880,0.9899,0.9919,0.9964,0.9977,0.9979,0.9985, Overall p-value after applying KStest on 269 p-values = 0.329281 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.