RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-14_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.82 10.7201 0.129263 2 to 25 15.55 14.7452 0.386171 3 to 26 15.68 20.7414 0.761927 4 to 27 15.93 19.1422 0.679568 5 to 28 16.08 12.5120 0.231810 6 to 29 16.03 17.7332 0.594143 7 to 30 15.80 13.9391 0.328593 8 to 31 15.71 27.5921 0.950064 9 to 32 15.61 18.7331 0.655937 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.961879 Tough bday spacings test for dh-ranFile-2016-04-14_08:31: 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 11 46 64 85 102 83 53 25 16 10 5 (O-E)^2/E 0.4 2.4 1.2 1.6 0.2 0.3 0.0 0.8 0.1 1.7 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.886, p= 0.457 RESULTS OF GCD FOR dh-ranFile-2016-04-14_08:31 Euclid's algorithm: p-value, steps to gcd: 0.573177 p-value, dist. of gcd's: 0.602751 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-14_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.669 0.635 0.487 0.802 0.891 0.426 0.823 0.930 Bits 8 to 15---> 0.032 0.614 0.006 0.607 0.008 0.039 0.456 0.039 Bits 16 to 23---> 0.631 0.353 0.403 0.265 0.347 0.233 0.753 0.411 Bits 24 to 31---> 0.913 0.161 0.949 0.191 0.339 0.906 0.543 0.962 KS test for the above 32 p values: 0.328 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-14_08:31, p-values for 5 runs: 0.1665, 0.7070, 0.0361, 0.2621, 0.5717 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-14_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 218 211.4 0.205 0.205 r= 29 5096 5134.0 0.281 0.486 r= 30 22893 23103.0 1.910 2.396 r= 31 11793 11551.5 5.048 7.444 chi-square = 7.444 with df = 3; p-value = 0.941 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-14_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 188 211.4 2.594 2.594 r= 30 5185 5134.0 0.506 3.100 r= 31 23022 23103.0 0.284 3.385 r= 32 11605 11551.5 0.248 3.632 chi-square = 3.632 with df = 3; p-value = 0.696 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-14_08:31 b-rank test for bits 1 to 8, p=0.69155 b-rank test for bits 2 to 9, p=0.76868 b-rank test for bits 3 to 10, p=0.24752 b-rank test for bits 4 to 11, p=0.23462 b-rank test for bits 5 to 12, p=0.07787 b-rank test for bits 6 to 13, p=0.32200 b-rank test for bits 7 to 14, p=0.19701 b-rank test for bits 8 to 15, p=0.19970 b-rank test for bits 9 to 16, p=0.49596 b-rank test for bits 10 to 17, p=0.20308 b-rank test for bits 11 to 18, p=0.77577 b-rank test for bits 12 to 19, p=0.36360 b-rank test for bits 13 to 20, p=0.97143 b-rank test for bits 14 to 21, p=0.80835 b-rank test for bits 15 to 22, p=0.29692 b-rank test for bits 16 to 23, p=0.84114 b-rank test for bits 17 to 24, p=0.53716 b-rank test for bits 18 to 25, p=0.13543 b-rank test for bits 19 to 26, p=0.13779 b-rank test for bits 20 to 27, p=0.76487 b-rank test for bits 21 to 28, p=0.71765 b-rank test for bits 22 to 29, p=0.91331 b-rank test for bits 23 to 30, p=0.56180 b-rank test for bits 24 to 31, p=0.24949 b-rank test for bits 25 to 32, p=0.95177 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 = 0.797390 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-14_08:31 (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 141915 0.01 0.505285 2 141871 -0.09 0.464320 3 141717 -0.45 0.326583 4 142039 0.30 0.619043 5 141637 -0.64 0.262295 6 141555 -0.83 0.203871 7 142288 0.88 0.811852 8 142242 0.78 0.781499 9 143035 2.63 0.995732 10 141524 -0.90 0.183979 11 141834 -0.18 0.430145 12 142636 1.70 0.955230 13 142298 0.91 0.818089 14 142726 1.91 0.971811 15 141497 -0.96 0.167676 16 141603 -0.72 0.237081 17 142278 0.86 0.805485 18 141732 -0.41 0.339319 19 142127 0.51 0.694475 20 142788 2.05 0.979962 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-14_08:31 Bits used No. missing words z-score p-value 23 to 32 141855 -0.1873 0.425695 22 to 31 142078 0.5816 0.719589 21 to 30 141819 -0.3115 0.377717 20 to 29 142238 1.1333 0.871465 19 to 28 142041 0.4540 0.675098 18 to 27 141730 -0.6184 0.268163 17 to 26 141405 -1.7391 0.041011 16 to 25 141771 -0.4770 0.316681 15 to 24 142046 0.4713 0.681278 14 to 23 141778 -0.4529 0.325324 13 to 22 141775 -0.4632 0.321608 12 to 21 141262 -2.2322 0.012802 11 to 20 141599 -1.0701 0.142286 10 to 19 141564 -1.1908 0.116867 9 to 18 141781 -0.4425 0.329058 8 to 17 141918 0.0299 0.511925 7 to 16 141679 -0.7942 0.213528 6 to 15 141785 -0.4287 0.334062 5 to 14 142174 0.9127 0.819288 4 to 13 141965 0.1920 0.576115 3 to 12 141487 -1.4563 0.072653 2 to 11 141737 -0.5942 0.276175 1 to 10 141713 -0.6770 0.249203 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-14_08:31 Bits used No. missing words z-score p-value 28 to 32 142506 2.0226 0.978443 27 to 31 141633 -0.9367 0.174453 26 to 30 141962 0.1785 0.570852 25 to 29 141964 0.1853 0.573512 24 to 28 141927 0.0599 0.523882 23 to 27 141852 -0.1943 0.422955 22 to 26 142245 1.1379 0.872411 21 to 25 142246 1.1413 0.873118 20 to 24 141932 0.0768 0.530628 19 to 23 142204 0.9989 0.841074 18 to 22 142195 0.9684 0.833571 17 to 21 141648 -0.8859 0.187845 16 to 20 141219 -2.3401 0.009639 15 to 19 141635 -0.9299 0.176203 14 to 18 141434 -1.6113 0.053558 13 to 17 142028 0.4023 0.656258 12 to 16 141790 -0.4045 0.342919 11 to 15 141895 -0.0486 0.480629 10 to 14 141947 0.1277 0.550805 9 to 13 141698 -0.7164 0.236881 8 to 12 141803 -0.3604 0.359259 7 to 11 142117 0.7040 0.759273 6 to 10 142089 0.6091 0.728755 5 to 9 141861 -0.1638 0.434932 4 to 8 141811 -0.3333 0.369446 3 to 7 141706 -0.6893 0.245332 2 to 6 141983 0.2497 0.598602 1 to 5 142150 0.8158 0.792702 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-14_08:31 Bits used No. missing words z-score p-value 31 to 32 141591 -0.9390 0.173859 30 to 31 141891 -0.0541 0.478439 29 to 30 142140 0.6804 0.751888 28 to 29 142420 1.5064 0.934018 27 to 28 141274 -1.8741 0.030456 26 to 27 141976 0.1967 0.577956 25 to 26 141827 -0.2429 0.404056 24 to 25 142232 0.9518 0.829408 23 to 24 141225 -2.0187 0.021761 22 to 23 142246 0.9931 0.839676 21 to 22 141509 -1.1809 0.118818 20 to 21 142032 0.3619 0.641271 19 to 20 141270 -1.8859 0.029652 18 to 19 141747 -0.4788 0.316023 17 to 18 141889 -0.0600 0.476090 16 to 17 141593 -0.9331 0.175377 15 to 16 142188 0.8220 0.794472 14 to 15 141981 0.2114 0.583719 13 to 14 141789 -0.3550 0.361311 12 to 13 141857 -0.1544 0.438661 11 to 12 141834 -0.2222 0.412074 10 to 11 142145 0.6952 0.756532 9 to 10 142066 0.4622 0.678014 8 to 9 141990 0.2380 0.594046 7 to 8 141587 -0.9508 0.170846 6 to 7 141635 -0.8092 0.209191 5 to 6 142331 1.2439 0.893225 4 to 5 141790 -0.3520 0.362417 3 to 4 142156 0.7276 0.766583 2 to 3 141791 -0.3491 0.363524 1 to 2 142161 0.7424 0.771074 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-14_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2445.01 -0.778 0.218374 Test results for specific bytes for dh-ranFile-2016-04-14_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2491.13 -0.125 0.450071 2 to 9 2468.87 -0.440 0.329870 3 to 10 2438.80 -0.865 0.193394 4 to 11 2572.29 1.022 0.846676 5 to 12 2489.72 -0.145 0.442184 6 to 13 2571.71 1.014 0.844748 7 to 14 2560.32 0.853 0.803200 8 to 15 2539.84 0.563 0.713404 9 to 16 2414.50 -1.209 0.113308 10 to 17 2543.42 0.614 0.730392 11 to 18 2471.15 -0.408 0.341637 12 to 19 2619.24 1.686 0.954134 13 to 20 2488.82 -0.158 0.437213 14 to 21 2579.83 1.129 0.870546 15 to 22 2455.60 -0.628 0.265053 16 to 23 2475.05 -0.353 0.362090 17 to 24 2551.22 0.724 0.765597 18 to 25 2522.29 0.315 0.623711 19 to 26 2498.29 -0.024 0.490367 20 to 27 2455.71 -0.626 0.265545 21 to 28 2447.34 -0.745 0.228236 22 to 29 2684.46 2.609 0.995456 23 to 30 2473.58 -0.374 0.354352 24 to 31 2506.22 0.088 0.535074 25 to 32 2534.18 0.483 0.685588 CDPARK for dh-ranFile-2016-04-14_08:31: 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 3498 -1.1416 0.126820 3523 0.0000 0.500000 3543 0.9132 0.819442 3528 0.2283 0.590298 3547 1.0959 0.863437 3554 1.4155 0.921543 3518 -0.2283 0.409702 3562 1.7808 0.962529 3545 1.0046 0.842447 Square side=100, avg. no. parked=3535.70 sample std.=18.06 p-value of the KSTEST for those 10 p-values: 0.073186 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-14_08:31 0.1641,0.9919,0.6793,0.5505,0.6614,0.1916,0.0832,0.2989,0.3776,0.8404, The KS test for those 10 p-values: 0.955821 The 3DSPHERES test for dh-ranFile-2016-04-14_08:31 sample no r^3 equiv. uni. 1 36.246 0.701269 2 20.928 0.502215 3 15.314 0.399782 4 16.438 0.421859 5 22.785 0.532097 6 26.123 0.581373 7 9.167 0.263286 8 8.861 0.255745 9 45.182 0.778222 10 15.498 0.403445 11 11.222 0.312077 12 19.725 0.481847 13 2.006 0.064672 14 10.670 0.299291 15 36.499 0.703776 16 46.558 0.788165 17 3.755 0.117660 18 1.536 0.049898 19 35.894 0.697740 20 34.575 0.684158 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.369588 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-14_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -0.3 -1.6 -0.4 -0.2 -0.4 -0.1 0.9 -0.9 1.1 -0.5 -1.4 1.0 -0.5 -0.8 -0.9 1.7 -0.2 0.7 -0.1 0.9 -1.2 -1.0 0.3 1.0 1.3 -0.6 0.8 0.4 0.1 -0.3 -0.7 -1.4 -0.4 -1.0 1.1 -0.5 -0.4 -0.8 -1.8 0.1 1.0 -0.1 Chi-square with 42 degrees of freedom:32.382747 z-score=-1.049328, p-value=0.142788 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-14_08:31 Test no p-value 1 0.585372 2 0.014833 3 0.602932 4 0.123038 5 0.736672 6 0.009446 7 0.513413 8 0.615130 9 0.400787 10 0.066915 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.092259 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-14_08:31: (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 66429 0.85 66670 0.00 3 25000.00 24997 0.00 24967 0.04 4 6666.67 6810 3.08 6695 0.12 5 1388.89 1429 1.16 1384 0.02 6 238.10 278 6.69 235 0.04 7 34.72 51 7.63 41 1.14 8 4.96 5 0.00 7 0.84 p=0.99647 p=0.09923 Number of rngs required: 690669, p-value: 0.997 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-14_08:31 No. of wins: Observed Expected 98921 98585.9 z-score= 1.499, pvalue=0.93306 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66780 66666.7 0.193 0.193 2 37927 37654.3 1.975 2.167 3 26722 26954.7 2.009 4.177 4 19308 19313.5 0.002 4.178 5 13694 13851.4 1.789 5.967 6 9763 9943.5 3.278 9.245 7 7180 7145.0 0.171 9.417 8 5167 5139.1 0.152 9.568 9 3726 3699.9 0.185 9.753 10 2690 2666.3 0.211 9.964 11 1966 1923.3 0.947 10.910 12 1371 1388.7 0.227 11.137 13 1000 1003.7 0.014 11.151 14 790 726.1 5.616 16.767 15 501 525.8 1.173 17.940 16 373 381.2 0.174 18.114 17 286 276.5 0.324 18.438 18 224 200.8 2.673 21.111 19 140 146.0 0.245 21.356 20 110 106.2 0.135 21.491 21 282 287.1 0.091 21.582 Chisq= 21.58 for 20 degrees of freedom, p= 0.63640 SUMMARY of craptest p-value for no. of wins: 0.933056 p-value for throws/game: 0.636398 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-14_08:31 No. of wins: Observed Expected 98538 98585.9 z-score=-0.214, pvalue=0.41525 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66875 66666.7 0.651 0.651 2 37576 37654.3 0.163 0.814 3 26851 26954.7 0.399 1.213 4 19206 19313.5 0.598 1.811 5 13811 13851.4 0.118 1.929 6 9993 9943.5 0.246 2.175 7 7094 7145.0 0.364 2.539 8 5048 5139.1 1.614 4.153 9 3783 3699.9 1.868 6.021 10 2681 2666.3 0.081 6.102 11 1937 1923.3 0.097 6.200 12 1351 1388.7 1.026 7.225 13 1027 1003.7 0.540 7.765 14 780 726.1 3.995 11.760 15 544 525.8 0.627 12.388 16 412 381.2 2.497 14.885 17 266 276.5 0.402 15.286 18 209 200.8 0.332 15.619 19 139 146.0 0.334 15.953 20 127 106.2 4.067 20.020 21 290 287.1 0.029 20.049 Chisq= 20.05 for 20 degrees of freedom, p= 0.54514 SUMMARY of craptest p-value for no. of wins: 0.415253 p-value for throws/game: 0.545139 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0056,0.0078,0.0094,0.0096,0.0128,0.0148,0.0218,0.0297,0.0305,0.0324, 0.0361,0.0388,0.0393,0.0410,0.0499,0.0536,0.0647,0.0669,0.0727,0.0732, 0.0779,0.0832,0.0923,0.0992,0.1133,0.1169,0.1177,0.1188,0.1230,0.1268, 0.1293,0.1354,0.1378,0.1423,0.1428,0.1605,0.1641,0.1665,0.1677,0.1708, 0.1739,0.1745,0.1754,0.1762,0.1840,0.1878,0.1905,0.1916,0.1934,0.1970, 0.1997,0.2031,0.2039,0.2092,0.2135,0.2184,0.2282,0.2318,0.2329,0.2346, 0.2369,0.2371,0.2453,0.2475,0.2492,0.2495,0.2557,0.2621,0.2623,0.2633, 0.2645,0.2651,0.2655,0.2682,0.2762,0.2969,0.2989,0.2993,0.3121,0.3160, 0.3167,0.3216,0.3220,0.3253,0.3266,0.3283,0.3286,0.3291,0.3299,0.3341, 0.3386,0.3393,0.3416,0.3429,0.3469,0.3527,0.3544,0.3593,0.3613,0.3621, 0.3624,0.3635,0.3636,0.3694,0.3696,0.3776,0.3777,0.3862,0.3998,0.4008, 0.4032,0.4034,0.4041,0.4097,0.4111,0.4121,0.4153,0.4219,0.4230,0.4257, 0.4259,0.4301,0.4349,0.4372,0.4387,0.4422,0.4501,0.4561,0.4571,0.4643, 0.4761,0.4784,0.4806,0.4818,0.4866,0.4904,0.4960,0.5000,0.5022,0.5053, 0.5119,0.5134,0.5239,0.5306,0.5321,0.5351,0.5372,0.5433,0.5451,0.5505, 0.5508,0.5618,0.5709,0.5717,0.5732,0.5735,0.5761,0.5780,0.5814,0.5837, 0.5854,0.5903,0.5940,0.5941,0.5986,0.6028,0.6029,0.6074,0.6141,0.6151, 0.6190,0.6237,0.6310,0.6354,0.6364,0.6413,0.6559,0.6563,0.6614,0.6686, 0.6751,0.6780,0.6793,0.6796,0.6813,0.6842,0.6856,0.6915,0.6945,0.6960, 0.6977,0.7013,0.7038,0.7070,0.7134,0.7176,0.7196,0.7288,0.7304,0.7367, 0.7519,0.7525,0.7565,0.7593,0.7619,0.7649,0.7656,0.7666,0.7675,0.7687, 0.7711,0.7758,0.7782,0.7815,0.7882,0.7927,0.7945,0.7974,0.8024,0.8032, 0.8055,0.8083,0.8119,0.8181,0.8193,0.8194,0.8229,0.8294,0.8336,0.8397, 0.8404,0.8411,0.8411,0.8424,0.8447,0.8467,0.8634,0.8705,0.8715,0.8724, 0.8731,0.8906,0.8932,0.9063,0.9128,0.9133,0.9215,0.9301,0.9331,0.9340, 0.9410,0.9486,0.9501,0.9518,0.9541,0.9552,0.9558,0.9619,0.9623,0.9625, 0.9714,0.9718,0.9784,0.9800,0.9919,0.9955,0.9957,0.9965,0.9967, Overall p-value after applying KStest on 269 p-values = 0.934996 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.