RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-25_11:31 (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 13.3256 0.285869 2 to 25 15.59 21.1513 0.780405 3 to 26 15.75 27.1740 0.944435 4 to 27 15.84 12.9337 0.259386 5 to 28 15.73 18.0230 0.612610 6 to 29 15.91 11.9226 0.195199 7 to 30 15.91 19.2666 0.686554 8 to 31 15.80 23.4884 0.865985 9 to 32 15.57 21.1287 0.779416 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.466896 Tough bday spacings test for dh-ranFile-2016-04-25_11:31: 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 5 36 85 112 91 67 41 38 16 6 3 (O-E)^2/E 1.9 0.0 1.9 2.1 0.5 1.6 2.4 2.3 0.1 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.984, p= 0.775 RESULTS OF GCD FOR dh-ranFile-2016-04-25_11:31 Euclid's algorithm: p-value, steps to gcd: 0.362611 p-value, dist. of gcd's: 0.393533 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-25_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.065 0.065 0.198 0.296 0.710 0.548 0.746 0.288 Bits 8 to 15---> 0.321 0.171 0.561 0.487 0.875 0.899 0.165 0.012 Bits 16 to 23---> 0.926 0.632 0.709 0.929 0.048 0.173 0.029 0.270 Bits 24 to 31---> 0.227 0.821 0.147 0.757 0.071 0.459 0.105 0.507 KS test for the above 32 p values: 0.896 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-25_11:31, p-values for 5 runs: 0.0224, 0.3051, 0.2222, 0.8927, 0.3658 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-25_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5123 5134.0 0.024 1.007 r= 30 23085 23103.0 0.014 1.021 r= 31 11595 11551.5 0.164 1.185 chi-square = 1.185 with df = 3; p-value = 0.243 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-25_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5071 5134.0 0.773 0.775 r= 31 23211 23103.0 0.504 1.279 r= 32 11506 11551.5 0.179 1.459 chi-square = 1.459 with df = 3; p-value = 0.308 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-25_11:31 b-rank test for bits 1 to 8, p=0.40128 b-rank test for bits 2 to 9, p=0.92587 b-rank test for bits 3 to 10, p=0.36523 b-rank test for bits 4 to 11, p=0.37243 b-rank test for bits 5 to 12, p=0.20322 b-rank test for bits 6 to 13, p=0.16433 b-rank test for bits 7 to 14, p=0.97623 b-rank test for bits 8 to 15, p=0.93588 b-rank test for bits 9 to 16, p=0.06237 b-rank test for bits 10 to 17, p=0.34876 b-rank test for bits 11 to 18, p=0.38832 b-rank test for bits 12 to 19, p=0.24569 b-rank test for bits 13 to 20, p=0.27158 b-rank test for bits 14 to 21, p=0.81143 b-rank test for bits 15 to 22, p=0.02332 b-rank test for bits 16 to 23, p=0.08707 b-rank test for bits 17 to 24, p=0.52588 b-rank test for bits 18 to 25, p=0.38303 b-rank test for bits 19 to 26, p=0.00700 b-rank test for bits 20 to 27, p=0.28576 b-rank test for bits 21 to 28, p=0.30458 b-rank test for bits 22 to 29, p=0.53188 b-rank test for bits 23 to 30, p=0.34876 b-rank test for bits 24 to 31, p=0.08788 b-rank test for bits 25 to 32, p=0.08983 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 = 0.018840 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-25_11:31 (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 142044 0.31 0.623486 2 142003 0.22 0.586619 3 141547 -0.85 0.198619 4 142270 0.84 0.800298 5 141648 -0.61 0.270738 6 141414 -1.16 0.123572 7 141820 -0.21 0.417335 8 142098 0.44 0.670328 9 141640 -0.63 0.264584 10 141868 -0.10 0.461536 11 141295 -1.44 0.075594 12 141839 -0.16 0.434739 13 141490 -0.98 0.163607 14 141890 -0.05 0.481989 15 142056 0.34 0.634083 16 141193 -1.67 0.047098 17 142949 2.43 0.992433 18 141533 -0.88 0.189626 19 141726 -0.43 0.334201 20 141483 -1.00 0.159601 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-25_11:31 Bits used No. missing words z-score p-value 23 to 32 142592 2.3540 0.990715 22 to 31 142263 1.2196 0.888683 21 to 30 142131 0.7644 0.777679 20 to 29 141961 0.1782 0.570706 19 to 28 142071 0.5575 0.711401 18 to 27 141627 -0.9736 0.165140 17 to 26 141781 -0.4425 0.329058 16 to 25 141715 -0.6701 0.251396 15 to 24 141579 -1.1391 0.127337 14 to 23 141773 -0.4701 0.319141 13 to 22 141551 -1.2356 0.108300 12 to 21 142325 1.4333 0.924120 11 to 20 141854 -0.1908 0.424344 10 to 19 142190 0.9678 0.833435 9 to 18 141957 0.1644 0.565284 8 to 17 141999 0.3092 0.621418 7 to 16 142342 1.4920 0.932146 6 to 15 141909 -0.0011 0.499546 5 to 14 141766 -0.4942 0.310568 4 to 13 142121 0.7299 0.767273 3 to 12 142193 0.9782 0.836006 2 to 11 141981 0.2471 0.597599 1 to 10 141438 -1.6253 0.052052 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-25_11:31 Bits used No. missing words z-score p-value 28 to 32 142060 0.5107 0.695236 27 to 31 142240 1.1209 0.868838 26 to 30 142217 1.0429 0.851514 25 to 29 141526 -1.2994 0.096899 24 to 28 141965 0.1887 0.574841 23 to 27 142451 1.8362 0.966834 22 to 26 141633 -0.9367 0.174453 21 to 25 142136 0.7684 0.778867 20 to 24 141529 -1.2893 0.098655 19 to 23 141613 -1.0045 0.157567 18 to 22 141954 0.1514 0.560179 17 to 21 142220 1.0531 0.853857 16 to 20 142345 1.4768 0.930142 15 to 19 141674 -0.7977 0.212514 14 to 18 141588 -1.0893 0.138021 13 to 17 142119 0.7107 0.761379 12 to 16 142235 1.1040 0.865196 11 to 15 142418 1.7243 0.957674 10 to 14 141931 0.0735 0.529279 9 to 13 142089 0.6091 0.728755 8 to 12 141843 -0.2248 0.411049 7 to 11 142479 1.9311 0.973264 6 to 10 141826 -0.2825 0.388790 5 to 9 142069 0.5413 0.705834 4 to 8 141694 -0.7299 0.232716 3 to 7 141833 -0.2587 0.397916 2 to 6 142097 0.6362 0.737667 1 to 5 142055 0.4938 0.689275 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-25_11:31 Bits used No. missing words z-score p-value 31 to 32 141917 0.0226 0.509025 30 to 31 141869 -0.1190 0.452651 29 to 30 141701 -0.6145 0.269428 28 to 29 142239 0.9725 0.834594 27 to 28 142008 0.2911 0.614498 26 to 27 142276 1.0816 0.860290 25 to 26 142295 1.1377 0.872371 24 to 25 142441 1.5683 0.941600 23 to 24 142142 0.6863 0.753751 22 to 23 141814 -0.2812 0.389275 21 to 22 141979 0.2055 0.581416 20 to 21 141877 -0.0954 0.462011 19 to 20 142273 1.0728 0.858314 18 to 19 141978 0.2026 0.580263 17 to 18 141711 -0.5850 0.279259 16 to 17 142659 2.2114 0.986496 15 to 16 140749 -3.4228 0.000310 14 to 15 141732 -0.5231 0.300453 13 to 14 142087 0.5241 0.699896 12 to 13 142055 0.4297 0.666295 11 to 12 142623 2.1052 0.982364 10 to 11 141403 -1.4936 0.067640 9 to 10 141976 0.1967 0.577956 8 to 9 142149 0.7070 0.760214 7 to 8 142385 1.4032 0.919715 6 to 7 142041 0.3884 0.651143 5 to 6 141758 -0.4464 0.327654 4 to 5 141734 -0.5172 0.302509 3 to 4 141640 -0.7945 0.213457 2 to 3 141897 -0.0364 0.485493 1 to 2 141591 -0.9390 0.173859 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-25_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2489.54 -0.148 0.441226 Test results for specific bytes for dh-ranFile-2016-04-25_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2448.99 -0.721 0.235338 2 to 9 2566.13 0.935 0.825153 3 to 10 2448.28 -0.731 0.232273 4 to 11 2562.04 0.877 0.809862 5 to 12 2451.94 -0.680 0.248336 6 to 13 2628.67 1.820 0.965596 7 to 14 2487.54 -0.176 0.430070 8 to 15 2436.61 -0.896 0.184999 9 to 16 2573.85 1.044 0.851850 10 to 17 2410.67 -1.263 0.103250 11 to 18 2537.19 0.526 0.700559 12 to 19 2390.95 -1.542 0.061520 13 to 20 2364.88 -1.911 0.028010 14 to 21 2492.92 -0.100 0.460123 15 to 22 2474.45 -0.361 0.358914 16 to 23 2478.42 -0.305 0.380100 17 to 24 2543.18 0.611 0.729271 18 to 25 2434.70 -0.923 0.177894 19 to 26 2565.30 0.923 0.822106 20 to 27 2550.84 0.719 0.763906 21 to 28 2513.39 0.189 0.575074 22 to 29 2557.93 0.819 0.793697 23 to 30 2434.86 -0.921 0.178470 24 to 31 2482.09 -0.253 0.400043 25 to 32 2457.16 -0.606 0.272285 CDPARK for dh-ranFile-2016-04-25_11:31: 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 3576 2.4201 0.992242 3536 0.5936 0.723613 3520 -0.1370 0.445521 3524 0.0457 0.518210 3544 0.9589 0.831196 3545 1.0046 0.842447 3559 1.6438 0.949895 3544 0.9589 0.831196 3537 0.6393 0.738676 3517 -0.2740 0.392053 Square side=100, avg. no. parked=3540.20 sample std.=17.10 p-value of the KSTEST for those 10 p-values: 0.019037 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-25_11:31 0.7220,0.6953,0.5562,0.3174,0.2376,0.5780,0.9746,0.3987,0.0255,0.5424, The KS test for those 10 p-values: 0.890456 The 3DSPHERES test for dh-ranFile-2016-04-25_11:31 sample no r^3 equiv. uni. 1 169.008 0.996424 2 7.311 0.216287 3 28.247 0.609986 4 11.119 0.309695 5 10.566 0.296866 6 47.250 0.792991 7 0.316 0.010476 8 25.134 0.567332 9 43.134 0.762554 10 8.912 0.257002 11 2.040 0.065735 12 56.263 0.846713 13 87.040 0.945050 14 5.930 0.179355 15 46.818 0.789987 16 108.058 0.972729 17 0.635 0.020941 18 2.433 0.077883 19 74.531 0.916621 20 41.485 0.749134 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.292140 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-25_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.2 0.3 0.0 0.1 -0.3 -0.1 -1.3 1.3 0.8 -0.6 0.9 2.1 -0.3 -0.2 2.1 -0.5 0.3 -0.4 -0.4 1.3 -0.4 -1.6 0.6 -1.6 -1.0 -1.7 -0.4 -1.5 -0.4 -0.5 -0.7 -0.4 1.0 -0.8 -0.1 1.0 0.8 -1.6 -0.1 0.9 0.0 0.8 Chi-square with 42 degrees of freedom:38.555111 z-score=-0.375868, p-value=0.377012 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-25_11:31 Test no p-value 1 0.378274 2 0.690183 3 0.046675 4 0.395149 5 0.056739 6 0.186871 7 0.402593 8 0.183522 9 0.040973 10 0.397628 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.018768 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-25_11:31: (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 66648 0.01 66694 0.01 3 25000.00 25060 0.14 25095 0.36 4 6666.67 6641 0.10 6576 1.23 5 1388.89 1393 0.01 1344 1.45 6 238.10 218 1.70 245 0.20 7 34.72 35 0.00 38 0.31 8 4.96 4 0.19 7 0.84 p=0.09404 p=0.37801 Number of rngs required: 688966, p-value: 0.742 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-25_11:31 No. of wins: Observed Expected 98474 98585.9 z-score=-0.500, pvalue=0.30843 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66700 66666.7 0.017 0.017 2 37935 37654.3 2.092 2.109 3 27007 26954.7 0.101 2.210 4 19156 19313.5 1.284 3.494 5 13666 13851.4 2.482 5.976 6 9958 9943.5 0.021 5.997 7 7117 7145.0 0.110 6.107 8 5198 5139.1 0.676 6.783 9 3683 3699.9 0.077 6.860 10 2609 2666.3 1.231 8.091 11 1949 1923.3 0.343 8.434 12 1398 1388.7 0.062 8.495 13 1004 1003.7 0.000 8.495 14 718 726.1 0.091 8.587 15 547 525.8 0.852 9.438 16 366 381.2 0.602 10.041 17 273 276.5 0.045 10.086 18 196 200.8 0.116 10.202 19 141 146.0 0.170 10.372 20 105 106.2 0.014 10.386 21 274 287.1 0.599 10.985 Chisq= 10.99 for 20 degrees of freedom, p= 0.05340 SUMMARY of craptest p-value for no. of wins: 0.308433 p-value for throws/game: 0.053395 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-25_11:31 No. of wins: Observed Expected 98438 98585.9 z-score=-0.661, pvalue=0.25421 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66434 66666.7 0.812 0.812 2 37700 37654.3 0.055 0.867 3 27311 26954.7 4.709 5.576 4 19323 19313.5 0.005 5.581 5 13810 13851.4 0.124 5.705 6 9952 9943.5 0.007 5.712 7 7082 7145.0 0.556 6.268 8 5123 5139.1 0.050 6.318 9 3757 3699.9 0.882 7.201 10 2572 2666.3 3.335 10.536 11 1956 1923.3 0.555 11.091 12 1358 1388.7 0.680 11.771 13 989 1003.7 0.216 11.987 14 718 726.1 0.091 12.078 15 544 525.8 0.627 12.705 16 351 381.2 2.385 15.090 17 257 276.5 1.381 16.471 18 232 200.8 4.838 21.309 19 158 146.0 0.989 22.298 20 107 106.2 0.006 22.304 21 266 287.1 1.553 23.856 Chisq= 23.86 for 20 degrees of freedom, p= 0.75127 SUMMARY of craptest p-value for no. of wins: 0.254207 p-value for throws/game: 0.751275 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0003,0.0070,0.0105,0.0115,0.0188,0.0188,0.0190,0.0209,0.0224,0.0233, 0.0255,0.0280,0.0289,0.0410,0.0467,0.0471,0.0483,0.0521,0.0534,0.0567, 0.0615,0.0624,0.0647,0.0653,0.0657,0.0676,0.0705,0.0756,0.0779,0.0871, 0.0879,0.0898,0.0940,0.0969,0.0987,0.1033,0.1048,0.1083,0.1236,0.1273, 0.1380,0.1471,0.1576,0.1596,0.1636,0.1643,0.1649,0.1651,0.1705,0.1732, 0.1739,0.1745,0.1779,0.1785,0.1794,0.1835,0.1850,0.1869,0.1896,0.1952, 0.1980,0.1986,0.2032,0.2125,0.2135,0.2163,0.2222,0.2268,0.2323,0.2327, 0.2353,0.2376,0.2433,0.2457,0.2483,0.2514,0.2542,0.2570,0.2594,0.2646, 0.2694,0.2696,0.2707,0.2716,0.2723,0.2793,0.2858,0.2859,0.2878,0.2921, 0.2963,0.2969,0.3005,0.3025,0.3046,0.3051,0.3082,0.3084,0.3097,0.3106, 0.3174,0.3191,0.3206,0.3277,0.3291,0.3342,0.3488,0.3488,0.3589,0.3626, 0.3652,0.3658,0.3724,0.3770,0.3780,0.3783,0.3801,0.3830,0.3883,0.3888, 0.3893,0.3921,0.3935,0.3951,0.3976,0.3979,0.3987,0.4000,0.4013,0.4026, 0.4110,0.4173,0.4243,0.4301,0.4347,0.4412,0.4455,0.4527,0.4594,0.4601, 0.4615,0.4620,0.4669,0.4820,0.4855,0.4870,0.4995,0.5072,0.5090,0.5182, 0.5259,0.5293,0.5319,0.5424,0.5485,0.5562,0.5602,0.5607,0.5653,0.5673, 0.5707,0.5748,0.5751,0.5780,0.5780,0.5803,0.5814,0.5866,0.5976,0.6100, 0.6126,0.6145,0.6214,0.6235,0.6320,0.6341,0.6511,0.6663,0.6703,0.6866, 0.6893,0.6902,0.6952,0.6953,0.6999,0.7006,0.7058,0.7086,0.7104,0.7114, 0.7220,0.7236,0.7288,0.7293,0.7377,0.7387,0.7420,0.7463,0.7491,0.7513, 0.7538,0.7571,0.7602,0.7614,0.7626,0.7639,0.7673,0.7754,0.7777,0.7789, 0.7794,0.7804,0.7900,0.7930,0.7937,0.8003,0.8099,0.8114,0.8209,0.8221, 0.8252,0.8312,0.8312,0.8334,0.8346,0.8360,0.8424,0.8467,0.8515,0.8519, 0.8539,0.8583,0.8603,0.8652,0.8660,0.8688,0.8724,0.8747,0.8887,0.8905, 0.8927,0.8964,0.8993,0.9166,0.9197,0.9241,0.9259,0.9260,0.9288,0.9301, 0.9321,0.9359,0.9416,0.9444,0.9450,0.9499,0.9577,0.9656,0.9668,0.9727, 0.9733,0.9746,0.9762,0.9824,0.9865,0.9907,0.9922,0.9924,0.9964, Overall p-value after applying KStest on 269 p-values = 0.219742 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.