RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-24_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.60 18.4744 0.640482 2 to 25 15.56 26.7737 0.938529 3 to 26 15.66 11.9022 0.193976 4 to 27 16.05 16.5089 0.511909 5 to 28 15.66 22.8800 0.846803 6 to 29 16.18 16.1012 0.483327 7 to 30 15.78 17.2066 0.559542 8 to 31 15.77 10.4984 0.118578 9 to 32 16.00 11.8420 0.190394 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.968357 Tough bday spacings test for dh-ranFile-2018-03-24_20:31: 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 8 38 82 92 101 85 44 22 20 4 4 (O-E)^2/E 0.1 0.1 1.0 0.3 0.1 0.6 1.3 2.0 1.8 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.363, p= 0.407 RESULTS OF GCD FOR dh-ranFile-2018-03-24_20:31 Euclid's algorithm: p-value, steps to gcd: 0.746054 p-value, dist. of gcd's: 0.465461 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-24_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.121 0.748 0.543 0.392 0.356 0.510 0.814 0.868 Bits 8 to 15---> 0.976 0.047 0.938 0.530 0.852 0.111 0.905 0.196 Bits 16 to 23---> 0.368 0.465 0.743 0.448 0.960 0.159 0.527 0.982 Bits 24 to 31---> 0.264 0.554 0.882 0.140 0.611 0.212 0.372 0.380 KS test for the above 32 p values: 0.293 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-24_20:31, p-values for 5 runs: 0.8668, 0.8263, 0.6487, 0.9681, 0.8057 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-24_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5122 5134.0 0.028 0.541 r= 30 23211 23103.0 0.504 1.046 r= 31 11466 11551.5 0.633 1.679 chi-square = 1.679 with df = 3; p-value = 0.358 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-24_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5051 5134.0 1.342 2.467 r= 31 23277 23103.0 1.310 3.776 r= 32 11476 11551.5 0.494 4.270 chi-square = 4.270 with df = 3; p-value = 0.766 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-24_20:31 b-rank test for bits 1 to 8, p=0.77168 b-rank test for bits 2 to 9, p=0.72782 b-rank test for bits 3 to 10, p=0.81940 b-rank test for bits 4 to 11, p=0.29920 b-rank test for bits 5 to 12, p=0.39592 b-rank test for bits 6 to 13, p=0.64018 b-rank test for bits 7 to 14, p=0.81150 b-rank test for bits 8 to 15, p=0.50397 b-rank test for bits 9 to 16, p=0.33403 b-rank test for bits 10 to 17, p=0.00394 b-rank test for bits 11 to 18, p=0.13556 b-rank test for bits 12 to 19, p=0.07202 b-rank test for bits 13 to 20, p=0.02902 b-rank test for bits 14 to 21, p=0.20995 b-rank test for bits 15 to 22, p=0.52422 b-rank test for bits 16 to 23, p=0.27666 b-rank test for bits 17 to 24, p=0.13652 b-rank test for bits 18 to 25, p=0.96690 b-rank test for bits 19 to 26, p=0.31774 b-rank test for bits 20 to 27, p=0.68181 b-rank test for bits 21 to 28, p=0.23337 b-rank test for bits 22 to 29, p=0.43953 b-rank test for bits 23 to 30, p=0.31814 b-rank test for bits 24 to 31, p=0.09966 b-rank test for bits 25 to 32, p=0.07259 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 = 0.106364 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-24_20:31 (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 141671 -0.56 0.288816 2 141475 -1.01 0.155103 3 141338 -1.33 0.090957 4 141687 -0.52 0.301719 5 142272 0.85 0.801603 6 141665 -0.57 0.284046 7 142059 0.35 0.636717 8 141314 -1.39 0.082119 9 142556 1.51 0.934594 10 141578 -0.77 0.219425 11 142298 0.91 0.818089 12 141829 -0.19 0.425561 13 142028 0.28 0.609212 14 141936 0.06 0.524843 15 141128 -1.83 0.033960 16 142231 0.75 0.773844 17 142190 0.66 0.744014 18 141776 -0.31 0.377703 19 142269 0.84 0.799644 20 142363 1.06 0.855422 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-24_20:31 Bits used No. missing words z-score p-value 23 to 32 141862 -0.1632 0.435178 22 to 31 141330 -1.9977 0.022875 21 to 30 142110 0.6920 0.755521 20 to 29 141705 -0.7046 0.240534 19 to 28 141360 -1.8942 0.029096 18 to 27 141987 0.2678 0.605584 17 to 26 141219 -2.3804 0.008646 16 to 25 141699 -0.7253 0.234141 15 to 24 141789 -0.4149 0.339096 14 to 23 141871 -0.1322 0.447424 13 to 22 141876 -0.1149 0.454250 12 to 21 141829 -0.2770 0.390890 11 to 20 141830 -0.2736 0.392215 10 to 19 141840 -0.2391 0.405526 9 to 18 141890 -0.0667 0.473428 8 to 17 142745 2.8816 0.998022 7 to 16 142589 2.3437 0.990453 6 to 15 141856 -0.1839 0.427047 5 to 14 141495 -1.4287 0.076542 4 to 13 141800 -0.3770 0.353087 3 to 12 141898 -0.0391 0.484418 2 to 11 141659 -0.8632 0.194012 1 to 10 142027 0.4058 0.657540 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-24_20:31 Bits used No. missing words z-score p-value 28 to 32 142287 1.2802 0.899769 27 to 31 141885 -0.0825 0.467135 26 to 30 141860 -0.1672 0.433598 25 to 29 141947 0.1277 0.550805 24 to 28 141559 -1.1876 0.117504 23 to 27 141987 0.2633 0.603836 22 to 26 141728 -0.6147 0.269384 21 to 25 141938 0.0972 0.538711 20 to 24 141660 -0.8452 0.199003 19 to 23 141826 -0.2825 0.388790 18 to 22 141092 -2.7706 0.002798 17 to 21 141598 -1.0554 0.145631 16 to 20 141644 -0.8994 0.184214 15 to 19 142042 0.4497 0.673547 14 to 18 141906 -0.0113 0.495497 13 to 17 141690 -0.7435 0.228592 12 to 16 141960 0.1718 0.568188 11 to 15 142142 0.7887 0.784860 10 to 14 142147 0.8057 0.789781 9 to 13 142117 0.7040 0.759273 8 to 12 142400 1.6633 0.951873 7 to 11 141736 -0.5876 0.278414 6 to 10 142194 0.9650 0.832723 5 to 9 141507 -1.3638 0.086310 4 to 8 141641 -0.9096 0.181519 3 to 7 141982 0.2463 0.597290 2 to 6 141840 -0.2350 0.407098 1 to 5 142006 0.3277 0.628429 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-24_20:31 Bits used No. missing words z-score p-value 31 to 32 142006 0.2852 0.612240 30 to 31 141742 -0.4936 0.310795 29 to 30 142586 1.9961 0.977037 28 to 29 141973 0.1878 0.574490 27 to 28 141897 -0.0364 0.485493 26 to 27 141352 -1.6440 0.050084 25 to 26 142148 0.7040 0.759297 24 to 25 141701 -0.6145 0.269428 23 to 24 142657 2.2055 0.986291 22 to 23 142401 1.4504 0.926520 21 to 22 141591 -0.9390 0.173859 20 to 21 142081 0.5064 0.693713 19 to 20 141198 -2.0983 0.017939 18 to 19 142555 1.9046 0.971586 17 to 18 142457 1.6155 0.946904 16 to 17 142324 1.2232 0.889376 15 to 16 141975 0.1937 0.576801 14 to 15 141693 -0.6381 0.261691 13 to 14 141674 -0.6942 0.243782 12 to 13 141236 -1.9862 0.023504 11 to 12 141779 -0.3845 0.350321 10 to 11 142213 0.8958 0.814815 9 to 10 141707 -0.5968 0.275306 8 to 9 141219 -2.0364 0.020857 7 to 8 141854 -0.1632 0.435174 6 to 7 142465 1.6391 0.949408 5 to 6 142081 0.5064 0.693713 4 to 5 141940 0.0905 0.536044 3 to 4 141634 -0.8122 0.208343 2 to 3 141613 -0.8741 0.191024 1 to 2 141575 -0.9862 0.162012 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-24_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2530.73 0.435 0.668044 Test results for specific bytes for dh-ranFile-2018-03-24_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2553.03 0.750 0.773362 2 to 9 2493.93 -0.086 0.465770 3 to 10 2452.16 -0.677 0.249352 4 to 11 2728.67 3.234 0.999390 5 to 12 2482.13 -0.253 0.400263 6 to 13 2468.57 -0.445 0.328325 7 to 14 2406.64 -1.320 0.093371 8 to 15 2542.24 0.597 0.724848 9 to 16 2425.76 -1.050 0.146887 10 to 17 2389.58 -1.562 0.059191 11 to 18 2517.36 0.246 0.596993 12 to 19 2456.28 -0.618 0.268199 13 to 20 2394.59 -1.491 0.068010 14 to 21 2549.14 0.695 0.756444 15 to 22 2524.79 0.351 0.637065 16 to 23 2407.66 -1.306 0.095786 17 to 24 2403.65 -1.363 0.086499 18 to 25 2495.82 -0.059 0.476430 19 to 26 2462.92 -0.524 0.300009 20 to 27 2544.91 0.635 0.737330 21 to 28 2564.31 0.910 0.818466 22 to 29 2495.76 -0.060 0.476112 23 to 30 2547.01 0.665 0.746907 24 to 31 2488.78 -0.159 0.436972 25 to 32 2515.08 0.213 0.584418 CDPARK for dh-ranFile-2018-03-24_20:31: 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 3504 -0.8676 0.192812 3521 -0.0913 0.463617 3550 1.2329 0.891189 3521 -0.0913 0.463617 3536 0.5936 0.723613 3516 -0.3196 0.374623 3540 0.7763 0.781201 3535 0.5479 0.708135 3518 -0.2283 0.409702 Square side=100, avg. no. parked=3526.10 sample std.=12.99 p-value of the KSTEST for those 10 p-values: 0.501574 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-24_20:31 0.9453,0.1845,0.5711,0.7357,0.0186,0.3668,0.5055,0.4222,0.9575,0.4652, The KS test for those 10 p-values: 0.882340 The 3DSPHERES test for dh-ranFile-2018-03-24_20:31 sample no r^3 equiv. uni. 1 9.474 0.270800 2 6.160 0.185629 3 10.755 0.301286 4 18.900 0.467413 5 55.208 0.841225 6 8.265 0.240796 7 1.001 0.032814 8 5.909 0.178786 9 32.859 0.665561 10 55.031 0.840285 11 10.177 0.287673 12 18.547 0.461100 13 30.254 0.635218 14 60.393 0.866424 15 49.276 0.806513 16 10.119 0.286298 17 13.999 0.372894 18 22.474 0.527226 19 78.415 0.926747 20 3.225 0.101934 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.793617 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-24_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.6 -0.6 0.5 2.1 -1.2 -1.1 -0.8 -1.6 0.5 -1.4 -0.6 0.7 -0.8 3.1 -0.7 -0.7 0.2 -0.9 0.7 0.9 0.2 -0.8 -1.2 -0.7 1.7 1.7 -0.5 1.0 1.2 -0.8 0.3 -1.0 -1.3 0.1 -0.7 1.7 -0.4 2.1 -1.8 -1.3 2.0 1.8 Chi-square with 42 degrees of freedom:64.326668 z-score=2.436039, p-value=0.985105 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-24_20:31 Test no p-value 1 0.731243 2 0.612078 3 0.167883 4 0.402192 5 0.048898 6 0.295555 7 0.523474 8 0.545598 9 0.195517 10 0.389459 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.326927 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-24_20:31: (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 66746 0.09 66786 0.21 3 25000.00 24834 1.10 25026 0.03 4 6666.67 6763 1.39 6534 2.64 5 1388.89 1377 0.10 1379 0.07 6 238.10 240 0.02 237 0.01 7 34.72 34 0.01 32 0.21 8 4.96 5 0.00 5 0.00 p=0.15702 p=0.21273 Number of rngs required: 688476, p-value: 0.533 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-24_20:31 No. of wins: Observed Expected 98822 98585.9 z-score= 1.056, pvalue=0.85455 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66447 66666.7 0.724 0.724 2 37710 37654.3 0.082 0.806 3 27032 26954.7 0.221 1.028 4 19087 19313.5 2.655 3.683 5 13816 13851.4 0.091 3.774 6 10003 9943.5 0.356 4.129 7 7256 7145.0 1.724 5.853 8 5196 5139.1 0.631 6.483 9 3778 3699.9 1.650 8.133 10 2687 2666.3 0.161 8.294 11 1979 1923.3 1.611 9.906 12 1377 1388.7 0.099 10.005 13 1037 1003.7 1.104 11.109 14 687 726.1 2.110 13.218 15 529 525.8 0.019 13.237 16 380 381.2 0.003 13.241 17 283 276.5 0.151 13.392 18 199 200.8 0.017 13.409 19 139 146.0 0.334 13.743 20 100 106.2 0.364 14.106 21 278 287.1 0.289 14.396 Chisq= 14.40 for 20 degrees of freedom, p= 0.19012 SUMMARY of craptest p-value for no. of wins: 0.854553 p-value for throws/game: 0.190118 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-24_20:31 No. of wins: Observed Expected 98514 98585.9 z-score=-0.321, pvalue=0.37396 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66624 66666.7 0.027 0.027 2 37950 37654.3 2.322 2.349 3 26737 26954.7 1.759 4.108 4 19213 19313.5 0.523 4.630 5 13687 13851.4 1.952 6.582 6 10104 9943.5 2.589 9.171 7 7196 7145.0 0.364 9.535 8 5110 5139.1 0.164 9.700 9 3769 3699.9 1.292 10.991 10 2587 2666.3 2.358 13.350 11 1909 1923.3 0.107 13.457 12 1419 1388.7 0.659 14.116 13 1010 1003.7 0.039 14.155 14 729 726.1 0.011 14.166 15 532 525.8 0.072 14.239 16 363 381.2 0.864 15.103 17 300 276.5 1.990 17.093 18 202 200.8 0.007 17.100 19 156 146.0 0.687 17.787 20 113 106.2 0.433 18.221 21 290 287.1 0.029 18.250 Chisq= 18.25 for 20 degrees of freedom, p= 0.42904 SUMMARY of craptest p-value for no. of wins: 0.373956 p-value for throws/game: 0.429039 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0028,0.0039,0.0086,0.0179,0.0186,0.0209,0.0229,0.0235,0.0290,0.0291, 0.0328,0.0340,0.0473,0.0489,0.0501,0.0592,0.0680,0.0720,0.0726,0.0765, 0.0821,0.0863,0.0865,0.0910,0.0934,0.0958,0.0997,0.1019,0.1064,0.1111, 0.1175,0.1186,0.1211,0.1356,0.1365,0.1398,0.1456,0.1469,0.1551,0.1570, 0.1588,0.1620,0.1679,0.1739,0.1788,0.1815,0.1842,0.1845,0.1856,0.1901, 0.1904,0.1910,0.1928,0.1940,0.1940,0.1955,0.1956,0.1990,0.2083,0.2099, 0.2115,0.2127,0.2194,0.2286,0.2334,0.2341,0.2405,0.2408,0.2438,0.2494, 0.2617,0.2640,0.2682,0.2694,0.2694,0.2708,0.2753,0.2767,0.2784,0.2840, 0.2863,0.2877,0.2888,0.2926,0.2956,0.2992,0.3000,0.3013,0.3017,0.3108, 0.3177,0.3181,0.3269,0.3283,0.3340,0.3391,0.3503,0.3531,0.3558,0.3584, 0.3668,0.3681,0.3721,0.3729,0.3740,0.3746,0.3777,0.3803,0.3888,0.3895, 0.3909,0.3916,0.3922,0.3959,0.4003,0.4022,0.4055,0.4066,0.4071,0.4097, 0.4222,0.4256,0.4270,0.4290,0.4336,0.4352,0.4352,0.4370,0.4395,0.4455, 0.4474,0.4480,0.4542,0.4611,0.4636,0.4636,0.4647,0.4652,0.4655,0.4658, 0.4671,0.4674,0.4734,0.4761,0.4764,0.4833,0.4844,0.4855,0.4955,0.5016, 0.5040,0.5055,0.5101,0.5119,0.5235,0.5242,0.5248,0.5272,0.5272,0.5301, 0.5335,0.5360,0.5387,0.5428,0.5456,0.5508,0.5538,0.5595,0.5682,0.5711, 0.5745,0.5768,0.5844,0.5970,0.5973,0.6038,0.6056,0.6092,0.6107,0.6121, 0.6122,0.6284,0.6352,0.6367,0.6371,0.6402,0.6405,0.6487,0.6575,0.6656, 0.6680,0.6735,0.6818,0.6937,0.6937,0.7081,0.7236,0.7248,0.7278,0.7312, 0.7357,0.7373,0.7429,0.7440,0.7461,0.7469,0.7485,0.7555,0.7564,0.7593, 0.7593,0.7663,0.7717,0.7734,0.7738,0.7812,0.7849,0.7898,0.7936,0.7996, 0.8016,0.8057,0.8065,0.8115,0.8139,0.8148,0.8181,0.8185,0.8194,0.8263, 0.8327,0.8403,0.8412,0.8468,0.8516,0.8546,0.8554,0.8664,0.8668,0.8676, 0.8818,0.8823,0.8894,0.8912,0.8998,0.9046,0.9265,0.9267,0.9346,0.9383, 0.9385,0.9453,0.9469,0.9494,0.9519,0.9575,0.9597,0.9669,0.9681,0.9684, 0.9716,0.9756,0.9770,0.9822,0.9851,0.9863,0.9905,0.9980,0.9994, Overall p-value after applying KStest on 269 p-values = 0.327344 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.