RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-08_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.94 18.1277 0.619175 2 to 25 15.60 30.6157 0.977769 3 to 26 16.01 5.2928 0.003185 4 to 27 15.97 10.7289 0.129697 5 to 28 15.80 12.2275 0.213829 6 to 29 15.67 22.9565 0.849328 7 to 30 15.83 18.2989 0.629775 8 to 31 15.71 25.4657 0.915240 9 to 32 15.89 10.8143 0.133947 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.425814 Tough bday spacings test for dh-ranFile-2015-09-08_00:31: 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 41 91 85 92 95 51 24 8 3 4 (O-E)^2/E 1.1 0.5 4.3 1.6 0.3 3.6 0.0 1.1 3.2 2.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 17.820, p= 0.942 RESULTS OF GCD FOR dh-ranFile-2015-09-08_00:31 Euclid's algorithm: p-value, steps to gcd: 0.945138 p-value, dist. of gcd's: 0.468773 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-08_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.638 0.625 0.124 0.165 0.569 0.116 0.319 0.185 Bits 8 to 15---> 0.345 0.773 0.696 0.380 0.324 0.982 0.687 0.018 Bits 16 to 23---> 0.563 0.929 0.060 0.512 0.030 0.051 0.852 0.985 Bits 24 to 31---> 0.233 0.936 0.704 0.827 0.061 0.193 0.740 0.345 KS test for the above 32 p values: 0.392 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-08_00:31, p-values for 5 runs: 0.6331, 0.8111, 0.4891, 0.2582, 0.5233 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-08_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5122 5134.0 0.028 0.901 r= 30 22968 23103.0 0.789 1.690 r= 31 11685 11551.5 1.542 3.232 chi-square = 3.232 with df = 3; p-value = 0.643 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-08_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5116 5134.0 0.063 0.412 r= 31 22865 23103.0 2.453 2.864 r= 32 11799 11551.5 5.302 8.166 chi-square = 8.166 with df = 3; p-value = 0.957 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-08_00:31 b-rank test for bits 1 to 8, p=0.60415 b-rank test for bits 2 to 9, p=0.26287 b-rank test for bits 3 to 10, p=0.05144 b-rank test for bits 4 to 11, p=0.69831 b-rank test for bits 5 to 12, p=0.88795 b-rank test for bits 6 to 13, p=0.93901 b-rank test for bits 7 to 14, p=0.22604 b-rank test for bits 8 to 15, p=0.69590 b-rank test for bits 9 to 16, p=0.55313 b-rank test for bits 10 to 17, p=0.76194 b-rank test for bits 11 to 18, p=0.09180 b-rank test for bits 12 to 19, p=0.23647 b-rank test for bits 13 to 20, p=0.42031 b-rank test for bits 14 to 21, p=0.41375 b-rank test for bits 15 to 22, p=0.38852 b-rank test for bits 16 to 23, p=0.02722 b-rank test for bits 17 to 24, p=0.33139 b-rank test for bits 18 to 25, p=0.21665 b-rank test for bits 19 to 26, p=0.01048 b-rank test for bits 20 to 27, p=0.02099 b-rank test for bits 21 to 28, p=0.57405 b-rank test for bits 22 to 29, p=0.17826 b-rank test for bits 23 to 30, p=0.73086 b-rank test for bits 24 to 31, p=0.50676 b-rank test for bits 25 to 32, p=0.14279 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 = 0.126060 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-08_00:31 (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 142369 1.07 0.858588 2 141911 0.00 0.501557 3 141140 -1.80 0.036128 4 141343 -1.32 0.092884 5 142266 0.83 0.797674 6 142113 0.48 0.682915 7 141588 -0.75 0.226395 8 141693 -0.51 0.306624 9 141695 -0.50 0.308266 10 142317 0.95 0.829578 11 141906 -0.01 0.496896 12 142524 1.44 0.924519 13 141473 -1.02 0.153992 14 142238 0.77 0.778733 15 141444 -1.09 0.138470 16 141829 -0.19 0.425561 17 142483 1.34 0.909934 18 141909 -0.00 0.499692 19 142322 0.96 0.832523 20 141764 -0.34 0.367095 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-08_00:31 Bits used No. missing words z-score p-value 23 to 32 141542 -1.2667 0.102639 22 to 31 141756 -0.5287 0.298498 21 to 30 141902 -0.0253 0.489918 20 to 29 141955 0.1575 0.562568 19 to 28 141861 -0.1667 0.433821 18 to 27 142597 2.3713 0.991137 17 to 26 141896 -0.0460 0.481669 16 to 25 141864 -0.1563 0.437894 15 to 24 141368 -1.8667 0.030975 14 to 23 142694 2.7058 0.996593 13 to 22 142089 0.6196 0.732224 12 to 21 141900 -0.0322 0.487167 11 to 20 141542 -1.2667 0.102639 10 to 19 142005 0.3299 0.629261 9 to 18 142153 0.8402 0.799614 8 to 17 141587 -1.1115 0.133180 7 to 16 141632 -0.9563 0.169458 6 to 15 141890 -0.0667 0.473428 5 to 14 141729 -0.6218 0.267028 4 to 13 141905 -0.0149 0.494044 3 to 12 141475 -1.4977 0.067107 2 to 11 141693 -0.7460 0.227844 1 to 10 141927 0.0609 0.524293 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-08_00:31 Bits used No. missing words z-score p-value 28 to 32 141991 0.2768 0.609051 27 to 31 142006 0.3277 0.628429 26 to 30 142160 0.8497 0.802262 25 to 29 142129 0.7446 0.771757 24 to 28 141878 -0.1062 0.457711 23 to 27 141638 -0.9198 0.178848 22 to 26 141414 -1.6791 0.046568 21 to 25 142013 0.3514 0.637365 20 to 24 142425 1.7480 0.959771 19 to 23 142144 0.7955 0.786836 18 to 22 141773 -0.4621 0.321992 17 to 21 141992 0.2802 0.610352 16 to 20 141959 0.1684 0.566855 15 to 19 141395 -1.7435 0.040624 14 to 18 141370 -1.8282 0.033757 13 to 17 141842 -0.2282 0.409731 12 to 16 141665 -0.8282 0.203768 11 to 15 142112 0.6870 0.753964 10 to 14 141412 -1.6859 0.045911 9 to 13 141733 -0.5977 0.275010 8 to 12 141819 -0.3062 0.379725 7 to 11 141713 -0.6655 0.252857 6 to 10 142278 1.2497 0.894301 5 to 9 141756 -0.5198 0.301615 4 to 8 141444 -1.5774 0.057353 3 to 7 141821 -0.2994 0.382308 2 to 6 141990 0.2735 0.607749 1 to 5 141855 -0.1842 0.426940 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-08_00:31 Bits used No. missing words z-score p-value 31 to 32 142255 1.0197 0.846059 30 to 31 142064 0.4563 0.675896 29 to 30 142019 0.3235 0.626846 28 to 29 141839 -0.2075 0.417824 27 to 28 141737 -0.5083 0.305605 26 to 27 142323 1.2203 0.888818 25 to 26 141756 -0.4523 0.325526 24 to 25 142255 1.0197 0.846059 23 to 24 142178 0.7925 0.785976 22 to 23 141491 -1.2340 0.108599 21 to 22 141955 0.1347 0.553583 20 to 21 141613 -0.8741 0.191024 19 to 20 142001 0.2704 0.606579 18 to 19 141890 -0.0570 0.477264 17 to 18 142006 0.2852 0.612240 16 to 17 142511 1.7748 0.962038 15 to 16 141632 -0.8181 0.206655 14 to 15 141836 -0.2163 0.414372 13 to 14 141934 0.0728 0.529007 12 to 13 142106 0.5801 0.719092 11 to 12 142000 0.2675 0.605444 10 to 11 142191 0.8309 0.796981 9 to 10 141933 0.0698 0.527833 8 to 9 142386 1.4061 0.920154 7 to 8 142293 1.1318 0.871134 6 to 7 142308 1.1760 0.880206 5 to 6 141910 0.0020 0.500789 4 to 5 141721 -0.5555 0.289261 3 to 4 142033 0.3648 0.642373 2 to 3 141854 -0.1632 0.435174 1 to 2 142312 1.1878 0.882547 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-08_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2467.56 -0.459 0.323178 Test results for specific bytes for dh-ranFile-2015-09-08_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2464.16 -0.507 0.306141 2 to 9 2496.25 -0.053 0.478865 3 to 10 2509.17 0.130 0.551591 4 to 11 2437.91 -0.878 0.189934 5 to 12 2460.94 -0.552 0.290316 6 to 13 2559.95 0.848 0.801730 7 to 14 2433.59 -0.939 0.173829 8 to 15 2494.18 -0.082 0.467225 9 to 16 2509.07 0.128 0.551028 10 to 17 2573.81 1.044 0.851717 11 to 18 2445.73 -0.767 0.221395 12 to 19 2556.52 0.799 0.787959 13 to 20 2441.22 -0.831 0.202921 14 to 21 2396.85 -1.459 0.072318 15 to 22 2426.08 -1.045 0.147909 16 to 23 2559.45 0.841 0.799764 17 to 24 2484.24 -0.223 0.411792 18 to 25 2579.09 1.118 0.868317 19 to 26 2514.36 0.203 0.580492 20 to 27 2561.73 0.873 0.808668 21 to 28 2541.40 0.585 0.720872 22 to 29 2374.87 -1.770 0.038400 23 to 30 2433.84 -0.936 0.174741 24 to 31 2529.07 0.411 0.659493 25 to 32 2406.47 -1.323 0.092954 CDPARK for dh-ranFile-2015-09-08_00:31: 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 3530 0.3196 0.625377 3545 1.0046 0.842447 3519 -0.1826 0.427537 3520 -0.1370 0.445521 3547 1.0959 0.863437 3509 -0.6393 0.261324 3548 1.1416 0.873180 3492 -1.4155 0.078457 3518 -0.2283 0.409702 3519 -0.1826 0.427537 Square side=100, avg. no. parked=3524.70 sample std.=17.11 p-value of the KSTEST for those 10 p-values: 0.775183 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-08_00:31 0.7746,0.2113,0.4506,0.9551,0.6806,0.6237,0.7004,0.8130,0.7072,0.3179, The KS test for those 10 p-values: 0.242978 The 3DSPHERES test for dh-ranFile-2015-09-08_00:31 sample no r^3 equiv. uni. 1 8.812 0.254515 2 0.684 0.022548 3 4.863 0.149646 4 20.872 0.501286 5 19.774 0.482697 6 36.569 0.704466 7 26.796 0.590662 8 34.181 0.679977 9 0.213 0.007079 10 0.305 0.010124 11 23.701 0.546172 12 1.588 0.051550 13 5.504 0.167614 14 5.518 0.168006 15 19.322 0.474851 16 19.148 0.471784 17 100.964 0.965454 18 4.097 0.127660 19 70.674 0.905182 20 70.659 0.905135 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.122282 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-08_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.9 1.5 1.9 -1.4 0.5 -0.0 1.9 -0.6 2.4 -0.0 0.8 0.5 -1.1 -1.6 -0.2 -0.4 -0.3 0.2 -0.6 -0.6 1.3 -0.0 0.8 -0.0 1.6 -0.9 -0.5 -0.7 0.2 1.0 -0.5 -0.0 0.1 -0.6 -0.7 0.7 -2.3 0.9 2.1 0.9 -1.0 -0.1 Chi-square with 42 degrees of freedom:45.970528 z-score=0.433220, p-value=0.688832 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-08_00:31 Test no p-value 1 0.433155 2 0.150510 3 0.899371 4 0.457763 5 0.840306 6 0.012994 7 0.025909 8 0.187363 9 0.035792 10 0.126794 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.024509 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-08_00:31: (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 66376 1.27 66828 0.39 3 25000.00 25143 0.82 24723 3.07 4 6666.67 6738 0.76 6778 1.86 5 1388.89 1454 3.05 1401 0.11 6 238.10 249 0.50 227 0.52 7 34.72 35 0.00 36 0.05 8 4.96 4 0.19 6 0.22 p=0.63940 p=0.59955 Number of rngs required: 688846, p-value: 0.695 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-08_00:31 No. of wins: Observed Expected 98280 98585.9 z-score=-1.368, pvalue=0.08566 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66608 66666.7 0.052 0.052 2 38152 37654.3 6.578 6.629 3 26968 26954.7 0.007 6.636 4 19383 19313.5 0.250 6.886 5 13679 13851.4 2.146 9.033 6 9886 9943.5 0.333 9.366 7 7083 7145.0 0.538 9.904 8 5021 5139.1 2.713 12.617 9 3603 3699.9 2.536 15.153 10 2628 2666.3 0.550 15.703 11 1917 1923.3 0.021 15.724 12 1377 1388.7 0.099 15.823 13 1003 1003.7 0.001 15.823 14 708 726.1 0.453 16.277 15 559 525.8 2.092 18.368 16 350 381.2 2.546 20.914 17 278 276.5 0.008 20.922 18 205 200.8 0.087 21.008 19 147 146.0 0.007 21.016 20 124 106.2 2.978 23.993 21 321 287.1 3.999 27.993 Chisq= 27.99 for 20 degrees of freedom, p= 0.89043 SUMMARY of craptest p-value for no. of wins: 0.085659 p-value for throws/game: 0.890430 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-08_00:31 No. of wins: Observed Expected 98734 98585.9 z-score= 0.663, pvalue=0.74620 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66689 66666.7 0.007 0.007 2 37911 37654.3 1.750 1.757 3 27098 26954.7 0.761 2.519 4 19463 19313.5 1.158 3.676 5 13633 13851.4 3.444 7.121 6 9957 9943.5 0.018 7.139 7 6962 7145.0 4.688 11.827 8 5078 5139.1 0.726 12.553 9 3665 3699.9 0.329 12.882 10 2583 2666.3 2.602 15.484 11 1890 1923.3 0.578 16.061 12 1356 1388.7 0.772 16.833 13 1017 1003.7 0.176 17.009 14 747 726.1 0.599 17.608 15 515 525.8 0.223 17.832 16 360 381.2 1.174 19.005 17 301 276.5 2.164 21.169 18 211 200.8 0.515 21.684 19 164 146.0 2.223 23.907 20 103 106.2 0.097 24.005 21 297 287.1 0.340 24.345 Chisq= 24.34 for 20 degrees of freedom, p= 0.77235 SUMMARY of craptest p-value for no. of wins: 0.746199 p-value for throws/game: 0.772350 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0032,0.0071,0.0101,0.0105,0.0130,0.0177,0.0210,0.0225,0.0245,0.0259, 0.0272,0.0303,0.0310,0.0338,0.0358,0.0361,0.0384,0.0406,0.0459,0.0466, 0.0510,0.0514,0.0516,0.0574,0.0601,0.0613,0.0671,0.0723,0.0785,0.0857, 0.0918,0.0929,0.0930,0.1026,0.1026,0.1086,0.1161,0.1223,0.1243,0.1261, 0.1268,0.1277,0.1297,0.1332,0.1339,0.1385,0.1428,0.1479,0.1496,0.1505, 0.1540,0.1646,0.1676,0.1680,0.1695,0.1738,0.1747,0.1783,0.1788,0.1849, 0.1874,0.1899,0.1910,0.1929,0.2029,0.2038,0.2067,0.2113,0.2138,0.2166, 0.2214,0.2260,0.2264,0.2278,0.2328,0.2365,0.2430,0.2529,0.2545,0.2582, 0.2613,0.2629,0.2670,0.2750,0.2893,0.2903,0.2985,0.3016,0.3056,0.3061, 0.3066,0.3083,0.3179,0.3188,0.3220,0.3232,0.3244,0.3255,0.3314,0.3448, 0.3454,0.3671,0.3795,0.3797,0.3823,0.3885,0.3924,0.4097,0.4097,0.4118, 0.4138,0.4144,0.4178,0.4203,0.4256,0.4258,0.4269,0.4275,0.4275,0.4332, 0.4338,0.4352,0.4379,0.4455,0.4506,0.4577,0.4578,0.4672,0.4688,0.4718, 0.4734,0.4749,0.4773,0.4789,0.4817,0.4827,0.4872,0.4891,0.4899,0.4940, 0.4969,0.4997,0.5008,0.5013,0.5016,0.5068,0.5117,0.5233,0.5243,0.5278, 0.5290,0.5462,0.5510,0.5516,0.5531,0.5536,0.5626,0.5632,0.5669,0.5691, 0.5740,0.5805,0.5907,0.5996,0.6042,0.6054,0.6066,0.6077,0.6091,0.6104, 0.6122,0.6192,0.6237,0.6253,0.6254,0.6268,0.6284,0.6293,0.6298,0.6331, 0.6374,0.6379,0.6394,0.6424,0.6428,0.6595,0.6759,0.6800,0.6806,0.6829, 0.6872,0.6888,0.6952,0.6957,0.6959,0.6983,0.7004,0.7036,0.7045,0.7072, 0.7191,0.7209,0.7309,0.7322,0.7405,0.7462,0.7540,0.7619,0.7718,0.7724, 0.7735,0.7746,0.7752,0.7787,0.7860,0.7868,0.7880,0.7970,0.7977,0.7996, 0.7998,0.8017,0.8023,0.8087,0.8111,0.8130,0.8267,0.8296,0.8325,0.8403, 0.8424,0.8461,0.8461,0.8493,0.8517,0.8520,0.8586,0.8634,0.8683,0.8711, 0.8732,0.8802,0.8825,0.8880,0.8888,0.8904,0.8943,0.8994,0.9051,0.9052, 0.9099,0.9152,0.9202,0.9245,0.9292,0.9362,0.9390,0.9419,0.9451,0.9551, 0.9573,0.9598,0.9620,0.9655,0.9778,0.9817,0.9849,0.9911,0.9966, Overall p-value after applying KStest on 269 p-values = 0.301284 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.