RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-13_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.52 21.2114 0.783025 2 to 25 15.66 20.0202 0.726801 3 to 26 15.86 7.8600 0.030551 4 to 27 15.94 26.3945 0.932433 5 to 28 15.80 21.8644 0.810008 6 to 29 15.72 12.8243 0.252137 7 to 30 15.83 23.1200 0.854616 8 to 31 16.03 11.1857 0.153253 9 to 32 15.74 11.3339 0.161314 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.550239 Tough bday spacings test for dh-ranFile-2016-02-13_04:31: 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 79 87 99 85 54 24 15 7 4 (O-E)^2/E 0.1 0.1 0.4 1.2 0.0 0.6 0.1 1.1 0.0 0.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 3.646, p= 0.038 RESULTS OF GCD FOR dh-ranFile-2016-02-13_04:31 Euclid's algorithm: p-value, steps to gcd: 0.127805 p-value, dist. of gcd's: 0.476696 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-13_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.290 0.037 0.553 0.317 0.678 0.626 0.303 0.839 Bits 8 to 15---> 0.141 0.947 0.967 0.186 0.645 0.810 0.062 0.335 Bits 16 to 23---> 0.910 0.504 0.440 0.605 0.338 0.109 0.797 0.450 Bits 24 to 31---> 0.070 0.740 0.227 0.619 0.876 0.713 0.441 0.676 KS test for the above 32 p values: 0.002 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-13_04:31, p-values for 5 runs: 0.1622, 0.8109, 0.2888, 0.0900, 0.6911 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-13_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 224 211.4 0.749 0.749 r= 29 5135 5134.0 0.000 0.749 r= 30 23169 23103.0 0.188 0.937 r= 31 11472 11551.5 0.547 1.485 chi-square = 1.485 with df = 3; p-value = 0.314 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-13_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5179 5134.0 0.394 0.589 r= 31 23040 23103.0 0.172 0.761 r= 32 11576 11551.5 0.052 0.813 chi-square = 0.813 with df = 3; p-value = 0.154 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-13_04:31 b-rank test for bits 1 to 8, p=0.88257 b-rank test for bits 2 to 9, p=0.49177 b-rank test for bits 3 to 10, p=0.13220 b-rank test for bits 4 to 11, p=0.42538 b-rank test for bits 5 to 12, p=0.59846 b-rank test for bits 6 to 13, p=0.34379 b-rank test for bits 7 to 14, p=0.00601 b-rank test for bits 8 to 15, p=0.75212 b-rank test for bits 9 to 16, p=0.29493 b-rank test for bits 10 to 17, p=0.63815 b-rank test for bits 11 to 18, p=0.51006 b-rank test for bits 12 to 19, p=0.61242 b-rank test for bits 13 to 20, p=0.44426 b-rank test for bits 14 to 21, p=0.37694 b-rank test for bits 15 to 22, p=0.09758 b-rank test for bits 16 to 23, p=0.12931 b-rank test for bits 17 to 24, p=0.43276 b-rank test for bits 18 to 25, p=0.55221 b-rank test for bits 19 to 26, p=0.74435 b-rank test for bits 20 to 27, p=0.07199 b-rank test for bits 21 to 28, p=0.64907 b-rank test for bits 22 to 29, p=0.80562 b-rank test for bits 23 to 30, p=0.40876 b-rank test for bits 24 to 31, p=0.97198 b-rank test for bits 25 to 32, p=0.10597 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 = 0.625022 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-13_04:31 (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 141892 -0.04 0.483851 2 142588 1.59 0.943594 3 141531 -0.88 0.188362 4 142386 1.11 0.867299 5 141743 -0.39 0.348778 6 141505 -0.94 0.172407 7 141881 -0.07 0.473613 8 141937 0.06 0.525774 9 141984 0.17 0.569249 10 142083 0.41 0.657545 11 141456 -1.06 0.144758 12 142980 2.50 0.993818 13 142806 2.10 0.981916 14 142742 1.95 0.974142 15 141186 -1.69 0.045512 16 142167 0.60 0.726424 17 141742 -0.39 0.347914 18 142670 1.78 0.962238 19 141696 -0.50 0.309089 20 142179 0.63 0.735676 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-13_04:31 Bits used No. missing words z-score p-value 23 to 32 141859 -0.1736 0.431109 22 to 31 142202 1.0092 0.843562 21 to 30 142172 0.9058 0.817468 20 to 29 141765 -0.4977 0.309351 19 to 28 141174 -2.5356 0.005612 18 to 27 141870 -0.1356 0.446061 17 to 26 142086 0.6092 0.728806 16 to 25 142083 0.5989 0.725368 15 to 24 142241 1.1437 0.873624 14 to 23 142359 1.5506 0.939500 13 to 22 142213 1.0471 0.852482 12 to 21 142064 0.5333 0.703103 11 to 20 142108 0.6851 0.753350 10 to 19 142061 0.5230 0.699513 9 to 18 142309 1.3782 0.915925 8 to 17 141962 0.1816 0.572060 7 to 16 141554 -1.2253 0.110236 6 to 15 141553 -1.2287 0.109588 5 to 14 142000 0.3127 0.622729 4 to 13 141926 0.0575 0.522920 3 to 12 142289 1.3092 0.904768 2 to 11 141959 0.1713 0.567997 1 to 10 141762 -0.5080 0.305715 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-13_04:31 Bits used No. missing words z-score p-value 28 to 32 141856 -0.1808 0.428270 27 to 31 142054 0.4904 0.688077 26 to 30 141713 -0.6655 0.252857 25 to 29 142317 1.3819 0.916504 24 to 28 141905 -0.0147 0.494145 23 to 27 142187 0.9413 0.826713 22 to 26 141789 -0.4079 0.341674 21 to 25 141986 0.2599 0.602529 20 to 24 141937 0.0938 0.537365 19 to 23 141892 -0.0587 0.476577 18 to 22 141821 -0.2994 0.382308 17 to 21 141837 -0.2452 0.403156 16 to 20 141776 -0.4520 0.325647 15 to 19 141870 -0.1333 0.446969 14 to 18 142083 0.5887 0.721973 13 to 17 141261 -2.1977 0.013984 12 to 16 142190 0.9514 0.829305 11 to 15 141784 -0.4248 0.335474 10 to 14 142040 0.4429 0.671099 9 to 13 141861 -0.1638 0.434932 8 to 12 142107 0.6701 0.748593 7 to 11 141793 -0.3943 0.346665 6 to 10 141921 0.0396 0.515778 5 to 9 141881 -0.0960 0.461747 4 to 8 141789 -0.4079 0.341674 3 to 7 141784 -0.4248 0.335474 2 to 6 141206 -2.3842 0.008559 1 to 5 141594 -1.0689 0.142554 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-13_04:31 Bits used No. missing words z-score p-value 31 to 32 141900 -0.0275 0.489022 30 to 31 141761 -0.4376 0.330856 29 to 30 141688 -0.6529 0.256913 28 to 29 142223 0.9253 0.822590 27 to 28 141773 -0.4022 0.343786 26 to 27 141809 -0.2960 0.383631 25 to 26 142050 0.4150 0.660913 24 to 25 142453 1.6037 0.945615 23 to 24 142193 0.8368 0.798643 22 to 23 141897 -0.0364 0.485493 21 to 22 141857 -0.1544 0.438661 20 to 21 141750 -0.4700 0.319178 19 to 20 141477 -1.2753 0.101100 18 to 19 142139 0.6775 0.750953 17 to 18 142069 0.4710 0.681181 16 to 17 142088 0.5271 0.700921 15 to 16 141565 -1.0157 0.154881 14 to 15 141833 -0.2252 0.410927 13 to 14 141815 -0.2783 0.390407 12 to 13 141716 -0.5703 0.284239 11 to 12 141710 -0.5880 0.278268 10 to 11 142793 2.6067 0.995429 9 to 10 142088 0.5271 0.700921 8 to 9 142226 0.9341 0.824882 7 to 8 142413 1.4858 0.931328 6 to 7 142175 0.7837 0.783388 5 to 6 141507 -1.1868 0.117650 4 to 5 142022 0.3324 0.630191 3 to 4 141727 -0.5378 0.295342 2 to 3 141657 -0.7443 0.228337 1 to 2 142883 2.8722 0.997962 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-13_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2536.33 0.514 0.696295 Test results for specific bytes for dh-ranFile-2016-02-13_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2450.98 -0.693 0.244098 2 to 9 2457.36 -0.603 0.273268 3 to 10 2281.68 -3.088 0.001009 4 to 11 2511.12 0.157 0.562456 5 to 12 2423.63 -1.080 0.140078 6 to 13 2448.16 -0.733 0.231736 7 to 14 2421.50 -1.110 0.133476 8 to 15 2293.38 -2.922 0.001738 9 to 16 2467.84 -0.455 0.324647 10 to 17 2450.36 -0.702 0.241331 11 to 18 2619.29 1.687 0.954196 12 to 19 2417.26 -1.170 0.120988 13 to 20 2477.89 -0.313 0.377248 14 to 21 2579.97 1.131 0.870963 15 to 22 2500.13 0.002 0.500726 16 to 23 2482.98 -0.241 0.404919 17 to 24 2522.41 0.317 0.624357 18 to 25 2565.86 0.931 0.824164 19 to 26 2485.09 -0.211 0.416477 20 to 27 2461.31 -0.547 0.292139 21 to 28 2591.38 1.292 0.901872 22 to 29 2544.62 0.631 0.736004 23 to 30 2597.72 1.382 0.916510 24 to 31 2500.45 0.006 0.502525 25 to 32 2618.11 1.670 0.952571 CDPARK for dh-ranFile-2016-02-13_04:31: 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 3544 0.9589 0.831196 3561 1.7352 0.958644 3540 0.7763 0.781201 3526 0.1370 0.554479 3508 -0.6849 0.246694 3506 -0.7763 0.218799 3544 0.9589 0.831196 3497 -1.1872 0.117571 3549 1.1872 0.882429 3529 0.2740 0.607947 Square side=100, avg. no. parked=3530.40 sample std.=19.95 p-value of the KSTEST for those 10 p-values: 0.390680 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-13_04:31 0.5939,0.8493,0.1608,0.1689,0.1634,0.5312,0.5335,0.6739,0.3477,0.8752, The KS test for those 10 p-values: 0.876203 The 3DSPHERES test for dh-ranFile-2016-02-13_04:31 sample no r^3 equiv. uni. 1 33.700 0.674804 2 7.755 0.227781 3 22.404 0.526120 4 1.574 0.051113 5 63.069 0.877826 6 8.989 0.258911 7 38.765 0.725324 8 47.205 0.792684 9 97.717 0.961505 10 63.807 0.880792 11 72.870 0.911874 12 16.037 0.414073 13 16.504 0.423123 14 101.259 0.965792 15 0.955 0.031323 16 13.260 0.357260 17 1.800 0.058246 18 10.225 0.288826 19 10.178 0.287702 20 19.962 0.485932 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.867913 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-13_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.3 1.1 -0.4 0.5 0.2 0.5 0.6 0.4 0.6 0.8 0.4 0.7 -1.1 -0.1 -0.2 0.5 -1.0 -1.1 0.2 -0.9 0.9 0.7 -0.1 -0.5 -1.0 1.6 0.8 0.1 -0.6 1.0 -1.5 -0.1 -0.1 -0.2 0.4 -1.4 -0.1 0.1 1.5 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:26.879348 z-score=-1.649798, p-value=0.033736 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-13_04:31 Test no p-value 1 0.308512 2 0.130889 3 0.053937 4 0.000523 5 0.000782 6 0.025175 7 0.203526 8 0.264181 9 0.596605 10 0.189181 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000069 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-13_04:31: (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 66710 0.03 66617 0.04 3 25000.00 24856 0.83 25044 0.08 4 6666.67 6745 0.92 6711 0.29 5 1388.89 1398 0.06 1375 0.14 6 238.10 253 0.93 209 3.56 7 34.72 31 0.40 38 0.31 8 4.96 6 0.22 5 0.00 p=0.24111 p=0.37913 Number of rngs required: 688852, p-value: 0.698 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-13_04:31 No. of wins: Observed Expected 98733 98585.9 z-score= 0.658, pvalue=0.74476 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66973 66666.7 1.408 1.408 2 37327 37654.3 2.845 4.253 3 26904 26954.7 0.095 4.348 4 19467 19313.5 1.221 5.569 5 13725 13851.4 1.154 6.723 6 9959 9943.5 0.024 6.747 7 7113 7145.0 0.144 6.890 8 5203 5139.1 0.795 7.686 9 3689 3699.9 0.032 7.718 10 2587 2666.3 2.358 10.076 11 1978 1923.3 1.554 11.630 12 1412 1388.7 0.390 12.019 13 978 1003.7 0.659 12.678 14 744 726.1 0.439 13.118 15 530 525.8 0.033 13.151 16 391 381.2 0.255 13.405 17 298 276.5 1.665 15.070 18 204 200.8 0.050 15.121 19 129 146.0 1.976 17.097 20 106 106.2 0.000 17.097 21 283 287.1 0.059 17.156 Chisq= 17.16 for 20 degrees of freedom, p= 0.35717 SUMMARY of craptest p-value for no. of wins: 0.744764 p-value for throws/game: 0.357174 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-13_04:31 No. of wins: Observed Expected 98207 98585.9 z-score=-1.694, pvalue=0.04509 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66414 66666.7 0.958 0.958 2 37471 37654.3 0.893 1.850 3 27309 26954.7 4.656 6.506 4 19268 19313.5 0.107 6.613 5 13944 13851.4 0.619 7.232 6 9979 9943.5 0.126 7.358 7 7242 7145.0 1.316 8.675 8 5156 5139.1 0.056 8.730 9 3739 3699.9 0.414 9.144 10 2580 2666.3 2.793 11.937 11 1873 1923.3 1.317 13.254 12 1321 1388.7 3.304 16.559 13 994 1003.7 0.094 16.653 14 737 726.1 0.162 16.815 15 556 525.8 1.730 18.545 16 378 381.2 0.026 18.572 17 271 276.5 0.111 18.683 18 209 200.8 0.332 19.015 19 166 146.0 2.744 21.759 20 107 106.2 0.006 21.765 21 286 287.1 0.004 21.769 Chisq= 21.77 for 20 degrees of freedom, p= 0.64684 SUMMARY of craptest p-value for no. of wins: 0.045087 p-value for throws/game: 0.646841 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0005,0.0008,0.0010,0.0017,0.0017,0.0056,0.0060,0.0086,0.0140, 0.0252,0.0306,0.0313,0.0337,0.0367,0.0381,0.0451,0.0455,0.0511,0.0539, 0.0582,0.0624,0.0695,0.0720,0.0900,0.0976,0.1011,0.1060,0.1093,0.1096, 0.1102,0.1176,0.1177,0.1210,0.1278,0.1293,0.1309,0.1322,0.1335,0.1401, 0.1412,0.1426,0.1448,0.1533,0.1536,0.1549,0.1608,0.1613,0.1622,0.1634, 0.1689,0.1724,0.1857,0.1884,0.1892,0.2035,0.2188,0.2273,0.2278,0.2283, 0.2317,0.2411,0.2413,0.2441,0.2467,0.2521,0.2529,0.2569,0.2589,0.2642, 0.2733,0.2783,0.2842,0.2877,0.2888,0.2888,0.2904,0.2921,0.2949,0.2953, 0.3028,0.3057,0.3085,0.3091,0.3094,0.3142,0.3167,0.3192,0.3246,0.3256, 0.3309,0.3354,0.3355,0.3355,0.3381,0.3417,0.3417,0.3438,0.3438,0.3467, 0.3477,0.3479,0.3488,0.3572,0.3573,0.3769,0.3772,0.3791,0.3823,0.3836, 0.3904,0.3907,0.4032,0.4049,0.4088,0.4109,0.4141,0.4165,0.4231,0.4254, 0.4283,0.4311,0.4328,0.4349,0.4387,0.4396,0.4409,0.4443,0.4461,0.4470, 0.4499,0.4617,0.4736,0.4766,0.4767,0.4839,0.4855,0.4859,0.4890,0.4918, 0.4941,0.5007,0.5025,0.5040,0.5101,0.5158,0.5229,0.5258,0.5261,0.5312, 0.5335,0.5374,0.5502,0.5522,0.5526,0.5545,0.5625,0.5680,0.5692,0.5721, 0.5939,0.5966,0.5985,0.6025,0.6051,0.6079,0.6124,0.6195,0.6227,0.6244, 0.6250,0.6256,0.6302,0.6382,0.6448,0.6468,0.6491,0.6575,0.6609,0.6711, 0.6739,0.6748,0.6763,0.6778,0.6812,0.6881,0.6911,0.6963,0.6976,0.6995, 0.7009,0.7009,0.7031,0.7130,0.7220,0.7253,0.7254,0.7264,0.7268,0.7288, 0.7357,0.7360,0.7400,0.7444,0.7448,0.7486,0.7510,0.7521,0.7533,0.7812, 0.7830,0.7834,0.7927,0.7969,0.7986,0.8056,0.8100,0.8103,0.8109,0.8175, 0.8226,0.8242,0.8249,0.8267,0.8293,0.8312,0.8312,0.8389,0.8436,0.8493, 0.8525,0.8546,0.8673,0.8679,0.8710,0.8736,0.8752,0.8762,0.8765,0.8778, 0.8808,0.8824,0.8826,0.9019,0.9048,0.9096,0.9119,0.9159,0.9165,0.9165, 0.9313,0.9324,0.9395,0.9436,0.9456,0.9467,0.9526,0.9542,0.9586,0.9615, 0.9622,0.9658,0.9668,0.9720,0.9741,0.9819,0.9938,0.9954,0.9980, Overall p-value after applying KStest on 269 p-values = 0.584001 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.