RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-22_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 15.47 30.7454 0.978556 2 to 25 15.34 26.6010 0.935815 3 to 26 15.69 18.7290 0.655692 4 to 27 15.61 28.3905 0.959423 5 to 28 16.08 22.1026 0.819194 6 to 29 16.19 23.2081 0.857402 7 to 30 16.01 8.1184 0.036051 8 to 31 15.88 24.8027 0.900787 9 to 32 16.07 14.1634 0.344497 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.011293 Tough bday spacings test for dh-ranFile-2015-06-22_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 18 37 68 88 101 82 60 28 12 3 3 (O-E)^2/E 8.5 0.0 0.4 1.0 0.1 0.2 1.2 0.1 0.6 2.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 14.300, p= 0.840 RESULTS OF GCD FOR dh-ranFile-2015-06-22_04:31 Euclid's algorithm: p-value, steps to gcd: 0.089301 p-value, dist. of gcd's: 0.442546 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-22_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.776 0.857 0.280 0.086 0.527 0.201 0.427 0.433 Bits 8 to 15---> 0.318 0.959 0.489 0.285 0.735 0.181 0.251 0.271 Bits 16 to 23---> 0.316 0.124 0.880 0.791 0.537 0.170 0.900 0.155 Bits 24 to 31---> 0.058 0.285 0.185 0.948 0.847 0.956 0.908 0.634 KS test for the above 32 p values: 0.422 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-22_04:31, p-values for 5 runs: 0.8486, 0.3127, 0.3288, 0.5656, 0.3899 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-22_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 5067 5134.0 0.875 2.150 r= 30 23018 23103.0 0.313 2.463 r= 31 11720 11551.5 2.457 4.920 chi-square = 4.920 with df = 3; p-value = 0.822 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-22_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 237 211.4 3.095 3.095 r= 30 5238 5134.0 2.106 5.202 r= 31 22998 23103.0 0.478 5.679 r= 32 11527 11551.5 0.052 5.731 chi-square = 5.731 with df = 3; p-value = 0.875 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-22_04:31 b-rank test for bits 1 to 8, p=0.35709 b-rank test for bits 2 to 9, p=0.94939 b-rank test for bits 3 to 10, p=0.00244 b-rank test for bits 4 to 11, p=0.90186 b-rank test for bits 5 to 12, p=0.00161 b-rank test for bits 6 to 13, p=0.07071 b-rank test for bits 7 to 14, p=0.20427 b-rank test for bits 8 to 15, p=0.04512 b-rank test for bits 9 to 16, p=0.33320 b-rank test for bits 10 to 17, p=0.62286 b-rank test for bits 11 to 18, p=0.84008 b-rank test for bits 12 to 19, p=0.88412 b-rank test for bits 13 to 20, p=0.51708 b-rank test for bits 14 to 21, p=0.39981 b-rank test for bits 15 to 22, p=0.84521 b-rank test for bits 16 to 23, p=0.77109 b-rank test for bits 17 to 24, p=0.92391 b-rank test for bits 18 to 25, p=0.47766 b-rank test for bits 19 to 26, p=0.94791 b-rank test for bits 20 to 27, p=0.93882 b-rank test for bits 21 to 28, p=0.84946 b-rank test for bits 22 to 29, p=0.29412 b-rank test for bits 23 to 30, p=0.75851 b-rank test for bits 24 to 31, p=0.28801 b-rank test for bits 25 to 32, p=0.23666 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 = 0.188904 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-22_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 141776 -0.31 0.377703 2 142537 1.47 0.928746 3 142751 1.97 0.975381 4 141623 -0.67 0.251749 5 140997 -2.13 0.016519 6 142220 0.73 0.766039 7 141552 -0.83 0.201892 8 141837 -0.17 0.432900 9 140973 -2.19 0.014346 10 141625 -0.66 0.253242 11 141693 -0.51 0.306624 12 142153 0.57 0.715431 13 142006 0.23 0.589347 14 141334 -1.34 0.089437 15 140906 -2.34 0.009533 16 141641 -0.63 0.265350 17 141669 -0.56 0.287222 18 141760 -0.35 0.363582 19 142117 0.49 0.686236 20 142636 1.70 0.955230 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-22_04:31 Bits used No. missing words z-score p-value 23 to 32 141976 0.2299 0.590914 22 to 31 142150 0.8299 0.796701 21 to 30 142284 1.2920 0.901815 20 to 29 141366 -1.8736 0.030496 19 to 28 141961 0.1782 0.570706 18 to 27 142109 0.6885 0.754436 17 to 26 141917 0.0264 0.510550 16 to 25 141684 -0.7770 0.218579 15 to 24 142066 0.5402 0.705485 14 to 23 142131 0.7644 0.777679 13 to 22 142016 0.3678 0.643499 12 to 21 141741 -0.5804 0.280806 11 to 20 142153 0.8402 0.799614 10 to 19 142149 0.8264 0.795725 9 to 18 142229 1.1023 0.864837 8 to 17 141599 -1.0701 0.142286 7 to 16 141455 -1.5667 0.058598 6 to 15 141899 -0.0356 0.485792 5 to 14 142367 1.5782 0.942737 4 to 13 142124 0.7402 0.770423 3 to 12 141891 -0.0632 0.474801 2 to 11 141726 -0.6322 0.263637 1 to 10 142131 0.7644 0.777679 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-22_04:31 Bits used No. missing words z-score p-value 28 to 32 142025 0.3921 0.652509 27 to 31 142063 0.5209 0.698787 26 to 30 142179 0.9141 0.819677 25 to 29 141886 -0.0791 0.468483 24 to 28 141769 -0.4757 0.317146 23 to 27 141771 -0.4689 0.319565 22 to 26 141937 0.0938 0.537365 21 to 25 141771 -0.4689 0.319565 20 to 24 141818 -0.3096 0.378435 19 to 23 141973 0.2158 0.585440 18 to 22 141870 -0.1333 0.446969 17 to 21 142516 2.0565 0.980133 16 to 20 141939 0.1006 0.540057 15 to 19 142068 0.5379 0.704665 14 to 18 141759 -0.5096 0.305168 13 to 17 142219 1.0497 0.853079 12 to 16 141921 0.0396 0.515778 11 to 15 141484 -1.4418 0.074680 10 to 14 141644 -0.8994 0.184214 9 to 13 141642 -0.9062 0.182414 8 to 12 141835 -0.2520 0.400534 7 to 11 141945 0.1209 0.548121 6 to 10 141881 -0.0960 0.461747 5 to 9 142102 0.6531 0.743160 4 to 8 141967 0.1955 0.577496 3 to 7 141847 -0.2113 0.416331 2 to 6 142045 0.4599 0.677205 1 to 5 142004 0.3209 0.625863 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-22_04:31 Bits used No. missing words z-score p-value 31 to 32 141194 -2.1101 0.017424 30 to 31 141700 -0.6175 0.268455 29 to 30 141839 -0.2075 0.417824 28 to 29 142278 1.0875 0.861597 27 to 28 141769 -0.4140 0.339454 26 to 27 142039 0.3825 0.648958 25 to 26 142163 0.7483 0.772857 24 to 25 142336 1.2586 0.895915 23 to 24 141883 -0.0777 0.469045 22 to 23 142523 1.8102 0.964870 21 to 22 142102 0.5683 0.715101 20 to 21 141559 -1.0334 0.150703 19 to 20 141323 -1.7296 0.041852 18 to 19 142179 0.7955 0.786835 17 to 18 141850 -0.1750 0.430534 16 to 17 142261 1.0374 0.850219 15 to 16 141673 -0.6971 0.242858 14 to 15 141858 -0.1514 0.439824 13 to 14 141584 -0.9597 0.168609 12 to 13 141571 -0.9980 0.159134 11 to 12 141522 -1.1426 0.126609 10 to 11 142215 0.9017 0.816387 9 to 10 141874 -0.1042 0.458498 8 to 9 141474 -1.2842 0.099543 7 to 8 141893 -0.0482 0.480790 6 to 7 141697 -0.6263 0.265545 5 to 6 141184 -2.1396 0.016193 4 to 5 141976 0.1967 0.577956 3 to 4 142194 0.8397 0.799471 2 to 3 141769 -0.4140 0.339454 1 to 2 141885 -0.0718 0.471393 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-22_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2497.05 -0.042 0.483373 Test results for specific bytes for dh-ranFile-2015-06-22_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2512.33 0.174 0.569207 2 to 9 2531.82 0.450 0.673627 3 to 10 2476.26 -0.336 0.368527 4 to 11 2567.15 0.950 0.828847 5 to 12 2467.34 -0.462 0.322070 6 to 13 2552.02 0.736 0.769046 7 to 14 2500.15 0.002 0.500846 8 to 15 2554.73 0.774 0.780531 9 to 16 2699.10 2.816 0.997567 10 to 17 2556.10 0.793 0.786209 11 to 18 2512.82 0.181 0.571935 12 to 19 2468.99 -0.439 0.330507 13 to 20 2440.64 -0.839 0.200598 14 to 21 2492.54 -0.106 0.457987 15 to 22 2546.31 0.655 0.743723 16 to 23 2506.29 0.089 0.535454 17 to 24 2446.57 -0.756 0.224939 18 to 25 2518.98 0.268 0.605807 19 to 26 2413.39 -1.225 0.110316 20 to 27 2499.03 -0.014 0.494540 21 to 28 2402.67 -1.376 0.084348 22 to 29 2628.17 1.813 0.965048 23 to 30 2565.90 0.932 0.824322 24 to 31 2568.73 0.972 0.834482 25 to 32 2591.60 1.295 0.902419 CDPARK for dh-ranFile-2015-06-22_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 3509 -0.6393 0.261324 3536 0.5936 0.723613 3521 -0.0913 0.463617 3511 -0.5479 0.291865 3533 0.4566 0.676028 3590 3.0594 0.998891 3493 -1.3699 0.085365 3548 1.1416 0.873180 3545 1.0046 0.842447 3508 -0.6849 0.246694 Square side=100, avg. no. parked=3529.40 sample std.=26.32 p-value of the KSTEST for those 10 p-values: 0.638865 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-22_04:31 0.0553,0.0444,0.1476,0.0334,0.5938,0.1815,0.4928,0.3890,0.2381,0.5819, The KS test for those 10 p-values: 0.019081 The 3DSPHERES test for dh-ranFile-2015-06-22_04:31 sample no r^3 equiv. uni. 1 5.597 0.170202 2 32.983 0.666942 3 1.581 0.051320 4 1.733 0.056144 5 7.072 0.210016 6 27.899 0.605437 7 87.393 0.945692 8 17.254 0.437369 9 51.331 0.819320 10 17.542 0.442745 11 21.532 0.512147 12 2.100 0.067595 13 15.115 0.395790 14 38.526 0.723131 15 28.686 0.615645 16 30.320 0.636023 17 25.923 0.578574 18 27.388 0.598649 19 6.447 0.193390 20 46.585 0.788353 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.718132 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-22_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.5 0.1 -1.1 -0.8 -0.6 -0.2 0.7 -0.8 -1.0 -0.7 1.7 3.0 -1.1 -0.2 -1.5 -0.4 1.1 1.2 -1.3 -0.3 1.0 0.9 -0.6 0.2 -0.1 -1.0 0.9 -1.0 -1.0 -0.2 -1.5 -0.4 0.1 0.1 -1.0 1.0 -0.7 -0.4 -0.7 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:39.433193 z-score=-0.280062, p-value=0.415748 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-22_04:31 Test no p-value 1 0.616913 2 0.229481 3 0.035149 4 0.317214 5 0.321513 6 0.087909 7 0.280582 8 0.567303 9 0.484522 10 0.058444 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.044668 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-22_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 66790 0.23 66783 0.20 3 25000.00 24985 0.01 24892 0.47 4 6666.67 6588 0.93 6672 0.00 5 1388.89 1369 0.28 1367 0.35 6 238.10 226 0.61 259 1.84 7 34.72 39 0.53 23 3.96 8 4.96 2 1.77 3 0.77 p=0.37176 p=0.72989 Number of rngs required: 687128, p-value: 0.068 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-22_04:31 No. of wins: Observed Expected 98506 98585.9 z-score=-0.357, pvalue=0.36048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67072 66666.7 2.464 2.464 2 37656 37654.3 0.000 2.465 3 26889 26954.7 0.160 2.625 4 19315 19313.5 0.000 2.625 5 13756 13851.4 0.657 3.282 6 9891 9943.5 0.278 3.560 7 7197 7145.0 0.378 3.938 8 5043 5139.1 1.796 5.734 9 3679 3699.9 0.118 5.852 10 2622 2666.3 0.736 6.588 11 1881 1923.3 0.932 7.519 12 1417 1388.7 0.575 8.094 13 989 1003.7 0.216 8.310 14 710 726.1 0.359 8.669 15 538 525.8 0.281 8.950 16 355 381.2 1.794 10.744 17 268 276.5 0.264 11.008 18 206 200.8 0.133 11.141 19 139 146.0 0.334 11.475 20 116 106.2 0.901 12.377 21 261 287.1 2.375 14.752 Chisq= 14.75 for 20 degrees of freedom, p= 0.20957 SUMMARY of craptest p-value for no. of wins: 0.360481 p-value for throws/game: 0.209573 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-22_04:31 No. of wins: Observed Expected 98315 98585.9 z-score=-1.211, pvalue=0.11286 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66902 66666.7 0.831 0.831 2 37608 37654.3 0.057 0.888 3 26917 26954.7 0.053 0.941 4 19156 19313.5 1.284 2.224 5 13984 13851.4 1.269 3.493 6 9902 9943.5 0.174 3.667 7 7204 7145.0 0.487 4.154 8 5066 5139.1 1.039 5.193 9 3695 3699.9 0.006 5.199 10 2588 2666.3 2.299 7.498 11 1912 1923.3 0.067 7.565 12 1359 1388.7 0.637 8.202 13 940 1003.7 4.045 12.247 14 785 726.1 4.771 17.018 15 533 525.8 0.098 17.115 16 387 381.2 0.090 17.205 17 263 276.5 0.663 17.868 18 218 200.8 1.468 19.336 19 153 146.0 0.337 19.673 20 132 106.2 6.260 25.932 21 296 287.1 0.275 26.207 Chisq= 26.21 for 20 degrees of freedom, p= 0.84093 SUMMARY of craptest p-value for no. of wins: 0.112864 p-value for throws/game: 0.840931 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0024,0.0095,0.0113,0.0143,0.0162,0.0165,0.0174,0.0191,0.0305, 0.0334,0.0351,0.0361,0.0419,0.0444,0.0447,0.0451,0.0513,0.0553,0.0561, 0.0581,0.0584,0.0586,0.0676,0.0682,0.0707,0.0747,0.0843,0.0854,0.0860, 0.0879,0.0893,0.0894,0.0995,0.1103,0.1129,0.1241,0.1266,0.1423,0.1476, 0.1507,0.1550,0.1591,0.1686,0.1702,0.1704,0.1809,0.1815,0.1824,0.1842, 0.1850,0.1889,0.1934,0.2006,0.2006,0.2019,0.2043,0.2096,0.2100,0.2186, 0.2249,0.2295,0.2367,0.2381,0.2429,0.2467,0.2512,0.2517,0.2532,0.2613, 0.2636,0.2653,0.2655,0.2685,0.2705,0.2800,0.2806,0.2808,0.2850,0.2851, 0.2872,0.2880,0.2919,0.2941,0.3052,0.3066,0.3127,0.3158,0.3171,0.3172, 0.3180,0.3196,0.3196,0.3215,0.3221,0.3288,0.3305,0.3332,0.3395,0.3395, 0.3445,0.3571,0.3605,0.3636,0.3685,0.3718,0.3777,0.3784,0.3890,0.3899, 0.3958,0.3998,0.4005,0.4157,0.4163,0.4178,0.4224,0.4273,0.4305,0.4329, 0.4333,0.4374,0.4398,0.4425,0.4427,0.4470,0.4580,0.4585,0.4617,0.4636, 0.4685,0.4690,0.4714,0.4748,0.4777,0.4808,0.4834,0.4845,0.4858,0.4889, 0.4928,0.4945,0.5008,0.5106,0.5121,0.5158,0.5171,0.5274,0.5355,0.5365, 0.5374,0.5401,0.5481,0.5656,0.5673,0.5692,0.5707,0.5719,0.5775,0.5780, 0.5786,0.5819,0.5854,0.5893,0.5909,0.5938,0.5986,0.6054,0.6058,0.6156, 0.6169,0.6229,0.6259,0.6343,0.6360,0.6389,0.6435,0.6490,0.6525,0.6557, 0.6669,0.6736,0.6760,0.6772,0.6862,0.6988,0.7047,0.7055,0.7151,0.7154, 0.7181,0.7231,0.7236,0.7299,0.7353,0.7432,0.7437,0.7544,0.7585,0.7660, 0.7690,0.7704,0.7711,0.7729,0.7757,0.7777,0.7777,0.7805,0.7862,0.7868, 0.7884,0.7906,0.7957,0.7967,0.7995,0.7996,0.8164,0.8192,0.8193,0.8197, 0.8222,0.8243,0.8288,0.8345,0.8401,0.8403,0.8409,0.8424,0.8452,0.8470, 0.8486,0.8495,0.8502,0.8531,0.8571,0.8574,0.8616,0.8648,0.8732,0.8746, 0.8801,0.8841,0.8959,0.8995,0.9008,0.9018,0.9019,0.9024,0.9081,0.9239, 0.9287,0.9358,0.9388,0.9427,0.9457,0.9475,0.9479,0.9494,0.9552,0.9561, 0.9586,0.9594,0.9649,0.9650,0.9754,0.9786,0.9801,0.9976,0.9989, Overall p-value after applying KStest on 269 p-values = 0.816832 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.