RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-28_08:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.93 14.9365 0.399946 2 to 25 15.63 11.9672 0.197878 3 to 26 15.35 33.5201 0.990323 4 to 27 15.97 30.4265 0.976571 5 to 28 16.26 13.9530 0.329572 6 to 29 16.03 14.2529 0.350871 7 to 30 15.92 11.5816 0.175219 8 to 31 15.73 24.6989 0.898344 9 to 32 15.75 13.7596 0.315957 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.248568 Tough bday spacings test for dh-ranFile-2016-02-28_08:31: 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 17 41 78 95 88 87 49 23 11 8 3 (O-E)^2/E 6.7 0.5 0.3 0.1 1.0 1.0 0.2 1.5 1.0 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 12.887, p= 0.770 RESULTS OF GCD FOR dh-ranFile-2016-02-28_08:31 Euclid's algorithm: p-value, steps to gcd: 0.161550 p-value, dist. of gcd's: 0.622001 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-28_08:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.010 0.659 0.454 0.830 0.289 0.034 0.181 0.198 Bits 8 to 15---> 0.811 0.284 0.770 0.813 0.324 0.698 0.039 0.750 Bits 16 to 23---> 0.707 0.502 0.369 0.034 0.493 0.519 0.613 0.445 Bits 24 to 31---> 0.203 0.921 0.997 0.205 0.631 0.191 0.668 0.797 KS test for the above 32 p values: 0.191 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-28_08:31, p-values for 5 runs: 0.6259, 0.2487, 0.5732, 0.4557, 0.7195 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-28_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 208 211.4 0.055 0.055 r= 29 5087 5134.0 0.430 0.486 r= 30 23072 23103.0 0.042 0.527 r= 31 11633 11551.5 0.575 1.102 chi-square = 1.102 with df = 3; p-value = 0.223 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-28_08:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5224 5134.0 1.577 1.638 r= 31 23027 23103.0 0.250 1.888 r= 32 11534 11551.5 0.027 1.915 chi-square = 1.915 with df = 3; p-value = 0.410 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-28_08:31 b-rank test for bits 1 to 8, p=0.60351 b-rank test for bits 2 to 9, p=0.90213 b-rank test for bits 3 to 10, p=0.07726 b-rank test for bits 4 to 11, p=0.31402 b-rank test for bits 5 to 12, p=0.51290 b-rank test for bits 6 to 13, p=0.90069 b-rank test for bits 7 to 14, p=0.14365 b-rank test for bits 8 to 15, p=0.14416 b-rank test for bits 9 to 16, p=0.73016 b-rank test for bits 10 to 17, p=0.81327 b-rank test for bits 11 to 18, p=0.67943 b-rank test for bits 12 to 19, p=0.37192 b-rank test for bits 13 to 20, p=0.09758 b-rank test for bits 14 to 21, p=0.13149 b-rank test for bits 15 to 22, p=0.51942 b-rank test for bits 16 to 23, p=0.60014 b-rank test for bits 17 to 24, p=0.45474 b-rank test for bits 18 to 25, p=0.27649 b-rank test for bits 19 to 26, p=0.38891 b-rank test for bits 20 to 27, p=0.61752 b-rank test for bits 21 to 28, p=0.54726 b-rank test for bits 22 to 29, p=0.42194 b-rank test for bits 23 to 30, p=0.85486 b-rank test for bits 24 to 31, p=0.62070 b-rank test for bits 25 to 32, p=0.16019 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 = 0.714612 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-28_08:31 (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 141947 0.09 0.535067 2 142056 0.34 0.634083 3 141478 -1.01 0.156780 4 142340 1.01 0.842850 5 142173 0.62 0.731070 6 141687 -0.52 0.301719 7 141384 -1.23 0.109835 8 141558 -0.82 0.205862 9 141815 -0.22 0.412781 10 141702 -0.48 0.314045 11 142217 0.72 0.763885 12 142375 1.09 0.861706 13 142551 1.50 0.933093 14 141076 -1.95 0.025765 15 142105 0.46 0.676227 16 142137 0.53 0.702616 17 142107 0.46 0.677904 18 141937 0.06 0.525774 19 142027 0.27 0.608315 20 141788 -0.28 0.388404 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-28_08:31 Bits used No. missing words z-score p-value 23 to 32 141520 -1.3425 0.089714 22 to 31 142262 1.2161 0.888027 21 to 30 141682 -0.7839 0.216550 20 to 29 141644 -0.9149 0.180114 19 to 28 142310 1.3816 0.916456 18 to 27 142289 1.3092 0.904768 17 to 26 141984 0.2575 0.601597 16 to 25 141936 0.0920 0.536637 15 to 24 142175 0.9161 0.820194 14 to 23 142135 0.7782 0.781766 13 to 22 142570 2.2782 0.988642 12 to 21 142236 1.1264 0.870012 11 to 20 142364 1.5678 0.941539 10 to 19 142118 0.7196 0.764100 9 to 18 142046 0.4713 0.681278 8 to 17 141514 -1.3632 0.086409 7 to 16 141711 -0.6839 0.247020 6 to 15 142015 0.3644 0.642213 5 to 14 141054 -2.9494 0.001592 4 to 13 141897 -0.0425 0.483043 3 to 12 141931 0.0747 0.529783 2 to 11 141690 -0.7563 0.224732 1 to 10 142319 1.4127 0.921121 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-28_08:31 Bits used No. missing words z-score p-value 28 to 32 141894 -0.0520 0.479278 27 to 31 141872 -0.1265 0.449651 26 to 30 141985 0.2565 0.601221 25 to 29 142284 1.2701 0.897970 24 to 28 141866 -0.1469 0.441613 23 to 27 142046 0.4633 0.678421 22 to 26 142078 0.5718 0.716259 21 to 25 141752 -0.5333 0.296905 20 to 24 142496 1.9887 0.976634 19 to 23 141799 -0.3740 0.354202 18 to 22 141617 -0.9909 0.160855 17 to 21 141506 -1.3672 0.085778 16 to 20 142099 0.6429 0.739872 15 to 19 141854 -0.1876 0.425611 14 to 18 141712 -0.6689 0.251775 13 to 17 142021 0.3785 0.647486 12 to 16 142279 1.2531 0.894919 11 to 15 142106 0.6667 0.747511 10 to 14 141650 -0.8791 0.189678 9 to 13 142116 0.7006 0.758216 8 to 12 141999 0.3040 0.619423 7 to 11 141902 -0.0248 0.490088 6 to 10 141797 -0.3808 0.351683 5 to 9 142310 1.3582 0.912800 4 to 8 141953 0.1480 0.558842 3 to 7 142051 0.4802 0.684471 2 to 6 142131 0.7514 0.773801 1 to 5 142212 1.0260 0.847554 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-28_08:31 Bits used No. missing words z-score p-value 31 to 32 142024 0.3383 0.632416 30 to 31 142057 0.4356 0.668438 29 to 30 141816 -0.2753 0.391539 28 to 29 141828 -0.2399 0.405199 27 to 28 141817 -0.2724 0.392673 26 to 27 142128 0.6450 0.740551 25 to 26 141323 -1.7296 0.041852 24 to 25 142294 1.1347 0.871754 23 to 24 141800 -0.3225 0.373534 22 to 23 141594 -0.9302 0.176140 21 to 22 141711 -0.5850 0.279259 20 to 21 142493 1.7217 0.957442 19 to 20 142244 0.9872 0.838234 18 to 19 142164 0.7512 0.773746 17 to 18 141433 -1.4051 0.079995 16 to 17 142380 1.3884 0.917493 15 to 16 141676 -0.6883 0.245635 14 to 15 141829 -0.2370 0.406343 13 to 14 141832 -0.2281 0.409780 12 to 13 142140 0.6804 0.751888 11 to 12 142167 0.7601 0.776399 10 to 11 141046 -2.5467 0.005437 9 to 10 142141 0.6834 0.752821 8 to 9 141758 -0.4464 0.327654 7 to 8 141899 -0.0305 0.487845 6 to 7 142421 1.5094 0.934395 5 to 6 141711 -0.5850 0.279259 4 to 5 141527 -1.1278 0.129699 3 to 4 141940 0.0905 0.536044 2 to 3 142423 1.5153 0.935146 1 to 2 142215 0.9017 0.816387 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-28_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2532.03 0.453 0.674713 Test results for specific bytes for dh-ranFile-2016-02-28_08:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2516.12 0.228 0.590166 2 to 9 2518.74 0.265 0.604504 3 to 10 2525.62 0.362 0.641442 4 to 11 2630.07 1.840 0.967081 5 to 12 2573.48 1.039 0.850627 6 to 13 2511.56 0.163 0.564927 7 to 14 2459.94 -0.567 0.285508 8 to 15 2455.97 -0.623 0.266726 9 to 16 2485.31 -0.208 0.417740 10 to 17 2502.00 0.028 0.511297 11 to 18 2518.05 0.255 0.600761 12 to 19 2461.25 -0.548 0.291862 13 to 20 2539.93 0.565 0.713859 14 to 21 2522.05 0.312 0.622434 15 to 22 2487.72 -0.174 0.431090 16 to 23 2432.98 -0.948 0.171627 17 to 24 2538.03 0.538 0.704667 18 to 25 2548.97 0.693 0.755690 19 to 26 2539.55 0.559 0.712032 20 to 27 2524.25 0.343 0.634184 21 to 28 2566.12 0.935 0.825141 22 to 29 2497.66 -0.033 0.486784 23 to 30 2670.82 2.416 0.992147 24 to 31 2635.60 1.918 0.972424 25 to 32 2467.87 -0.454 0.324762 CDPARK for dh-ranFile-2016-02-28_08:31: 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 3531 0.3653 0.642555 3530 0.3196 0.625377 3517 -0.2740 0.392053 3530 0.3196 0.625377 3521 -0.0913 0.463617 3539 0.7306 0.767486 3506 -0.7763 0.218799 3495 -1.2785 0.100530 3479 -2.0091 0.022262 Square side=100, avg. no. parked=3515.70 sample std.=17.69 p-value of the KSTEST for those 10 p-values: 0.515317 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-28_08:31 0.1294,0.6084,0.7967,0.5940,0.4712,0.1129,0.0867,0.1716,0.6529,0.0603, The KS test for those 10 p-values: 0.171971 The 3DSPHERES test for dh-ranFile-2016-02-28_08:31 sample no r^3 equiv. uni. 1 24.544 0.558753 2 126.751 0.985375 3 93.302 0.955402 4 16.287 0.418941 5 115.462 0.978693 6 87.514 0.945912 7 35.951 0.698313 8 69.651 0.901894 9 19.351 0.475354 10 34.551 0.683905 11 21.738 0.515483 12 1.352 0.044061 13 3.802 0.119021 14 17.798 0.447487 15 5.535 0.168474 16 113.438 0.977206 17 45.504 0.780585 18 7.793 0.228758 19 25.423 0.571489 20 57.842 0.854573 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.060969 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-28_08:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 2.2 -0.1 1.9 -0.2 0.4 0.2 -0.6 0.3 1.6 1.9 -0.5 1.3 -0.1 -0.4 -2.6 -1.5 -0.2 1.5 0.3 -0.9 -0.5 -0.5 0.5 -0.1 1.2 0.6 1.5 0.4 -0.2 0.8 -1.0 -0.9 1.4 0.8 -0.5 -0.9 0.5 0.1 0.4 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:44.469177 z-score=0.269409, p-value=0.631857 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-28_08:31 Test no p-value 1 0.758432 2 0.952972 3 0.179026 4 0.084085 5 0.067202 6 0.029152 7 0.425445 8 0.058025 9 0.115929 10 0.063897 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003378 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-28_08:31: (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 66721 0.04 66576 0.12 3 25000.00 25041 0.07 25166 1.10 4 6666.67 6623 0.29 6624 0.27 5 1388.89 1361 0.56 1392 0.01 6 238.10 225 0.72 204 4.88 7 34.72 24 3.31 31 0.40 8 4.96 4 0.19 6 0.22 p=0.47824 p=0.67959 Number of rngs required: 687074, p-value: 0.060 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-28_08:31 No. of wins: Observed Expected 98737 98585.9 z-score= 0.676, pvalue=0.75048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66696 66666.7 0.013 0.013 2 37614 37654.3 0.043 0.056 3 27146 26954.7 1.357 1.413 4 19295 19313.5 0.018 1.431 5 13998 13851.4 1.551 2.982 6 9878 9943.5 0.432 3.414 7 6924 7145.0 6.837 10.251 8 5170 5139.1 0.186 10.438 9 3768 3699.9 1.255 11.692 10 2636 2666.3 0.344 12.037 11 1897 1923.3 0.360 12.397 12 1374 1388.7 0.156 12.553 13 979 1003.7 0.609 13.162 14 716 726.1 0.142 13.304 15 496 525.8 1.693 14.996 16 390 381.2 0.205 15.202 17 289 276.5 0.561 15.763 18 207 200.8 0.190 15.953 19 138 146.0 0.437 16.390 20 98 106.2 0.635 17.025 21 291 287.1 0.053 17.078 Chisq= 17.08 for 20 degrees of freedom, p= 0.35207 SUMMARY of craptest p-value for no. of wins: 0.750477 p-value for throws/game: 0.352074 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-28_08:31 No. of wins: Observed Expected 98799 98585.9 z-score= 0.953, pvalue=0.82978 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66763 66666.7 0.139 0.139 2 38085 37654.3 4.926 5.065 3 26803 26954.7 0.854 5.919 4 19069 19313.5 3.094 9.014 5 13860 13851.4 0.005 9.019 6 9736 9943.5 4.332 13.351 7 6998 7145.0 3.025 16.376 8 5166 5139.1 0.141 16.517 9 3756 3699.9 0.852 17.369 10 2717 2666.3 0.964 18.333 11 1934 1923.3 0.059 18.392 12 1378 1388.7 0.083 18.475 13 1032 1003.7 0.797 19.272 14 758 726.1 1.398 20.670 15 556 525.8 1.730 22.401 16 382 381.2 0.002 22.403 17 271 276.5 0.111 22.514 18 203 200.8 0.023 22.537 19 126 146.0 2.736 25.273 20 97 106.2 0.800 26.072 21 310 287.1 1.824 27.896 Chisq= 27.90 for 20 degrees of freedom, p= 0.88813 SUMMARY of craptest p-value for no. of wins: 0.829779 p-value for throws/game: 0.888127 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0034,0.0054,0.0099,0.0223,0.0258,0.0292,0.0340,0.0344,0.0386, 0.0419,0.0441,0.0580,0.0601,0.0603,0.0610,0.0639,0.0672,0.0773,0.0800, 0.0841,0.0858,0.0864,0.0867,0.0897,0.0976,0.1005,0.1098,0.1129,0.1159, 0.1190,0.1294,0.1297,0.1315,0.1437,0.1442,0.1568,0.1602,0.1609,0.1615, 0.1685,0.1716,0.1716,0.1720,0.1752,0.1761,0.1790,0.1801,0.1808,0.1897, 0.1906,0.1910,0.1978,0.1979,0.2029,0.2047,0.2059,0.2166,0.2188,0.2234, 0.2247,0.2288,0.2456,0.2470,0.2486,0.2487,0.2518,0.2613,0.2667,0.2765, 0.2793,0.2793,0.2839,0.2855,0.2888,0.2919,0.2969,0.3017,0.3140,0.3140, 0.3160,0.3240,0.3248,0.3277,0.3296,0.3509,0.3517,0.3521,0.3542,0.3690, 0.3719,0.3735,0.3884,0.3889,0.3915,0.3921,0.3927,0.3999,0.4052,0.4063, 0.4098,0.4098,0.4128,0.4177,0.4189,0.4219,0.4254,0.4256,0.4311,0.4416, 0.4451,0.4475,0.4497,0.4539,0.4547,0.4557,0.4636,0.4712,0.4754,0.4782, 0.4793,0.4830,0.4868,0.4878,0.4901,0.4935,0.5018,0.5113,0.5129,0.5153, 0.5155,0.5193,0.5194,0.5258,0.5298,0.5351,0.5360,0.5366,0.5473,0.5588, 0.5588,0.5649,0.5715,0.5732,0.5902,0.5940,0.6001,0.6008,0.6012,0.6016, 0.6035,0.6045,0.6083,0.6084,0.6131,0.6175,0.6194,0.6207,0.6220,0.6224, 0.6254,0.6254,0.6259,0.6310,0.6319,0.6324,0.6341,0.6342,0.6414,0.6422, 0.6426,0.6475,0.6529,0.6593,0.6680,0.6684,0.6747,0.6762,0.6779,0.6784, 0.6794,0.6796,0.6813,0.6839,0.6845,0.6981,0.6983,0.7026,0.7047,0.7069, 0.7120,0.7139,0.7146,0.7163,0.7195,0.7302,0.7311,0.7399,0.7406,0.7475, 0.7496,0.7505,0.7519,0.7528,0.7557,0.7582,0.7584,0.7639,0.7641,0.7675, 0.7699,0.7704,0.7737,0.7738,0.7764,0.7806,0.7818,0.7967,0.7967,0.8112, 0.8131,0.8133,0.8164,0.8202,0.8251,0.8298,0.8303,0.8382,0.8428,0.8476, 0.8506,0.8546,0.8549,0.8617,0.8700,0.8718,0.8880,0.8881,0.8949,0.8980, 0.8983,0.9007,0.9019,0.9021,0.9048,0.9128,0.9165,0.9175,0.9211,0.9211, 0.9331,0.9344,0.9351,0.9415,0.9459,0.9530,0.9554,0.9574,0.9671,0.9724, 0.9766,0.9766,0.9772,0.9787,0.9854,0.9886,0.9903,0.9921,0.9973, Overall p-value after applying KStest on 269 p-values = 0.710936 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.