RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-04_23:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 24.1422 0.884378 2 to 25 15.76 13.3778 0.289449 3 to 26 15.67 16.7146 0.526144 4 to 27 15.69 17.5944 0.585153 5 to 28 15.89 17.6316 0.587569 6 to 29 15.87 13.3728 0.289105 7 to 30 15.93 16.1203 0.484673 8 to 31 15.53 24.4933 0.893360 9 to 32 15.87 23.0473 0.852282 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.372782 Tough bday spacings test for dh-ranFile-2016-05-04_23:31: 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 12 31 71 81 118 72 51 39 17 6 2 (O-E)^2/E 0.9 0.9 0.1 2.8 4.2 0.5 0.0 2.9 0.3 0.1 1.0 Birthday Spacings: Sum(O-E)^2/E= 13.668, p= 0.811 RESULTS OF GCD FOR dh-ranFile-2016-05-04_23:31 Euclid's algorithm: p-value, steps to gcd: 0.214218 p-value, dist. of gcd's: 0.929728 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-04_23:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.846 0.340 0.479 0.530 0.789 0.797 0.870 0.494 Bits 8 to 15---> 0.156 0.925 0.990 0.919 0.870 0.550 0.149 0.480 Bits 16 to 23---> 0.897 0.332 0.761 0.389 0.873 0.377 0.521 0.526 Bits 24 to 31---> 0.728 0.225 0.474 0.605 0.816 0.862 0.227 0.706 KS test for the above 32 p values: 0.961 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-04_23:31, p-values for 5 runs: 0.4727, 0.2634, 0.3420, 0.7508, 0.3166 Rank test for binary matrices (31x31) for dh-ranFile-2016-05-04_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 5068 5134.0 0.849 2.124 r= 30 23100 23103.0 0.000 2.124 r= 31 11637 11551.5 0.632 2.757 chi-square = 2.757 with df = 3; p-value = 0.569 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-05-04_23:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5140 5134.0 0.007 0.756 r= 31 23004 23103.0 0.425 1.180 r= 32 11632 11551.5 0.561 1.741 chi-square = 1.741 with df = 3; p-value = 0.372 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-05-04_23:31 b-rank test for bits 1 to 8, p=0.71195 b-rank test for bits 2 to 9, p=0.52664 b-rank test for bits 3 to 10, p=0.93991 b-rank test for bits 4 to 11, p=0.11713 b-rank test for bits 5 to 12, p=0.74073 b-rank test for bits 6 to 13, p=0.05204 b-rank test for bits 7 to 14, p=0.60407 b-rank test for bits 8 to 15, p=0.19678 b-rank test for bits 9 to 16, p=0.93531 b-rank test for bits 10 to 17, p=0.47856 b-rank test for bits 11 to 18, p=0.06212 b-rank test for bits 12 to 19, p=0.00876 b-rank test for bits 13 to 20, p=0.20688 b-rank test for bits 14 to 21, p=0.23255 b-rank test for bits 15 to 22, p=0.47936 b-rank test for bits 16 to 23, p=0.60982 b-rank test for bits 17 to 24, p=0.87216 b-rank test for bits 18 to 25, p=0.96921 b-rank test for bits 19 to 26, p=0.63164 b-rank test for bits 20 to 27, p=0.65671 b-rank test for bits 21 to 28, p=0.58621 b-rank test for bits 22 to 29, p=0.96626 b-rank test for bits 23 to 30, p=0.91107 b-rank test for bits 24 to 31, p=0.77356 b-rank test for bits 25 to 32, p=0.10803 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 = 0.512854 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-04_23:31 (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 142379 1.10 0.863758 2 142179 0.63 0.735676 3 142091 0.42 0.664386 4 141003 -2.12 0.017105 5 141326 -1.36 0.086454 6 141596 -0.73 0.232060 7 141781 -0.30 0.382151 8 142054 0.34 0.632324 9 141679 -0.54 0.295235 10 142193 0.66 0.746264 11 141999 0.21 0.582975 12 142122 0.50 0.690368 13 142418 1.19 0.882678 14 142042 0.31 0.621711 15 141079 -1.94 0.026188 16 140691 -2.85 0.002210 17 142274 0.85 0.802902 18 141770 -0.33 0.372387 19 142012 0.24 0.594790 20 142000 0.21 0.583886 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-05-04_23:31 Bits used No. missing words z-score p-value 23 to 32 141819 -0.3115 0.377717 22 to 31 141738 -0.5908 0.277330 21 to 30 141877 -0.1115 0.455617 20 to 29 141608 -1.0391 0.149386 19 to 28 141852 -0.1977 0.421644 18 to 27 142697 2.7161 0.996697 17 to 26 141719 -0.6563 0.255812 16 to 25 141519 -1.3460 0.089157 15 to 24 141598 -1.0736 0.141512 14 to 23 141620 -0.9977 0.159215 13 to 22 141482 -1.4736 0.070301 12 to 21 141688 -0.7632 0.222670 11 to 20 142046 0.4713 0.681278 10 to 19 141371 -1.8563 0.031705 9 to 18 141765 -0.4977 0.309351 8 to 17 142179 0.9299 0.823788 7 to 16 142183 0.9437 0.827336 6 to 15 141896 -0.0460 0.481669 5 to 14 142142 0.8023 0.788813 4 to 13 141847 -0.2149 0.414911 3 to 12 141999 0.3092 0.621418 2 to 11 142372 1.5954 0.944690 1 to 10 141726 -0.6322 0.263637 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-05-04_23:31 Bits used No. missing words z-score p-value 28 to 32 142450 1.8328 0.966582 27 to 31 142135 0.7650 0.777859 26 to 30 141923 0.0463 0.518480 25 to 29 141997 0.2972 0.616838 24 to 28 141967 0.1955 0.577496 23 to 27 141818 -0.3096 0.378435 22 to 26 141795 -0.3876 0.349171 21 to 25 142085 0.5955 0.724243 20 to 24 141915 0.0192 0.507667 19 to 23 142100 0.6463 0.740970 18 to 22 142092 0.6192 0.732114 17 to 21 141866 -0.1469 0.441613 16 to 20 142248 1.1480 0.874523 15 to 19 141516 -1.3333 0.091213 14 to 18 141855 -0.1842 0.426940 13 to 17 142512 2.0429 0.979471 12 to 16 141823 -0.2926 0.384897 11 to 15 141759 -0.5096 0.305168 10 to 14 141690 -0.7435 0.228592 9 to 13 142263 1.1989 0.884713 8 to 12 142029 0.4057 0.657504 7 to 11 141898 -0.0384 0.484682 6 to 10 141600 -1.0486 0.147187 5 to 9 141625 -0.9638 0.167565 4 to 8 141408 -1.6994 0.044620 3 to 7 142068 0.5379 0.704665 2 to 6 142021 0.3785 0.647486 1 to 5 141618 -0.9876 0.161684 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-05-04_23:31 Bits used No. missing words z-score p-value 31 to 32 142075 0.4887 0.687474 30 to 31 141780 -0.3815 0.351415 29 to 30 141646 -0.7768 0.218643 28 to 29 141835 -0.2193 0.413223 27 to 28 141966 0.1672 0.566381 26 to 27 141730 -0.5290 0.298404 25 to 26 142206 0.8751 0.809249 24 to 25 142088 0.5271 0.700921 23 to 24 142366 1.3471 0.911027 22 to 23 142107 0.5831 0.720086 21 to 22 141743 -0.4906 0.311837 20 to 21 142161 0.7424 0.771074 19 to 20 141490 -1.2370 0.108051 18 to 19 142817 2.6775 0.996291 17 to 18 142311 1.1849 0.881965 16 to 17 142257 1.0256 0.847454 15 to 16 142451 1.5978 0.944961 14 to 15 142085 0.5182 0.697841 13 to 14 141785 -0.3668 0.356901 12 to 13 141532 -1.1131 0.132840 11 to 12 142023 0.3353 0.631304 10 to 11 141963 0.1583 0.562897 9 to 10 142082 0.5094 0.694747 8 to 9 141171 -2.1780 0.014704 7 to 8 142002 0.2734 0.607713 6 to 7 141531 -1.1160 0.132207 5 to 6 142331 1.2439 0.893225 4 to 5 141901 -0.0246 0.490198 3 to 4 142076 0.4917 0.688517 2 to 3 141583 -0.9626 0.167868 1 to 2 142020 0.3265 0.627962 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-04_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2539.41 0.557 0.711350 Test results for specific bytes for dh-ranFile-2016-05-04_23:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2695.84 2.770 0.997194 2 to 9 2542.97 0.608 0.728296 3 to 10 2477.71 -0.315 0.376307 4 to 11 2392.42 -1.521 0.064077 5 to 12 2455.91 -0.624 0.266467 6 to 13 2667.99 2.376 0.991244 7 to 14 2446.59 -0.755 0.225009 8 to 15 2652.84 2.161 0.984669 9 to 16 2438.60 -0.868 0.192624 10 to 17 2509.55 0.135 0.553727 11 to 18 2580.75 1.142 0.873278 12 to 19 2377.42 -1.734 0.041501 13 to 20 2449.73 -0.711 0.238573 14 to 21 2605.36 1.490 0.931896 15 to 22 2526.80 0.379 0.647675 16 to 23 2514.78 0.209 0.582777 17 to 24 2491.57 -0.119 0.452530 18 to 25 2589.80 1.270 0.897945 19 to 26 2497.52 -0.035 0.485996 20 to 27 2546.06 0.651 0.742605 21 to 28 2549.04 0.694 0.756018 22 to 29 2473.13 -0.380 0.351956 23 to 30 2602.74 1.453 0.926876 24 to 31 2470.61 -0.416 0.338815 25 to 32 2528.29 0.400 0.655439 CDPARK for dh-ranFile-2016-05-04_23:31: 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 3502 -0.9589 0.168804 3535 0.5479 0.708135 3529 0.2740 0.607947 3521 -0.0913 0.463617 3524 0.0457 0.518210 3535 0.5479 0.708135 3512 -0.5023 0.307734 3539 0.7306 0.767486 3548 1.1416 0.873180 3530 0.3196 0.625377 Square side=100, avg. no. parked=3527.50 sample std.=12.72 p-value of the KSTEST for those 10 p-values: 0.408133 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-04_23:31 0.1469,0.5973,0.0763,0.4559,0.3302,0.8935,0.3434,0.2064,0.4028,0.0762, The KS test for those 10 p-values: 0.171127 The 3DSPHERES test for dh-ranFile-2016-05-04_23:31 sample no r^3 equiv. uni. 1 0.567 0.018721 2 1.971 0.063584 3 82.945 0.937012 4 40.705 0.742526 5 2.536 0.081058 6 0.305 0.010121 7 34.006 0.678107 8 3.984 0.124354 9 44.888 0.776034 10 13.826 0.369271 11 40.790 0.743254 12 25.922 0.578555 13 54.138 0.835462 14 11.390 0.315902 15 1.211 0.039566 16 3.950 0.123360 17 81.363 0.933603 18 22.268 0.523971 19 3.186 0.100749 20 12.110 0.332125 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.107834 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-04_23:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 1.8 0.1 -0.3 0.3 -0.3 1.3 -1.8 -0.5 -0.9 0.0 -0.0 -0.2 -0.2 -1.2 -0.3 1.2 0.6 1.0 0.2 -1.3 2.0 -0.1 -1.5 -0.4 0.4 0.2 -0.9 -0.8 0.5 1.0 0.2 1.4 1.3 -0.5 1.5 1.2 -1.3 0.9 -0.1 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:37.612863 z-score=-0.478676, p-value=0.336160 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-05-04_23:31 Test no p-value 1 0.090866 2 0.705551 3 0.441083 4 0.139259 5 0.116628 6 0.196777 7 0.187034 8 0.030234 9 0.250681 10 0.152910 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.003332 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-04_23:31: (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 66756 0.12 66534 0.26 3 25000.00 24979 0.02 25007 0.00 4 6666.67 6583 1.05 6797 2.55 5 1388.89 1414 0.45 1403 0.14 6 238.10 232 0.16 224 0.83 7 34.72 29 0.94 30 0.64 8 4.96 6 0.22 4 0.19 p=0.18588 p=0.40649 Number of rngs required: 687776, p-value: 0.235 RESULTS OF CRAPS TEST for dh-ranFile-2016-05-04_23:31 No. of wins: Observed Expected 98430 98585.9 z-score=-0.697, pvalue=0.24287 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66710 66666.7 0.028 0.028 2 37786 37654.3 0.460 0.489 3 27013 26954.7 0.126 0.615 4 19193 19313.5 0.751 1.366 5 13917 13851.4 0.310 1.676 6 9892 9943.5 0.267 1.944 7 7043 7145.0 1.457 3.400 8 5101 5139.1 0.282 3.683 9 3685 3699.9 0.060 3.742 10 2641 2666.3 0.240 3.982 11 1911 1923.3 0.079 4.061 12 1452 1388.7 2.882 6.943 13 996 1003.7 0.059 7.002 14 768 726.1 2.413 9.415 15 503 525.8 0.992 10.407 16 391 381.2 0.255 10.661 17 287 276.5 0.396 11.057 18 204 200.8 0.050 11.107 19 124 146.0 3.311 14.418 20 110 106.2 0.135 14.553 21 273 287.1 0.694 15.247 Chisq= 15.25 for 20 degrees of freedom, p= 0.23787 SUMMARY of craptest p-value for no. of wins: 0.242873 p-value for throws/game: 0.237872 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-04_23:31 No. of wins: Observed Expected 98752 98585.9 z-score= 0.743, pvalue=0.77128 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66883 66666.7 0.702 0.702 2 37874 37654.3 1.282 1.984 3 26824 26954.7 0.634 2.618 4 19334 19313.5 0.022 2.640 5 13878 13851.4 0.051 2.691 6 9918 9943.5 0.066 2.756 7 6973 7145.0 4.142 6.898 8 4988 5139.1 4.441 11.339 9 3729 3699.9 0.229 11.568 10 2629 2666.3 0.522 12.090 11 1985 1923.3 1.977 14.068 12 1330 1388.7 2.485 16.552 13 1005 1003.7 0.002 16.554 14 727 726.1 0.001 16.555 15 531 525.8 0.051 16.605 16 361 381.2 1.065 17.671 17 285 276.5 0.259 17.930 18 201 200.8 0.000 17.930 19 140 146.0 0.245 18.175 20 114 106.2 0.571 18.746 21 291 287.1 0.053 18.798 Chisq= 18.80 for 20 degrees of freedom, p= 0.46503 SUMMARY of craptest p-value for no. of wins: 0.771284 p-value for throws/game: 0.465029 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0022,0.0033,0.0088,0.0101,0.0147,0.0171,0.0187,0.0262,0.0302,0.0317, 0.0396,0.0415,0.0446,0.0520,0.0621,0.0636,0.0641,0.0703,0.0762,0.0763, 0.0811,0.0865,0.0892,0.0909,0.0912,0.1007,0.1078,0.1080,0.1081,0.1166, 0.1171,0.1234,0.1244,0.1322,0.1328,0.1393,0.1415,0.1469,0.1472,0.1490, 0.1494,0.1529,0.1563,0.1592,0.1617,0.1676,0.1679,0.1688,0.1711,0.1859, 0.1870,0.1926,0.1968,0.1968,0.2064,0.2069,0.2142,0.2186,0.2227,0.2248, 0.2250,0.2267,0.2286,0.2321,0.2325,0.2345,0.2379,0.2386,0.2429,0.2507, 0.2558,0.2634,0.2636,0.2665,0.2773,0.2891,0.2894,0.2952,0.2984,0.3052, 0.3077,0.3094,0.3118,0.3159,0.3166,0.3302,0.3321,0.3324,0.3362,0.3388, 0.3396,0.3420,0.3434,0.3492,0.3514,0.3520,0.3569,0.3693,0.3722,0.3724, 0.3728,0.3763,0.3768,0.3777,0.3784,0.3822,0.3849,0.3894,0.4028,0.4065, 0.4081,0.4132,0.4149,0.4216,0.4269,0.4411,0.4416,0.4525,0.4556,0.4559, 0.4636,0.4650,0.4727,0.4740,0.4786,0.4787,0.4794,0.4804,0.4817,0.4847, 0.4847,0.4860,0.4902,0.4943,0.5077,0.5129,0.5182,0.5185,0.5210,0.5240, 0.5258,0.5261,0.5266,0.5296,0.5496,0.5537,0.5629,0.5664,0.5693,0.5775, 0.5786,0.5828,0.5830,0.5839,0.5852,0.5862,0.5876,0.5948,0.5973,0.6041, 0.6053,0.6077,0.6079,0.6098,0.6168,0.6214,0.6217,0.6254,0.6280,0.6313, 0.6316,0.6323,0.6475,0.6477,0.6554,0.6567,0.6575,0.6644,0.6781,0.6813, 0.6875,0.6885,0.6904,0.6947,0.6978,0.7009,0.7047,0.7056,0.7064,0.7081, 0.7081,0.7113,0.7119,0.7201,0.7242,0.7282,0.7283,0.7321,0.7357,0.7407, 0.7410,0.7425,0.7426,0.7433,0.7463,0.7508,0.7560,0.7614,0.7675,0.7711, 0.7713,0.7736,0.7760,0.7779,0.7888,0.7894,0.7973,0.8029,0.8092,0.8113, 0.8158,0.8238,0.8273,0.8355,0.8457,0.8475,0.8523,0.8618,0.8638,0.8699, 0.8702,0.8722,0.8726,0.8732,0.8733,0.8745,0.8820,0.8827,0.8844,0.8847, 0.8932,0.8934,0.8935,0.8970,0.8979,0.9110,0.9111,0.9189,0.9248,0.9269, 0.9297,0.9319,0.9336,0.9353,0.9370,0.9399,0.9447,0.9450,0.9606,0.9663, 0.9666,0.9692,0.9795,0.9847,0.9902,0.9912,0.9963,0.9967,0.9972, Overall p-value after applying KStest on 269 p-values = 0.999778 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.