RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-27_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.14 20.0151 0.726543 2 to 25 15.80 23.8030 0.875113 3 to 26 15.93 6.3327 0.009343 4 to 27 15.58 16.7485 0.528473 5 to 28 15.71 21.9299 0.812568 6 to 29 15.69 21.8469 0.809320 7 to 30 15.82 31.4130 0.982218 8 to 31 15.91 11.2868 0.158729 9 to 32 15.94 20.1002 0.730864 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.173300 Tough bday spacings test for dh-ranFile-2015-08-27_06:31: 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 9 30 86 94 95 71 59 31 14 5 6 (O-E)^2/E 0.0 1.2 2.2 0.1 0.1 0.7 0.9 0.1 0.1 0.4 0.9 Birthday Spacings: Sum(O-E)^2/E= 6.616, p= 0.239 RESULTS OF GCD FOR dh-ranFile-2015-08-27_06:31 Euclid's algorithm: p-value, steps to gcd: 0.562254 p-value, dist. of gcd's: 0.589543 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-27_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.312 0.606 0.823 0.324 0.457 0.959 0.523 0.568 Bits 8 to 15---> 0.257 0.202 0.262 0.213 0.634 0.989 0.195 0.160 Bits 16 to 23---> 0.901 0.731 0.204 0.292 0.338 0.985 0.774 0.267 Bits 24 to 31---> 0.897 0.062 0.718 0.513 0.011 0.676 0.510 0.941 KS test for the above 32 p values: 0.192 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-27_06:31, p-values for 5 runs: 0.6801, 0.7160, 0.5648, 0.1300, 0.0478 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-27_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5194 5134.0 0.701 1.573 r= 30 23218 23103.0 0.572 2.145 r= 31 11363 11551.5 3.077 5.222 chi-square = 5.222 with df = 3; p-value = 0.844 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-27_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5113 5134.0 0.086 0.147 r= 31 23013 23103.0 0.351 0.498 r= 32 11659 11551.5 1.000 1.498 chi-square = 1.498 with df = 3; p-value = 0.317 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-27_06:31 b-rank test for bits 1 to 8, p=0.57462 b-rank test for bits 2 to 9, p=0.01838 b-rank test for bits 3 to 10, p=0.12673 b-rank test for bits 4 to 11, p=0.31016 b-rank test for bits 5 to 12, p=0.98285 b-rank test for bits 6 to 13, p=0.43861 b-rank test for bits 7 to 14, p=0.84632 b-rank test for bits 8 to 15, p=0.60465 b-rank test for bits 9 to 16, p=0.58507 b-rank test for bits 10 to 17, p=0.08804 b-rank test for bits 11 to 18, p=0.95459 b-rank test for bits 12 to 19, p=0.93555 b-rank test for bits 13 to 20, p=0.87493 b-rank test for bits 14 to 21, p=0.34474 b-rank test for bits 15 to 22, p=0.17969 b-rank test for bits 16 to 23, p=0.33940 b-rank test for bits 17 to 24, p=0.69601 b-rank test for bits 18 to 25, p=0.83746 b-rank test for bits 19 to 26, p=0.13238 b-rank test for bits 20 to 27, p=0.93312 b-rank test for bits 21 to 28, p=0.90477 b-rank test for bits 22 to 29, p=0.91206 b-rank test for bits 23 to 30, p=0.04560 b-rank test for bits 24 to 31, p=0.12040 b-rank test for bits 25 to 32, p=0.06979 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 = 0.251749 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-27_06:31 (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 142208 0.70 0.757357 2 141241 -1.56 0.059201 3 142794 2.07 0.980632 4 141379 -1.24 0.107656 5 141912 0.01 0.502489 6 141506 -0.94 0.173004 7 142408 1.17 0.878014 8 141841 -0.16 0.436579 9 142125 0.50 0.692835 10 141710 -0.47 0.320706 11 141746 -0.38 0.351375 12 142181 0.63 0.737202 13 141976 0.16 0.561893 14 142225 0.74 0.769605 15 141710 -0.47 0.320706 16 142245 0.78 0.783561 17 142227 0.74 0.771023 18 141363 -1.28 0.100894 19 142226 0.74 0.770315 20 141534 -0.88 0.190260 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-27_06:31 Bits used No. missing words z-score p-value 23 to 32 141743 -0.5736 0.283136 22 to 31 141838 -0.2460 0.402855 21 to 30 141774 -0.4667 0.320373 20 to 29 142325 1.4333 0.924120 19 to 28 141804 -0.3632 0.358225 18 to 27 141568 -1.1770 0.119598 17 to 26 142085 0.6058 0.727663 16 to 25 142155 0.8471 0.801541 15 to 24 142027 0.4058 0.657540 14 to 23 142023 0.3920 0.652458 13 to 22 142249 1.1713 0.879256 12 to 21 141931 0.0747 0.529783 11 to 20 142162 0.8713 0.808198 10 to 19 141801 -0.3736 0.354369 9 to 18 141734 -0.6046 0.272727 8 to 17 141567 -1.1804 0.118911 7 to 16 142176 0.9196 0.821097 6 to 15 141530 -1.3080 0.095431 5 to 14 141639 -0.9322 0.175624 4 to 13 141863 -0.1598 0.436536 3 to 12 142007 0.3368 0.631864 2 to 11 142122 0.7333 0.768326 1 to 10 141721 -0.6494 0.258036 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-27_06:31 Bits used No. missing words z-score p-value 28 to 32 142160 0.8497 0.802262 27 to 31 142063 0.5209 0.698787 26 to 30 142266 1.2091 0.886678 25 to 29 141996 0.2938 0.615543 24 to 28 141684 -0.7638 0.222484 23 to 27 142188 0.9446 0.827580 22 to 26 141477 -1.4655 0.071389 21 to 25 141790 -0.4045 0.342919 20 to 24 141746 -0.5537 0.289905 19 to 23 141934 0.0836 0.533324 18 to 22 141936 0.0904 0.536018 17 to 21 141867 -0.1435 0.442951 16 to 20 141521 -1.3164 0.094024 15 to 19 141953 0.1480 0.558842 14 to 18 141927 0.0599 0.523882 13 to 17 141600 -1.0486 0.147187 12 to 16 142000 0.3074 0.620714 11 to 15 142169 0.8802 0.810635 10 to 14 141852 -0.1943 0.422955 9 to 13 142017 0.3650 0.642438 8 to 12 141884 -0.0859 0.465787 7 to 11 142134 0.7616 0.776849 6 to 10 142075 0.5616 0.712803 5 to 9 141977 0.2294 0.590717 4 to 8 141796 -0.3842 0.350426 3 to 7 142393 1.6396 0.949452 2 to 6 141932 0.0768 0.530628 1 to 5 142185 0.9345 0.824970 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-27_06:31 Bits used No. missing words z-score p-value 31 to 32 142371 1.3619 0.913379 30 to 31 141631 -0.8210 0.205814 29 to 30 142009 0.2940 0.615626 28 to 29 141375 -1.5762 0.057490 27 to 28 142263 1.0433 0.851589 26 to 27 141784 -0.3697 0.355801 25 to 26 142111 0.5949 0.724044 24 to 25 142042 0.3914 0.652233 23 to 24 141836 -0.2163 0.414372 22 to 23 142058 0.4386 0.669508 21 to 22 142013 0.3058 0.620126 20 to 21 141426 -1.4258 0.076970 19 to 20 141995 0.2527 0.599755 18 to 19 142495 1.7276 0.957974 17 to 18 141326 -1.7207 0.042649 16 to 17 141984 0.2203 0.587168 15 to 16 141978 0.2026 0.580263 14 to 15 142314 1.1937 0.883706 13 to 14 141100 -2.3874 0.008484 12 to 13 143075 3.4386 0.999708 11 to 12 142264 1.0462 0.852271 10 to 11 141351 -1.6470 0.049780 9 to 10 141992 0.2439 0.596332 8 to 9 141846 -0.1868 0.425903 7 to 8 141700 -0.6175 0.268455 6 to 7 142162 0.7453 0.771967 5 to 6 141437 -1.3933 0.081764 4 to 5 141875 -0.1013 0.459669 3 to 4 141741 -0.4965 0.309754 2 to 3 142400 1.4474 0.926108 1 to 2 141670 -0.7060 0.240098 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-27_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2535.08 0.496 0.690100 Test results for specific bytes for dh-ranFile-2015-08-27_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2467.28 -0.463 0.321776 2 to 9 2592.47 1.308 0.904515 3 to 10 2451.10 -0.692 0.244594 4 to 11 2543.45 0.614 0.730545 5 to 12 2453.09 -0.663 0.253542 6 to 13 2506.22 0.088 0.535065 7 to 14 2582.46 1.166 0.878229 8 to 15 2656.18 2.209 0.986405 9 to 16 2642.16 2.011 0.977811 10 to 17 2584.18 1.191 0.883082 11 to 18 2506.19 0.088 0.534868 12 to 19 2455.59 -0.628 0.264970 13 to 20 2464.59 -0.501 0.308241 14 to 21 2426.68 -1.037 0.149890 15 to 22 2515.16 0.214 0.584897 16 to 23 2536.27 0.513 0.696010 17 to 24 2397.70 -1.447 0.073977 18 to 25 2596.33 1.362 0.913440 19 to 26 2566.37 0.939 0.826031 20 to 27 2521.97 0.311 0.621960 21 to 28 2470.02 -0.424 0.335775 22 to 29 2470.28 -0.420 0.337132 23 to 30 2420.72 -1.121 0.131105 24 to 31 2472.14 -0.394 0.346812 25 to 32 2404.37 -1.352 0.088112 CDPARK for dh-ranFile-2015-08-27_06:31: 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 3516 -0.3196 0.374623 3524 0.0457 0.518210 3529 0.2740 0.607947 3561 1.7352 0.958644 3535 0.5479 0.708135 3525 0.0913 0.536383 3516 -0.3196 0.374623 3548 1.1416 0.873180 3530 0.3196 0.625377 3511 -0.5479 0.291865 Square side=100, avg. no. parked=3529.50 sample std.=14.57 p-value of the KSTEST for those 10 p-values: 0.383388 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-27_06:31 0.2232,0.2946,0.5337,0.8313,0.3289,0.9860,0.9502,0.0063,0.6253,0.1185, The KS test for those 10 p-values: 0.713253 The 3DSPHERES test for dh-ranFile-2015-08-27_06:31 sample no r^3 equiv. uni. 1 30.867 0.642597 2 20.121 0.488645 3 2.007 0.064724 4 81.908 0.934797 5 60.981 0.869020 6 82.627 0.936343 7 3.894 0.121741 8 16.578 0.424545 9 16.501 0.423074 10 12.673 0.344557 11 32.128 0.657314 12 80.573 0.931830 13 50.009 0.811178 14 89.079 0.948661 15 39.129 0.728642 16 13.259 0.357238 17 1.295 0.042243 18 13.087 0.353528 19 47.771 0.796553 20 23.224 0.538891 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.406214 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-27_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.7 2.3 1.2 -0.2 0.7 -1.1 -1.6 -0.6 0.4 -1.0 0.7 0.4 0.7 0.4 0.4 0.5 -0.2 -0.3 1.5 -1.3 0.9 -1.5 -0.2 -0.8 -1.3 2.0 -1.3 -0.7 1.4 0.2 0.2 -1.4 -0.5 -0.2 0.1 0.0 0.2 -0.8 -0.1 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:39.524510 z-score=-0.270098, p-value=0.419797 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-27_06:31 Test no p-value 1 0.118651 2 0.902792 3 0.031321 4 0.218900 5 0.388357 6 0.473654 7 0.651441 8 0.115331 9 0.799833 10 0.131995 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.299097 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-27_06:31: (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 66426 0.87 66594 0.08 3 25000.00 25174 1.21 24989 0.00 4 6666.67 6689 0.07 6789 2.24 5 1388.89 1460 3.64 1375 0.14 6 238.10 226 0.61 214 2.44 7 34.72 17 9.04 31 0.40 8 4.96 7 0.84 7 0.84 p=0.98773 p=0.59271 Number of rngs required: 689718, p-value: 0.938 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-27_06:31 No. of wins: Observed Expected 98497 98585.9 z-score=-0.397, pvalue=0.34553 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66721 66666.7 0.044 0.044 2 37551 37654.3 0.284 0.328 3 26579 26954.7 5.237 5.565 4 19338 19313.5 0.031 5.596 5 13808 13851.4 0.136 5.733 6 9994 9943.5 0.256 5.989 7 7325 7145.0 4.533 10.522 8 5197 5139.1 0.653 11.175 9 3738 3699.9 0.393 11.568 10 2725 2666.3 1.292 12.860 11 1966 1923.3 0.947 13.807 12 1360 1388.7 0.595 14.402 13 1042 1003.7 1.460 15.862 14 727 726.1 0.001 15.863 15 549 525.8 1.020 16.884 16 360 381.2 1.174 18.057 17 251 276.5 2.359 20.416 18 190 200.8 0.584 21.000 19 151 146.0 0.172 21.172 20 117 106.2 1.095 22.267 21 311 287.1 1.987 24.255 Chisq= 24.25 for 20 degrees of freedom, p= 0.76855 SUMMARY of craptest p-value for no. of wins: 0.345526 p-value for throws/game: 0.768548 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-27_06:31 No. of wins: Observed Expected 98531 98585.9 z-score=-0.245, pvalue=0.40309 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66712 66666.7 0.031 0.031 2 37452 37654.3 1.087 1.118 3 27083 26954.7 0.610 1.728 4 19506 19313.5 1.919 3.648 5 13803 13851.4 0.169 3.817 6 9800 9943.5 2.072 5.889 7 6991 7145.0 3.320 9.209 8 5157 5139.1 0.063 9.272 9 3659 3699.9 0.451 9.723 10 2684 2666.3 0.118 9.841 11 1953 1923.3 0.458 10.299 12 1428 1388.7 1.110 11.409 13 1068 1003.7 4.117 15.526 14 757 726.1 1.311 16.837 15 552 525.8 1.302 18.139 16 392 381.2 0.309 18.448 17 268 276.5 0.264 18.712 18 205 200.8 0.087 18.798 19 138 146.0 0.437 19.235 20 106 106.2 0.000 19.235 21 286 287.1 0.004 19.240 Chisq= 19.24 for 20 degrees of freedom, p= 0.49370 SUMMARY of craptest p-value for no. of wins: 0.403089 p-value for throws/game: 0.493698 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0063,0.0085,0.0093,0.0113,0.0184,0.0313,0.0422,0.0426,0.0456,0.0478, 0.0498,0.0575,0.0592,0.0622,0.0647,0.0698,0.0714,0.0740,0.0770,0.0818, 0.0880,0.0881,0.0940,0.0954,0.1009,0.1077,0.1153,0.1185,0.1187,0.1189, 0.1196,0.1204,0.1217,0.1267,0.1300,0.1311,0.1320,0.1324,0.1472,0.1499, 0.1587,0.1598,0.1730,0.1733,0.1756,0.1797,0.1903,0.1922,0.1950,0.2017, 0.2042,0.2058,0.2130,0.2189,0.2225,0.2232,0.2389,0.2401,0.2446,0.2517, 0.2535,0.2572,0.2580,0.2621,0.2650,0.2669,0.2685,0.2727,0.2831,0.2899, 0.2919,0.2924,0.2946,0.2991,0.3082,0.3098,0.3102,0.3117,0.3172,0.3204, 0.3207,0.3207,0.3218,0.3237,0.3289,0.3358,0.3371,0.3380,0.3394,0.3429, 0.3446,0.3447,0.3455,0.3468,0.3504,0.3514,0.3535,0.3544,0.3558,0.3572, 0.3582,0.3746,0.3746,0.3834,0.3884,0.4029,0.4031,0.4062,0.4144,0.4198, 0.4230,0.4231,0.4245,0.4259,0.4365,0.4366,0.4386,0.4430,0.4566,0.4597, 0.4658,0.4737,0.4886,0.4937,0.5025,0.5102,0.5131,0.5182,0.5226,0.5239, 0.5285,0.5298,0.5306,0.5333,0.5337,0.5349,0.5351,0.5360,0.5364,0.5389, 0.5588,0.5619,0.5623,0.5648,0.5675,0.5746,0.5803,0.5849,0.5851,0.5872, 0.5895,0.5907,0.5927,0.5963,0.5998,0.6046,0.6061,0.6079,0.6155,0.6156, 0.6201,0.6207,0.6220,0.6253,0.6254,0.6319,0.6337,0.6424,0.6426,0.6514, 0.6522,0.6525,0.6573,0.6575,0.6695,0.6761,0.6801,0.6901,0.6928,0.6960, 0.6960,0.6988,0.7081,0.7128,0.7133,0.7160,0.7179,0.7240,0.7265,0.7277, 0.7286,0.7305,0.7306,0.7309,0.7372,0.7574,0.7683,0.7685,0.7696,0.7703, 0.7710,0.7720,0.7741,0.7768,0.7836,0.7966,0.7998,0.8015,0.8023,0.8082, 0.8093,0.8106,0.8112,0.8126,0.8211,0.8229,0.8250,0.8260,0.8276,0.8313, 0.8375,0.8438,0.8463,0.8516,0.8523,0.8690,0.8732,0.8749,0.8751,0.8780, 0.8782,0.8793,0.8831,0.8837,0.8867,0.8965,0.9013,0.9028,0.9045,0.9048, 0.9121,0.9134,0.9134,0.9241,0.9261,0.9318,0.9331,0.9348,0.9355,0.9363, 0.9379,0.9409,0.9487,0.9495,0.9502,0.9546,0.9580,0.9586,0.9587,0.9778, 0.9806,0.9822,0.9829,0.9853,0.9860,0.9864,0.9877,0.9894,0.9997, Overall p-value after applying KStest on 269 p-values = 0.545880 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.