RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_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 15.69 22.3131 0.827024 2 to 25 15.60 18.9622 0.669292 3 to 26 15.57 26.4869 0.933965 4 to 27 15.77 19.0599 0.674895 5 to 28 15.93 22.9872 0.850331 6 to 29 15.66 16.0606 0.480460 7 to 30 15.82 18.0012 0.611236 8 to 31 15.86 26.2796 0.930485 9 to 32 15.65 10.8871 0.137630 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.093753 Tough bday spacings test for dh-ranFile-2018-06-29_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 7 40 72 102 99 78 52 24 16 5 5 (O-E)^2/E 0.5 0.3 0.0 0.2 0.0 0.0 0.0 1.1 0.1 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 2.860, p= 0.015 RESULTS OF GCD FOR dh-ranFile-2018-06-29_06:31 Euclid's algorithm: p-value, steps to gcd: 0.740644 p-value, dist. of gcd's: 0.505206 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.639 0.307 0.837 0.143 0.785 0.701 0.729 0.244 Bits 8 to 15---> 0.978 0.096 0.553 0.780 0.853 0.344 0.135 0.950 Bits 16 to 23---> 0.171 0.313 0.336 0.857 0.189 0.841 0.253 0.734 Bits 24 to 31---> 0.773 0.894 0.436 0.179 0.776 0.034 0.062 0.150 KS test for the above 32 p values: 0.396 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_06:31, p-values for 5 runs: 0.4421, 0.8540, 0.3974, 0.5165, 0.6545 Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5097 5134.0 0.267 0.539 r= 30 23032 23103.0 0.218 0.757 r= 31 11652 11551.5 0.874 1.631 chi-square = 1.631 with df = 3; p-value = 0.348 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 229 211.4 1.462 1.462 r= 30 4838 5134.0 17.067 18.529 r= 31 23315 23103.0 1.944 20.474 r= 32 11618 11551.5 0.383 20.856 chi-square = 20.856 with df = 3; p-value = 1.000 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_06:31 b-rank test for bits 1 to 8, p=0.20149 b-rank test for bits 2 to 9, p=0.43365 b-rank test for bits 3 to 10, p=0.55827 b-rank test for bits 4 to 11, p=0.47255 b-rank test for bits 5 to 12, p=0.53746 b-rank test for bits 6 to 13, p=0.71958 b-rank test for bits 7 to 14, p=0.86238 b-rank test for bits 8 to 15, p=0.78840 b-rank test for bits 9 to 16, p=0.82630 b-rank test for bits 10 to 17, p=0.99535 b-rank test for bits 11 to 18, p=0.84188 b-rank test for bits 12 to 19, p=0.18166 b-rank test for bits 13 to 20, p=0.35518 b-rank test for bits 14 to 21, p=0.23766 b-rank test for bits 15 to 22, p=0.73884 b-rank test for bits 16 to 23, p=0.66735 b-rank test for bits 17 to 24, p=0.03516 b-rank test for bits 18 to 25, p=0.35356 b-rank test for bits 19 to 26, p=0.23656 b-rank test for bits 20 to 27, p=0.63631 b-rank test for bits 21 to 28, p=0.95536 b-rank test for bits 22 to 29, p=0.80393 b-rank test for bits 23 to 30, p=0.34203 b-rank test for bits 24 to 31, p=0.00520 b-rank test for bits 25 to 32, p=0.44151 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 = 0.892450 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_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 141788 -0.28 0.388404 2 142271 0.85 0.800951 3 141826 -0.19 0.422815 4 141953 0.10 0.540635 5 142387 1.12 0.867800 6 142027 0.27 0.608315 7 141945 0.08 0.533210 8 141475 -1.01 0.155103 9 141585 -0.76 0.224291 10 141352 -1.30 0.096429 11 142470 1.31 0.904898 12 141545 -0.85 0.197319 13 142489 1.35 0.912191 14 141534 -0.88 0.190260 15 142052 0.33 0.630562 16 142278 0.86 0.805485 17 141740 -0.40 0.346189 18 142231 0.75 0.773844 19 141926 0.04 0.515534 20 143111 2.81 0.997505 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-06-29_06:31 Bits used No. missing words z-score p-value 23 to 32 141980 0.2437 0.596264 22 to 31 141952 0.1471 0.558488 21 to 30 141747 -0.5598 0.287822 20 to 29 141418 -1.6942 0.045110 19 to 28 141458 -1.5563 0.059817 18 to 27 141748 -0.5563 0.288999 17 to 26 141953 0.1506 0.559849 16 to 25 142212 1.0437 0.851686 15 to 24 141738 -0.5908 0.277330 14 to 23 141743 -0.5736 0.283136 13 to 22 142058 0.5127 0.695904 12 to 21 141923 0.0471 0.518798 11 to 20 141184 -2.5011 0.006190 10 to 19 142033 0.4264 0.665109 9 to 18 142279 1.2747 0.898797 8 to 17 142506 2.0575 0.980180 7 to 16 142174 0.9127 0.819288 6 to 15 141831 -0.2701 0.393540 5 to 14 142015 0.3644 0.642213 4 to 13 141506 -1.3908 0.082144 3 to 12 141867 -0.1460 0.441974 2 to 11 142066 0.5402 0.705485 1 to 10 142428 1.7885 0.963154 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-06-29_06:31 Bits used No. missing words z-score p-value 28 to 32 141986 0.2599 0.602529 27 to 31 142076 0.5650 0.713957 26 to 30 142179 0.9141 0.819677 25 to 29 141797 -0.3808 0.351683 24 to 28 141723 -0.6316 0.263815 23 to 27 142124 0.7277 0.766600 22 to 26 141865 -0.1503 0.440275 21 to 25 141743 -0.5638 0.286435 20 to 24 141732 -0.6011 0.273881 19 to 23 142201 0.9887 0.838598 18 to 22 142189 0.9480 0.828444 17 to 21 142634 2.4565 0.992985 16 to 20 141848 -0.2079 0.417654 15 to 19 142100 0.6463 0.740970 14 to 18 141788 -0.4113 0.340431 13 to 17 142442 1.8057 0.964514 12 to 16 142010 0.3413 0.633544 11 to 15 142280 1.2565 0.895534 10 to 14 142258 1.1819 0.881384 9 to 13 142167 0.8735 0.808793 8 to 12 142141 0.7853 0.783868 7 to 11 141985 0.2565 0.601221 6 to 10 141784 -0.4248 0.335474 5 to 9 141146 -2.5876 0.004833 4 to 8 142009 0.3379 0.632267 3 to 7 141781 -0.4350 0.331775 2 to 6 141560 -1.1842 0.118173 1 to 5 141461 -1.5198 0.064285 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-06-29_06:31 Bits used No. missing words z-score p-value 31 to 32 142286 1.1111 0.866742 30 to 31 142011 0.2999 0.617878 29 to 30 141893 -0.0482 0.480790 28 to 29 141840 -0.2045 0.418976 27 to 28 142259 1.0315 0.848841 26 to 27 142042 0.3914 0.652233 25 to 26 141581 -0.9685 0.166391 24 to 25 141784 -0.3697 0.355801 23 to 24 141715 -0.5732 0.283240 22 to 23 142130 0.6509 0.742459 21 to 22 141913 0.0108 0.504319 20 to 21 141992 0.2439 0.596332 19 to 20 141803 -0.3137 0.376891 18 to 19 141733 -0.5201 0.301480 17 to 18 141898 -0.0334 0.486669 16 to 17 142196 0.8456 0.801122 15 to 16 142017 0.3176 0.624610 14 to 15 142074 0.4858 0.686429 13 to 14 141294 -1.8151 0.034752 12 to 13 141439 -1.3874 0.082659 11 to 12 141650 -0.7650 0.222140 10 to 11 141630 -0.8240 0.204975 9 to 10 141915 0.0167 0.506672 8 to 9 142684 2.2852 0.988848 7 to 8 141723 -0.5496 0.291281 6 to 7 141800 -0.3225 0.373534 5 to 6 141848 -0.1809 0.428217 4 to 5 142198 0.8515 0.802764 3 to 4 141303 -1.7886 0.036841 2 to 3 141822 -0.2576 0.398354 1 to 2 142057 0.4356 0.668438 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2536.26 0.513 0.695948 Test results for specific bytes for dh-ranFile-2018-06-29_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2524.06 0.340 0.633179 2 to 9 2396.34 -1.466 0.071318 3 to 10 2316.28 -2.598 0.004686 4 to 11 2538.12 0.539 0.705082 5 to 12 2656.41 2.212 0.986514 6 to 13 2521.38 0.302 0.618798 7 to 14 2592.27 1.305 0.904028 8 to 15 2443.04 -0.806 0.210237 9 to 16 2497.32 -0.038 0.484886 10 to 17 2503.70 0.052 0.520857 11 to 18 2458.61 -0.585 0.279146 12 to 19 2556.58 0.800 0.788191 13 to 20 2640.99 1.994 0.976919 14 to 21 2561.22 0.866 0.806679 15 to 22 2525.07 0.354 0.638515 16 to 23 2479.02 -0.297 0.383363 17 to 24 2390.31 -1.551 0.060419 18 to 25 2449.53 -0.714 0.237691 19 to 26 2462.48 -0.531 0.297855 20 to 27 2491.60 -0.119 0.452746 21 to 28 2476.01 -0.339 0.367180 22 to 29 2507.80 0.110 0.543942 23 to 30 2634.65 1.904 0.971556 24 to 31 2550.24 0.711 0.761325 25 to 32 2608.62 1.536 0.937753 CDPARK for dh-ranFile-2018-06-29_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 3499 -1.0959 0.136563 3514 -0.4110 0.340551 3531 0.3653 0.642555 3528 0.2283 0.590298 3507 -0.7306 0.232514 3584 2.7854 0.997327 3539 0.7306 0.767486 3551 1.2785 0.899470 3516 -0.3196 0.374623 3523 0.0000 0.500000 Square side=100, avg. no. parked=3529.20 sample std.=23.30 p-value of the KSTEST for those 10 p-values: 0.763366 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_06:31 0.2171,0.7411,0.3033,0.0465,0.5148,0.6966,0.0513,0.2117,0.5555,0.6848, The KS test for those 10 p-values: 0.411320 The 3DSPHERES test for dh-ranFile-2018-06-29_06:31 sample no r^3 equiv. uni. 1 10.583 0.297259 2 17.296 0.438163 3 21.677 0.514500 4 18.715 0.464111 5 28.664 0.615366 6 38.493 0.722825 7 36.104 0.699850 8 66.309 0.890334 9 16.012 0.413582 10 5.279 0.161367 11 66.772 0.892010 12 4.733 0.145937 13 8.475 0.246106 14 46.284 0.786215 15 40.076 0.737073 16 139.917 0.990570 17 32.752 0.664362 18 0.843 0.027693 19 0.047 0.001556 20 35.096 0.689587 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.843289 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 2.6 0.6 -0.4 -1.2 0.3 1.5 -0.0 -1.3 1.1 0.3 1.3 0.3 -0.1 -0.4 0.5 -0.6 -0.8 -0.2 -0.3 0.3 -3.1 0.8 2.3 -0.9 0.0 0.9 -0.8 0.8 0.0 0.3 1.1 2.7 0.4 -1.0 -1.2 0.5 0.8 -0.4 0.4 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:48.447643 z-score=0.703496, p-value=0.771062 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-06-29_06:31 Test no p-value 1 0.571318 2 0.048049 3 0.166474 4 0.147375 5 0.529615 6 0.194192 7 0.248072 8 0.052853 9 0.997440 10 0.181723 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.028606 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_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 66646 0.01 66837 0.44 3 25000.00 24970 0.04 24813 1.40 4 6666.67 6739 0.78 6680 0.03 5 1388.89 1378 0.09 1380 0.06 6 238.10 228 0.43 235 0.04 7 34.72 32 0.21 45 3.04 8 4.96 6 0.22 9 3.29 p=0.06055 p=0.78253 Number of rngs required: 687985, p-value: 0.315 RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_06:31 No. of wins: Observed Expected 98866 98585.9 z-score= 1.253, pvalue=0.89489 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66435 66666.7 0.805 0.805 2 37973 37654.3 2.697 3.502 3 27038 26954.7 0.257 3.759 4 19349 19313.5 0.065 3.825 5 13765 13851.4 0.539 4.364 6 9830 9943.5 1.297 5.660 7 7067 7145.0 0.852 6.512 8 5114 5139.1 0.122 6.635 9 3707 3699.9 0.014 6.649 10 2676 2666.3 0.035 6.684 11 1951 1923.3 0.398 7.082 12 1411 1388.7 0.357 7.439 13 1005 1003.7 0.002 7.440 14 734 726.1 0.085 7.525 15 551 525.8 1.204 8.730 16 371 381.2 0.270 9.000 17 280 276.5 0.043 9.043 18 197 200.8 0.073 9.116 19 146 146.0 0.000 9.116 20 114 106.2 0.571 9.687 21 286 287.1 0.004 9.691 Chisq= 9.69 for 20 degrees of freedom, p= 0.02657 SUMMARY of craptest p-value for no. of wins: 0.894889 p-value for throws/game: 0.026569 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_06:31 No. of wins: Observed Expected 98633 98585.9 z-score= 0.211, pvalue=0.58350 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66853 66666.7 0.521 0.521 2 37415 37654.3 1.521 2.042 3 27106 26954.7 0.849 2.891 4 19367 19313.5 0.148 3.039 5 13803 13851.4 0.169 3.208 6 9982 9943.5 0.149 3.357 7 7034 7145.0 1.725 5.082 8 5213 5139.1 1.063 6.146 9 3646 3699.9 0.784 6.930 10 2684 2666.3 0.118 7.048 11 1921 1923.3 0.003 7.050 12 1373 1388.7 0.178 7.229 13 993 1003.7 0.114 7.343 14 733 726.1 0.065 7.408 15 479 525.8 4.172 11.580 16 395 381.2 0.503 12.083 17 282 276.5 0.108 12.191 18 192 200.8 0.388 12.579 19 152 146.0 0.248 12.827 20 104 106.2 0.046 12.873 21 273 287.1 0.694 13.567 Chisq= 13.57 for 20 degrees of freedom, p= 0.14824 SUMMARY of craptest p-value for no. of wins: 0.583495 p-value for throws/game: 0.148238 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0047,0.0048,0.0052,0.0062,0.0155,0.0266,0.0277,0.0286,0.0340, 0.0348,0.0352,0.0368,0.0451,0.0465,0.0480,0.0513,0.0529,0.0598,0.0604, 0.0605,0.0619,0.0643,0.0713,0.0821,0.0827,0.0938,0.0964,0.0964,0.1182, 0.1351,0.1366,0.1376,0.1431,0.1459,0.1474,0.1482,0.1499,0.1551,0.1614, 0.1664,0.1665,0.1714,0.1792,0.1817,0.1817,0.1886,0.1903,0.1942,0.1973, 0.2015,0.2050,0.2102,0.2117,0.2171,0.2221,0.2243,0.2325,0.2366,0.2377, 0.2377,0.2438,0.2461,0.2481,0.2525,0.2638,0.2739,0.2773,0.2791,0.2831, 0.2832,0.2864,0.2878,0.2890,0.2913,0.2973,0.2979,0.3015,0.3033,0.3068, 0.3131,0.3150,0.3318,0.3355,0.3359,0.3404,0.3406,0.3420,0.3439,0.3462, 0.3477,0.3517,0.3536,0.3552,0.3558,0.3672,0.3735,0.3746,0.3769,0.3834, 0.3884,0.3935,0.3955,0.3974,0.3984,0.4113,0.4136,0.4177,0.4190,0.4228, 0.4282,0.4337,0.4359,0.4382,0.4403,0.4415,0.4420,0.4421,0.4527,0.4641, 0.4725,0.4805,0.4808,0.4849,0.4867,0.5000,0.5043,0.5052,0.5067,0.5145, 0.5148,0.5155,0.5165,0.5188,0.5209,0.5296,0.5332,0.5375,0.5406,0.5439, 0.5529,0.5555,0.5583,0.5585,0.5598,0.5713,0.5835,0.5903,0.5963,0.5963, 0.6012,0.6025,0.6083,0.6112,0.6154,0.6179,0.6188,0.6246,0.6306,0.6323, 0.6332,0.6335,0.6363,0.6385,0.6391,0.6422,0.6426,0.6522,0.6545,0.6644, 0.6651,0.6674,0.6684,0.6693,0.6749,0.6848,0.6864,0.6896,0.6959,0.6959, 0.6966,0.6999,0.7013,0.7051,0.7055,0.7140,0.7196,0.7228,0.7292,0.7337, 0.7371,0.7388,0.7406,0.7410,0.7411,0.7425,0.7613,0.7634,0.7666,0.7675, 0.7711,0.7730,0.7738,0.7765,0.7804,0.7825,0.7839,0.7854,0.7862,0.7882, 0.7884,0.8010,0.8011,0.8028,0.8039,0.8055,0.8067,0.8088,0.8193,0.8197, 0.8263,0.8270,0.8284,0.8366,0.8386,0.8415,0.8419,0.8433,0.8488,0.8503, 0.8517,0.8527,0.8540,0.8566,0.8624,0.8667,0.8678,0.8814,0.8903,0.8920, 0.8925,0.8941,0.8949,0.8955,0.8988,0.8995,0.9040,0.9049,0.9122,0.9305, 0.9340,0.9378,0.9495,0.9554,0.9632,0.9645,0.9716,0.9769,0.9782,0.9802, 0.9865,0.9888,0.9906,0.9930,0.9954,0.9973,0.9974,0.9975,0.9999, Overall p-value after applying KStest on 269 p-values = 0.519242 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.