RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-29_03:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.91 12.7993 0.250486 2 to 25 15.84 12.2356 0.214337 3 to 26 15.83 8.1150 0.035974 4 to 27 15.69 18.6954 0.653709 5 to 28 15.86 16.5836 0.517098 6 to 29 15.94 18.7136 0.654784 7 to 30 15.97 27.0564 0.942754 8 to 31 15.37 28.1659 0.956963 9 to 32 15.90 8.6286 0.048803 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.666452 Tough bday spacings test for dh-ranFile-2015-08-29_03:31: 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 15 38 75 104 93 73 47 31 12 6 6 (O-E)^2/E 3.7 0.1 0.0 0.4 0.2 0.3 0.5 0.1 0.6 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 6.877, p= 0.263 RESULTS OF GCD FOR dh-ranFile-2015-08-29_03:31 Euclid's algorithm: p-value, steps to gcd: 0.792897 p-value, dist. of gcd's: 0.360508 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-29_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.020 0.894 0.919 0.541 0.703 0.109 0.366 0.197 Bits 8 to 15---> 0.893 0.686 0.771 0.023 0.265 0.855 0.372 0.498 Bits 16 to 23---> 0.462 0.625 0.918 0.607 0.579 0.095 0.910 0.159 Bits 24 to 31---> 0.195 0.684 0.606 0.743 0.006 0.264 0.711 0.223 KS test for the above 32 p values: 0.166 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-29_03:31, p-values for 5 runs: 0.0809, 0.4279, 0.2844, 0.6693, 0.9675 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-29_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5062 5134.0 1.010 1.993 r= 30 23129 23103.0 0.029 2.022 r= 31 11612 11551.5 0.317 2.339 chi-square = 2.339 with df = 3; p-value = 0.495 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-29_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 205 211.4 0.195 0.195 r= 30 5181 5134.0 0.430 0.625 r= 31 23122 23103.0 0.016 0.640 r= 32 11492 11551.5 0.307 0.947 chi-square = 0.947 with df = 3; p-value = 0.186 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-29_03:31 b-rank test for bits 1 to 8, p=0.33061 b-rank test for bits 2 to 9, p=0.91406 b-rank test for bits 3 to 10, p=0.86620 b-rank test for bits 4 to 11, p=0.38784 b-rank test for bits 5 to 12, p=0.20356 b-rank test for bits 6 to 13, p=0.41986 b-rank test for bits 7 to 14, p=0.83885 b-rank test for bits 8 to 15, p=0.74262 b-rank test for bits 9 to 16, p=0.74937 b-rank test for bits 10 to 17, p=0.23767 b-rank test for bits 11 to 18, p=0.83150 b-rank test for bits 12 to 19, p=0.01270 b-rank test for bits 13 to 20, p=0.63154 b-rank test for bits 14 to 21, p=0.83047 b-rank test for bits 15 to 22, p=0.76273 b-rank test for bits 16 to 23, p=0.63426 b-rank test for bits 17 to 24, p=0.56472 b-rank test for bits 18 to 25, p=0.14948 b-rank test for bits 19 to 26, p=0.64218 b-rank test for bits 20 to 27, p=0.84322 b-rank test for bits 21 to 28, p=0.92520 b-rank test for bits 22 to 29, p=0.91261 b-rank test for bits 23 to 30, p=0.75550 b-rank test for bits 24 to 31, p=0.26631 b-rank test for bits 25 to 32, p=0.71817 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 = 0.070001 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-29_03:31 (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 141746 -0.38 0.351375 2 142251 0.80 0.787650 3 142263 0.83 0.795692 4 141768 -0.33 0.370621 5 142648 1.73 0.957814 6 142029 0.28 0.610109 7 141634 -0.64 0.260017 8 142818 2.12 0.983126 9 142298 0.91 0.818089 10 142038 0.30 0.618152 11 142126 0.51 0.693655 12 141343 -1.32 0.092884 13 141706 -0.48 0.317369 14 141591 -0.74 0.228510 15 141320 -1.38 0.084266 16 142346 1.02 0.846197 17 142542 1.48 0.930323 18 141283 -1.46 0.071681 19 141791 -0.28 0.391093 20 142561 1.52 0.936070 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-29_03:31 Bits used No. missing words z-score p-value 23 to 32 141593 -1.0908 0.137682 22 to 31 141894 -0.0529 0.478921 21 to 30 142312 1.3885 0.917510 20 to 29 141711 -0.6839 0.247020 19 to 28 141931 0.0747 0.529783 18 to 27 141883 -0.0908 0.463829 17 to 26 141443 -1.6080 0.053914 16 to 25 141322 -2.0253 0.021420 15 to 24 141694 -0.7425 0.228887 14 to 23 141485 -1.4632 0.071705 13 to 22 141846 -0.2184 0.413567 12 to 21 141428 -1.6598 0.048482 11 to 20 142319 1.4127 0.921121 10 to 19 142181 0.9368 0.825568 9 to 18 142101 0.6609 0.745672 8 to 17 141592 -1.0942 0.136925 7 to 16 141845 -0.2218 0.412224 6 to 15 141779 -0.4494 0.326567 5 to 14 141909 -0.0011 0.499546 4 to 13 141825 -0.2908 0.385605 3 to 12 141861 -0.1667 0.433821 2 to 11 141777 -0.4563 0.324083 1 to 10 141946 0.1264 0.550312 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-29_03:31 Bits used No. missing words z-score p-value 28 to 32 142077 0.5684 0.715109 27 to 31 141829 -0.2723 0.392694 26 to 30 141854 -0.1876 0.425611 25 to 29 142376 1.5819 0.943167 24 to 28 142096 0.6328 0.736561 23 to 27 142140 0.7819 0.782873 22 to 26 141681 -0.7740 0.219465 21 to 25 142389 1.6260 0.948025 20 to 24 141875 -0.1164 0.453679 19 to 23 142455 1.8497 0.967824 18 to 22 142157 0.8396 0.799422 17 to 21 141207 -2.3808 0.008638 16 to 20 141950 0.1379 0.554826 15 to 19 141897 -0.0418 0.483330 14 to 18 141949 0.1345 0.553486 13 to 17 141722 -0.6350 0.262709 12 to 16 141771 -0.4689 0.319565 11 to 15 141946 0.1243 0.549463 10 to 14 141959 0.1684 0.566855 9 to 13 141749 -0.5435 0.293396 8 to 12 142075 0.5616 0.712803 7 to 11 141720 -0.6418 0.260503 6 to 10 142077 0.5684 0.715109 5 to 9 142027 0.3989 0.655010 4 to 8 141808 -0.3435 0.365614 3 to 7 142117 0.7040 0.759273 2 to 6 141519 -1.3232 0.092892 1 to 5 141714 -0.6621 0.253942 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-29_03:31 Bits used No. missing words z-score p-value 31 to 32 142027 0.3471 0.635745 30 to 31 141793 -0.3432 0.365740 29 to 30 142129 0.6480 0.741506 28 to 29 142149 0.7070 0.760214 27 to 28 142086 0.5212 0.698869 26 to 27 142650 2.1849 0.985551 25 to 26 141587 -0.9508 0.170846 24 to 25 142455 1.6096 0.946262 23 to 24 142083 0.5123 0.695780 22 to 23 142160 0.7394 0.770180 21 to 22 141399 -1.5054 0.066111 20 to 21 141772 -0.4051 0.342701 19 to 20 141383 -1.5526 0.060260 18 to 19 142037 0.3766 0.646767 17 to 18 142177 0.7896 0.785116 16 to 17 141903 -0.0187 0.492551 15 to 16 141860 -0.1455 0.442152 14 to 15 141847 -0.1839 0.427060 13 to 14 141965 0.1642 0.565220 12 to 13 142015 0.3117 0.622370 11 to 12 141176 -2.1632 0.015262 10 to 11 141275 -1.8712 0.030660 9 to 10 142136 0.6686 0.748138 8 to 9 142560 1.9194 0.972532 7 to 8 141791 -0.3491 0.363524 6 to 7 142159 0.7365 0.769284 5 to 6 142046 0.4032 0.656583 4 to 5 142130 0.6509 0.742459 3 to 4 141920 0.0315 0.512555 2 to 3 142074 0.4858 0.686429 1 to 2 141691 -0.6440 0.259774 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-29_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2436.19 -0.902 0.183412 Test results for specific bytes for dh-ranFile-2015-08-29_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2462.72 -0.527 0.299042 2 to 9 2586.12 1.218 0.888384 3 to 10 2467.85 -0.455 0.324664 4 to 11 2482.98 -0.241 0.404910 5 to 12 2467.20 -0.464 0.321398 6 to 13 2477.65 -0.316 0.375987 7 to 14 2598.07 1.387 0.917260 8 to 15 2460.66 -0.556 0.289006 9 to 16 2443.19 -0.803 0.210852 10 to 17 2463.01 -0.523 0.300466 11 to 18 2563.64 0.900 0.815941 12 to 19 2573.79 1.044 0.851656 13 to 20 2470.74 -0.414 0.339518 14 to 21 2517.49 0.247 0.597671 15 to 22 2447.62 -0.741 0.229435 16 to 23 2454.28 -0.647 0.258939 17 to 24 2275.77 -3.171 0.000759 18 to 25 2605.61 1.494 0.932347 19 to 26 2542.08 0.595 0.724097 20 to 27 2411.34 -1.254 0.104960 21 to 28 2535.98 0.509 0.694577 22 to 29 2425.70 -1.051 0.146675 23 to 30 2586.26 1.220 0.888755 24 to 31 2412.22 -1.241 0.107239 25 to 32 2518.66 0.264 0.604084 CDPARK for dh-ranFile-2015-08-29_03:31: 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 3565 1.9178 0.972432 3494 -1.3242 0.092718 3574 2.3288 0.990064 3547 1.0959 0.863437 3531 0.3653 0.642555 3569 2.1005 0.982156 3520 -0.1370 0.445521 3522 -0.0457 0.481790 3539 0.7306 0.767486 3555 1.4612 0.928018 Square side=100, avg. no. parked=3541.60 sample std.=24.07 p-value of the KSTEST for those 10 p-values: 0.009147 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-29_03:31 0.0094,0.8044,0.5263,0.2262,0.3759,0.3190,0.9509,0.0824,0.4746,0.8579, The KS test for those 10 p-values: 0.898409 The 3DSPHERES test for dh-ranFile-2015-08-29_03:31 sample no r^3 equiv. uni. 1 12.866 0.348752 2 14.683 0.387033 3 52.888 0.828457 4 45.441 0.780127 5 1.363 0.044403 6 48.850 0.803747 7 7.185 0.212966 8 77.304 0.923984 9 37.589 0.714340 10 14.815 0.389708 11 0.278 0.009233 12 4.646 0.143468 13 23.976 0.550305 14 37.719 0.715575 15 58.394 0.857224 16 77.139 0.923565 17 6.443 0.193262 18 76.567 0.922092 19 10.381 0.292520 20 22.586 0.528987 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.814088 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-29_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.7 -0.8 0.2 -0.5 1.3 0.3 1.0 0.4 0.8 -0.2 1.6 -1.4 -0.4 0.3 0.0 0.9 1.6 -0.1 -2.0 -0.2 -2.3 -1.0 2.2 -1.2 0.9 -0.0 1.7 -1.5 -1.1 1.6 1.0 -0.8 0.0 -1.3 0.8 -1.2 0.2 -0.4 0.4 0.9 -1.0 -1.1 Chi-square with 42 degrees of freedom:51.016819 z-score=0.983816, p-value=0.839572 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-29_03:31 Test no p-value 1 0.274171 2 0.611771 3 0.119478 4 0.714593 5 0.090610 6 0.520101 7 0.028473 8 0.398327 9 0.176385 10 0.120679 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.051814 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-29_03:31: (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 66857 0.54 66509 0.37 3 25000.00 24951 0.10 25133 0.71 4 6666.67 6532 2.72 6619 0.34 5 1388.89 1348 1.20 1439 1.81 6 238.10 259 1.84 258 1.66 7 34.72 47 4.34 33 0.09 8 4.96 5 0.00 8 1.86 p=0.90334 p=0.66427 Number of rngs required: 689480, p-value: 0.895 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-29_03:31 No. of wins: Observed Expected 98842 98585.9 z-score= 1.146, pvalue=0.87402 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66501 66666.7 0.412 0.412 2 37726 37654.3 0.136 0.548 3 26838 26954.7 0.506 1.054 4 19413 19313.5 0.513 1.567 5 14016 13851.4 1.956 3.522 6 9943 9943.5 0.000 3.522 7 7101 7145.0 0.271 3.793 8 4992 5139.1 4.209 8.002 9 3696 3699.9 0.004 8.006 10 2671 2666.3 0.008 8.015 11 1949 1923.3 0.343 8.357 12 1389 1388.7 0.000 8.357 13 1083 1003.7 6.263 14.620 14 748 726.1 0.658 15.278 15 541 525.8 0.437 15.716 16 392 381.2 0.309 16.024 17 273 276.5 0.045 16.070 18 229 200.8 3.951 20.021 19 128 146.0 2.216 22.237 20 103 106.2 0.097 22.334 21 268 287.1 1.272 23.607 Chisq= 23.61 for 20 degrees of freedom, p= 0.74000 SUMMARY of craptest p-value for no. of wins: 0.874023 p-value for throws/game: 0.739997 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-29_03:31 No. of wins: Observed Expected 98217 98585.9 z-score=-1.650, pvalue=0.04950 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66425 66666.7 0.876 0.876 2 37714 37654.3 0.095 0.971 3 27048 26954.7 0.323 1.293 4 19398 19313.5 0.370 1.663 5 13809 13851.4 0.130 1.793 6 10102 9943.5 2.525 4.318 7 7157 7145.0 0.020 4.338 8 5134 5139.1 0.005 4.343 9 3789 3699.9 2.147 6.491 10 2612 2666.3 1.106 7.597 11 1944 1923.3 0.222 7.819 12 1355 1388.7 0.820 8.639 13 951 1003.7 2.769 11.407 14 745 726.1 0.490 11.897 15 522 525.8 0.028 11.925 16 356 381.2 1.660 13.584 17 280 276.5 0.043 13.628 18 180 200.8 2.160 15.788 19 129 146.0 1.976 17.764 20 86 106.2 3.847 21.612 21 264 287.1 1.861 23.472 Chisq= 23.47 for 20 degrees of freedom, p= 0.73381 SUMMARY of craptest p-value for no. of wins: 0.049497 p-value for throws/game: 0.733806 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0008,0.0059,0.0086,0.0091,0.0092,0.0094,0.0127,0.0153,0.0204,0.0214, 0.0225,0.0285,0.0307,0.0360,0.0444,0.0485,0.0488,0.0495,0.0518,0.0539, 0.0603,0.0661,0.0700,0.0717,0.0717,0.0809,0.0824,0.0843,0.0906,0.0927, 0.0929,0.0929,0.0945,0.1050,0.1072,0.1094,0.1195,0.1207,0.1369,0.1377, 0.1435,0.1467,0.1495,0.1589,0.1663,0.1708,0.1764,0.1834,0.1860,0.1933, 0.1950,0.1969,0.2036,0.2109,0.2130,0.2143,0.2195,0.2226,0.2262,0.2285, 0.2289,0.2294,0.2377,0.2470,0.2505,0.2539,0.2589,0.2598,0.2600,0.2605, 0.2627,0.2630,0.2635,0.2652,0.2663,0.2742,0.2844,0.2890,0.2925,0.2934, 0.2990,0.3005,0.3174,0.3190,0.3196,0.3214,0.3241,0.3247,0.3266,0.3306, 0.3395,0.3427,0.3488,0.3514,0.3605,0.3635,0.3656,0.3657,0.3662,0.3706, 0.3720,0.3759,0.3760,0.3856,0.3870,0.3878,0.3897,0.3911,0.3927,0.3983, 0.4049,0.4122,0.4136,0.4199,0.4256,0.4271,0.4279,0.4338,0.4422,0.4455, 0.4537,0.4617,0.4638,0.4746,0.4789,0.4818,0.4833,0.4926,0.4949,0.4985, 0.4995,0.5126,0.5171,0.5201,0.5263,0.5290,0.5298,0.5415,0.5495,0.5503, 0.5503,0.5535,0.5548,0.5647,0.5652,0.5669,0.5789,0.5977,0.6041,0.6061, 0.6070,0.6101,0.6118,0.6182,0.6224,0.6248,0.6315,0.6343,0.6357,0.6422, 0.6426,0.6468,0.6537,0.6548,0.6550,0.6566,0.6643,0.6665,0.6693,0.6838, 0.6864,0.6865,0.6937,0.6946,0.6958,0.6989,0.7031,0.7108,0.7128,0.7143, 0.7146,0.7151,0.7151,0.7156,0.7182,0.7241,0.7338,0.7366,0.7400,0.7415, 0.7425,0.7426,0.7434,0.7457,0.7481,0.7494,0.7555,0.7593,0.7602,0.7627, 0.7675,0.7693,0.7702,0.7714,0.7801,0.7829,0.7851,0.7877,0.7929,0.7957, 0.7994,0.8037,0.8044,0.8141,0.8159,0.8181,0.8256,0.8285,0.8305,0.8315, 0.8388,0.8396,0.8432,0.8462,0.8517,0.8552,0.8572,0.8579,0.8634,0.8662, 0.8740,0.8884,0.8888,0.8928,0.8943,0.8948,0.8984,0.9033,0.9098,0.9126, 0.9141,0.9173,0.9175,0.9184,0.9195,0.9211,0.9221,0.9236,0.9240,0.9252, 0.9280,0.9303,0.9323,0.9361,0.9428,0.9432,0.9463,0.9480,0.9509,0.9570, 0.9578,0.9675,0.9678,0.9724,0.9725,0.9822,0.9831,0.9856,0.9901, Overall p-value after applying KStest on 269 p-values = 0.437252 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.