RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-15_15:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 13.5109 0.298632 2 to 25 15.80 10.8907 0.137810 3 to 26 15.80 10.7640 0.131436 4 to 27 15.47 22.6042 0.837414 5 to 28 15.79 19.1558 0.680335 6 to 29 15.81 21.4922 0.794956 7 to 30 15.48 19.7835 0.714549 8 to 31 15.83 14.8394 0.392954 9 to 32 15.74 21.1839 0.781826 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.767009 Tough bday spacings test for dh-ranFile-2016-03-15_15:31: 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 10 30 65 104 105 79 52 31 14 4 6 (O-E)^2/E 0.1 1.2 0.9 0.4 0.5 0.0 0.0 0.1 0.1 1.0 0.9 Birthday Spacings: Sum(O-E)^2/E= 5.233, p= 0.125 RESULTS OF GCD FOR dh-ranFile-2016-03-15_15:31 Euclid's algorithm: p-value, steps to gcd: 0.871335 p-value, dist. of gcd's: 0.194065 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-15_15:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.861 0.737 0.078 0.729 0.459 0.704 0.617 0.025 Bits 8 to 15---> 0.753 0.457 0.816 0.136 0.952 0.261 0.011 0.466 Bits 16 to 23---> 0.220 0.474 0.408 0.841 0.559 0.176 0.059 0.154 Bits 24 to 31---> 0.492 0.592 0.083 0.615 0.809 0.194 0.282 0.448 KS test for the above 32 p values: 0.446 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-15_15:31, p-values for 5 runs: 0.7443, 0.5675, 0.7224, 0.7187, 0.4262 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-15_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5314 5134.0 6.310 6.570 r= 30 23030 23103.0 0.231 6.801 r= 31 11452 11551.5 0.857 7.659 chi-square = 7.659 with df = 3; p-value = 0.946 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-15_15:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5106 5134.0 0.153 0.882 r= 31 23284 23103.0 1.417 2.300 r= 32 11411 11551.5 1.709 4.009 chi-square = 4.009 with df = 3; p-value = 0.740 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-15_15:31 b-rank test for bits 1 to 8, p=0.55243 b-rank test for bits 2 to 9, p=0.75754 b-rank test for bits 3 to 10, p=0.57547 b-rank test for bits 4 to 11, p=0.48422 b-rank test for bits 5 to 12, p=0.30138 b-rank test for bits 6 to 13, p=0.70429 b-rank test for bits 7 to 14, p=0.22062 b-rank test for bits 8 to 15, p=0.20967 b-rank test for bits 9 to 16, p=0.18069 b-rank test for bits 10 to 17, p=0.92248 b-rank test for bits 11 to 18, p=0.44404 b-rank test for bits 12 to 19, p=0.22134 b-rank test for bits 13 to 20, p=0.48534 b-rank test for bits 14 to 21, p=0.21639 b-rank test for bits 15 to 22, p=0.20389 b-rank test for bits 16 to 23, p=0.47034 b-rank test for bits 17 to 24, p=0.60738 b-rank test for bits 18 to 25, p=0.59658 b-rank test for bits 19 to 26, p=0.23494 b-rank test for bits 20 to 27, p=0.08893 b-rank test for bits 21 to 28, p=0.08019 b-rank test for bits 22 to 29, p=0.08423 b-rank test for bits 23 to 30, p=0.14174 b-rank test for bits 24 to 31, p=0.98017 b-rank test for bits 25 to 32, p=0.04146 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 = 0.079062 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-15_15:31 (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 142441 1.24 0.892922 2 141657 -0.59 0.277744 3 141922 0.03 0.511808 4 141885 -0.06 0.477334 5 141786 -0.29 0.386614 6 141625 -0.66 0.253242 7 142298 0.91 0.818089 8 143154 2.91 0.998182 9 141909 -0.00 0.499692 10 141941 0.07 0.529493 11 141757 -0.36 0.360954 12 141718 -0.45 0.327426 13 142866 2.24 0.987298 14 142259 0.82 0.793032 15 142147 0.56 0.710657 16 142240 0.77 0.780119 17 141944 0.08 0.532281 18 141868 -0.10 0.461536 19 141926 0.04 0.515534 20 141157 -1.76 0.039392 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-15_15:31 Bits used No. missing words z-score p-value 23 to 32 141627 -0.9736 0.165140 22 to 31 141739 -0.5873 0.278486 21 to 30 142325 1.4333 0.924120 20 to 29 142029 0.4127 0.660070 19 to 28 141750 -0.5494 0.291361 18 to 27 141883 -0.0908 0.463829 17 to 26 142243 1.1506 0.875049 16 to 25 141911 0.0058 0.502297 15 to 24 142020 0.3816 0.648629 14 to 23 141451 -1.5804 0.057002 13 to 22 142030 0.4161 0.661333 12 to 21 141535 -1.2908 0.098388 11 to 20 141878 -0.1080 0.456984 10 to 19 141816 -0.3218 0.373792 9 to 18 142068 0.5471 0.707858 8 to 17 141728 -0.6253 0.265895 7 to 16 142453 1.8747 0.969585 6 to 15 141519 -1.3460 0.089157 5 to 14 141492 -1.4391 0.075066 4 to 13 142129 0.7575 0.775620 3 to 12 141271 -2.2011 0.013863 2 to 11 141439 -1.6218 0.052420 1 to 10 141468 -1.5218 0.064026 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-15_15:31 Bits used No. missing words z-score p-value 28 to 32 141641 -0.9096 0.181519 27 to 31 141799 -0.3740 0.354202 26 to 30 142150 0.8158 0.792702 25 to 29 142124 0.7277 0.766600 24 to 28 141610 -1.0147 0.155130 23 to 27 141981 0.2429 0.595978 22 to 26 141879 -0.1028 0.459056 21 to 25 141837 -0.2452 0.403156 20 to 24 142182 0.9243 0.822336 19 to 23 141323 -1.9876 0.023430 18 to 22 142089 0.6091 0.728755 17 to 21 141903 -0.0215 0.491440 16 to 20 141790 -0.4045 0.342919 15 to 19 142136 0.7684 0.778867 14 to 18 141212 -2.3638 0.009044 13 to 17 141492 -1.4147 0.078581 12 to 16 141389 -1.7638 0.038880 11 to 15 141875 -0.1164 0.453679 10 to 14 142010 0.3413 0.633544 9 to 13 141404 -1.7130 0.043358 8 to 12 142242 1.1277 0.870276 7 to 11 141912 0.0091 0.503611 6 to 10 141527 -1.2960 0.097482 5 to 9 141672 -0.8045 0.210552 4 to 8 142266 1.2091 0.886678 3 to 7 141811 -0.3333 0.369446 2 to 6 141435 -1.6079 0.053929 1 to 5 141747 -0.5503 0.291067 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-15_15:31 Bits used No. missing words z-score p-value 31 to 32 141684 -0.6647 0.253124 30 to 31 141872 -0.1101 0.456158 29 to 30 141926 0.0492 0.519610 28 to 29 141730 -0.5290 0.298404 27 to 28 141947 0.1111 0.544240 26 to 27 142108 0.5860 0.721078 25 to 26 141368 -1.5968 0.055150 24 to 25 142361 1.3324 0.908629 23 to 24 141726 -0.5408 0.294324 22 to 23 141779 -0.3845 0.350321 21 to 22 141996 0.2557 0.600895 20 to 21 141174 -2.1691 0.015037 19 to 20 141445 -1.3697 0.085390 18 to 19 141842 -0.1986 0.421283 17 to 18 141571 -0.9980 0.159134 16 to 17 141438 -1.3904 0.082211 15 to 16 142103 0.5713 0.716101 14 to 15 142244 0.9872 0.838234 13 to 14 141947 0.1111 0.544240 12 to 13 141654 -0.7532 0.225669 11 to 12 142162 0.7453 0.771967 10 to 11 141987 0.2291 0.590610 9 to 10 142500 1.7424 0.959280 8 to 9 142334 1.2527 0.894845 7 to 8 141908 -0.0039 0.498435 6 to 7 142060 0.4445 0.671643 5 to 6 141713 -0.5791 0.281246 4 to 5 141871 -0.1131 0.454988 3 to 4 141736 -0.5113 0.304571 2 to 3 141550 -1.0600 0.144579 1 to 2 141938 0.0846 0.533699 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-15_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2352.69 -2.083 0.018611 Test results for specific bytes for dh-ranFile-2016-03-15_15:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2685.58 2.624 0.995661 2 to 9 2508.24 0.116 0.546368 3 to 10 2399.62 -1.420 0.077867 4 to 11 2611.33 1.574 0.942308 5 to 12 2449.71 -0.711 0.238471 6 to 13 2403.18 -1.369 0.085463 7 to 14 2530.45 0.431 0.666612 8 to 15 2584.96 1.202 0.885228 9 to 16 2508.46 0.120 0.547600 10 to 17 2463.43 -0.517 0.302536 11 to 18 2571.93 1.017 0.845492 12 to 19 2433.91 -0.935 0.174992 13 to 20 2627.41 1.802 0.964220 14 to 21 2565.71 0.929 0.823635 15 to 22 2586.07 1.217 0.888246 16 to 23 2600.85 1.426 0.923095 17 to 24 2460.91 -0.553 0.290187 18 to 25 2462.58 -0.529 0.298318 19 to 26 2564.76 0.916 0.820110 20 to 27 2457.68 -0.598 0.274766 21 to 28 2495.29 -0.067 0.473426 22 to 29 2527.80 0.393 0.652911 23 to 30 2421.39 -1.112 0.133137 24 to 31 2524.10 0.341 0.633357 25 to 32 2506.82 0.096 0.538404 CDPARK for dh-ranFile-2016-03-15_15:31: 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 3542 0.8676 0.807188 3524 0.0457 0.518210 3516 -0.3196 0.374623 3511 -0.5479 0.291865 3479 -2.0091 0.022262 3525 0.0913 0.536383 3532 0.4110 0.659449 3496 -1.2329 0.108811 3511 -0.5479 0.291865 3489 -1.5525 0.060270 Square side=100, avg. no. parked=3512.50 sample std.=18.71 p-value of the KSTEST for those 10 p-values: 0.252134 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-15_15:31 0.9086,0.6618,0.3679,0.2483,0.0083,0.3710,0.0616,0.5386,0.7132,0.0372, The KS test for those 10 p-values: 0.278098 The 3DSPHERES test for dh-ranFile-2016-03-15_15:31 sample no r^3 equiv. uni. 1 21.137 0.505669 2 3.128 0.099014 3 73.166 0.912739 4 44.384 0.772244 5 66.719 0.891822 6 6.137 0.184989 7 32.704 0.663828 8 51.042 0.817573 9 22.335 0.525036 10 27.653 0.602184 11 8.926 0.257348 12 29.233 0.622598 13 1.973 0.063647 14 33.267 0.670078 15 12.217 0.334517 16 62.648 0.876097 17 25.769 0.576407 18 39.819 0.734808 19 123.403 0.983649 20 13.969 0.372254 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.492244 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-15_15:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 1.3 1.5 -0.4 0.8 0.5 0.6 0.7 2.8 0.4 0.0 0.8 -0.3 0.1 -0.2 0.9 0.2 -1.7 -1.1 -0.1 -1.0 -1.0 0.7 0.6 1.2 0.1 -0.3 -0.3 -0.3 0.7 -1.4 -0.4 0.8 0.8 -2.0 -0.8 -1.2 1.5 0.5 0.4 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:39.985744 z-score=-0.219773, p-value=0.440274 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-15_15:31 Test no p-value 1 0.762832 2 0.038881 3 0.853727 4 0.115969 5 0.724213 6 0.425973 7 0.006109 8 0.073359 9 0.123464 10 0.740309 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.097763 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-15_15:31: (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 66624 0.03 66787 0.22 3 25000.00 25138 0.76 24913 0.30 4 6666.67 6617 0.37 6626 0.25 5 1388.89 1346 1.32 1399 0.07 6 238.10 237 0.01 235 0.04 7 34.72 31 0.40 37 0.15 8 4.96 6 0.22 2 1.77 p=0.20448 p=0.16627 Number of rngs required: 687091, p-value: 0.063 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-15_15:31 No. of wins: Observed Expected 98707 98585.9 z-score= 0.542, pvalue=0.70603 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67045 66666.7 2.147 2.147 2 37502 37654.3 0.616 2.763 3 27049 26954.7 0.330 3.093 4 19053 19313.5 3.513 6.605 5 13809 13851.4 0.130 6.735 6 9887 9943.5 0.322 7.057 7 7220 7145.0 0.787 7.844 8 5084 5139.1 0.590 8.434 9 3790 3699.9 2.196 10.630 10 2640 2666.3 0.259 10.889 11 1842 1923.3 3.439 14.328 12 1394 1388.7 0.020 14.348 13 1023 1003.7 0.371 14.719 14 739 726.1 0.228 14.946 15 541 525.8 0.437 15.384 16 380 381.2 0.003 15.387 17 264 276.5 0.569 15.956 18 214 200.8 0.864 16.819 19 157 146.0 0.831 17.651 20 87 106.2 3.476 21.127 21 280 287.1 0.176 21.303 Chisq= 21.30 for 20 degrees of freedom, p= 0.62050 SUMMARY of craptest p-value for no. of wins: 0.706027 p-value for throws/game: 0.620505 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-15_15:31 No. of wins: Observed Expected 98524 98585.9 z-score=-0.277, pvalue=0.39102 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66710 66666.7 0.028 0.028 2 37451 37654.3 1.098 1.126 3 26940 26954.7 0.008 1.134 4 19461 19313.5 1.127 2.261 5 13829 13851.4 0.036 2.297 6 10198 9943.5 6.512 8.809 7 7211 7145.0 0.609 9.418 8 5045 5139.1 1.722 11.140 9 3691 3699.9 0.021 11.161 10 2568 2666.3 3.624 14.785 11 1936 1923.3 0.083 14.869 12 1392 1388.7 0.008 14.876 13 979 1003.7 0.609 15.485 14 696 726.1 1.251 16.736 15 511 525.8 0.419 17.155 16 401 381.2 1.034 18.188 17 269 276.5 0.206 18.394 18 182 200.8 1.765 20.159 19 138 146.0 0.437 20.596 20 104 106.2 0.046 20.642 21 288 287.1 0.003 20.645 Chisq= 20.65 for 20 degrees of freedom, p= 0.58172 SUMMARY of craptest p-value for no. of wins: 0.391018 p-value for throws/game: 0.581721 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0061,0.0083,0.0090,0.0109,0.0139,0.0150,0.0186,0.0223,0.0234,0.0247, 0.0372,0.0389,0.0389,0.0394,0.0415,0.0434,0.0524,0.0539,0.0552,0.0570, 0.0589,0.0603,0.0616,0.0626,0.0636,0.0640,0.0734,0.0751,0.0776,0.0779, 0.0786,0.0791,0.0802,0.0822,0.0833,0.0842,0.0854,0.0855,0.0889,0.0892, 0.0975,0.0978,0.0984,0.0990,0.1088,0.1160,0.1235,0.1249,0.1314,0.1331, 0.1365,0.1378,0.1417,0.1446,0.1544,0.1551,0.1591,0.1651,0.1663,0.1750, 0.1759,0.1807,0.1815,0.1850,0.1941,0.1943,0.2039,0.2045,0.2097,0.2106, 0.2164,0.2198,0.2206,0.2213,0.2257,0.2349,0.2385,0.2483,0.2521,0.2531, 0.2532,0.2573,0.2614,0.2659,0.2748,0.2777,0.2781,0.2785,0.2812,0.2818, 0.2902,0.2911,0.2914,0.2919,0.2919,0.2943,0.2983,0.2984,0.2986,0.3014, 0.3025,0.3046,0.3274,0.3345,0.3429,0.3503,0.3542,0.3610,0.3679,0.3694, 0.3710,0.3723,0.3738,0.3746,0.3866,0.3910,0.3930,0.4032,0.4078,0.4213, 0.4260,0.4262,0.4403,0.4440,0.4457,0.4479,0.4537,0.4550,0.4562,0.4570, 0.4571,0.4591,0.4593,0.4615,0.4638,0.4664,0.4703,0.4734,0.4737,0.4773, 0.4842,0.4853,0.4914,0.4916,0.4922,0.4984,0.4997,0.5023,0.5036,0.5057, 0.5118,0.5155,0.5182,0.5196,0.5250,0.5295,0.5323,0.5337,0.5364,0.5384, 0.5386,0.5442,0.5442,0.5464,0.5476,0.5524,0.5585,0.5675,0.5755,0.5764, 0.5817,0.5906,0.5924,0.5960,0.5966,0.6009,0.6022,0.6074,0.6145,0.6168, 0.6205,0.6226,0.6334,0.6335,0.6486,0.6529,0.6594,0.6601,0.6613,0.6618, 0.6638,0.6666,0.6701,0.6716,0.6803,0.7038,0.7043,0.7060,0.7079,0.7107, 0.7132,0.7145,0.7161,0.7187,0.7211,0.7224,0.7242,0.7288,0.7295,0.7348, 0.7374,0.7395,0.7403,0.7443,0.7532,0.7575,0.7628,0.7666,0.7670,0.7720, 0.7722,0.7756,0.7789,0.7801,0.7818,0.7927,0.7930,0.7950,0.8072,0.8086, 0.8156,0.8176,0.8181,0.8201,0.8223,0.8236,0.8374,0.8382,0.8406,0.8455, 0.8537,0.8610,0.8703,0.8713,0.8750,0.8761,0.8852,0.8867,0.8882,0.8918, 0.8929,0.8948,0.9086,0.9086,0.9127,0.9225,0.9231,0.9241,0.9423,0.9464, 0.9522,0.9593,0.9642,0.9696,0.9802,0.9836,0.9873,0.9957,0.9982, Overall p-value after applying KStest on 269 p-values = 0.028660 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.