RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-30_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 12.2580 0.215729 2 to 25 15.42 24.4229 0.891607 3 to 26 15.34 30.4546 0.976753 4 to 27 15.56 35.3616 0.994425 5 to 28 15.67 17.3909 0.571800 6 to 29 15.70 19.0238 0.672832 7 to 30 16.20 9.7586 0.086571 8 to 31 15.69 26.0841 0.927059 9 to 32 15.72 14.6679 0.380611 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.106062 Tough bday spacings test for dh-ranFile-2016-01-30_04:31: 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 11 33 67 85 119 79 52 29 17 5 3 (O-E)^2/E 0.4 0.4 0.5 1.6 4.7 0.0 0.0 0.0 0.3 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.568, p= 0.427 RESULTS OF GCD FOR dh-ranFile-2016-01-30_04:31 Euclid's algorithm: p-value, steps to gcd: 0.182727 p-value, dist. of gcd's: 0.384246 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-30_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.520 0.681 0.347 0.637 0.074 0.157 0.293 0.062 Bits 8 to 15---> 0.561 0.082 0.903 0.026 0.261 0.036 0.613 0.911 Bits 16 to 23---> 0.902 0.873 0.422 0.801 0.736 0.246 0.823 0.533 Bits 24 to 31---> 0.951 0.454 0.260 0.693 0.766 0.591 0.228 0.213 KS test for the above 32 p values: 0.021 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-30_04:31, p-values for 5 runs: 0.5312, 0.5780, 0.5841, 0.7925, 0.6374 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-30_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5148 5134.0 0.038 0.911 r= 30 23172 23103.0 0.206 1.116 r= 31 11455 11551.5 0.807 1.923 chi-square = 1.923 with df = 3; p-value = 0.411 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-30_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5223 5134.0 1.542 2.291 r= 31 22975 23103.0 0.710 3.001 r= 32 11578 11551.5 0.061 3.062 chi-square = 3.062 with df = 3; p-value = 0.618 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-30_04:31 b-rank test for bits 1 to 8, p=0.11454 b-rank test for bits 2 to 9, p=0.03123 b-rank test for bits 3 to 10, p=0.29662 b-rank test for bits 4 to 11, p=0.58083 b-rank test for bits 5 to 12, p=0.58420 b-rank test for bits 6 to 13, p=0.08580 b-rank test for bits 7 to 14, p=0.38659 b-rank test for bits 8 to 15, p=0.43197 b-rank test for bits 9 to 16, p=0.09875 b-rank test for bits 10 to 17, p=0.81157 b-rank test for bits 11 to 18, p=0.59527 b-rank test for bits 12 to 19, p=0.20006 b-rank test for bits 13 to 20, p=0.93797 b-rank test for bits 14 to 21, p=0.69186 b-rank test for bits 15 to 22, p=0.75807 b-rank test for bits 16 to 23, p=0.13347 b-rank test for bits 17 to 24, p=0.29297 b-rank test for bits 18 to 25, p=0.50164 b-rank test for bits 19 to 26, p=0.99907 b-rank test for bits 20 to 27, p=0.56418 b-rank test for bits 21 to 28, p=0.88108 b-rank test for bits 22 to 29, p=0.73741 b-rank test for bits 23 to 30, p=0.01198 b-rank test for bits 24 to 31, p=0.69831 b-rank test for bits 25 to 32, p=0.60485 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 = 0.850952 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-30_04:31 (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 141957 0.11 0.544342 2 142193 0.66 0.746264 3 141613 -0.69 0.244356 4 141775 -0.31 0.376816 5 141041 -2.03 0.021239 6 141495 -0.97 0.166507 7 142503 1.39 0.917291 8 141928 0.04 0.517397 9 142382 1.10 0.865284 10 142147 0.56 0.710657 11 141397 -1.20 0.115647 12 142218 0.72 0.764604 13 141499 -0.96 0.168851 14 142794 2.07 0.980632 15 141698 -0.49 0.310737 16 141266 -1.50 0.066406 17 142592 1.60 0.944647 18 141966 0.13 0.552669 19 141916 0.02 0.506217 20 141732 -0.41 0.339319 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-30_04:31 Bits used No. missing words z-score p-value 23 to 32 142104 0.6713 0.748978 22 to 31 142107 0.6816 0.752261 21 to 30 141779 -0.4494 0.326567 20 to 29 142142 0.8023 0.788813 19 to 28 142216 1.0575 0.854854 18 to 27 141754 -0.5356 0.296110 17 to 26 142189 0.9644 0.832572 16 to 25 142223 1.0816 0.860289 15 to 24 142229 1.1023 0.864837 14 to 23 142282 1.2851 0.900616 13 to 22 142194 0.9816 0.836857 12 to 21 141988 0.2713 0.606911 11 to 20 142007 0.3368 0.631864 10 to 19 142093 0.6333 0.736746 9 to 18 142196 0.9885 0.838550 8 to 17 142126 0.7471 0.772510 7 to 16 142149 0.8264 0.795725 6 to 15 142212 1.0437 0.851686 5 to 14 142474 1.9471 0.974241 4 to 13 142029 0.4127 0.660070 3 to 12 141881 -0.0977 0.461089 2 to 11 141826 -0.2873 0.386924 1 to 10 141805 -0.3598 0.359514 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-30_04:31 Bits used No. missing words z-score p-value 28 to 32 141650 -0.8791 0.189678 27 to 31 141919 0.0328 0.513075 26 to 30 141865 -0.1503 0.440275 25 to 29 142666 2.5650 0.994841 24 to 28 142470 1.9006 0.971321 23 to 27 142013 0.3514 0.637365 22 to 26 141975 0.2226 0.588081 21 to 25 141704 -0.6960 0.243204 20 to 24 141900 -0.0316 0.487385 19 to 23 141327 -1.9740 0.024191 18 to 22 141513 -1.3435 0.089556 17 to 21 141720 -0.6418 0.260503 16 to 20 141439 -1.5943 0.055430 15 to 19 141449 -1.5604 0.059328 14 to 18 141956 0.1582 0.562852 13 to 17 141750 -0.5401 0.294564 12 to 16 141589 -1.0859 0.138770 11 to 15 141655 -0.8621 0.194306 10 to 14 142023 0.3853 0.650001 9 to 13 141906 -0.0113 0.495497 8 to 12 141938 0.0972 0.538711 7 to 11 141615 -0.9977 0.159205 6 to 10 141653 -0.8689 0.192447 5 to 9 141412 -1.6859 0.045911 4 to 8 141918 0.0294 0.511723 3 to 7 142513 2.0463 0.979638 2 to 6 141779 -0.4418 0.329318 1 to 5 141435 -1.6079 0.053929 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-30_04:31 Bits used No. missing words z-score p-value 31 to 32 141141 -2.2665 0.011712 30 to 31 141748 -0.4759 0.317073 29 to 30 141957 0.1406 0.555915 28 to 29 142055 0.4297 0.666295 27 to 28 141728 -0.5349 0.296361 26 to 27 141270 -1.8859 0.029652 25 to 26 141663 -0.7266 0.233724 24 to 25 141317 -1.7473 0.040294 23 to 24 141910 0.0020 0.500789 22 to 23 141316 -1.7502 0.040039 21 to 22 141515 -1.1632 0.122371 20 to 21 142194 0.8397 0.799471 19 to 20 141633 -0.8151 0.207498 18 to 19 141668 -0.7119 0.238267 17 to 18 141457 -1.3343 0.091052 16 to 17 141529 -1.1219 0.130949 15 to 16 142153 0.7188 0.763865 14 to 15 141001 -2.6794 0.003687 13 to 14 141779 -0.3845 0.350321 12 to 13 142027 0.3471 0.635745 11 to 12 142599 2.0344 0.979046 10 to 11 142235 0.9607 0.831643 9 to 10 141797 -0.3314 0.370187 8 to 9 141488 -1.2429 0.106959 7 to 8 142010 0.2970 0.616752 6 to 7 141792 -0.3461 0.364632 5 to 6 141688 -0.6529 0.256913 4 to 5 141454 -1.3432 0.089611 3 to 4 142022 0.3324 0.630191 2 to 3 142231 0.9489 0.828659 1 to 2 142065 0.4592 0.676956 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-30_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2577.62 1.098 0.863841 Test results for specific bytes for dh-ranFile-2016-01-30_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2587.49 1.237 0.892022 2 to 9 2521.84 0.309 0.621277 3 to 10 2494.73 -0.075 0.470285 4 to 11 2443.01 -0.806 0.210115 5 to 12 2456.58 -0.614 0.269592 6 to 13 2506.27 0.089 0.535310 7 to 14 2446.14 -0.762 0.223131 8 to 15 2425.95 -1.047 0.147493 9 to 16 2525.23 0.357 0.639396 10 to 17 2605.81 1.496 0.932729 11 to 18 2614.63 1.621 0.947508 12 to 19 2476.62 -0.331 0.370453 13 to 20 2428.16 -1.016 0.154819 14 to 21 2408.04 -1.301 0.096714 15 to 22 2401.82 -1.388 0.082500 16 to 23 2488.35 -0.165 0.434596 17 to 24 2529.13 0.412 0.659814 18 to 25 2478.27 -0.307 0.379285 19 to 26 2529.94 0.423 0.664028 20 to 27 2486.14 -0.196 0.422294 21 to 28 2583.62 1.183 0.881517 22 to 29 2405.01 -1.343 0.089574 23 to 30 2547.57 0.673 0.749446 24 to 31 2421.70 -1.107 0.134063 25 to 32 2452.43 -0.673 0.250564 CDPARK for dh-ranFile-2016-01-30_04:31: 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 3523 0.0000 0.500000 3523 0.0000 0.500000 3528 0.2283 0.590298 3509 -0.6393 0.261324 3511 -0.5479 0.291865 3512 -0.5023 0.307734 3518 -0.2283 0.409702 3574 2.3288 0.990064 3532 0.4110 0.659449 3542 0.8676 0.807188 Square side=100, avg. no. parked=3527.20 sample std.=18.38 p-value of the KSTEST for those 10 p-values: 0.558451 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-30_04:31 0.9834,0.5937,0.1870,0.2142,0.8926,0.6622,0.1912,0.4430,0.8671,0.3488, The KS test for those 10 p-values: 0.820298 The 3DSPHERES test for dh-ranFile-2016-01-30_04:31 sample no r^3 equiv. uni. 1 10.852 0.303541 2 39.337 0.730511 3 51.376 0.819591 4 17.040 0.433340 5 25.613 0.574194 6 24.474 0.557721 7 58.478 0.857620 8 2.327 0.074627 9 4.678 0.144384 10 60.394 0.866429 11 50.620 0.814989 12 34.903 0.687592 13 6.684 0.199732 14 11.901 0.327471 15 11.728 0.323569 16 34.952 0.688098 17 20.800 0.500090 18 87.441 0.945779 19 29.701 0.628435 20 42.013 0.753508 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.516985 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-30_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 -0.6 1.2 -0.5 0.0 0.8 -0.8 0.6 0.5 -2.4 0.3 2.3 0.8 -0.5 0.5 -0.2 -0.3 1.3 0.7 0.1 -0.1 -1.4 -0.4 -0.2 -1.5 -0.8 -2.2 -0.7 0.1 2.2 -0.3 0.5 -0.8 -1.3 1.5 0.5 -2.0 0.1 -0.7 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:43.488052 z-score=0.162360, p-value=0.592154 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-30_04:31 Test no p-value 1 0.031300 2 0.195578 3 0.376077 4 0.896732 5 0.282208 6 0.626292 7 0.840253 8 0.667437 9 0.477002 10 0.009915 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.682822 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-30_04:31: (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 66600 0.07 66817 0.34 3 25000.00 25098 0.38 24923 0.24 4 6666.67 6660 0.01 6592 0.84 5 1388.89 1366 0.38 1379 0.07 6 238.10 243 0.10 243 0.10 7 34.72 30 0.64 38 0.31 8 4.96 2 1.77 7 0.84 p=0.23539 p=0.15845 Number of rngs required: 687348, p-value: 0.110 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-30_04:31 No. of wins: Observed Expected 98105 98585.9 z-score=-2.151, pvalue=0.01575 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66428 66666.7 0.854 0.854 2 37733 37654.3 0.164 1.019 3 26955 26954.7 0.000 1.019 4 19205 19313.5 0.609 1.628 5 13933 13851.4 0.480 2.108 6 9974 9943.5 0.093 2.202 7 7293 7145.0 3.065 5.266 8 5169 5139.1 0.174 5.441 9 3667 3699.9 0.292 5.732 10 2696 2666.3 0.331 6.063 11 1965 1923.3 0.903 6.966 12 1410 1388.7 0.325 7.292 13 959 1003.7 1.992 9.284 14 721 726.1 0.036 9.320 15 542 525.8 0.497 9.817 16 354 381.2 1.934 11.751 17 297 276.5 1.514 13.265 18 203 200.8 0.023 13.288 19 132 146.0 1.340 14.628 20 119 106.2 1.539 16.167 21 245 287.1 6.177 22.344 Chisq= 22.34 for 20 degrees of freedom, p= 0.67786 SUMMARY of craptest p-value for no. of wins: 0.015751 p-value for throws/game: 0.677864 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-30_04:31 No. of wins: Observed Expected 98674 98585.9 z-score= 0.394, pvalue=0.65329 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66640 66666.7 0.011 0.011 2 37707 37654.3 0.074 0.084 3 26730 26954.7 1.874 1.958 4 19407 19313.5 0.453 2.411 5 14018 13851.4 2.003 4.414 6 9862 9943.5 0.669 5.083 7 7198 7145.0 0.393 5.476 8 5074 5139.1 0.824 6.300 9 3750 3699.9 0.679 6.979 10 2610 2666.3 1.189 8.168 11 1937 1923.3 0.097 8.265 12 1437 1388.7 1.677 9.942 13 1004 1003.7 0.000 9.942 14 711 726.1 0.316 10.258 15 537 525.8 0.237 10.495 16 363 381.2 0.864 11.359 17 239 276.5 5.096 16.455 18 203 200.8 0.023 16.479 19 169 146.0 3.629 20.107 20 121 106.2 2.058 22.165 21 283 287.1 0.059 22.224 Chisq= 22.22 for 20 degrees of freedom, p= 0.67152 SUMMARY of craptest p-value for no. of wins: 0.653291 p-value for throws/game: 0.671525 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0037,0.0099,0.0117,0.0120,0.0158,0.0212,0.0214,0.0242,0.0256,0.0297, 0.0312,0.0313,0.0357,0.0400,0.0403,0.0459,0.0539,0.0554,0.0593,0.0625, 0.0664,0.0739,0.0746,0.0821,0.0825,0.0858,0.0866,0.0896,0.0896,0.0896, 0.0911,0.0967,0.0987,0.1061,0.1070,0.1100,0.1145,0.1156,0.1224,0.1309, 0.1335,0.1341,0.1388,0.1444,0.1475,0.1548,0.1571,0.1584,0.1592,0.1665, 0.1689,0.1827,0.1870,0.1897,0.1912,0.1924,0.1943,0.1956,0.1997,0.2001, 0.2075,0.2101,0.2133,0.2142,0.2157,0.2231,0.2276,0.2337,0.2354,0.2383, 0.2432,0.2444,0.2460,0.2506,0.2569,0.2597,0.2605,0.2613,0.2614,0.2696, 0.2822,0.2919,0.2929,0.2930,0.2946,0.2961,0.2964,0.2966,0.3035,0.3077, 0.3107,0.3171,0.3236,0.3266,0.3275,0.3293,0.3393,0.3467,0.3488,0.3503, 0.3595,0.3646,0.3702,0.3705,0.3761,0.3768,0.3793,0.3806,0.3842,0.3866, 0.3869,0.4097,0.4115,0.4221,0.4223,0.4265,0.4320,0.4333,0.4346,0.4403, 0.4430,0.4544,0.4611,0.4703,0.4770,0.4874,0.4955,0.5000,0.5000,0.5001, 0.5008,0.5016,0.5062,0.5117,0.5131,0.5170,0.5174,0.5197,0.5312,0.5333, 0.5353,0.5387,0.5443,0.5527,0.5559,0.5577,0.5585,0.5610,0.5629,0.5642, 0.5718,0.5742,0.5780,0.5808,0.5841,0.5842,0.5881,0.5903,0.5910,0.5922, 0.5937,0.5953,0.6048,0.6069,0.6129,0.6168,0.6178,0.6213,0.6263,0.6284, 0.6302,0.6319,0.6357,0.6368,0.6374,0.6374,0.6394,0.6500,0.6533,0.6594, 0.6598,0.6601,0.6622,0.6640,0.6663,0.6674,0.6715,0.6728,0.6770,0.6779, 0.6809,0.6828,0.6876,0.6881,0.6919,0.6935,0.6983,0.7107,0.7305,0.7364, 0.7367,0.7374,0.7463,0.7490,0.7494,0.7523,0.7535,0.7581,0.7639,0.7646, 0.7655,0.7725,0.7888,0.7925,0.7957,0.7995,0.8006,0.8072,0.8116,0.8150, 0.8196,0.8203,0.8231,0.8287,0.8316,0.8326,0.8369,0.8386,0.8403,0.8510, 0.8517,0.8549,0.8576,0.8603,0.8638,0.8648,0.8653,0.8664,0.8671,0.8733, 0.8811,0.8815,0.8916,0.8920,0.8926,0.8967,0.9006,0.9019,0.9027,0.9111, 0.9173,0.9271,0.9327,0.9380,0.9446,0.9458,0.9475,0.9512,0.9713,0.9742, 0.9768,0.9790,0.9796,0.9806,0.9834,0.9901,0.9944,0.9948,0.9991, Overall p-value after applying KStest on 269 p-values = 0.841880 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.