RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-29_20:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 14.4475 0.364789 2 to 25 15.85 17.4215 0.573820 3 to 26 15.82 14.2718 0.352223 4 to 27 15.86 38.6116 0.997976 5 to 28 15.71 16.6573 0.522196 6 to 29 15.72 14.1192 0.341354 7 to 30 15.98 16.8025 0.532176 8 to 31 15.72 19.8170 0.716303 9 to 32 15.79 21.2802 0.785992 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.297241 Tough bday spacings test for dh-ranFile-2016-02-29_20:31: 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 45 68 89 104 70 52 32 15 9 5 (O-E)^2/E 0.4 1.9 0.4 0.8 0.4 0.8 0.0 0.2 0.0 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 5.932, p= 0.179 RESULTS OF GCD FOR dh-ranFile-2016-02-29_20:31 Euclid's algorithm: p-value, steps to gcd: 0.846276 p-value, dist. of gcd's: 0.697006 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-29_20:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.342 0.746 0.423 0.913 0.907 0.207 0.642 0.419 Bits 8 to 15---> 0.993 0.008 0.712 0.010 0.130 0.001 0.309 0.121 Bits 16 to 23---> 0.858 0.729 0.420 0.216 0.597 0.460 0.542 0.675 Bits 24 to 31---> 0.783 0.183 0.468 0.740 0.257 0.264 0.639 0.791 KS test for the above 32 p values: 0.253 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-29_20:31, p-values for 5 runs: 0.3337, 0.4598, 0.5629, 0.4797, 0.0892 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-29_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 237 211.4 3.095 3.095 r= 29 5170 5134.0 0.252 3.348 r= 30 23103 23103.0 0.000 3.348 r= 31 11490 11551.5 0.328 3.675 chi-square = 3.675 with df = 3; p-value = 0.701 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-29_20:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 213 211.4 0.012 0.012 r= 30 5174 5134.0 0.311 0.323 r= 31 23001 23103.0 0.451 0.774 r= 32 11612 11551.5 0.317 1.091 chi-square = 1.091 with df = 3; p-value = 0.221 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-29_20:31 b-rank test for bits 1 to 8, p=0.16426 b-rank test for bits 2 to 9, p=0.15996 b-rank test for bits 3 to 10, p=0.97143 b-rank test for bits 4 to 11, p=0.12452 b-rank test for bits 5 to 12, p=0.59491 b-rank test for bits 6 to 13, p=0.11316 b-rank test for bits 7 to 14, p=0.24068 b-rank test for bits 8 to 15, p=0.76242 b-rank test for bits 9 to 16, p=0.78808 b-rank test for bits 10 to 17, p=0.68901 b-rank test for bits 11 to 18, p=0.58807 b-rank test for bits 12 to 19, p=0.72608 b-rank test for bits 13 to 20, p=0.65702 b-rank test for bits 14 to 21, p=0.44057 b-rank test for bits 15 to 22, p=0.18607 b-rank test for bits 16 to 23, p=0.73334 b-rank test for bits 17 to 24, p=0.59229 b-rank test for bits 18 to 25, p=0.74576 b-rank test for bits 19 to 26, p=0.07263 b-rank test for bits 20 to 27, p=0.45216 b-rank test for bits 21 to 28, p=0.41049 b-rank test for bits 22 to 29, p=0.96992 b-rank test for bits 23 to 30, p=0.18461 b-rank test for bits 24 to 31, p=0.82788 b-rank test for bits 25 to 32, p=0.19907 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 = 0.770060 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-29_20:31 (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 141988 0.18 0.572918 2 142164 0.60 0.724086 3 141548 -0.84 0.199271 4 140807 -2.58 0.005004 5 141932 0.05 0.521121 6 142286 0.88 0.810589 7 142742 1.95 0.974142 8 141185 -1.69 0.045289 9 142174 0.62 0.731840 10 141717 -0.45 0.326583 11 140730 -2.76 0.002931 12 141852 -0.13 0.446722 13 142234 0.76 0.775947 14 141787 -0.29 0.387509 15 141399 -1.19 0.116560 16 141636 -0.64 0.261535 17 142156 0.58 0.717805 18 141176 -1.71 0.043321 19 142027 0.27 0.608315 20 142417 1.19 0.882217 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-29_20:31 Bits used No. missing words z-score p-value 23 to 32 141990 0.2782 0.609560 22 to 31 142024 0.3954 0.653731 21 to 30 142612 2.4230 0.992304 20 to 29 142250 1.1747 0.879947 19 to 28 142157 0.8540 0.803457 18 to 27 141734 -0.6046 0.272727 17 to 26 142092 0.6299 0.735619 16 to 25 141721 -0.6494 0.258036 15 to 24 141640 -0.9287 0.176516 14 to 23 141463 -1.5391 0.061894 13 to 22 141344 -1.9494 0.025623 12 to 21 141997 0.3023 0.618792 11 to 20 141685 -0.7736 0.219598 10 to 19 141674 -0.8115 0.208544 9 to 18 141622 -0.9908 0.160893 8 to 17 141916 0.0230 0.509175 7 to 16 141693 -0.7460 0.227844 6 to 15 141591 -1.0977 0.136170 5 to 14 142183 0.9437 0.827336 4 to 13 141614 -1.0184 0.154249 3 to 12 142218 1.0644 0.856422 2 to 11 141758 -0.5218 0.300895 1 to 10 142374 1.6023 0.945457 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-29_20:31 Bits used No. missing words z-score p-value 28 to 32 141744 -0.5604 0.287589 27 to 31 141760 -0.5062 0.306357 26 to 30 142090 0.6124 0.729877 25 to 29 141776 -0.4520 0.325647 24 to 28 142292 1.2972 0.902717 23 to 27 141463 -1.5130 0.065142 22 to 26 141644 -0.8994 0.184214 21 to 25 141856 -0.1808 0.428270 20 to 24 141872 -0.1265 0.449651 19 to 23 141831 -0.2655 0.395302 18 to 22 142420 1.7311 0.958282 17 to 21 142089 0.6091 0.728755 16 to 20 141758 -0.5130 0.303982 15 to 19 142094 0.6260 0.734343 14 to 18 142420 1.7311 0.958282 13 to 17 142205 1.0023 0.841894 12 to 16 142220 1.0531 0.853857 11 to 15 141850 -0.2011 0.420303 10 to 14 141778 -0.4452 0.328093 9 to 13 141827 -0.2791 0.390090 8 to 12 142021 0.3785 0.647486 7 to 11 141354 -1.8825 0.029886 6 to 10 141904 -0.0181 0.492792 5 to 9 142147 0.8057 0.789781 4 to 8 141583 -1.1062 0.134319 3 to 7 141946 0.1243 0.549463 2 to 6 142497 1.9921 0.976820 1 to 5 141993 0.2836 0.611652 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-29_20:31 Bits used No. missing words z-score p-value 31 to 32 142095 0.5477 0.708051 30 to 31 142022 0.3324 0.630191 29 to 30 141590 -0.9420 0.173102 28 to 29 141903 -0.0187 0.492551 27 to 28 141980 0.2085 0.582568 26 to 27 141919 0.0285 0.511378 25 to 26 141671 -0.7030 0.241016 24 to 25 141898 -0.0334 0.486669 23 to 24 142263 1.0433 0.851589 22 to 23 142368 1.3530 0.911974 21 to 22 141697 -0.6263 0.265545 20 to 21 141584 -0.9597 0.168609 19 to 20 142045 0.4002 0.655498 18 to 19 142085 0.5182 0.697841 17 to 18 141782 -0.3756 0.353605 16 to 17 141795 -0.3373 0.367962 15 to 16 141698 -0.6234 0.266513 14 to 15 141775 -0.3963 0.345959 13 to 14 142332 1.2468 0.893767 12 to 13 141679 -0.6794 0.248430 11 to 12 142251 1.0079 0.843243 10 to 11 141035 -2.5791 0.004952 9 to 10 141848 -0.1809 0.428217 8 to 9 141735 -0.5142 0.303539 7 to 8 141740 -0.4995 0.308714 6 to 7 142510 1.7719 0.961793 5 to 6 142011 0.2999 0.617878 4 to 5 142157 0.7306 0.767485 3 to 4 141107 -2.3668 0.008972 2 to 3 141761 -0.4376 0.330856 1 to 2 141615 -0.8682 0.192634 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-29_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2436.55 -0.897 0.184790 Test results for specific bytes for dh-ranFile-2016-02-29_20:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2467.85 -0.455 0.324685 2 to 9 2629.65 1.834 0.966637 3 to 10 2450.96 -0.693 0.244003 4 to 11 2551.20 0.724 0.765495 5 to 12 2469.14 -0.436 0.331244 6 to 13 2377.76 -1.729 0.041934 7 to 14 2527.02 0.382 0.648833 8 to 15 2465.05 -0.494 0.310558 9 to 16 2379.90 -1.698 0.044712 10 to 17 2377.31 -1.735 0.041366 11 to 18 2488.93 -0.157 0.437782 12 to 19 2562.25 0.880 0.810671 13 to 20 2453.00 -0.665 0.253106 14 to 21 2417.72 -1.164 0.122279 15 to 22 2525.91 0.366 0.642989 16 to 23 2503.80 0.054 0.521401 17 to 24 2393.87 -1.501 0.066697 18 to 25 2498.33 -0.024 0.490601 19 to 26 2333.62 -2.353 0.009311 20 to 27 2451.15 -0.691 0.244818 21 to 28 2569.28 0.980 0.836411 22 to 29 2399.66 -1.419 0.077946 23 to 30 2365.39 -1.904 0.028474 24 to 31 2561.52 0.870 0.807841 25 to 32 2449.15 -0.719 0.236022 CDPARK for dh-ranFile-2016-02-29_20:31: 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 3507 -0.7306 0.232514 3560 1.6895 0.954438 3505 -0.8219 0.205562 3524 0.0457 0.518210 3504 -0.8676 0.192812 3525 0.0913 0.536383 3531 0.3653 0.642555 3520 -0.1370 0.445521 3537 0.6393 0.738676 3509 -0.6393 0.261324 Square side=100, avg. no. parked=3522.20 sample std.=16.65 p-value of the KSTEST for those 10 p-values: 0.752600 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-29_20:31 0.8246,0.5191,0.4845,0.4439,0.9260,0.4932,0.5376,0.5975,0.1003,0.1023, The KS test for those 10 p-values: 0.698462 The 3DSPHERES test for dh-ranFile-2016-02-29_20:31 sample no r^3 equiv. uni. 1 21.000 0.503415 2 27.229 0.596527 3 39.538 0.732310 4 7.455 0.220029 5 56.008 0.845402 6 41.527 0.749488 7 15.523 0.403946 8 11.208 0.311742 9 59.252 0.861248 10 38.032 0.718530 11 32.827 0.665207 12 74.677 0.917026 13 50.146 0.812043 14 2.793 0.088907 15 74.907 0.917659 16 30.874 0.642679 17 111.363 0.975574 18 4.191 0.130386 19 27.590 0.601353 20 29.739 0.628902 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.114424 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-29_20:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 0.9 1.8 1.1 -0.6 -1.3 2.2 -0.8 -0.2 1.0 0.2 0.7 0.5 1.9 1.1 0.6 0.4 -1.2 0.2 -0.2 -1.8 -0.7 -1.5 -0.2 -1.8 -0.2 0.6 1.1 0.3 0.8 -0.3 -0.9 0.8 -0.3 -1.5 -1.4 -0.5 0.2 0.1 -0.1 -1.3 0.0 -0.1 Chi-square with 42 degrees of freedom:42.870251 z-score=0.094952, p-value=0.566315 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-29_20:31 Test no p-value 1 0.142143 2 0.001997 3 0.538151 4 0.328582 5 0.877378 6 0.001936 7 0.000605 8 0.686203 9 0.249144 10 0.667538 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.005615 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-29_20:31: (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 67100 2.82 66689 0.01 3 25000.00 24653 4.82 25001 0.00 4 6666.67 6676 0.01 6619 0.34 5 1388.89 1303 5.31 1409 0.29 6 238.10 238 0.00 244 0.15 7 34.72 28 1.30 35 0.00 8 4.96 1 3.16 2 1.77 p=0.99214 p=0.13770 Number of rngs required: 687574, p-value: 0.169 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-29_20:31 No. of wins: Observed Expected 98773 98585.9 z-score= 0.837, pvalue=0.79871 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66864 66666.7 0.584 0.584 2 37761 37654.3 0.302 0.886 3 26899 26954.7 0.115 1.002 4 19264 19313.5 0.127 1.128 5 13886 13851.4 0.086 1.215 6 9836 9943.5 1.163 2.378 7 7093 7145.0 0.379 2.757 8 5045 5139.1 1.722 4.479 9 3682 3699.9 0.086 4.565 10 2730 2666.3 1.522 6.087 11 1895 1923.3 0.417 6.504 12 1368 1388.7 0.310 6.814 13 989 1003.7 0.216 7.030 14 699 726.1 1.014 8.044 15 542 525.8 0.497 8.541 16 395 381.2 0.503 9.044 17 296 276.5 1.369 10.414 18 209 200.8 0.332 10.746 19 149 146.0 0.062 10.808 20 109 106.2 0.073 10.881 21 289 287.1 0.012 10.894 Chisq= 10.89 for 20 degrees of freedom, p= 0.05106 SUMMARY of craptest p-value for no. of wins: 0.798705 p-value for throws/game: 0.051064 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-29_20:31 No. of wins: Observed Expected 98295 98585.9 z-score=-1.301, pvalue=0.09665 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66420 66666.7 0.913 0.913 2 37835 37654.3 0.867 1.780 3 27101 26954.7 0.794 2.573 4 19295 19313.5 0.018 2.591 5 13696 13851.4 1.744 4.335 6 9900 9943.5 0.191 4.526 7 7136 7145.0 0.011 4.537 8 5182 5139.1 0.359 4.896 9 3778 3699.9 1.650 6.546 10 2595 2666.3 1.907 8.452 11 1979 1923.3 1.611 10.064 12 1476 1388.7 5.483 15.546 13 975 1003.7 0.822 16.368 14 697 726.1 1.169 17.537 15 538 525.8 0.281 17.819 16 410 381.2 2.184 20.002 17 284 276.5 0.201 20.204 18 204 200.8 0.050 20.254 19 139 146.0 0.334 20.588 20 85 106.2 4.237 24.825 21 275 287.1 0.511 25.336 Chisq= 25.34 for 20 degrees of freedom, p= 0.81114 SUMMARY of craptest p-value for no. of wins: 0.096648 p-value for throws/game: 0.811137 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0006,0.0014,0.0019,0.0020,0.0029,0.0050,0.0050,0.0056,0.0085,0.0090, 0.0093,0.0097,0.0256,0.0285,0.0299,0.0414,0.0419,0.0433,0.0447,0.0453, 0.0511,0.0619,0.0651,0.0667,0.0726,0.0779,0.0889,0.0892,0.0966,0.1003, 0.1023,0.1132,0.1144,0.1166,0.1212,0.1223,0.1245,0.1303,0.1304,0.1343, 0.1362,0.1377,0.1421,0.1542,0.1600,0.1609,0.1643,0.1685,0.1686,0.1731, 0.1765,0.1791,0.1828,0.1842,0.1846,0.1848,0.1861,0.1926,0.1928,0.1991, 0.1993,0.2056,0.2070,0.2085,0.2163,0.2196,0.2200,0.2207,0.2278,0.2325, 0.2360,0.2407,0.2410,0.2440,0.2448,0.2484,0.2491,0.2531,0.2532,0.2572, 0.2580,0.2613,0.2615,0.2636,0.2655,0.2665,0.2727,0.2876,0.2972,0.3009, 0.3035,0.3040,0.3064,0.3087,0.3089,0.3106,0.3117,0.3247,0.3256,0.3266, 0.3281,0.3286,0.3309,0.3312,0.3337,0.3414,0.3423,0.3460,0.3522,0.3536, 0.3648,0.3680,0.3875,0.3901,0.3953,0.4039,0.4105,0.4194,0.4195,0.4203, 0.4235,0.4282,0.4283,0.4378,0.4406,0.4439,0.4455,0.4467,0.4497,0.4522, 0.4598,0.4599,0.4683,0.4797,0.4845,0.4867,0.4906,0.4926,0.4928,0.4932, 0.5034,0.5092,0.5114,0.5182,0.5191,0.5211,0.5214,0.5222,0.5322,0.5364, 0.5376,0.5382,0.5421,0.5495,0.5629,0.5663,0.5729,0.5738,0.5826,0.5881, 0.5923,0.5949,0.5965,0.5970,0.5975,0.6014,0.6083,0.6096,0.6117,0.6179, 0.6188,0.6289,0.6302,0.6394,0.6424,0.6426,0.6427,0.6430,0.6475,0.6488, 0.6537,0.6555,0.6570,0.6652,0.6675,0.6748,0.6862,0.6890,0.6970,0.6978, 0.6985,0.7013,0.7081,0.7117,0.7163,0.7178,0.7185,0.7241,0.7261,0.7288, 0.7290,0.7299,0.7318,0.7323,0.7333,0.7343,0.7356,0.7387,0.7398,0.7458, 0.7463,0.7495,0.7526,0.7624,0.7655,0.7675,0.7701,0.7759,0.7832,0.7860, 0.7881,0.7898,0.7914,0.7987,0.8035,0.8078,0.8106,0.8107,0.8111,0.8120, 0.8246,0.8273,0.8279,0.8364,0.8419,0.8432,0.8454,0.8463,0.8516,0.8539, 0.8564,0.8577,0.8612,0.8774,0.8799,0.8822,0.8938,0.9027,0.9066,0.9120, 0.9130,0.9170,0.9177,0.9260,0.9455,0.9544,0.9583,0.9583,0.9618,0.9666, 0.9699,0.9714,0.9741,0.9756,0.9768,0.9921,0.9923,0.9927,0.9980, Overall p-value after applying KStest on 269 p-values = 0.183877 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.