RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-26_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 15.0684 0.409442 2 to 25 15.88 22.1344 0.820396 3 to 26 15.73 20.7330 0.761539 4 to 27 15.90 12.9153 0.258160 5 to 28 15.50 20.9642 0.772103 6 to 29 16.03 26.6868 0.937177 7 to 30 15.53 26.0749 0.926893 8 to 31 15.86 30.4231 0.976550 9 to 32 15.64 10.0841 0.099954 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.092146 Tough bday spacings test for dh-ranFile-2015-06-26_22:31: 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 42 59 91 113 87 40 32 14 8 3 (O-E)^2/E 0.4 0.8 2.8 0.5 2.4 1.0 2.8 0.2 0.1 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 11.394, p= 0.672 RESULTS OF GCD FOR dh-ranFile-2015-06-26_22:31 Euclid's algorithm: p-value, steps to gcd: 0.319789 p-value, dist. of gcd's: 0.352584 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-26_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.160 0.241 0.072 0.570 0.916 0.949 0.226 0.388 Bits 8 to 15---> 0.329 0.419 0.956 0.894 0.973 0.202 0.139 0.227 Bits 16 to 23---> 0.483 0.286 0.638 0.511 0.778 0.292 0.847 0.549 Bits 24 to 31---> 0.335 0.259 0.709 0.862 0.079 0.002 0.819 0.864 KS test for the above 32 p values: 0.210 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-26_22:31, p-values for 5 runs: 0.2992, 0.0034, 0.8681, 0.5398, 0.1706 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-26_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5060 5134.0 1.067 1.339 r= 30 23279 23103.0 1.340 2.679 r= 31 11442 11551.5 1.038 3.717 chi-square = 3.717 with df = 3; p-value = 0.706 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-26_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5243 5134.0 2.314 2.323 r= 31 22973 23103.0 0.732 3.055 r= 32 11574 11551.5 0.044 3.099 chi-square = 3.099 with df = 3; p-value = 0.623 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-26_22:31 b-rank test for bits 1 to 8, p=0.91540 b-rank test for bits 2 to 9, p=0.08468 b-rank test for bits 3 to 10, p=0.60341 b-rank test for bits 4 to 11, p=0.53398 b-rank test for bits 5 to 12, p=0.20309 b-rank test for bits 6 to 13, p=0.53902 b-rank test for bits 7 to 14, p=0.80070 b-rank test for bits 8 to 15, p=0.02347 b-rank test for bits 9 to 16, p=0.77062 b-rank test for bits 10 to 17, p=0.74123 b-rank test for bits 11 to 18, p=0.72964 b-rank test for bits 12 to 19, p=0.26321 b-rank test for bits 13 to 20, p=0.06598 b-rank test for bits 14 to 21, p=0.63026 b-rank test for bits 15 to 22, p=0.76885 b-rank test for bits 16 to 23, p=0.98602 b-rank test for bits 17 to 24, p=0.79796 b-rank test for bits 18 to 25, p=0.66312 b-rank test for bits 19 to 26, p=0.13020 b-rank test for bits 20 to 27, p=0.60218 b-rank test for bits 21 to 28, p=0.35818 b-rank test for bits 22 to 29, p=0.64764 b-rank test for bits 23 to 30, p=0.57844 b-rank test for bits 24 to 31, p=0.96292 b-rank test for bits 25 to 32, p=0.08986 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 = 0.534772 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-26_22:31 (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 142518 1.42 0.922505 2 142870 2.24 0.987602 3 142024 0.27 0.605620 4 141923 0.03 0.512740 5 141594 -0.74 0.230637 6 141694 -0.50 0.307444 7 142294 0.90 0.815610 8 141552 -0.83 0.201892 9 141513 -0.93 0.177222 10 142218 0.72 0.764604 11 142028 0.28 0.609212 12 141551 -0.84 0.201235 13 141996 0.20 0.580237 14 141736 -0.40 0.342747 15 142060 0.35 0.637593 16 142068 0.37 0.644579 17 142121 0.49 0.689543 18 141879 -0.07 0.471753 19 141157 -1.76 0.039392 20 142068 0.37 0.644579 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-26_22:31 Bits used No. missing words z-score p-value 23 to 32 142072 0.5609 0.712578 22 to 31 141448 -1.5908 0.055828 21 to 30 142088 0.6161 0.731087 20 to 29 141415 -1.7046 0.044136 19 to 28 141949 0.1368 0.554403 18 to 27 142039 0.4471 0.672612 17 to 26 141702 -0.7149 0.237326 16 to 25 141850 -0.2046 0.418948 15 to 24 141974 0.2230 0.588232 14 to 23 142065 0.5368 0.704295 13 to 22 142012 0.3540 0.638344 12 to 21 142508 2.0644 0.980509 11 to 20 141861 -0.1667 0.433821 10 to 19 141971 0.2127 0.584202 9 to 18 142192 0.9747 0.835151 8 to 17 142002 0.3196 0.625346 7 to 16 141982 0.2506 0.598933 6 to 15 142282 1.2851 0.900616 5 to 14 142065 0.5368 0.704295 4 to 13 141714 -0.6736 0.250298 3 to 12 141695 -0.7391 0.229933 2 to 11 141996 0.2989 0.617477 1 to 10 141713 -0.6770 0.249203 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-26_22:31 Bits used No. missing words z-score p-value 28 to 32 142157 0.8396 0.799422 27 to 31 142162 0.8565 0.804142 26 to 30 141674 -0.7977 0.212514 25 to 29 142676 2.5989 0.995324 24 to 28 141994 0.2870 0.612950 23 to 27 141909 -0.0011 0.499554 22 to 26 141944 0.1175 0.546778 21 to 25 141519 -1.3232 0.092892 20 to 24 142213 1.0294 0.848352 19 to 23 141669 -0.8147 0.207628 18 to 22 141754 -0.5265 0.299256 17 to 21 141400 -1.7265 0.042125 16 to 20 141703 -0.6994 0.242144 15 to 19 142395 1.6463 0.950153 14 to 18 141641 -0.9096 0.181519 13 to 17 142138 0.7752 0.780875 12 to 16 141663 -0.8350 0.201854 11 to 15 142110 0.6802 0.751823 10 to 14 141964 0.1853 0.573512 9 to 13 141946 0.1243 0.549463 8 to 12 141698 -0.7164 0.236881 7 to 11 141706 -0.6893 0.245332 6 to 10 141713 -0.6655 0.252857 5 to 9 141801 -0.3672 0.356727 4 to 8 141689 -0.7469 0.227568 3 to 7 141958 0.1650 0.565521 2 to 6 141845 -0.2181 0.413688 1 to 5 142224 1.0667 0.856941 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-26_22:31 Bits used No. missing words z-score p-value 31 to 32 141822 -0.2576 0.398354 30 to 31 142040 0.3855 0.650051 29 to 30 142040 0.3855 0.650051 28 to 29 141981 0.2114 0.583719 27 to 28 141558 -1.0364 0.150014 26 to 27 141421 -1.4405 0.074863 25 to 26 142246 0.9931 0.839676 24 to 25 142223 0.9253 0.822590 23 to 24 142616 2.0846 0.981446 22 to 23 141779 -0.3845 0.350321 21 to 22 141669 -0.7089 0.239182 20 to 21 141788 -0.3579 0.360207 19 to 20 141661 -0.7325 0.231921 18 to 19 141497 -1.2163 0.111933 17 to 18 141785 -0.3668 0.356901 16 to 17 142273 1.0728 0.858314 15 to 16 142486 1.7011 0.955537 14 to 15 141698 -0.6234 0.266513 13 to 14 141595 -0.9272 0.176904 12 to 13 142163 0.7483 0.772857 11 to 12 142358 1.3235 0.907167 10 to 11 141376 -1.5732 0.057831 9 to 10 141809 -0.2960 0.383631 8 to 9 142151 0.7129 0.762043 7 to 8 141525 -1.1337 0.128457 6 to 7 141380 -1.5614 0.059209 5 to 6 142225 0.9312 0.824120 4 to 5 142122 0.6273 0.734784 3 to 4 141708 -0.5939 0.276292 2 to 3 142253 1.0138 0.844655 1 to 2 142483 1.6922 0.954700 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-26_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2495.89 -0.058 0.476800 Test results for specific bytes for dh-ranFile-2015-06-26_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2531.55 0.446 0.672260 2 to 9 2602.47 1.449 0.926361 3 to 10 2540.51 0.573 0.716651 4 to 11 2528.01 0.396 0.654012 5 to 12 2432.42 -0.956 0.169603 6 to 13 2415.06 -1.201 0.114838 7 to 14 2472.04 -0.395 0.346290 8 to 15 2533.75 0.477 0.683437 9 to 16 2382.77 -1.658 0.048672 10 to 17 2598.03 1.386 0.917170 11 to 18 2479.42 -0.291 0.385514 12 to 19 2493.52 -0.092 0.463475 13 to 20 2605.87 1.497 0.932842 14 to 21 2589.38 1.264 0.896900 15 to 22 2500.09 0.001 0.500523 16 to 23 2460.00 -0.566 0.285800 17 to 24 2469.59 -0.430 0.333587 18 to 25 2492.88 -0.101 0.459925 19 to 26 2390.14 -1.554 0.060139 20 to 27 2392.84 -1.515 0.064831 21 to 28 2296.76 -2.874 0.002025 22 to 29 2501.51 0.021 0.508520 23 to 30 2358.32 -2.004 0.022555 24 to 31 2491.60 -0.119 0.452728 25 to 32 2459.26 -0.576 0.282255 CDPARK for dh-ranFile-2015-06-26_22:31: 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 3553 1.3699 0.914635 3536 0.5936 0.723613 3518 -0.2283 0.409702 3509 -0.6393 0.261324 3514 -0.4110 0.340551 3506 -0.7763 0.218799 3541 0.8219 0.794438 3529 0.2740 0.607947 3521 -0.0913 0.463617 3525 0.0913 0.536383 Square side=100, avg. no. parked=3525.20 sample std.=14.07 p-value of the KSTEST for those 10 p-values: 0.769543 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-26_22:31 0.0968,0.0736,0.6653,0.1647,0.9932,0.6172,0.2406,0.0471,0.8692,0.3401, The KS test for those 10 p-values: 0.312711 The 3DSPHERES test for dh-ranFile-2015-06-26_22:31 sample no r^3 equiv. uni. 1 9.105 0.261762 2 17.722 0.446086 3 15.726 0.407968 4 127.394 0.985685 5 27.497 0.600104 6 0.933 0.030612 7 3.215 0.101631 8 55.732 0.843974 9 15.111 0.395717 10 10.300 0.290605 11 43.346 0.764225 12 35.498 0.693724 13 23.210 0.538678 14 12.382 0.338172 15 14.375 0.380696 16 49.826 0.810023 17 21.045 0.504162 18 20.724 0.498829 19 35.226 0.690933 20 34.477 0.683120 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.700359 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-26_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 1.1 0.3 -0.6 -1.5 -1.3 1.2 0.7 -0.2 1.2 -0.4 -1.5 0.5 -1.8 1.1 -0.1 0.3 -1.3 0.2 0.3 2.1 -1.0 1.3 -1.2 -0.9 0.6 -0.2 0.7 2.2 1.2 -1.3 0.7 -1.3 -1.0 0.6 -1.6 -0.7 -0.8 -1.8 -0.6 2.0 -1.1 Chi-square with 42 degrees of freedom:54.976106 z-score=1.415809, p-value=0.913529 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-26_22:31 Test no p-value 1 0.313858 2 0.293251 3 0.897590 4 0.778661 5 0.026495 6 0.289745 7 0.955341 8 0.442829 9 0.074981 10 0.323126 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.575626 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-26_22:31: (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 66685 0.01 66777 0.18 3 25000.00 24934 0.17 24850 0.90 4 6666.67 6714 0.34 6747 0.97 5 1388.89 1354 0.88 1378 0.09 6 238.10 262 2.40 214 2.44 7 34.72 42 1.53 27 1.72 8 4.96 8 1.86 6 0.22 p=0.69561 p=0.63135 Number of rngs required: 688919, p-value: 0.724 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-26_22:31 No. of wins: Observed Expected 98704 98585.9 z-score= 0.528, pvalue=0.70139 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66630 66666.7 0.020 0.020 2 37830 37654.3 0.820 0.840 3 26718 26954.7 2.079 2.919 4 19395 19313.5 0.344 3.263 5 13831 13851.4 0.030 3.293 6 9963 9943.5 0.038 3.331 7 7262 7145.0 1.915 5.246 8 5075 5139.1 0.799 6.045 9 3716 3699.9 0.070 6.116 10 2692 2666.3 0.248 6.363 11 1910 1923.3 0.092 6.456 12 1366 1388.7 0.372 6.828 13 1014 1003.7 0.105 6.933 14 734 726.1 0.085 7.019 15 550 525.8 1.110 8.129 16 364 381.2 0.772 8.901 17 294 276.5 1.102 10.003 18 176 200.8 3.070 13.073 19 122 146.0 3.940 17.014 20 100 106.2 0.364 17.377 21 258 287.1 2.952 20.329 Chisq= 20.33 for 20 degrees of freedom, p= 0.56250 SUMMARY of craptest p-value for no. of wins: 0.701388 p-value for throws/game: 0.562501 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-26_22:31 No. of wins: Observed Expected 98335 98585.9 z-score=-1.122, pvalue=0.13093 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66641 66666.7 0.010 0.010 2 37493 37654.3 0.691 0.701 3 26952 26954.7 0.000 0.701 4 19361 19313.5 0.117 0.818 5 13995 13851.4 1.488 2.307 6 9882 9943.5 0.381 2.688 7 7051 7145.0 1.237 3.925 8 5170 5139.1 0.186 4.111 9 3707 3699.9 0.014 4.125 10 2721 2666.3 1.122 5.247 11 1914 1923.3 0.045 5.292 12 1405 1388.7 0.190 5.483 13 1062 1003.7 3.385 8.867 14 745 726.1 0.490 9.357 15 504 525.8 0.907 10.264 16 397 381.2 0.659 10.923 17 312 276.5 4.547 15.470 18 173 200.8 3.857 19.326 19 117 146.0 5.755 25.081 20 104 106.2 0.046 25.127 21 294 287.1 0.165 25.293 Chisq= 25.29 for 20 degrees of freedom, p= 0.80953 SUMMARY of craptest p-value for no. of wins: 0.130934 p-value for throws/game: 0.809531 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0020,0.0034,0.0226,0.0235,0.0265,0.0306,0.0394,0.0421,0.0441, 0.0471,0.0487,0.0558,0.0578,0.0592,0.0601,0.0648,0.0660,0.0721,0.0736, 0.0749,0.0750,0.0790,0.0847,0.0899,0.0921,0.0929,0.0968,0.1000,0.1016, 0.1119,0.1148,0.1285,0.1302,0.1309,0.1393,0.1500,0.1599,0.1647,0.1696, 0.1706,0.1769,0.1772,0.1815,0.2012,0.2016,0.2019,0.2019,0.2031,0.2076, 0.2095,0.2125,0.2188,0.2262,0.2266,0.2276,0.2299,0.2306,0.2319,0.2369, 0.2373,0.2392,0.2406,0.2408,0.2421,0.2453,0.2492,0.2503,0.2529,0.2582, 0.2589,0.2613,0.2618,0.2632,0.2665,0.2763,0.2823,0.2857,0.2858,0.2897, 0.2906,0.2917,0.2933,0.2992,0.2993,0.3074,0.3127,0.3139,0.3198,0.3231, 0.3288,0.3336,0.3353,0.3382,0.3401,0.3406,0.3427,0.3463,0.3503,0.3526, 0.3567,0.3569,0.3582,0.3602,0.3807,0.3836,0.3855,0.3883,0.3957,0.3984, 0.4080,0.4094,0.4097,0.4137,0.4189,0.4194,0.4338,0.4428,0.4461,0.4527, 0.4599,0.4635,0.4636,0.4718,0.4768,0.4829,0.4988,0.4996,0.5005,0.5042, 0.5085,0.5106,0.5127,0.5340,0.5348,0.5364,0.5387,0.5390,0.5398,0.5468, 0.5493,0.5495,0.5544,0.5625,0.5655,0.5698,0.5735,0.5756,0.5784,0.5802, 0.5837,0.5842,0.5882,0.5989,0.6001,0.6022,0.6034,0.6056,0.6079,0.6092, 0.6130,0.6172,0.6175,0.6234,0.6253,0.6303,0.6313,0.6376,0.6380,0.6383, 0.6446,0.6446,0.6476,0.6501,0.6501,0.6540,0.6631,0.6653,0.6723,0.6723, 0.6726,0.6831,0.6834,0.6895,0.6909,0.6937,0.6956,0.7004,0.7014,0.7043, 0.7043,0.7063,0.7087,0.7126,0.7167,0.7236,0.7241,0.7296,0.7311,0.7348, 0.7412,0.7518,0.7615,0.7620,0.7642,0.7646,0.7689,0.7695,0.7706,0.7721, 0.7729,0.7784,0.7787,0.7809,0.7944,0.7980,0.7994,0.8007,0.8041,0.8095, 0.8100,0.8156,0.8190,0.8204,0.8226,0.8241,0.8352,0.8397,0.8440,0.8447, 0.8474,0.8484,0.8569,0.8583,0.8625,0.8640,0.8681,0.8692,0.8943,0.8969, 0.8976,0.9006,0.9072,0.9135,0.9146,0.9154,0.9159,0.9172,0.9225,0.9264, 0.9269,0.9328,0.9372,0.9486,0.9502,0.9547,0.9553,0.9555,0.9555,0.9629, 0.9727,0.9765,0.9805,0.9814,0.9857,0.9860,0.9876,0.9932,0.9953, Overall p-value after applying KStest on 269 p-values = 0.939611 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.