RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-14_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 15.66 14.9656 0.402044 2 to 25 15.63 17.3287 0.567683 3 to 26 15.64 36.7754 0.996391 4 to 27 15.61 16.9845 0.544580 5 to 28 15.67 23.3475 0.861723 6 to 29 15.87 21.9741 0.814282 7 to 30 15.46 34.4928 0.992752 8 to 31 15.55 15.8670 0.466718 9 to 32 15.91 24.9031 0.903101 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.012898 Tough bday spacings test for dh-ranFile-2017-01-14_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 4 40 80 102 80 62 61 39 19 4 9 (O-E)^2/E 2.9 0.3 0.6 0.2 3.2 3.3 1.5 2.9 1.1 1.0 6.0 Birthday Spacings: Sum(O-E)^2/E= 23.104, p= 0.990 RESULTS OF GCD FOR dh-ranFile-2017-01-14_03:31 Euclid's algorithm: p-value, steps to gcd: 0.717827 p-value, dist. of gcd's: 0.030635 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-14_03:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.184 0.776 0.569 0.034 0.394 0.529 0.620 0.227 Bits 8 to 15---> 0.674 0.535 0.642 0.152 0.559 0.067 0.588 0.447 Bits 16 to 23---> 0.824 0.557 0.493 0.522 0.886 0.580 0.250 0.864 Bits 24 to 31---> 0.494 0.716 0.701 0.547 0.947 0.564 0.801 0.645 KS test for the above 32 p values: 0.873 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-14_03:31, p-values for 5 runs: 0.4520, 0.7343, 0.7873, 0.7330, 0.8240 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-14_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5163 5134.0 0.164 0.256 r= 30 23141 23103.0 0.062 0.318 r= 31 11489 11551.5 0.338 0.657 chi-square = 0.657 with df = 3; p-value = 0.117 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-14_03:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 196 211.4 1.124 1.124 r= 30 5183 5134.0 0.467 1.592 r= 31 23074 23103.0 0.037 1.628 r= 32 11547 11551.5 0.002 1.630 chi-square = 1.630 with df = 3; p-value = 0.347 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-14_03:31 b-rank test for bits 1 to 8, p=0.47971 b-rank test for bits 2 to 9, p=0.29707 b-rank test for bits 3 to 10, p=0.34515 b-rank test for bits 4 to 11, p=0.08130 b-rank test for bits 5 to 12, p=0.14840 b-rank test for bits 6 to 13, p=0.08379 b-rank test for bits 7 to 14, p=0.54226 b-rank test for bits 8 to 15, p=0.72482 b-rank test for bits 9 to 16, p=0.50050 b-rank test for bits 10 to 17, p=0.51249 b-rank test for bits 11 to 18, p=0.51716 b-rank test for bits 12 to 19, p=0.96106 b-rank test for bits 13 to 20, p=0.49768 b-rank test for bits 14 to 21, p=0.10803 b-rank test for bits 15 to 22, p=0.16603 b-rank test for bits 16 to 23, p=0.89828 b-rank test for bits 17 to 24, p=0.02466 b-rank test for bits 18 to 25, p=0.41552 b-rank test for bits 19 to 26, p=0.08078 b-rank test for bits 20 to 27, p=0.73200 b-rank test for bits 21 to 28, p=0.52766 b-rank test for bits 22 to 29, p=0.77776 b-rank test for bits 23 to 30, p=0.87038 b-rank test for bits 24 to 31, p=0.03158 b-rank test for bits 25 to 32, p=0.23096 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 = 0.261685 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-14_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 141415 -1.15 0.124050 2 142123 0.50 0.691191 3 142191 0.66 0.744765 4 142311 0.94 0.826001 5 142077 0.39 0.652379 6 141977 0.16 0.562814 7 142033 0.29 0.613690 8 141386 -1.22 0.110715 9 141981 0.17 0.566493 10 141894 -0.04 0.485714 11 142317 0.95 0.829578 12 142386 1.11 0.867299 13 141412 -1.16 0.122621 14 141833 -0.18 0.429228 15 141690 -0.51 0.304167 16 141694 -0.50 0.307444 17 142295 0.90 0.816232 18 141211 -1.63 0.051381 19 141799 -0.26 0.398288 20 141769 -0.33 0.371504 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-14_03:31 Bits used No. missing words z-score p-value 23 to 32 142244 1.1540 0.875757 22 to 31 141889 -0.0701 0.472056 21 to 30 142266 1.2299 0.890632 20 to 29 142119 0.7230 0.765160 19 to 28 142069 0.5506 0.709041 18 to 27 141960 0.1747 0.569352 17 to 26 142134 0.7747 0.780749 16 to 25 142048 0.4782 0.683736 15 to 24 141700 -0.7218 0.235200 14 to 23 141969 0.2058 0.581510 13 to 22 142510 2.0713 0.980833 12 to 21 142110 0.6920 0.755521 11 to 20 141676 -0.8046 0.210529 10 to 19 142217 1.0609 0.855639 9 to 18 141680 -0.7908 0.214532 8 to 17 141937 0.0954 0.538007 7 to 16 141371 -1.8563 0.031705 6 to 15 142363 1.5644 0.941136 5 to 14 142261 1.2127 0.887369 4 to 13 142096 0.6437 0.740112 3 to 12 142182 0.9402 0.826453 2 to 11 141832 -0.2667 0.394867 1 to 10 141499 -1.4149 0.078544 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-14_03:31 Bits used No. missing words z-score p-value 28 to 32 142179 0.9141 0.819677 27 to 31 141906 -0.0113 0.495497 26 to 30 141922 0.0429 0.517129 25 to 29 142126 0.7345 0.768670 24 to 28 141529 -1.2893 0.098655 23 to 27 141901 -0.0282 0.488737 22 to 26 142204 0.9989 0.841074 21 to 25 142431 1.7684 0.961501 20 to 24 142538 2.1311 0.983459 19 to 23 142360 1.5277 0.936706 18 to 22 141640 -0.9130 0.180626 17 to 21 142052 0.4836 0.685675 16 to 20 142050 0.4768 0.683265 15 to 19 142009 0.3379 0.632267 14 to 18 142188 0.9446 0.827580 13 to 17 141489 -1.4248 0.077101 12 to 16 142183 0.9277 0.823217 11 to 15 142163 0.8599 0.805077 10 to 14 142374 1.5752 0.942389 9 to 13 141797 -0.3808 0.351683 8 to 12 141129 -2.6452 0.004082 7 to 11 141830 -0.2689 0.393998 6 to 10 141846 -0.2147 0.415009 5 to 9 142143 0.7921 0.785849 4 to 8 142173 0.8938 0.814285 3 to 7 141931 0.0735 0.529279 2 to 6 141904 -0.0181 0.492792 1 to 5 141899 -0.0350 0.486033 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-14_03:31 Bits used No. missing words z-score p-value 31 to 32 142227 0.9371 0.825641 30 to 31 142366 1.3471 0.911027 29 to 30 142066 0.4622 0.678014 28 to 29 141834 -0.2222 0.412074 27 to 28 142211 0.8899 0.813235 26 to 27 141615 -0.8682 0.192634 25 to 26 141511 -1.1750 0.119994 24 to 25 141931 0.0639 0.525484 23 to 24 141466 -1.3078 0.095478 22 to 23 142012 0.3029 0.619002 21 to 22 142147 0.7011 0.758377 20 to 21 142349 1.2970 0.902678 19 to 20 141901 -0.0246 0.490198 18 to 19 142155 0.7247 0.765679 17 to 18 142321 1.2144 0.887696 16 to 17 141466 -1.3078 0.095478 15 to 16 141811 -0.2901 0.385886 14 to 15 142579 1.9754 0.975890 13 to 14 141759 -0.4435 0.328720 12 to 13 141661 -0.7325 0.231921 11 to 12 142183 0.8073 0.790249 10 to 11 141846 -0.1868 0.425903 9 to 10 141925 0.0462 0.518434 8 to 9 141918 0.0256 0.510202 7 to 8 141558 -1.0364 0.150014 6 to 7 141499 -1.2104 0.113060 5 to 6 141562 -1.0246 0.152783 4 to 5 141626 -0.8358 0.201639 3 to 4 142116 0.6096 0.728952 2 to 3 142129 0.6480 0.741506 1 to 2 141893 -0.0482 0.480790 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-14_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2453.45 -0.658 0.255155 Test results for specific bytes for dh-ranFile-2017-01-14_03:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2481.56 -0.261 0.397133 2 to 9 2494.29 -0.081 0.467836 3 to 10 2436.48 -0.898 0.184505 4 to 11 2593.18 1.318 0.906199 5 to 12 2571.53 1.012 0.844117 6 to 13 2447.04 -0.749 0.226946 7 to 14 2370.36 -1.833 0.033374 8 to 15 2491.59 -0.119 0.452648 9 to 16 2539.69 0.561 0.712711 10 to 17 2487.63 -0.175 0.430566 11 to 18 2432.16 -0.959 0.168682 12 to 19 2474.65 -0.358 0.359997 13 to 20 2430.11 -0.988 0.161485 14 to 21 2534.59 0.489 0.687661 15 to 22 2554.64 0.773 0.780158 16 to 23 2546.43 0.657 0.744297 17 to 24 2542.28 0.598 0.725045 18 to 25 2582.73 1.170 0.879009 19 to 26 2537.04 0.524 0.699814 20 to 27 2574.43 1.053 0.853751 21 to 28 2647.44 2.085 0.981468 22 to 29 2670.84 2.416 0.992155 23 to 30 2499.19 -0.012 0.495411 24 to 31 2423.88 -1.076 0.140855 25 to 32 2422.15 -1.101 0.135442 CDPARK for dh-ranFile-2017-01-14_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 3556 1.5068 0.934075 3555 1.4612 0.928018 3521 -0.0913 0.463617 3495 -1.2785 0.100530 3524 0.0457 0.518210 3509 -0.6393 0.261324 3506 -0.7763 0.218799 3536 0.5936 0.723613 3538 0.6849 0.753306 3497 -1.1872 0.117571 Square side=100, avg. no. parked=3523.70 sample std.=21.10 p-value of the KSTEST for those 10 p-values: 0.958892 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-14_03:31 0.9539,0.3479,0.1745,0.5386,0.7316,0.2789,0.2260,0.5184,0.8638,0.4479, The KS test for those 10 p-values: 0.924302 The 3DSPHERES test for dh-ranFile-2017-01-14_03:31 sample no r^3 equiv. uni. 1 39.595 0.732824 2 97.685 0.961464 3 0.850 0.027951 4 36.878 0.707495 5 27.679 0.602531 6 12.870 0.348830 7 47.592 0.795339 8 17.422 0.440509 9 16.158 0.416427 10 0.164 0.005446 11 35.813 0.696922 12 11.805 0.325307 13 6.325 0.190083 14 9.828 0.279338 15 20.213 0.490220 16 121.866 0.982789 17 14.038 0.373706 18 68.367 0.897602 19 13.279 0.357664 20 6.462 0.193770 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.903722 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-14_03:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.3 3.4 0.8 0.2 -0.3 0.5 1.2 0.2 -0.3 -0.2 0.5 1.5 1.3 0.5 0.7 -0.7 0.5 -0.7 -3.1 1.6 -0.4 -1.4 0.5 0.2 -0.4 1.0 -1.0 -0.6 -0.8 -0.2 -1.4 0.6 0.3 0.2 -0.1 -1.2 -1.0 0.9 1.0 -1.3 -1.0 -1.1 Chi-square with 42 degrees of freedom:51.033279 z-score=0.985612, p-value=0.839956 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-14_03:31 Test no p-value 1 0.329417 2 0.574172 3 0.993796 4 0.156741 5 0.025079 6 0.157991 7 0.023849 8 0.960199 9 0.047444 10 0.082400 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.013658 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-14_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 66471 0.57 66673 0.00 3 25000.00 25237 2.25 24984 0.01 4 6666.67 6602 0.63 6727 0.55 5 1388.89 1396 0.04 1346 1.32 6 238.10 260 2.02 228 0.43 7 34.72 27 1.72 33 0.09 8 4.96 6 0.22 8 1.86 p=0.71749 p=0.35816 Number of rngs required: 687748, p-value: 0.225 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-14_03:31 No. of wins: Observed Expected 98264 98585.9 z-score=-1.440, pvalue=0.07500 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66353 66666.7 1.476 1.476 2 37952 37654.3 2.353 3.829 3 26939 26954.7 0.009 3.838 4 19427 19313.5 0.667 4.506 5 13927 13851.4 0.412 4.918 6 9928 9943.5 0.024 4.942 7 7185 7145.0 0.224 5.166 8 5141 5139.1 0.001 5.167 9 3662 3699.9 0.388 5.554 10 2622 2666.3 0.736 6.290 11 1866 1923.3 1.709 7.999 12 1380 1388.7 0.055 8.054 13 1005 1003.7 0.002 8.056 14 708 726.1 0.453 8.509 15 500 525.8 1.269 9.778 16 379 381.2 0.012 9.790 17 284 276.5 0.201 9.992 18 182 200.8 1.765 11.757 19 173 146.0 4.999 16.757 20 116 106.2 0.901 17.658 21 271 287.1 0.904 18.562 Chisq= 18.56 for 20 degrees of freedom, p= 0.44959 SUMMARY of craptest p-value for no. of wins: 0.074999 p-value for throws/game: 0.449594 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-14_03:31 No. of wins: Observed Expected 98147 98585.9 z-score=-1.963, pvalue=0.02483 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66609 66666.7 0.050 0.050 2 37631 37654.3 0.014 0.064 3 27238 26954.7 2.977 3.041 4 19409 19313.5 0.473 3.514 5 13870 13851.4 0.025 3.539 6 9869 9943.5 0.559 4.098 7 7000 7145.0 2.944 7.041 8 5113 5139.1 0.132 7.173 9 3646 3699.9 0.784 7.958 10 2613 2666.3 1.065 9.023 11 1900 1923.3 0.283 9.306 12 1463 1388.7 3.971 13.277 13 1050 1003.7 2.134 15.411 14 700 726.1 0.941 16.352 15 520 525.8 0.065 16.417 16 383 381.2 0.009 16.426 17 285 276.5 0.259 16.685 18 196 200.8 0.116 16.801 19 148 146.0 0.028 16.829 20 72 106.2 11.022 27.851 21 285 287.1 0.016 27.866 Chisq= 27.87 for 20 degrees of freedom, p= 0.88740 SUMMARY of craptest p-value for no. of wins: 0.024833 p-value for throws/game: 0.887395 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0041,0.0054,0.0129,0.0137,0.0238,0.0247,0.0248,0.0251,0.0280,0.0306, 0.0316,0.0317,0.0334,0.0341,0.0474,0.0514,0.0668,0.0750,0.0771,0.0785, 0.0808,0.0813,0.0824,0.0838,0.0955,0.0955,0.0987,0.1005,0.1080,0.1107, 0.1131,0.1167,0.1176,0.1200,0.1226,0.1241,0.1354,0.1409,0.1484,0.1500, 0.1523,0.1528,0.1567,0.1580,0.1615,0.1660,0.1687,0.1745,0.1806,0.1837, 0.1845,0.1901,0.1926,0.1938,0.2016,0.2105,0.2145,0.2188,0.2246,0.2260, 0.2266,0.2269,0.2310,0.2319,0.2352,0.2502,0.2552,0.2613,0.2617,0.2789, 0.2793,0.2971,0.3042,0.3074,0.3253,0.3287,0.3294,0.3452,0.3474,0.3479, 0.3488,0.3517,0.3577,0.3582,0.3600,0.3715,0.3737,0.3859,0.3940,0.3940, 0.3949,0.3971,0.3983,0.4020,0.4121,0.4150,0.4155,0.4164,0.4259,0.4292, 0.4306,0.4405,0.4468,0.4479,0.4496,0.4520,0.4526,0.4636,0.4667,0.4678, 0.4721,0.4797,0.4808,0.4857,0.4860,0.4887,0.4902,0.4902,0.4928,0.4928, 0.4941,0.4954,0.4955,0.4977,0.5005,0.5102,0.5125,0.5171,0.5172,0.5182, 0.5184,0.5184,0.5216,0.5255,0.5277,0.5287,0.5293,0.5349,0.5380,0.5386, 0.5423,0.5446,0.5469,0.5566,0.5592,0.5628,0.5642,0.5665,0.5677,0.5692, 0.5694,0.5742,0.5795,0.5815,0.5881,0.6025,0.6137,0.6190,0.6203,0.6323, 0.6423,0.6453,0.6524,0.6737,0.6780,0.6833,0.6837,0.6857,0.6877,0.6912, 0.6969,0.6998,0.7013,0.7075,0.7090,0.7127,0.7157,0.7175,0.7178,0.7236, 0.7248,0.7250,0.7290,0.7316,0.7320,0.7328,0.7330,0.7343,0.7401,0.7415, 0.7443,0.7448,0.7533,0.7555,0.7584,0.7652,0.7657,0.7687,0.7761,0.7778, 0.7802,0.7807,0.7858,0.7873,0.7902,0.7953,0.8013,0.8051,0.8132,0.8143, 0.8143,0.8162,0.8197,0.8232,0.8239,0.8240,0.8256,0.8260,0.8265,0.8276, 0.8296,0.8400,0.8411,0.8441,0.8538,0.8556,0.8617,0.8638,0.8644,0.8673, 0.8704,0.8732,0.8758,0.8790,0.8859,0.8874,0.8874,0.8877,0.8906,0.8976, 0.8983,0.9027,0.9031,0.9037,0.9062,0.9110,0.9243,0.9280,0.9341,0.9367, 0.9411,0.9424,0.9467,0.9539,0.9589,0.9602,0.9611,0.9615,0.9615,0.9759, 0.9808,0.9815,0.9828,0.9835,0.9896,0.9922,0.9928,0.9938,0.9964, Overall p-value after applying KStest on 269 p-values = 0.175355 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.