RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-12-01_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 20.7858 0.763981 2 to 25 15.78 34.4132 0.992577 3 to 26 15.63 21.0143 0.774347 4 to 27 15.32 26.1675 0.928538 5 to 28 15.40 33.6111 0.990579 6 to 29 15.50 32.1724 0.985677 7 to 30 15.94 21.2715 0.785620 8 to 31 15.89 29.2488 0.967700 9 to 32 15.84 17.0819 0.551168 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.000027 Tough bday spacings test for dh-ranFile-2015-12-01_00:31: 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 12 30 69 100 94 68 65 35 18 6 3 (O-E)^2/E 0.9 1.2 0.2 0.1 0.1 1.3 3.2 0.9 0.7 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.944, p= 0.463 RESULTS OF GCD FOR dh-ranFile-2015-12-01_00:31 Euclid's algorithm: p-value, steps to gcd: 0.471210 p-value, dist. of gcd's: 0.146076 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-12-01_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.690 0.996 0.326 0.179 0.758 0.784 0.634 0.638 Bits 8 to 15---> 0.270 0.311 0.165 0.963 0.354 0.259 0.610 0.318 Bits 16 to 23---> 0.587 0.460 0.444 0.333 0.482 0.585 0.710 0.583 Bits 24 to 31---> 0.912 0.679 0.827 0.879 0.932 0.600 0.268 0.631 KS test for the above 32 p values: 0.845 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-12-01_00:31, p-values for 5 runs: 0.6578, 0.4166, 0.0261, 0.5952, 0.3950 Rank test for binary matrices (31x31) for dh-ranFile-2015-12-01_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 186 211.4 3.056 3.056 r= 29 5162 5134.0 0.153 3.209 r= 30 23096 23103.0 0.002 3.211 r= 31 11556 11551.5 0.002 3.212 chi-square = 3.212 with df = 3; p-value = 0.640 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-12-01_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 231 211.4 1.814 1.814 r= 30 5123 5134.0 0.024 1.837 r= 31 23155 23103.0 0.117 1.954 r= 32 11491 11551.5 0.317 2.271 chi-square = 2.271 with df = 3; p-value = 0.482 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-12-01_00:31 b-rank test for bits 1 to 8, p=0.63500 b-rank test for bits 2 to 9, p=0.42554 b-rank test for bits 3 to 10, p=0.21992 b-rank test for bits 4 to 11, p=0.67101 b-rank test for bits 5 to 12, p=0.62320 b-rank test for bits 6 to 13, p=0.88016 b-rank test for bits 7 to 14, p=0.68457 b-rank test for bits 8 to 15, p=0.00856 b-rank test for bits 9 to 16, p=0.44209 b-rank test for bits 10 to 17, p=0.20017 b-rank test for bits 11 to 18, p=0.61438 b-rank test for bits 12 to 19, p=0.36051 b-rank test for bits 13 to 20, p=0.92318 b-rank test for bits 14 to 21, p=0.97220 b-rank test for bits 15 to 22, p=0.09532 b-rank test for bits 16 to 23, p=0.99436 b-rank test for bits 17 to 24, p=0.31341 b-rank test for bits 18 to 25, p=0.95521 b-rank test for bits 19 to 26, p=0.68018 b-rank test for bits 20 to 27, p=0.69550 b-rank test for bits 21 to 28, p=0.97860 b-rank test for bits 22 to 29, p=0.62452 b-rank test for bits 23 to 30, p=0.11255 b-rank test for bits 24 to 31, p=0.13740 b-rank test for bits 25 to 32, p=0.13012 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 = 0.446786 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-12-01_00:31 (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 142429 1.21 0.887661 2 141435 -1.11 0.133877 3 142677 1.79 0.963563 4 141617 -0.68 0.247299 5 141700 -0.49 0.312389 6 141833 -0.18 0.429228 7 140735 -2.74 0.003037 8 142297 0.91 0.817471 9 142590 1.59 0.944122 10 141707 -0.47 0.318202 11 142285 0.88 0.809956 12 142392 1.13 0.870284 13 142028 0.28 0.609212 14 141415 -1.15 0.124050 15 141780 -0.30 0.381260 16 142152 0.57 0.714638 17 142513 1.41 0.920796 18 141586 -0.76 0.224991 19 141317 -1.38 0.083187 20 141882 -0.06 0.474543 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-12-01_00:31 Bits used No. missing words z-score p-value 23 to 32 141622 -0.9908 0.160893 22 to 31 141897 -0.0425 0.483043 21 to 30 142109 0.6885 0.754436 20 to 29 141909 -0.0011 0.499546 19 to 28 142393 1.6678 0.952325 18 to 27 141691 -0.7529 0.225766 17 to 26 141512 -1.3701 0.085327 16 to 25 142082 0.5954 0.724217 15 to 24 141659 -0.8632 0.194012 14 to 23 142642 2.5264 0.994239 13 to 22 142181 0.9368 0.825568 12 to 21 141882 -0.0942 0.462459 11 to 20 141779 -0.4494 0.326567 10 to 19 141781 -0.4425 0.329058 9 to 18 141915 0.0196 0.507800 8 to 17 142064 0.5333 0.703103 7 to 16 142133 0.7713 0.779728 6 to 15 142099 0.6540 0.743455 5 to 14 141742 -0.5770 0.281970 4 to 13 141829 -0.2770 0.390890 3 to 12 141945 0.1230 0.548947 2 to 11 141962 0.1816 0.572060 1 to 10 141671 -0.8218 0.205588 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-12-01_00:31 Bits used No. missing words z-score p-value 28 to 32 142407 1.6870 0.954200 27 to 31 142364 1.5413 0.938373 26 to 30 142089 0.6091 0.728755 25 to 29 142131 0.7514 0.773801 24 to 28 141640 -0.9130 0.180626 23 to 27 142131 0.7514 0.773801 22 to 26 142214 1.0328 0.849147 21 to 25 142025 0.3921 0.652509 20 to 24 142503 2.0124 0.977913 19 to 23 142193 0.9616 0.831873 18 to 22 142156 0.8362 0.798470 17 to 21 142253 1.1650 0.877987 16 to 20 141927 0.0599 0.523882 15 to 19 141931 0.0735 0.529279 14 to 18 142185 0.9345 0.824970 13 to 17 141778 -0.4452 0.328093 12 to 16 141749 -0.5435 0.293396 11 to 15 141696 -0.7232 0.234793 10 to 14 142002 0.3141 0.623291 9 to 13 142077 0.5684 0.715109 8 to 12 141524 -1.3062 0.095742 7 to 11 142520 2.0701 0.980777 6 to 10 141607 -1.0248 0.152718 5 to 9 141843 -0.2248 0.411049 4 to 8 141689 -0.7469 0.227568 3 to 7 142158 0.8429 0.800372 2 to 6 141730 -0.6079 0.271628 1 to 5 141963 0.1819 0.572182 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-12-01_00:31 Bits used No. missing words z-score p-value 31 to 32 140995 -2.6971 0.003497 30 to 31 142573 1.9577 0.974869 29 to 30 141675 -0.6912 0.244708 28 to 29 141946 0.1082 0.543070 27 to 28 142027 0.3471 0.635745 26 to 27 141822 -0.2576 0.398354 25 to 26 141572 -0.9951 0.159850 24 to 25 141686 -0.6588 0.255015 23 to 24 141587 -0.9508 0.170846 22 to 23 142053 0.4238 0.664146 21 to 22 141847 -0.1839 0.427060 20 to 21 141628 -0.8299 0.203303 19 to 20 142005 0.2822 0.611110 18 to 19 142171 0.7719 0.779910 17 to 18 141400 -1.5024 0.066491 16 to 17 141449 -1.3579 0.087247 15 to 16 141866 -0.1278 0.449147 14 to 15 141895 -0.0423 0.483141 13 to 14 142233 0.9548 0.830155 12 to 13 141425 -1.4287 0.076545 11 to 12 141594 -0.9302 0.176140 10 to 11 141950 0.1200 0.547747 9 to 10 141921 0.0344 0.513731 8 to 9 141885 -0.0718 0.471393 7 to 8 142649 2.1819 0.985442 6 to 7 141610 -0.8830 0.188624 5 to 6 142319 1.2085 0.886566 4 to 5 141734 -0.5172 0.302509 3 to 4 141980 0.2085 0.582568 2 to 3 142268 1.0580 0.854978 1 to 2 141889 -0.0600 0.476090 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-12-01_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2552.49 0.742 0.771033 Test results for specific bytes for dh-ranFile-2015-12-01_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2486.17 -0.196 0.422454 2 to 9 2645.20 2.053 0.979987 3 to 10 2442.52 -0.813 0.208134 4 to 11 2417.95 -1.160 0.122939 5 to 12 2471.40 -0.405 0.342911 6 to 13 2492.20 -0.110 0.456085 7 to 14 2661.96 2.290 0.989003 8 to 15 2353.60 -2.070 0.019206 9 to 16 2542.10 0.595 0.724198 10 to 17 2418.77 -1.149 0.125337 11 to 18 2433.97 -0.934 0.175186 12 to 19 2478.79 -0.300 0.382118 13 to 20 2554.41 0.769 0.779188 14 to 21 2434.48 -0.927 0.177059 15 to 22 2450.45 -0.701 0.241739 16 to 23 2526.29 0.372 0.644984 17 to 24 2525.41 0.359 0.640326 18 to 25 2524.97 0.353 0.638022 19 to 26 2419.02 -1.145 0.126059 20 to 27 2571.48 1.011 0.843958 21 to 28 2468.56 -0.445 0.328310 22 to 29 2580.06 1.132 0.871216 23 to 30 2443.12 -0.804 0.210576 24 to 31 2383.72 -1.644 0.050045 25 to 32 2517.37 0.246 0.596998 CDPARK for dh-ranFile-2015-12-01_00:31: 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 3501 -1.0046 0.157553 3518 -0.2283 0.409702 3530 0.3196 0.625377 3502 -0.9589 0.168804 3539 0.7306 0.767486 3489 -1.5525 0.060270 3539 0.7306 0.767486 3518 -0.2283 0.409702 3500 -1.0502 0.146807 3531 0.3653 0.642555 Square side=100, avg. no. parked=3516.70 sample std.=16.99 p-value of the KSTEST for those 10 p-values: 0.509334 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-12-01_00:31 0.0351,0.5475,0.1403,0.5966,0.4487,0.7267,0.5317,0.2572,0.4700,0.7206, The KS test for those 10 p-values: 0.552741 The 3DSPHERES test for dh-ranFile-2015-12-01_00:31 sample no r^3 equiv. uni. 1 28.484 0.613056 2 2.241 0.071978 3 10.460 0.294376 4 29.632 0.627580 5 11.786 0.324871 6 25.969 0.579215 7 5.855 0.177314 8 103.868 0.968641 9 1.586 0.051488 10 25.101 0.566867 11 11.285 0.313523 12 34.898 0.687536 13 23.597 0.544596 14 2.102 0.067658 15 48.593 0.802055 16 0.428 0.014179 17 34.890 0.687449 18 16.837 0.429490 19 25.038 0.565947 20 41.588 0.749990 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.563362 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-12-01_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 2.0 0.5 0.1 -0.8 1.0 -1.0 0.7 0.5 0.1 -0.0 -0.6 -0.9 -0.3 0.1 0.2 -0.0 -0.4 0.8 -0.3 -0.7 0.5 -0.7 0.0 0.6 0.5 1.4 0.5 -0.6 0.2 0.3 0.2 -0.3 -0.5 -1.5 0.1 -1.6 -0.2 1.1 0.9 -0.7 -0.6 -1.0 -0.1 Chi-square with 42 degrees of freedom:23.628240 z-score=-2.004523, p-value=0.009906 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-12-01_00:31 Test no p-value 1 0.878492 2 0.817187 3 0.039926 4 0.677052 5 0.344516 6 0.393192 7 0.025516 8 0.349808 9 0.838873 10 0.607016 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.802194 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-12-01_00:31: (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 66365 1.37 66810 0.31 3 25000.00 25119 0.57 25079 0.25 4 6666.67 6825 3.76 6523 3.10 5 1388.89 1413 0.42 1330 2.50 6 238.10 239 0.00 218 1.70 7 34.72 32 0.21 35 0.00 8 4.96 6 0.22 4 0.19 p=0.63501 p=0.76445 Number of rngs required: 688100, p-value: 0.364 RESULTS OF CRAPS TEST for dh-ranFile-2015-12-01_00:31 No. of wins: Observed Expected 98493 98585.9 z-score=-0.415, pvalue=0.33895 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66658 66666.7 0.001 0.001 2 37641 37654.3 0.005 0.006 3 26913 26954.7 0.065 0.070 4 19409 19313.5 0.473 0.543 5 13846 13851.4 0.002 0.545 6 9866 9943.5 0.605 1.150 7 7215 7145.0 0.685 1.835 8 5191 5139.1 0.525 2.360 9 3672 3699.9 0.210 2.570 10 2607 2666.3 1.319 3.888 11 1934 1923.3 0.059 3.948 12 1381 1388.7 0.043 3.991 13 1012 1003.7 0.068 4.059 14 774 726.1 3.154 7.214 15 540 525.8 0.382 7.595 16 380 381.2 0.003 7.599 17 266 276.5 0.402 8.000 18 180 200.8 2.160 10.161 19 141 146.0 0.170 10.331 20 127 106.2 4.067 14.398 21 247 287.1 5.605 20.003 Chisq= 20.00 for 20 degrees of freedom, p= 0.54224 SUMMARY of craptest p-value for no. of wins: 0.338955 p-value for throws/game: 0.542239 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-12-01_00:31 No. of wins: Observed Expected 98701 98585.9 z-score= 0.515, pvalue=0.69672 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66632 66666.7 0.018 0.018 2 37518 37654.3 0.494 0.512 3 27075 26954.7 0.537 1.048 4 19403 19313.5 0.415 1.463 5 14037 13851.4 2.486 3.950 6 9737 9943.5 4.290 8.240 7 7196 7145.0 0.364 8.604 8 5081 5139.1 0.656 9.260 9 3714 3699.9 0.054 9.314 10 2716 2666.3 0.927 10.240 11 1858 1923.3 2.219 12.459 12 1383 1388.7 0.024 12.483 13 1045 1003.7 1.698 14.181 14 725 726.1 0.002 14.183 15 515 525.8 0.223 14.406 16 393 381.2 0.368 14.775 17 263 276.5 0.663 15.438 18 159 200.8 8.713 24.150 19 165 146.0 2.477 26.627 20 102 106.2 0.167 26.794 21 283 287.1 0.059 26.853 Chisq= 26.85 for 20 degrees of freedom, p= 0.86056 SUMMARY of craptest p-value for no. of wins: 0.696716 p-value for throws/game: 0.860556 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0030,0.0035,0.0086,0.0099,0.0142,0.0192,0.0255,0.0261,0.0351, 0.0399,0.0500,0.0515,0.0603,0.0665,0.0677,0.0720,0.0765,0.0832,0.0853, 0.0872,0.0953,0.0957,0.1126,0.1229,0.1241,0.1253,0.1261,0.1301,0.1339, 0.1374,0.1403,0.1461,0.1468,0.1527,0.1576,0.1599,0.1609,0.1648,0.1688, 0.1708,0.1752,0.1761,0.1771,0.1773,0.1791,0.1806,0.1886,0.1940,0.2002, 0.2033,0.2056,0.2081,0.2106,0.2199,0.2250,0.2258,0.2276,0.2348,0.2417, 0.2447,0.2473,0.2550,0.2572,0.2594,0.2679,0.2704,0.2716,0.2820,0.2934, 0.2944,0.3025,0.3106,0.3124,0.3134,0.3135,0.3182,0.3183,0.3249,0.3261, 0.3266,0.3281,0.3283,0.3291,0.3330,0.3390,0.3429,0.3445,0.3498,0.3539, 0.3605,0.3636,0.3813,0.3821,0.3909,0.3932,0.3950,0.3984,0.4097,0.4097, 0.4110,0.4166,0.4225,0.4255,0.4271,0.4292,0.4295,0.4421,0.4442,0.4468, 0.4487,0.4491,0.4561,0.4602,0.4625,0.4626,0.4700,0.4712,0.4714,0.4745, 0.4761,0.4820,0.4825,0.4830,0.4831,0.4995,0.5078,0.5093,0.5137,0.5239, 0.5293,0.5317,0.5422,0.5431,0.5446,0.5475,0.5477,0.5489,0.5512,0.5527, 0.5634,0.5659,0.5669,0.5721,0.5722,0.5792,0.5826,0.5833,0.5853,0.5868, 0.5952,0.5966,0.5970,0.6000,0.6070,0.6092,0.6097,0.6111,0.6131,0.6144, 0.6232,0.6233,0.6245,0.6254,0.6276,0.6310,0.6341,0.6350,0.6350,0.6357, 0.6380,0.6381,0.6400,0.6403,0.6426,0.6450,0.6525,0.6578,0.6641,0.6710, 0.6771,0.6794,0.6802,0.6846,0.6874,0.6875,0.6895,0.6955,0.6967,0.7031, 0.7102,0.7146,0.7151,0.7206,0.7242,0.7242,0.7267,0.7288,0.7435,0.7500, 0.7544,0.7583,0.7640,0.7645,0.7675,0.7675,0.7710,0.7738,0.7738,0.7743, 0.7792,0.7797,0.7799,0.7837,0.7856,0.7985,0.8004,0.8021,0.8022,0.8100, 0.8172,0.8175,0.8250,0.8256,0.8271,0.8302,0.8319,0.8389,0.8440,0.8451, 0.8491,0.8550,0.8606,0.8703,0.8712,0.8780,0.8785,0.8793,0.8802,0.8866, 0.8877,0.9119,0.9208,0.9232,0.9285,0.9316,0.9384,0.9441,0.9523,0.9542, 0.9552,0.9628,0.9636,0.9677,0.9686,0.9722,0.9749,0.9779,0.9786,0.9800, 0.9808,0.9854,0.9857,0.9890,0.9906,0.9926,0.9942,0.9944,0.9961, Overall p-value after applying KStest on 269 p-values = 0.389924 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.