RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-08-11_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.84 22.8334 0.845247 2 to 25 15.80 32.6603 0.987558 3 to 26 15.98 15.2442 0.422101 4 to 27 15.99 23.4418 0.864586 5 to 28 15.80 16.5727 0.516340 6 to 29 15.87 11.8338 0.189902 7 to 30 15.74 8.1236 0.036169 8 to 31 15.60 18.9077 0.666143 9 to 32 15.70 17.3777 0.570927 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.775233 Tough bday spacings test for dh-ranFile-2015-08-11_19:31: 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 10 26 78 95 109 69 52 34 14 6 7 (O-E)^2/E 0.1 3.1 0.3 0.1 1.3 1.1 0.0 0.6 0.1 0.1 2.1 Birthday Spacings: Sum(O-E)^2/E= 8.753, p= 0.444 RESULTS OF GCD FOR dh-ranFile-2015-08-11_19:31 Euclid's algorithm: p-value, steps to gcd: 0.653419 p-value, dist. of gcd's: 0.998643 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-08-11_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.400 0.546 0.575 0.894 0.235 0.892 0.660 0.071 Bits 8 to 15---> 0.714 0.276 0.395 0.292 0.566 0.164 0.401 0.397 Bits 16 to 23---> 0.180 0.966 0.870 0.027 0.418 0.358 0.685 0.209 Bits 24 to 31---> 0.834 0.978 0.155 0.376 0.533 0.959 0.098 0.802 KS test for the above 32 p values: 0.043 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-08-11_19:31, p-values for 5 runs: 0.6691, 0.7697, 0.2321, 0.8656, 0.3428 Rank test for binary matrices (31x31) for dh-ranFile-2015-08-11_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 204 211.4 0.260 0.260 r= 29 5144 5134.0 0.019 0.280 r= 30 23166 23103.0 0.172 0.451 r= 31 11486 11551.5 0.372 0.823 chi-square = 0.823 with df = 3; p-value = 0.156 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-08-11_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 227 211.4 1.148 1.148 r= 30 5150 5134.0 0.050 1.198 r= 31 23111 23103.0 0.003 1.201 r= 32 11512 11551.5 0.135 1.336 chi-square = 1.336 with df = 3; p-value = 0.279 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-08-11_19:31 b-rank test for bits 1 to 8, p=0.19798 b-rank test for bits 2 to 9, p=0.49516 b-rank test for bits 3 to 10, p=0.70565 b-rank test for bits 4 to 11, p=0.14144 b-rank test for bits 5 to 12, p=0.72877 b-rank test for bits 6 to 13, p=0.42826 b-rank test for bits 7 to 14, p=0.95927 b-rank test for bits 8 to 15, p=0.78342 b-rank test for bits 9 to 16, p=0.29417 b-rank test for bits 10 to 17, p=0.76853 b-rank test for bits 11 to 18, p=0.91099 b-rank test for bits 12 to 19, p=0.41125 b-rank test for bits 13 to 20, p=0.15538 b-rank test for bits 14 to 21, p=0.53430 b-rank test for bits 15 to 22, p=0.52971 b-rank test for bits 16 to 23, p=0.24420 b-rank test for bits 17 to 24, p=0.95696 b-rank test for bits 18 to 25, p=0.99338 b-rank test for bits 19 to 26, p=0.62243 b-rank test for bits 20 to 27, p=0.32738 b-rank test for bits 21 to 28, p=0.73588 b-rank test for bits 22 to 29, p=0.59812 b-rank test for bits 23 to 30, p=0.40212 b-rank test for bits 24 to 31, p=0.10265 b-rank test for bits 25 to 32, p=0.61032 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 = 0.638979 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-08-11_19:31 (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 142251 0.80 0.787650 2 141668 -0.56 0.286426 3 141574 -0.78 0.216672 4 142855 2.21 0.986430 5 141837 -0.17 0.432900 6 141767 -0.33 0.369738 7 142477 1.33 0.907635 8 141318 -1.38 0.083545 9 142169 0.61 0.727977 10 142285 0.88 0.809956 11 141776 -0.31 0.377703 12 142118 0.49 0.687065 13 141221 -1.61 0.053890 14 141935 0.06 0.523913 15 140946 -2.25 0.012200 16 141553 -0.83 0.202550 17 142431 1.22 0.888550 18 141803 -0.25 0.401899 19 142450 1.26 0.896750 20 142427 1.21 0.886766 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-08-11_19:31 Bits used No. missing words z-score p-value 23 to 32 141744 -0.5701 0.284304 22 to 31 141616 -1.0115 0.155893 21 to 30 142269 1.2402 0.892557 20 to 29 141692 -0.7494 0.226804 19 to 28 141653 -0.8839 0.188376 18 to 27 141962 0.1816 0.572060 17 to 26 142075 0.5713 0.716094 16 to 25 141719 -0.6563 0.255812 15 to 24 142182 0.9402 0.826453 14 to 23 142056 0.5058 0.693487 13 to 22 141800 -0.3770 0.353087 12 to 21 141815 -0.3253 0.372486 11 to 20 141693 -0.7460 0.227844 10 to 19 141863 -0.1598 0.436536 9 to 18 141854 -0.1908 0.424344 8 to 17 142485 1.9851 0.976432 7 to 16 142642 2.5264 0.994239 6 to 15 141320 -2.0322 0.021068 5 to 14 141927 0.0609 0.524293 4 to 13 141977 0.2333 0.592253 3 to 12 141854 -0.1908 0.424344 2 to 11 142083 0.5989 0.725368 1 to 10 142141 0.7989 0.787815 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-08-11_19:31 Bits used No. missing words z-score p-value 28 to 32 142356 1.5141 0.935004 27 to 31 142026 0.3955 0.653760 26 to 30 142126 0.7345 0.768670 25 to 29 141743 -0.5638 0.286435 24 to 28 141612 -1.0079 0.156752 23 to 27 141961 0.1752 0.569520 22 to 26 141755 -0.5232 0.300434 21 to 25 142207 1.0091 0.843525 20 to 24 141973 0.2158 0.585440 19 to 23 141902 -0.0248 0.490088 18 to 22 141861 -0.1638 0.434932 17 to 21 142161 0.8531 0.803203 16 to 20 141935 0.0870 0.534671 15 to 19 142173 0.8938 0.814285 14 to 18 142200 0.9853 0.837767 13 to 17 141839 -0.2384 0.405783 12 to 16 141917 0.0260 0.510371 11 to 15 141813 -0.3265 0.372007 10 to 14 142134 0.7616 0.776849 9 to 13 141288 -2.1062 0.017593 8 to 12 142236 1.1074 0.865930 7 to 11 142068 0.5379 0.704665 6 to 10 142101 0.6497 0.742066 5 to 9 141805 -0.3537 0.361797 4 to 8 141691 -0.7401 0.229619 3 to 7 141879 -0.1028 0.459056 2 to 6 142138 0.7752 0.780875 1 to 5 141994 0.2870 0.612950 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-08-11_19:31 Bits used No. missing words z-score p-value 31 to 32 142267 1.0551 0.854304 30 to 31 142000 0.2675 0.605444 29 to 30 142339 1.2675 0.897505 28 to 29 141892 -0.0511 0.479615 27 to 28 142059 0.4415 0.670576 26 to 27 141459 -1.3284 0.092022 25 to 26 141428 -1.4199 0.077825 24 to 25 142474 1.6657 0.952113 23 to 24 141286 -1.8387 0.032977 22 to 23 141310 -1.7679 0.038536 21 to 22 142438 1.5595 0.940561 20 to 21 142129 0.6480 0.741506 19 to 20 141753 -0.4612 0.322345 18 to 19 142304 1.1642 0.877832 17 to 18 142205 0.8722 0.808446 16 to 17 141510 -1.1780 0.119405 15 to 16 141836 -0.2163 0.414372 14 to 15 142460 1.6244 0.947854 13 to 14 142073 0.4828 0.685382 12 to 13 141918 0.0256 0.510202 11 to 12 142247 0.9961 0.840394 10 to 11 142215 0.9017 0.816387 9 to 10 141961 0.1524 0.560572 8 to 9 142191 0.8309 0.796981 7 to 8 141912 0.0079 0.503142 6 to 7 142437 1.5565 0.940211 5 to 6 142168 0.7630 0.777280 4 to 5 141671 -0.7030 0.241016 3 to 4 141585 -0.9567 0.169353 2 to 3 141690 -0.6470 0.258819 1 to 2 142080 0.5035 0.692677 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-08-11_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2499.35 -0.009 0.496357 Test results for specific bytes for dh-ranFile-2015-08-11_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2441.09 -0.833 0.202371 2 to 9 2592.53 1.309 0.904651 3 to 10 2477.10 -0.324 0.372998 4 to 11 2459.73 -0.569 0.284528 5 to 12 2355.43 -2.045 0.020451 6 to 13 2493.61 -0.090 0.464012 7 to 14 2499.41 -0.008 0.496676 8 to 15 2485.16 -0.210 0.416897 9 to 16 2567.28 0.952 0.829326 10 to 17 2412.97 -1.231 0.109201 11 to 18 2438.09 -0.876 0.190643 12 to 19 2436.38 -0.900 0.184145 13 to 20 2600.58 1.422 0.922549 14 to 21 2489.17 -0.153 0.439125 15 to 22 2532.02 0.453 0.674676 16 to 23 2505.38 0.076 0.530306 17 to 24 2466.00 -0.481 0.315309 18 to 25 2550.22 0.710 0.761207 19 to 26 2368.65 -1.858 0.031620 20 to 27 2466.33 -0.476 0.316994 21 to 28 2400.78 -1.403 0.080285 22 to 29 2350.85 -2.109 0.017457 23 to 30 2702.22 2.860 0.997881 24 to 31 2387.05 -1.597 0.055091 25 to 32 2523.11 0.327 0.628119 CDPARK for dh-ranFile-2015-08-11_19:31: 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 3512 -0.5023 0.307734 3544 0.9589 0.831196 3531 0.3653 0.642555 3523 0.0000 0.500000 3536 0.5936 0.723613 3516 -0.3196 0.374623 3518 -0.2283 0.409702 3538 0.6849 0.753306 3497 -1.1872 0.117571 3483 -1.8265 0.033889 Square side=100, avg. no. parked=3519.80 sample std.=18.08 p-value of the KSTEST for those 10 p-values: 0.921988 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-08-11_19:31 0.7724,0.5182,0.9277,0.5957,0.8172,0.1542,0.9997,0.0073,0.8506,0.9944, The KS test for those 10 p-values: 0.019618 The 3DSPHERES test for dh-ranFile-2015-08-11_19:31 sample no r^3 equiv. uni. 1 29.114 0.621098 2 0.624 0.020581 3 0.823 0.027066 4 42.176 0.754843 5 66.202 0.889939 6 19.193 0.472585 7 0.519 0.017140 8 49.663 0.808990 9 46.886 0.790463 10 0.099 0.003282 11 9.720 0.276740 12 6.498 0.194746 13 25.508 0.572704 14 31.963 0.655422 15 48.999 0.804718 16 19.207 0.472835 17 14.348 0.380146 18 24.545 0.558755 19 55.602 0.843296 20 66.932 0.892585 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.287765 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-08-11_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.2 -0.1 1.6 1.0 3.1 1.7 0.9 -2.5 1.2 0.1 -0.1 -0.3 -1.8 0.7 -0.5 0.5 -0.8 1.3 -0.2 -1.4 0.9 -0.1 0.6 -0.0 -1.5 0.2 1.4 2.0 -1.2 0.6 -1.8 -0.2 0.9 -2.2 0.2 0.3 0.8 -0.4 1.5 -1.3 -1.0 -1.1 Chi-square with 42 degrees of freedom:61.901710 z-score=2.171455, p-value=0.975611 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-08-11_19:31 Test no p-value 1 0.096737 2 0.021721 3 0.661710 4 0.186057 5 0.077279 6 0.647165 7 0.970178 8 0.909159 9 0.828283 10 0.134127 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.287653 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-08-11_19:31: (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 66783 0.20 66583 0.11 3 25000.00 24914 0.30 24925 0.23 4 6666.67 6643 0.08 6810 3.08 5 1388.89 1391 0.00 1377 0.10 6 238.10 232 0.16 258 1.66 7 34.72 34 0.01 38 0.31 8 4.96 2 1.77 8 1.86 p=0.13417 p=0.71035 Number of rngs required: 687702, p-value: 0.209 RESULTS OF CRAPS TEST for dh-ranFile-2015-08-11_19:31 No. of wins: Observed Expected 98867 98585.9 z-score= 1.257, pvalue=0.89570 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66925 66666.7 1.001 1.001 2 37655 37654.3 0.000 1.001 3 26835 26954.7 0.532 1.533 4 19016 19313.5 4.581 6.114 5 13799 13851.4 0.198 6.313 6 9988 9943.5 0.199 6.512 7 7301 7145.0 3.405 9.916 8 5065 5139.1 1.068 10.984 9 3796 3699.9 2.498 13.482 10 2720 2666.3 1.082 14.564 11 1902 1923.3 0.237 14.800 12 1470 1388.7 4.755 19.555 13 935 1003.7 4.704 24.259 14 716 726.1 0.142 24.401 15 479 525.8 4.172 28.572 16 394 381.2 0.433 29.006 17 276 276.5 0.001 29.007 18 194 200.8 0.232 29.239 19 146 146.0 0.000 29.239 20 96 106.2 0.982 30.221 21 292 287.1 0.083 30.305 Chisq= 30.30 for 20 degrees of freedom, p= 0.93493 SUMMARY of craptest p-value for no. of wins: 0.895701 p-value for throws/game: 0.934933 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-08-11_19:31 No. of wins: Observed Expected 98719 98585.9 z-score= 0.595, pvalue=0.72424 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66592 66666.7 0.084 0.084 2 37630 37654.3 0.016 0.099 3 27138 26954.7 1.246 1.345 4 19110 19313.5 2.143 3.489 5 13883 13851.4 0.072 3.561 6 9840 9943.5 1.078 4.639 7 7182 7145.0 0.191 4.830 8 5142 5139.1 0.002 4.832 9 3698 3699.9 0.001 4.833 10 2745 2666.3 2.323 7.156 11 2019 1923.3 4.759 11.915 12 1380 1388.7 0.055 11.970 13 1055 1003.7 2.620 14.590 14 716 726.1 0.142 14.732 15 514 525.8 0.266 14.998 16 371 381.2 0.270 15.269 17 268 276.5 0.264 15.532 18 194 200.8 0.232 15.765 19 141 146.0 0.170 15.935 20 106 106.2 0.000 15.935 21 276 287.1 0.430 16.366 Chisq= 16.37 for 20 degrees of freedom, p= 0.30630 SUMMARY of craptest p-value for no. of wins: 0.724241 p-value for throws/game: 0.306296 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0033,0.0073,0.0122,0.0171,0.0175,0.0176,0.0196,0.0205,0.0206,0.0211, 0.0217,0.0269,0.0271,0.0316,0.0330,0.0339,0.0362,0.0385,0.0429,0.0539, 0.0551,0.0708,0.0773,0.0778,0.0803,0.0835,0.0920,0.0967,0.0982,0.1027, 0.1092,0.1176,0.1194,0.1341,0.1342,0.1414,0.1542,0.1553,0.1554,0.1559, 0.1560,0.1568,0.1641,0.1694,0.1800,0.1841,0.1861,0.1884,0.1899,0.1906, 0.1947,0.1980,0.2024,0.2026,0.2089,0.2091,0.2167,0.2268,0.2278,0.2296, 0.2321,0.2348,0.2410,0.2442,0.2558,0.2588,0.2757,0.2767,0.2794,0.2843, 0.2845,0.2864,0.2864,0.2877,0.2878,0.2923,0.2942,0.3004,0.3063,0.3077, 0.3153,0.3170,0.3223,0.3274,0.3428,0.3531,0.3583,0.3618,0.3697,0.3720, 0.3725,0.3730,0.3746,0.3759,0.3777,0.3801,0.3946,0.3974,0.4004,0.4005, 0.4019,0.4021,0.4058,0.4097,0.4112,0.4144,0.4169,0.4181,0.4221,0.4243, 0.4243,0.4283,0.4329,0.4349,0.4365,0.4391,0.4443,0.4591,0.4640,0.4726, 0.4728,0.4796,0.4901,0.4952,0.4964,0.4967,0.5000,0.5031,0.5102,0.5104, 0.5163,0.5182,0.5239,0.5243,0.5297,0.5303,0.5325,0.5343,0.5347,0.5463, 0.5588,0.5606,0.5662,0.5695,0.5709,0.5721,0.5727,0.5747,0.5854,0.5923, 0.5957,0.5981,0.6054,0.6103,0.6130,0.6211,0.6224,0.6281,0.6390,0.6426, 0.6472,0.6534,0.6538,0.6554,0.6598,0.6617,0.6661,0.6691,0.6706,0.6747, 0.6853,0.6854,0.6871,0.6927,0.6935,0.7047,0.7056,0.7104,0.7144,0.7161, 0.7236,0.7242,0.7254,0.7280,0.7288,0.7359,0.7415,0.7421,0.7533,0.7548, 0.7612,0.7685,0.7687,0.7697,0.7724,0.7752,0.7768,0.7773,0.7809,0.7834, 0.7877,0.7878,0.7905,0.7970,0.8021,0.8032,0.8047,0.8084,0.8090,0.8100, 0.8143,0.8164,0.8172,0.8265,0.8283,0.8293,0.8312,0.8345,0.8378,0.8404, 0.8433,0.8435,0.8452,0.8506,0.8543,0.8646,0.8656,0.8659,0.8695,0.8778, 0.8868,0.8886,0.8899,0.8923,0.8926,0.8926,0.8939,0.8957,0.8967,0.8975, 0.9047,0.9076,0.9092,0.9110,0.9220,0.9225,0.9277,0.9349,0.9350,0.9402, 0.9406,0.9479,0.9521,0.9570,0.9593,0.9594,0.9662,0.9702,0.9756,0.9764, 0.9776,0.9864,0.9876,0.9934,0.9942,0.9944,0.9979,0.9986,0.9997, Overall p-value after applying KStest on 269 p-values = 0.222396 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.