RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-20_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.77 15.9699 0.474029 2 to 25 15.91 20.7651 0.763024 3 to 26 15.81 28.1264 0.956517 4 to 27 15.89 8.4409 0.043811 5 to 28 15.82 14.0862 0.339008 6 to 29 15.82 23.1525 0.855650 7 to 30 15.68 16.2845 0.496234 8 to 31 15.59 27.9439 0.954402 9 to 32 15.59 22.8255 0.844981 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.198170 Tough bday spacings test for dh-ranFile-2018-03-20_05:31: 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 8 33 61 96 104 84 53 27 23 6 5 (O-E)^2/E 0.1 0.4 2.1 0.0 0.4 0.4 0.0 0.3 4.4 0.1 0.2 Birthday Spacings: Sum(O-E)^2/E= 8.404, p= 0.411 RESULTS OF GCD FOR dh-ranFile-2018-03-20_05:31 Euclid's algorithm: p-value, steps to gcd: 0.876996 p-value, dist. of gcd's: 0.095815 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-20_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.216 0.908 0.589 0.703 0.501 0.455 0.722 0.804 Bits 8 to 15---> 0.704 0.515 0.246 0.505 0.627 0.491 0.136 0.110 Bits 16 to 23---> 0.750 0.076 0.607 0.127 0.044 0.837 0.151 0.145 Bits 24 to 31---> 0.715 0.569 0.630 0.115 0.477 0.653 0.612 0.257 KS test for the above 32 p values: 0.693 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-20_05:31, p-values for 5 runs: 0.5189, 0.6318, 0.7152, 0.3292, 0.3827 Rank test for binary matrices (31x31) for dh-ranFile-2018-03-20_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 201 211.4 0.513 0.513 r= 29 5072 5134.0 0.749 1.262 r= 30 23172 23103.0 0.206 1.468 r= 31 11555 11551.5 0.001 1.469 chi-square = 1.469 with df = 3; p-value = 0.311 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-03-20_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 192 211.4 1.783 1.783 r= 30 5045 5134.0 1.543 3.327 r= 31 23176 23103.0 0.230 3.557 r= 32 11587 11551.5 0.109 3.666 chi-square = 3.666 with df = 3; p-value = 0.700 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-03-20_05:31 b-rank test for bits 1 to 8, p=0.68362 b-rank test for bits 2 to 9, p=0.18422 b-rank test for bits 3 to 10, p=0.42100 b-rank test for bits 4 to 11, p=0.78753 b-rank test for bits 5 to 12, p=0.24692 b-rank test for bits 6 to 13, p=0.44294 b-rank test for bits 7 to 14, p=0.89819 b-rank test for bits 8 to 15, p=0.16071 b-rank test for bits 9 to 16, p=0.42893 b-rank test for bits 10 to 17, p=0.10113 b-rank test for bits 11 to 18, p=0.08019 b-rank test for bits 12 to 19, p=0.99581 b-rank test for bits 13 to 20, p=0.21987 b-rank test for bits 14 to 21, p=0.10566 b-rank test for bits 15 to 22, p=0.85482 b-rank test for bits 16 to 23, p=0.25353 b-rank test for bits 17 to 24, p=0.13215 b-rank test for bits 18 to 25, p=0.41711 b-rank test for bits 19 to 26, p=0.73877 b-rank test for bits 20 to 27, p=0.04590 b-rank test for bits 21 to 28, p=0.74828 b-rank test for bits 22 to 29, p=0.62532 b-rank test for bits 23 to 30, p=0.14682 b-rank test for bits 24 to 31, p=0.41051 b-rank test for bits 25 to 32, p=0.81541 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 = 0.366362 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-20_05:31 (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 141779 -0.30 0.380370 2 141752 -0.37 0.356588 3 141979 0.16 0.564654 4 142296 0.90 0.816852 5 142090 0.42 0.663534 6 141685 -0.52 0.300092 7 141177 -1.71 0.043536 8 142570 1.54 0.938660 9 142125 0.50 0.692835 10 141710 -0.47 0.320706 11 141865 -0.10 0.458753 12 142069 0.37 0.645448 13 142201 0.68 0.752214 14 141714 -0.46 0.324059 15 142703 1.85 0.968157 16 142567 1.54 0.937806 17 141951 0.10 0.538780 18 142284 0.88 0.809321 19 141332 -1.35 0.088684 20 141726 -0.43 0.334201 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-03-20_05:31 Bits used No. missing words z-score p-value 23 to 32 141722 -0.6460 0.259151 22 to 31 142236 1.1264 0.870012 21 to 30 141980 0.2437 0.596264 20 to 29 141749 -0.5529 0.290179 19 to 28 141627 -0.9736 0.165140 18 to 27 141810 -0.3425 0.365981 17 to 26 142116 0.7127 0.761970 16 to 25 141498 -1.4184 0.078040 15 to 24 142252 1.1816 0.881322 14 to 23 141916 0.0230 0.509175 13 to 22 142060 0.5196 0.698312 12 to 21 141979 0.2402 0.594928 11 to 20 141601 -1.0632 0.143844 10 to 19 141576 -1.1494 0.125193 9 to 18 142247 1.1644 0.877865 8 to 17 141745 -0.5667 0.285474 7 to 16 141214 -2.3977 0.008249 6 to 15 141880 -0.1011 0.459721 5 to 14 141880 -0.1011 0.459721 4 to 13 141960 0.1747 0.569352 3 to 12 141951 0.1437 0.557127 2 to 11 141905 -0.0149 0.494044 1 to 10 141510 -1.3770 0.084256 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-03-20_05:31 Bits used No. missing words z-score p-value 28 to 32 141949 0.1345 0.553486 27 to 31 141456 -1.5367 0.062182 26 to 30 142166 0.8701 0.807868 25 to 29 141941 0.1074 0.542747 24 to 28 141615 -0.9977 0.159205 23 to 27 141926 0.0565 0.522532 22 to 26 141643 -0.9028 0.183312 21 to 25 141432 -1.6181 0.052824 20 to 24 141981 0.2429 0.595978 19 to 23 142052 0.4836 0.685675 18 to 22 141587 -1.0926 0.137275 17 to 21 142148 0.8091 0.790757 16 to 20 141857 -0.1774 0.429601 15 to 19 142113 0.6904 0.755031 14 to 18 141679 -0.7808 0.217466 13 to 17 141638 -0.9198 0.178848 12 to 16 142085 0.5955 0.724243 11 to 15 141702 -0.7028 0.241086 10 to 14 141607 -1.0248 0.152718 9 to 13 142037 0.4328 0.667413 8 to 12 141952 0.1446 0.557504 7 to 11 141802 -0.3638 0.357992 6 to 10 141599 -1.0520 0.146408 5 to 9 141443 -1.5808 0.056964 4 to 8 142229 1.0836 0.860735 3 to 7 142177 0.9074 0.817891 2 to 6 142123 0.7243 0.765561 1 to 5 142200 0.9853 0.837767 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-03-20_05:31 Bits used No. missing words z-score p-value 31 to 32 142075 0.4887 0.687474 30 to 31 141340 -1.6794 0.046533 29 to 30 141684 -0.6647 0.253124 28 to 29 141904 -0.0157 0.493728 27 to 28 141336 -1.6912 0.045396 26 to 27 142704 2.3442 0.990465 25 to 26 141905 -0.0128 0.494905 24 to 25 142119 0.6185 0.731876 23 to 24 141663 -0.7266 0.233724 22 to 23 141901 -0.0246 0.490198 21 to 22 142109 0.5890 0.722068 20 to 21 141690 -0.6470 0.258819 19 to 20 142423 1.5153 0.935146 18 to 19 141729 -0.5319 0.297381 17 to 18 141782 -0.3756 0.353605 16 to 17 141631 -0.8210 0.205814 15 to 16 141004 -2.6706 0.003786 14 to 15 141581 -0.9685 0.166391 13 to 14 141886 -0.0688 0.472566 12 to 13 142345 1.2852 0.900632 11 to 12 141788 -0.3579 0.360207 10 to 11 142178 0.7925 0.785976 9 to 10 142077 0.4946 0.689559 8 to 9 142233 0.9548 0.830155 7 to 8 142290 1.1229 0.869264 6 to 7 142087 0.5241 0.699896 5 to 6 141853 -0.1662 0.434014 4 to 5 141976 0.1967 0.577956 3 to 4 141930 0.0610 0.524310 2 to 3 142001 0.2704 0.606579 1 to 2 142081 0.5064 0.693713 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-20_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2522.70 0.321 0.625883 Test results for specific bytes for dh-ranFile-2018-03-20_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2551.20 0.724 0.765476 2 to 9 2309.90 -2.688 0.003590 3 to 10 2585.10 1.203 0.885599 4 to 11 2365.59 -1.901 0.028663 5 to 12 2459.29 -0.576 0.282379 6 to 13 2482.12 -0.253 0.400173 7 to 14 2549.49 0.700 0.757987 8 to 15 2454.08 -0.649 0.258045 9 to 16 2602.59 1.451 0.926580 10 to 17 2525.28 0.357 0.639625 11 to 18 2434.58 -0.925 0.177438 12 to 19 2501.48 0.021 0.508351 13 to 20 2533.26 0.470 0.680952 14 to 21 2465.60 -0.487 0.313291 15 to 22 2535.84 0.507 0.693871 16 to 23 2637.48 1.944 0.974071 17 to 24 2521.78 0.308 0.620975 18 to 25 2516.52 0.234 0.592338 19 to 26 2511.16 0.158 0.562687 20 to 27 2570.50 0.997 0.840638 21 to 28 2602.62 1.451 0.926652 22 to 29 2462.78 -0.526 0.299308 23 to 30 2381.41 -1.677 0.046764 24 to 31 2582.26 1.163 0.877659 25 to 32 2454.08 -0.649 0.258021 CDPARK for dh-ranFile-2018-03-20_05:31: 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 3510 -0.5936 0.276387 3536 0.5936 0.723613 3544 0.9589 0.831196 3501 -1.0046 0.157553 3555 1.4612 0.928018 3471 -2.3744 0.008788 3511 -0.5479 0.291865 3507 -0.7306 0.232514 3558 1.5982 0.944998 3532 0.4110 0.659449 Square side=100, avg. no. parked=3522.50 sample std.=25.87 p-value of the KSTEST for those 10 p-values: 0.746750 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-20_05:31 0.3872,0.1730,0.9182,0.0747,0.2967,0.6848,0.7066,0.3476,0.2528,0.6684, The KS test for those 10 p-values: 0.842084 The 3DSPHERES test for dh-ranFile-2018-03-20_05:31 sample no r^3 equiv. uni. 1 15.610 0.405687 2 5.490 0.167234 3 23.449 0.542343 4 12.913 0.349763 5 18.751 0.464756 6 42.753 0.759512 7 12.485 0.340437 8 36.699 0.705744 9 25.382 0.570897 10 20.812 0.500301 11 11.318 0.314263 12 2.640 0.084228 13 54.960 0.839905 14 26.963 0.592928 15 3.181 0.100593 16 0.070 0.002318 17 2.846 0.090508 18 23.733 0.546651 19 29.458 0.625415 20 18.153 0.453983 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.218375 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-20_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 1.3 -1.3 -2.9 -0.1 2.7 -1.2 1.3 -0.3 -0.2 0.7 0.6 0.7 -0.6 -1.6 -1.9 0.3 0.2 0.9 -0.5 -0.4 1.2 0.5 0.2 0.8 -0.7 -0.4 0.2 0.9 -0.4 -0.3 0.1 0.7 1.4 0.3 -0.8 -0.7 -0.1 0.9 1.5 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:43.878402 z-score=0.204950, p-value=0.608160 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-03-20_05:31 Test no p-value 1 0.259388 2 0.017576 3 0.375809 4 0.580642 5 0.439248 6 0.192770 7 0.225313 8 0.036667 9 0.944618 10 0.025504 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.034343 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-20_05:31: (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 66609 0.05 66688 0.01 3 25000.00 24993 0.00 24960 0.06 4 6666.67 6734 0.68 6679 0.02 5 1388.89 1394 0.02 1378 0.09 6 238.10 225 0.72 246 0.26 7 34.72 38 0.31 43 1.97 8 4.96 6 0.22 5 0.00 p=0.08019 p=0.12229 Number of rngs required: 688565, p-value: 0.574 RESULTS OF CRAPS TEST for dh-ranFile-2018-03-20_05:31 No. of wins: Observed Expected 98783 98585.9 z-score= 0.882, pvalue=0.81104 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66390 66666.7 1.148 1.148 2 37992 37654.3 3.028 4.176 3 26860 26954.7 0.333 4.509 4 19364 19313.5 0.132 4.642 5 13960 13851.4 0.851 5.493 6 9793 9943.5 2.279 7.772 7 7129 7145.0 0.036 7.808 8 5147 5139.1 0.012 7.820 9 3690 3699.9 0.026 7.846 10 2641 2666.3 0.240 8.086 11 1924 1923.3 0.000 8.087 12 1393 1388.7 0.013 8.100 13 999 1003.7 0.022 8.122 14 716 726.1 0.142 8.264 15 574 525.8 4.412 12.675 16 379 381.2 0.012 12.687 17 285 276.5 0.259 12.946 18 179 200.8 2.373 15.319 19 157 146.0 0.831 16.150 20 125 106.2 3.322 19.472 21 303 287.1 0.879 20.351 Chisq= 20.35 for 20 degrees of freedom, p= 0.56385 SUMMARY of craptest p-value for no. of wins: 0.811039 p-value for throws/game: 0.563847 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-20_05:31 No. of wins: Observed Expected 98785 98585.9 z-score= 0.891, pvalue=0.81345 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66927 66666.7 1.017 1.017 2 37592 37654.3 0.103 1.120 3 26916 26954.7 0.056 1.175 4 19339 19313.5 0.034 1.209 5 13885 13851.4 0.081 1.291 6 9918 9943.5 0.066 1.356 7 7081 7145.0 0.574 1.930 8 5042 5139.1 1.834 3.764 9 3752 3699.9 0.735 4.498 10 2683 2666.3 0.105 4.603 11 1926 1923.3 0.004 4.607 12 1377 1388.7 0.099 4.706 13 1012 1003.7 0.068 4.774 14 708 726.1 0.453 5.227 15 499 525.8 1.370 6.597 16 386 381.2 0.062 6.659 17 261 276.5 0.873 7.532 18 183 200.8 1.583 9.115 19 130 146.0 1.750 10.865 20 112 106.2 0.315 11.180 21 271 287.1 0.904 12.084 Chisq= 12.08 for 20 degrees of freedom, p= 0.08686 SUMMARY of craptest p-value for no. of wins: 0.813449 p-value for throws/game: 0.086859 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0036,0.0038,0.0082,0.0088,0.0176,0.0255,0.0287,0.0343,0.0367, 0.0435,0.0438,0.0443,0.0454,0.0459,0.0465,0.0468,0.0528,0.0570,0.0622, 0.0747,0.0758,0.0780,0.0802,0.0802,0.0842,0.0843,0.0869,0.0887,0.0905, 0.0958,0.1006,0.1011,0.1057,0.1097,0.1148,0.1223,0.1252,0.1266,0.1322, 0.1362,0.1373,0.1438,0.1449,0.1464,0.1468,0.1507,0.1527,0.1576,0.1592, 0.1607,0.1651,0.1664,0.1672,0.1730,0.1774,0.1788,0.1833,0.1842,0.1928, 0.1982,0.2058,0.2163,0.2175,0.2184,0.2199,0.2253,0.2325,0.2337,0.2411, 0.2455,0.2469,0.2528,0.2531,0.2535,0.2569,0.2580,0.2580,0.2588,0.2592, 0.2594,0.2764,0.2824,0.2855,0.2902,0.2919,0.2967,0.2974,0.2993,0.3001, 0.3106,0.3133,0.3143,0.3207,0.3241,0.3292,0.3342,0.3390,0.3404,0.3476, 0.3498,0.3536,0.3566,0.3580,0.3602,0.3660,0.3664,0.3758,0.3804,0.3827, 0.3872,0.4002,0.4057,0.4105,0.4106,0.4171,0.4210,0.4289,0.4296,0.4340, 0.4392,0.4429,0.4540,0.4551,0.4588,0.4597,0.4597,0.4648,0.4726,0.4740, 0.4772,0.4902,0.4907,0.4937,0.4940,0.4949,0.4962,0.5003,0.5012,0.5047, 0.5084,0.5092,0.5147,0.5189,0.5225,0.5243,0.5388,0.5423,0.5427,0.5467, 0.5535,0.5571,0.5575,0.5627,0.5638,0.5647,0.5693,0.5694,0.5709,0.5739, 0.5780,0.5806,0.5893,0.5923,0.5929,0.5949,0.5960,0.5963,0.6066,0.6073, 0.6082,0.6118,0.6210,0.6253,0.6254,0.6259,0.6269,0.6297,0.6318,0.6396, 0.6454,0.6532,0.6594,0.6635,0.6674,0.6684,0.6810,0.6836,0.6848,0.6857, 0.6875,0.6896,0.6925,0.6928,0.6937,0.6939,0.6983,0.6999,0.7001,0.7033, 0.7042,0.7057,0.7066,0.7152,0.7154,0.7220,0.7221,0.7236,0.7242,0.7319, 0.7388,0.7468,0.7483,0.7504,0.7522,0.7550,0.7580,0.7595,0.7620,0.7630, 0.7655,0.7656,0.7860,0.7875,0.7908,0.8040,0.8079,0.8093,0.8110,0.8134, 0.8154,0.8169,0.8179,0.8302,0.8312,0.8370,0.8378,0.8399,0.8406,0.8421, 0.8450,0.8548,0.8557,0.8607,0.8693,0.8700,0.8770,0.8777,0.8779,0.8813, 0.8856,0.8982,0.9006,0.9079,0.9182,0.9266,0.9267,0.9280,0.9351,0.9378, 0.9387,0.9446,0.9450,0.9544,0.9565,0.9682,0.9741,0.9905,0.9958, Overall p-value after applying KStest on 269 p-values = 0.198698 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.