RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-03-25_02:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.62 16.1337 0.485622 2 to 25 15.50 17.2944 0.565398 3 to 26 15.35 35.0516 0.993875 4 to 27 15.39 37.9540 0.997506 5 to 28 15.66 23.9764 0.879923 6 to 29 15.33 45.0468 0.999760 7 to 30 15.53 23.3978 0.863257 8 to 31 15.61 18.0599 0.614931 9 to 32 15.72 21.9051 0.811604 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.000199 Tough bday spacings test for dh-ranFile-2017-03-25_02:31: 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 9 22 77 123 102 82 42 21 11 9 2 (O-E)^2/E 0.0 5.8 0.2 6.6 0.2 0.2 2.0 2.6 1.0 0.9 1.0 Birthday Spacings: Sum(O-E)^2/E= 20.444, p= 0.975 RESULTS OF GCD FOR dh-ranFile-2017-03-25_02:31 Euclid's algorithm: p-value, steps to gcd: 0.796449 p-value, dist. of gcd's: 0.268201 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-03-25_02:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.249 0.561 0.944 0.110 0.877 0.087 0.378 0.058 Bits 8 to 15---> 0.923 0.201 0.123 0.670 0.326 0.882 0.608 0.681 Bits 16 to 23---> 0.832 0.155 0.383 0.414 0.408 0.987 0.863 0.924 Bits 24 to 31---> 0.293 0.570 0.881 0.655 0.444 0.878 0.613 0.316 KS test for the above 32 p values: 0.404 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-03-25_02:31, p-values for 5 runs: 0.1483, 0.8004, 0.7796, 0.1597, 0.3032 Rank test for binary matrices (31x31) for dh-ranFile-2017-03-25_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5107 5134.0 0.142 0.477 r= 30 23208 23103.0 0.477 0.954 r= 31 11482 11551.5 0.418 1.372 chi-square = 1.372 with df = 3; p-value = 0.288 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-03-25_02:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 216 211.4 0.099 0.099 r= 30 5096 5134.0 0.281 0.381 r= 31 23053 23103.0 0.108 0.489 r= 32 11635 11551.5 0.603 1.092 chi-square = 1.092 with df = 3; p-value = 0.221 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-03-25_02:31 b-rank test for bits 1 to 8, p=0.43875 b-rank test for bits 2 to 9, p=0.58979 b-rank test for bits 3 to 10, p=0.16557 b-rank test for bits 4 to 11, p=0.36807 b-rank test for bits 5 to 12, p=0.34936 b-rank test for bits 6 to 13, p=0.64243 b-rank test for bits 7 to 14, p=0.48331 b-rank test for bits 8 to 15, p=0.71770 b-rank test for bits 9 to 16, p=0.59226 b-rank test for bits 10 to 17, p=0.66059 b-rank test for bits 11 to 18, p=0.40864 b-rank test for bits 12 to 19, p=0.93269 b-rank test for bits 13 to 20, p=0.30956 b-rank test for bits 14 to 21, p=0.37566 b-rank test for bits 15 to 22, p=0.03708 b-rank test for bits 16 to 23, p=0.29532 b-rank test for bits 17 to 24, p=0.48436 b-rank test for bits 18 to 25, p=0.80194 b-rank test for bits 19 to 26, p=0.82357 b-rank test for bits 20 to 27, p=0.99369 b-rank test for bits 21 to 28, p=0.53039 b-rank test for bits 22 to 29, p=0.19129 b-rank test for bits 23 to 30, p=0.64156 b-rank test for bits 24 to 31, p=0.79304 b-rank test for bits 25 to 32, p=0.73362 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 = 0.499662 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-03-25_02:31 (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 142090 0.42 0.663534 2 140972 -2.19 0.014261 3 141627 -0.66 0.254739 4 141441 -1.09 0.136927 5 142203 0.69 0.753689 6 141784 -0.29 0.384827 7 141513 -0.93 0.177222 8 141113 -1.86 0.031401 9 141769 -0.33 0.371504 10 142242 0.78 0.781499 11 141909 -0.00 0.499692 12 141742 -0.39 0.347914 13 142189 0.65 0.743262 14 141551 -0.84 0.201235 15 141897 -0.03 0.488509 16 141884 -0.06 0.476404 17 140980 -2.17 0.014953 18 141760 -0.35 0.363582 19 141037 -2.04 0.020767 20 141711 -0.46 0.321543 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-03-25_02:31 Bits used No. missing words z-score p-value 23 to 32 141823 -0.2977 0.382970 22 to 31 141732 -0.6115 0.270440 21 to 30 142303 1.3575 0.912686 20 to 29 142048 0.4782 0.683736 19 to 28 141884 -0.0873 0.465199 18 to 27 141592 -1.0942 0.136925 17 to 26 141585 -1.1184 0.131703 16 to 25 142075 0.5713 0.716094 15 to 24 141968 0.2023 0.580163 14 to 23 141965 0.1920 0.576115 13 to 22 142210 1.0368 0.850084 12 to 21 142208 1.0299 0.848471 11 to 20 142088 0.6161 0.731087 10 to 19 141719 -0.6563 0.255812 9 to 18 141708 -0.6942 0.243765 8 to 17 141729 -0.6218 0.267028 7 to 16 142062 0.5264 0.700712 6 to 15 141725 -0.6356 0.262512 5 to 14 142018 0.3747 0.646067 4 to 13 142074 0.5678 0.714924 3 to 12 142211 1.0402 0.850886 2 to 11 142037 0.4402 0.670119 1 to 10 141704 -0.7080 0.239462 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-03-25_02:31 Bits used No. missing words z-score p-value 28 to 32 142309 1.3548 0.912262 27 to 31 142322 1.3989 0.919076 26 to 30 142177 0.9074 0.817891 25 to 29 141958 0.1650 0.565521 24 to 28 141819 -0.3062 0.379725 23 to 27 141895 -0.0486 0.480629 22 to 26 141969 0.2023 0.580148 21 to 25 141440 -1.5909 0.055811 20 to 24 141715 -0.6587 0.255030 19 to 23 141786 -0.4181 0.337949 18 to 22 142024 0.3887 0.651255 17 to 21 141800 -0.3706 0.355464 16 to 20 141584 -1.1028 0.135054 15 to 19 141459 -1.5265 0.063437 14 to 18 142068 0.5379 0.704665 13 to 17 141898 -0.0384 0.484682 12 to 16 141389 -1.7638 0.038880 11 to 15 142138 0.7752 0.780875 10 to 14 142107 0.6701 0.748593 9 to 13 142035 0.4260 0.664946 8 to 12 142066 0.5311 0.702320 7 to 11 142087 0.6023 0.726503 6 to 10 142154 0.8294 0.796558 5 to 9 141863 -0.1571 0.437602 4 to 8 141667 -0.8215 0.205693 3 to 7 142256 1.1752 0.880033 2 to 6 142168 0.8768 0.809715 1 to 5 142021 0.3785 0.647486 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-03-25_02:31 Bits used No. missing words z-score p-value 31 to 32 142048 0.4091 0.658751 30 to 31 142028 0.3501 0.636853 29 to 30 141687 -0.6558 0.255963 28 to 29 141312 -1.7620 0.039032 27 to 28 142154 0.7217 0.764773 26 to 27 141436 -1.3963 0.081319 25 to 26 141882 -0.0806 0.467872 24 to 25 141581 -0.9685 0.166391 23 to 24 142658 2.2085 0.986394 22 to 23 141992 0.2439 0.596332 21 to 22 141860 -0.1455 0.442152 20 to 21 141432 -1.4081 0.079558 19 to 20 141924 0.0433 0.517259 18 to 19 141636 -0.8063 0.210040 17 to 18 142142 0.6863 0.753751 16 to 17 141966 0.1672 0.566381 15 to 16 141479 -1.2694 0.102147 14 to 15 142077 0.4946 0.689559 13 to 14 142287 1.1141 0.867376 12 to 13 141673 -0.6971 0.242858 11 to 12 141899 -0.0305 0.487845 10 to 11 141580 -0.9715 0.165656 9 to 10 141509 -1.1809 0.118818 8 to 9 141596 -0.9243 0.177671 7 to 8 141541 -1.0865 0.138625 6 to 7 141553 -1.0511 0.146602 5 to 6 141886 -0.0688 0.472566 4 to 5 141728 -0.5349 0.296361 3 to 4 141995 0.2527 0.599755 2 to 3 141936 0.0787 0.531354 1 to 2 142577 1.9695 0.975554 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-03-25_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2532.67 0.462 0.677951 Test results for specific bytes for dh-ranFile-2017-03-25_02:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2389.54 -1.562 0.059134 2 to 9 2402.70 -1.376 0.084406 3 to 10 2600.13 1.416 0.921613 4 to 11 2548.74 0.689 0.754666 5 to 12 2543.72 0.618 0.731824 6 to 13 2517.42 0.246 0.597284 7 to 14 2543.13 0.610 0.729032 8 to 15 2487.54 -0.176 0.430078 9 to 16 2433.76 -0.937 0.174441 10 to 17 2495.36 -0.066 0.473860 11 to 18 2416.89 -1.175 0.119922 12 to 19 2521.95 0.310 0.621901 13 to 20 2467.53 -0.459 0.323061 14 to 21 2491.82 -0.116 0.453940 15 to 22 2682.89 2.586 0.995151 16 to 23 2491.16 -0.125 0.450261 17 to 24 2490.87 -0.129 0.448624 18 to 25 2462.77 -0.527 0.299256 19 to 26 2337.82 -2.294 0.010907 20 to 27 2574.32 1.051 0.853371 21 to 28 2439.44 -0.856 0.195878 22 to 29 2377.22 -1.736 0.041244 23 to 30 2529.51 0.417 0.661793 24 to 31 2485.72 -0.202 0.419985 25 to 32 2627.73 1.806 0.964573 CDPARK for dh-ranFile-2017-03-25_02:31: 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 3533 0.4566 0.676028 3530 0.3196 0.625377 3557 1.5525 0.939730 3500 -1.0502 0.146807 3535 0.5479 0.708135 3538 0.6849 0.753306 3519 -0.1826 0.427537 3550 1.2329 0.891189 3546 1.0502 0.853193 3541 0.8219 0.794438 Square side=100, avg. no. parked=3534.90 sample std.=15.44 p-value of the KSTEST for those 10 p-values: 0.067707 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-03-25_02:31 0.5446,0.2062,0.6229,0.2968,0.0006,0.5565,0.3162,0.3604,0.8758,0.5903, The KS test for those 10 p-values: 0.383108 The 3DSPHERES test for dh-ranFile-2017-03-25_02:31 sample no r^3 equiv. uni. 1 22.801 0.532348 2 20.629 0.497231 3 42.986 0.761375 4 3.473 0.109303 5 5.308 0.162177 6 12.125 0.332470 7 93.272 0.955357 8 16.587 0.424713 9 2.597 0.082916 10 13.929 0.371423 11 26.462 0.586071 12 1.087 0.035595 13 54.761 0.838843 14 2.746 0.087454 15 45.795 0.782707 16 23.159 0.537900 17 16.872 0.430166 18 61.137 0.869696 19 1.739 0.056329 20 8.029 0.234807 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.531142 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-03-25_02:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 1.3 0.1 0.2 0.6 0.8 -0.7 -0.8 -0.9 -1.2 1.0 -0.4 -0.3 -0.2 -2.4 0.7 -0.8 1.0 -0.7 0.1 0.1 -0.4 0.4 2.1 -1.1 1.3 1.7 2.1 0.6 0.4 0.2 -0.4 1.2 -1.0 -0.5 -1.7 1.7 0.8 0.5 0.4 -0.6 1.0 3.7 Chi-square with 42 degrees of freedom:56.261242 z-score=1.556029, p-value=0.930456 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-03-25_02:31 Test no p-value 1 0.313561 2 0.316085 3 0.948694 4 0.000199 5 0.908580 6 0.314620 7 0.619339 8 0.083580 9 0.654420 10 0.017872 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.159934 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-03-25_02:31: (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 66549 0.21 66623 0.03 3 25000.00 25023 0.02 24989 0.00 4 6666.67 6762 1.36 6698 0.15 5 1388.89 1407 0.24 1416 0.53 6 238.10 213 2.65 227 0.52 7 34.72 38 0.31 41 1.14 8 4.96 7 0.84 5 0.00 p=0.53317 p=0.11654 Number of rngs required: 689227, p-value: 0.830 RESULTS OF CRAPS TEST for dh-ranFile-2017-03-25_02:31 No. of wins: Observed Expected 98730 98585.9 z-score= 0.645, pvalue=0.74043 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66726 66666.7 0.053 0.053 2 37697 37654.3 0.048 0.101 3 26804 26954.7 0.843 0.944 4 19251 19313.5 0.202 1.146 5 13831 13851.4 0.030 1.176 6 9938 9943.5 0.003 1.179 7 7348 7145.0 5.766 6.945 8 5206 5139.1 0.872 7.817 9 3594 3699.9 3.029 10.846 10 2670 2666.3 0.005 10.851 11 1921 1923.3 0.003 10.854 12 1335 1388.7 2.080 12.934 13 1000 1003.7 0.014 12.947 14 723 726.1 0.014 12.961 15 538 525.8 0.281 13.242 16 392 381.2 0.309 13.551 17 278 276.5 0.008 13.559 18 213 200.8 0.737 14.296 19 144 146.0 0.027 14.323 20 91 106.2 2.180 16.503 21 300 287.1 0.578 17.081 Chisq= 17.08 for 20 degrees of freedom, p= 0.35231 SUMMARY of craptest p-value for no. of wins: 0.740434 p-value for throws/game: 0.352312 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-03-25_02:31 No. of wins: Observed Expected 98561 98585.9 z-score=-0.111, pvalue=0.45574 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66768 66666.7 0.154 0.154 2 37400 37654.3 1.718 1.872 3 26719 26954.7 2.062 3.933 4 19363 19313.5 0.127 4.060 5 13974 13851.4 1.085 5.145 6 9971 9943.5 0.076 5.221 7 7297 7145.0 3.232 8.453 8 5244 5139.1 2.142 10.596 9 3643 3699.9 0.874 11.470 10 2650 2666.3 0.100 11.569 11 1952 1923.3 0.427 11.997 12 1421 1388.7 0.749 12.746 13 1023 1003.7 0.371 13.117 14 687 726.1 2.110 15.227 15 467 525.8 6.583 21.810 16 386 381.2 0.062 21.871 17 291 276.5 0.756 22.628 18 195 200.8 0.169 22.797 19 138 146.0 0.437 23.233 20 121 106.2 2.058 25.291 21 290 287.1 0.029 25.320 Chisq= 25.32 for 20 degrees of freedom, p= 0.81056 SUMMARY of craptest p-value for no. of wins: 0.455736 p-value for throws/game: 0.810555 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0002,0.0006,0.0109,0.0143,0.0150,0.0179,0.0208,0.0314,0.0356, 0.0371,0.0389,0.0390,0.0412,0.0558,0.0563,0.0579,0.0591,0.0634,0.0677, 0.0796,0.0813,0.0829,0.0836,0.0844,0.0870,0.0875,0.1021,0.1093,0.1103, 0.1165,0.1188,0.1199,0.1228,0.1317,0.1351,0.1369,0.1369,0.1386,0.1466, 0.1468,0.1483,0.1553,0.1597,0.1599,0.1622,0.1656,0.1657,0.1664,0.1744, 0.1772,0.1777,0.1913,0.1959,0.2008,0.2012,0.2057,0.2062,0.2100,0.2211, 0.2348,0.2395,0.2429,0.2438,0.2487,0.2547,0.2550,0.2558,0.2560,0.2625, 0.2670,0.2682,0.2704,0.2880,0.2929,0.2953,0.2964,0.2968,0.2993,0.3032, 0.3096,0.3136,0.3146,0.3159,0.3161,0.3162,0.3215,0.3231,0.3259,0.3325, 0.3379,0.3479,0.3494,0.3523,0.3555,0.3604,0.3636,0.3681,0.3714,0.3715, 0.3757,0.3783,0.3797,0.3830,0.3831,0.3835,0.3848,0.4036,0.4085,0.4086, 0.4141,0.4200,0.4247,0.4275,0.4301,0.4302,0.4376,0.4387,0.4422,0.4440, 0.4486,0.4503,0.4539,0.4557,0.4652,0.4679,0.4726,0.4739,0.4764,0.4806, 0.4833,0.4844,0.4847,0.4856,0.4878,0.4885,0.4972,0.4997,0.4997,0.5173, 0.5304,0.5311,0.5314,0.5323,0.5332,0.5379,0.5446,0.5565,0.5610,0.5654, 0.5655,0.5664,0.5702,0.5761,0.5801,0.5802,0.5861,0.5898,0.5903,0.5923, 0.5963,0.5973,0.5998,0.6076,0.6125,0.6149,0.6193,0.6219,0.6229,0.6254, 0.6369,0.6416,0.6424,0.6461,0.6475,0.6513,0.6544,0.6547,0.6588,0.6606, 0.6618,0.6635,0.6649,0.6697,0.6701,0.6760,0.6780,0.6812,0.6837,0.6896, 0.7007,0.7023,0.7047,0.7081,0.7149,0.7161,0.7177,0.7265,0.7290,0.7311, 0.7318,0.7336,0.7404,0.7433,0.7486,0.7533,0.7537,0.7538,0.7547,0.7614, 0.7648,0.7796,0.7809,0.7815,0.7827,0.7930,0.7944,0.7964,0.7966,0.8004, 0.8019,0.8097,0.8106,0.8116,0.8179,0.8236,0.8300,0.8322,0.8388,0.8485, 0.8501,0.8509,0.8532,0.8534,0.8629,0.8633,0.8674,0.8697,0.8758,0.8766, 0.8779,0.8799,0.8800,0.8811,0.8822,0.8912,0.9086,0.9123,0.9127,0.9191, 0.9216,0.9227,0.9242,0.9305,0.9327,0.9397,0.9443,0.9487,0.9554,0.9646, 0.9747,0.9756,0.9864,0.9870,0.9937,0.9939,0.9952,0.9975,0.9998, Overall p-value after applying KStest on 269 p-values = 0.960832 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.