RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-04-02_14:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.10 8.4963 0.045247 2 to 25 15.84 12.9883 0.263030 3 to 26 15.83 18.1526 0.620726 4 to 27 15.92 18.0483 0.614203 5 to 28 15.92 10.4802 0.117726 6 to 29 15.52 26.5205 0.934515 7 to 30 15.61 19.4093 0.694450 8 to 31 15.76 20.2713 0.739411 9 to 32 15.44 31.5110 0.982705 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.665131 Tough bday spacings test for dh-ranFile-2018-04-02_14:31: 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 6 44 79 100 102 74 47 25 11 7 5 (O-E)^2/E 1.1 1.5 0.4 0.1 0.2 0.2 0.5 0.8 1.0 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.000, p= 0.185 RESULTS OF GCD FOR dh-ranFile-2018-04-02_14:31 Euclid's algorithm: p-value, steps to gcd: 0.238500 p-value, dist. of gcd's: 0.192469 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-04-02_14:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.878 0.977 0.016 0.388 0.487 0.159 0.156 0.090 Bits 8 to 15---> 0.704 0.365 0.805 0.276 0.779 0.947 0.157 0.370 Bits 16 to 23---> 0.177 0.491 0.925 0.667 0.058 0.262 0.142 0.475 Bits 24 to 31---> 0.099 0.569 0.974 0.702 0.480 0.851 0.982 0.425 KS test for the above 32 p values: 0.238 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-04-02_14:31, p-values for 5 runs: 0.7064, 0.7879, 0.7991, 0.5521, 0.7976 Rank test for binary matrices (31x31) for dh-ranFile-2018-04-02_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5310 5134.0 6.033 6.045 r= 30 23086 23103.0 0.013 6.057 r= 31 11391 11551.5 2.231 8.288 chi-square = 8.288 with df = 3; p-value = 0.960 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2018-04-02_14:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5094 5134.0 0.312 0.373 r= 31 23256 23103.0 1.013 1.385 r= 32 11435 11551.5 1.175 2.561 chi-square = 2.561 with df = 3; p-value = 0.536 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2018-04-02_14:31 b-rank test for bits 1 to 8, p=0.50851 b-rank test for bits 2 to 9, p=0.14250 b-rank test for bits 3 to 10, p=0.88994 b-rank test for bits 4 to 11, p=0.38916 b-rank test for bits 5 to 12, p=0.81974 b-rank test for bits 6 to 13, p=0.25677 b-rank test for bits 7 to 14, p=0.24714 b-rank test for bits 8 to 15, p=0.75951 b-rank test for bits 9 to 16, p=0.36286 b-rank test for bits 10 to 17, p=0.82043 b-rank test for bits 11 to 18, p=0.60210 b-rank test for bits 12 to 19, p=0.42394 b-rank test for bits 13 to 20, p=0.66175 b-rank test for bits 14 to 21, p=0.09435 b-rank test for bits 15 to 22, p=0.06634 b-rank test for bits 16 to 23, p=0.53645 b-rank test for bits 17 to 24, p=0.83736 b-rank test for bits 18 to 25, p=0.52537 b-rank test for bits 19 to 26, p=0.78392 b-rank test for bits 20 to 27, p=0.80587 b-rank test for bits 21 to 28, p=0.59452 b-rank test for bits 22 to 29, p=0.51335 b-rank test for bits 23 to 30, p=0.07088 b-rank test for bits 24 to 31, p=0.06929 b-rank test for bits 25 to 32, p=0.28384 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 = 0.785289 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-04-02_14:31 (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 141176 -1.71 0.043321 2 142076 0.39 0.651516 3 141995 0.20 0.579324 4 141475 -1.01 0.155103 5 142303 0.92 0.821159 6 141640 -0.63 0.264584 7 141990 0.19 0.574750 8 141968 0.14 0.554516 9 142028 0.28 0.609212 10 142637 1.70 0.955450 11 142214 0.71 0.761720 12 142796 2.07 0.980851 13 141254 -1.53 0.062867 14 141390 -1.21 0.112491 15 141891 -0.04 0.482920 16 141975 0.15 0.560972 17 141551 -0.84 0.201235 18 141735 -0.41 0.341889 19 142952 2.44 0.992578 20 142436 1.23 0.890752 ---------------------------------------------------------------- OPSO test for dh-ranFile-2018-04-02_14:31 Bits used No. missing words z-score p-value 23 to 32 142175 0.9161 0.820194 22 to 31 142454 1.8782 0.969821 21 to 30 141940 0.1058 0.542113 20 to 29 142076 0.5747 0.717261 19 to 28 142435 1.8127 0.965058 18 to 27 142301 1.3506 0.911586 17 to 26 141649 -0.8977 0.184676 16 to 25 142193 0.9782 0.836006 15 to 24 142047 0.4747 0.682508 14 to 23 141975 0.2264 0.589574 13 to 22 142074 0.5678 0.714924 12 to 21 141710 -0.6873 0.245933 11 to 20 141441 -1.6149 0.053163 10 to 19 142163 0.8747 0.809138 9 to 18 142178 0.9264 0.822894 8 to 17 141793 -0.4011 0.344159 7 to 16 142309 1.3782 0.915925 6 to 15 141859 -0.1736 0.431109 5 to 14 141422 -1.6804 0.046435 4 to 13 141921 0.0402 0.516050 3 to 12 141661 -0.8563 0.195913 2 to 11 141888 -0.0736 0.470684 1 to 10 141998 0.3058 0.620106 ----------------------------------------------------------------- OQSO test for dh-ranFile-2018-04-02_14:31 Bits used No. missing words z-score p-value 28 to 32 142273 1.2328 0.891171 27 to 31 141995 0.2904 0.614248 26 to 30 142054 0.4904 0.688077 25 to 29 142535 2.1209 0.983036 24 to 28 141687 -0.7537 0.225526 23 to 27 141872 -0.1265 0.449651 22 to 26 141948 0.1311 0.552146 21 to 25 142103 0.6565 0.744252 20 to 24 142207 1.0091 0.843525 19 to 23 141903 -0.0215 0.491440 18 to 22 141190 -2.4384 0.007376 17 to 21 141596 -1.0621 0.144087 16 to 20 142100 0.6463 0.740970 15 to 19 141521 -1.3164 0.094024 14 to 18 142321 1.3955 0.918566 13 to 17 141965 0.1887 0.574841 12 to 16 141820 -0.3028 0.381016 11 to 15 141790 -0.4045 0.342919 10 to 14 141708 -0.6825 0.247470 9 to 13 141550 -1.2181 0.111599 8 to 12 141811 -0.3333 0.369446 7 to 11 142033 0.4192 0.662473 6 to 10 142361 1.5311 0.937126 5 to 9 141992 0.2802 0.610352 4 to 8 141785 -0.4215 0.336711 3 to 7 142283 1.2667 0.897365 2 to 6 142385 1.6124 0.946567 1 to 5 141731 -0.6045 0.272753 ----------------------------------------------------------------- DNA test for dh-ranFile-2018-04-02_14:31 Bits used No. missing words z-score p-value 31 to 32 142041 0.3884 0.651143 30 to 31 141786 -0.3638 0.358002 29 to 30 142605 2.0521 0.979921 28 to 29 141311 -1.7650 0.038783 27 to 28 141584 -0.9597 0.168609 26 to 27 141845 -0.1898 0.424747 25 to 26 141540 -1.0895 0.137974 24 to 25 142059 0.4415 0.670576 23 to 24 141880 -0.0865 0.465527 22 to 23 141651 -0.7620 0.223019 21 to 22 141975 0.1937 0.576801 20 to 21 141773 -0.4022 0.343786 19 to 20 141450 -1.3550 0.087716 18 to 19 142404 1.4592 0.927745 17 to 18 141928 0.0551 0.521960 16 to 17 141969 0.1760 0.569860 15 to 16 142456 1.6126 0.946584 14 to 15 141936 0.0787 0.531354 13 to 14 141379 -1.5644 0.058862 12 to 13 141553 -1.0511 0.146602 11 to 12 141999 0.2645 0.604308 10 to 11 142525 1.8161 0.965325 9 to 10 141766 -0.4228 0.336220 8 to 9 141968 0.1731 0.568701 7 to 8 141562 -1.0246 0.152783 6 to 7 141988 0.2321 0.591756 5 to 6 142661 2.2173 0.986699 4 to 5 142056 0.4327 0.667367 3 to 4 141838 -0.2104 0.416673 2 to 3 142151 0.7129 0.762043 1 to 2 141661 -0.7325 0.231921 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2018-04-02_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2436.68 -0.895 0.185271 Test results for specific bytes for dh-ranFile-2018-04-02_14:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2476.65 -0.330 0.370634 2 to 9 2430.84 -0.978 0.164005 3 to 10 2398.93 -1.429 0.076460 4 to 11 2485.92 -0.199 0.421085 5 to 12 2526.21 0.371 0.644531 6 to 13 2487.49 -0.177 0.429810 7 to 14 2493.77 -0.088 0.464904 8 to 15 2522.44 0.317 0.624537 9 to 16 2439.74 -0.852 0.197059 10 to 17 2475.58 -0.345 0.364891 11 to 18 2446.34 -0.759 0.223949 12 to 19 2479.60 -0.288 0.386490 13 to 20 2481.09 -0.267 0.394565 14 to 21 2455.91 -0.623 0.266481 15 to 22 2589.57 1.267 0.897369 16 to 23 2479.26 -0.293 0.384626 17 to 24 2285.34 -3.036 0.001199 18 to 25 2492.53 -0.106 0.457954 19 to 26 2512.77 0.181 0.571661 20 to 27 2558.05 0.821 0.794151 21 to 28 2543.38 0.614 0.730237 22 to 29 2568.61 0.970 0.834053 23 to 30 2353.82 -2.067 0.019355 24 to 31 2398.78 -1.432 0.076141 25 to 32 2535.38 0.500 0.691581 CDPARK for dh-ranFile-2018-04-02_14:31: 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 3519 -0.1826 0.427537 3563 1.8265 0.966111 3502 -0.9589 0.168804 3524 0.0457 0.518210 3533 0.4566 0.676028 3523 0.0000 0.500000 3500 -1.0502 0.146807 3529 0.2740 0.607947 3498 -1.1416 0.126820 3543 0.9132 0.819442 Square side=100, avg. no. parked=3523.40 sample std.=19.36 p-value of the KSTEST for those 10 p-values: 0.957372 Results for the MINIMUM DISTANCE test for dh-ranFile-2018-04-02_14:31 0.1250,0.8132,0.1883,0.4087,0.7638,0.6537,0.7979,0.7559,0.9818,0.2595, The KS test for those 10 p-values: 0.587077 The 3DSPHERES test for dh-ranFile-2018-04-02_14:31 sample no r^3 equiv. uni. 1 16.978 0.432174 2 10.131 0.286603 3 50.722 0.815617 4 33.362 0.671118 5 69.641 0.901861 6 30.888 0.642847 7 13.735 0.367344 8 0.089 0.002979 9 20.851 0.500940 10 1.663 0.053911 11 30.678 0.640341 12 13.416 0.360587 13 27.194 0.596045 14 11.344 0.314852 15 39.559 0.732499 16 9.943 0.282116 17 6.609 0.197711 18 20.801 0.500107 19 104.696 0.969496 20 7.665 0.225460 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.843698 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-04-02_14:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 -0.7 -1.1 -1.6 -0.5 0.6 -1.6 0.2 -0.2 -0.6 0.5 -0.6 -0.9 1.5 1.4 -1.7 -1.2 -0.8 1.7 0.9 0.4 -0.8 0.4 -0.6 0.7 -0.2 -0.9 1.8 0.8 0.4 -1.0 -0.5 -0.9 -0.6 0.5 1.3 0.3 -0.1 -0.4 0.4 1.6 -1.0 -1.1 Chi-square with 42 degrees of freedom:40.201281 z-score=-0.196256, p-value=0.449847 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2018-04-02_14:31 Test no p-value 1 0.005367 2 0.487701 3 0.679338 4 0.000432 5 0.019872 6 0.265619 7 0.011008 8 0.076950 9 0.224854 10 0.994194 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000543 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-04-02_14:31: (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 66531 0.28 66649 0.00 3 25000.00 25029 0.03 24965 0.05 4 6666.67 6736 0.72 6832 4.10 5 1388.89 1424 0.89 1287 7.47 6 238.10 239 0.00 227 0.52 7 34.72 32 0.21 36 0.05 8 4.96 8 1.86 3 0.77 p=0.32306 p=0.95644 Number of rngs required: 689477, p-value: 0.894 RESULTS OF CRAPS TEST for dh-ranFile-2018-04-02_14:31 No. of wins: Observed Expected 98552 98585.9 z-score=-0.151, pvalue=0.43982 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66647 66666.7 0.006 0.006 2 37813 37654.3 0.669 0.674 3 26909 26954.7 0.078 0.752 4 19321 19313.5 0.003 0.755 5 13979 13851.4 1.175 1.930 6 9870 9943.5 0.544 2.474 7 7070 7145.0 0.788 3.262 8 5042 5139.1 1.834 5.095 9 3732 3699.9 0.279 5.375 10 2592 2666.3 2.070 7.445 11 2011 1923.3 3.996 11.441 12 1324 1388.7 3.018 14.459 13 1022 1003.7 0.333 14.792 14 770 726.1 2.649 17.441 15 562 525.8 2.487 19.929 16 374 381.2 0.134 20.063 17 268 276.5 0.264 20.326 18 187 200.8 0.952 21.279 19 146 146.0 0.000 21.279 20 110 106.2 0.135 21.414 21 251 287.1 4.543 25.956 Chisq= 25.96 for 20 degrees of freedom, p= 0.83274 SUMMARY of craptest p-value for no. of wins: 0.439816 p-value for throws/game: 0.832738 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2018-04-02_14:31 No. of wins: Observed Expected 98420 98585.9 z-score=-0.742, pvalue=0.22910 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66902 66666.7 0.831 0.831 2 37380 37654.3 1.998 2.829 3 27033 26954.7 0.227 3.056 4 19455 19313.5 1.037 4.094 5 13760 13851.4 0.603 4.697 6 9893 9943.5 0.257 4.954 7 7119 7145.0 0.095 5.049 8 5101 5139.1 0.282 5.331 9 3803 3699.9 2.875 8.206 10 2585 2666.3 2.479 10.685 11 1976 1923.3 1.442 12.127 12 1371 1388.7 0.227 12.354 13 992 1003.7 0.137 12.490 14 733 726.1 0.065 12.555 15 502 525.8 1.080 13.636 16 392 381.2 0.309 13.944 17 276 276.5 0.001 13.946 18 189 200.8 0.697 14.642 19 150 146.0 0.110 14.753 20 105 106.2 0.014 14.767 21 283 287.1 0.059 14.826 Chisq= 14.83 for 20 degrees of freedom, p= 0.21371 SUMMARY of craptest p-value for no. of wins: 0.229099 p-value for throws/game: 0.213706 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0004,0.0005,0.0012,0.0030,0.0054,0.0074,0.0110,0.0158,0.0194,0.0199, 0.0388,0.0433,0.0452,0.0464,0.0532,0.0539,0.0578,0.0589,0.0629,0.0663, 0.0693,0.0709,0.0761,0.0765,0.0770,0.0877,0.0896,0.0940,0.0944,0.0994, 0.1116,0.1125,0.1177,0.1250,0.1268,0.1380,0.1415,0.1425,0.1441,0.1466, 0.1468,0.1528,0.1551,0.1564,0.1574,0.1590,0.1640,0.1686,0.1688,0.1767, 0.1847,0.1848,0.1853,0.1883,0.1925,0.1959,0.1971,0.1977,0.2012,0.2137, 0.2230,0.2239,0.2249,0.2255,0.2255,0.2291,0.2319,0.2379,0.2385,0.2459, 0.2471,0.2475,0.2568,0.2595,0.2619,0.2630,0.2646,0.2656,0.2665,0.2728, 0.2762,0.2821,0.2838,0.2866,0.3149,0.3231,0.3362,0.3367,0.3419,0.3429, 0.3438,0.3442,0.3580,0.3606,0.3629,0.3649,0.3655,0.3673,0.3694,0.3703, 0.3706,0.3810,0.3846,0.3865,0.3880,0.3892,0.3946,0.4087,0.4167,0.4211, 0.4239,0.4247,0.4250,0.4275,0.4298,0.4311,0.4322,0.4398,0.4497,0.4498, 0.4580,0.4649,0.4655,0.4707,0.4749,0.4798,0.4829,0.4874,0.4877,0.4909, 0.4914,0.5000,0.5001,0.5009,0.5085,0.5133,0.5160,0.5182,0.5220,0.5254, 0.5314,0.5355,0.5364,0.5421,0.5521,0.5521,0.5545,0.5610,0.5687,0.5693, 0.5699,0.5717,0.5748,0.5748,0.5768,0.5793,0.5871,0.5896,0.5918,0.5945, 0.5960,0.6021,0.6043,0.6079,0.6092,0.6104,0.6142,0.6142,0.6201,0.6207, 0.6245,0.6403,0.6428,0.6445,0.6511,0.6515,0.6537,0.6618,0.6625,0.6651, 0.6667,0.6674,0.6706,0.6711,0.6760,0.6793,0.6825,0.6881,0.6916,0.6944, 0.7023,0.7039,0.7064,0.7149,0.7173,0.7302,0.7325,0.7394,0.7410,0.7443, 0.7559,0.7595,0.7617,0.7620,0.7638,0.7791,0.7839,0.7853,0.7879,0.7942, 0.7976,0.7979,0.7991,0.8047,0.8059,0.8091,0.8132,0.8156,0.8194,0.8197, 0.8202,0.8204,0.8212,0.8229,0.8327,0.8341,0.8360,0.8374,0.8435,0.8437, 0.8511,0.8780,0.8899,0.8908,0.8912,0.8942,0.8974,0.8974,0.9019,0.9116, 0.9159,0.9186,0.9254,0.9277,0.9345,0.9371,0.9466,0.9466,0.9467,0.9554, 0.9564,0.9574,0.9596,0.9651,0.9653,0.9661,0.9695,0.9698,0.9739,0.9771, 0.9799,0.9809,0.9817,0.9818,0.9827,0.9830,0.9867,0.9926,0.9942, Overall p-value after applying KStest on 269 p-values = 0.768489 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.