RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-21_04:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.69 15.4038 0.433576 2 to 25 15.76 14.6685 0.380654 3 to 26 15.84 16.1185 0.484549 4 to 27 16.24 12.4588 0.228407 5 to 28 15.90 19.4288 0.695517 6 to 29 15.77 17.9807 0.609941 7 to 30 15.75 14.8058 0.390531 8 to 31 15.59 20.2350 0.737612 9 to 32 15.72 16.3085 0.497923 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.311309 Tough bday spacings test for dh-ranFile-2017-01-21_04:31: 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 5 49 79 84 97 80 55 33 11 5 2 (O-E)^2/E 1.9 4.2 0.4 1.9 0.0 0.0 0.2 0.4 1.0 0.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 11.449, p= 0.676 RESULTS OF GCD FOR dh-ranFile-2017-01-21_04:31 Euclid's algorithm: p-value, steps to gcd: 0.750887 p-value, dist. of gcd's: 0.460138 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-21_04:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.479 0.999 0.677 0.464 0.854 0.222 0.757 0.541 Bits 8 to 15---> 0.210 0.833 0.442 0.213 0.996 0.496 0.782 0.446 Bits 16 to 23---> 0.609 0.762 0.658 0.048 0.750 0.047 0.488 0.813 Bits 24 to 31---> 0.299 0.029 0.799 0.404 0.643 0.140 0.574 0.799 KS test for the above 32 p values: 0.570 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-21_04:31, p-values for 5 runs: 0.6942, 0.6156, 0.0973, 0.6684, 0.6079 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-21_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 207 211.4 0.092 0.092 r= 29 5178 5134.0 0.377 0.469 r= 30 23005 23103.0 0.416 0.885 r= 31 11610 11551.5 0.296 1.181 chi-square = 1.181 with df = 3; p-value = 0.243 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-21_04:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 220 211.4 0.348 0.348 r= 30 5149 5134.0 0.044 0.392 r= 31 22978 23103.0 0.677 1.069 r= 32 11653 11551.5 0.891 1.960 chi-square = 1.960 with df = 3; p-value = 0.419 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-21_04:31 b-rank test for bits 1 to 8, p=0.96663 b-rank test for bits 2 to 9, p=0.62452 b-rank test for bits 3 to 10, p=0.87057 b-rank test for bits 4 to 11, p=0.91858 b-rank test for bits 5 to 12, p=0.98422 b-rank test for bits 6 to 13, p=0.54978 b-rank test for bits 7 to 14, p=0.29985 b-rank test for bits 8 to 15, p=0.46544 b-rank test for bits 9 to 16, p=0.56323 b-rank test for bits 10 to 17, p=0.69385 b-rank test for bits 11 to 18, p=0.68905 b-rank test for bits 12 to 19, p=0.52148 b-rank test for bits 13 to 20, p=0.98940 b-rank test for bits 14 to 21, p=0.67169 b-rank test for bits 15 to 22, p=0.17334 b-rank test for bits 16 to 23, p=0.37115 b-rank test for bits 17 to 24, p=0.99327 b-rank test for bits 18 to 25, p=0.77527 b-rank test for bits 19 to 26, p=0.20851 b-rank test for bits 20 to 27, p=0.16532 b-rank test for bits 21 to 28, p=0.84002 b-rank test for bits 22 to 29, p=0.66044 b-rank test for bits 23 to 30, p=0.01403 b-rank test for bits 24 to 31, p=0.07356 b-rank test for bits 25 to 32, p=0.61340 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 = 0.134264 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-21_04:31 (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 141404 -1.18 0.118865 2 142284 0.88 0.809321 3 142048 0.32 0.627029 4 142082 0.40 0.656686 5 141767 -0.33 0.369738 6 142096 0.44 0.668634 7 141153 -1.77 0.038604 8 141857 -0.12 0.451344 9 142559 1.52 0.935483 10 141613 -0.69 0.244356 11 141471 -1.02 0.152886 12 141991 0.19 0.575666 13 142150 0.56 0.713049 14 141803 -0.25 0.401899 15 141572 -0.79 0.215303 16 141828 -0.19 0.424645 17 142076 0.39 0.651516 18 142233 0.76 0.775247 19 142509 1.40 0.919408 20 141345 -1.32 0.093663 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-21_04:31 Bits used No. missing words z-score p-value 23 to 32 141258 -2.2460 0.012353 22 to 31 141695 -0.7391 0.229933 21 to 30 141518 -1.3494 0.088602 20 to 29 141339 -1.9667 0.024611 19 to 28 141957 0.1644 0.565284 18 to 27 142224 1.0851 0.861054 17 to 26 141855 -0.1873 0.425695 16 to 25 141687 -0.7667 0.221643 15 to 24 141677 -0.8011 0.211526 14 to 23 142081 0.5920 0.723063 13 to 22 142155 0.8471 0.801541 12 to 21 141232 -2.3356 0.009756 11 to 20 141794 -0.3977 0.345430 10 to 19 141964 0.1885 0.574764 9 to 18 141373 -1.8494 0.032199 8 to 17 142141 0.7989 0.787815 7 to 16 141436 -1.6322 0.051322 6 to 15 141931 0.0747 0.529783 5 to 14 141369 -1.8632 0.031217 4 to 13 141866 -0.1494 0.440614 3 to 12 142002 0.3196 0.625346 2 to 11 141473 -1.5046 0.066215 1 to 10 141488 -1.4529 0.073131 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-21_04:31 Bits used No. missing words z-score p-value 28 to 32 141937 0.0938 0.537365 27 to 31 141915 0.0192 0.507667 26 to 30 141586 -1.0960 0.136532 25 to 29 142072 0.5514 0.709328 24 to 28 141868 -0.1401 0.444290 23 to 27 141645 -0.8960 0.185117 22 to 26 141786 -0.4181 0.337949 21 to 25 141791 -0.4011 0.344166 20 to 24 141919 0.0328 0.513075 19 to 23 141900 -0.0316 0.487385 18 to 22 142222 1.0599 0.855405 17 to 21 141956 0.1582 0.562852 16 to 20 141787 -0.4147 0.339189 15 to 19 141897 -0.0418 0.483330 14 to 18 141900 -0.0316 0.487385 13 to 17 141506 -1.3672 0.085778 12 to 16 142212 1.0260 0.847554 11 to 15 141757 -0.5164 0.302797 10 to 14 141656 -0.8587 0.195240 9 to 13 142444 1.8124 0.965041 8 to 12 141467 -1.4994 0.066882 7 to 11 142048 0.4701 0.680847 6 to 10 141733 -0.5977 0.275010 5 to 9 142044 0.4565 0.675988 4 to 8 142058 0.5040 0.692857 3 to 7 141982 0.2463 0.597290 2 to 6 141982 0.2463 0.597290 1 to 5 142091 0.6158 0.730997 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-21_04:31 Bits used No. missing words z-score p-value 31 to 32 142093 0.5418 0.706022 30 to 31 142057 0.4356 0.668438 29 to 30 141844 -0.1927 0.423592 28 to 29 142191 0.8309 0.796981 27 to 28 142382 1.3943 0.918388 26 to 27 141335 -1.6942 0.045115 25 to 26 141986 0.2262 0.589464 24 to 25 142248 0.9990 0.841109 23 to 24 142053 0.4238 0.664146 22 to 23 141996 0.2557 0.600895 21 to 22 140971 -2.7679 0.002821 20 to 21 141688 -0.6529 0.256913 19 to 20 141637 -0.8033 0.210891 18 to 19 142132 0.6568 0.744359 17 to 18 141751 -0.4671 0.320232 16 to 17 141941 0.0934 0.537216 15 to 16 141933 0.0698 0.527833 14 to 15 142079 0.5005 0.691639 13 to 14 141836 -0.2163 0.414372 12 to 13 141936 0.0787 0.531354 11 to 12 141330 -1.7089 0.043731 10 to 11 141853 -0.1662 0.434014 9 to 10 141998 0.2616 0.603171 8 to 9 142261 1.0374 0.850219 7 to 8 141644 -0.7827 0.216906 6 to 7 142246 0.9931 0.839676 5 to 6 141964 0.1613 0.564059 4 to 5 142349 1.2970 0.902678 3 to 4 142246 0.9931 0.839676 2 to 3 142056 0.4327 0.667367 1 to 2 142137 0.6716 0.749079 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-21_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2587.43 1.236 0.891853 Test results for specific bytes for dh-ranFile-2017-01-21_04:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2564.60 0.914 0.819542 2 to 9 2365.52 -1.902 0.028599 3 to 10 2538.96 0.551 0.709177 4 to 11 2478.02 -0.311 0.377965 5 to 12 2542.22 0.597 0.724766 6 to 13 2519.41 0.275 0.608159 7 to 14 2454.13 -0.649 0.258273 8 to 15 2532.39 0.458 0.676546 9 to 16 2485.59 -0.204 0.419233 10 to 17 2402.78 -1.375 0.084587 11 to 18 2456.24 -0.619 0.267995 12 to 19 2569.95 0.989 0.838743 13 to 20 2508.61 0.122 0.548453 14 to 21 2478.18 -0.309 0.378825 15 to 22 2389.97 -1.556 0.059842 16 to 23 2532.63 0.461 0.677761 17 to 24 2438.01 -0.877 0.190333 18 to 25 2659.13 2.250 0.987788 19 to 26 2461.50 -0.544 0.293066 20 to 27 2544.92 0.635 0.737380 21 to 28 2441.94 -0.821 0.205801 22 to 29 2533.64 0.476 0.682890 23 to 30 2505.73 0.081 0.532312 24 to 31 2587.06 1.231 0.890871 25 to 32 2529.54 0.418 0.661964 CDPARK for dh-ranFile-2017-01-21_04:31: 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 3487 -1.6438 0.050105 3515 -0.3653 0.357445 3501 -1.0046 0.157553 3504 -0.8676 0.192812 3541 0.8219 0.794438 3524 0.0457 0.518210 3542 0.8676 0.807188 3507 -0.7306 0.232514 3554 1.4155 0.921543 3514 -0.4110 0.340551 Square side=100, avg. no. parked=3518.90 sample std.=20.05 p-value of the KSTEST for those 10 p-values: 0.768044 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-21_04:31 0.5124,0.7312,0.2194,0.8898,0.5408,0.3872,0.8067,0.7397,0.5203,0.0754, The KS test for those 10 p-values: 0.829169 The 3DSPHERES test for dh-ranFile-2017-01-21_04:31 sample no r^3 equiv. uni. 1 24.660 0.560449 2 6.679 0.199605 3 36.851 0.707227 4 17.755 0.446690 5 3.447 0.108540 6 17.063 0.433782 7 69.955 0.902884 8 43.381 0.764500 9 31.122 0.645624 10 42.857 0.760345 11 71.119 0.906578 12 14.452 0.382281 13 71.142 0.906651 14 1.743 0.056437 15 6.359 0.190996 16 1.165 0.038098 17 93.130 0.955146 18 9.874 0.280462 19 2.666 0.085022 20 10.379 0.292476 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.913318 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-21_04:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 -1.3 2.5 -0.9 -1.4 0.1 0.6 0.9 -1.2 -0.3 0.8 -2.0 1.9 -0.6 0.5 -0.8 2.0 -0.3 -0.6 -0.1 -1.5 0.8 -1.0 -0.4 0.7 0.3 0.8 -0.4 -0.0 -0.1 0.5 1.2 0.4 -0.2 1.1 -0.2 0.2 0.1 2.1 -1.3 -1.0 0.8 Chi-square with 42 degrees of freedom:45.932706 z-score=0.429093, p-value=0.687459 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-21_04:31 Test no p-value 1 0.005163 2 0.134429 3 0.282491 4 0.713148 5 0.191161 6 0.072633 7 0.094786 8 0.087191 9 0.008485 10 0.863556 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001511 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-21_04:31: (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 66605 0.06 66662 0.00 3 25000.00 24870 0.68 25078 0.24 4 6666.67 6805 2.87 6584 1.03 5 1388.89 1477 5.59 1402 0.12 6 238.10 210 3.32 232 0.16 7 34.72 29 0.94 39 0.53 8 4.96 3 0.77 2 1.77 p=0.97278 p=0.30204 Number of rngs required: 688479, p-value: 0.535 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-21_04:31 No. of wins: Observed Expected 98299 98585.9 z-score=-1.283, pvalue=0.09975 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66836 66666.7 0.430 0.430 2 37402 37654.3 1.691 2.121 3 27027 26954.7 0.194 2.315 4 19267 19313.5 0.112 2.426 5 13715 13851.4 1.344 3.770 6 10039 9943.5 0.916 4.686 7 7182 7145.0 0.191 4.878 8 5122 5139.1 0.057 4.934 9 3682 3699.9 0.086 5.021 10 2620 2666.3 0.804 5.825 11 1932 1923.3 0.039 5.864 12 1446 1388.7 2.361 8.225 13 1008 1003.7 0.018 8.243 14 747 726.1 0.599 8.842 15 528 525.8 0.009 8.851 16 389 381.2 0.162 9.013 17 282 276.5 0.108 9.120 18 211 200.8 0.515 9.635 19 169 146.0 3.629 13.264 20 113 106.2 0.433 13.697 21 283 287.1 0.059 13.756 Chisq= 13.76 for 20 degrees of freedom, p= 0.15737 SUMMARY of craptest p-value for no. of wins: 0.099746 p-value for throws/game: 0.157373 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-21_04:31 No. of wins: Observed Expected 98750 98585.9 z-score= 0.734, pvalue=0.76857 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67241 66666.7 4.948 4.948 2 37108 37654.3 7.926 12.874 3 26999 26954.7 0.073 12.947 4 19199 19313.5 0.678 13.625 5 13876 13851.4 0.044 13.669 6 10021 9943.5 0.603 14.272 7 7127 7145.0 0.045 14.318 8 5136 5139.1 0.002 14.320 9 3717 3699.9 0.079 14.399 10 2668 2666.3 0.001 14.400 11 1943 1923.3 0.201 14.601 12 1357 1388.7 0.725 15.327 13 961 1003.7 1.818 17.145 14 677 726.1 3.326 20.470 15 526 525.8 0.000 20.470 16 430 381.2 6.261 26.731 17 269 276.5 0.206 26.936 18 207 200.8 0.190 27.126 19 156 146.0 0.687 27.813 20 112 106.2 0.315 28.128 21 270 287.1 1.020 29.148 Chisq= 29.15 for 20 degrees of freedom, p= 0.91512 SUMMARY of craptest p-value for no. of wins: 0.768567 p-value for throws/game: 0.915120 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0015,0.0028,0.0052,0.0085,0.0098,0.0124,0.0140,0.0246,0.0286,0.0286, 0.0312,0.0322,0.0381,0.0386,0.0437,0.0451,0.0469,0.0483,0.0501,0.0513, 0.0564,0.0598,0.0662,0.0669,0.0726,0.0731,0.0736,0.0754,0.0846,0.0850, 0.0858,0.0872,0.0886,0.0937,0.0948,0.0973,0.0997,0.1085,0.1189,0.1343, 0.1344,0.1365,0.1401,0.1529,0.1574,0.1576,0.1653,0.1733,0.1851,0.1903, 0.1910,0.1912,0.1928,0.1952,0.1996,0.2058,0.2085,0.2099,0.2109,0.2115, 0.2127,0.2153,0.2169,0.2194,0.2215,0.2216,0.2284,0.2299,0.2325,0.2425, 0.2444,0.2569,0.2583,0.2680,0.2750,0.2805,0.2825,0.2925,0.2931,0.2988, 0.2998,0.3020,0.3028,0.3113,0.3202,0.3379,0.3392,0.3406,0.3442,0.3454, 0.3574,0.3697,0.3711,0.3780,0.3788,0.3807,0.3823,0.3872,0.3905,0.4019, 0.4038,0.4144,0.4192,0.4193,0.4236,0.4246,0.4257,0.4336,0.4338,0.4340, 0.4406,0.4423,0.4443,0.4456,0.4467,0.4513,0.4601,0.4637,0.4654,0.4792, 0.4833,0.4845,0.4874,0.4874,0.4881,0.4957,0.4979,0.5077,0.5124,0.5131, 0.5182,0.5203,0.5215,0.5278,0.5298,0.5314,0.5323,0.5348,0.5372,0.5374, 0.5405,0.5408,0.5485,0.5498,0.5604,0.5629,0.5632,0.5641,0.5653,0.5704, 0.5742,0.5748,0.5757,0.5895,0.5973,0.5973,0.6009,0.6032,0.6079,0.6082, 0.6089,0.6099,0.6134,0.6156,0.6245,0.6253,0.6270,0.6431,0.6456,0.6515, 0.6567,0.6578,0.6604,0.6620,0.6641,0.6674,0.6684,0.6684,0.6686,0.6717, 0.6760,0.6764,0.6765,0.6772,0.6778,0.6808,0.6829,0.6875,0.6891,0.6916, 0.6929,0.6938,0.6942,0.6955,0.7060,0.7072,0.7092,0.7093,0.7130,0.7131, 0.7231,0.7248,0.7310,0.7312,0.7374,0.7376,0.7397,0.7444,0.7491,0.7501, 0.7509,0.7574,0.7603,0.7623,0.7645,0.7680,0.7686,0.7752,0.7753,0.7823, 0.7878,0.7944,0.7970,0.7988,0.7994,0.8015,0.8067,0.8072,0.8093,0.8134, 0.8195,0.8292,0.8334,0.8387,0.8397,0.8397,0.8400,0.8411,0.8476,0.8502, 0.8537,0.8554,0.8611,0.8636,0.8706,0.8898,0.8909,0.8919,0.9027,0.9029, 0.9066,0.9067,0.9133,0.9151,0.9184,0.9186,0.9194,0.9215,0.9355,0.9551, 0.9650,0.9666,0.9728,0.9842,0.9878,0.9894,0.9933,0.9957,0.9990, Overall p-value after applying KStest on 269 p-values = 0.342367 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.