RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-08-14_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 15.82 17.2601 0.563118 2 to 25 15.46 37.3832 0.997015 3 to 26 15.83 15.2655 0.423633 4 to 27 15.88 13.7344 0.314196 5 to 28 15.74 23.0448 0.852202 6 to 29 15.59 14.7946 0.389729 7 to 30 15.71 33.6764 0.990759 8 to 31 15.87 14.3704 0.359267 9 to 32 15.35 31.5626 0.982956 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.024270 Tough bday spacings test for dh-ranFile-2016-08-14_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 7 36 72 106 102 81 39 30 17 8 2 (O-E)^2/E 0.5 0.0 0.0 0.7 0.2 0.1 3.3 0.0 0.3 0.3 1.0 Birthday Spacings: Sum(O-E)^2/E= 6.479, p= 0.226 RESULTS OF GCD FOR dh-ranFile-2016-08-14_19:31 Euclid's algorithm: p-value, steps to gcd: 0.308831 p-value, dist. of gcd's: 0.177558 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-08-14_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.124 0.862 0.314 0.553 0.656 0.392 0.883 0.845 Bits 8 to 15---> 0.889 0.212 0.127 0.816 0.895 0.816 0.834 0.957 Bits 16 to 23---> 0.012 0.244 0.489 0.639 0.855 0.057 0.451 0.753 Bits 24 to 31---> 0.969 0.260 0.823 0.521 0.511 0.140 0.984 0.585 KS test for the above 32 p values: 0.841 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-08-14_19:31, p-values for 5 runs: 0.5931, 0.8253, 0.7062, 0.6057, 0.5107 Rank test for binary matrices (31x31) for dh-ranFile-2016-08-14_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 5152 5134.0 0.063 1.338 r= 30 23079 23103.0 0.025 1.363 r= 31 11574 11551.5 0.044 1.407 chi-square = 1.407 with df = 3; p-value = 0.296 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-08-14_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 222 211.4 0.530 0.530 r= 30 5107 5134.0 0.142 0.672 r= 31 23250 23103.0 0.935 1.606 r= 32 11421 11551.5 1.475 3.081 chi-square = 3.081 with df = 3; p-value = 0.621 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-08-14_19:31 b-rank test for bits 1 to 8, p=0.03251 b-rank test for bits 2 to 9, p=0.76346 b-rank test for bits 3 to 10, p=0.87752 b-rank test for bits 4 to 11, p=0.88115 b-rank test for bits 5 to 12, p=0.57932 b-rank test for bits 6 to 13, p=0.28088 b-rank test for bits 7 to 14, p=0.08535 b-rank test for bits 8 to 15, p=0.26729 b-rank test for bits 9 to 16, p=0.23393 b-rank test for bits 10 to 17, p=0.13813 b-rank test for bits 11 to 18, p=0.99321 b-rank test for bits 12 to 19, p=0.26614 b-rank test for bits 13 to 20, p=0.22034 b-rank test for bits 14 to 21, p=0.12452 b-rank test for bits 15 to 22, p=0.20469 b-rank test for bits 16 to 23, p=0.33204 b-rank test for bits 17 to 24, p=0.78024 b-rank test for bits 18 to 25, p=0.44327 b-rank test for bits 19 to 26, p=0.88097 b-rank test for bits 20 to 27, p=0.94267 b-rank test for bits 21 to 28, p=0.35861 b-rank test for bits 22 to 29, p=0.65005 b-rank test for bits 23 to 30, p=0.20408 b-rank test for bits 24 to 31, p=0.92016 b-rank test for bits 25 to 32, p=0.95649 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 = 0.416124 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-08-14_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 141264 -1.51 0.065805 2 141151 -1.77 0.038214 3 142008 0.23 0.591163 4 141629 -0.65 0.256241 5 142118 0.49 0.687065 6 142036 0.30 0.616369 7 141761 -0.35 0.364459 8 142330 0.98 0.837165 9 142258 0.81 0.792364 10 141846 -0.15 0.441184 11 142167 0.60 0.726424 12 141357 -1.29 0.098440 13 141704 -0.48 0.315705 14 141400 -1.19 0.117019 15 141318 -1.38 0.083545 16 141733 -0.41 0.340175 17 141516 -0.92 0.179049 18 141740 -0.40 0.346189 19 142072 0.38 0.648053 20 141845 -0.15 0.440263 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-08-14_19:31 Bits used No. missing words z-score p-value 23 to 32 141919 0.0333 0.513300 22 to 31 142284 1.2920 0.901815 21 to 30 141897 -0.0425 0.483043 20 to 29 141998 0.3058 0.620106 19 to 28 142510 2.0713 0.980833 18 to 27 141587 -1.1115 0.133180 17 to 26 142059 0.5161 0.697109 16 to 25 141541 -1.2701 0.102024 15 to 24 141582 -1.1287 0.129507 14 to 23 142222 1.0782 0.859522 13 to 22 142679 2.6540 0.996023 12 to 21 141980 0.2437 0.596264 11 to 20 141961 0.1782 0.570706 10 to 19 142071 0.5575 0.711401 9 to 18 141456 -1.5632 0.059002 8 to 17 141749 -0.5529 0.290179 7 to 16 142361 1.5575 0.940322 6 to 15 142109 0.6885 0.754436 5 to 14 142067 0.5437 0.706673 4 to 13 142001 0.3161 0.624038 3 to 12 141907 -0.0080 0.496795 2 to 11 142220 1.0713 0.857977 1 to 10 141358 -1.9011 0.028642 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-08-14_19:31 Bits used No. missing words z-score p-value 28 to 32 141555 -1.2011 0.114853 27 to 31 142072 0.5514 0.709328 26 to 30 142243 1.1311 0.870990 25 to 29 141697 -0.7198 0.235836 24 to 28 142163 0.8599 0.805077 23 to 27 142128 0.7413 0.770730 22 to 26 141931 0.0735 0.529279 21 to 25 141795 -0.3876 0.349171 20 to 24 141969 0.2023 0.580148 19 to 23 141857 -0.1774 0.429601 18 to 22 142334 1.4396 0.925004 17 to 21 142036 0.4294 0.666180 16 to 20 141575 -1.1333 0.128540 15 to 19 141909 -0.0011 0.499554 14 to 18 141427 -1.6350 0.051023 13 to 17 142237 1.1107 0.866661 12 to 16 142013 0.3514 0.637365 11 to 15 142086 0.5989 0.725374 10 to 14 142143 0.7921 0.785849 9 to 13 141976 0.2260 0.589399 8 to 12 141875 -0.1164 0.453679 7 to 11 141517 -1.3299 0.091770 6 to 10 141896 -0.0452 0.481979 5 to 9 142043 0.4531 0.674768 4 to 8 142101 0.6497 0.742066 3 to 7 142088 0.6057 0.727630 2 to 6 142209 1.0158 0.845145 1 to 5 142121 0.7175 0.763475 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-08-14_19:31 Bits used No. missing words z-score p-value 31 to 32 142248 0.9990 0.841109 30 to 31 141335 -1.6942 0.045115 29 to 30 141233 -1.9951 0.023017 28 to 29 141867 -0.1249 0.450314 27 to 28 141588 -0.9479 0.171596 26 to 27 142401 1.4504 0.926520 25 to 26 141834 -0.2222 0.412074 24 to 25 142002 0.2734 0.607713 23 to 24 141351 -1.6470 0.049780 22 to 23 141976 0.1967 0.577956 21 to 22 141756 -0.4523 0.325526 20 to 21 141585 -0.9567 0.169353 19 to 20 142116 0.6096 0.728952 18 to 19 141902 -0.0216 0.491375 17 to 18 141864 -0.1337 0.446813 16 to 17 142140 0.6804 0.751888 15 to 16 141813 -0.2842 0.388144 14 to 15 142362 1.3353 0.909113 13 to 14 142627 2.1170 0.982871 12 to 13 141660 -0.7355 0.231022 11 to 12 141792 -0.3461 0.364632 10 to 11 142113 0.6008 0.726012 9 to 10 141922 0.0374 0.514907 8 to 9 141533 -1.1101 0.133474 7 to 8 142639 2.1524 0.984318 6 to 7 141396 -1.5142 0.064982 5 to 6 141660 -0.7355 0.231022 4 to 5 141840 -0.2045 0.418976 3 to 4 142600 2.0374 0.979194 2 to 3 141507 -1.1868 0.117650 1 to 2 141763 -0.4317 0.332997 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-08-14_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2455.09 -0.635 0.262661 Test results for specific bytes for dh-ranFile-2016-08-14_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2694.66 2.753 0.997047 2 to 9 2532.93 0.466 0.679275 3 to 10 2543.75 0.619 0.731971 4 to 11 2545.64 0.645 0.740673 5 to 12 2439.87 -0.850 0.197559 6 to 13 2362.09 -1.950 0.025565 7 to 14 2533.26 0.470 0.680936 8 to 15 2559.11 0.836 0.798414 9 to 16 2503.56 0.050 0.520076 10 to 17 2433.88 -0.935 0.174880 11 to 18 2568.54 0.969 0.833809 12 to 19 2451.45 -0.687 0.246155 13 to 20 2393.64 -1.504 0.066272 14 to 21 2546.17 0.653 0.743106 15 to 22 2531.88 0.451 0.673971 16 to 23 2560.90 0.861 0.805442 17 to 24 2469.66 -0.429 0.333910 18 to 25 2441.80 -0.823 0.205232 19 to 26 2376.43 -1.748 0.040266 20 to 27 2584.46 1.194 0.883840 21 to 28 2405.43 -1.337 0.090540 22 to 29 2562.29 0.881 0.810807 23 to 30 2504.08 0.058 0.522989 24 to 31 2395.19 -1.482 0.069129 25 to 32 2505.77 0.082 0.532507 CDPARK for dh-ranFile-2016-08-14_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 3539 0.7306 0.767486 3521 -0.0913 0.463617 3541 0.8219 0.794438 3541 0.8219 0.794438 3534 0.5023 0.692266 3495 -1.2785 0.100530 3482 -1.8721 0.030593 3532 0.4110 0.659449 3537 0.6393 0.738676 3527 0.1826 0.572463 Square side=100, avg. no. parked=3524.90 sample std.=19.37 p-value of the KSTEST for those 10 p-values: 0.338611 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-08-14_19:31 0.5409,0.2078,0.4109,0.9431,0.9928,0.2969,0.4110,0.1043,0.4519,0.3001, The KS test for those 10 p-values: 0.471653 The 3DSPHERES test for dh-ranFile-2016-08-14_19:31 sample no r^3 equiv. uni. 1 2.204 0.070844 2 12.497 0.340689 3 4.788 0.147515 4 27.507 0.600247 5 8.382 0.243761 6 5.658 0.171875 7 24.330 0.555587 8 110.714 0.975040 9 12.924 0.350019 10 3.449 0.108592 11 31.982 0.655644 12 60.750 0.868008 13 6.676 0.199511 14 12.894 0.349359 15 108.788 0.973385 16 1.428 0.046491 17 66.969 0.892720 18 29.337 0.623904 19 33.052 0.667711 20 20.117 0.488587 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.825698 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-08-14_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 1.8 0.6 -0.1 -0.3 0.1 1.2 0.7 0.4 0.9 1.3 -1.7 -0.3 -1.2 0.2 -0.4 -0.2 -0.3 0.4 -0.8 -0.6 1.7 -0.1 0.2 -0.6 0.6 0.0 0.8 0.5 0.7 -0.9 -1.1 0.8 1.5 0.8 0.2 1.7 1.1 3.8 1.0 -0.6 0.0 -0.1 Chi-square with 42 degrees of freedom:44.530895 z-score=0.276143, p-value=0.634294 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-08-14_19:31 Test no p-value 1 0.706473 2 0.233917 3 0.097881 4 0.216218 5 0.006331 6 0.040580 7 0.464533 8 0.654203 9 0.321654 10 0.974913 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.194111 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-08-14_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 66730 0.06 66518 0.33 3 25000.00 24819 1.31 25151 0.91 4 6666.67 6768 1.54 6686 0.06 5 1388.89 1397 0.05 1390 0.00 6 238.10 243 0.10 232 0.16 7 34.72 35 0.00 19 7.12 8 4.96 7 0.84 3 0.77 p=0.30985 p=0.84510 Number of rngs required: 688923, p-value: 0.726 RESULTS OF CRAPS TEST for dh-ranFile-2016-08-14_19:31 No. of wins: Observed Expected 98676 98585.9 z-score= 0.403, pvalue=0.65659 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67144 66666.7 3.418 3.418 2 37232 37654.3 4.737 8.154 3 26944 26954.7 0.004 8.159 4 19531 19313.5 2.450 10.609 5 13717 13851.4 1.304 11.913 6 10024 9943.5 0.651 12.564 7 7208 7145.0 0.555 13.119 8 5018 5139.1 2.852 15.972 9 3639 3699.9 1.001 16.973 10 2620 2666.3 0.804 17.777 11 1865 1923.3 1.769 19.546 12 1424 1388.7 0.895 20.441 13 983 1003.7 0.428 20.869 14 686 726.1 2.219 23.088 15 541 525.8 0.437 23.525 16 381 381.2 0.000 23.525 17 264 276.5 0.569 24.094 18 214 200.8 0.864 24.957 19 166 146.0 2.744 27.702 20 110 106.2 0.135 27.836 21 289 287.1 0.012 27.849 Chisq= 27.85 for 20 degrees of freedom, p= 0.88697 SUMMARY of craptest p-value for no. of wins: 0.656587 p-value for throws/game: 0.886972 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-08-14_19:31 No. of wins: Observed Expected 98726 98585.9 z-score= 0.627, pvalue=0.73460 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66778 66666.7 0.186 0.186 2 37732 37654.3 0.160 0.346 3 26815 26954.7 0.724 1.071 4 19358 19313.5 0.103 1.173 5 13760 13851.4 0.603 1.777 6 9920 9943.5 0.056 1.832 7 7172 7145.0 0.102 1.934 8 5171 5139.1 0.198 2.133 9 3631 3699.9 1.282 3.414 10 2713 2666.3 0.818 4.232 11 1888 1923.3 0.649 4.881 12 1426 1388.7 1.000 5.881 13 996 1003.7 0.059 5.940 14 694 726.1 1.423 7.363 15 527 525.8 0.003 7.365 16 382 381.2 0.002 7.367 17 287 276.5 0.396 7.763 18 205 200.8 0.087 7.850 19 153 146.0 0.337 8.187 20 104 106.2 0.046 8.233 21 288 287.1 0.003 8.236 Chisq= 8.24 for 20 degrees of freedom, p= 0.00981 SUMMARY of craptest p-value for no. of wins: 0.734603 p-value for throws/game: 0.009810 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0063,0.0098,0.0122,0.0230,0.0243,0.0256,0.0286,0.0306,0.0325,0.0382, 0.0403,0.0406,0.0451,0.0465,0.0498,0.0510,0.0573,0.0590,0.0650,0.0658, 0.0663,0.0691,0.0708,0.0835,0.0853,0.0905,0.0918,0.0979,0.0984,0.1005, 0.1020,0.1043,0.1086,0.1149,0.1170,0.1177,0.1242,0.1245,0.1266,0.1285, 0.1295,0.1332,0.1335,0.1381,0.1404,0.1475,0.1694,0.1716,0.1719,0.1749, 0.1776,0.1790,0.1941,0.1976,0.1995,0.2041,0.2047,0.2052,0.2078,0.2118, 0.2162,0.2203,0.2264,0.2310,0.2310,0.2339,0.2339,0.2358,0.2437,0.2438, 0.2462,0.2562,0.2604,0.2627,0.2661,0.2673,0.2809,0.2902,0.2961,0.2969, 0.3001,0.3088,0.3099,0.3142,0.3143,0.3157,0.3217,0.3255,0.3320,0.3330, 0.3339,0.3386,0.3402,0.3407,0.3462,0.3492,0.3494,0.3500,0.3586,0.3593, 0.3645,0.3646,0.3881,0.3897,0.3916,0.4109,0.4110,0.4121,0.4161,0.4190, 0.4236,0.4296,0.4403,0.4412,0.4433,0.4468,0.4503,0.4511,0.4519,0.4537, 0.4636,0.4645,0.4717,0.4820,0.4830,0.4886,0.4888,0.4914,0.4968,0.4996, 0.5107,0.5111,0.5133,0.5149,0.5201,0.5207,0.5230,0.5293,0.5325,0.5409, 0.5530,0.5556,0.5631,0.5707,0.5725,0.5780,0.5793,0.5801,0.5853,0.5894, 0.5912,0.5931,0.5963,0.6002,0.6057,0.6077,0.6164,0.6201,0.6207,0.6239, 0.6240,0.6343,0.6374,0.6387,0.6481,0.6500,0.6542,0.6556,0.6559,0.6566, 0.6594,0.6662,0.6677,0.6740,0.6748,0.6793,0.6809,0.6871,0.6923,0.6971, 0.7062,0.7065,0.7067,0.7093,0.7114,0.7254,0.7257,0.7260,0.7264,0.7276, 0.7290,0.7320,0.7346,0.7387,0.7407,0.7421,0.7431,0.7519,0.7525,0.7544, 0.7635,0.7635,0.7675,0.7707,0.7802,0.7858,0.7924,0.7944,0.7944,0.7984, 0.8051,0.8054,0.8108,0.8160,0.8163,0.8233,0.8253,0.8257,0.8338,0.8338, 0.8372,0.8407,0.8411,0.8451,0.8451,0.8454,0.8522,0.8547,0.8580,0.8595, 0.8622,0.8667,0.8680,0.8710,0.8775,0.8810,0.8811,0.8829,0.8838,0.8870, 0.8886,0.8927,0.8950,0.9018,0.9091,0.9202,0.9250,0.9265,0.9403,0.9427, 0.9431,0.9565,0.9572,0.9690,0.9734,0.9749,0.9750,0.9792,0.9808,0.9829, 0.9830,0.9838,0.9843,0.9908,0.9928,0.9932,0.9960,0.9970,0.9970, Overall p-value after applying KStest on 269 p-values = 0.613824 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.