RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-17_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.98 14.2201 0.348534 2 to 25 15.87 16.2130 0.491209 3 to 26 15.58 16.6906 0.524491 4 to 27 15.68 15.2020 0.419062 5 to 28 15.52 15.1485 0.415216 6 to 29 15.66 11.5096 0.171121 7 to 30 15.49 24.0329 0.881455 8 to 31 15.81 23.3641 0.862233 9 to 32 15.95 8.8531 0.055243 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.838971 Tough bday spacings test for dh-ranFile-2016-03-17_09:31: 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 12 35 75 95 94 83 51 31 14 7 3 (O-E)^2/E 0.9 0.1 0.0 0.1 0.1 0.3 0.0 0.1 0.1 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 1.938, p= 0.003 RESULTS OF GCD FOR dh-ranFile-2016-03-17_09:31 Euclid's algorithm: p-value, steps to gcd: 0.380759 p-value, dist. of gcd's: 0.508882 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-17_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.562 0.404 0.794 0.487 0.911 0.916 0.891 0.052 Bits 8 to 15---> 0.771 0.765 0.876 0.718 0.063 0.557 0.755 0.518 Bits 16 to 23---> 0.939 0.902 0.137 0.394 0.636 0.163 0.433 0.201 Bits 24 to 31---> 0.088 0.915 0.175 0.288 0.064 0.312 0.643 0.147 KS test for the above 32 p values: 0.215 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-17_09:31, p-values for 5 runs: 0.2176, 0.9812, 0.4723, 0.7323, 0.0179 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-17_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 227 211.4 1.148 1.148 r= 29 5148 5134.0 0.038 1.187 r= 30 23186 23103.0 0.298 1.484 r= 31 11439 11551.5 1.096 2.580 chi-square = 2.580 with df = 3; p-value = 0.539 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-17_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 221 211.4 0.434 0.434 r= 30 5160 5134.0 0.132 0.566 r= 31 23063 23103.0 0.069 0.635 r= 32 11556 11551.5 0.002 0.637 chi-square = 0.637 with df = 3; p-value = 0.112 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-17_09:31 b-rank test for bits 1 to 8, p=0.57051 b-rank test for bits 2 to 9, p=0.06757 b-rank test for bits 3 to 10, p=0.09762 b-rank test for bits 4 to 11, p=0.54178 b-rank test for bits 5 to 12, p=0.39921 b-rank test for bits 6 to 13, p=0.18724 b-rank test for bits 7 to 14, p=0.44690 b-rank test for bits 8 to 15, p=0.86306 b-rank test for bits 9 to 16, p=0.07263 b-rank test for bits 10 to 17, p=0.46063 b-rank test for bits 11 to 18, p=0.48528 b-rank test for bits 12 to 19, p=0.71013 b-rank test for bits 13 to 20, p=0.88792 b-rank test for bits 14 to 21, p=0.53702 b-rank test for bits 15 to 22, p=0.42444 b-rank test for bits 16 to 23, p=0.53457 b-rank test for bits 17 to 24, p=0.12037 b-rank test for bits 18 to 25, p=0.98607 b-rank test for bits 19 to 26, p=0.73387 b-rank test for bits 20 to 27, p=0.70287 b-rank test for bits 21 to 28, p=0.30740 b-rank test for bits 22 to 29, p=0.20024 b-rank test for bits 23 to 30, p=0.40027 b-rank test for bits 24 to 31, p=0.20852 b-rank test for bits 25 to 32, p=0.22407 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 = 0.494568 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-17_09:31 (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 142808 2.10 0.982122 2 142561 1.52 0.936070 3 142407 1.16 0.877541 4 141698 -0.49 0.310737 5 141986 0.18 0.571084 6 142268 0.84 0.798989 7 141188 -1.69 0.045960 8 141687 -0.52 0.301719 9 142248 0.79 0.785611 10 141183 -1.70 0.044845 11 142084 0.41 0.658403 12 142157 0.58 0.718594 13 141547 -0.85 0.198619 14 141212 -1.63 0.051627 15 141603 -0.72 0.237081 16 142129 0.51 0.696111 17 142435 1.23 0.890314 18 141737 -0.40 0.343607 19 141657 -0.59 0.277744 20 142086 0.41 0.660116 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-17_09:31 Bits used No. missing words z-score p-value 23 to 32 141600 -1.0667 0.143064 22 to 31 141814 -0.3287 0.371182 21 to 30 141900 -0.0322 0.487167 20 to 29 141938 0.0989 0.539376 19 to 28 141904 -0.0184 0.492668 18 to 27 141789 -0.4149 0.339096 17 to 26 141613 -1.0218 0.153431 16 to 25 141136 -2.6667 0.003831 15 to 24 142149 0.8264 0.795725 14 to 23 141575 -1.1529 0.124484 13 to 22 141362 -1.8873 0.029557 12 to 21 142064 0.5333 0.703103 11 to 20 141751 -0.5460 0.292545 10 to 19 141973 0.2196 0.586890 9 to 18 141967 0.1989 0.578815 8 to 17 142243 1.1506 0.875049 7 to 16 141464 -1.5356 0.062316 6 to 15 142015 0.3644 0.642213 5 to 14 142326 1.4368 0.924612 4 to 13 141496 -1.4253 0.077039 3 to 12 142276 1.2644 0.896953 2 to 11 141711 -0.6839 0.247020 1 to 10 141749 -0.5529 0.290179 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-17_09:31 Bits used No. missing words z-score p-value 28 to 32 141373 -1.8181 0.034527 27 to 31 141813 -0.3265 0.372007 26 to 30 141920 0.0362 0.514426 25 to 29 142422 1.7379 0.958883 24 to 28 141331 -1.9604 0.024972 23 to 27 141837 -0.2452 0.403156 22 to 26 142305 1.3413 0.910081 21 to 25 141907 -0.0079 0.496849 20 to 24 141899 -0.0350 0.486033 19 to 23 142406 1.6836 0.953873 18 to 22 141553 -1.2079 0.113543 17 to 21 141806 -0.3503 0.363068 16 to 20 141938 0.0972 0.538711 15 to 19 141655 -0.8621 0.194306 14 to 18 141809 -0.3401 0.366890 13 to 17 141851 -0.1977 0.421629 12 to 16 142761 2.8870 0.998055 11 to 15 141561 -1.1808 0.118845 10 to 14 141708 -0.6825 0.247470 9 to 13 141468 -1.4960 0.067322 8 to 12 141899 -0.0350 0.486033 7 to 11 141468 -1.4960 0.067322 6 to 10 141895 -0.0486 0.480629 5 to 9 141785 -0.4215 0.336711 4 to 8 142380 1.5955 0.944699 3 to 7 142040 0.4429 0.671099 2 to 6 141702 -0.7028 0.241086 1 to 5 142148 0.8091 0.790757 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-17_09:31 Bits used No. missing words z-score p-value 31 to 32 141354 -1.6381 0.050696 30 to 31 141331 -1.7060 0.044005 29 to 30 141890 -0.0570 0.477264 28 to 29 141868 -0.1219 0.451482 27 to 28 141847 -0.1839 0.427060 26 to 27 142065 0.4592 0.676956 25 to 26 142714 2.3737 0.991194 24 to 25 141148 -2.2458 0.012358 23 to 24 141339 -1.6824 0.046247 22 to 23 141437 -1.3933 0.081764 21 to 22 142086 0.5212 0.698869 20 to 21 141970 0.1790 0.571018 19 to 20 142359 1.3265 0.907656 18 to 19 141467 -1.3048 0.095979 17 to 18 141827 -0.2429 0.404056 16 to 17 141851 -0.1721 0.431693 15 to 16 141463 -1.3166 0.093985 14 to 15 141814 -0.2812 0.389275 13 to 14 141426 -1.4258 0.076970 12 to 13 141730 -0.5290 0.298404 11 to 12 142372 1.3648 0.913843 10 to 11 142575 1.9636 0.975213 9 to 10 141676 -0.6883 0.245635 8 to 9 141634 -0.8122 0.208343 7 to 8 142053 0.4238 0.664146 6 to 7 141935 0.0757 0.530180 5 to 6 142566 1.9371 0.973632 4 to 5 141984 0.2203 0.587168 3 to 4 141575 -0.9862 0.162012 2 to 3 142028 0.3501 0.636853 1 to 2 142019 0.3235 0.626846 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-17_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2473.08 -0.381 0.351696 Test results for specific bytes for dh-ranFile-2016-03-17_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2298.02 -2.856 0.002142 2 to 9 2519.42 0.275 0.608179 3 to 10 2547.66 0.674 0.749869 4 to 11 2430.51 -0.983 0.162878 5 to 12 2576.16 1.077 0.859272 6 to 13 2457.35 -0.603 0.273191 7 to 14 2368.61 -1.858 0.031572 8 to 15 2347.75 -2.153 0.015652 9 to 16 2459.00 -0.580 0.281006 10 to 17 2650.55 2.129 0.983377 11 to 18 2478.26 -0.307 0.379249 12 to 19 2477.74 -0.315 0.376436 13 to 20 2491.28 -0.123 0.450931 14 to 21 2462.70 -0.528 0.298913 15 to 22 2412.30 -1.240 0.107439 16 to 23 2573.50 1.039 0.850696 17 to 24 2627.06 1.797 0.963830 18 to 25 2473.15 -0.380 0.352098 19 to 26 2529.06 0.411 0.659451 20 to 27 2512.56 0.178 0.570483 21 to 28 2488.48 -0.163 0.435292 22 to 29 2484.05 -0.226 0.410778 23 to 30 2476.98 -0.325 0.372401 24 to 31 2522.14 0.313 0.622874 25 to 32 2523.89 0.338 0.632270 CDPARK for dh-ranFile-2016-03-17_09:31: 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 3477 -2.1005 0.017844 3519 -0.1826 0.427537 3505 -0.8219 0.205562 3545 1.0046 0.842447 3519 -0.1826 0.427537 3535 0.5479 0.708135 3537 0.6393 0.738676 3517 -0.2740 0.392053 3520 -0.1370 0.445521 3544 0.9589 0.831196 Square side=100, avg. no. parked=3521.80 sample std.=19.41 p-value of the KSTEST for those 10 p-values: 0.818220 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-17_09:31 0.2396,0.5082,0.7734,0.5291,0.2696,0.3243,0.2035,0.6405,0.1925,0.6812, The KS test for those 10 p-values: 0.425749 The 3DSPHERES test for dh-ranFile-2016-03-17_09:31 sample no r^3 equiv. uni. 1 42.235 0.755326 2 55.676 0.843681 3 30.420 0.637240 4 16.130 0.415893 5 22.752 0.531587 6 16.871 0.430139 7 1.018 0.033380 8 38.201 0.720112 9 1.149 0.037585 10 45.964 0.783926 11 51.965 0.823098 12 92.546 0.954264 13 72.244 0.910018 14 63.334 0.878900 15 35.571 0.694469 16 11.985 0.329347 17 96.007 0.959248 18 6.255 0.188202 19 24.012 0.550857 20 1.765 0.057150 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.299717 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-17_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -1.2 0.3 0.9 -0.6 -0.4 -1.2 -0.1 -0.3 -0.4 -0.2 -0.9 0.3 -0.3 0.6 -1.3 -0.8 -1.0 0.5 0.9 3.6 0.5 -0.7 -0.2 0.2 -1.6 -0.0 -0.9 -0.1 -0.1 0.2 1.8 1.2 2.2 0.8 -0.8 0.3 0.8 0.9 0.4 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:41.604664 z-score=-0.043135, p-value=0.511810 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-17_09:31 Test no p-value 1 0.398293 2 0.013384 3 0.578998 4 0.363623 5 0.800688 6 0.793017 7 0.001048 8 0.116146 9 0.607856 10 0.092909 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.108785 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-17_09:31: (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 66298 2.04 66798 0.26 3 25000.00 25309 3.82 24873 0.65 4 6666.67 6690 0.08 6674 0.01 5 1388.89 1404 0.16 1340 1.72 6 238.10 255 1.20 277 6.36 7 34.72 39 0.53 33 0.09 8 4.96 4 0.19 4 0.19 p=0.76319 p=0.84058 Number of rngs required: 688757, p-value: 0.658 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-17_09:31 No. of wins: Observed Expected 98648 98585.9 z-score= 0.278, pvalue=0.60947 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66461 66666.7 0.634 0.634 2 37395 37654.3 1.786 2.420 3 27146 26954.7 1.357 3.778 4 19286 19313.5 0.039 3.817 5 14041 13851.4 2.595 6.411 6 9894 9943.5 0.247 6.658 7 7146 7145.0 0.000 6.658 8 5316 5139.1 6.091 12.750 9 3674 3699.9 0.181 12.930 10 2670 2666.3 0.005 12.936 11 2007 1923.3 3.640 16.576 12 1335 1388.7 2.080 18.655 13 967 1003.7 1.343 19.998 14 752 726.1 0.921 20.919 15 469 525.8 6.143 27.062 16 438 381.2 8.479 35.541 17 282 276.5 0.108 35.649 18 195 200.8 0.169 35.819 19 144 146.0 0.027 35.845 20 87 106.2 3.476 39.322 21 295 287.1 0.217 39.538 Chisq= 39.54 for 20 degrees of freedom, p= 0.99429 SUMMARY of craptest p-value for no. of wins: 0.609468 p-value for throws/game: 0.994289 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-17_09:31 No. of wins: Observed Expected 98363 98585.9 z-score=-0.997, pvalue=0.15944 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66842 66666.7 0.461 0.461 2 37542 37654.3 0.335 0.796 3 26829 26954.7 0.586 1.383 4 19359 19313.5 0.107 1.490 5 13907 13851.4 0.223 1.713 6 9956 9943.5 0.016 1.729 7 7023 7145.0 2.084 3.813 8 5133 5139.1 0.007 3.820 9 3745 3699.9 0.551 4.370 10 2618 2666.3 0.875 5.245 11 1962 1923.3 0.778 6.023 12 1430 1388.7 1.226 7.249 13 1068 1003.7 4.117 11.366 14 754 726.1 1.069 12.435 15 504 525.8 0.907 13.342 16 394 381.2 0.433 13.775 17 261 276.5 0.873 14.648 18 171 200.8 4.431 19.079 19 123 146.0 3.619 22.697 20 89 106.2 2.790 25.488 21 290 287.1 0.029 25.517 Chisq= 25.52 for 20 degrees of freedom, p= 0.81762 SUMMARY of craptest p-value for no. of wins: 0.159442 p-value for throws/game: 0.817624 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0010,0.0021,0.0032,0.0038,0.0124,0.0134,0.0157,0.0178,0.0179,0.0250, 0.0296,0.0316,0.0334,0.0345,0.0376,0.0440,0.0448,0.0460,0.0462,0.0507, 0.0516,0.0524,0.0552,0.0572,0.0623,0.0626,0.0640,0.0673,0.0673,0.0676, 0.0726,0.0770,0.0770,0.0818,0.0879,0.0929,0.0940,0.0960,0.0976,0.1074, 0.1088,0.1121,0.1135,0.1161,0.1188,0.1204,0.1245,0.1365,0.1431,0.1470, 0.1534,0.1594,0.1620,0.1629,0.1635,0.1711,0.1748,0.1872,0.1882,0.1925, 0.1943,0.1986,0.2002,0.2006,0.2035,0.2056,0.2083,0.2085,0.2154,0.2176, 0.2241,0.2371,0.2396,0.2411,0.2456,0.2470,0.2475,0.2696,0.2732,0.2777, 0.2810,0.2877,0.2902,0.2925,0.2984,0.2989,0.2997,0.3017,0.3074,0.3107, 0.3124,0.3243,0.3293,0.3367,0.3391,0.3436,0.3485,0.3517,0.3521,0.3631, 0.3636,0.3669,0.3712,0.3720,0.3724,0.3764,0.3792,0.3808,0.3893,0.3921, 0.3936,0.3983,0.3992,0.4003,0.4032,0.4041,0.4042,0.4108,0.4152,0.4159, 0.4191,0.4216,0.4244,0.4257,0.4271,0.4275,0.4275,0.4301,0.4317,0.4331, 0.4353,0.4455,0.4469,0.4509,0.4515,0.4606,0.4723,0.4773,0.4806,0.4853, 0.4860,0.4860,0.4865,0.4872,0.4912,0.4927,0.4946,0.4968,0.5082,0.5089, 0.5118,0.5144,0.5180,0.5245,0.5291,0.5302,0.5316,0.5346,0.5370,0.5387, 0.5391,0.5394,0.5418,0.5509,0.5566,0.5617,0.5705,0.5705,0.5710,0.5711, 0.5788,0.5790,0.5869,0.5872,0.6079,0.6082,0.6095,0.6229,0.6268,0.6323, 0.6364,0.6369,0.6372,0.6405,0.6422,0.6431,0.6583,0.6584,0.6595,0.6601, 0.6641,0.6711,0.6770,0.6812,0.6945,0.6961,0.6989,0.7029,0.7031,0.7081, 0.7101,0.7175,0.7186,0.7201,0.7323,0.7339,0.7387,0.7499,0.7552,0.7553, 0.7632,0.7646,0.7711,0.7734,0.7839,0.7856,0.7908,0.7930,0.7937,0.7957, 0.7990,0.8007,0.8176,0.8182,0.8231,0.8312,0.8390,0.8406,0.8424,0.8437, 0.8507,0.8593,0.8622,0.8631,0.8750,0.8756,0.8775,0.8789,0.8815,0.8879, 0.8903,0.8906,0.8970,0.9018,0.9077,0.9100,0.9101,0.9115,0.9138,0.9146, 0.9157,0.9246,0.9361,0.9385,0.9447,0.9539,0.9543,0.9589,0.9592,0.9638, 0.9736,0.9752,0.9812,0.9821,0.9834,0.9861,0.9912,0.9943,0.9981, Overall p-value after applying KStest on 269 p-values = 0.145026 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.