RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-10-16_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 16.11 13.8861 0.324850 2 to 25 15.82 10.5525 0.121139 3 to 26 15.60 21.0713 0.776883 4 to 27 15.90 21.0985 0.778084 5 to 28 15.74 12.0643 0.203770 6 to 29 15.98 14.8476 0.393541 7 to 30 15.61 23.0598 0.852685 8 to 31 15.94 24.5386 0.894477 9 to 32 16.04 16.7395 0.527858 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.900798 Tough bday spacings test for dh-ranFile-2016-10-16_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 11 45 76 104 98 60 38 41 15 7 5 (O-E)^2/E 0.4 1.9 0.1 0.4 0.0 4.2 3.8 4.2 0.0 0.0 0.2 Birthday Spacings: Sum(O-E)^2/E= 15.297, p= 0.878 RESULTS OF GCD FOR dh-ranFile-2016-10-16_09:31 Euclid's algorithm: p-value, steps to gcd: 0.424105 p-value, dist. of gcd's: 0.931911 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-10-16_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.244 0.430 0.579 0.173 0.294 0.703 0.300 0.914 Bits 8 to 15---> 0.193 0.971 0.779 0.559 0.051 0.442 0.620 0.037 Bits 16 to 23---> 0.113 0.468 0.712 0.679 0.773 0.398 0.133 0.000 Bits 24 to 31---> 0.636 0.438 0.765 0.357 0.186 0.008 0.520 0.375 KS test for the above 32 p values: 0.746 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-10-16_09:31, p-values for 5 runs: 0.7649, 0.3585, 0.7151, 0.1603, 0.5903 Rank test for binary matrices (31x31) for dh-ranFile-2016-10-16_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 216 211.4 0.099 0.099 r= 29 5170 5134.0 0.252 0.352 r= 30 23157 23103.0 0.126 0.478 r= 31 11457 11551.5 0.773 1.251 chi-square = 1.251 with df = 3; p-value = 0.259 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-10-16_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 225 211.4 0.873 0.873 r= 30 5085 5134.0 0.468 1.340 r= 31 23122 23103.0 0.016 1.356 r= 32 11568 11551.5 0.024 1.379 chi-square = 1.379 with df = 3; p-value = 0.290 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-10-16_09:31 b-rank test for bits 1 to 8, p=0.43734 b-rank test for bits 2 to 9, p=0.26703 b-rank test for bits 3 to 10, p=0.43376 b-rank test for bits 4 to 11, p=0.56345 b-rank test for bits 5 to 12, p=0.44461 b-rank test for bits 6 to 13, p=0.38603 b-rank test for bits 7 to 14, p=0.87462 b-rank test for bits 8 to 15, p=0.26168 b-rank test for bits 9 to 16, p=0.97978 b-rank test for bits 10 to 17, p=0.69401 b-rank test for bits 11 to 18, p=0.00849 b-rank test for bits 12 to 19, p=0.95355 b-rank test for bits 13 to 20, p=0.70831 b-rank test for bits 14 to 21, p=0.85570 b-rank test for bits 15 to 22, p=0.34460 b-rank test for bits 16 to 23, p=0.07355 b-rank test for bits 17 to 24, p=0.54966 b-rank test for bits 18 to 25, p=0.68182 b-rank test for bits 19 to 26, p=0.96496 b-rank test for bits 20 to 27, p=0.50568 b-rank test for bits 21 to 28, p=0.85702 b-rank test for bits 22 to 29, p=0.40226 b-rank test for bits 23 to 30, p=0.42414 b-rank test for bits 24 to 31, p=0.56736 b-rank test for bits 25 to 32, p=0.51814 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 = 0.399702 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-10-16_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 141417 -1.15 0.125009 2 141396 -1.20 0.115192 3 141780 -0.30 0.381260 4 141817 -0.22 0.414601 5 142156 0.58 0.717805 6 142041 0.31 0.620822 7 141197 -1.66 0.048024 8 140945 -2.25 0.012126 9 142018 0.25 0.600214 10 142017 0.25 0.599312 11 141987 0.18 0.572001 12 142391 1.13 0.869790 13 142597 1.61 0.945941 14 141540 -0.86 0.194091 15 141938 0.07 0.526704 16 141748 -0.38 0.353109 17 142448 1.26 0.895908 18 142415 1.18 0.881292 19 141047 -2.01 0.021963 20 142564 1.53 0.936942 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-10-16_09:31 Bits used No. missing words z-score p-value 23 to 32 141793 -0.4011 0.344159 22 to 31 141911 0.0058 0.502297 21 to 30 141872 -0.1287 0.448788 20 to 29 142511 2.0747 0.980994 19 to 28 142413 1.7368 0.958788 18 to 27 141320 -2.0322 0.021068 17 to 26 141564 -1.1908 0.116867 16 to 25 142071 0.5575 0.711401 15 to 24 142173 0.9092 0.818380 14 to 23 141769 -0.4839 0.314230 13 to 22 141578 -1.1425 0.126620 12 to 21 142333 1.4609 0.927983 11 to 20 142181 0.9368 0.825568 10 to 19 142012 0.3540 0.638344 9 to 18 141916 0.0230 0.509175 8 to 17 142184 0.9471 0.828216 7 to 16 142481 1.9713 0.975654 6 to 15 141937 0.0954 0.538007 5 to 14 142467 1.9230 0.972760 4 to 13 142062 0.5264 0.700712 3 to 12 142549 2.2058 0.986300 2 to 11 141793 -0.4011 0.344159 1 to 10 142353 1.5299 0.936979 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-10-16_09:31 Bits used No. missing words z-score p-value 28 to 32 141678 -0.7842 0.216470 27 to 31 141976 0.2260 0.589399 26 to 30 142375 1.5785 0.942779 25 to 29 141064 -2.8655 0.002082 24 to 28 142339 1.4565 0.927374 23 to 27 142329 1.4226 0.922575 22 to 26 141746 -0.5537 0.289905 21 to 25 141728 -0.6147 0.269384 20 to 24 142461 1.8701 0.969263 19 to 23 142201 0.9887 0.838598 18 to 22 142265 1.2057 0.886026 17 to 21 141890 -0.0655 0.473878 16 to 20 142152 0.8226 0.794635 15 to 19 141980 0.2396 0.594664 14 to 18 141940 0.1040 0.541402 13 to 17 141750 -0.5401 0.294564 12 to 16 141882 -0.0926 0.463093 11 to 15 141917 0.0260 0.510371 10 to 14 141487 -1.4316 0.076125 9 to 13 142321 1.3955 0.918566 8 to 12 142153 0.8260 0.795598 7 to 11 142750 2.8497 0.997812 6 to 10 141792 -0.3977 0.345415 5 to 9 142014 0.3548 0.638635 4 to 8 141913 0.0124 0.504963 3 to 7 142048 0.4701 0.680847 2 to 6 141886 -0.0791 0.468483 1 to 5 142344 1.4735 0.929686 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-10-16_09:31 Bits used No. missing words z-score p-value 31 to 32 141675 -0.6912 0.244708 30 to 31 142073 0.4828 0.685382 29 to 30 142075 0.4887 0.687474 28 to 29 141775 -0.3963 0.345959 27 to 28 141505 -1.1927 0.116491 26 to 27 142174 0.7807 0.782522 25 to 26 142025 0.3412 0.633527 24 to 25 141766 -0.4228 0.336220 23 to 24 141863 -0.1367 0.445647 22 to 23 142428 1.5300 0.936992 21 to 22 141838 -0.2104 0.416673 20 to 21 141965 0.1642 0.565220 19 to 20 141706 -0.5998 0.274322 18 to 19 141437 -1.3933 0.081764 17 to 18 141965 0.1642 0.565220 16 to 17 141791 -0.3491 0.363524 15 to 16 142064 0.4563 0.675896 14 to 15 142386 1.4061 0.920154 13 to 14 141149 -2.2429 0.012453 12 to 13 141532 -1.1131 0.132840 11 to 12 141873 -0.1072 0.457328 10 to 11 142149 0.7070 0.760214 9 to 10 141777 -0.3904 0.348137 8 to 9 141934 0.0728 0.529007 7 to 8 141877 -0.0954 0.462011 6 to 7 142485 1.6981 0.955259 5 to 6 142879 2.8604 0.997884 4 to 5 142191 0.8309 0.796981 3 to 4 142009 0.2940 0.615626 2 to 3 141932 0.0669 0.526659 1 to 2 142160 0.7394 0.770180 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-10-16_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2522.77 0.322 0.626259 Test results for specific bytes for dh-ranFile-2016-10-16_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2553.23 0.753 0.774194 2 to 9 2594.50 1.336 0.909285 3 to 10 2597.59 1.380 0.916219 4 to 11 2534.40 0.486 0.686694 5 to 12 2329.88 -2.406 0.008069 6 to 13 2505.75 0.081 0.532421 7 to 14 2505.14 0.073 0.528989 8 to 15 2436.12 -0.903 0.183150 9 to 16 2483.59 -0.232 0.408249 10 to 17 2372.93 -1.797 0.036169 11 to 18 2533.03 0.467 0.679799 12 to 19 2510.34 0.146 0.558137 13 to 20 2370.82 -1.827 0.033863 14 to 21 2435.55 -0.912 0.181011 15 to 22 2481.05 -0.268 0.394375 16 to 23 2495.30 -0.066 0.473519 17 to 24 2425.39 -1.055 0.145679 18 to 25 2519.56 0.277 0.608968 19 to 26 2399.73 -1.418 0.078088 20 to 27 2507.23 0.102 0.540694 21 to 28 2636.41 1.929 0.973144 22 to 29 2481.51 -0.261 0.396880 23 to 30 2629.51 1.831 0.966486 24 to 31 2606.02 1.499 0.933110 25 to 32 2435.64 -0.910 0.181349 CDPARK for dh-ranFile-2016-10-16_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 3538 0.6849 0.753306 3511 -0.5479 0.291865 3524 0.0457 0.518210 3531 0.3653 0.642555 3514 -0.4110 0.340551 3513 -0.4566 0.323972 3532 0.4110 0.659449 3518 -0.2283 0.409702 3529 0.2740 0.607947 3502 -0.9589 0.168804 Square side=100, avg. no. parked=3521.20 sample std.=10.80 p-value of the KSTEST for those 10 p-values: 0.424062 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-10-16_09:31 0.7452,0.8510,0.2277,0.5327,0.9224,0.2737,0.5146,0.1712,0.0612,0.7566, The KS test for those 10 p-values: 0.993451 The 3DSPHERES test for dh-ranFile-2016-10-16_09:31 sample no r^3 equiv. uni. 1 46.276 0.786158 2 36.334 0.702142 3 2.994 0.094996 4 0.572 0.018873 5 2.124 0.068351 6 47.140 0.792229 7 71.738 0.908487 8 44.725 0.774819 9 119.313 0.981260 10 142.289 0.991287 11 6.755 0.201626 12 16.602 0.425010 13 3.632 0.114025 14 6.674 0.199462 15 116.030 0.979093 16 49.977 0.810982 17 11.434 0.316907 18 85.214 0.941602 19 53.417 0.831459 20 7.093 0.210562 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.094741 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-10-16_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.6 0.5 -0.1 1.2 -0.6 -0.5 0.4 -1.1 -1.6 0.1 0.2 -0.4 1.6 1.8 0.2 -1.2 -0.7 -0.7 1.0 -0.1 0.4 -1.9 0.9 -1.3 0.9 1.5 -0.4 -0.1 1.9 0.3 -1.0 -0.5 -0.8 0.1 -0.2 -0.4 -1.6 -1.3 -0.6 0.0 0.8 Chi-square with 42 degrees of freedom:36.614419 z-score=-0.587615, p-value=0.294195 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-10-16_09:31 Test no p-value 1 0.209795 2 0.092663 3 0.487154 4 0.766163 5 0.432164 6 0.248196 7 0.330201 8 0.778775 9 0.157540 10 0.435122 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.342816 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-10-16_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 66836 0.43 66597 0.07 3 25000.00 24619 5.81 24972 0.03 4 6666.67 6880 6.83 6733 0.66 5 1388.89 1382 0.03 1403 0.14 6 238.10 239 0.00 253 0.93 7 34.72 37 0.15 37 0.15 8 4.96 6 0.22 4 0.19 p=0.96383 p=0.09718 Number of rngs required: 688862, p-value: 0.702 RESULTS OF CRAPS TEST for dh-ranFile-2016-10-16_09:31 No. of wins: Observed Expected 98768 98585.9 z-score= 0.815, pvalue=0.79236 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 67029 66666.7 1.969 1.969 2 37496 37654.3 0.666 2.635 3 27210 26954.7 2.417 5.052 4 19215 19313.5 0.502 5.554 5 13805 13851.4 0.156 5.710 6 9811 9943.5 1.767 7.477 7 7191 7145.0 0.296 7.772 8 5082 5139.1 0.634 8.406 9 3685 3699.9 0.060 8.466 10 2544 2666.3 5.610 14.076 11 1879 1923.3 1.022 15.097 12 1335 1388.7 2.080 17.177 13 972 1003.7 1.002 18.179 14 766 726.1 2.188 20.367 15 531 525.8 0.051 20.418 16 377 381.2 0.045 20.463 17 277 276.5 0.001 20.464 18 190 200.8 0.584 21.048 19 173 146.0 4.999 26.047 20 114 106.2 0.571 26.618 21 318 287.1 3.323 29.940 Chisq= 29.94 for 20 degrees of freedom, p= 0.92917 SUMMARY of craptest p-value for no. of wins: 0.792362 p-value for throws/game: 0.929171 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-10-16_09:31 No. of wins: Observed Expected 98011 98585.9 z-score=-2.571, pvalue=0.00507 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66206 66666.7 3.183 3.183 2 37626 37654.3 0.021 3.205 3 27177 26954.7 1.833 5.037 4 19264 19313.5 0.127 5.164 5 14039 13851.4 2.540 7.704 6 9980 9943.5 0.134 7.838 7 7066 7145.0 0.874 8.712 8 5132 5139.1 0.010 8.722 9 3757 3699.9 0.882 9.604 10 2753 2666.3 2.819 12.423 11 1913 1923.3 0.055 12.479 12 1403 1388.7 0.146 12.625 13 1015 1003.7 0.127 12.752 14 723 726.1 0.014 12.766 15 541 525.8 0.437 13.203 16 383 381.2 0.009 13.212 17 268 276.5 0.264 13.476 18 185 200.8 1.248 14.723 19 153 146.0 0.337 15.061 20 126 106.2 3.685 18.746 21 290 287.1 0.029 18.775 Chisq= 18.77 for 20 degrees of freedom, p= 0.46351 SUMMARY of craptest p-value for no. of wins: 0.005069 p-value for throws/game: 0.463506 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0021,0.0051,0.0081,0.0083,0.0085,0.0121,0.0125,0.0189,0.0211, 0.0220,0.0339,0.0362,0.0372,0.0480,0.0507,0.0612,0.0684,0.0735,0.0761, 0.0781,0.0818,0.0927,0.0947,0.0950,0.0972,0.1134,0.1140,0.1152,0.1165, 0.1169,0.1211,0.1250,0.1266,0.1328,0.1329,0.1457,0.1575,0.1603,0.1688, 0.1712,0.1733,0.1810,0.1813,0.1831,0.1856,0.1931,0.1941,0.1995,0.2016, 0.2038,0.2098,0.2106,0.2165,0.2277,0.2439,0.2447,0.2482,0.2592,0.2617, 0.2670,0.2694,0.2737,0.2743,0.2896,0.2899,0.2919,0.2941,0.2942,0.2946, 0.2998,0.3142,0.3169,0.3240,0.3249,0.3302,0.3362,0.3406,0.3428,0.3442, 0.3442,0.3446,0.3454,0.3460,0.3481,0.3531,0.3571,0.3585,0.3635,0.3751, 0.3813,0.3860,0.3935,0.3944,0.3969,0.3977,0.3997,0.4023,0.4082,0.4097, 0.4146,0.4167,0.4241,0.4241,0.4241,0.4250,0.4298,0.4322,0.4338,0.4351, 0.4373,0.4380,0.4420,0.4446,0.4456,0.4488,0.4573,0.4620,0.4631,0.4635, 0.4681,0.4685,0.4735,0.4739,0.4872,0.5023,0.5050,0.5057,0.5092,0.5104, 0.5146,0.5181,0.5182,0.5199,0.5267,0.5267,0.5279,0.5290,0.5290,0.5324, 0.5327,0.5380,0.5407,0.5414,0.5497,0.5581,0.5590,0.5635,0.5652,0.5652, 0.5674,0.5720,0.5794,0.5894,0.5903,0.5947,0.5993,0.6002,0.6079,0.6090, 0.6156,0.6196,0.6208,0.6263,0.6335,0.6355,0.6383,0.6386,0.6426,0.6594, 0.6759,0.6789,0.6798,0.6808,0.6818,0.6854,0.6867,0.6875,0.6940,0.7007, 0.7016,0.7021,0.7032,0.7083,0.7114,0.7121,0.7151,0.7178,0.7452,0.7461, 0.7533,0.7566,0.7602,0.7647,0.7649,0.7662,0.7702,0.7733,0.7742,0.7748, 0.7769,0.7781,0.7788,0.7795,0.7825,0.7862,0.7922,0.7924,0.7946,0.7956, 0.7970,0.8110,0.8184,0.8256,0.8282,0.8315,0.8386,0.8510,0.8527,0.8557, 0.8570,0.8698,0.8746,0.8784,0.8813,0.8860,0.8945,0.8959,0.9008,0.9085, 0.9093,0.9137,0.9162,0.9186,0.9202,0.9224,0.9226,0.9274,0.9280,0.9292, 0.9297,0.9319,0.9331,0.9369,0.9370,0.9370,0.9416,0.9428,0.9459,0.9536, 0.9553,0.9588,0.9638,0.9650,0.9665,0.9693,0.9708,0.9728,0.9731,0.9757, 0.9791,0.9798,0.9810,0.9813,0.9863,0.9913,0.9935,0.9978,0.9979, Overall p-value after applying KStest on 269 p-values = 0.133558 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.