RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-01-25_21:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 15.0672 0.409357 2 to 25 15.89 12.9734 0.262032 3 to 26 15.70 16.7917 0.531435 4 to 27 15.65 21.6752 0.802465 5 to 28 15.83 20.9983 0.773634 6 to 29 15.51 19.6170 0.705711 7 to 30 15.71 14.6597 0.380022 8 to 31 15.71 20.2871 0.740191 9 to 32 15.58 21.9581 0.813664 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.273450 Tough bday spacings test for dh-ranFile-2017-01-25_21:31: 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 9 39 66 88 113 84 58 23 10 7 3 (O-E)^2/E 0.0 0.2 0.7 1.0 2.4 0.4 0.7 1.5 1.6 0.0 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.789, p= 0.448 RESULTS OF GCD FOR dh-ranFile-2017-01-25_21:31 Euclid's algorithm: p-value, steps to gcd: 0.417670 p-value, dist. of gcd's: 0.582060 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-01-25_21:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.846 0.899 0.154 0.198 0.844 0.150 0.539 0.754 Bits 8 to 15---> 0.481 0.274 0.008 0.437 0.758 0.425 0.478 0.311 Bits 16 to 23---> 0.860 0.826 0.069 0.948 0.192 0.129 0.074 0.535 Bits 24 to 31---> 0.366 0.471 0.280 0.935 0.521 0.838 0.709 0.149 KS test for the above 32 p values: 0.110 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-01-25_21:31, p-values for 5 runs: 0.6775, 0.8360, 0.0352, 0.6582, 0.1223 Rank test for binary matrices (31x31) for dh-ranFile-2017-01-25_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 219 211.4 0.272 0.272 r= 29 5122 5134.0 0.028 0.300 r= 30 23078 23103.0 0.027 0.327 r= 31 11581 11551.5 0.075 0.402 chi-square = 0.402 with df = 3; p-value = 0.060 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2017-01-25_21:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 208 211.4 0.055 0.055 r= 30 5205 5134.0 0.982 1.037 r= 31 23138 23103.0 0.053 1.090 r= 32 11449 11551.5 0.910 2.000 chi-square = 2.000 with df = 3; p-value = 0.428 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2017-01-25_21:31 b-rank test for bits 1 to 8, p=0.94488 b-rank test for bits 2 to 9, p=0.10539 b-rank test for bits 3 to 10, p=0.57814 b-rank test for bits 4 to 11, p=0.03880 b-rank test for bits 5 to 12, p=0.42936 b-rank test for bits 6 to 13, p=0.43101 b-rank test for bits 7 to 14, p=0.43638 b-rank test for bits 8 to 15, p=0.27554 b-rank test for bits 9 to 16, p=0.32100 b-rank test for bits 10 to 17, p=0.96956 b-rank test for bits 11 to 18, p=0.16815 b-rank test for bits 12 to 19, p=0.37319 b-rank test for bits 13 to 20, p=0.34548 b-rank test for bits 14 to 21, p=0.10737 b-rank test for bits 15 to 22, p=0.16398 b-rank test for bits 16 to 23, p=0.19935 b-rank test for bits 17 to 24, p=0.54485 b-rank test for bits 18 to 25, p=0.67020 b-rank test for bits 19 to 26, p=0.88878 b-rank test for bits 20 to 27, p=0.85211 b-rank test for bits 21 to 28, p=0.13375 b-rank test for bits 22 to 29, p=0.29560 b-rank test for bits 23 to 30, p=0.97167 b-rank test for bits 24 to 31, p=0.95135 b-rank test for bits 25 to 32, p=0.84459 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 = 0.538813 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-01-25_21:31 (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 141429 -1.12 0.130875 2 142093 0.43 0.666088 3 141913 0.01 0.503421 4 141761 -0.35 0.364459 5 141162 -1.75 0.040397 6 142021 0.26 0.602920 7 141510 -0.93 0.175406 8 141867 -0.10 0.460608 9 142316 0.95 0.828985 10 142519 1.42 0.922844 11 142235 0.76 0.776645 12 141347 -1.31 0.094447 13 142060 0.35 0.637593 14 141582 -0.76 0.222198 15 141223 -1.60 0.054404 16 142164 0.60 0.724086 17 142407 1.16 0.877541 18 142225 0.74 0.769605 19 142144 0.55 0.708255 20 141446 -1.08 0.139505 ---------------------------------------------------------------- OPSO test for dh-ranFile-2017-01-25_21:31 Bits used No. missing words z-score p-value 23 to 32 142086 0.6092 0.728806 22 to 31 141615 -1.0149 0.155069 21 to 30 141865 -0.1529 0.439254 20 to 29 141971 0.2127 0.584202 19 to 28 141603 -1.0563 0.145413 18 to 27 141939 0.1023 0.540745 17 to 26 141826 -0.2873 0.386924 16 to 25 141954 0.1540 0.561209 15 to 24 142037 0.4402 0.670119 14 to 23 141769 -0.4839 0.314230 13 to 22 141494 -1.4322 0.076047 12 to 21 141624 -0.9839 0.162583 11 to 20 142195 0.9851 0.837705 10 to 19 141890 -0.0667 0.473428 9 to 18 141913 0.0127 0.505049 8 to 17 141637 -0.9391 0.173848 7 to 16 141554 -1.2253 0.110236 6 to 15 141948 0.1333 0.553040 5 to 14 142263 1.2196 0.888683 4 to 13 142147 0.8196 0.793764 3 to 12 142064 0.5333 0.703103 2 to 11 141941 0.1092 0.543481 1 to 10 141868 -0.1425 0.443336 ----------------------------------------------------------------- OQSO test for dh-ranFile-2017-01-25_21:31 Bits used No. missing words z-score p-value 28 to 32 141620 -0.9808 0.163351 27 to 31 142095 0.6294 0.735453 26 to 30 141731 -0.6045 0.272753 25 to 29 141568 -1.1571 0.123626 24 to 28 141667 -0.8215 0.205693 23 to 27 142087 0.6023 0.726503 22 to 26 141759 -0.5096 0.305168 21 to 25 142074 0.5582 0.711647 20 to 24 141872 -0.1265 0.449651 19 to 23 142330 1.4260 0.923066 18 to 22 142149 0.8124 0.791731 17 to 21 142021 0.3785 0.647486 16 to 20 141909 -0.0011 0.499554 15 to 19 141511 -1.3503 0.088465 14 to 18 142000 0.3074 0.620714 13 to 17 142294 1.3040 0.903877 12 to 16 141555 -1.2011 0.114853 11 to 15 141936 0.0904 0.536018 10 to 14 141522 -1.3130 0.094594 9 to 13 141689 -0.7469 0.227568 8 to 12 141436 -1.6045 0.054301 7 to 11 141822 -0.2960 0.383602 6 to 10 141700 -0.7096 0.238978 5 to 9 141803 -0.3604 0.359259 4 to 8 141806 -0.3503 0.363068 3 to 7 141882 -0.0926 0.463093 2 to 6 142120 0.7141 0.762428 1 to 5 141909 -0.0011 0.499554 ----------------------------------------------------------------- DNA test for dh-ranFile-2017-01-25_21:31 Bits used No. missing words z-score p-value 31 to 32 142149 0.7070 0.760214 30 to 31 141815 -0.2783 0.390407 29 to 30 141845 -0.1898 0.424747 28 to 29 141751 -0.4671 0.320232 27 to 28 141559 -1.0334 0.150703 26 to 27 141546 -1.0718 0.141912 25 to 26 141702 -0.6116 0.270404 24 to 25 142745 2.4651 0.993151 23 to 24 141685 -0.6617 0.254069 22 to 23 141970 0.1790 0.571018 21 to 22 142502 1.7483 0.959793 20 to 21 141862 -0.1396 0.444482 19 to 20 141889 -0.0600 0.476090 18 to 19 141921 0.0344 0.513731 17 to 18 141729 -0.5319 0.297381 16 to 17 141802 -0.3166 0.375771 15 to 16 141887 -0.0659 0.473741 14 to 15 142167 0.7601 0.776399 13 to 14 142304 1.1642 0.877832 12 to 13 141796 -0.3343 0.369074 11 to 12 141804 -0.3107 0.378011 10 to 11 141665 -0.7207 0.235536 9 to 10 142174 0.7807 0.782522 8 to 9 142080 0.5035 0.692677 7 to 8 142006 0.2852 0.612240 6 to 7 142009 0.2940 0.615626 5 to 6 142493 1.7217 0.957442 4 to 5 142046 0.4032 0.656583 3 to 4 141910 0.0020 0.500789 2 to 3 142429 1.5329 0.937356 1 to 2 142251 1.0079 0.843243 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2017-01-25_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2634.45 1.901 0.971376 Test results for specific bytes for dh-ranFile-2017-01-25_21:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2436.74 -0.895 0.185495 2 to 9 2534.31 0.485 0.686256 3 to 10 2536.39 0.515 0.696577 4 to 11 2531.52 0.446 0.672103 5 to 12 2572.30 1.023 0.846731 6 to 13 2570.00 0.990 0.838913 7 to 14 2651.48 2.142 0.983913 8 to 15 2584.60 1.196 0.884239 9 to 16 2615.69 1.636 0.949086 10 to 17 2521.41 0.303 0.618972 11 to 18 2498.78 -0.017 0.493104 12 to 19 2615.52 1.634 0.948845 13 to 20 2499.00 -0.014 0.494368 14 to 21 2544.23 0.626 0.734184 15 to 22 2384.89 -1.628 0.051779 16 to 23 2518.57 0.263 0.603591 17 to 24 2567.93 0.961 0.831645 18 to 25 2452.63 -0.670 0.251477 19 to 26 2552.87 0.748 0.772696 20 to 27 2457.27 -0.604 0.272830 21 to 28 2474.54 -0.360 0.359400 22 to 29 2548.87 0.691 0.755256 23 to 30 2432.99 -0.948 0.171646 24 to 31 2446.71 -0.754 0.225548 25 to 32 2637.65 1.947 0.974214 CDPARK for dh-ranFile-2017-01-25_21:31: 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 3522 -0.0457 0.481790 3537 0.6393 0.738676 3522 -0.0457 0.481790 3522 -0.0457 0.481790 3505 -0.8219 0.205562 3530 0.3196 0.625377 3526 0.1370 0.554479 3510 -0.5936 0.276387 3476 -2.1461 0.015932 3528 0.2283 0.590298 Square side=100, avg. no. parked=3517.80 sample std.=16.47 p-value of the KSTEST for those 10 p-values: 0.383855 Results for the MINIMUM DISTANCE test for dh-ranFile-2017-01-25_21:31 0.5927,0.0956,0.1183,0.4518,0.0486,0.0345,0.4722,0.0108,0.1312,0.8014, The KS test for those 10 p-values: 0.009088 The 3DSPHERES test for dh-ranFile-2017-01-25_21:31 sample no r^3 equiv. uni. 1 4.252 0.132136 2 6.468 0.193942 3 11.224 0.312122 4 14.900 0.391448 5 23.632 0.545130 6 54.085 0.835171 7 19.165 0.472096 8 32.020 0.656078 9 52.769 0.827779 10 29.874 0.630569 11 28.014 0.606945 12 33.749 0.675339 13 16.407 0.421263 14 35.041 0.689024 15 21.172 0.506252 16 1.410 0.045898 17 29.133 0.621337 18 49.011 0.804795 19 214.356 0.999211 20 3.105 0.098312 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.659046 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-01-25_21:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 1.3 0.1 -0.1 0.9 2.5 1.1 -0.2 0.8 0.3 -0.8 -0.6 -0.8 0.3 0.9 0.2 0.5 -0.2 0.2 1.3 -0.8 -1.1 -1.0 0.2 -0.1 -0.5 -0.1 -0.6 -0.7 0.5 1.5 0.8 0.2 0.3 -0.3 0.9 -1.4 -1.2 -1.3 -0.8 1.0 -0.6 3.0 0.8 Chi-square with 42 degrees of freedom:40.535884 z-score=-0.159748, p-value=0.464696 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2017-01-25_21:31 Test no p-value 1 0.414361 2 0.262291 3 0.283766 4 0.721129 5 0.987631 6 0.130073 7 0.871609 8 0.200098 9 0.150517 10 0.008568 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.293408 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-01-25_21:31: (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 66673 0.00 66539 0.24 3 25000.00 25059 0.14 24964 0.05 4 6666.67 6636 0.14 6774 1.73 5 1388.89 1367 0.35 1422 0.79 6 238.10 230 0.28 253 0.93 7 34.72 33 0.09 39 0.53 8 4.96 1 3.16 8 1.86 p=0.34334 p=0.59203 Number of rngs required: 688949, p-value: 0.736 RESULTS OF CRAPS TEST for dh-ranFile-2017-01-25_21:31 No. of wins: Observed Expected 98506 98585.9 z-score=-0.357, pvalue=0.36048 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66424 66666.7 0.883 0.883 2 37661 37654.3 0.001 0.884 3 26926 26954.7 0.031 0.915 4 19328 19313.5 0.011 0.926 5 13968 13851.4 0.981 1.907 6 9787 9943.5 2.464 4.372 7 7104 7145.0 0.236 4.607 8 5151 5139.1 0.028 4.635 9 3743 3699.9 0.503 5.138 10 2725 2666.3 1.292 6.430 11 2023 1923.3 5.165 11.595 12 1359 1388.7 0.637 12.232 13 1042 1003.7 1.460 13.693 14 783 726.1 4.452 18.145 15 544 525.8 0.627 18.772 16 399 381.2 0.836 19.608 17 290 276.5 0.655 20.263 18 192 200.8 0.388 20.652 19 171 146.0 4.287 24.938 20 99 106.2 0.490 25.428 21 281 287.1 0.130 25.559 Chisq= 25.56 for 20 degrees of freedom, p= 0.81911 SUMMARY of craptest p-value for no. of wins: 0.360481 p-value for throws/game: 0.819113 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2017-01-25_21:31 No. of wins: Observed Expected 98881 98585.9 z-score= 1.320, pvalue=0.90659 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66454 66666.7 0.678 0.678 2 37776 37654.3 0.393 1.072 3 26974 26954.7 0.014 1.085 4 19233 19313.5 0.335 1.421 5 13868 13851.4 0.020 1.440 6 10093 9943.5 2.246 3.687 7 7049 7145.0 1.291 4.977 8 5189 5139.1 0.485 5.462 9 3628 3699.9 1.396 6.858 10 2629 2666.3 0.522 7.380 11 2019 1923.3 4.759 12.139 12 1388 1388.7 0.000 12.139 13 1034 1003.7 0.914 13.053 14 734 726.1 0.085 13.138 15 546 525.8 0.773 13.911 16 360 381.2 1.174 15.085 17 276 276.5 0.001 15.086 18 190 200.8 0.584 15.670 19 174 146.0 5.376 21.047 20 107 106.2 0.006 21.052 21 279 287.1 0.229 21.282 Chisq= 21.28 for 20 degrees of freedom, p= 0.61928 SUMMARY of craptest p-value for no. of wins: 0.906590 p-value for throws/game: 0.619280 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0079,0.0086,0.0091,0.0108,0.0159,0.0345,0.0352,0.0388,0.0404,0.0459, 0.0486,0.0518,0.0543,0.0544,0.0602,0.0689,0.0743,0.0760,0.0885,0.0944, 0.0946,0.0956,0.0983,0.1054,0.1074,0.1096,0.1102,0.1149,0.1183,0.1223, 0.1236,0.1290,0.1301,0.1309,0.1312,0.1321,0.1338,0.1395,0.1419,0.1454, 0.1493,0.1497,0.1505,0.1507,0.1538,0.1551,0.1626,0.1634,0.1640,0.1682, 0.1716,0.1738,0.1754,0.1855,0.1923,0.1939,0.1981,0.1994,0.2001,0.2056, 0.2057,0.2222,0.2255,0.2276,0.2355,0.2390,0.2515,0.2541,0.2620,0.2623, 0.2704,0.2728,0.2728,0.2735,0.2744,0.2755,0.2764,0.2803,0.2838,0.2934, 0.2956,0.2974,0.3052,0.3107,0.3121,0.3142,0.3202,0.3210,0.3433,0.3455, 0.3593,0.3594,0.3605,0.3631,0.3645,0.3657,0.3691,0.3732,0.3758,0.3780, 0.3800,0.3836,0.3839,0.3869,0.3904,0.3914,0.4094,0.4144,0.4177,0.4213, 0.4247,0.4247,0.4275,0.4294,0.4310,0.4364,0.4369,0.4393,0.4433,0.4445, 0.4478,0.4497,0.4518,0.4606,0.4631,0.4647,0.4712,0.4721,0.4722,0.4734, 0.4737,0.4761,0.4780,0.4810,0.4818,0.4818,0.4818,0.4931,0.4944,0.4996, 0.4996,0.5008,0.5034,0.5050,0.5063,0.5137,0.5214,0.5314,0.5350,0.5360, 0.5385,0.5388,0.5407,0.5435,0.5448,0.5451,0.5530,0.5545,0.5612,0.5710, 0.5781,0.5821,0.5842,0.5903,0.5920,0.5927,0.6029,0.6036,0.6069,0.6122, 0.6156,0.6190,0.6193,0.6207,0.6213,0.6254,0.6306,0.6376,0.6475,0.6561, 0.6566,0.6582,0.6590,0.6661,0.6701,0.6702,0.6721,0.6753,0.6775,0.6863, 0.6890,0.6927,0.6966,0.7031,0.7057,0.7083,0.7086,0.7116,0.7211,0.7241, 0.7265,0.7288,0.7342,0.7355,0.7356,0.7387,0.7402,0.7543,0.7553,0.7583, 0.7602,0.7624,0.7696,0.7727,0.7736,0.7764,0.7766,0.7825,0.7917,0.7938, 0.8014,0.8025,0.8048,0.8137,0.8191,0.8256,0.8278,0.8290,0.8316,0.8352, 0.8360,0.8377,0.8384,0.8389,0.8432,0.8439,0.8446,0.8458,0.8467,0.8521, 0.8598,0.8716,0.8775,0.8778,0.8842,0.8887,0.8888,0.8987,0.9039,0.9066, 0.9228,0.9231,0.9354,0.9374,0.9449,0.9477,0.9488,0.9491,0.9513,0.9574, 0.9598,0.9696,0.9714,0.9717,0.9742,0.9839,0.9876,0.9932,0.9992, Overall p-value after applying KStest on 269 p-values = 0.730420 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.