RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-14_05:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.79 26.1981 0.929074 2 to 25 15.72 18.5107 0.642673 3 to 26 15.82 20.1444 0.733089 4 to 27 15.92 9.9114 0.092715 5 to 28 15.70 17.4220 0.573849 6 to 29 15.70 21.3665 0.789676 7 to 30 15.73 16.6785 0.523656 8 to 31 15.73 20.3055 0.741097 9 to 32 15.68 12.2122 0.212881 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.579536 Tough bday spacings test for dh-ranFile-2016-04-14_05:31: 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 13 40 73 101 79 74 53 31 22 12 2 (O-E)^2/E 1.6 0.3 0.0 0.1 3.6 0.2 0.0 0.1 3.4 4.4 1.0 Birthday Spacings: Sum(O-E)^2/E= 14.728, p= 0.858 RESULTS OF GCD FOR dh-ranFile-2016-04-14_05:31 Euclid's algorithm: p-value, steps to gcd: 0.425257 p-value, dist. of gcd's: 0.112720 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-14_05:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.142 0.543 0.649 0.652 0.732 0.065 0.034 0.338 Bits 8 to 15---> 0.041 0.370 0.532 0.822 0.797 0.657 0.416 0.975 Bits 16 to 23---> 0.961 0.435 0.776 0.758 0.995 0.179 0.717 0.117 Bits 24 to 31---> 0.034 0.664 0.348 0.372 0.973 0.615 0.168 0.746 KS test for the above 32 p values: 0.324 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-14_05:31, p-values for 5 runs: 0.6846, 0.6569, 0.6603, 0.7971, 0.9764 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-14_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5087 5134.0 0.430 1.303 r= 30 23277 23103.0 1.310 2.613 r= 31 11411 11551.5 1.709 4.322 chi-square = 4.322 with df = 3; p-value = 0.771 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-14_05:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 226 211.4 1.006 1.006 r= 30 5206 5134.0 1.009 2.015 r= 31 23031 23103.0 0.225 2.240 r= 32 11537 11551.5 0.018 2.258 chi-square = 2.258 with df = 3; p-value = 0.479 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-14_05:31 b-rank test for bits 1 to 8, p=0.79892 b-rank test for bits 2 to 9, p=0.06875 b-rank test for bits 3 to 10, p=0.17972 b-rank test for bits 4 to 11, p=0.08940 b-rank test for bits 5 to 12, p=0.17106 b-rank test for bits 6 to 13, p=0.03720 b-rank test for bits 7 to 14, p=0.18064 b-rank test for bits 8 to 15, p=0.38975 b-rank test for bits 9 to 16, p=0.15419 b-rank test for bits 10 to 17, p=0.46359 b-rank test for bits 11 to 18, p=0.65438 b-rank test for bits 12 to 19, p=0.56735 b-rank test for bits 13 to 20, p=0.42046 b-rank test for bits 14 to 21, p=0.64117 b-rank test for bits 15 to 22, p=0.76779 b-rank test for bits 16 to 23, p=0.85682 b-rank test for bits 17 to 24, p=0.97736 b-rank test for bits 18 to 25, p=0.91202 b-rank test for bits 19 to 26, p=0.34573 b-rank test for bits 20 to 27, p=0.81516 b-rank test for bits 21 to 28, p=0.51925 b-rank test for bits 22 to 29, p=0.86752 b-rank test for bits 23 to 30, p=0.25047 b-rank test for bits 24 to 31, p=0.48804 b-rank test for bits 25 to 32, p=0.76858 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 = 0.996395 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-14_05:31 (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 141782 -0.30 0.383042 2 141298 -1.43 0.076597 3 141882 -0.06 0.474543 4 141588 -0.75 0.226395 5 141177 -1.71 0.043536 6 142252 0.80 0.788327 7 142060 0.35 0.637593 8 141736 -0.40 0.342747 9 142364 1.06 0.855953 10 141673 -0.55 0.290415 11 142045 0.32 0.624373 12 141428 -1.12 0.130379 13 141314 -1.39 0.082119 14 141794 -0.27 0.393787 15 141944 0.08 0.532281 16 142211 0.70 0.759544 17 141624 -0.67 0.252495 18 141696 -0.50 0.309089 19 141260 -1.52 0.064617 20 142336 1.00 0.840592 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-14_05:31 Bits used No. missing words z-score p-value 23 to 32 142061 0.5230 0.699513 22 to 31 142221 1.0747 0.858751 21 to 30 141760 -0.5149 0.303301 20 to 29 141616 -1.0115 0.155893 19 to 28 142073 0.5644 0.713752 18 to 27 142497 2.0264 0.978641 17 to 26 142031 0.4196 0.662594 16 to 25 141534 -1.2942 0.097791 15 to 24 142067 0.5437 0.706673 14 to 23 141764 -0.5011 0.308137 13 to 22 141398 -1.7632 0.038933 12 to 21 142600 2.3816 0.991382 11 to 20 141736 -0.5977 0.275024 10 to 19 141791 -0.4080 0.341624 9 to 18 141959 0.1713 0.567997 8 to 17 141991 0.2816 0.610883 7 to 16 141458 -1.5563 0.059817 6 to 15 141958 0.1678 0.566641 5 to 14 141790 -0.4115 0.340359 4 to 13 142153 0.8402 0.799614 3 to 12 141824 -0.2942 0.384287 2 to 11 141428 -1.6598 0.048482 1 to 10 141989 0.2747 0.608236 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-14_05:31 Bits used No. missing words z-score p-value 28 to 32 142089 0.6091 0.728755 27 to 31 141789 -0.4079 0.341674 26 to 30 142017 0.3650 0.642438 25 to 29 141741 -0.5706 0.284132 24 to 28 141838 -0.2418 0.404469 23 to 27 142121 0.7175 0.763475 22 to 26 141841 -0.2316 0.408414 21 to 25 141784 -0.4248 0.335474 20 to 24 142132 0.7548 0.774820 19 to 23 142432 1.7718 0.961783 18 to 22 141498 -1.3943 0.081608 17 to 21 141661 -0.8418 0.199951 16 to 20 141964 0.1853 0.573512 15 to 19 141464 -1.5096 0.065574 14 to 18 141746 -0.5537 0.289905 13 to 17 142068 0.5379 0.704665 12 to 16 141977 0.2294 0.590717 11 to 15 141775 -0.4554 0.324427 10 to 14 141852 -0.1943 0.422955 9 to 13 141796 -0.3842 0.350426 8 to 12 142040 0.4429 0.671099 7 to 11 142113 0.6904 0.755031 6 to 10 141808 -0.3435 0.365614 5 to 9 141633 -0.9367 0.174453 4 to 8 142010 0.3413 0.633544 3 to 7 141990 0.2735 0.607749 2 to 6 141741 -0.5706 0.284132 1 to 5 142177 0.9074 0.817891 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-14_05:31 Bits used No. missing words z-score p-value 31 to 32 141957 0.1406 0.555915 30 to 31 141954 0.1318 0.552417 29 to 30 142070 0.4740 0.682233 28 to 29 141615 -0.8682 0.192634 27 to 28 141569 -1.0039 0.157708 26 to 27 141988 0.2321 0.591756 25 to 26 142474 1.6657 0.952113 24 to 25 142171 0.7719 0.779910 23 to 24 142053 0.4238 0.664146 22 to 23 141832 -0.2281 0.409780 21 to 22 142044 0.3973 0.654411 20 to 21 141574 -0.9892 0.161289 19 to 20 141787 -0.3609 0.359104 18 to 19 142099 0.5595 0.712089 17 to 18 141653 -0.7561 0.224784 16 to 17 141943 0.0993 0.539559 15 to 16 142051 0.4179 0.661992 14 to 15 141740 -0.4995 0.308714 13 to 14 141760 -0.4405 0.329787 12 to 13 141834 -0.2222 0.412074 11 to 12 142272 1.0698 0.857651 10 to 11 141787 -0.3609 0.359104 9 to 10 141672 -0.7001 0.241936 8 to 9 141451 -1.3520 0.088187 7 to 8 142115 0.6067 0.727974 6 to 7 141922 0.0374 0.514907 5 to 6 142114 0.6037 0.726994 4 to 5 142201 0.8604 0.805211 3 to 4 141400 -1.5024 0.066491 2 to 3 142102 0.5683 0.715101 1 to 2 141791 -0.3491 0.363524 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-14_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2493.89 -0.086 0.465583 Test results for specific bytes for dh-ranFile-2016-04-14_05:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2535.92 0.508 0.694249 2 to 9 2570.14 0.992 0.839370 3 to 10 2493.40 -0.093 0.462797 4 to 11 2540.19 0.568 0.715123 5 to 12 2482.28 -0.251 0.401049 6 to 13 2347.17 -2.161 0.015333 7 to 14 2428.44 -1.012 0.155774 8 to 15 2409.00 -1.287 0.099058 9 to 16 2462.12 -0.536 0.296068 10 to 17 2602.46 1.449 0.926333 11 to 18 2473.97 -0.368 0.356379 12 to 19 2510.59 0.150 0.559505 13 to 20 2476.70 -0.329 0.370896 14 to 21 2390.06 -1.555 0.059992 15 to 22 2502.21 0.031 0.512477 16 to 23 2352.52 -2.086 0.018501 17 to 24 2531.91 0.451 0.674093 18 to 25 2422.00 -1.103 0.134999 19 to 26 2480.29 -0.279 0.390211 20 to 27 2553.60 0.758 0.775780 21 to 28 2425.23 -1.057 0.145148 22 to 29 2488.68 -0.160 0.436416 23 to 30 2550.72 0.717 0.763388 24 to 31 2429.49 -0.997 0.159350 25 to 32 2593.52 1.323 0.907007 CDPARK for dh-ranFile-2016-04-14_05:31: 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 3516 -0.3196 0.374623 3551 1.2785 0.899470 3498 -1.1416 0.126820 3499 -1.0959 0.136563 3509 -0.6393 0.261324 3548 1.1416 0.873180 3513 -0.4566 0.323972 3536 0.5936 0.723613 3532 0.4110 0.659449 3556 1.5068 0.934075 Square side=100, avg. no. parked=3525.80 sample std.=20.53 p-value of the KSTEST for those 10 p-values: 0.859316 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-14_05:31 0.3485,0.9730,0.3505,0.8819,0.1258,0.5667,0.8841,0.6898,0.0275,0.5507, The KS test for those 10 p-values: 0.896729 The 3DSPHERES test for dh-ranFile-2016-04-14_05:31 sample no r^3 equiv. uni. 1 65.511 0.887377 2 34.457 0.682913 3 0.895 0.029405 4 18.926 0.467863 5 37.424 0.712765 6 32.037 0.656273 7 34.393 0.682236 8 0.625 0.020602 9 30.170 0.634200 10 9.984 0.283093 11 7.718 0.226849 12 65.537 0.887473 13 20.658 0.497721 14 0.959 0.031471 15 4.505 0.139425 16 65.336 0.886718 17 12.543 0.341694 18 44.770 0.775153 19 13.130 0.354460 20 14.520 0.383678 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.772218 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-14_05:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 -0.6 -0.5 -0.5 0.8 -0.6 -0.6 -0.2 0.1 0.3 -0.8 -1.1 -0.2 1.0 1.6 -0.6 -0.6 -0.1 0.2 0.3 0.6 0.3 0.6 -0.5 0.4 -0.3 -1.9 -1.2 -0.3 1.0 1.6 -0.2 0.2 0.2 -2.1 0.5 -2.0 -0.8 -0.7 0.9 1.0 -0.1 Chi-square with 42 degrees of freedom:30.800295 z-score=-1.221988, p-value=0.100825 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-14_05:31 Test no p-value 1 0.743327 2 0.554806 3 0.231026 4 0.329254 5 0.027105 6 0.179743 7 0.119205 8 0.916685 9 0.960999 10 0.057881 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.345961 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-14_05:31: (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 66629 0.02 66765 0.15 3 25000.00 25056 0.13 24939 0.15 4 6666.67 6640 0.11 6666 0.00 5 1388.89 1378 0.09 1361 0.56 6 238.10 253 0.93 235 0.04 7 34.72 34 0.01 30 0.64 8 4.96 9 3.29 3 0.77 p=0.40097 p=0.11095 Number of rngs required: 688178, p-value: 0.398 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-14_05:31 No. of wins: Observed Expected 98517 98585.9 z-score=-0.308, pvalue=0.37905 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66442 66666.7 0.757 0.757 2 37511 37654.3 0.546 1.303 3 27032 26954.7 0.221 1.524 4 19398 19313.5 0.370 1.894 5 13969 13851.4 0.998 2.892 6 9987 9943.5 0.190 3.082 7 7183 7145.0 0.202 3.284 8 5140 5139.1 0.000 3.284 9 3754 3699.9 0.792 4.076 10 2675 2666.3 0.028 4.105 11 1922 1923.3 0.001 4.106 12 1342 1388.7 1.573 5.679 13 1001 1003.7 0.007 5.686 14 743 726.1 0.391 6.077 15 508 525.8 0.605 6.682 16 361 381.2 1.065 7.748 17 272 276.5 0.075 7.822 18 187 200.8 0.952 8.775 19 160 146.0 1.346 10.120 20 105 106.2 0.014 10.134 21 308 287.1 1.519 11.654 Chisq= 11.65 for 20 degrees of freedom, p= 0.07252 SUMMARY of craptest p-value for no. of wins: 0.379050 p-value for throws/game: 0.072515 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-14_05:31 No. of wins: Observed Expected 98812 98585.9 z-score= 1.011, pvalue=0.84410 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66686 66666.7 0.006 0.006 2 37505 37654.3 0.592 0.598 3 26979 26954.7 0.022 0.620 4 19317 19313.5 0.001 0.620 5 13928 13851.4 0.423 1.044 6 10038 9943.5 0.897 1.941 7 7070 7145.0 0.788 2.729 8 5058 5139.1 1.279 4.008 9 3750 3699.9 0.679 4.687 10 2713 2666.3 0.818 5.505 11 1950 1923.3 0.370 5.875 12 1409 1388.7 0.296 6.170 13 1028 1003.7 0.588 6.758 14 701 726.1 0.870 7.628 15 540 525.8 0.382 8.010 16 344 381.2 3.621 11.631 17 275 276.5 0.009 11.640 18 195 200.8 0.169 11.809 19 139 146.0 0.334 12.143 20 97 106.2 0.800 12.943 21 278 287.1 0.289 13.232 Chisq= 13.23 for 20 degrees of freedom, p= 0.13278 SUMMARY of craptest p-value for no. of wins: 0.844096 p-value for throws/game: 0.132784 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0153,0.0185,0.0206,0.0271,0.0275,0.0294,0.0315,0.0337,0.0338,0.0372, 0.0389,0.0406,0.0435,0.0485,0.0579,0.0598,0.0600,0.0646,0.0651,0.0656, 0.0665,0.0687,0.0725,0.0766,0.0816,0.0821,0.0882,0.0894,0.0927,0.0978, 0.0991,0.1008,0.1109,0.1127,0.1169,0.1192,0.1258,0.1268,0.1304,0.1328, 0.1350,0.1366,0.1394,0.1417,0.1451,0.1542,0.1558,0.1559,0.1577,0.1593, 0.1613,0.1676,0.1711,0.1745,0.1786,0.1797,0.1797,0.1806,0.1926,0.2000, 0.2129,0.2248,0.2264,0.2268,0.2310,0.2419,0.2505,0.2525,0.2613,0.2750, 0.2831,0.2841,0.2841,0.2899,0.2904,0.2961,0.3033,0.3081,0.3087,0.3091, 0.3239,0.3240,0.3244,0.3293,0.3298,0.3355,0.3380,0.3404,0.3416,0.3417, 0.3417,0.3427,0.3457,0.3460,0.3485,0.3485,0.3504,0.3505,0.3545,0.3564, 0.3591,0.3591,0.3635,0.3656,0.3703,0.3709,0.3723,0.3746,0.3791,0.3830, 0.3837,0.3843,0.3898,0.3902,0.3938,0.3978,0.4010,0.4010,0.4045,0.4084, 0.4098,0.4121,0.4160,0.4205,0.4230,0.4253,0.4348,0.4364,0.4628,0.4636, 0.4656,0.4679,0.4745,0.4794,0.4880,0.4977,0.5125,0.5149,0.5192,0.5237, 0.5315,0.5323,0.5396,0.5429,0.5507,0.5524,0.5548,0.5559,0.5595,0.5666, 0.5667,0.5673,0.5680,0.5735,0.5738,0.5795,0.5907,0.5918,0.6077,0.6082, 0.6109,0.6150,0.6244,0.6335,0.6342,0.6376,0.6412,0.6424,0.6427,0.6490, 0.6515,0.6544,0.6544,0.6563,0.6569,0.6574,0.6594,0.6603,0.6620,0.6626, 0.6639,0.6641,0.6711,0.6741,0.6822,0.6822,0.6829,0.6846,0.6898,0.6942, 0.6995,0.7047,0.7067,0.7121,0.7128,0.7138,0.7151,0.7151,0.7173,0.7236, 0.7270,0.7280,0.7288,0.7317,0.7331,0.7411,0.7433,0.7458,0.7550,0.7585, 0.7595,0.7634,0.7635,0.7678,0.7686,0.7713,0.7722,0.7748,0.7752,0.7758, 0.7764,0.7799,0.7883,0.7897,0.7971,0.7973,0.7989,0.7996,0.8052,0.8152, 0.8179,0.8218,0.8394,0.8406,0.8441,0.8560,0.8568,0.8577,0.8577,0.8588, 0.8593,0.8675,0.8732,0.8819,0.8841,0.8867,0.8874,0.8875,0.8967,0.8995, 0.9070,0.9120,0.9167,0.9263,0.9291,0.9341,0.9521,0.9607,0.9610,0.9618, 0.9730,0.9732,0.9747,0.9764,0.9774,0.9786,0.9914,0.9949,0.9964, Overall p-value after applying KStest on 269 p-values = 0.509740 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.