RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-08_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.62 15.3190 0.427485 2 to 25 15.76 24.2029 0.885974 3 to 26 16.12 21.6426 0.801145 4 to 27 15.94 14.5617 0.372981 5 to 28 15.92 15.9194 0.470444 6 to 29 15.73 21.8804 0.810637 7 to 30 15.75 25.3317 0.912472 8 to 31 15.90 22.6054 0.837455 9 to 32 16.09 12.4573 0.228309 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.195574 Tough bday spacings test for dh-ranFile-2016-06-08_18:31: 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 8 38 92 99 89 66 44 32 16 11 5 (O-E)^2/E 0.1 0.1 4.8 0.0 0.8 1.9 1.3 0.2 0.1 2.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 12.297, p= 0.734 RESULTS OF GCD FOR dh-ranFile-2016-06-08_18:31 Euclid's algorithm: p-value, steps to gcd: 0.332637 p-value, dist. of gcd's: 0.434192 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-08_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.910 0.313 0.281 0.962 0.745 0.541 0.171 0.845 Bits 8 to 15---> 0.320 0.522 0.235 0.195 0.672 0.837 0.729 0.595 Bits 16 to 23---> 0.044 0.199 0.463 0.454 0.930 0.508 0.108 0.819 Bits 24 to 31---> 0.060 0.507 0.519 0.384 0.746 0.636 0.539 0.196 KS test for the above 32 p values: 0.047 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-08_18:31, p-values for 5 runs: 0.4465, 0.2524, 0.6104, 0.3736, 0.8516 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-08_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 212 211.4 0.002 0.002 r= 29 5106 5134.0 0.153 0.154 r= 30 23048 23103.0 0.131 0.286 r= 31 11634 11551.5 0.589 0.874 chi-square = 0.874 with df = 3; p-value = 0.168 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-08_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5097 5134.0 0.267 0.472 r= 31 23141 23103.0 0.062 0.534 r= 32 11544 11551.5 0.005 0.539 chi-square = 0.539 with df = 3; p-value = 0.090 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-08_18:31 b-rank test for bits 1 to 8, p=0.12396 b-rank test for bits 2 to 9, p=0.11375 b-rank test for bits 3 to 10, p=0.63867 b-rank test for bits 4 to 11, p=0.79599 b-rank test for bits 5 to 12, p=0.74388 b-rank test for bits 6 to 13, p=0.53480 b-rank test for bits 7 to 14, p=0.18760 b-rank test for bits 8 to 15, p=0.84878 b-rank test for bits 9 to 16, p=0.68158 b-rank test for bits 10 to 17, p=0.98408 b-rank test for bits 11 to 18, p=0.95220 b-rank test for bits 12 to 19, p=0.63920 b-rank test for bits 13 to 20, p=0.93700 b-rank test for bits 14 to 21, p=0.60744 b-rank test for bits 15 to 22, p=0.40049 b-rank test for bits 16 to 23, p=0.12792 b-rank test for bits 17 to 24, p=0.18909 b-rank test for bits 18 to 25, p=0.71136 b-rank test for bits 19 to 26, p=0.80706 b-rank test for bits 20 to 27, p=0.35912 b-rank test for bits 21 to 28, p=0.41473 b-rank test for bits 22 to 29, p=0.27501 b-rank test for bits 23 to 30, p=0.69964 b-rank test for bits 24 to 31, p=0.09771 b-rank test for bits 25 to 32, p=0.02184 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 = 0.936003 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-08_18:31 (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 142127 0.51 0.694475 2 141195 -1.67 0.047559 3 141958 0.11 0.545268 4 141407 -1.17 0.120264 5 142318 0.95 0.830170 6 141895 -0.03 0.486645 7 141763 -0.34 0.366216 8 141908 -0.00 0.498760 9 142443 1.25 0.893782 10 141396 -1.20 0.115192 11 141489 -0.98 0.163030 12 141419 -1.15 0.125974 13 141944 0.08 0.532281 14 142495 1.37 0.914405 15 141998 0.21 0.582063 16 142052 0.33 0.630562 17 141793 -0.27 0.392888 18 141284 -1.46 0.072001 19 141798 -0.26 0.397387 20 142088 0.42 0.661827 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-08_18:31 Bits used No. missing words z-score p-value 23 to 32 141849 -0.2080 0.417601 22 to 31 141711 -0.6839 0.247020 21 to 30 142076 0.5747 0.717261 20 to 29 142275 1.2609 0.896333 19 to 28 141727 -0.6287 0.264765 18 to 27 141532 -1.3011 0.096606 17 to 26 141482 -1.4736 0.070301 16 to 25 141416 -1.7011 0.044459 15 to 24 141542 -1.2667 0.102639 14 to 23 141490 -1.4460 0.074093 13 to 22 141987 0.2678 0.605584 12 to 21 142415 1.7437 0.959393 11 to 20 141936 0.0920 0.536637 10 to 19 142137 0.7851 0.783793 9 to 18 142055 0.5023 0.692275 8 to 17 141646 -0.9080 0.181930 7 to 16 141485 -1.4632 0.071705 6 to 15 142152 0.8368 0.798646 5 to 14 142361 1.5575 0.940322 4 to 13 142006 0.3333 0.630563 3 to 12 141471 -1.5115 0.065333 2 to 11 141323 -2.0218 0.021597 1 to 10 141806 -0.3563 0.360804 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-08_18:31 Bits used No. missing words z-score p-value 28 to 32 142505 2.0192 0.978268 27 to 31 142325 1.4091 0.920590 26 to 30 142108 0.6735 0.749672 25 to 29 141764 -0.4926 0.311132 24 to 28 142458 1.8599 0.968550 23 to 27 142760 2.8836 0.998034 22 to 26 141694 -0.7299 0.232716 21 to 25 141395 -1.7435 0.040624 20 to 24 141974 0.2192 0.586761 19 to 23 141688 -0.7503 0.226546 18 to 22 141836 -0.2486 0.401844 17 to 21 141933 0.0802 0.531976 16 to 20 141993 0.2836 0.611652 15 to 19 142078 0.5718 0.716259 14 to 18 142543 2.1480 0.984144 13 to 17 141909 -0.0011 0.499554 12 to 16 141581 -1.1130 0.132858 11 to 15 142127 0.7379 0.769702 10 to 14 141998 0.3006 0.618131 9 to 13 141990 0.2735 0.607749 8 to 12 141395 -1.7435 0.040624 7 to 11 141804 -0.3571 0.360527 6 to 10 142099 0.6429 0.739872 5 to 9 141964 0.1853 0.573512 4 to 8 141942 0.1107 0.544091 3 to 7 142031 0.4124 0.659992 2 to 6 141293 -2.0893 0.018342 1 to 5 141921 0.0396 0.515778 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-08_18:31 Bits used No. missing words z-score p-value 31 to 32 141897 -0.0364 0.485493 30 to 31 142391 1.4209 0.922321 29 to 30 141985 0.2232 0.588316 28 to 29 141812 -0.2871 0.387014 27 to 28 141870 -0.1160 0.453819 26 to 27 141541 -1.0865 0.138625 25 to 26 142089 0.5300 0.701944 24 to 25 141670 -0.7060 0.240098 23 to 24 142403 1.4563 0.927339 22 to 23 141868 -0.1219 0.451482 21 to 22 141797 -0.3314 0.370187 20 to 21 141545 -1.0747 0.141250 19 to 20 142078 0.4976 0.690600 18 to 19 142200 0.8574 0.804397 17 to 18 141460 -1.3255 0.092510 16 to 17 141803 -0.3137 0.376891 15 to 16 141779 -0.3845 0.350321 14 to 15 141763 -0.4317 0.332997 13 to 14 141938 0.0846 0.533699 12 to 13 141625 -0.8387 0.200810 11 to 12 141935 0.0757 0.530180 10 to 11 142016 0.3147 0.623490 9 to 10 141679 -0.6794 0.248430 8 to 9 141931 0.0639 0.525484 7 to 8 141808 -0.2989 0.382505 6 to 7 142338 1.2645 0.896977 5 to 6 142384 1.4002 0.919274 4 to 5 141316 -1.7502 0.040039 3 to 4 141475 -1.2812 0.100060 2 to 3 141637 -0.8033 0.210891 1 to 2 141886 -0.0688 0.472566 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-08_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2438.32 -0.872 0.191535 Test results for specific bytes for dh-ranFile-2016-06-08_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2486.07 -0.197 0.421896 2 to 9 2422.26 -1.099 0.135798 3 to 10 2590.45 1.279 0.899581 4 to 11 2502.29 0.032 0.512899 5 to 12 2546.53 0.658 0.744743 6 to 13 2545.16 0.639 0.738478 7 to 14 2451.85 -0.681 0.247938 8 to 15 2465.72 -0.485 0.313891 9 to 16 2563.91 0.904 0.816950 10 to 17 2530.07 0.425 0.664678 11 to 18 2417.52 -1.166 0.121719 12 to 19 2534.55 0.489 0.687421 13 to 20 2523.51 0.332 0.630215 14 to 21 2513.45 0.190 0.575450 15 to 22 2443.61 -0.797 0.212605 16 to 23 2497.55 -0.035 0.486198 17 to 24 2544.67 0.632 0.736238 18 to 25 2550.87 0.719 0.764048 19 to 26 2345.61 -2.183 0.014504 20 to 27 2509.70 0.137 0.554574 21 to 28 2433.93 -0.934 0.175042 22 to 29 2548.38 0.684 0.753084 23 to 30 2514.58 0.206 0.581653 24 to 31 2549.63 0.702 0.758603 25 to 32 2485.68 -0.203 0.419734 CDPARK for dh-ranFile-2016-06-08_18:31: 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 3517 -0.2740 0.392053 3532 0.4110 0.659449 3520 -0.1370 0.445521 3573 2.2831 0.988788 3506 -0.7763 0.218799 3561 1.7352 0.958644 3536 0.5936 0.723613 3537 0.6393 0.738676 3497 -1.1872 0.117571 3520 -0.1370 0.445521 Square side=100, avg. no. parked=3529.90 sample std.=22.21 p-value of the KSTEST for those 10 p-values: 0.626935 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-08_18:31 0.5601,0.7805,0.1601,0.8607,0.0792,0.4654,0.4218,0.5691,0.9144,0.1808, The KS test for those 10 p-values: 0.991591 The 3DSPHERES test for dh-ranFile-2016-06-08_18:31 sample no r^3 equiv. uni. 1 37.119 0.709834 2 178.296 0.997376 3 130.112 0.986925 4 51.885 0.822626 5 10.521 0.295802 6 17.755 0.446692 7 44.053 0.769712 8 27.330 0.597878 9 105.116 0.969919 10 12.219 0.334546 11 1.133 0.037060 12 10.786 0.302003 13 10.795 0.302214 14 171.577 0.996718 15 18.170 0.454290 16 1.930 0.062300 17 6.925 0.206132 18 40.776 0.743137 19 61.706 0.872145 20 17.553 0.442945 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.138568 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-08_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 2.2 0.3 0.9 0.1 0.3 -0.0 0.0 -0.3 0.1 0.0 -0.5 -0.8 -0.2 1.1 -1.1 -0.6 0.1 -0.4 1.0 -1.9 1.4 1.4 -0.2 1.2 -0.0 -0.7 0.3 0.9 0.9 -1.2 -0.7 -0.1 0.0 1.0 -0.1 0.7 -0.1 -0.4 -0.7 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:27.283675 z-score=-1.605683, p-value=0.038434 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-08_18:31 Test no p-value 1 0.937373 2 0.645248 3 0.707302 4 0.006858 5 0.317974 6 0.430567 7 0.045253 8 0.449064 9 0.972678 10 0.678633 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.682084 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-08_18:31: (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 66631 0.02 66549 0.21 3 25000.00 25053 0.11 25041 0.07 4 6666.67 6693 0.10 6768 1.54 5 1388.89 1346 1.32 1367 0.35 6 238.10 242 0.06 232 0.16 7 34.72 29 0.94 35 0.00 8 4.96 5 0.00 7 0.84 p=0.13906 p=0.21116 Number of rngs required: 688226, p-value: 0.419 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-08_18:31 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 66740 66666.7 0.081 0.081 2 37782 37654.3 0.433 0.514 3 27084 26954.7 0.620 1.134 4 19122 19313.5 1.898 3.032 5 13928 13851.4 0.423 3.455 6 9881 9943.5 0.393 3.848 7 7147 7145.0 0.001 3.849 8 5201 5139.1 0.746 4.595 9 3604 3699.9 2.484 7.079 10 2639 2666.3 0.279 7.359 11 1904 1923.3 0.194 7.553 12 1358 1388.7 0.680 8.233 13 973 1003.7 0.940 9.173 14 738 726.1 0.194 9.367 15 530 525.8 0.033 9.400 16 386 381.2 0.062 9.462 17 267 276.5 0.329 9.791 18 193 200.8 0.305 10.096 19 134 146.0 0.984 11.080 20 102 106.2 0.167 11.247 21 287 287.1 0.000 11.247 Chisq= 11.25 for 20 degrees of freedom, p= 0.06044 SUMMARY of craptest p-value for no. of wins: 0.656587 p-value for throws/game: 0.060437 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-08_18:31 No. of wins: Observed Expected 98622 98585.9 z-score= 0.162, pvalue=0.56421 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66411 66666.7 0.980 0.980 2 37571 37654.3 0.184 1.165 3 26983 26954.7 0.030 1.194 4 19367 19313.5 0.148 1.343 5 14069 13851.4 3.418 4.761 6 10035 9943.5 0.841 5.602 7 7051 7145.0 1.237 6.839 8 5196 5139.1 0.631 7.470 9 3689 3699.9 0.032 7.502 10 2706 2666.3 0.591 8.093 11 1881 1923.3 0.932 9.025 12 1415 1388.7 0.497 9.521 13 1003 1003.7 0.001 9.522 14 762 726.1 1.771 11.292 15 490 525.8 2.442 13.735 16 373 381.2 0.174 13.909 17 267 276.5 0.329 14.238 18 210 200.8 0.419 14.657 19 136 146.0 0.683 15.340 20 96 106.2 0.982 16.322 21 289 287.1 0.012 16.334 Chisq= 16.33 for 20 degrees of freedom, p= 0.30433 SUMMARY of craptest p-value for no. of wins: 0.564207 p-value for throws/game: 0.304329 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0069,0.0145,0.0183,0.0216,0.0218,0.0371,0.0384,0.0400,0.0406,0.0406, 0.0435,0.0445,0.0453,0.0475,0.0476,0.0604,0.0604,0.0623,0.0653,0.0703, 0.0717,0.0720,0.0741,0.0792,0.0897,0.0925,0.0966,0.0977,0.1001,0.1026, 0.1080,0.1137,0.1152,0.1176,0.1203,0.1217,0.1240,0.1260,0.1279,0.1329, 0.1358,0.1386,0.1386,0.1391,0.1413,0.1601,0.1630,0.1684,0.1714,0.1750, 0.1808,0.1819,0.1876,0.1891,0.1915,0.1946,0.1956,0.1962,0.1992,0.2008, 0.2061,0.2109,0.2112,0.2126,0.2188,0.2265,0.2283,0.2327,0.2347,0.2401, 0.2470,0.2479,0.2484,0.2524,0.2648,0.2750,0.2813,0.2958,0.3020,0.3022, 0.3043,0.3111,0.3133,0.3139,0.3180,0.3198,0.3326,0.3330,0.3345,0.3503, 0.3591,0.3605,0.3608,0.3662,0.3702,0.3730,0.3736,0.3769,0.3825,0.3836, 0.3870,0.3921,0.3929,0.3974,0.4005,0.4018,0.4147,0.4176,0.4193,0.4197, 0.4218,0.4219,0.4275,0.4306,0.4342,0.4429,0.4455,0.4455,0.4465,0.4467, 0.4491,0.4515,0.4536,0.4538,0.4543,0.4630,0.4654,0.4704,0.4726,0.4855, 0.4862,0.4866,0.4988,0.4996,0.5070,0.5078,0.5129,0.5158,0.5187,0.5222, 0.5255,0.5302,0.5320,0.5323,0.5337,0.5348,0.5366,0.5385,0.5410,0.5441, 0.5453,0.5546,0.5601,0.5642,0.5691,0.5735,0.5755,0.5817,0.5821,0.5868, 0.5883,0.5948,0.5979,0.6056,0.6074,0.6077,0.6104,0.6117,0.6181,0.6235, 0.6269,0.6302,0.6306,0.6306,0.6360,0.6387,0.6392,0.6452,0.6566,0.6594, 0.6600,0.6618,0.6647,0.6724,0.6786,0.6816,0.6821,0.6874,0.6906,0.6923, 0.6945,0.6996,0.7019,0.7073,0.7098,0.7114,0.7163,0.7173,0.7236,0.7289, 0.7343,0.7362,0.7385,0.7387,0.7399,0.7431,0.7439,0.7447,0.7453,0.7455, 0.7497,0.7531,0.7586,0.7640,0.7697,0.7697,0.7805,0.7838,0.7960,0.7986, 0.8011,0.8044,0.8071,0.8106,0.8169,0.8188,0.8226,0.8302,0.8375,0.8375, 0.8445,0.8488,0.8516,0.8607,0.8721,0.8860,0.8938,0.8963,0.8970,0.8996, 0.9099,0.9125,0.9144,0.9144,0.9193,0.9206,0.9223,0.9273,0.9295,0.9360, 0.9370,0.9374,0.9403,0.9522,0.9586,0.9594,0.9620,0.9686,0.9699,0.9727, 0.9783,0.9841,0.9841,0.9869,0.9888,0.9916,0.9967,0.9974,0.9980, Overall p-value after applying KStest on 269 p-values = 0.891935 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.