RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-06_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.52 27.9546 0.954529 2 to 25 15.94 23.2812 0.859682 3 to 26 16.13 20.2856 0.740119 4 to 27 15.77 14.3193 0.355612 5 to 28 15.86 10.6185 0.124304 6 to 29 15.55 19.7368 0.712088 7 to 30 15.52 18.2200 0.624908 8 to 31 15.60 17.5211 0.580363 9 to 32 15.75 20.1794 0.734845 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.269321 Tough bday spacings test for dh-ranFile-2016-04-06_10:31: 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 10 34 62 93 99 78 63 27 20 8 6 (O-E)^2/E 0.1 0.2 1.7 0.2 0.0 0.0 2.3 0.3 1.8 0.3 0.9 Birthday Spacings: Sum(O-E)^2/E= 7.747, p= 0.346 RESULTS OF GCD FOR dh-ranFile-2016-04-06_10:31 Euclid's algorithm: p-value, steps to gcd: 0.466502 p-value, dist. of gcd's: 0.606647 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-06_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.454 0.063 0.287 0.554 0.243 0.658 0.468 0.241 Bits 8 to 15---> 0.816 0.280 0.540 0.476 0.147 0.827 0.742 0.640 Bits 16 to 23---> 0.697 0.121 0.747 0.788 0.373 0.431 0.890 0.254 Bits 24 to 31---> 0.010 0.323 0.267 0.467 0.979 0.947 0.617 0.003 KS test for the above 32 p values: 0.106 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-06_10:31, p-values for 5 runs: 0.3488, 0.5280, 0.9227, 0.2197, 0.8914 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-06_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 225 211.4 0.873 0.873 r= 29 5127 5134.0 0.010 0.882 r= 30 23039 23103.0 0.178 1.060 r= 31 11609 11551.5 0.286 1.346 chi-square = 1.346 with df = 3; p-value = 0.282 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-06_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 232 211.4 2.004 2.004 r= 30 5134 5134.0 0.000 2.004 r= 31 23115 23103.0 0.006 2.010 r= 32 11519 11551.5 0.092 2.101 chi-square = 2.101 with df = 3; p-value = 0.448 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-06_10:31 b-rank test for bits 1 to 8, p=0.17215 b-rank test for bits 2 to 9, p=0.34461 b-rank test for bits 3 to 10, p=0.48194 b-rank test for bits 4 to 11, p=0.02316 b-rank test for bits 5 to 12, p=0.48726 b-rank test for bits 6 to 13, p=0.64286 b-rank test for bits 7 to 14, p=0.75133 b-rank test for bits 8 to 15, p=0.35545 b-rank test for bits 9 to 16, p=0.45017 b-rank test for bits 10 to 17, p=0.26246 b-rank test for bits 11 to 18, p=0.18059 b-rank test for bits 12 to 19, p=0.09016 b-rank test for bits 13 to 20, p=0.67017 b-rank test for bits 14 to 21, p=0.10226 b-rank test for bits 15 to 22, p=0.39595 b-rank test for bits 16 to 23, p=0.00008 b-rank test for bits 17 to 24, p=0.93636 b-rank test for bits 18 to 25, p=0.14665 b-rank test for bits 19 to 26, p=0.85715 b-rank test for bits 20 to 27, p=0.27535 b-rank test for bits 21 to 28, p=0.05860 b-rank test for bits 22 to 29, p=0.02982 b-rank test for bits 23 to 30, p=0.31695 b-rank test for bits 24 to 31, p=0.64810 b-rank test for bits 25 to 32, p=0.32064 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 = 0.020245 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-06_10:31 (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 141905 -0.01 0.495964 2 142257 0.81 0.791694 3 141971 0.14 0.557285 4 142156 0.58 0.717805 5 141161 -1.75 0.040194 6 142100 0.45 0.672017 7 142142 0.54 0.706649 8 142879 2.27 0.988262 9 141944 0.08 0.532281 10 141194 -1.67 0.047328 11 141688 -0.52 0.302534 12 141786 -0.29 0.386614 13 142059 0.35 0.636717 14 142056 0.34 0.634083 15 141725 -0.43 0.333351 16 141831 -0.18 0.427394 17 142081 0.40 0.655826 18 141669 -0.56 0.287222 19 141862 -0.11 0.455973 20 142029 0.28 0.610109 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-06_10:31 Bits used No. missing words z-score p-value 23 to 32 141567 -1.1804 0.118911 22 to 31 141911 0.0058 0.502297 21 to 30 142028 0.4092 0.658806 20 to 29 142120 0.7264 0.766218 19 to 28 141885 -0.0839 0.466569 18 to 27 141504 -1.3977 0.081103 17 to 26 141518 -1.3494 0.088602 16 to 25 141821 -0.3046 0.380341 15 to 24 141868 -0.1425 0.443336 14 to 23 142180 0.9333 0.824679 13 to 22 142617 2.4402 0.992661 12 to 21 141607 -1.0425 0.148586 11 to 20 142092 0.6299 0.735619 10 to 19 141905 -0.0149 0.494044 9 to 18 141671 -0.8218 0.205588 8 to 17 142153 0.8402 0.799614 7 to 16 142079 0.5851 0.720749 6 to 15 141869 -0.1391 0.444698 5 to 14 141250 -2.2736 0.011496 4 to 13 142234 1.1196 0.868548 3 to 12 142081 0.5920 0.723063 2 to 11 141807 -0.3529 0.362096 1 to 10 141645 -0.9115 0.181021 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-06_10:31 Bits used No. missing words z-score p-value 28 to 32 141430 -1.6248 0.052098 27 to 31 142655 2.5277 0.994259 26 to 30 141865 -0.1503 0.440275 25 to 29 141754 -0.5265 0.299256 24 to 28 141794 -0.3909 0.347917 23 to 27 142129 0.7446 0.771757 22 to 26 141766 -0.4859 0.313532 21 to 25 141657 -0.8554 0.196177 20 to 24 141795 -0.3876 0.349171 19 to 23 141337 -1.9401 0.026184 18 to 22 141780 -0.4384 0.330546 17 to 21 141829 -0.2723 0.392694 16 to 20 141730 -0.6079 0.271628 15 to 19 141818 -0.3096 0.378435 14 to 18 142389 1.6260 0.948025 13 to 17 142080 0.5785 0.718551 12 to 16 141668 -0.8181 0.206659 11 to 15 141921 0.0396 0.515778 10 to 14 141490 -1.4215 0.077592 9 to 13 142309 1.3548 0.912262 8 to 12 142768 2.9107 0.998197 7 to 11 142295 1.3074 0.904454 6 to 10 142572 2.2463 0.987659 5 to 9 142118 0.7074 0.760327 4 to 8 142257 1.1785 0.880710 3 to 7 141461 -1.5198 0.064285 2 to 6 141994 0.2870 0.612950 1 to 5 141955 0.1548 0.561516 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-06_10:31 Bits used No. missing words z-score p-value 31 to 32 142023 0.3353 0.631304 30 to 31 141972 0.1849 0.573333 29 to 30 141586 -0.9538 0.170099 28 to 29 142258 1.0285 0.848149 27 to 28 141560 -1.0305 0.151394 26 to 27 141224 -2.0216 0.021608 25 to 26 142712 2.3678 0.991052 24 to 25 142261 1.0374 0.850219 23 to 24 142029 0.3530 0.637959 22 to 23 141630 -0.8240 0.204975 21 to 22 142023 0.3353 0.631304 20 to 21 141552 -1.0541 0.145925 19 to 20 141210 -2.0629 0.019560 18 to 19 142068 0.4681 0.680127 17 to 18 141991 0.2409 0.595189 16 to 17 142469 1.6509 0.950625 15 to 16 142109 0.5890 0.722068 14 to 15 141855 -0.1603 0.436336 13 to 14 141926 0.0492 0.519610 12 to 13 142234 0.9577 0.830900 11 to 12 141796 -0.3343 0.369074 10 to 11 142267 1.0551 0.854304 9 to 10 142017 0.3176 0.624610 8 to 9 142373 1.3678 0.914306 7 to 8 141974 0.1908 0.575646 6 to 7 142351 1.3029 0.903689 5 to 6 142179 0.7955 0.786835 4 to 5 141801 -0.3196 0.374652 3 to 4 141566 -1.0128 0.155584 2 to 3 141923 0.0403 0.516083 1 to 2 142221 0.9194 0.821052 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-06_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2611.25 1.573 0.942172 Test results for specific bytes for dh-ranFile-2016-04-06_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2443.35 -0.801 0.211538 2 to 9 2331.96 -2.376 0.008741 3 to 10 2475.48 -0.347 0.364399 4 to 11 2513.83 0.196 0.577550 5 to 12 2467.28 -0.463 0.321778 6 to 13 2557.80 0.817 0.793164 7 to 14 2559.45 0.841 0.799768 8 to 15 2647.60 2.087 0.981573 9 to 16 2546.92 0.664 0.746514 10 to 17 2457.03 -0.608 0.271695 11 to 18 2483.42 -0.235 0.407295 12 to 19 2552.94 0.749 0.772986 13 to 20 2508.82 0.125 0.549632 14 to 21 2634.83 1.907 0.971723 15 to 22 2509.35 0.132 0.552604 16 to 23 2440.14 -0.847 0.198610 17 to 24 2399.50 -1.421 0.077614 18 to 25 2445.58 -0.770 0.220763 19 to 26 2496.17 -0.054 0.478425 20 to 27 2473.54 -0.374 0.354127 21 to 28 2456.14 -0.620 0.267555 22 to 29 2426.75 -1.036 0.150123 23 to 30 2570.28 0.994 0.839880 24 to 31 2484.40 -0.221 0.412693 25 to 32 2511.81 0.167 0.566305 CDPARK for dh-ranFile-2016-04-06_10:31: 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 3488 -1.5982 0.055002 3530 0.3196 0.625377 3537 0.6393 0.738676 3492 -1.4155 0.078457 3497 -1.1872 0.117571 3503 -0.9132 0.180558 3516 -0.3196 0.374623 3520 -0.1370 0.445521 3506 -0.7763 0.218799 Square side=100, avg. no. parked=3512.70 sample std.=17.37 p-value of the KSTEST for those 10 p-values: 0.199030 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-06_10:31 0.9304,0.6947,0.4421,0.8884,0.4939,0.6233,0.9052,0.5190,0.8954,0.5905, The KS test for those 10 p-values: 0.036926 The 3DSPHERES test for dh-ranFile-2016-04-06_10:31 sample no r^3 equiv. uni. 1 67.660 0.895162 2 46.384 0.786931 3 72.976 0.912187 4 17.262 0.437518 5 10.519 0.295760 6 24.552 0.558867 7 23.207 0.538638 8 59.754 0.863549 9 27.976 0.606446 10 26.584 0.587757 11 5.022 0.154137 12 38.429 0.722233 13 28.591 0.614434 14 3.865 0.120894 15 7.411 0.218881 16 53.283 0.830704 17 8.350 0.242961 18 5.803 0.175873 19 68.446 0.897873 20 7.278 0.215402 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.721431 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-06_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 0.1 -0.1 1.1 0.1 1.0 1.8 1.2 -0.2 -0.0 -0.3 0.3 -0.2 -0.6 1.5 1.3 -0.4 0.2 -0.1 0.2 -0.6 -2.8 0.2 -0.9 1.2 0.4 -1.6 1.1 -1.5 0.1 0.7 0.1 -0.3 0.4 -0.2 -0.1 -0.5 0.2 -0.4 -0.7 -0.6 2.0 -1.1 Chi-square with 42 degrees of freedom:36.359545 z-score=-0.615424, p-value=0.283766 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-06_10:31 Test no p-value 1 0.378998 2 0.303249 3 0.006826 4 0.781669 5 0.057483 6 0.042533 7 0.489891 8 0.522985 9 0.059935 10 0.092090 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.009362 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-06_10:31: (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 66688 0.01 3 25000.00 25065 0.17 24909 0.33 4 6666.67 6678 0.02 6765 1.45 5 1388.89 1343 1.52 1366 0.38 6 238.10 238 0.00 236 0.02 7 34.72 40 0.80 31 0.40 8 4.96 6 0.22 4 0.19 p=0.16012 p=0.16270 Number of rngs required: 688670, p-value: 0.621 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-06_10:31 No. of wins: Observed Expected 98555 98585.9 z-score=-0.138, pvalue=0.44511 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66649 66666.7 0.005 0.005 2 37799 37654.3 0.556 0.561 3 26980 26954.7 0.024 0.584 4 19292 19313.5 0.024 0.608 5 13666 13851.4 2.482 3.090 6 9951 9943.5 0.006 3.096 7 7189 7145.0 0.271 3.366 8 5073 5139.1 0.849 4.216 9 3766 3699.9 1.182 5.398 10 2669 2666.3 0.003 5.401 11 1968 1923.3 1.038 6.438 12 1387 1388.7 0.002 6.441 13 989 1003.7 0.216 6.656 14 691 726.1 1.701 8.357 15 501 525.8 1.173 9.530 16 386 381.2 0.062 9.592 17 278 276.5 0.008 9.599 18 214 200.8 0.864 10.463 19 140 146.0 0.245 10.708 20 114 106.2 0.571 11.279 21 298 287.1 0.413 11.692 Chisq= 11.69 for 20 degrees of freedom, p= 0.07372 SUMMARY of craptest p-value for no. of wins: 0.445113 p-value for throws/game: 0.073718 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-06_10:31 No. of wins: Observed Expected 98654 98585.9 z-score= 0.305, pvalue=0.61973 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66540 66666.7 0.241 0.241 2 37460 37654.3 1.003 1.243 3 27023 26954.7 0.173 1.416 4 19429 19313.5 0.691 2.108 5 13812 13851.4 0.112 2.220 6 10143 9943.5 4.001 6.221 7 7108 7145.0 0.192 6.413 8 5088 5139.1 0.508 6.920 9 3660 3699.9 0.430 7.350 10 2683 2666.3 0.105 7.454 11 1987 1923.3 2.108 9.562 12 1398 1388.7 0.062 9.624 13 1001 1003.7 0.007 9.631 14 713 726.1 0.238 9.869 15 557 525.8 1.847 11.716 16 386 381.2 0.062 11.778 17 276 276.5 0.001 11.779 18 199 200.8 0.017 11.795 19 137 146.0 0.553 12.348 20 117 106.2 1.095 13.443 21 283 287.1 0.059 13.502 Chisq= 13.50 for 20 degrees of freedom, p= 0.14519 SUMMARY of craptest p-value for no. of wins: 0.619729 p-value for throws/game: 0.145189 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0025,0.0068,0.0087,0.0094,0.0100,0.0115,0.0196,0.0202,0.0216, 0.0232,0.0262,0.0298,0.0369,0.0402,0.0425,0.0473,0.0521,0.0550,0.0575, 0.0586,0.0599,0.0633,0.0643,0.0737,0.0776,0.0776,0.0785,0.0811,0.0886, 0.0902,0.0921,0.1023,0.1062,0.1176,0.1189,0.1209,0.1209,0.1243,0.1452, 0.1459,0.1466,0.1475,0.1486,0.1501,0.1514,0.1541,0.1556,0.1601,0.1627, 0.1701,0.1721,0.1759,0.1806,0.1806,0.1810,0.1962,0.1986,0.1990,0.2050, 0.2056,0.2067,0.2115,0.2154,0.2188,0.2189,0.2197,0.2208,0.2406,0.2428, 0.2430,0.2544,0.2625,0.2666,0.2676,0.2693,0.2716,0.2717,0.2753,0.2801, 0.2817,0.2838,0.2867,0.2872,0.2958,0.2993,0.3025,0.3032,0.3135,0.3170, 0.3206,0.3218,0.3234,0.3305,0.3334,0.3446,0.3464,0.3479,0.3488,0.3492, 0.3541,0.3555,0.3556,0.3621,0.3644,0.3691,0.3727,0.3746,0.3747,0.3784, 0.3790,0.3803,0.3866,0.3927,0.3959,0.4073,0.4127,0.4274,0.4313,0.4363, 0.4375,0.4403,0.4421,0.4433,0.4447,0.4451,0.4455,0.4484,0.4502,0.4537, 0.4560,0.4665,0.4665,0.4666,0.4678,0.4757,0.4784,0.4819,0.4873,0.4899, 0.4939,0.4940,0.4960,0.5023,0.5158,0.5161,0.5190,0.5196,0.5230,0.5280, 0.5323,0.5386,0.5402,0.5496,0.5526,0.5544,0.5573,0.5589,0.5615,0.5663, 0.5733,0.5756,0.5775,0.5804,0.5878,0.5905,0.5952,0.6064,0.6066,0.6101, 0.6130,0.6144,0.6172,0.6197,0.6207,0.6233,0.6246,0.6249,0.6254,0.6313, 0.6313,0.6341,0.6367,0.6380,0.6401,0.6429,0.6481,0.6558,0.6584,0.6588, 0.6702,0.6720,0.6801,0.6947,0.6972,0.7066,0.7121,0.7178,0.7186,0.7207, 0.7214,0.7221,0.7222,0.7231,0.7348,0.7356,0.7387,0.7401,0.7425,0.7465, 0.7466,0.7513,0.7533,0.7603,0.7662,0.7718,0.7730,0.7817,0.7868,0.7869, 0.7885,0.7917,0.7932,0.7996,0.7998,0.8160,0.8211,0.8247,0.8267,0.8307, 0.8309,0.8399,0.8481,0.8502,0.8543,0.8571,0.8597,0.8635,0.8685,0.8807, 0.8884,0.8896,0.8914,0.8952,0.8954,0.8979,0.9037,0.9045,0.9052,0.9122, 0.9123,0.9143,0.9227,0.9304,0.9364,0.9422,0.9474,0.9480,0.9506,0.9545, 0.9717,0.9792,0.9816,0.9877,0.9883,0.9911,0.9927,0.9943,0.9982, Overall p-value after applying KStest on 269 p-values = 0.417998 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.