RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-02-04_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 15.93 16.5807 0.516892 2 to 25 16.04 17.3183 0.566989 3 to 26 15.66 35.4523 0.994577 4 to 27 15.69 17.2074 0.559597 5 to 28 15.76 16.6807 0.523806 6 to 29 15.52 16.4984 0.511185 7 to 30 15.46 25.4800 0.915531 8 to 31 15.52 27.0076 0.942044 9 to 32 15.71 24.9239 0.903575 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.020930 Tough bday spacings test for dh-ranFile-2016-02-04_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 12 43 88 92 101 74 45 24 11 5 5 (O-E)^2/E 0.9 1.1 3.0 0.3 0.1 0.2 1.0 1.1 1.0 0.4 0.2 Birthday Spacings: Sum(O-E)^2/E= 9.326, p= 0.499 RESULTS OF GCD FOR dh-ranFile-2016-02-04_18:31 Euclid's algorithm: p-value, steps to gcd: 0.798453 p-value, dist. of gcd's: 0.912695 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-02-04_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.931 0.663 0.107 0.231 0.707 0.279 0.472 0.990 Bits 8 to 15---> 0.700 0.759 0.261 0.411 0.163 0.050 0.313 0.948 Bits 16 to 23---> 0.198 0.965 0.647 0.551 0.970 0.795 0.002 0.729 Bits 24 to 31---> 0.847 0.799 0.105 0.533 0.642 0.530 0.704 0.799 KS test for the above 32 p values: 0.607 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-02-04_18:31, p-values for 5 runs: 0.5268, 0.7263, 0.9919, 0.2954, 0.7580 Rank test for binary matrices (31x31) for dh-ranFile-2016-02-04_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 230 211.4 1.633 1.633 r= 29 5234 5134.0 1.947 3.581 r= 30 23017 23103.0 0.320 3.901 r= 31 11519 11551.5 0.092 3.993 chi-square = 3.993 with df = 3; p-value = 0.738 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-02-04_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 210 211.4 0.010 0.010 r= 30 5267 5134.0 3.445 3.454 r= 31 23032 23103.0 0.218 3.673 r= 32 11491 11551.5 0.317 3.990 chi-square = 3.990 with df = 3; p-value = 0.737 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-02-04_18:31 b-rank test for bits 1 to 8, p=0.63718 b-rank test for bits 2 to 9, p=0.66081 b-rank test for bits 3 to 10, p=0.17969 b-rank test for bits 4 to 11, p=0.43078 b-rank test for bits 5 to 12, p=0.75667 b-rank test for bits 6 to 13, p=0.58777 b-rank test for bits 7 to 14, p=0.67528 b-rank test for bits 8 to 15, p=0.43241 b-rank test for bits 9 to 16, p=0.05858 b-rank test for bits 10 to 17, p=0.09518 b-rank test for bits 11 to 18, p=0.02493 b-rank test for bits 12 to 19, p=0.65879 b-rank test for bits 13 to 20, p=0.22370 b-rank test for bits 14 to 21, p=0.88282 b-rank test for bits 15 to 22, p=0.92558 b-rank test for bits 16 to 23, p=0.34573 b-rank test for bits 17 to 24, p=0.46016 b-rank test for bits 18 to 25, p=0.71647 b-rank test for bits 19 to 26, p=0.61094 b-rank test for bits 20 to 27, p=0.40169 b-rank test for bits 21 to 28, p=0.28513 b-rank test for bits 22 to 29, p=0.37089 b-rank test for bits 23 to 30, p=0.34099 b-rank test for bits 24 to 31, p=0.34012 b-rank test for bits 25 to 32, p=0.37609 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 = 0.445056 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-02-04_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 141730 -0.42 0.337610 2 141823 -0.20 0.420073 3 142334 0.99 0.839455 4 141676 -0.55 0.292821 5 141841 -0.16 0.436579 6 141700 -0.49 0.312389 7 141721 -0.44 0.329960 8 142637 1.70 0.955450 9 142120 0.49 0.688718 10 142434 1.23 0.889875 11 142590 1.59 0.944122 12 141860 -0.12 0.454121 13 141928 0.04 0.517397 14 141907 -0.01 0.497828 15 141582 -0.76 0.222198 16 141860 -0.12 0.454121 17 141332 -1.35 0.088684 18 141676 -0.55 0.292821 19 141795 -0.27 0.394686 20 142364 1.06 0.855953 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-02-04_18:31 Bits used No. missing words z-score p-value 23 to 32 142414 1.7402 0.959092 22 to 31 142210 1.0368 0.850084 21 to 30 141745 -0.5667 0.285474 20 to 29 142399 1.6885 0.954344 19 to 28 142143 0.8058 0.789809 18 to 27 141779 -0.4494 0.326567 17 to 26 142121 0.7299 0.767273 16 to 25 141945 0.1230 0.548947 15 to 24 142030 0.4161 0.661333 14 to 23 141341 -1.9598 0.025012 13 to 22 141702 -0.7149 0.237326 12 to 21 141967 0.1989 0.578815 11 to 20 141691 -0.7529 0.225766 10 to 19 141582 -1.1287 0.129507 9 to 18 142109 0.6885 0.754436 8 to 17 141733 -0.6080 0.271582 7 to 16 141877 -0.1115 0.455617 6 to 15 141845 -0.2218 0.412224 5 to 14 141659 -0.8632 0.194012 4 to 13 142260 1.2092 0.886708 3 to 12 141377 -1.8356 0.033207 2 to 11 141888 -0.0736 0.470684 1 to 10 141776 -0.4598 0.322845 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-02-04_18:31 Bits used No. missing words z-score p-value 28 to 32 142085 0.5955 0.724243 27 to 31 141808 -0.3435 0.365614 26 to 30 141266 -2.1808 0.014600 25 to 29 141778 -0.4452 0.328093 24 to 28 141937 0.0938 0.537365 23 to 27 142065 0.5277 0.701145 22 to 26 141819 -0.3062 0.379725 21 to 25 141609 -1.0181 0.154323 20 to 24 142211 1.0226 0.846754 19 to 23 141840 -0.2350 0.407098 18 to 22 141934 0.0836 0.533324 17 to 21 141372 -1.8215 0.034269 16 to 20 142129 0.7446 0.771757 15 to 19 141639 -0.9164 0.179736 14 to 18 142046 0.4633 0.678421 13 to 17 142135 0.7650 0.777859 12 to 16 142305 1.3413 0.910081 11 to 15 141946 0.1243 0.549463 10 to 14 141967 0.1955 0.577496 9 to 13 142433 1.7752 0.962064 8 to 12 141934 0.0836 0.533324 7 to 11 142088 0.6057 0.727630 6 to 10 142222 1.0599 0.855405 5 to 9 141984 0.2531 0.599912 4 to 8 142121 0.7175 0.763475 3 to 7 141647 -0.8893 0.186933 2 to 6 142253 1.1650 0.877987 1 to 5 141858 -0.1740 0.430933 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-02-04_18:31 Bits used No. missing words z-score p-value 31 to 32 141643 -0.7856 0.216041 30 to 31 141657 -0.7443 0.228337 29 to 30 141924 0.0433 0.517259 28 to 29 142018 0.3206 0.625728 27 to 28 142372 1.3648 0.913843 26 to 27 141625 -0.8387 0.200810 25 to 26 142288 1.1170 0.868007 24 to 25 142391 1.4209 0.922321 23 to 24 142006 0.2852 0.612240 22 to 23 141817 -0.2724 0.392673 21 to 22 141846 -0.1868 0.425903 20 to 21 141740 -0.4995 0.308714 19 to 20 141854 -0.1632 0.435174 18 to 19 141664 -0.7237 0.234629 17 to 18 141620 -0.8535 0.196696 16 to 17 141946 0.1082 0.543070 15 to 16 141910 0.0020 0.500789 14 to 15 142058 0.4386 0.669508 13 to 14 142055 0.4297 0.666295 12 to 13 142070 0.4740 0.682233 11 to 12 141639 -0.7974 0.212600 10 to 11 141686 -0.6588 0.255015 9 to 10 141224 -2.0216 0.021608 8 to 9 141658 -0.7414 0.229230 7 to 8 142186 0.8161 0.792789 6 to 7 141640 -0.7945 0.213457 5 to 6 142286 1.1111 0.866742 4 to 5 141644 -0.7827 0.216906 3 to 4 141586 -0.9538 0.170099 2 to 3 141574 -0.9892 0.161289 1 to 2 142266 1.0521 0.853629 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-02-04_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2504.95 0.070 0.527924 Test results for specific bytes for dh-ranFile-2016-02-04_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2448.17 -0.733 0.231783 2 to 9 2506.28 0.089 0.535385 3 to 10 2609.55 1.549 0.939334 4 to 11 2521.21 0.300 0.617918 5 to 12 2411.27 -1.255 0.104765 6 to 13 2558.35 0.825 0.795376 7 to 14 2423.47 -1.082 0.139574 8 to 15 2343.06 -2.219 0.013228 9 to 16 2537.55 0.531 0.702281 10 to 17 2573.58 1.041 0.850964 11 to 18 2489.66 -0.146 0.441853 12 to 19 2431.35 -0.971 0.165794 13 to 20 2546.71 0.661 0.745581 14 to 21 2467.02 -0.466 0.320446 15 to 22 2360.54 -1.972 0.024293 16 to 23 2477.85 -0.313 0.377063 17 to 24 2515.05 0.213 0.584248 18 to 25 2523.99 0.339 0.632793 19 to 26 2588.26 1.248 0.894007 20 to 27 2625.08 1.769 0.961543 21 to 28 2571.46 1.011 0.843906 22 to 29 2413.98 -1.216 0.111904 23 to 30 2385.09 -1.625 0.052073 24 to 31 2623.24 1.743 0.959320 25 to 32 2555.05 0.779 0.781885 CDPARK for dh-ranFile-2016-02-04_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 3471 -2.3744 0.008788 3544 0.9589 0.831196 3504 -0.8676 0.192812 3548 1.1416 0.873180 3520 -0.1370 0.445521 3562 1.7808 0.962529 3543 0.9132 0.819442 3527 0.1826 0.572463 3558 1.5982 0.944998 3530 0.3196 0.625377 Square side=100, avg. no. parked=3530.70 sample std.=26.00 p-value of the KSTEST for those 10 p-values: 0.180473 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-02-04_18:31 0.2816,0.5616,0.9832,0.4806,0.6825,0.5442,0.3873,0.2205,0.2644,0.2172, The KS test for those 10 p-values: 0.496302 The 3DSPHERES test for dh-ranFile-2016-02-04_18:31 sample no r^3 equiv. uni. 1 87.822 0.946465 2 4.171 0.129805 3 1.499 0.048732 4 21.369 0.509486 5 21.142 0.505768 6 5.148 0.157692 7 42.512 0.757575 8 23.058 0.536333 9 30.962 0.643732 10 8.857 0.255635 11 5.299 0.161915 12 4.539 0.140423 13 93.471 0.955653 14 17.850 0.448434 15 14.576 0.384845 16 17.685 0.445400 17 29.607 0.627266 18 45.116 0.777732 19 49.406 0.807348 20 13.109 0.354012 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.946625 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-02-04_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 0.1 -0.4 -0.8 3.3 1.9 -0.8 0.8 0.3 -1.5 -0.6 0.4 -0.1 -0.3 0.6 0.9 -0.7 -0.8 0.2 0.6 -1.7 1.1 0.6 0.2 0.5 -0.6 0.3 0.6 -0.3 -1.3 -1.2 0.6 -0.4 -1.1 0.3 0.6 0.5 -0.7 0.1 -0.1 0.1 -1.0 -1.1 Chi-square with 42 degrees of freedom:35.931762 z-score=-0.662099, p-value=0.266562 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-02-04_18:31 Test no p-value 1 0.164040 2 0.253792 3 0.236977 4 0.050380 5 0.148544 6 0.001056 7 0.677639 8 0.011376 9 0.345501 10 0.221530 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.001051 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-02-04_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 66866 0.60 66602 0.06 3 25000.00 24872 0.66 24915 0.29 4 6666.67 6585 1.00 6806 2.91 5 1388.89 1358 0.69 1363 0.48 6 238.10 281 7.73 270 4.28 7 34.72 32 0.21 40 0.80 8 4.96 5 0.00 3 0.77 p=0.90796 p=0.85741 Number of rngs required: 687536, p-value: 0.158 RESULTS OF CRAPS TEST for dh-ranFile-2016-02-04_18:31 No. of wins: Observed Expected 98691 98585.9 z-score= 0.470, pvalue=0.68091 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66806 66666.7 0.291 0.291 2 37209 37654.3 5.267 5.558 3 27052 26954.7 0.351 5.909 4 19208 19313.5 0.576 6.485 5 14008 13851.4 1.770 8.255 6 9994 9943.5 0.256 8.511 7 7208 7145.0 0.555 9.066 8 5235 5139.1 1.791 10.856 9 3559 3699.9 5.363 16.220 10 2708 2666.3 0.652 16.872 11 1935 1923.3 0.071 16.943 12 1398 1388.7 0.062 17.004 13 992 1003.7 0.137 17.141 14 730 726.1 0.021 17.162 15 515 525.8 0.223 17.385 16 369 381.2 0.387 17.772 17 278 276.5 0.008 17.780 18 226 200.8 3.155 20.935 19 177 146.0 6.590 27.524 20 98 106.2 0.635 28.160 21 295 287.1 0.217 28.376 Chisq= 28.38 for 20 degrees of freedom, p= 0.89921 SUMMARY of craptest p-value for no. of wins: 0.680913 p-value for throws/game: 0.899209 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-02-04_18:31 No. of wins: Observed Expected 98741 98585.9 z-score= 0.694, pvalue=0.75612 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66715 66666.7 0.035 0.035 2 37626 37654.3 0.021 0.056 3 26784 26954.7 1.081 1.138 4 19468 19313.5 1.237 2.374 5 13809 13851.4 0.130 2.504 6 9967 9943.5 0.055 2.560 7 7069 7145.0 0.809 3.369 8 5081 5139.1 0.656 4.025 9 3754 3699.9 0.792 4.817 10 2622 2666.3 0.736 5.553 11 1958 1923.3 0.625 6.178 12 1389 1388.7 0.000 6.178 13 1097 1003.7 8.670 14.848 14 717 726.1 0.115 14.963 15 557 525.8 1.847 16.810 16 387 381.2 0.090 16.899 17 280 276.5 0.043 16.943 18 184 200.8 1.410 18.353 19 117 146.0 5.755 24.108 20 128 106.2 4.468 28.576 21 291 287.1 0.053 28.628 Chisq= 28.63 for 20 degrees of freedom, p= 0.90466 SUMMARY of craptest p-value for no. of wins: 0.756122 p-value for throws/game: 0.904664 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0011,0.0011,0.0019,0.0088,0.0114,0.0132,0.0146,0.0209,0.0216,0.0243, 0.0249,0.0250,0.0332,0.0343,0.0487,0.0496,0.0504,0.0521,0.0586,0.0887, 0.0952,0.1046,0.1048,0.1069,0.1119,0.1295,0.1298,0.1396,0.1404,0.1485, 0.1543,0.1575,0.1577,0.1613,0.1619,0.1628,0.1640,0.1658,0.1701,0.1797, 0.1797,0.1805,0.1869,0.1928,0.1940,0.1967,0.1976,0.2008,0.2126,0.2135, 0.2160,0.2169,0.2172,0.2205,0.2215,0.2222,0.2237,0.2258,0.2283,0.2292, 0.2307,0.2318,0.2346,0.2370,0.2373,0.2538,0.2550,0.2556,0.2613,0.2644, 0.2666,0.2716,0.2787,0.2816,0.2851,0.2855,0.2928,0.2928,0.2954,0.3087, 0.3124,0.3128,0.3204,0.3228,0.3266,0.3281,0.3300,0.3376,0.3401,0.3410, 0.3455,0.3457,0.3540,0.3656,0.3709,0.3761,0.3771,0.3797,0.3848,0.3873, 0.3927,0.3947,0.4017,0.4071,0.4115,0.4122,0.4201,0.4259,0.4308,0.4309, 0.4324,0.4352,0.4366,0.4419,0.4451,0.4454,0.4455,0.4484,0.4541,0.4541, 0.4556,0.4602,0.4707,0.4720,0.4806,0.4963,0.4978,0.4985,0.5008,0.5058, 0.5095,0.5112,0.5169,0.5173,0.5174,0.5238,0.5268,0.5279,0.5302,0.5333, 0.5333,0.5333,0.5354,0.5363,0.5374,0.5431,0.5442,0.5489,0.5495,0.5510, 0.5596,0.5616,0.5670,0.5725,0.5775,0.5788,0.5842,0.5878,0.5999,0.6074, 0.6109,0.6122,0.6179,0.6254,0.6257,0.6273,0.6328,0.6372,0.6419,0.6437, 0.6474,0.6588,0.6608,0.6613,0.6628,0.6663,0.6695,0.6753,0.6776,0.6784, 0.6809,0.6822,0.6825,0.6887,0.6998,0.7011,0.7023,0.7037,0.7075,0.7165, 0.7242,0.7263,0.7276,0.7292,0.7375,0.7377,0.7456,0.7544,0.7561,0.7567, 0.7576,0.7580,0.7589,0.7635,0.7673,0.7718,0.7777,0.7779,0.7819,0.7898, 0.7928,0.7952,0.7954,0.7985,0.7985,0.7987,0.8073,0.8194,0.8312,0.8395, 0.8439,0.8466,0.8468,0.8501,0.8510,0.8536,0.8554,0.8560,0.8574,0.8667, 0.8680,0.8732,0.8780,0.8828,0.8867,0.8899,0.8940,0.8992,0.9036,0.9047, 0.9080,0.9101,0.9127,0.9138,0.9155,0.9223,0.9256,0.9309,0.9393,0.9420, 0.9441,0.9450,0.9465,0.9466,0.9484,0.9543,0.9554,0.9557,0.9591,0.9593, 0.9615,0.9621,0.9625,0.9651,0.9699,0.9832,0.9900,0.9919,0.9946, Overall p-value after applying KStest on 269 p-values = 0.668276 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.