RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-02_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 15.53 26.3071 0.930955 2 to 25 16.05 11.7533 0.185161 3 to 26 15.84 17.2993 0.565725 4 to 27 15.94 32.5552 0.987173 5 to 28 16.01 10.6580 0.126221 6 to 29 15.77 29.1164 0.966532 7 to 30 15.92 30.7830 0.978779 8 to 31 15.72 20.5978 0.755199 9 to 32 16.02 9.9784 0.095485 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.039923 Tough bday spacings test for dh-ranFile-2016-03-02_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 9 32 83 121 89 67 41 33 17 2 6 (O-E)^2/E 0.0 0.6 1.3 5.6 0.8 1.6 2.4 0.4 0.3 3.2 0.9 Birthday Spacings: Sum(O-E)^2/E= 16.965, p= 0.925 RESULTS OF GCD FOR dh-ranFile-2016-03-02_10:31 Euclid's algorithm: p-value, steps to gcd: 0.549211 p-value, dist. of gcd's: 0.940706 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-02_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.850 0.014 0.075 0.859 0.249 0.704 0.508 0.253 Bits 8 to 15---> 0.668 0.948 0.407 0.373 0.981 0.561 0.773 0.826 Bits 16 to 23---> 0.699 0.334 0.037 0.243 0.708 0.981 0.161 0.159 Bits 24 to 31---> 0.148 0.152 0.650 0.749 0.427 0.613 0.870 0.854 KS test for the above 32 p values: 0.157 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-02_10:31, p-values for 5 runs: 0.5876, 0.4439, 0.8100, 0.1115, 0.4667 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-02_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 188 211.4 2.594 2.594 r= 29 5145 5134.0 0.024 2.617 r= 30 23160 23103.0 0.140 2.758 r= 31 11507 11551.5 0.172 2.929 chi-square = 2.929 with df = 3; p-value = 0.597 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-02_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 215 211.4 0.061 0.061 r= 30 5113 5134.0 0.086 0.147 r= 31 23011 23103.0 0.367 0.513 r= 32 11661 11551.5 1.038 1.551 chi-square = 1.551 with df = 3; p-value = 0.329 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-02_10:31 b-rank test for bits 1 to 8, p=0.39072 b-rank test for bits 2 to 9, p=0.73405 b-rank test for bits 3 to 10, p=0.42601 b-rank test for bits 4 to 11, p=0.29214 b-rank test for bits 5 to 12, p=0.85501 b-rank test for bits 6 to 13, p=0.14365 b-rank test for bits 7 to 14, p=0.52837 b-rank test for bits 8 to 15, p=0.16799 b-rank test for bits 9 to 16, p=0.62498 b-rank test for bits 10 to 17, p=0.00615 b-rank test for bits 11 to 18, p=0.51492 b-rank test for bits 12 to 19, p=0.51204 b-rank test for bits 13 to 20, p=0.43538 b-rank test for bits 14 to 21, p=0.40960 b-rank test for bits 15 to 22, p=0.28256 b-rank test for bits 16 to 23, p=0.78317 b-rank test for bits 17 to 24, p=0.51107 b-rank test for bits 18 to 25, p=0.50050 b-rank test for bits 19 to 26, p=0.99672 b-rank test for bits 20 to 27, p=0.03646 b-rank test for bits 21 to 28, p=0.35182 b-rank test for bits 22 to 29, p=0.16929 b-rank test for bits 23 to 30, p=0.58310 b-rank test for bits 24 to 31, p=0.98820 b-rank test for bits 25 to 32, p=0.97664 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 = 0.552453 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-02_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 142162 0.59 0.722522 2 141715 -0.45 0.324899 3 142393 1.13 0.870777 4 141639 -0.63 0.263820 5 142201 0.68 0.752214 6 142354 1.04 0.850586 7 142006 0.23 0.589347 8 140945 -2.25 0.012126 9 141786 -0.29 0.386614 10 141658 -0.59 0.278528 11 141381 -1.23 0.108524 12 141296 -1.43 0.075927 13 142165 0.60 0.724866 14 142132 0.52 0.698558 15 141503 -0.95 0.171216 16 141288 -1.45 0.073292 17 142358 1.05 0.852749 18 141957 0.11 0.544342 19 141383 -1.23 0.109397 20 141414 -1.16 0.123572 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-02_10:31 Bits used No. missing words z-score p-value 23 to 32 141908 -0.0046 0.498170 22 to 31 142064 0.5333 0.703103 21 to 30 141871 -0.1322 0.447424 20 to 29 141772 -0.4736 0.317910 19 to 28 141697 -0.7322 0.232032 18 to 27 141691 -0.7529 0.225766 17 to 26 141450 -1.5839 0.056609 16 to 25 141918 0.0299 0.511925 15 to 24 141872 -0.1287 0.448788 14 to 23 141519 -1.3460 0.089157 13 to 22 141815 -0.3253 0.372486 12 to 21 142017 0.3713 0.644784 11 to 20 141496 -1.4253 0.077039 10 to 19 142229 1.1023 0.864837 9 to 18 141724 -0.6391 0.261389 8 to 17 141877 -0.1115 0.455617 7 to 16 141610 -1.0322 0.150996 6 to 15 141330 -1.9977 0.022875 5 to 14 142019 0.3782 0.647349 4 to 13 141490 -1.4460 0.074093 3 to 12 142498 2.0299 0.978816 2 to 11 141586 -1.1149 0.132440 1 to 10 141605 -1.0494 0.146994 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-02_10:31 Bits used No. missing words z-score p-value 28 to 32 141950 0.1379 0.554826 27 to 31 141122 -2.6689 0.003805 26 to 30 142069 0.5413 0.705834 25 to 29 141629 -0.9503 0.170987 24 to 28 141738 -0.5808 0.280695 23 to 27 141489 -1.4248 0.077101 22 to 26 141364 -1.8486 0.032260 21 to 25 142189 0.9480 0.828444 20 to 24 142050 0.4768 0.683265 19 to 23 142073 0.5548 0.710489 18 to 22 141657 -0.8554 0.196177 17 to 21 142189 0.9480 0.828444 16 to 20 141892 -0.0587 0.476577 15 to 19 141237 -2.2791 0.011331 14 to 18 141865 -0.1503 0.440275 13 to 17 141698 -0.7164 0.236881 12 to 16 142018 0.3684 0.643702 11 to 15 142570 2.2396 0.987440 10 to 14 141899 -0.0350 0.486033 9 to 13 142017 0.3650 0.642438 8 to 12 142107 0.6701 0.748593 7 to 11 141600 -1.0486 0.147187 6 to 10 142237 1.1107 0.866661 5 to 9 141574 -1.1367 0.127829 4 to 8 142115 0.6972 0.757157 3 to 7 142438 1.7921 0.963442 2 to 6 141513 -1.3435 0.089556 1 to 5 141563 -1.1740 0.120198 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-02_10:31 Bits used No. missing words z-score p-value 31 to 32 141636 -0.8063 0.210040 30 to 31 142558 1.9135 0.972157 29 to 30 142044 0.3973 0.654411 28 to 29 141424 -1.4317 0.076122 27 to 28 141509 -1.1809 0.118818 26 to 27 141381 -1.5585 0.059558 25 to 26 141525 -1.1337 0.128457 24 to 25 141642 -0.7886 0.215178 23 to 24 141891 -0.0541 0.478439 22 to 23 141503 -1.1986 0.115339 21 to 22 141838 -0.2104 0.416673 20 to 21 142071 0.4769 0.683284 19 to 20 142074 0.4858 0.686429 18 to 19 141250 -1.9449 0.025892 17 to 18 141806 -0.3048 0.380256 16 to 17 141732 -0.5231 0.300453 15 to 16 141768 -0.4169 0.338375 14 to 15 141960 0.1495 0.559408 13 to 14 141960 0.1495 0.559408 12 to 13 141881 -0.0836 0.466699 11 to 12 142076 0.4917 0.688517 10 to 11 141794 -0.3402 0.366851 9 to 10 141639 -0.7974 0.212600 8 to 9 141658 -0.7414 0.229230 7 to 8 141617 -0.8623 0.194253 6 to 7 142085 0.5182 0.697841 5 to 6 141076 -2.4582 0.006982 4 to 5 141473 -1.2871 0.099028 3 to 4 141904 -0.0157 0.493728 2 to 3 141530 -1.1190 0.131577 1 to 2 142263 1.0433 0.851589 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-02_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2479.88 -0.285 0.387988 Test results for specific bytes for dh-ranFile-2016-03-02_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2521.65 0.306 0.620290 2 to 9 2490.00 -0.141 0.443790 3 to 10 2520.16 0.285 0.612216 4 to 11 2558.12 0.822 0.794457 5 to 12 2446.31 -0.759 0.223837 6 to 13 2550.51 0.714 0.762500 7 to 14 2623.56 1.747 0.959713 8 to 15 2533.80 0.478 0.683660 9 to 16 2525.38 0.359 0.640179 10 to 17 2497.81 -0.031 0.487630 11 to 18 2508.90 0.126 0.550097 12 to 19 2439.72 -0.853 0.196968 13 to 20 2625.43 1.774 0.961958 14 to 21 2521.11 0.299 0.617351 15 to 22 2440.11 -0.847 0.198501 16 to 23 2556.38 0.797 0.787354 17 to 24 2521.90 0.310 0.621624 18 to 25 2581.13 1.147 0.874380 19 to 26 2408.02 -1.301 0.096656 20 to 27 2541.42 0.586 0.721006 21 to 28 2407.68 -1.306 0.095843 22 to 29 2544.37 0.628 0.734850 23 to 30 2554.96 0.777 0.781489 24 to 31 2434.60 -0.925 0.177516 25 to 32 2521.75 0.308 0.620803 CDPARK for dh-ranFile-2016-03-02_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 3514 -0.4110 0.340551 3528 0.2283 0.590298 3507 -0.7306 0.232514 3539 0.7306 0.767486 3517 -0.2740 0.392053 3529 0.2740 0.607947 3521 -0.0913 0.463617 3532 0.4110 0.659449 3524 0.0457 0.518210 3543 0.9132 0.819442 Square side=100, avg. no. parked=3525.40 sample std.=10.58 p-value of the KSTEST for those 10 p-values: 0.400461 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-02_10:31 0.7631,0.1530,0.9525,0.3650,0.1907,0.0410,0.5152,0.9143,0.8974,0.3480, The KS test for those 10 p-values: 0.828929 The 3DSPHERES test for dh-ranFile-2016-03-02_10:31 sample no r^3 equiv. uni. 1 31.111 0.645496 2 41.041 0.745395 3 13.945 0.371753 4 68.491 0.898027 5 74.487 0.916498 6 15.955 0.412466 7 15.804 0.409499 8 13.136 0.354596 9 12.295 0.336239 10 64.189 0.882302 11 30.423 0.637276 12 34.004 0.678089 13 11.860 0.326543 14 29.412 0.624837 15 131.853 0.987663 16 78.685 0.927403 17 3.775 0.118246 18 40.531 0.741027 19 7.308 0.216198 20 82.600 0.936286 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.130405 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-02_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 0.1 1.4 -1.0 -0.2 0.4 0.4 -0.0 0.0 0.1 -1.1 -0.1 -0.5 1.3 3.0 0.6 -1.1 -1.5 0.3 -1.1 -0.6 0.7 -0.3 0.5 -1.3 1.4 -1.3 -1.0 1.1 0.1 -0.4 -1.6 0.1 -0.5 0.1 0.3 1.1 -0.4 -0.1 2.4 1.0 -1.1 Chi-square with 42 degrees of freedom:42.105624 z-score=0.011525, p-value=0.533599 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-02_10:31 Test no p-value 1 0.012512 2 0.030371 3 0.864029 4 0.786703 5 0.523903 6 0.002721 7 0.146607 8 0.028560 9 0.913445 10 0.215885 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.010891 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-02_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 66898 0.80 66672 0.00 3 25000.00 24837 1.06 24976 0.02 4 6666.67 6520 3.23 6714 0.34 5 1388.89 1455 3.15 1361 0.56 6 238.10 254 1.06 231 0.21 7 34.72 31 0.40 38 0.31 8 4.96 4 0.19 7 0.84 p=0.87046 p=0.10776 Number of rngs required: 687109, p-value: 0.065 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-02_10:31 No. of wins: Observed Expected 98352 98585.9 z-score=-1.046, pvalue=0.14779 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66443 66666.7 0.750 0.750 2 37757 37654.3 0.280 1.030 3 26782 26954.7 1.107 2.137 4 19415 19313.5 0.534 2.671 5 14021 13851.4 2.076 4.747 6 9946 9943.5 0.001 4.748 7 7285 7145.0 2.742 7.490 8 5200 5139.1 0.722 8.212 9 3712 3699.9 0.040 8.252 10 2669 2666.3 0.003 8.255 11 1900 1923.3 0.283 8.538 12 1349 1388.7 1.137 9.675 13 995 1003.7 0.076 9.751 14 677 726.1 3.326 13.076 15 500 525.8 1.269 14.346 16 361 381.2 1.065 15.411 17 261 276.5 0.873 16.284 18 198 200.8 0.040 16.324 19 142 146.0 0.109 16.433 20 104 106.2 0.046 16.479 21 283 287.1 0.059 16.538 Chisq= 16.54 for 20 degrees of freedom, p= 0.31726 SUMMARY of craptest p-value for no. of wins: 0.147792 p-value for throws/game: 0.317262 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-02_10:31 No. of wins: Observed Expected 98283 98585.9 z-score=-1.355, pvalue=0.08778 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66449 66666.7 0.711 0.711 2 37982 37654.3 2.852 3.562 3 26839 26954.7 0.497 4.059 4 19435 19313.5 0.765 4.824 5 13855 13851.4 0.001 4.825 6 9973 9943.5 0.087 4.912 7 7071 7145.0 0.767 5.679 8 5057 5139.1 1.311 6.990 9 3673 3699.9 0.195 7.185 10 2689 2666.3 0.193 7.378 11 1972 1923.3 1.232 8.610 12 1379 1388.7 0.068 8.678 13 998 1003.7 0.033 8.711 14 740 726.1 0.265 8.975 15 513 525.8 0.313 9.289 16 365 381.2 0.684 9.973 17 289 276.5 0.561 10.534 18 186 200.8 1.095 11.629 19 141 146.0 0.170 11.800 20 101 106.2 0.256 12.056 21 293 287.1 0.121 12.176 Chisq= 12.18 for 20 degrees of freedom, p= 0.09013 SUMMARY of craptest p-value for no. of wins: 0.087779 p-value for throws/game: 0.090128 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0027,0.0038,0.0061,0.0070,0.0109,0.0113,0.0121,0.0125,0.0138,0.0229, 0.0259,0.0286,0.0304,0.0323,0.0365,0.0368,0.0399,0.0410,0.0566,0.0596, 0.0653,0.0733,0.0741,0.0748,0.0759,0.0761,0.0770,0.0771,0.0878,0.0892, 0.0896,0.0901,0.0955,0.0958,0.0967,0.0990,0.1078,0.1085,0.1094,0.1115, 0.1153,0.1182,0.1188,0.1202,0.1236,0.1262,0.1278,0.1285,0.1304,0.1316, 0.1324,0.1436,0.1466,0.1470,0.1472,0.1477,0.1478,0.1510,0.1522,0.1530, 0.1571,0.1585,0.1611,0.1680,0.1693,0.1710,0.1712,0.1775,0.1852,0.1907, 0.1943,0.1962,0.1970,0.1985,0.2100,0.2126,0.2152,0.2159,0.2162,0.2238, 0.2258,0.2292,0.2320,0.2325,0.2369,0.2431,0.2493,0.2528,0.2614,0.2638, 0.2785,0.2807,0.2826,0.2921,0.3005,0.3173,0.3179,0.3249,0.3265,0.3294, 0.3339,0.3362,0.3384,0.3406,0.3480,0.3518,0.3546,0.3650,0.3669,0.3718, 0.3725,0.3726,0.3803,0.3866,0.3880,0.3907,0.3921,0.4005,0.4069,0.4095, 0.4096,0.4125,0.4167,0.4260,0.4267,0.4354,0.4403,0.4438,0.4439,0.4474, 0.4488,0.4556,0.4636,0.4667,0.4667,0.4766,0.4784,0.4860,0.4876,0.4937, 0.4982,0.5005,0.5084,0.5111,0.5119,0.5120,0.5149,0.5152,0.5182,0.5239, 0.5284,0.5336,0.5443,0.5492,0.5501,0.5525,0.5548,0.5594,0.5594,0.5612, 0.5657,0.5831,0.5876,0.5893,0.5903,0.5974,0.6079,0.6122,0.6133,0.6174, 0.6203,0.6208,0.6216,0.6248,0.6250,0.6373,0.6402,0.6424,0.6437,0.6448, 0.6455,0.6473,0.6496,0.6544,0.6594,0.6679,0.6781,0.6833,0.6833,0.6837, 0.6864,0.6885,0.6978,0.6986,0.6988,0.7031,0.7041,0.7058,0.7084,0.7105, 0.7210,0.7225,0.7249,0.7341,0.7349,0.7410,0.7454,0.7486,0.7488,0.7522, 0.7552,0.7572,0.7625,0.7631,0.7675,0.7733,0.7815,0.7832,0.7867,0.7874, 0.7945,0.8100,0.8194,0.8263,0.8284,0.8284,0.8289,0.8501,0.8506,0.8516, 0.8527,0.8543,0.8550,0.8586,0.8640,0.8648,0.8667,0.8697,0.8705,0.8708, 0.8744,0.8823,0.8974,0.8980,0.9134,0.9143,0.9165,0.9249,0.9274,0.9310, 0.9363,0.9407,0.9480,0.9525,0.9597,0.9620,0.9634,0.9665,0.9722,0.9766, 0.9788,0.9788,0.9810,0.9813,0.9872,0.9874,0.9877,0.9882,0.9967, Overall p-value after applying KStest on 269 p-values = 0.074393 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.