RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-06-28_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 15.58 17.4802 0.577683 2 to 25 15.62 15.4472 0.436693 3 to 26 15.38 36.6232 0.996216 4 to 27 15.86 10.5144 0.119334 5 to 28 15.83 13.0069 0.264276 6 to 29 15.82 15.2878 0.425238 7 to 30 16.16 9.8543 0.090391 8 to 31 15.64 14.1101 0.340706 9 to 32 15.77 16.3122 0.498176 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.366852 Tough bday spacings test for dh-ranFile-2016-06-28_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 7 45 69 114 83 73 48 32 15 6 8 (O-E)^2/E 0.5 1.9 0.2 2.7 2.2 0.3 0.3 0.2 0.0 0.1 3.8 Birthday Spacings: Sum(O-E)^2/E= 12.293, p= 0.734 RESULTS OF GCD FOR dh-ranFile-2016-06-28_18:31 Euclid's algorithm: p-value, steps to gcd: 0.532378 p-value, dist. of gcd's: 0.518420 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-06-28_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.826 0.360 0.650 0.058 0.187 0.912 0.624 0.233 Bits 8 to 15---> 0.091 0.662 0.861 0.155 0.221 0.711 0.326 0.126 Bits 16 to 23---> 0.420 0.103 0.767 0.362 0.106 0.076 0.829 0.570 Bits 24 to 31---> 0.180 0.067 0.210 0.745 0.119 0.654 0.814 0.767 KS test for the above 32 p values: 0.854 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-06-28_18:31, p-values for 5 runs: 0.7411, 0.4160, 0.4495, 0.0889, 0.2919 Rank test for binary matrices (31x31) for dh-ranFile-2016-06-28_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 213 211.4 0.012 0.012 r= 29 5184 5134.0 0.487 0.499 r= 30 22967 23103.0 0.801 1.300 r= 31 11636 11551.5 0.618 1.918 chi-square = 1.918 with df = 3; p-value = 0.410 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-06-28_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 230 211.4 1.633 1.633 r= 30 5054 5134.0 1.247 2.880 r= 31 23303 23103.0 1.731 4.611 r= 32 11413 11551.5 1.661 6.272 chi-square = 6.272 with df = 3; p-value = 0.901 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-06-28_18:31 b-rank test for bits 1 to 8, p=0.95639 b-rank test for bits 2 to 9, p=0.22275 b-rank test for bits 3 to 10, p=0.12595 b-rank test for bits 4 to 11, p=0.55327 b-rank test for bits 5 to 12, p=0.22101 b-rank test for bits 6 to 13, p=0.68240 b-rank test for bits 7 to 14, p=0.66259 b-rank test for bits 8 to 15, p=0.63886 b-rank test for bits 9 to 16, p=0.64760 b-rank test for bits 10 to 17, p=0.07236 b-rank test for bits 11 to 18, p=0.66773 b-rank test for bits 12 to 19, p=0.04194 b-rank test for bits 13 to 20, p=0.31126 b-rank test for bits 14 to 21, p=0.30118 b-rank test for bits 15 to 22, p=0.36560 b-rank test for bits 16 to 23, p=0.13291 b-rank test for bits 17 to 24, p=0.51009 b-rank test for bits 18 to 25, p=0.36961 b-rank test for bits 19 to 26, p=0.92328 b-rank test for bits 20 to 27, p=0.31017 b-rank test for bits 21 to 28, p=0.02814 b-rank test for bits 22 to 29, p=0.44336 b-rank test for bits 23 to 30, p=0.04927 b-rank test for bits 24 to 31, p=0.65178 b-rank test for bits 25 to 32, p=0.19378 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 = 0.146452 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-06-28_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 141985 0.18 0.570167 2 142039 0.30 0.619043 3 141871 -0.09 0.464320 4 141055 -2.00 0.022962 5 141557 -0.82 0.205197 6 142409 1.17 0.878486 7 141316 -1.39 0.082830 8 141681 -0.53 0.296850 9 142239 0.77 0.779426 10 142231 0.75 0.773844 11 142219 0.72 0.765322 12 142539 1.47 0.929380 13 141951 0.10 0.538780 14 142044 0.31 0.623486 15 140846 -2.48 0.006488 16 142481 1.34 0.909173 17 141338 -1.33 0.090957 18 141439 -1.10 0.135905 19 141377 -1.24 0.106794 20 142393 1.13 0.870777 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-06-28_18:31 Bits used No. missing words z-score p-value 23 to 32 141868 -0.1425 0.443336 22 to 31 141672 -0.8184 0.206570 21 to 30 141907 -0.0080 0.496795 20 to 29 142061 0.5230 0.699513 19 to 28 141579 -1.1391 0.127337 18 to 27 142249 1.1713 0.879256 17 to 26 141902 -0.0253 0.489918 16 to 25 141788 -0.4184 0.337835 15 to 24 142044 0.4644 0.678812 14 to 23 141888 -0.0736 0.470684 13 to 22 142124 0.7402 0.770423 12 to 21 142051 0.4885 0.687408 11 to 20 141623 -0.9873 0.161737 10 to 19 142044 0.4644 0.678812 9 to 18 141305 -2.0839 0.018585 8 to 17 141994 0.2920 0.614844 7 to 16 142103 0.6678 0.747878 6 to 15 142071 0.5575 0.711401 5 to 14 142025 0.3989 0.655003 4 to 13 141602 -1.0598 0.144627 3 to 12 142098 0.6506 0.742343 2 to 11 141935 0.0885 0.535267 1 to 10 142091 0.6264 0.734490 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-06-28_18:31 Bits used No. missing words z-score p-value 28 to 32 142297 1.3141 0.905600 27 to 31 141478 -1.4621 0.071852 26 to 30 141361 -1.8587 0.031532 25 to 29 141979 0.2362 0.593349 24 to 28 141980 0.2396 0.594664 23 to 27 141890 -0.0655 0.473878 22 to 26 141519 -1.3232 0.092892 21 to 25 141606 -1.0282 0.151919 20 to 24 141776 -0.4520 0.325647 19 to 23 141857 -0.1774 0.429601 18 to 22 141933 0.0802 0.531976 17 to 21 141795 -0.3876 0.349171 16 to 20 141740 -0.5740 0.282984 15 to 19 141479 -1.4587 0.072318 14 to 18 141575 -1.1333 0.128540 13 to 17 141746 -0.5537 0.289905 12 to 16 141410 -1.6926 0.045262 11 to 15 142742 2.8226 0.997618 10 to 14 142061 0.5141 0.696421 9 to 13 141992 0.2802 0.610352 8 to 12 141842 -0.2282 0.409731 7 to 11 141981 0.2429 0.595978 6 to 10 141442 -1.5842 0.056578 5 to 9 142179 0.9141 0.819677 4 to 8 142128 0.7413 0.770730 3 to 7 141768 -0.4791 0.315939 2 to 6 141900 -0.0316 0.487385 1 to 5 141678 -0.7842 0.216470 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-06-28_18:31 Bits used No. missing words z-score p-value 31 to 32 142196 0.8456 0.801122 30 to 31 141414 -1.4612 0.071987 29 to 30 142534 1.8427 0.967312 28 to 29 141898 -0.0334 0.486669 27 to 28 141676 -0.6883 0.245635 26 to 27 141901 -0.0246 0.490198 25 to 26 141883 -0.0777 0.469045 24 to 25 141994 0.2498 0.598615 23 to 24 142364 1.3412 0.910074 22 to 23 141904 -0.0157 0.493728 21 to 22 142290 1.1229 0.869264 20 to 21 141639 -0.7974 0.212600 19 to 20 141659 -0.7384 0.230125 18 to 19 141494 -1.2252 0.110257 17 to 18 141237 -1.9833 0.023668 16 to 17 141755 -0.4553 0.324464 15 to 16 141855 -0.1603 0.436336 14 to 15 142070 0.4740 0.682233 13 to 14 141905 -0.0128 0.494905 12 to 13 141746 -0.4818 0.314974 11 to 12 141729 -0.5319 0.297381 10 to 11 142090 0.5329 0.702966 9 to 10 142353 1.3088 0.904692 8 to 9 141960 0.1495 0.559408 7 to 8 141637 -0.8033 0.210891 6 to 7 141326 -1.7207 0.042649 5 to 6 141628 -0.8299 0.203303 4 to 5 141908 -0.0039 0.498435 3 to 4 141990 0.2380 0.594046 2 to 3 142376 1.3766 0.915683 1 to 2 142354 1.3117 0.905191 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-06-28_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2419.50 -1.138 0.127466 Test results for specific bytes for dh-ranFile-2016-06-28_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2474.05 -0.367 0.356790 2 to 9 2480.99 -0.269 0.394036 3 to 10 2531.28 0.442 0.670896 4 to 11 2594.67 1.339 0.909698 5 to 12 2496.83 -0.045 0.482124 6 to 13 2472.00 -0.396 0.346046 7 to 14 2581.54 1.153 0.875590 8 to 15 2429.77 -0.993 0.160308 9 to 16 2424.53 -1.067 0.142916 10 to 17 2483.35 -0.236 0.406899 11 to 18 2575.14 1.063 0.856030 12 to 19 2601.40 1.434 0.924223 13 to 20 2498.26 -0.025 0.490195 14 to 21 2518.76 0.265 0.604619 15 to 22 2530.23 0.427 0.665482 16 to 23 2567.86 0.960 0.831408 17 to 24 2502.12 0.030 0.511935 18 to 25 2488.78 -0.159 0.436943 19 to 26 2510.12 0.143 0.556917 20 to 27 2554.28 0.768 0.778662 21 to 28 2489.91 -0.143 0.443257 22 to 29 2324.57 -2.481 0.006552 23 to 30 2478.05 -0.310 0.378126 24 to 31 2562.50 0.884 0.811623 25 to 32 2495.04 -0.070 0.472067 CDPARK for dh-ranFile-2016-06-28_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 3519 -0.1826 0.427537 3535 0.5479 0.708135 3539 0.7306 0.767486 3517 -0.2740 0.392053 3494 -1.3242 0.092718 3521 -0.0913 0.463617 3490 -1.5068 0.065925 3513 -0.4566 0.323972 3517 -0.2740 0.392053 3548 1.1416 0.873180 Square side=100, avg. no. parked=3519.30 sample std.=17.35 p-value of the KSTEST for those 10 p-values: 0.766300 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-06-28_18:31 0.5512,0.8308,0.6642,0.5315,0.4390,0.5568,0.8105,0.6796,0.3061,0.2209, The KS test for those 10 p-values: 0.394460 The 3DSPHERES test for dh-ranFile-2016-06-28_18:31 sample no r^3 equiv. uni. 1 3.869 0.120989 2 23.602 0.544664 3 5.091 0.156074 4 117.886 0.980347 5 5.152 0.157794 6 19.257 0.473713 7 7.878 0.230950 8 6.387 0.191756 9 80.824 0.932398 10 39.148 0.728813 11 129.806 0.986791 12 26.126 0.581410 13 22.994 0.535351 14 1.434 0.046685 15 6.611 0.197763 16 199.892 0.998723 17 5.413 0.165079 18 37.739 0.715766 19 11.245 0.312590 20 32.873 0.665713 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.324790 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-06-28_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 -1.6 -0.4 -1.6 -0.8 0.7 0.6 -0.5 -1.6 -0.9 1.1 -0.4 0.9 -1.4 -0.6 -2.1 1.6 0.6 1.5 -0.1 -0.1 0.1 -0.9 -0.3 0.3 0.0 1.0 1.1 -0.3 0.4 -0.3 -0.3 1.5 0.1 0.8 2.8 -1.9 -0.4 0.5 2.1 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:48.399666 z-score=0.698261, p-value=0.769618 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-06-28_18:31 Test no p-value 1 0.448681 2 0.179861 3 0.280965 4 0.517174 5 0.909652 6 0.205067 7 0.438128 8 0.208188 9 0.399692 10 0.682591 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.411151 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-06-28_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 66831 0.41 66664 0.00 3 25000.00 24897 0.42 25113 0.51 4 6666.67 6615 0.40 6612 0.45 5 1388.89 1392 0.01 1326 2.85 6 238.10 229 0.35 235 0.04 7 34.72 26 2.19 41 1.14 8 4.96 9 3.29 8 1.86 p=0.68512 p=0.66470 Number of rngs required: 687359, p-value: 0.112 RESULTS OF CRAPS TEST for dh-ranFile-2016-06-28_18:31 No. of wins: Observed Expected 98745 98585.9 z-score= 0.712, pvalue=0.76170 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66426 66666.7 0.869 0.869 2 37654 37654.3 0.000 0.869 3 26770 26954.7 1.266 2.135 4 19332 19313.5 0.018 2.153 5 14030 13851.4 2.302 4.455 6 9967 9943.5 0.055 4.510 7 7253 7145.0 1.632 6.142 8 5095 5139.1 0.378 6.520 9 3785 3699.9 1.959 8.479 10 2688 2666.3 0.177 8.656 11 1908 1923.3 0.122 8.778 12 1376 1388.7 0.117 8.895 13 1041 1003.7 1.385 10.280 14 732 726.1 0.047 10.327 15 553 525.8 1.403 11.730 16 404 381.2 1.370 13.100 17 248 276.5 2.945 16.045 18 189 200.8 0.697 16.742 19 165 146.0 2.477 19.219 20 104 106.2 0.046 19.265 21 280 287.1 0.176 19.442 Chisq= 19.44 for 20 degrees of freedom, p= 0.50669 SUMMARY of craptest p-value for no. of wins: 0.761697 p-value for throws/game: 0.506691 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-06-28_18:31 No. of wins: Observed Expected 98658 98585.9 z-score= 0.323, pvalue=0.62652 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66773 66666.7 0.170 0.170 2 37698 37654.3 0.051 0.220 3 26908 26954.7 0.081 0.301 4 19278 19313.5 0.065 0.366 5 13821 13851.4 0.067 0.433 6 9825 9943.5 1.413 1.846 7 7091 7145.0 0.409 2.255 8 5152 5139.1 0.033 2.287 9 3826 3699.9 4.300 6.588 10 2601 2666.3 1.599 8.187 11 1938 1923.3 0.112 8.299 12 1400 1388.7 0.091 8.390 13 1014 1003.7 0.105 8.495 14 736 726.1 0.134 8.629 15 554 525.8 1.508 10.138 16 385 381.2 0.039 10.177 17 266 276.5 0.402 10.578 18 208 200.8 0.256 10.834 19 132 146.0 1.340 12.174 20 98 106.2 0.635 12.809 21 296 287.1 0.275 13.084 Chisq= 13.08 for 20 degrees of freedom, p= 0.12626 SUMMARY of craptest p-value for no. of wins: 0.626523 p-value for throws/game: 0.126262 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0065,0.0066,0.0186,0.0230,0.0237,0.0281,0.0315,0.0419,0.0426,0.0453, 0.0467,0.0493,0.0566,0.0582,0.0659,0.0672,0.0719,0.0720,0.0723,0.0724, 0.0763,0.0828,0.0889,0.0904,0.0908,0.0910,0.0927,0.0929,0.1032,0.1062, 0.1068,0.1103,0.1125,0.1193,0.1193,0.1210,0.1260,0.1262,0.1263,0.1273, 0.1275,0.1285,0.1329,0.1359,0.1429,0.1446,0.1465,0.1519,0.1550,0.1561, 0.1578,0.1603,0.1617,0.1651,0.1799,0.1800,0.1875,0.1918,0.1938,0.1978, 0.2033,0.2051,0.2052,0.2066,0.2082,0.2105,0.2109,0.2126,0.2165,0.2209, 0.2210,0.2211,0.2228,0.2301,0.2310,0.2326,0.2456,0.2643,0.2810,0.2830, 0.2899,0.2919,0.2969,0.2974,0.3012,0.3061,0.3102,0.3113,0.3126,0.3150, 0.3159,0.3240,0.3245,0.3248,0.3256,0.3261,0.3378,0.3407,0.3460,0.3492, 0.3568,0.3595,0.3624,0.3656,0.3669,0.3696,0.3781,0.3921,0.3921,0.3940, 0.3945,0.3997,0.4069,0.4097,0.4103,0.4112,0.4160,0.4201,0.4252,0.4275, 0.4296,0.4363,0.4367,0.4369,0.4381,0.4390,0.4433,0.4433,0.4434,0.4487, 0.4495,0.4636,0.4643,0.4690,0.4707,0.4721,0.4737,0.4739,0.4821,0.4867, 0.4874,0.4899,0.4902,0.4902,0.4937,0.4949,0.4968,0.4982,0.4984,0.5067, 0.5101,0.5119,0.5172,0.5184,0.5315,0.5320,0.5324,0.5353,0.5354,0.5388, 0.5447,0.5512,0.5533,0.5568,0.5569,0.5594,0.5702,0.5702,0.5777,0.5814, 0.5933,0.5940,0.5947,0.5960,0.5986,0.6046,0.6104,0.6148,0.6190,0.6235, 0.6236,0.6265,0.6389,0.6476,0.6497,0.6518,0.6536,0.6550,0.6620,0.6626, 0.6642,0.6647,0.6655,0.6657,0.6677,0.6709,0.6788,0.6788,0.6796,0.6822, 0.6824,0.6826,0.6851,0.6874,0.6964,0.6995,0.7030,0.7081,0.7108,0.7114, 0.7158,0.7288,0.7341,0.7345,0.7411,0.7423,0.7451,0.7479,0.7617,0.7653, 0.7663,0.7668,0.7669,0.7675,0.7696,0.7704,0.7707,0.7738,0.7787,0.7794, 0.8011,0.8105,0.8116,0.8138,0.8197,0.8263,0.8289,0.8308,0.8314,0.8543, 0.8560,0.8605,0.8693,0.8708,0.8732,0.8756,0.8785,0.8793,0.9009,0.9047, 0.9052,0.9056,0.9092,0.9097,0.9097,0.9101,0.9124,0.9157,0.9233,0.9242, 0.9294,0.9324,0.9564,0.9673,0.9803,0.9868,0.9962,0.9976,0.9987, Overall p-value after applying KStest on 269 p-values = 0.066350 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.