RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-11-25_11:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.57 14.6235 0.377418 2 to 25 15.81 7.5346 0.024488 3 to 26 15.86 19.3361 0.690418 4 to 27 15.53 28.2160 0.957523 5 to 28 15.87 17.9478 0.607862 6 to 29 15.78 16.1940 0.489877 7 to 30 15.82 13.2282 0.279222 8 to 31 15.62 15.5487 0.443979 9 to 32 15.52 19.4427 0.696280 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.898240 Tough bday spacings test for dh-ranFile-2016-11-25_11:31: 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 45 87 93 92 77 51 24 11 6 6 (O-E)^2/E 0.1 1.9 2.6 0.2 0.3 0.0 0.0 1.1 1.0 0.1 0.9 Birthday Spacings: Sum(O-E)^2/E= 8.339, p= 0.404 RESULTS OF GCD FOR dh-ranFile-2016-11-25_11:31 Euclid's algorithm: p-value, steps to gcd: 0.014739 p-value, dist. of gcd's: 0.088389 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-11-25_11:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.199 0.206 0.250 0.636 0.003 0.582 0.658 0.363 Bits 8 to 15---> 0.562 0.150 0.279 0.966 0.016 0.147 0.466 0.807 Bits 16 to 23---> 0.189 0.636 0.863 0.593 0.783 0.835 0.275 0.608 Bits 24 to 31---> 0.473 0.777 0.711 0.330 0.240 0.175 0.709 0.994 KS test for the above 32 p values: 0.170 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-11-25_11:31, p-values for 5 runs: 0.5827, 0.2656, 0.0130, 0.3109, 0.4860 Rank test for binary matrices (31x31) for dh-ranFile-2016-11-25_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 192 211.4 1.783 1.783 r= 29 5112 5134.0 0.094 1.878 r= 30 23030 23103.0 0.231 2.109 r= 31 11666 11551.5 1.134 3.243 chi-square = 3.243 with df = 3; p-value = 0.644 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-11-25_11:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 206 211.4 0.139 0.139 r= 30 5195 5134.0 0.725 0.863 r= 31 23307 23103.0 1.800 2.664 r= 32 11292 11551.5 5.831 8.494 chi-square = 8.494 with df = 3; p-value = 0.963 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-11-25_11:31 b-rank test for bits 1 to 8, p=0.54938 b-rank test for bits 2 to 9, p=0.15774 b-rank test for bits 3 to 10, p=0.62532 b-rank test for bits 4 to 11, p=0.86554 b-rank test for bits 5 to 12, p=0.46653 b-rank test for bits 6 to 13, p=0.44467 b-rank test for bits 7 to 14, p=0.27293 b-rank test for bits 8 to 15, p=0.90394 b-rank test for bits 9 to 16, p=0.14989 b-rank test for bits 10 to 17, p=0.60546 b-rank test for bits 11 to 18, p=0.12533 b-rank test for bits 12 to 19, p=0.70267 b-rank test for bits 13 to 20, p=0.51129 b-rank test for bits 14 to 21, p=0.30704 b-rank test for bits 15 to 22, p=0.79844 b-rank test for bits 16 to 23, p=0.27581 b-rank test for bits 17 to 24, p=0.24239 b-rank test for bits 18 to 25, p=0.56133 b-rank test for bits 19 to 26, p=0.79176 b-rank test for bits 20 to 27, p=0.76426 b-rank test for bits 21 to 28, p=0.62610 b-rank test for bits 22 to 29, p=0.54427 b-rank test for bits 23 to 30, p=0.86486 b-rank test for bits 24 to 31, p=0.56649 b-rank test for bits 25 to 32, p=0.42984 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 = 0.421349 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-11-25_11:31 (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 142138 0.53 0.703425 2 142005 0.22 0.588438 3 142385 1.11 0.866797 4 141662 -0.58 0.281675 5 142370 1.08 0.859111 6 141565 -0.80 0.210551 7 142152 0.57 0.714638 8 141420 -1.14 0.126458 9 141701 -0.49 0.313217 10 141764 -0.34 0.367095 11 142861 2.22 0.986910 12 141095 -1.90 0.028544 13 141796 -0.26 0.395586 14 141997 0.20 0.581150 15 143152 2.90 0.998155 16 141060 -1.98 0.023605 17 142026 0.27 0.607417 18 141581 -0.77 0.221503 19 141942 0.08 0.530422 20 141630 -0.65 0.256994 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-11-25_11:31 Bits used No. missing words z-score p-value 23 to 32 142334 1.4644 0.928455 22 to 31 141547 -1.2494 0.105757 21 to 30 142007 0.3368 0.631864 20 to 29 142029 0.4127 0.660070 19 to 28 141709 -0.6908 0.244848 18 to 27 142453 1.8747 0.969585 17 to 26 142071 0.5575 0.711401 16 to 25 141921 0.0402 0.516050 15 to 24 141845 -0.2218 0.412224 14 to 23 141925 0.0540 0.521546 13 to 22 141820 -0.3080 0.379028 12 to 21 142124 0.7402 0.770423 11 to 20 142268 1.2368 0.891918 10 to 19 141446 -1.5977 0.055056 9 to 18 141785 -0.4287 0.334062 8 to 17 141596 -1.0804 0.139971 7 to 16 141720 -0.6529 0.256923 6 to 15 142094 0.6368 0.737870 5 to 14 142199 0.9989 0.841069 4 to 13 141944 0.1196 0.547581 3 to 12 142158 0.8575 0.804411 2 to 11 141717 -0.6632 0.253599 1 to 10 141676 -0.8046 0.210529 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-11-25_11:31 Bits used No. missing words z-score p-value 28 to 32 141924 0.0497 0.519831 27 to 31 141686 -0.7571 0.224510 26 to 30 142438 1.7921 0.963442 25 to 29 142231 1.0904 0.862233 24 to 28 141918 0.0294 0.511723 23 to 27 142382 1.6023 0.945452 22 to 26 141779 -0.4418 0.329318 21 to 25 141986 0.2599 0.602529 20 to 24 142262 1.1955 0.884053 19 to 23 141963 0.1819 0.572182 18 to 22 141848 -0.2079 0.417654 17 to 21 142060 0.5107 0.695236 16 to 20 142143 0.7921 0.785849 15 to 19 141544 -1.2384 0.107783 14 to 18 141441 -1.5876 0.056193 13 to 17 141596 -1.0621 0.144087 12 to 16 142279 1.2531 0.894919 11 to 15 141877 -0.1096 0.456366 10 to 14 141923 0.0463 0.518480 9 to 13 142092 0.6192 0.732114 8 to 12 142012 0.3480 0.636093 7 to 11 142078 0.5718 0.716259 6 to 10 141766 -0.4859 0.313532 5 to 9 141999 0.3040 0.619423 4 to 8 142251 1.1582 0.876610 3 to 7 141646 -0.8926 0.186024 2 to 6 141586 -1.0960 0.136532 1 to 5 142176 0.9040 0.816993 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-11-25_11:31 Bits used No. missing words z-score p-value 31 to 32 141347 -1.6588 0.048579 30 to 31 141798 -0.3284 0.371302 29 to 30 141476 -1.2783 0.100579 28 to 29 141187 -2.1308 0.016554 27 to 28 142139 0.6775 0.750953 26 to 27 142483 1.6922 0.954700 25 to 26 142192 0.8338 0.797813 24 to 25 141895 -0.0423 0.483141 23 to 24 141594 -0.9302 0.176140 22 to 23 142003 0.2763 0.608846 21 to 22 141838 -0.2104 0.416673 20 to 21 141810 -0.2930 0.384758 19 to 20 141407 -1.4818 0.069197 18 to 19 141697 -0.6263 0.265545 17 to 18 142239 0.9725 0.834594 16 to 17 141540 -1.0895 0.137974 15 to 16 141383 -1.5526 0.060260 14 to 15 142447 1.5860 0.943636 13 to 14 141938 0.0846 0.533699 12 to 13 142504 1.7542 0.960301 11 to 12 141807 -0.3019 0.381380 10 to 11 142280 1.0934 0.862896 9 to 10 141599 -0.9154 0.179984 8 to 9 141257 -1.9243 0.027160 7 to 8 141779 -0.3845 0.350321 6 to 7 141789 -0.3550 0.361311 5 to 6 142234 0.9577 0.830900 4 to 5 141376 -1.5732 0.057831 3 to 4 142203 0.8663 0.806833 2 to 3 142050 0.4150 0.660913 1 to 2 142275 1.0787 0.859633 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-11-25_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2583.96 1.187 0.882458 Test results for specific bytes for dh-ranFile-2016-11-25_11:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2399.72 -1.418 0.078080 2 to 9 2543.97 0.622 0.732986 3 to 10 2488.13 -0.168 0.433322 4 to 11 2378.74 -1.715 0.043190 5 to 12 2654.61 2.187 0.985611 6 to 13 2371.90 -1.812 0.035027 7 to 14 2660.13 2.265 0.988232 8 to 15 2561.10 0.864 0.806229 9 to 16 2468.51 -0.445 0.328024 10 to 17 2344.57 -2.198 0.013972 11 to 18 2553.81 0.761 0.776687 12 to 19 2451.67 -0.683 0.247170 13 to 20 2552.47 0.742 0.770954 14 to 21 2598.71 1.396 0.918644 15 to 22 2596.36 1.363 0.913517 16 to 23 2442.20 -0.817 0.206852 17 to 24 2417.22 -1.171 0.120861 18 to 25 2444.62 -0.783 0.216765 19 to 26 2551.20 0.724 0.765475 20 to 27 2451.90 -0.680 0.248190 21 to 28 2458.38 -0.589 0.278081 22 to 29 2418.01 -1.160 0.123119 23 to 30 2504.07 0.058 0.522971 24 to 31 2623.53 1.747 0.959680 25 to 32 2572.04 1.019 0.845836 CDPARK for dh-ranFile-2016-11-25_11:31: 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 3516 -0.3196 0.374623 3522 -0.0457 0.481790 3506 -0.7763 0.218799 3513 -0.4566 0.323972 3542 0.8676 0.807188 3526 0.1370 0.554479 3538 0.6849 0.753306 3538 0.6849 0.753306 3505 -0.8219 0.205562 3530 0.3196 0.625377 Square side=100, avg. no. parked=3523.60 sample std.=12.76 p-value of the KSTEST for those 10 p-values: 0.675397 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-11-25_11:31 0.7357,0.7376,0.9629,0.4411,0.3463,0.4664,0.7504,0.1299,0.7136,0.6778, The KS test for those 10 p-values: 0.359399 The 3DSPHERES test for dh-ranFile-2016-11-25_11:31 sample no r^3 equiv. uni. 1 23.980 0.550374 2 65.375 0.886864 3 36.731 0.706059 4 27.603 0.601527 5 9.769 0.277928 6 13.869 0.370159 7 33.171 0.669022 8 52.053 0.823616 9 33.607 0.673799 10 19.111 0.471143 11 7.925 0.232149 12 17.365 0.439450 13 70.988 0.906169 14 22.913 0.534088 15 39.615 0.732994 16 9.697 0.276190 17 24.833 0.562969 18 1.353 0.044084 19 19.714 0.481671 20 21.464 0.511040 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.350183 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-11-25_11:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) 0.6 2.2 -0.1 0.0 1.0 -0.1 0.3 -0.6 -0.2 -1.5 0.2 0.8 1.1 -0.6 -0.1 -0.5 0.1 -1.1 0.2 1.4 -0.3 -0.0 -0.8 0.8 0.7 -0.4 -0.9 0.5 0.3 -0.8 0.9 0.5 1.5 -0.8 -0.4 -1.4 -0.7 2.7 -0.8 -0.1 -0.6 0.0 1.8 Chi-square with 42 degrees of freedom:36.317276 z-score=-0.620036, p-value=0.282049 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-11-25_11:31 Test no p-value 1 0.456871 2 0.670663 3 0.793655 4 0.754769 5 0.583489 6 0.000191 7 0.019184 8 0.346357 9 0.528077 10 0.000011 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.011786 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-11-25_11:31: (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 66696 0.01 66694 0.01 3 25000.00 25070 0.20 24941 0.14 4 6666.67 6583 1.05 6688 0.07 5 1388.89 1397 0.05 1380 0.06 6 238.10 228 0.43 248 0.41 7 34.72 25 2.72 47 4.34 8 4.96 0 4.96 1 3.16 p=0.84848 p=0.77566 Number of rngs required: 688552, p-value: 0.568 RESULTS OF CRAPS TEST for dh-ranFile-2016-11-25_11:31 No. of wins: Observed Expected 98522 98585.9 z-score=-0.286, pvalue=0.38759 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66613 66666.7 0.043 0.043 2 37426 37654.3 1.384 1.428 3 27186 26954.7 1.984 3.412 4 19179 19313.5 0.936 4.348 5 14081 13851.4 3.805 8.153 6 9969 9943.5 0.065 8.218 7 7189 7145.0 0.271 8.489 8 5165 5139.1 0.131 8.620 9 3697 3699.9 0.002 8.622 10 2648 2666.3 0.126 8.748 11 1836 1923.3 3.965 12.713 12 1384 1388.7 0.016 12.729 13 1036 1003.7 1.038 13.767 14 680 726.1 2.932 16.699 15 535 525.8 0.160 16.859 16 348 381.2 2.883 19.742 17 281 276.5 0.072 19.814 18 191 200.8 0.481 20.295 19 146 146.0 0.000 20.295 20 103 106.2 0.097 20.393 21 307 287.1 1.377 21.770 Chisq= 21.77 for 20 degrees of freedom, p= 0.64688 SUMMARY of craptest p-value for no. of wins: 0.387587 p-value for throws/game: 0.646883 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-11-25_11:31 No. of wins: Observed Expected 98254 98585.9 z-score=-1.484, pvalue=0.06887 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66757 66666.7 0.122 0.122 2 37696 37654.3 0.046 0.169 3 26741 26954.7 1.695 1.863 4 19334 19313.5 0.022 1.885 5 13923 13851.4 0.370 2.255 6 9917 9943.5 0.071 2.326 7 7244 7145.0 1.371 3.697 8 5165 5139.1 0.131 3.828 9 3722 3699.9 0.132 3.960 10 2657 2666.3 0.032 3.993 11 1895 1923.3 0.417 4.410 12 1330 1388.7 2.485 6.894 13 996 1003.7 0.059 6.954 14 734 726.1 0.085 7.039 15 506 525.8 0.748 7.787 16 383 381.2 0.009 7.796 17 249 276.5 2.743 10.539 18 184 200.8 1.410 11.949 19 153 146.0 0.337 12.286 20 122 106.2 2.346 14.632 21 292 287.1 0.083 14.715 Chisq= 14.72 for 20 degrees of freedom, p= 0.20752 SUMMARY of craptest p-value for no. of wins: 0.068869 p-value for throws/game: 0.207524 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0002,0.0031,0.0118,0.0130,0.0140,0.0147,0.0159,0.0166,0.0192, 0.0236,0.0245,0.0272,0.0285,0.0350,0.0432,0.0441,0.0486,0.0551,0.0562, 0.0578,0.0603,0.0689,0.0692,0.0781,0.0884,0.1006,0.1058,0.1078,0.1209, 0.1231,0.1253,0.1265,0.1299,0.1365,0.1380,0.1400,0.1441,0.1468,0.1499, 0.1505,0.1577,0.1703,0.1748,0.1761,0.1800,0.1860,0.1891,0.1990,0.2056, 0.2057,0.2069,0.2075,0.2105,0.2106,0.2168,0.2188,0.2215,0.2245,0.2321, 0.2398,0.2424,0.2448,0.2472,0.2482,0.2499,0.2536,0.2569,0.2570,0.2655, 0.2656,0.2729,0.2754,0.2758,0.2762,0.2779,0.2781,0.2789,0.2792,0.2817, 0.2820,0.3070,0.3109,0.3132,0.3135,0.3240,0.3280,0.3293,0.3298,0.3341, 0.3463,0.3464,0.3502,0.3503,0.3594,0.3613,0.3630,0.3671,0.3702,0.3713, 0.3746,0.3774,0.3790,0.3814,0.3848,0.3876,0.3956,0.4042,0.4122,0.4167, 0.4177,0.4213,0.4298,0.4333,0.4394,0.4411,0.4440,0.4447,0.4564,0.4569, 0.4658,0.4664,0.4665,0.4711,0.4732,0.4817,0.4818,0.4831,0.4860,0.4899, 0.5110,0.5113,0.5117,0.5160,0.5185,0.5198,0.5215,0.5230,0.5281,0.5304, 0.5337,0.5341,0.5443,0.5476,0.5494,0.5504,0.5545,0.5613,0.5619,0.5630, 0.5665,0.5681,0.5722,0.5812,0.5824,0.5827,0.5835,0.5884,0.5927,0.6015, 0.6025,0.6055,0.6074,0.6077,0.6079,0.6088,0.6194,0.6253,0.6254,0.6261, 0.6319,0.6355,0.6359,0.6361,0.6444,0.6469,0.6578,0.6601,0.6609,0.6690, 0.6707,0.6738,0.6754,0.6778,0.6904,0.6952,0.6963,0.7027,0.7034,0.7061, 0.7085,0.7114,0.7114,0.7136,0.7146,0.7163,0.7321,0.7330,0.7330,0.7357, 0.7376,0.7379,0.7504,0.7510,0.7533,0.7533,0.7548,0.7643,0.7655,0.7704, 0.7710,0.7757,0.7767,0.7769,0.7828,0.7858,0.7918,0.7937,0.7978,0.7984, 0.8044,0.8062,0.8066,0.8068,0.8072,0.8170,0.8236,0.8309,0.8346,0.8349, 0.8411,0.8458,0.8485,0.8591,0.8596,0.8622,0.8625,0.8629,0.8649,0.8655, 0.8668,0.8766,0.8825,0.8841,0.8869,0.8919,0.8949,0.8982,0.9039,0.9062, 0.9135,0.9186,0.9285,0.9436,0.9455,0.9547,0.9575,0.9597,0.9603,0.9629, 0.9632,0.9634,0.9662,0.9696,0.9856,0.9869,0.9882,0.9939,0.9982, Overall p-value after applying KStest on 269 p-values = 0.841814 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.