RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-07-28_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 15.68 21.1293 0.779441 2 to 25 15.88 13.9350 0.328301 3 to 26 15.94 15.7246 0.456566 4 to 27 15.65 13.5283 0.299837 5 to 28 15.91 10.4510 0.116361 6 to 29 15.54 17.7909 0.597855 7 to 30 16.02 6.4726 0.010594 8 to 31 15.64 18.0387 0.613596 9 to 32 15.76 15.2745 0.424281 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.448852 Tough bday spacings test for dh-ranFile-2015-07-28_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 5 40 57 105 97 82 57 35 17 2 3 (O-E)^2/E 1.9 0.3 3.6 0.5 0.0 0.2 0.5 0.9 0.3 3.2 0.3 Birthday Spacings: Sum(O-E)^2/E= 11.730, p= 0.697 RESULTS OF GCD FOR dh-ranFile-2015-07-28_18:31 Euclid's algorithm: p-value, steps to gcd: 0.972380 p-value, dist. of gcd's: 0.707970 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-07-28_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.922 0.601 0.535 0.651 0.739 0.296 0.233 0.498 Bits 8 to 15---> 0.153 0.691 0.998 0.330 0.112 0.523 0.289 0.192 Bits 16 to 23---> 0.407 0.626 0.233 0.790 0.554 0.724 0.509 0.357 Bits 24 to 31---> 0.479 0.537 0.208 0.859 0.097 0.044 0.717 0.536 KS test for the above 32 p values: 0.429 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-07-28_18:31, p-values for 5 runs: 0.5943, 0.5208, 0.1985, 0.2759, 0.2239 Rank test for binary matrices (31x31) for dh-ranFile-2015-07-28_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 220 211.4 0.348 0.348 r= 29 5135 5134.0 0.000 0.349 r= 30 23066 23103.0 0.059 0.408 r= 31 11579 11551.5 0.065 0.473 chi-square = 0.473 with df = 3; p-value = 0.075 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-07-28_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 193 211.4 1.605 1.605 r= 30 5147 5134.0 0.033 1.637 r= 31 23185 23103.0 0.291 1.928 r= 32 11475 11551.5 0.507 2.435 chi-square = 2.435 with df = 3; p-value = 0.513 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-07-28_18:31 b-rank test for bits 1 to 8, p=0.38354 b-rank test for bits 2 to 9, p=0.10448 b-rank test for bits 3 to 10, p=0.18454 b-rank test for bits 4 to 11, p=0.38768 b-rank test for bits 5 to 12, p=0.29083 b-rank test for bits 6 to 13, p=0.20804 b-rank test for bits 7 to 14, p=0.43833 b-rank test for bits 8 to 15, p=0.90016 b-rank test for bits 9 to 16, p=0.03409 b-rank test for bits 10 to 17, p=0.84710 b-rank test for bits 11 to 18, p=0.03112 b-rank test for bits 12 to 19, p=0.61242 b-rank test for bits 13 to 20, p=0.66223 b-rank test for bits 14 to 21, p=0.84905 b-rank test for bits 15 to 22, p=0.23041 b-rank test for bits 16 to 23, p=0.71857 b-rank test for bits 17 to 24, p=0.07652 b-rank test for bits 18 to 25, p=0.36074 b-rank test for bits 19 to 26, p=0.50904 b-rank test for bits 20 to 27, p=0.51683 b-rank test for bits 21 to 28, p=0.24114 b-rank test for bits 22 to 29, p=0.73765 b-rank test for bits 23 to 30, p=0.68651 b-rank test for bits 24 to 31, p=0.39539 b-rank test for bits 25 to 32, p=0.21213 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 = 0.332198 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-07-28_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 142255 0.81 0.790351 2 141632 -0.65 0.258503 3 142302 0.92 0.820547 4 141579 -0.77 0.220117 5 142077 0.39 0.652379 6 142037 0.30 0.617261 7 141927 0.04 0.516466 8 141918 0.02 0.508081 9 142159 0.58 0.720168 10 142422 1.20 0.884508 11 141851 -0.14 0.445798 12 141970 0.14 0.556362 13 141355 -1.30 0.097632 14 142352 1.03 0.849496 15 142151 0.56 0.713844 16 141673 -0.55 0.290415 17 142158 0.58 0.719381 18 142638 1.70 0.955669 19 141930 0.05 0.519259 20 141945 0.08 0.533210 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-07-28_18:31 Bits used No. missing words z-score p-value 23 to 32 142354 1.5333 0.937405 22 to 31 142545 2.1920 0.985809 21 to 30 142398 1.6851 0.954012 20 to 29 141765 -0.4977 0.309351 19 to 28 142362 1.5609 0.940730 18 to 27 142207 1.0264 0.847660 17 to 26 142050 0.4851 0.686186 16 to 25 142011 0.3506 0.637051 15 to 24 141740 -0.5839 0.279645 14 to 23 141665 -0.8425 0.199749 13 to 22 142071 0.5575 0.711401 12 to 21 142398 1.6851 0.954012 11 to 20 142451 1.8678 0.969107 10 to 19 141749 -0.5529 0.290179 9 to 18 141784 -0.4322 0.332808 8 to 17 142112 0.6989 0.757681 7 to 16 141663 -0.8494 0.197826 6 to 15 141650 -0.8942 0.185596 5 to 14 142303 1.3575 0.912686 4 to 13 141532 -1.3011 0.096606 3 to 12 142402 1.6989 0.955327 2 to 11 141662 -0.8529 0.196868 1 to 10 142004 0.3264 0.627957 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-07-28_18:31 Bits used No. missing words z-score p-value 28 to 32 142377 1.5853 0.943553 27 to 31 142339 1.4565 0.927374 26 to 30 141840 -0.2350 0.407098 25 to 29 142157 0.8396 0.799422 24 to 28 141786 -0.4181 0.337949 23 to 27 141732 -0.6011 0.273881 22 to 26 141739 -0.5774 0.281838 21 to 25 141419 -1.6621 0.048243 20 to 24 141381 -1.7909 0.036651 19 to 23 141360 -1.8621 0.031292 18 to 22 141849 -0.2045 0.418978 17 to 21 141780 -0.4384 0.330546 16 to 20 141571 -1.1469 0.125715 15 to 19 142339 1.4565 0.927374 14 to 18 141491 -1.4181 0.078086 13 to 17 141775 -0.4554 0.324427 12 to 16 141959 0.1684 0.566855 11 to 15 141909 -0.0011 0.499554 10 to 14 141710 -0.6757 0.249617 9 to 13 141547 -1.2282 0.109679 8 to 12 141885 -0.0825 0.467135 7 to 11 141970 0.2057 0.581472 6 to 10 141656 -0.8587 0.195240 5 to 9 141742 -0.5672 0.285282 4 to 8 141815 -0.3198 0.374574 3 to 7 142160 0.8497 0.802262 2 to 6 141820 -0.3028 0.381016 1 to 5 142082 0.5853 0.720834 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-07-28_18:31 Bits used No. missing words z-score p-value 31 to 32 141867 -0.1249 0.450314 30 to 31 141710 -0.5880 0.278268 29 to 30 141459 -1.3284 0.092022 28 to 29 141765 -0.4258 0.335144 27 to 28 141562 -1.0246 0.152783 26 to 27 142361 1.3324 0.908629 25 to 26 142140 0.6804 0.751888 24 to 25 141768 -0.4169 0.338375 23 to 24 141975 0.1937 0.576801 22 to 23 141496 -1.2193 0.111372 21 to 22 141636 -0.8063 0.210040 20 to 21 142058 0.4386 0.669508 19 to 20 142142 0.6863 0.753751 18 to 19 142505 1.7571 0.960553 17 to 18 141728 -0.5349 0.296361 16 to 17 142029 0.3530 0.637959 15 to 16 141913 0.0108 0.504319 14 to 15 141595 -0.9272 0.176904 13 to 14 141917 0.0226 0.509025 12 to 13 141718 -0.5644 0.286243 11 to 12 141889 -0.0600 0.476090 10 to 11 142239 0.9725 0.834594 9 to 10 141695 -0.6322 0.263614 8 to 9 141829 -0.2370 0.406343 7 to 8 141922 0.0374 0.514907 6 to 7 141976 0.1967 0.577956 5 to 6 142730 2.4209 0.992258 4 to 5 141963 0.1583 0.562897 3 to 4 142105 0.5772 0.718097 2 to 3 141370 -1.5909 0.055811 1 to 2 141502 -1.2016 0.114766 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-07-28_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2442.98 -0.806 0.210005 Test results for specific bytes for dh-ranFile-2015-07-28_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2570.06 0.991 0.839118 2 to 9 2366.10 -1.894 0.029141 3 to 10 2547.53 0.672 0.749283 4 to 11 2445.63 -0.769 0.220959 5 to 12 2466.43 -0.475 0.317457 6 to 13 2554.11 0.765 0.777926 7 to 14 2436.47 -0.898 0.184467 8 to 15 2563.55 0.899 0.815590 9 to 16 2444.97 -0.778 0.218222 10 to 17 2537.91 0.536 0.704088 11 to 18 2492.71 -0.103 0.458938 12 to 19 2571.42 1.010 0.843773 13 to 20 2563.41 0.897 0.815076 14 to 21 2582.43 1.166 0.878137 15 to 22 2492.21 -0.110 0.456113 16 to 23 2483.81 -0.229 0.409468 17 to 24 2409.35 -1.282 0.099916 18 to 25 2467.15 -0.465 0.321130 19 to 26 2399.91 -1.416 0.078460 20 to 27 2499.27 -0.010 0.495888 21 to 28 2471.56 -0.402 0.343767 22 to 29 2570.41 0.996 0.840325 23 to 30 2517.17 0.243 0.595919 24 to 31 2344.04 -2.206 0.013704 25 to 32 2580.01 1.132 0.871081 CDPARK for dh-ranFile-2015-07-28_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 3522 -0.0457 0.481790 3504 -0.8676 0.192812 3558 1.5982 0.944998 3561 1.7352 0.958644 3550 1.2329 0.891189 3557 1.5525 0.939730 3509 -0.6393 0.261324 3498 -1.1416 0.126820 3517 -0.2740 0.392053 3535 0.5479 0.708135 Square side=100, avg. no. parked=3531.10 sample std.=22.94 p-value of the KSTEST for those 10 p-values: 0.273851 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-07-28_18:31 0.7232,0.2500,0.3020,0.9505,0.5755,0.2922,0.1787,0.0083,0.9598,0.5612, The KS test for those 10 p-values: 0.782627 The 3DSPHERES test for dh-ranFile-2015-07-28_18:31 sample no r^3 equiv. uni. 1 29.646 0.627752 2 50.753 0.815804 3 6.867 0.204588 4 13.615 0.364811 5 62.093 0.873786 6 5.360 0.163602 7 100.449 0.964856 8 50.190 0.812317 9 0.376 0.012442 10 7.507 0.221374 11 2.308 0.074037 12 78.032 0.925806 13 24.662 0.560473 14 1.954 0.063043 15 6.307 0.189596 16 54.427 0.837036 17 23.900 0.549166 18 21.849 0.517278 19 0.690 0.022729 20 48.590 0.802032 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.528819 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-07-28_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.3 0.3 0.0 -0.1 1.1 2.0 0.2 -0.8 0.6 1.9 -2.8 -1.2 -0.4 -0.5 0.1 1.0 -1.1 -0.7 0.7 0.7 1.3 0.7 -0.1 -0.6 -0.3 0.3 0.2 1.1 -0.2 -1.4 0.0 0.9 -0.3 -1.2 -0.1 -0.2 0.8 0.9 0.4 0.1 -1.0 0.8 Chi-square with 42 degrees of freedom:35.209957 z-score=-0.740854, p-value=0.238487 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-07-28_18:31 Test no p-value 1 0.326452 2 0.029869 3 0.025256 4 0.346183 5 0.938980 6 0.103082 7 0.002334 8 0.364714 9 0.984463 10 0.216255 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.018616 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-07-28_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 66713 0.03 66626 0.02 3 25000.00 24959 0.07 24978 0.02 4 6666.67 6647 0.06 6730 0.60 5 1388.89 1420 0.70 1392 0.01 6 238.10 233 0.11 241 0.04 7 34.72 25 2.72 29 0.94 8 4.96 2 1.77 3 0.77 p=0.51260 p=0.12106 Number of rngs required: 687732, p-value: 0.219 RESULTS OF CRAPS TEST for dh-ranFile-2015-07-28_18:31 No. of wins: Observed Expected 98630 98585.9 z-score= 0.197, pvalue=0.57825 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66498 66666.7 0.427 0.427 2 37604 37654.3 0.067 0.494 3 27015 26954.7 0.135 0.629 4 19133 19313.5 1.686 2.315 5 13790 13851.4 0.272 2.587 6 10082 9943.5 1.928 4.515 7 7086 7145.0 0.488 5.003 8 5256 5139.1 2.660 7.663 9 3705 3699.9 0.007 7.670 10 2762 2666.3 3.435 11.105 11 1952 1923.3 0.427 11.533 12 1376 1388.7 0.117 11.650 13 1059 1003.7 3.045 14.695 14 738 726.1 0.194 14.889 15 543 525.8 0.560 15.449 16 397 381.2 0.659 16.108 17 296 276.5 1.369 17.477 18 193 200.8 0.305 17.783 19 124 146.0 3.311 21.093 20 91 106.2 2.180 23.273 21 300 287.1 0.578 23.851 Chisq= 23.85 for 20 degrees of freedom, p= 0.75105 SUMMARY of craptest p-value for no. of wins: 0.578253 p-value for throws/game: 0.751049 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-07-28_18:31 No. of wins: Observed Expected 98818 98585.9 z-score= 1.038, pvalue=0.85043 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66517 66666.7 0.336 0.336 2 37506 37654.3 0.584 0.920 3 27130 26954.7 1.140 2.060 4 19288 19313.5 0.034 2.093 5 14165 13851.4 7.099 9.193 6 9919 9943.5 0.061 9.253 7 7037 7145.0 1.633 10.886 8 5148 5139.1 0.016 10.902 9 3719 3699.9 0.099 11.001 10 2658 2666.3 0.026 11.027 11 1890 1923.3 0.578 11.604 12 1416 1388.7 0.535 12.139 13 1015 1003.7 0.127 12.266 14 724 726.1 0.006 12.272 15 514 525.8 0.266 12.539 16 368 381.2 0.454 12.993 17 291 276.5 0.756 13.749 18 167 200.8 5.699 19.447 19 153 146.0 0.337 19.785 20 101 106.2 0.256 20.041 21 274 287.1 0.599 20.640 Chisq= 20.64 for 20 degrees of freedom, p= 0.58139 SUMMARY of craptest p-value for no. of wins: 0.850428 p-value for throws/game: 0.581391 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0023,0.0083,0.0106,0.0124,0.0137,0.0186,0.0227,0.0253,0.0291,0.0299, 0.0311,0.0313,0.0341,0.0367,0.0439,0.0482,0.0558,0.0630,0.0740,0.0753, 0.0765,0.0781,0.0785,0.0920,0.0966,0.0968,0.0976,0.0999,0.1031,0.1045, 0.1097,0.1114,0.1117,0.1148,0.1164,0.1211,0.1257,0.1268,0.1526,0.1528, 0.1636,0.1769,0.1787,0.1845,0.1845,0.1856,0.1896,0.1919,0.1928,0.1952, 0.1969,0.1978,0.1985,0.1997,0.2046,0.2080,0.2080,0.2100,0.2100,0.2121, 0.2163,0.2182,0.2191,0.2201,0.2210,0.2214,0.2239,0.2304,0.2330,0.2334, 0.2385,0.2411,0.2496,0.2500,0.2585,0.2613,0.2636,0.2739,0.2739,0.2759, 0.2783,0.2796,0.2818,0.2853,0.2862,0.2893,0.2902,0.2904,0.2908,0.2922, 0.2962,0.2964,0.2998,0.3020,0.3094,0.3175,0.3211,0.3244,0.3265,0.3283, 0.3299,0.3305,0.3322,0.3328,0.3351,0.3379,0.3384,0.3438,0.3462,0.3567, 0.3607,0.3647,0.3648,0.3746,0.3810,0.3835,0.3877,0.3921,0.3954,0.4063, 0.4069,0.4071,0.4095,0.4190,0.4243,0.4292,0.4383,0.4458,0.4489,0.4503, 0.4561,0.4566,0.4589,0.4671,0.4761,0.4790,0.4818,0.4959,0.4981,0.4996, 0.5043,0.5081,0.5090,0.5090,0.5095,0.5126,0.5129,0.5149,0.5165,0.5168, 0.5173,0.5193,0.5208,0.5231,0.5288,0.5332,0.5349,0.5363,0.5366,0.5492, 0.5541,0.5564,0.5605,0.5612,0.5629,0.5669,0.5755,0.5768,0.5780,0.5783, 0.5814,0.5815,0.5943,0.5959,0.5979,0.6010,0.6124,0.6136,0.6173,0.6258, 0.6278,0.6280,0.6371,0.6380,0.6513,0.6524,0.6622,0.6695,0.6862,0.6865, 0.6910,0.6965,0.7041,0.7080,0.7081,0.7114,0.7138,0.7170,0.7181,0.7186, 0.7194,0.7202,0.7208,0.7232,0.7244,0.7377,0.7391,0.7493,0.7510,0.7519, 0.7538,0.7577,0.7779,0.7794,0.7826,0.7899,0.7904,0.7994,0.8020,0.8023, 0.8123,0.8151,0.8156,0.8158,0.8205,0.8346,0.8370,0.8391,0.8403,0.8438, 0.8471,0.8477,0.8490,0.8495,0.8504,0.8589,0.8711,0.8738,0.8781,0.8845, 0.8912,0.9002,0.9086,0.9127,0.9217,0.9258,0.9274,0.9274,0.9374,0.9390, 0.9397,0.9407,0.9436,0.9450,0.9505,0.9540,0.9540,0.9553,0.9557,0.9586, 0.9598,0.9606,0.9649,0.9691,0.9724,0.9845,0.9858,0.9923,0.9980, Overall p-value after applying KStest on 269 p-values = 0.349198 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.