RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-25_19:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.67 19.0230 0.672785 2 to 25 16.00 12.6648 0.241677 3 to 26 15.63 23.4571 0.865048 4 to 27 15.72 13.3799 0.289594 5 to 28 15.59 17.6139 0.586422 6 to 29 15.63 18.7286 0.655670 7 to 30 15.66 25.4380 0.914674 8 to 31 15.89 12.9957 0.263524 9 to 32 15.38 29.1000 0.966385 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.423177 Tough bday spacings test for dh-ranFile-2015-11-25_19:31: 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 30 80 95 102 78 42 33 14 10 4 (O-E)^2/E 0.9 1.2 0.6 0.1 0.2 0.0 2.0 0.4 0.1 1.7 0.0 Birthday Spacings: Sum(O-E)^2/E= 7.060, p= 0.280 RESULTS OF GCD FOR dh-ranFile-2015-11-25_19:31 Euclid's algorithm: p-value, steps to gcd: 0.247580 p-value, dist. of gcd's: 0.439714 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-25_19:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.637 0.285 0.618 0.595 0.023 0.920 0.365 0.343 Bits 8 to 15---> 0.996 0.393 0.245 0.851 0.023 0.587 0.385 0.976 Bits 16 to 23---> 0.853 0.547 0.780 0.699 0.940 0.790 0.238 0.518 Bits 24 to 31---> 0.939 0.332 0.899 0.482 0.942 0.230 0.738 0.183 KS test for the above 32 p values: 0.786 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-25_19:31, p-values for 5 runs: 0.5459, 0.2492, 0.3822, 0.3764, 0.9446 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-25_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 203 211.4 0.335 0.335 r= 29 5102 5134.0 0.200 0.535 r= 30 23270 23103.0 1.206 1.741 r= 31 11425 11551.5 1.386 3.127 chi-square = 3.127 with df = 3; p-value = 0.628 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-25_19:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 176 211.4 5.933 5.933 r= 30 5286 5134.0 4.500 10.433 r= 31 23087 23103.0 0.011 10.444 r= 32 11451 11551.5 0.875 11.319 chi-square = 11.319 with df = 3; p-value = 0.990 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-25_19:31 b-rank test for bits 1 to 8, p=0.53922 b-rank test for bits 2 to 9, p=0.59663 b-rank test for bits 3 to 10, p=0.72757 b-rank test for bits 4 to 11, p=0.37445 b-rank test for bits 5 to 12, p=0.01561 b-rank test for bits 6 to 13, p=0.59387 b-rank test for bits 7 to 14, p=0.60213 b-rank test for bits 8 to 15, p=0.91588 b-rank test for bits 9 to 16, p=0.98696 b-rank test for bits 10 to 17, p=0.95096 b-rank test for bits 11 to 18, p=0.04140 b-rank test for bits 12 to 19, p=0.62140 b-rank test for bits 13 to 20, p=0.47927 b-rank test for bits 14 to 21, p=0.43173 b-rank test for bits 15 to 22, p=0.19678 b-rank test for bits 16 to 23, p=0.31026 b-rank test for bits 17 to 24, p=0.80615 b-rank test for bits 18 to 25, p=0.28403 b-rank test for bits 19 to 26, p=0.62164 b-rank test for bits 20 to 27, p=0.61467 b-rank test for bits 21 to 28, p=0.86801 b-rank test for bits 22 to 29, p=0.63741 b-rank test for bits 23 to 30, p=0.83148 b-rank test for bits 24 to 31, p=0.50878 b-rank test for bits 25 to 32, p=0.29635 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 = 0.445779 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-25_19:31 (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 141368 -1.26 0.102973 2 141724 -0.43 0.332502 3 142427 1.21 0.886766 4 142475 1.32 0.906859 5 142837 2.17 0.984900 6 141561 -0.81 0.207864 7 140836 -2.51 0.006075 8 142237 0.77 0.778038 9 141976 0.16 0.561893 10 141763 -0.34 0.366216 11 142080 0.40 0.654966 12 142798 2.08 0.981068 13 141734 -0.41 0.341032 14 142147 0.56 0.710657 15 141825 -0.20 0.421901 16 142320 0.96 0.831349 17 141773 -0.32 0.375042 18 141936 0.06 0.524843 19 141456 -1.06 0.144758 20 141579 -0.77 0.220117 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-25_19:31 Bits used No. missing words z-score p-value 23 to 32 142089 0.6196 0.732224 22 to 31 141195 -2.4632 0.006885 21 to 30 141589 -1.1046 0.134669 20 to 29 141837 -0.2494 0.401520 19 to 28 142104 0.6713 0.748978 18 to 27 141698 -0.7287 0.233085 17 to 26 141895 -0.0494 0.480295 16 to 25 141924 0.0506 0.520172 15 to 24 142423 1.7713 0.961743 14 to 23 141779 -0.4494 0.326567 13 to 22 142230 1.1058 0.865585 12 to 21 141623 -0.9873 0.161737 11 to 20 142062 0.5264 0.700712 10 to 19 142051 0.4885 0.687408 9 to 18 141569 -1.1736 0.120287 8 to 17 141854 -0.1908 0.424344 7 to 16 141857 -0.1804 0.428400 6 to 15 142083 0.5989 0.725368 5 to 14 141958 0.1678 0.566641 4 to 13 141642 -0.9218 0.178309 3 to 12 141926 0.0575 0.522920 2 to 11 142029 0.4127 0.660070 1 to 10 141820 -0.3080 0.379028 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-25_19:31 Bits used No. missing words z-score p-value 28 to 32 141908 -0.0045 0.498201 27 to 31 141655 -0.8621 0.194306 26 to 30 142390 1.6294 0.948385 25 to 29 141732 -0.6011 0.273881 24 to 28 142424 1.7446 0.959477 23 to 27 142159 0.8463 0.801318 22 to 26 142239 1.1175 0.868115 21 to 25 141454 -1.5435 0.061356 20 to 24 142380 1.5955 0.944699 19 to 23 141785 -0.4215 0.336711 18 to 22 141956 0.1582 0.562852 17 to 21 142355 1.5107 0.934573 16 to 20 141845 -0.2181 0.413688 15 to 19 141978 0.2328 0.592034 14 to 18 141828 -0.2757 0.391391 13 to 17 142475 1.9175 0.972414 12 to 16 141907 -0.0079 0.496849 11 to 15 142084 0.5921 0.723109 10 to 14 142046 0.4633 0.678421 9 to 13 141371 -1.8248 0.034012 8 to 12 142095 0.6294 0.735453 7 to 11 141842 -0.2282 0.409731 6 to 10 142045 0.4599 0.677205 5 to 9 141582 -1.1096 0.133587 4 to 8 142097 0.6362 0.737667 3 to 7 141781 -0.4350 0.331775 2 to 6 142081 0.5819 0.719694 1 to 5 142066 0.5311 0.702320 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-25_19:31 Bits used No. missing words z-score p-value 31 to 32 141707 -0.5968 0.275306 30 to 31 141613 -0.8741 0.191024 29 to 30 142301 1.1554 0.876030 28 to 29 142474 1.6657 0.952113 27 to 28 141972 0.1849 0.573333 26 to 27 141902 -0.0216 0.491375 25 to 26 142196 0.8456 0.801122 24 to 25 141691 -0.6440 0.259774 23 to 24 141174 -2.1691 0.015037 22 to 23 141795 -0.3373 0.367962 21 to 22 141906 -0.0098 0.496081 20 to 21 141937 0.0816 0.532527 19 to 20 142100 0.5624 0.713095 18 to 19 141965 0.1642 0.565220 17 to 18 141639 -0.7974 0.212600 16 to 17 141849 -0.1780 0.429375 15 to 16 142020 0.3265 0.627962 14 to 15 142242 0.9813 0.836784 13 to 14 141301 -1.7945 0.036368 12 to 13 141624 -0.8417 0.199983 11 to 12 141944 0.1023 0.540729 10 to 11 141336 -1.6912 0.045396 9 to 10 141539 -1.0924 0.137325 8 to 9 142625 2.1111 0.982619 7 to 8 141622 -0.8476 0.198336 6 to 7 142123 0.6303 0.735749 5 to 6 142009 0.2940 0.615626 4 to 5 142032 0.3619 0.641271 3 to 4 141718 -0.5644 0.286243 2 to 3 141696 -0.6293 0.264579 1 to 2 141664 -0.7237 0.234629 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-25_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2553.36 0.755 0.774750 Test results for specific bytes for dh-ranFile-2015-11-25_19:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2567.42 0.953 0.829813 2 to 9 2549.86 0.705 0.759621 3 to 10 2467.33 -0.462 0.322018 4 to 11 2543.78 0.619 0.732078 5 to 12 2442.62 -0.811 0.208545 6 to 13 2537.23 0.527 0.700733 7 to 14 2321.41 -2.526 0.005774 8 to 15 2519.57 0.277 0.609007 9 to 16 2386.22 -1.609 0.053804 10 to 17 2584.66 1.197 0.884408 11 to 18 2603.36 1.462 0.928091 12 to 19 2513.69 0.194 0.576785 13 to 20 2456.89 -0.610 0.271054 14 to 21 2571.58 1.012 0.844288 15 to 22 2456.67 -0.613 0.270016 16 to 23 2462.30 -0.533 0.296970 17 to 24 2620.35 1.702 0.955617 18 to 25 2510.04 0.142 0.556453 19 to 26 2609.73 1.552 0.939652 20 to 27 2612.06 1.585 0.943484 21 to 28 2499.26 -0.011 0.495804 22 to 29 2523.46 0.332 0.629946 23 to 30 2434.69 -0.924 0.177824 24 to 31 2456.91 -0.609 0.271158 25 to 32 2497.28 -0.038 0.484653 CDPARK for dh-ranFile-2015-11-25_19:31: 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 3518 -0.2283 0.409702 3436 -3.9726 0.000036 3517 -0.2740 0.392053 3513 -0.4566 0.323972 3560 1.6895 0.954438 3534 0.5023 0.692266 3557 1.5525 0.939730 3502 -0.9589 0.168804 3542 0.8676 0.807188 Square side=100, avg. no. parked=3519.50 sample std.=33.32 p-value of the KSTEST for those 10 p-values: 0.378745 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-25_19:31 0.1410,0.0347,0.8616,0.2924,0.5589,0.1933,0.0390,0.4716,0.2580,0.7699, The KS test for those 10 p-values: 0.212280 The 3DSPHERES test for dh-ranFile-2015-11-25_19:31 sample no r^3 equiv. uni. 1 29.083 0.620702 2 2.242 0.071994 3 2.861 0.090958 4 19.924 0.485287 5 5.123 0.156994 6 46.145 0.785224 7 12.863 0.348692 8 5.322 0.162542 9 28.851 0.617762 10 45.501 0.780568 11 20.652 0.497626 12 16.827 0.429304 13 0.462 0.015269 14 31.630 0.651577 15 72.380 0.910425 16 11.374 0.315552 17 74.361 0.916148 18 30.379 0.636742 19 37.278 0.711370 20 150.636 0.993403 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.978528 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-25_19:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.1 -0.1 -0.3 0.7 1.1 -1.1 -0.2 -0.0 0.2 0.4 0.0 -0.0 0.5 1.2 1.2 -0.3 -1.2 -2.8 -0.4 0.6 -0.1 -0.0 -0.7 0.9 0.3 0.0 0.7 2.1 0.2 0.9 0.9 -1.1 -1.0 -1.2 -0.5 0.3 -1.0 1.3 -1.3 -1.3 -1.0 -0.1 Chi-square with 42 degrees of freedom:35.417140 z-score=-0.718249, p-value=0.246415 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-25_19:31 Test no p-value 1 0.519629 2 0.291396 3 0.107125 4 0.280196 5 0.001286 6 0.358045 7 0.101249 8 0.211248 9 0.054381 10 0.519492 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.006480 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-25_19:31: (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 66596 0.07 66658 0.00 3 25000.00 25106 0.45 24977 0.02 4 6666.67 6639 0.11 6687 0.06 5 1388.89 1383 0.02 1404 0.16 6 238.10 231 0.21 239 0.00 7 34.72 35 0.00 28 1.30 8 4.96 9 3.29 6 0.22 p=0.34612 p=0.06048 Number of rngs required: 689927, p-value: 0.963 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-25_19:31 No. of wins: Observed Expected 98743 98585.9 z-score= 0.703, pvalue=0.75892 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66609 66666.7 0.050 0.050 2 37890 37654.3 1.475 1.525 3 26757 26954.7 1.451 2.976 4 19283 19313.5 0.048 3.024 5 13899 13851.4 0.163 3.187 6 9934 9943.5 0.009 3.196 7 7082 7145.0 0.556 3.752 8 5036 5139.1 2.067 5.819 9 3663 3699.9 0.367 6.187 10 2726 2666.3 1.337 7.524 11 1956 1923.3 0.555 8.078 12 1418 1388.7 0.616 8.695 13 1007 1003.7 0.011 8.706 14 754 726.1 1.069 9.775 15 545 525.8 0.698 10.473 16 395 381.2 0.503 10.976 17 274 276.5 0.023 11.000 18 210 200.8 0.419 11.418 19 154 146.0 0.440 11.858 20 98 106.2 0.635 12.494 21 310 287.1 1.824 14.318 Chisq= 14.32 for 20 degrees of freedom, p= 0.18599 SUMMARY of craptest p-value for no. of wins: 0.758919 p-value for throws/game: 0.185990 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-25_19:31 No. of wins: Observed Expected 98736 98585.9 z-score= 0.672, pvalue=0.74906 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66680 66666.7 0.003 0.003 2 37537 37654.3 0.366 0.368 3 26603 26954.7 4.590 4.958 4 19398 19313.5 0.370 5.328 5 13886 13851.4 0.086 5.414 6 10104 9943.5 2.589 8.004 7 7092 7145.0 0.394 8.397 8 5117 5139.1 0.095 8.492 9 3753 3699.9 0.763 9.255 10 2712 2666.3 0.783 10.038 11 1931 1923.3 0.031 10.069 12 1428 1388.7 1.110 11.179 13 1031 1003.7 0.742 11.921 14 773 726.1 3.024 14.945 15 543 525.8 0.560 15.505 16 408 381.2 1.891 17.396 17 285 276.5 0.259 17.655 18 194 200.8 0.232 17.887 19 140 146.0 0.245 18.133 20 115 106.2 0.727 18.859 21 270 287.1 1.020 19.879 Chisq= 19.88 for 20 degrees of freedom, p= 0.53449 SUMMARY of craptest p-value for no. of wins: 0.749055 p-value for throws/game: 0.534493 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0000,0.0013,0.0058,0.0061,0.0065,0.0069,0.0150,0.0153,0.0156,0.0231, 0.0232,0.0340,0.0347,0.0364,0.0390,0.0414,0.0454,0.0538,0.0544,0.0605, 0.0614,0.0720,0.0910,0.1012,0.1030,0.1071,0.1203,0.1336,0.1347,0.1373, 0.1410,0.1448,0.1570,0.1617,0.1625,0.1688,0.1778,0.1783,0.1830,0.1860, 0.1910,0.1933,0.1943,0.1968,0.1983,0.2000,0.2079,0.2085,0.2112,0.2123, 0.2126,0.2201,0.2300,0.2331,0.2346,0.2385,0.2417,0.2450,0.2464,0.2476, 0.2492,0.2580,0.2598,0.2635,0.2646,0.2700,0.2711,0.2712,0.2739,0.2753, 0.2802,0.2802,0.2840,0.2847,0.2862,0.2896,0.2914,0.2924,0.2964,0.2970, 0.3103,0.3156,0.3220,0.3240,0.3266,0.3318,0.3323,0.3325,0.3367,0.3410, 0.3431,0.3461,0.3487,0.3580,0.3646,0.3662,0.3680,0.3744,0.3746,0.3750, 0.3764,0.3787,0.3790,0.3822,0.3854,0.3914,0.3921,0.3933,0.4015,0.4097, 0.4097,0.4137,0.4219,0.4232,0.4243,0.4284,0.4293,0.4294,0.4317,0.4397, 0.4458,0.4716,0.4793,0.4803,0.4820,0.4847,0.4853,0.4914,0.4958,0.4961, 0.4968,0.4976,0.4982,0.5088,0.5180,0.5195,0.5196,0.5202,0.5229,0.5248, 0.5325,0.5345,0.5392,0.5407,0.5459,0.5474,0.5565,0.5589,0.5619,0.5629, 0.5652,0.5666,0.5733,0.5768,0.5864,0.5869,0.5920,0.5939,0.5954,0.5966, 0.6021,0.6090,0.6147,0.6156,0.6178,0.6178,0.6207,0.6214,0.6216,0.6276, 0.6280,0.6299,0.6367,0.6370,0.6374,0.6413,0.6516,0.6550,0.6557,0.6601, 0.6728,0.6772,0.6784,0.6874,0.6923,0.6990,0.7007,0.7007,0.7023,0.7107, 0.7114,0.7131,0.7197,0.7231,0.7254,0.7276,0.7321,0.7322,0.7355,0.7357, 0.7377,0.7382,0.7490,0.7491,0.7589,0.7596,0.7699,0.7748,0.7780,0.7804, 0.7806,0.7852,0.7863,0.7898,0.8011,0.8013,0.8062,0.8072,0.8298,0.8313, 0.8315,0.8368,0.8443,0.8515,0.8533,0.8616,0.8650,0.8656,0.8680,0.8681, 0.8760,0.8844,0.8868,0.8991,0.9069,0.9104,0.9147,0.9159,0.9161,0.9195, 0.9281,0.9346,0.9388,0.9397,0.9397,0.9397,0.9417,0.9435,0.9446,0.9447, 0.9484,0.9510,0.9521,0.9544,0.9556,0.9595,0.9617,0.9633,0.9664,0.9724, 0.9755,0.9785,0.9811,0.9826,0.9849,0.9870,0.9899,0.9934,0.9958, Overall p-value after applying KStest on 269 p-values = 0.494401 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.