RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-01-05_00:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.99 13.6929 0.311295 2 to 25 15.80 23.3671 0.862322 3 to 26 15.71 10.7595 0.131209 4 to 27 15.76 13.0642 0.268123 5 to 28 15.93 18.0148 0.612090 6 to 29 15.63 19.8918 0.720199 7 to 30 15.81 17.3391 0.568367 8 to 31 15.64 19.0524 0.674469 9 to 32 15.79 20.6878 0.759433 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.735387 Tough bday spacings test for dh-ranFile-2016-01-05_00:31: 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 40 76 91 88 86 58 23 21 4 4 (O-E)^2/E 0.0 0.3 0.1 0.5 1.0 0.8 0.7 1.5 2.5 1.0 0.0 Birthday Spacings: Sum(O-E)^2/E= 8.377, p= 0.408 RESULTS OF GCD FOR dh-ranFile-2016-01-05_00:31 Euclid's algorithm: p-value, steps to gcd: 0.007148 p-value, dist. of gcd's: 0.524405 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-01-05_00:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.885 0.341 0.048 0.596 0.225 0.191 0.260 0.608 Bits 8 to 15---> 0.778 0.101 0.496 0.025 0.916 0.484 0.341 0.254 Bits 16 to 23---> 0.427 0.686 0.593 0.141 0.919 0.664 0.463 0.246 Bits 24 to 31---> 0.324 0.452 0.828 0.796 0.403 0.080 0.547 0.027 KS test for the above 32 p values: 0.534 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-01-05_00:31, p-values for 5 runs: 0.7859, 0.2091, 0.3781, 0.5763, 0.9831 Rank test for binary matrices (31x31) for dh-ranFile-2016-01-05_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5065 5134.0 0.928 0.955 r= 30 23088 23103.0 0.010 0.965 r= 31 11638 11551.5 0.647 1.612 chi-square = 1.612 with df = 3; p-value = 0.343 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-01-05_00:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 224 211.4 0.749 0.749 r= 30 5202 5134.0 0.900 1.649 r= 31 23069 23103.0 0.050 1.699 r= 32 11505 11551.5 0.187 1.887 chi-square = 1.887 with df = 3; p-value = 0.404 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-01-05_00:31 b-rank test for bits 1 to 8, p=0.18527 b-rank test for bits 2 to 9, p=0.79380 b-rank test for bits 3 to 10, p=0.12584 b-rank test for bits 4 to 11, p=0.80246 b-rank test for bits 5 to 12, p=0.29258 b-rank test for bits 6 to 13, p=0.68413 b-rank test for bits 7 to 14, p=0.08632 b-rank test for bits 8 to 15, p=0.24701 b-rank test for bits 9 to 16, p=0.46360 b-rank test for bits 10 to 17, p=0.85431 b-rank test for bits 11 to 18, p=0.43446 b-rank test for bits 12 to 19, p=0.84532 b-rank test for bits 13 to 20, p=0.94935 b-rank test for bits 14 to 21, p=0.67450 b-rank test for bits 15 to 22, p=0.98047 b-rank test for bits 16 to 23, p=0.03669 b-rank test for bits 17 to 24, p=0.60643 b-rank test for bits 18 to 25, p=0.23403 b-rank test for bits 19 to 26, p=0.29304 b-rank test for bits 20 to 27, p=0.96538 b-rank test for bits 21 to 28, p=0.66318 b-rank test for bits 22 to 29, p=0.51845 b-rank test for bits 23 to 30, p=0.78973 b-rank test for bits 24 to 31, p=0.93854 b-rank test for bits 25 to 32, p=0.79474 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 = 0.343018 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-01-05_00:31 (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 141076 -1.95 0.025765 2 141419 -1.15 0.125974 3 141893 -0.04 0.484782 4 142586 1.58 0.943062 5 141951 0.10 0.538780 6 142148 0.56 0.711455 7 141869 -0.09 0.462464 8 140869 -2.43 0.007535 9 142080 0.40 0.654966 10 141245 -1.55 0.060310 11 141753 -0.37 0.357460 12 141763 -0.34 0.366216 13 142308 0.93 0.824195 14 142183 0.64 0.738724 15 141886 -0.05 0.478265 16 141620 -0.68 0.249519 17 141605 -0.71 0.238526 18 142580 1.57 0.941441 19 141378 -1.24 0.107224 20 142260 0.82 0.793699 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-01-05_00:31 Bits used No. missing words z-score p-value 23 to 32 142054 0.4989 0.691062 22 to 31 141975 0.2264 0.589574 21 to 30 142188 0.9609 0.831707 20 to 29 141829 -0.2770 0.390890 19 to 28 142379 1.6196 0.947336 18 to 27 141521 -1.3391 0.090274 17 to 26 142112 0.6989 0.757681 16 to 25 142591 2.3506 0.990628 15 to 24 141909 -0.0011 0.499546 14 to 23 142316 1.4023 0.919589 13 to 22 141863 -0.1598 0.436536 12 to 21 142229 1.1023 0.864837 11 to 20 142006 0.3333 0.630563 10 to 19 141917 0.0264 0.510550 9 to 18 142008 0.3402 0.633163 8 to 17 142365 1.5713 0.941941 7 to 16 141550 -1.2391 0.107660 6 to 15 141667 -0.8356 0.201684 5 to 14 141892 -0.0598 0.476174 4 to 13 142185 0.9506 0.829093 3 to 12 142099 0.6540 0.743455 2 to 11 141459 -1.5529 0.060228 1 to 10 142009 0.3437 0.634460 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-01-05_00:31 Bits used No. missing words z-score p-value 28 to 32 142060 0.5107 0.695236 27 to 31 141818 -0.3096 0.378435 26 to 30 141919 0.0328 0.513075 25 to 29 142148 0.8091 0.790757 24 to 28 142468 1.8938 0.970874 23 to 27 142536 2.1243 0.983178 22 to 26 141801 -0.3672 0.356727 21 to 25 141629 -0.9503 0.170987 20 to 24 141720 -0.6418 0.260503 19 to 23 141687 -0.7537 0.225526 18 to 22 142025 0.3921 0.652509 17 to 21 142010 0.3413 0.633544 16 to 20 142250 1.1548 0.875917 15 to 19 141509 -1.3571 0.087383 14 to 18 141957 0.1616 0.564187 13 to 17 142269 1.2192 0.888620 12 to 16 141900 -0.0316 0.487385 11 to 15 142122 0.7209 0.764519 10 to 14 141864 -0.1537 0.438939 9 to 13 142100 0.6463 0.740970 8 to 12 141766 -0.4859 0.313532 7 to 11 141929 0.0667 0.526581 6 to 10 141396 -1.7401 0.040921 5 to 9 141455 -1.5401 0.061768 4 to 8 142231 1.0904 0.862233 3 to 7 142317 1.3819 0.916504 2 to 6 141912 0.0091 0.503611 1 to 5 141727 -0.6181 0.268265 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-01-05_00:31 Bits used No. missing words z-score p-value 31 to 32 142595 2.0226 0.978444 30 to 31 141918 0.0256 0.510202 29 to 30 141787 -0.3609 0.359104 28 to 29 141667 -0.7148 0.237355 27 to 28 142302 1.1583 0.876633 26 to 27 142077 0.4946 0.689559 25 to 26 142335 1.2557 0.895381 24 to 25 141776 -0.3933 0.347048 23 to 24 142016 0.3147 0.623490 22 to 23 142006 0.2852 0.612240 21 to 22 142190 0.8279 0.796146 20 to 21 141185 -2.1367 0.016313 19 to 20 142024 0.3383 0.632416 18 to 19 142180 0.7984 0.787691 17 to 18 141076 -2.4582 0.006982 16 to 17 141478 -1.2724 0.101623 15 to 16 142396 1.4356 0.924443 14 to 15 141868 -0.1219 0.451482 13 to 14 141942 0.0964 0.538387 12 to 13 141810 -0.2930 0.384758 11 to 12 141336 -1.6912 0.045396 10 to 11 141756 -0.4523 0.325526 9 to 10 141834 -0.2222 0.412074 8 to 9 141796 -0.3343 0.369074 7 to 8 142271 1.0669 0.856985 6 to 7 141544 -1.0777 0.140591 5 to 6 141786 -0.3638 0.358002 4 to 5 141838 -0.2104 0.416673 3 to 4 141206 -2.0747 0.019006 2 to 3 141470 -1.2960 0.097495 1 to 2 141872 -0.1101 0.456158 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-01-05_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2409.78 -1.276 0.101000 Test results for specific bytes for dh-ranFile-2016-01-05_00:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2601.49 1.435 0.924407 2 to 9 2657.60 2.229 0.987087 3 to 10 2500.18 0.003 0.501036 4 to 11 2564.26 0.909 0.818260 5 to 12 2427.36 -1.027 0.152148 6 to 13 2469.83 -0.427 0.334803 7 to 14 2477.41 -0.319 0.374685 8 to 15 2638.64 1.961 0.975041 9 to 16 2568.06 0.962 0.832095 10 to 17 2490.99 -0.127 0.449310 11 to 18 2450.98 -0.693 0.244078 12 to 19 2535.54 0.503 0.692379 13 to 20 2487.90 -0.171 0.432054 14 to 21 2512.97 0.183 0.572741 15 to 22 2478.92 -0.298 0.382822 16 to 23 2569.68 0.985 0.837795 17 to 24 2582.76 1.170 0.879069 18 to 25 2456.25 -0.619 0.268061 19 to 26 2378.46 -1.719 0.042821 20 to 27 2592.71 1.311 0.905088 21 to 28 2589.36 1.264 0.896832 22 to 29 2497.04 -0.042 0.483282 23 to 30 2411.86 -1.246 0.106295 24 to 31 2551.29 0.725 0.765874 25 to 32 2433.96 -0.934 0.175168 CDPARK for dh-ranFile-2016-01-05_00:31: 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 3562 1.7808 0.962529 3491 -1.4612 0.071982 3528 0.2283 0.590298 3488 -1.5982 0.055002 3538 0.6849 0.753306 3505 -0.8219 0.205562 3503 -0.9132 0.180558 3477 -2.1005 0.017844 3504 -0.8676 0.192812 3528 0.2283 0.590298 Square side=100, avg. no. parked=3512.40 sample std.=24.74 p-value of the KSTEST for those 10 p-values: 0.118216 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-01-05_00:31 0.6058,0.1724,0.6681,0.6321,0.6593,0.3880,0.9772,0.3503,0.7093,0.0391, The KS test for those 10 p-values: 0.819301 The 3DSPHERES test for dh-ranFile-2016-01-05_00:31 sample no r^3 equiv. uni. 1 25.360 0.570583 2 7.581 0.223298 3 26.852 0.591415 4 90.619 0.951230 5 10.350 0.291771 6 17.592 0.443676 7 61.173 0.869854 8 39.295 0.730136 9 39.004 0.727504 10 13.972 0.372329 11 51.233 0.818732 12 52.811 0.828021 13 41.358 0.748065 14 6.199 0.186693 15 75.839 0.920179 16 2.495 0.079811 17 9.279 0.266033 18 14.492 0.383115 19 49.022 0.804866 20 36.993 0.708614 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.384651 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-01-05_00:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -1.6 -0.1 -0.5 0.8 -1.3 -1.9 0.6 -0.3 -1.3 -0.2 1.7 -1.2 0.3 0.2 0.1 0.3 -0.4 -0.8 -0.1 1.4 -1.5 -1.2 0.2 0.8 2.7 0.1 1.6 -0.3 -1.2 0.5 -0.3 2.4 -0.6 -0.1 1.1 -0.9 -1.0 -0.8 1.5 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:47.048737 z-score=0.550862, p-value=0.726526 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-01-05_00:31 Test no p-value 1 0.752543 2 0.548492 3 0.710344 4 0.075813 5 0.486985 6 0.439882 7 0.137309 8 0.602674 9 0.206759 10 0.077340 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.419448 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-01-05_00:31: (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 66598 0.07 66683 0.00 3 25000.00 25185 1.37 25125 0.62 4 6666.67 6589 0.90 6509 3.73 5 1388.89 1362 0.52 1391 0.00 6 238.10 234 0.07 254 1.06 7 34.72 26 2.19 32 0.21 8 4.96 5 0.00 5 0.00 p=0.47225 p=0.53495 Number of rngs required: 687879, p-value: 0.273 RESULTS OF CRAPS TEST for dh-ranFile-2016-01-05_00:31 No. of wins: Observed Expected 97936 98585.9 z-score=-2.907, pvalue=0.00183 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66483 66666.7 0.506 0.506 2 37589 37654.3 0.113 0.619 3 27037 26954.7 0.251 0.870 4 19343 19313.5 0.045 0.916 5 13734 13851.4 0.995 1.911 6 9953 9943.5 0.009 1.920 7 7213 7145.0 0.647 2.567 8 5120 5139.1 0.071 2.637 9 3754 3699.9 0.792 3.429 10 2655 2666.3 0.048 3.477 11 1927 1923.3 0.007 3.484 12 1466 1388.7 4.298 7.783 13 1067 1003.7 3.990 11.773 14 759 726.1 1.487 13.260 15 527 525.8 0.003 13.262 16 397 381.2 0.659 13.921 17 272 276.5 0.075 13.996 18 220 200.8 1.830 15.826 19 133 146.0 1.155 16.981 20 89 106.2 2.790 19.771 21 262 287.1 2.197 21.968 Chisq= 21.97 for 20 degrees of freedom, p= 0.65772 SUMMARY of craptest p-value for no. of wins: 0.001827 p-value for throws/game: 0.657725 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-01-05_00:31 No. of wins: Observed Expected 98486 98585.9 z-score=-0.447, pvalue=0.32757 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66304 66666.7 1.973 1.973 2 37779 37654.3 0.413 2.386 3 27074 26954.7 0.528 2.913 4 19199 19313.5 0.678 3.592 5 13940 13851.4 0.566 4.158 6 10018 9943.5 0.558 4.716 7 7151 7145.0 0.005 4.721 8 5054 5139.1 1.408 6.129 9 3701 3699.9 0.000 6.129 10 2709 2666.3 0.684 6.813 11 1935 1923.3 0.071 6.884 12 1412 1388.7 0.390 7.274 13 1053 1003.7 2.420 9.694 14 701 726.1 0.870 10.564 15 533 525.8 0.098 10.662 16 382 381.2 0.002 10.664 17 287 276.5 0.396 11.059 18 227 200.8 3.410 14.470 19 138 146.0 0.437 14.906 20 108 106.2 0.030 14.936 21 295 287.1 0.217 15.153 Chisq= 15.15 for 20 degrees of freedom, p= 0.23241 SUMMARY of craptest p-value for no. of wins: 0.327573 p-value for throws/game: 0.232406 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0018,0.0070,0.0071,0.0075,0.0163,0.0178,0.0190,0.0252,0.0258,0.0269, 0.0367,0.0391,0.0409,0.0428,0.0454,0.0482,0.0550,0.0602,0.0603,0.0618, 0.0720,0.0758,0.0773,0.0798,0.0801,0.0863,0.0874,0.0903,0.0975,0.1006, 0.1010,0.1016,0.1063,0.1072,0.1077,0.1182,0.1258,0.1260,0.1312,0.1373, 0.1406,0.1414,0.1521,0.1710,0.1724,0.1752,0.1806,0.1853,0.1867,0.1906, 0.1928,0.2017,0.2056,0.2068,0.2091,0.2233,0.2248,0.2255,0.2324,0.2340, 0.2374,0.2385,0.2441,0.2459,0.2470,0.2495,0.2545,0.2604,0.2605,0.2660, 0.2681,0.2681,0.2683,0.2728,0.2918,0.2926,0.2930,0.3113,0.3135,0.3238, 0.3255,0.3276,0.3348,0.3411,0.3412,0.3430,0.3434,0.3470,0.3503,0.3567, 0.3575,0.3580,0.3591,0.3662,0.3691,0.3723,0.3747,0.3781,0.3784,0.3828, 0.3831,0.3847,0.3848,0.3880,0.3909,0.4028,0.4038,0.4079,0.4121,0.4167, 0.4194,0.4267,0.4321,0.4345,0.4365,0.4389,0.4399,0.4437,0.4493,0.4515, 0.4524,0.4562,0.4625,0.4628,0.4636,0.4722,0.4762,0.4783,0.4833,0.4838, 0.4848,0.4870,0.4874,0.4964,0.4995,0.5010,0.5036,0.5102,0.5106,0.5131, 0.5184,0.5244,0.5266,0.5342,0.5349,0.5384,0.5388,0.5467,0.5485,0.5642, 0.5684,0.5706,0.5727,0.5763,0.5896,0.5903,0.5903,0.5914,0.5935,0.5957, 0.6027,0.6058,0.6064,0.6078,0.6121,0.6122,0.6235,0.6306,0.6321,0.6324, 0.6332,0.6335,0.6345,0.6525,0.6550,0.6577,0.6593,0.6632,0.6640,0.6681, 0.6745,0.6745,0.6841,0.6859,0.6896,0.6911,0.6924,0.6952,0.7086,0.7093, 0.7103,0.7115,0.7202,0.7265,0.7275,0.7301,0.7354,0.7387,0.7410,0.7435, 0.7481,0.7525,0.7533,0.7577,0.7594,0.7645,0.7659,0.7776,0.7859,0.7877, 0.7897,0.7908,0.7937,0.7938,0.7947,0.7961,0.7963,0.8025,0.8049,0.8183, 0.8187,0.8193,0.8242,0.8280,0.8284,0.8291,0.8317,0.8321,0.8378,0.8453, 0.8543,0.8570,0.8622,0.8623,0.8648,0.8699,0.8759,0.8766,0.8791,0.8846, 0.8886,0.8954,0.8968,0.9051,0.9156,0.9165,0.9189,0.9196,0.9202,0.9244, 0.9244,0.9385,0.9414,0.9419,0.9431,0.9473,0.9493,0.9512,0.9625,0.9654, 0.9709,0.9750,0.9772,0.9784,0.9805,0.9831,0.9832,0.9871,0.9906, Overall p-value after applying KStest on 269 p-values = 0.996033 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.