RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-04-14_22:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.75 26.7198 0.937692 2 to 25 16.06 14.8168 0.391326 3 to 26 15.87 11.6332 0.178177 4 to 27 16.03 18.8167 0.660849 5 to 28 15.72 12.2155 0.213082 6 to 29 15.74 16.0195 0.477544 7 to 30 15.67 25.0736 0.906925 8 to 31 15.45 20.5517 0.753014 9 to 32 15.39 28.4282 0.959823 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.389722 Tough bday spacings test for dh-ranFile-2016-04-14_22:31: 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 11 29 74 98 90 84 53 33 16 8 4 (O-E)^2/E 0.4 1.6 0.0 0.0 0.6 0.4 0.0 0.4 0.1 0.3 0.0 Birthday Spacings: Sum(O-E)^2/E= 3.752, p= 0.042 RESULTS OF GCD FOR dh-ranFile-2016-04-14_22:31 Euclid's algorithm: p-value, steps to gcd: 0.637123 p-value, dist. of gcd's: 0.875564 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-04-14_22:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.714 0.299 0.779 0.867 0.297 0.991 0.619 0.976 Bits 8 to 15---> 0.834 0.938 0.074 0.579 0.224 0.321 0.656 0.762 Bits 16 to 23---> 0.357 0.964 0.401 0.541 0.829 0.135 0.830 0.088 Bits 24 to 31---> 0.546 0.770 0.686 0.666 0.454 0.656 0.402 0.748 KS test for the above 32 p values: 0.891 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-04-14_22:31, p-values for 5 runs: 0.6712, 0.5632, 0.8201, 0.8005, 0.6894 Rank test for binary matrices (31x31) for dh-ranFile-2016-04-14_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 197 211.4 0.983 0.983 r= 29 5078 5134.0 0.611 1.594 r= 30 23079 23103.0 0.025 1.619 r= 31 11646 11551.5 0.773 2.392 chi-square = 2.392 with df = 3; p-value = 0.505 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-04-14_22:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 212 211.4 0.002 0.002 r= 30 5069 5134.0 0.823 0.825 r= 31 23048 23103.0 0.131 0.956 r= 32 11671 11551.5 1.236 2.192 chi-square = 2.192 with df = 3; p-value = 0.466 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-04-14_22:31 b-rank test for bits 1 to 8, p=0.05698 b-rank test for bits 2 to 9, p=0.10390 b-rank test for bits 3 to 10, p=0.97285 b-rank test for bits 4 to 11, p=0.58372 b-rank test for bits 5 to 12, p=0.65057 b-rank test for bits 6 to 13, p=0.68761 b-rank test for bits 7 to 14, p=0.73001 b-rank test for bits 8 to 15, p=0.00032 b-rank test for bits 9 to 16, p=0.76344 b-rank test for bits 10 to 17, p=0.39704 b-rank test for bits 11 to 18, p=0.38288 b-rank test for bits 12 to 19, p=0.63945 b-rank test for bits 13 to 20, p=0.79063 b-rank test for bits 14 to 21, p=0.24554 b-rank test for bits 15 to 22, p=0.17500 b-rank test for bits 16 to 23, p=0.46529 b-rank test for bits 17 to 24, p=0.11944 b-rank test for bits 18 to 25, p=0.24406 b-rank test for bits 19 to 26, p=0.71447 b-rank test for bits 20 to 27, p=0.57186 b-rank test for bits 21 to 28, p=0.02229 b-rank test for bits 22 to 29, p=0.70751 b-rank test for bits 23 to 30, p=0.20940 b-rank test for bits 24 to 31, p=0.86516 b-rank test for bits 25 to 32, p=0.68723 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 = 0.559137 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-04-14_22:31 (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 141596 -0.73 0.232060 2 141149 -1.78 0.037828 3 142306 0.93 0.822985 4 142655 1.74 0.959265 5 141433 -1.11 0.132871 6 141984 0.17 0.569249 7 142536 1.46 0.928428 8 142063 0.36 0.640218 9 141700 -0.49 0.312389 10 142323 0.97 0.833108 11 142666 1.77 0.961463 12 141757 -0.36 0.360954 13 141857 -0.12 0.451344 14 142022 0.26 0.603820 15 141580 -0.77 0.220809 16 141564 -0.81 0.209878 17 141972 0.15 0.558207 18 142236 0.76 0.777342 19 142522 1.43 0.923853 20 141919 0.02 0.509013 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-04-14_22:31 Bits used No. missing words z-score p-value 23 to 32 141904 -0.0184 0.492668 22 to 31 142030 0.4161 0.661333 21 to 30 141866 -0.1494 0.440614 20 to 29 142013 0.3575 0.639635 19 to 28 142447 1.8540 0.968133 18 to 27 141677 -0.8011 0.211526 17 to 26 141923 0.0471 0.518798 16 to 25 141739 -0.5873 0.278486 15 to 24 141933 0.0816 0.532526 14 to 23 141740 -0.5839 0.279645 13 to 22 141891 -0.0632 0.474801 12 to 21 141752 -0.5425 0.293731 11 to 20 142084 0.6023 0.726516 10 to 19 142152 0.8368 0.798646 9 to 18 142222 1.0782 0.859522 8 to 17 141960 0.1747 0.569352 7 to 16 142016 0.3678 0.643499 6 to 15 142546 2.1954 0.985933 5 to 14 142455 1.8816 0.970056 4 to 13 141964 0.1885 0.574764 3 to 12 141676 -0.8046 0.210529 2 to 11 142072 0.5609 0.712578 1 to 10 141979 0.2402 0.594928 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-04-14_22:31 Bits used No. missing words z-score p-value 28 to 32 142314 1.3718 0.914931 27 to 31 141701 -0.7062 0.240031 26 to 30 141805 -0.3537 0.361797 25 to 29 142218 1.0463 0.852298 24 to 28 142009 0.3379 0.632267 23 to 27 141392 -1.7537 0.039744 22 to 26 142024 0.3887 0.651255 21 to 25 142253 1.1650 0.877987 20 to 24 140779 -3.8316 0.000064 19 to 23 141904 -0.0181 0.492792 18 to 22 142084 0.5921 0.723109 17 to 21 141605 -1.0316 0.151123 16 to 20 142079 0.5752 0.717406 15 to 19 142061 0.5141 0.696421 14 to 18 141655 -0.8621 0.194306 13 to 17 141490 -1.4215 0.077592 12 to 16 141675 -0.7943 0.213499 11 to 15 142040 0.4429 0.671099 10 to 14 141731 -0.6045 0.272753 9 to 13 141712 -0.6689 0.251775 8 to 12 141881 -0.0960 0.461747 7 to 11 141973 0.2158 0.585440 6 to 10 141894 -0.0520 0.479278 5 to 9 141919 0.0328 0.513075 4 to 8 141401 -1.7232 0.042430 3 to 7 141910 0.0023 0.500906 2 to 6 142132 0.7548 0.774820 1 to 5 141324 -1.9842 0.023618 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-04-14_22:31 Bits used No. missing words z-score p-value 31 to 32 142332 1.2468 0.893767 30 to 31 142029 0.3530 0.637959 29 to 30 141794 -0.3402 0.366851 28 to 29 142106 0.5801 0.719092 27 to 28 142140 0.6804 0.751888 26 to 27 141603 -0.9036 0.183096 25 to 26 141891 -0.0541 0.478439 24 to 25 141427 -1.4228 0.077397 23 to 24 141631 -0.8210 0.205814 22 to 23 142235 0.9607 0.831643 21 to 22 142035 0.3707 0.644573 20 to 21 142192 0.8338 0.797813 19 to 20 142124 0.6332 0.736713 18 to 19 142555 1.9046 0.971586 17 to 18 142185 0.8132 0.791944 16 to 17 142128 0.6450 0.740551 15 to 16 142607 2.0580 0.980206 14 to 15 141768 -0.4169 0.338375 13 to 14 141424 -1.4317 0.076122 12 to 13 141978 0.2026 0.580263 11 to 12 141585 -0.9567 0.169353 10 to 11 141972 0.1849 0.573333 9 to 10 141973 0.1878 0.574490 8 to 9 141730 -0.5290 0.298404 7 to 8 141767 -0.4199 0.337297 6 to 7 141829 -0.2370 0.406343 5 to 6 141847 -0.1839 0.427060 4 to 5 141909 -0.0010 0.499612 3 to 4 141829 -0.2370 0.406343 2 to 3 142106 0.5801 0.719092 1 to 2 141481 -1.2635 0.103203 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-04-14_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2376.18 -1.751 0.039960 Test results for specific bytes for dh-ranFile-2016-04-14_22:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2474.99 -0.354 0.361779 2 to 9 2535.08 0.496 0.690096 3 to 10 2493.70 -0.089 0.464495 4 to 11 2510.49 0.148 0.558947 5 to 12 2505.72 0.081 0.532256 6 to 13 2571.49 1.011 0.843998 7 to 14 2531.21 0.441 0.670551 8 to 15 2528.30 0.400 0.655493 9 to 16 2415.38 -1.197 0.115708 10 to 17 2464.85 -0.497 0.309554 11 to 18 2427.87 -1.020 0.153843 12 to 19 2383.65 -1.645 0.049934 13 to 20 2645.76 2.061 0.980363 14 to 21 2484.87 -0.214 0.415261 15 to 22 2581.22 1.149 0.874640 16 to 23 2380.49 -1.690 0.045498 17 to 24 2430.85 -0.978 0.164052 18 to 25 2602.33 1.447 0.926079 19 to 26 2397.42 -1.451 0.073439 20 to 27 2360.36 -1.975 0.024149 21 to 28 2611.54 1.577 0.942644 22 to 29 2603.86 1.469 0.929049 23 to 30 2445.06 -0.777 0.218593 24 to 31 2579.76 1.128 0.870349 25 to 32 2434.16 -0.931 0.175885 CDPARK for dh-ranFile-2016-04-14_22:31: 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 3481 -1.9178 0.027568 3489 -1.5525 0.060270 3505 -0.8219 0.205562 3571 2.1918 0.985802 3541 0.8219 0.794438 3555 1.4612 0.928018 3513 -0.4566 0.323972 3506 -0.7763 0.218799 3531 0.3653 0.642555 3527 0.1826 0.572463 Square side=100, avg. no. parked=3521.90 sample std.=27.12 p-value of the KSTEST for those 10 p-values: 0.741439 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-04-14_22:31 0.8940,0.3443,0.8254,0.2189,0.6473,0.0140,0.7926,0.7878,0.5481,0.2574, The KS test for those 10 p-values: 0.850670 The 3DSPHERES test for dh-ranFile-2016-04-14_22:31 sample no r^3 equiv. uni. 1 87.755 0.946344 2 13.105 0.353919 3 12.785 0.347000 4 7.152 0.212123 5 94.852 0.957648 6 37.481 0.713311 7 29.810 0.629788 8 26.285 0.583620 9 40.853 0.743791 10 30.864 0.642564 11 53.510 0.831981 12 37.875 0.717058 13 12.627 0.343540 14 100.964 0.965454 15 0.789 0.025947 16 6.254 0.188162 17 3.949 0.123352 18 9.281 0.266079 19 2.940 0.093358 20 57.140 0.851126 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.885254 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-04-14_22:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 0.5 0.1 -1.1 -1.2 0.5 0.7 1.7 0.1 -0.8 1.9 0.5 -0.3 0.8 0.6 1.1 0.0 -0.6 -0.9 -0.8 -1.3 0.8 0.1 -2.6 -0.0 0.5 0.4 0.7 -0.5 0.6 0.3 1.4 -1.1 -1.2 0.6 -0.7 -0.5 0.8 0.5 -0.7 -0.6 -1.0 0.8 Chi-square with 42 degrees of freedom:35.355657 z-score=-0.724957, p-value=0.244051 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-04-14_22:31 Test no p-value 1 0.000730 2 0.447559 3 0.125116 4 0.691625 5 0.013323 6 0.085095 7 0.243687 8 0.150977 9 0.968399 10 0.016826 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.002535 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-04-14_22:31: (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 66703 0.02 66772 0.17 3 25000.00 24933 0.18 24914 0.30 4 6666.67 6690 0.08 6656 0.02 5 1388.89 1417 0.57 1367 0.35 6 238.10 221 1.23 232 0.16 7 34.72 26 2.19 47 4.34 8 4.96 9 3.29 11 7.36 p=0.72770 p=0.95157 Number of rngs required: 687885, p-value: 0.275 RESULTS OF CRAPS TEST for dh-ranFile-2016-04-14_22:31 No. of wins: Observed Expected 98430 98585.9 z-score=-0.697, pvalue=0.24287 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 65983 66666.7 7.011 7.011 2 37996 37654.3 3.100 10.111 3 26949 26954.7 0.001 10.113 4 19372 19313.5 0.177 10.290 5 13958 13851.4 0.820 11.110 6 10099 9943.5 2.430 13.541 7 7223 7145.0 0.851 14.392 8 5146 5139.1 0.009 14.401 9 3675 3699.9 0.167 14.568 10 2678 2666.3 0.051 14.619 11 1945 1923.3 0.244 14.863 12 1402 1388.7 0.127 14.990 13 1003 1003.7 0.001 14.991 14 697 726.1 1.169 16.160 15 515 525.8 0.223 16.383 16 356 381.2 1.660 18.043 17 270 276.5 0.155 18.198 18 186 200.8 1.095 19.293 19 141 146.0 0.170 19.463 20 109 106.2 0.073 19.536 21 297 287.1 0.340 19.876 Chisq= 19.88 for 20 degrees of freedom, p= 0.53430 SUMMARY of craptest p-value for no. of wins: 0.242873 p-value for throws/game: 0.534305 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-04-14_22:31 No. of wins: Observed Expected 98684 98585.9 z-score= 0.439, pvalue=0.66965 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66855 66666.7 0.532 0.532 2 37812 37654.3 0.660 1.192 3 26690 26954.7 2.600 3.792 4 19353 19313.5 0.081 3.873 5 13824 13851.4 0.054 3.928 6 9904 9943.5 0.157 4.085 7 7118 7145.0 0.102 4.187 8 5160 5139.1 0.085 4.272 9 3664 3699.9 0.348 4.620 10 2712 2666.3 0.783 5.403 11 1872 1923.3 1.370 6.773 12 1344 1388.7 1.441 8.215 13 1026 1003.7 0.495 8.709 14 698 726.1 1.091 9.800 15 537 525.8 0.237 10.037 16 412 381.2 2.497 12.534 17 304 276.5 2.727 15.261 18 187 200.8 0.952 16.213 19 163 146.0 1.983 18.196 20 88 106.2 3.124 21.320 21 277 287.1 0.356 21.676 Chisq= 21.68 for 20 degrees of freedom, p= 0.64167 SUMMARY of craptest p-value for no. of wins: 0.669650 p-value for throws/game: 0.641674 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0001,0.0003,0.0007,0.0025,0.0133,0.0140,0.0168,0.0223,0.0236,0.0241, 0.0259,0.0276,0.0378,0.0397,0.0400,0.0422,0.0424,0.0455,0.0499,0.0570, 0.0603,0.0734,0.0740,0.0761,0.0774,0.0776,0.0851,0.0883,0.0934,0.1032, 0.1039,0.1157,0.1194,0.1234,0.1251,0.1329,0.1354,0.1510,0.1511,0.1538, 0.1641,0.1694,0.1750,0.1759,0.1782,0.1831,0.1882,0.1943,0.2056,0.2058, 0.2094,0.2099,0.2105,0.2115,0.2121,0.2131,0.2135,0.2186,0.2188,0.2189, 0.2208,0.2239,0.2321,0.2400,0.2429,0.2437,0.2441,0.2441,0.2455,0.2518, 0.2574,0.2661,0.2728,0.2751,0.2785,0.2796,0.2937,0.2975,0.2984,0.2993, 0.3096,0.3124,0.3214,0.3240,0.3373,0.3384,0.3435,0.3443,0.3470,0.3539, 0.3567,0.3610,0.3618,0.3618,0.3669,0.3829,0.3897,0.3913,0.3970,0.4006, 0.4023,0.4063,0.4063,0.4153,0.4271,0.4406,0.4476,0.4513,0.4535,0.4617, 0.4645,0.4653,0.4664,0.4748,0.4775,0.4784,0.4793,0.4927,0.4928,0.4996, 0.5009,0.5049,0.5090,0.5131,0.5188,0.5323,0.5325,0.5343,0.5413,0.5464, 0.5481,0.5582,0.5589,0.5591,0.5632,0.5692,0.5694,0.5719,0.5725,0.5733, 0.5745,0.5748,0.5790,0.5803,0.5836,0.5837,0.5854,0.5949,0.6038,0.6192, 0.6298,0.6323,0.6371,0.6380,0.6394,0.6396,0.6402,0.6417,0.6426,0.6426, 0.6435,0.6446,0.6473,0.6506,0.6513,0.6555,0.6561,0.6562,0.6608,0.6613, 0.6657,0.6696,0.6706,0.6711,0.6712,0.6863,0.6872,0.6876,0.6894,0.6901, 0.6916,0.6964,0.7075,0.7126,0.7133,0.7141,0.7145,0.7171,0.7174,0.7191, 0.7191,0.7231,0.7265,0.7277,0.7300,0.7367,0.7406,0.7414,0.7438,0.7478, 0.7519,0.7530,0.7622,0.7634,0.7702,0.7748,0.7773,0.7786,0.7878,0.7906, 0.7919,0.7926,0.7944,0.7978,0.7986,0.8005,0.8201,0.8230,0.8254,0.8288, 0.8301,0.8316,0.8320,0.8331,0.8340,0.8440,0.8507,0.8511,0.8523,0.8595, 0.8652,0.8670,0.8703,0.8746,0.8756,0.8780,0.8853,0.8915,0.8938,0.8940, 0.9069,0.9149,0.9239,0.9261,0.9280,0.9284,0.9290,0.9376,0.9377,0.9426, 0.9463,0.9516,0.9576,0.9593,0.9598,0.9615,0.9635,0.9655,0.9681,0.9684, 0.9701,0.9716,0.9728,0.9757,0.9802,0.9804,0.9858,0.9859,0.9907, Overall p-value after applying KStest on 269 p-values = 0.250102 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.