RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-09-11_01:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.54 17.0228 0.547178 2 to 25 15.65 19.3183 0.689427 3 to 26 15.93 26.7427 0.938049 4 to 27 15.73 12.9003 0.257167 5 to 28 16.04 19.8783 0.719497 6 to 29 15.54 21.2503 0.784708 7 to 30 15.76 21.0200 0.774601 8 to 31 15.70 17.9968 0.610955 9 to 32 15.95 8.3928 0.042588 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.431654 Tough bday spacings test for dh-ranFile-2015-09-11_01:31: 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 14 34 83 112 96 72 44 20 10 10 5 (O-E)^2/E 2.6 0.2 1.3 2.1 0.0 0.5 1.3 3.2 1.6 1.7 0.2 Birthday Spacings: Sum(O-E)^2/E= 14.668, p= 0.855 RESULTS OF GCD FOR dh-ranFile-2015-09-11_01:31 Euclid's algorithm: p-value, steps to gcd: 0.072024 p-value, dist. of gcd's: 0.346305 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-09-11_01:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.475 0.008 0.845 0.528 0.227 0.920 0.911 0.190 Bits 8 to 15---> 0.870 0.869 0.949 0.853 0.915 0.676 0.646 0.895 Bits 16 to 23---> 0.636 0.664 0.885 0.474 0.241 0.323 0.692 0.725 Bits 24 to 31---> 0.275 0.319 0.494 0.721 0.743 0.972 0.100 0.356 KS test for the above 32 p values: 0.949 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-09-11_01:31, p-values for 5 runs: 0.7719, 0.1348, 0.4696, 0.5468, 0.0055 Rank test for binary matrices (31x31) for dh-ranFile-2015-09-11_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 234 211.4 2.412 2.412 r= 29 5130 5134.0 0.003 2.415 r= 30 23217 23103.0 0.562 2.977 r= 31 11419 11551.5 1.520 4.498 chi-square = 4.498 with df = 3; p-value = 0.787 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-09-11_01:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 214 211.4 0.032 0.032 r= 30 5197 5134.0 0.773 0.804 r= 31 23161 23103.0 0.145 0.950 r= 32 11428 11551.5 1.321 2.271 chi-square = 2.271 with df = 3; p-value = 0.482 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-09-11_01:31 b-rank test for bits 1 to 8, p=0.10526 b-rank test for bits 2 to 9, p=0.06908 b-rank test for bits 3 to 10, p=0.07754 b-rank test for bits 4 to 11, p=0.60546 b-rank test for bits 5 to 12, p=0.38912 b-rank test for bits 6 to 13, p=0.11798 b-rank test for bits 7 to 14, p=0.46894 b-rank test for bits 8 to 15, p=0.61094 b-rank test for bits 9 to 16, p=0.82987 b-rank test for bits 10 to 17, p=0.73935 b-rank test for bits 11 to 18, p=0.55613 b-rank test for bits 12 to 19, p=0.16182 b-rank test for bits 13 to 20, p=0.28061 b-rank test for bits 14 to 21, p=0.04428 b-rank test for bits 15 to 22, p=0.28078 b-rank test for bits 16 to 23, p=0.02099 b-rank test for bits 17 to 24, p=0.77489 b-rank test for bits 18 to 25, p=0.86029 b-rank test for bits 19 to 26, p=0.40851 b-rank test for bits 20 to 27, p=0.60270 b-rank test for bits 21 to 28, p=0.24993 b-rank test for bits 22 to 29, p=0.73400 b-rank test for bits 23 to 30, p=0.74324 b-rank test for bits 24 to 31, p=0.40141 b-rank test for bits 25 to 32, p=0.13468 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 = 0.180518 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-09-11_01:31 (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 140870 -2.43 0.007584 2 141525 -0.90 0.184602 3 142234 0.76 0.775947 4 142036 0.30 0.616369 5 141627 -0.66 0.254739 6 141841 -0.16 0.436579 7 141538 -0.87 0.192808 8 142121 0.49 0.689543 9 142206 0.69 0.755894 10 141897 -0.03 0.488509 11 140917 -2.32 0.010210 12 143258 3.15 0.999187 13 142425 1.20 0.885867 14 142190 0.66 0.744014 15 141403 -1.18 0.118402 16 141776 -0.31 0.377703 17 141812 -0.23 0.410054 18 141589 -0.75 0.227099 19 142574 1.55 0.939785 20 141863 -0.11 0.456900 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-09-11_01:31 Bits used No. missing words z-score p-value 23 to 32 142004 0.3264 0.627957 22 to 31 142307 1.3713 0.914856 21 to 30 141953 0.1506 0.559849 20 to 29 141884 -0.0873 0.465199 19 to 28 141997 0.3023 0.618792 18 to 27 141984 0.2575 0.601597 17 to 26 141981 0.2471 0.597599 16 to 25 141814 -0.3287 0.371182 15 to 24 141764 -0.5011 0.308137 14 to 23 141993 0.2885 0.613525 13 to 22 141845 -0.2218 0.412224 12 to 21 141937 0.0954 0.538007 11 to 20 141928 0.0644 0.525666 10 to 19 142105 0.6747 0.750075 9 to 18 142011 0.3506 0.637051 8 to 17 141852 -0.1977 0.421644 7 to 16 141880 -0.1011 0.459721 6 to 15 141999 0.3092 0.621418 5 to 14 141821 -0.3046 0.380341 4 to 13 141585 -1.1184 0.131703 3 to 12 141840 -0.2391 0.405526 2 to 11 141884 -0.0873 0.465199 1 to 10 141844 -0.2253 0.410882 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-09-11_01:31 Bits used No. missing words z-score p-value 28 to 32 141848 -0.2079 0.417654 27 to 31 141993 0.2836 0.611652 26 to 30 141801 -0.3672 0.356727 25 to 29 142502 2.0091 0.977734 24 to 28 142008 0.3345 0.630989 23 to 27 141956 0.1582 0.562852 22 to 26 141719 -0.6452 0.259403 21 to 25 141922 0.0429 0.517129 20 to 24 141699 -0.7130 0.237928 19 to 23 142069 0.5413 0.705834 18 to 22 141479 -1.4587 0.072318 17 to 21 141704 -0.6960 0.243204 16 to 20 142271 1.2260 0.889901 15 to 19 141896 -0.0452 0.481979 14 to 18 142061 0.5141 0.696421 13 to 17 141636 -0.9265 0.177082 12 to 16 141491 -1.4181 0.078086 11 to 15 142230 1.0870 0.861485 10 to 14 142307 1.3480 0.911176 9 to 13 141880 -0.0994 0.460401 8 to 12 142073 0.5548 0.710489 7 to 11 142211 1.0226 0.846754 6 to 10 141810 -0.3367 0.368167 5 to 9 141706 -0.6893 0.245332 4 to 8 141966 0.1921 0.576169 3 to 7 141861 -0.1638 0.434932 2 to 6 142107 0.6701 0.748593 1 to 5 141715 -0.6587 0.255030 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-09-11_01:31 Bits used No. missing words z-score p-value 31 to 32 142228 0.9400 0.826399 30 to 31 141604 -0.9007 0.183880 29 to 30 141500 -1.2075 0.113627 28 to 29 142432 1.5418 0.938439 27 to 28 141738 -0.5054 0.306640 26 to 27 141950 0.1200 0.547747 25 to 26 141941 0.0934 0.537216 24 to 25 142273 1.0728 0.858314 23 to 24 142131 0.6539 0.743410 22 to 23 141750 -0.4700 0.319178 21 to 22 141848 -0.1809 0.428217 20 to 21 141746 -0.4818 0.314974 19 to 20 142341 1.2734 0.898555 18 to 19 141924 0.0433 0.517259 17 to 18 141328 -1.7148 0.043188 16 to 17 141990 0.2380 0.594046 15 to 16 142155 0.7247 0.765679 14 to 15 141826 -0.2458 0.402914 13 to 14 141827 -0.2429 0.404056 12 to 13 142404 1.4592 0.927745 11 to 12 141650 -0.7650 0.222140 10 to 11 141445 -1.3697 0.085390 9 to 10 141397 -1.5113 0.065356 8 to 9 141624 -0.8417 0.199983 7 to 8 141836 -0.2163 0.414372 6 to 7 141500 -1.2075 0.113627 5 to 6 142330 1.2409 0.892681 4 to 5 141320 -1.7384 0.041067 3 to 4 141914 0.0138 0.505496 2 to 3 141672 -0.7001 0.241936 1 to 2 141252 -1.9390 0.026249 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-09-11_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2537.17 0.526 0.700421 Test results for specific bytes for dh-ranFile-2015-09-11_01:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2584.57 1.196 0.884158 2 to 9 2340.48 -2.256 0.012035 3 to 10 2577.17 1.091 0.862431 4 to 11 2504.56 0.064 0.525710 5 to 12 2503.95 0.056 0.522279 6 to 13 2594.02 1.330 0.908194 7 to 14 2590.24 1.276 0.899047 8 to 15 2519.45 0.275 0.608357 9 to 16 2478.50 -0.304 0.380565 10 to 17 2595.61 1.352 0.911841 11 to 18 2465.59 -0.487 0.313261 12 to 19 2661.72 2.287 0.988903 13 to 20 2438.17 -0.874 0.190936 14 to 21 2509.47 0.134 0.553297 15 to 22 2484.91 -0.213 0.415493 16 to 23 2411.82 -1.247 0.106200 17 to 24 2475.14 -0.352 0.362576 18 to 25 2541.64 0.589 0.722011 19 to 26 2566.45 0.940 0.826325 20 to 27 2326.20 -2.458 0.006987 21 to 28 2554.70 0.774 0.780413 22 to 29 2504.58 0.065 0.525842 23 to 30 2476.84 -0.328 0.371644 24 to 31 2528.87 0.408 0.658457 25 to 32 2422.20 -1.100 0.135625 CDPARK for dh-ranFile-2015-09-11_01:31: 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 3514 -0.4110 0.340551 3521 -0.0913 0.463617 3508 -0.6849 0.246694 3475 -2.1918 0.014198 3527 0.1826 0.572463 3486 -1.6895 0.045562 3523 0.0000 0.500000 3491 -1.4612 0.071982 3480 -1.9635 0.024796 3541 0.8219 0.794438 Square side=100, avg. no. parked=3506.60 sample std.=21.23 p-value of the KSTEST for those 10 p-values: 0.030446 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-09-11_01:31 0.4830,0.6565,0.9894,0.4204,0.8452,0.9917,0.0543,0.0226,0.7509,0.6762, The KS test for those 10 p-values: 0.197598 The 3DSPHERES test for dh-ranFile-2015-09-11_01:31 sample no r^3 equiv. uni. 1 16.739 0.427629 2 37.463 0.713145 3 35.452 0.693258 4 8.146 0.237790 5 13.067 0.353104 6 150.593 0.993394 7 20.991 0.503261 8 18.372 0.457943 9 5.588 0.169934 10 50.755 0.815821 11 25.960 0.579095 12 41.445 0.748801 13 50.652 0.815184 14 71.646 0.908206 15 60.606 0.867369 16 31.010 0.644295 17 17.629 0.444361 18 56.073 0.845737 19 15.564 0.404763 20 44.237 0.771119 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.086477 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-09-11_01:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -1.5 -0.7 0.6 -0.5 -0.3 1.1 0.3 -1.7 1.0 -0.1 0.6 0.2 0.6 0.2 0.5 0.2 -1.1 0.2 -0.3 -0.1 -0.4 0.2 -0.9 0.1 -1.6 3.3 0.0 0.2 0.1 -0.1 -1.7 -0.2 -1.0 0.5 -0.2 0.1 0.7 0.5 -1.2 1.0 0.1 0.0 -0.1 Chi-square with 42 degrees of freedom:32.915169 z-score=-0.991236, p-value=0.158866 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-09-11_01:31 Test no p-value 1 0.979226 2 0.450989 3 0.013632 4 0.521067 5 0.879894 6 0.015150 7 0.323123 8 0.292190 9 0.472274 10 0.157510 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.290955 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-09-11_01:31: (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 66847 0.49 66660 0.00 3 25000.00 24772 2.08 25053 0.11 4 6666.67 6766 1.48 6665 0.00 5 1388.89 1338 1.86 1377 0.10 6 238.10 224 0.83 213 2.65 7 34.72 46 3.66 30 0.64 8 4.96 6 0.22 1 3.16 p=0.89946 p=0.64691 Number of rngs required: 688271, p-value: 0.440 RESULTS OF CRAPS TEST for dh-ranFile-2015-09-11_01:31 No. of wins: Observed Expected 98338 98585.9 z-score=-1.109, pvalue=0.13381 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66438 66666.7 0.784 0.784 2 38015 37654.3 3.455 4.239 3 26689 26954.7 2.620 6.859 4 19352 19313.5 0.077 6.936 5 13906 13851.4 0.215 7.151 6 10154 9943.5 4.454 11.605 7 7036 7145.0 1.664 13.269 8 5172 5139.1 0.211 13.480 9 3634 3699.9 1.173 14.652 10 2599 2666.3 1.699 16.351 11 1905 1923.3 0.175 16.526 12 1383 1388.7 0.024 16.549 13 960 1003.7 1.904 18.453 14 818 726.1 11.621 30.074 15 566 525.8 3.068 33.142 16 393 381.2 0.368 33.510 17 239 276.5 5.096 38.606 18 194 200.8 0.232 38.838 19 154 146.0 0.440 39.278 20 109 106.2 0.073 39.351 21 284 287.1 0.034 39.385 Chisq= 39.39 for 20 degrees of freedom, p= 0.99403 SUMMARY of craptest p-value for no. of wins: 0.133808 p-value for throws/game: 0.994031 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-09-11_01:31 No. of wins: Observed Expected 98488 98585.9 z-score=-0.438, pvalue=0.33081 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66753 66666.7 0.112 0.112 2 37809 37654.3 0.635 0.747 3 26759 26954.7 1.421 2.169 4 19004 19313.5 4.959 7.127 5 13953 13851.4 0.745 7.872 6 10007 9943.5 0.405 8.277 7 7157 7145.0 0.020 8.297 8 5209 5139.1 0.952 9.249 9 3652 3699.9 0.619 9.868 10 2682 2666.3 0.092 9.960 11 1938 1923.3 0.112 10.072 12 1433 1388.7 1.411 11.483 13 1032 1003.7 0.797 12.280 14 717 726.1 0.115 12.395 15 507 525.8 0.675 13.070 16 375 381.2 0.099 13.169 17 275 276.5 0.009 13.177 18 208 200.8 0.256 13.433 19 158 146.0 0.989 14.422 20 90 106.2 2.475 16.898 21 282 287.1 0.091 16.989 Chisq= 16.99 for 20 degrees of freedom, p= 0.34631 SUMMARY of craptest p-value for no. of wins: 0.330809 p-value for throws/game: 0.346309 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0055,0.0070,0.0076,0.0077,0.0102,0.0120,0.0136,0.0142,0.0151,0.0210, 0.0226,0.0248,0.0262,0.0304,0.0411,0.0426,0.0432,0.0443,0.0456,0.0543, 0.0654,0.0691,0.0720,0.0720,0.0723,0.0775,0.0781,0.0854,0.0865,0.1002, 0.1053,0.1062,0.1136,0.1136,0.1180,0.1184,0.1317,0.1338,0.1347,0.1348, 0.1356,0.1575,0.1589,0.1618,0.1699,0.1771,0.1805,0.1839,0.1846,0.1904, 0.1909,0.1928,0.1976,0.2000,0.2221,0.2268,0.2271,0.2378,0.2379,0.2413, 0.2419,0.2432,0.2453,0.2467,0.2499,0.2547,0.2550,0.2572,0.2594,0.2755, 0.2806,0.2808,0.2910,0.2922,0.3066,0.3081,0.3133,0.3150,0.3190,0.3192, 0.3231,0.3233,0.3308,0.3406,0.3463,0.3463,0.3531,0.3563,0.3567,0.3626, 0.3682,0.3712,0.3716,0.3777,0.3803,0.3806,0.3891,0.4014,0.4029,0.4041, 0.4048,0.4055,0.4085,0.4101,0.4109,0.4122,0.4144,0.4155,0.4177,0.4204, 0.4216,0.4276,0.4282,0.4317,0.4349,0.4366,0.4396,0.4444,0.4510,0.4569, 0.4579,0.4597,0.4604,0.4636,0.4652,0.4652,0.4689,0.4696,0.4723,0.4737, 0.4748,0.4818,0.4820,0.4830,0.4885,0.4943,0.5000,0.5033,0.5055,0.5171, 0.5173,0.5211,0.5223,0.5257,0.5257,0.5258,0.5285,0.5372,0.5380,0.5468, 0.5472,0.5477,0.5533,0.5561,0.5598,0.5629,0.5725,0.5762,0.5791,0.5940, 0.5976,0.6016,0.6027,0.6055,0.6084,0.6109,0.6110,0.6117,0.6135,0.6164, 0.6188,0.6214,0.6280,0.6310,0.6356,0.6371,0.6443,0.6460,0.6469,0.6565, 0.6585,0.6645,0.6758,0.6762,0.6894,0.6895,0.6923,0.6933,0.6964,0.7004, 0.7058,0.7105,0.7131,0.7195,0.7208,0.7220,0.7248,0.7340,0.7394,0.7432, 0.7433,0.7434,0.7440,0.7486,0.7488,0.7501,0.7509,0.7559,0.7657,0.7711, 0.7719,0.7746,0.7749,0.7759,0.7804,0.7847,0.7875,0.7944,0.8152,0.8158, 0.8263,0.8264,0.8299,0.8452,0.8452,0.8457,0.8468,0.8527,0.8554,0.8583, 0.8603,0.8615,0.8624,0.8674,0.8688,0.8697,0.8799,0.8842,0.8853,0.8859, 0.8899,0.8927,0.8952,0.8986,0.8990,0.8995,0.9082,0.9082,0.9112,0.9113, 0.9118,0.9149,0.9155,0.9204,0.9277,0.9380,0.9384,0.9398,0.9487,0.9488, 0.9721,0.9777,0.9792,0.9889,0.9894,0.9917,0.9934,0.9940,0.9992, Overall p-value after applying KStest on 269 p-values = 0.770055 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.