RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-10-29_09:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.59 24.1289 0.884026 2 to 25 15.82 18.4982 0.641915 3 to 26 15.76 10.2143 0.105618 4 to 27 16.09 18.7611 0.657586 5 to 28 15.65 26.1612 0.928426 6 to 29 15.74 11.8248 0.189370 7 to 30 15.88 15.2452 0.422177 8 to 31 15.60 15.2154 0.420030 9 to 32 15.73 27.6762 0.951133 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.648854 Tough bday spacings test for dh-ranFile-2015-10-29_09:31: 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 48 73 87 104 71 57 25 15 5 3 (O-E)^2/E 0.9 3.5 0.0 1.2 0.4 0.7 0.5 0.8 0.0 0.4 0.3 Birthday Spacings: Sum(O-E)^2/E= 8.542, p= 0.424 RESULTS OF GCD FOR dh-ranFile-2015-10-29_09:31 Euclid's algorithm: p-value, steps to gcd: 0.457792 p-value, dist. of gcd's: 0.065750 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-10-29_09:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.653 0.920 0.168 0.377 0.418 0.597 0.375 0.301 Bits 8 to 15---> 0.944 0.541 0.056 0.505 0.595 0.849 0.209 0.451 Bits 16 to 23---> 0.187 0.780 0.627 0.447 0.539 0.629 0.933 0.568 Bits 24 to 31---> 0.149 0.825 0.753 0.633 0.016 0.700 0.172 0.385 KS test for the above 32 p values: 0.228 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-10-29_09:31, p-values for 5 runs: 0.3136, 0.3796, 0.8720, 0.8169, 0.1983 Rank test for binary matrices (31x31) for dh-ranFile-2015-10-29_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 233 211.4 2.203 2.203 r= 29 5183 5134.0 0.467 2.671 r= 30 23049 23103.0 0.126 2.797 r= 31 11535 11551.5 0.024 2.821 chi-square = 2.821 with df = 3; p-value = 0.580 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-10-29_09:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 191 211.4 1.972 1.972 r= 30 5223 5134.0 1.542 3.514 r= 31 22928 23103.0 1.326 4.841 r= 32 11658 11551.5 0.981 5.822 chi-square = 5.822 with df = 3; p-value = 0.879 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-10-29_09:31 b-rank test for bits 1 to 8, p=0.47597 b-rank test for bits 2 to 9, p=0.99070 b-rank test for bits 3 to 10, p=0.61659 b-rank test for bits 4 to 11, p=0.84408 b-rank test for bits 5 to 12, p=0.96528 b-rank test for bits 6 to 13, p=0.98152 b-rank test for bits 7 to 14, p=0.99509 b-rank test for bits 8 to 15, p=0.81341 b-rank test for bits 9 to 16, p=0.34092 b-rank test for bits 10 to 17, p=0.50798 b-rank test for bits 11 to 18, p=0.70947 b-rank test for bits 12 to 19, p=0.07394 b-rank test for bits 13 to 20, p=0.85835 b-rank test for bits 14 to 21, p=0.33914 b-rank test for bits 15 to 22, p=0.00394 b-rank test for bits 16 to 23, p=0.35304 b-rank test for bits 17 to 24, p=0.77909 b-rank test for bits 18 to 25, p=0.97624 b-rank test for bits 19 to 26, p=0.81738 b-rank test for bits 20 to 27, p=0.73148 b-rank test for bits 21 to 28, p=0.91764 b-rank test for bits 22 to 29, p=0.66695 b-rank test for bits 23 to 30, p=0.68821 b-rank test for bits 24 to 31, p=0.82818 b-rank test for bits 25 to 32, p=0.15669 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 = 0.004215 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-10-29_09:31 (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 141144 -1.79 0.036876 2 142119 0.49 0.687892 3 142287 0.88 0.811222 4 141204 -1.65 0.049680 5 142386 1.11 0.867299 6 142205 0.69 0.755160 7 142199 0.68 0.750733 8 141805 -0.24 0.403708 9 141221 -1.61 0.053890 10 140942 -2.26 0.011907 11 141673 -0.55 0.290415 12 142425 1.20 0.885867 13 141171 -1.73 0.042257 14 142417 1.19 0.882217 15 141104 -1.88 0.029944 16 141754 -0.36 0.358332 17 142724 1.90 0.971508 18 143002 2.55 0.994660 19 142207 0.70 0.756626 20 141406 -1.18 0.119797 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-10-29_09:31 Bits used No. missing words z-score p-value 23 to 32 141901 -0.0287 0.488542 22 to 31 141677 -0.8011 0.211526 21 to 30 141533 -1.2977 0.097197 20 to 29 141545 -1.2563 0.104502 19 to 28 141604 -1.0529 0.146202 18 to 27 141401 -1.7529 0.039813 17 to 26 141764 -0.5011 0.308137 16 to 25 142152 0.8368 0.798646 15 to 24 141766 -0.4942 0.310568 14 to 23 141927 0.0609 0.524293 13 to 22 141579 -1.1391 0.127337 12 to 21 142424 1.7747 0.962028 11 to 20 141769 -0.4839 0.314230 10 to 19 141756 -0.5287 0.298498 9 to 18 141797 -0.3873 0.349251 8 to 17 142155 0.8471 0.801541 7 to 16 142276 1.2644 0.896953 6 to 15 142104 0.6713 0.748978 5 to 14 141757 -0.5253 0.299696 4 to 13 141804 -0.3632 0.358225 3 to 12 141731 -0.6149 0.269300 2 to 11 142223 1.0816 0.860289 1 to 10 141844 -0.2253 0.410882 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-10-29_09:31 Bits used No. missing words z-score p-value 28 to 32 142227 1.0768 0.859226 27 to 31 141983 0.2497 0.598602 26 to 30 141827 -0.2791 0.390090 25 to 29 141579 -1.1198 0.131407 24 to 28 141916 0.0226 0.509019 23 to 27 141854 -0.1876 0.425611 22 to 26 141683 -0.7672 0.221475 21 to 25 141882 -0.0926 0.463093 20 to 24 141980 0.2396 0.594664 19 to 23 141429 -1.6282 0.051737 18 to 22 142003 0.3175 0.624578 17 to 21 141499 -1.3909 0.082120 16 to 20 141671 -0.8079 0.209575 15 to 19 141771 -0.4689 0.319565 14 to 18 141778 -0.4452 0.328093 13 to 17 142431 1.7684 0.961501 12 to 16 142169 0.8802 0.810635 11 to 15 142191 0.9548 0.830164 10 to 14 142338 1.4531 0.926905 9 to 13 142198 0.9785 0.836097 8 to 12 141854 -0.1876 0.425611 7 to 11 141857 -0.1774 0.429601 6 to 10 142166 0.8701 0.807868 5 to 9 141678 -0.7842 0.216470 4 to 8 141825 -0.2859 0.387491 3 to 7 141584 -1.1028 0.135054 2 to 6 141451 -1.5537 0.060133 1 to 5 141386 -1.7740 0.038032 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-10-29_09:31 Bits used No. missing words z-score p-value 31 to 32 141829 -0.2370 0.406343 30 to 31 141687 -0.6558 0.255963 29 to 30 141629 -0.8269 0.204138 28 to 29 141841 -0.2016 0.420129 27 to 28 141977 0.1996 0.579110 26 to 27 141542 -1.0836 0.139278 25 to 26 142085 0.5182 0.697841 24 to 25 141234 -1.9921 0.023179 23 to 24 141693 -0.6381 0.261691 22 to 23 141999 0.2645 0.604308 21 to 22 141855 -0.1603 0.436336 20 to 21 142581 1.9813 0.976223 19 to 20 141994 0.2498 0.598615 18 to 19 142622 2.1023 0.982235 17 to 18 141825 -0.2488 0.401773 16 to 17 142115 0.6067 0.727974 15 to 16 141761 -0.4376 0.330856 14 to 15 142306 1.1701 0.879023 13 to 14 141423 -1.4346 0.075700 12 to 13 141691 -0.6440 0.259774 11 to 12 142479 1.6804 0.953564 10 to 11 142268 1.0580 0.854978 9 to 10 142163 0.7483 0.772857 8 to 9 142352 1.3058 0.904192 7 to 8 141657 -0.7443 0.228337 6 to 7 142040 0.3855 0.650051 5 to 6 141379 -1.5644 0.058862 4 to 5 141426 -1.4258 0.076970 3 to 4 141875 -0.1013 0.459669 2 to 3 141841 -0.2016 0.420129 1 to 2 141731 -0.5260 0.299428 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-10-29_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2556.95 0.805 0.789715 Test results for specific bytes for dh-ranFile-2015-10-29_09:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2502.44 0.035 0.513761 2 to 9 2529.80 0.421 0.663258 3 to 10 2403.38 -1.366 0.085909 4 to 11 2381.87 -1.671 0.047402 5 to 12 2463.45 -0.517 0.302628 6 to 13 2529.26 0.414 0.660493 7 to 14 2423.07 -1.088 0.138294 8 to 15 2567.17 0.950 0.828930 9 to 16 2423.44 -1.083 0.139463 10 to 17 2446.96 -0.750 0.226580 11 to 18 2517.02 0.241 0.595106 12 to 19 2419.20 -1.143 0.126577 13 to 20 2493.75 -0.088 0.464788 14 to 21 2552.61 0.744 0.771552 15 to 22 2518.64 0.264 0.603948 16 to 23 2492.68 -0.104 0.458751 17 to 24 2522.60 0.320 0.625391 18 to 25 2632.09 1.868 0.969124 19 to 26 2570.83 1.002 0.841736 20 to 27 2615.89 1.639 0.949387 21 to 28 2558.54 0.828 0.796130 22 to 29 2545.49 0.643 0.739981 23 to 30 2475.76 -0.343 0.365860 24 to 31 2578.04 1.104 0.865121 25 to 32 2426.89 -1.034 0.150568 CDPARK for dh-ranFile-2015-10-29_09:31: 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 3524 0.0457 0.518210 3528 0.2283 0.590298 3501 -1.0046 0.157553 3518 -0.2283 0.409702 3526 0.1370 0.554479 3506 -0.7763 0.218799 3541 0.8219 0.794438 3543 0.9132 0.819442 3552 1.3242 0.907282 3552 1.3242 0.907282 Square side=100, avg. no. parked=3529.10 sample std.=16.93 p-value of the KSTEST for those 10 p-values: 0.560214 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-10-29_09:31 0.2746,0.4445,0.2236,0.2671,0.0661,0.1389,0.4302,0.1670,0.7251,0.0594, The KS test for those 10 p-values: 0.023344 The 3DSPHERES test for dh-ranFile-2015-10-29_09:31 sample no r^3 equiv. uni. 1 41.155 0.746362 2 22.793 0.532227 3 12.642 0.343864 4 24.587 0.559378 5 18.459 0.459519 6 19.992 0.486442 7 42.075 0.754015 8 14.025 0.373425 9 122.646 0.983231 10 5.905 0.178660 11 11.749 0.324055 12 7.063 0.209769 13 34.567 0.684066 14 9.350 0.267780 15 3.297 0.104084 16 28.319 0.610923 17 64.922 0.885141 18 13.393 0.360101 19 4.563 0.141107 20 27.283 0.597246 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.698908 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-10-29_09:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -1.6 -0.6 0.9 -0.5 -1.1 -0.2 -0.7 1.2 -0.2 -0.3 -0.3 0.2 0.9 0.1 -0.2 0.1 -0.7 -1.1 -0.1 -0.4 0.0 1.9 1.0 0.4 0.9 -0.5 -0.6 -0.6 1.3 0.4 -1.1 -2.0 -0.6 -0.5 0.8 0.3 -0.7 0.1 -1.8 -0.6 0.0 -1.1 Chi-square with 42 degrees of freedom:30.872303 z-score=-1.214131, p-value=0.102542 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-10-29_09:31 Test no p-value 1 0.587059 2 0.573597 3 0.001302 4 0.573261 5 0.096611 6 0.501852 7 0.498992 8 0.171797 9 0.292861 10 0.015310 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.045838 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-10-29_09:31: (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 66508 0.38 66592 0.08 3 25000.00 25241 2.32 25021 0.02 4 6666.67 6562 1.64 6712 0.31 5 1388.89 1420 0.70 1394 0.02 6 238.10 235 0.04 238 0.00 7 34.72 26 2.19 35 0.00 8 4.96 7 0.84 7 0.84 p=0.76987 p=0.02669 Number of rngs required: 689506, p-value: 0.900 RESULTS OF CRAPS TEST for dh-ranFile-2015-10-29_09:31 No. of wins: Observed Expected 98437 98585.9 z-score=-0.666, pvalue=0.25278 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66375 66666.7 1.276 1.276 2 37624 37654.3 0.024 1.300 3 27092 26954.7 0.699 1.999 4 19507 19313.5 1.939 3.939 5 13830 13851.4 0.033 3.972 6 9905 9943.5 0.149 4.121 7 7127 7145.0 0.045 4.167 8 5166 5139.1 0.141 4.308 9 3759 3699.9 0.945 5.253 10 2773 2666.3 4.270 9.523 11 1937 1923.3 0.097 9.620 12 1319 1388.7 3.502 13.123 13 986 1003.7 0.313 13.435 14 669 726.1 4.496 17.932 15 518 525.8 0.117 18.049 16 387 381.2 0.090 18.138 17 293 276.5 0.980 19.118 18 207 200.8 0.190 19.308 19 146 146.0 0.000 19.308 20 107 106.2 0.006 19.314 21 273 287.1 0.694 20.007 Chisq= 20.01 for 20 degrees of freedom, p= 0.54253 SUMMARY of craptest p-value for no. of wins: 0.252775 p-value for throws/game: 0.542529 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-10-29_09:31 No. of wins: Observed Expected 98337 98585.9 z-score=-1.113, pvalue=0.13285 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66602 66666.7 0.063 0.063 2 37737 37654.3 0.182 0.244 3 27083 26954.7 0.610 0.855 4 19345 19313.5 0.051 0.906 5 13535 13851.4 7.228 8.134 6 10060 9943.5 1.364 9.498 7 7121 7145.0 0.081 9.579 8 5204 5139.1 0.820 10.399 9 3708 3699.9 0.018 10.417 10 2649 2666.3 0.112 10.530 11 1964 1923.3 0.860 11.390 12 1337 1388.7 1.928 13.317 13 927 1003.7 5.863 19.181 14 762 726.1 1.771 20.952 15 521 525.8 0.044 20.996 16 401 381.2 1.034 22.030 17 267 276.5 0.329 22.359 18 220 200.8 1.830 24.189 19 143 146.0 0.061 24.250 20 104 106.2 0.046 24.296 21 310 287.1 1.824 26.120 Chisq= 26.12 for 20 degrees of freedom, p= 0.83812 SUMMARY of craptest p-value for no. of wins: 0.132845 p-value for throws/game: 0.838119 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0013,0.0039,0.0042,0.0119,0.0153,0.0159,0.0232,0.0233,0.0267,0.0299, 0.0369,0.0380,0.0398,0.0423,0.0458,0.0474,0.0497,0.0517,0.0539,0.0560, 0.0589,0.0594,0.0601,0.0657,0.0661,0.0739,0.0757,0.0770,0.0821,0.0859, 0.0966,0.0972,0.1025,0.1041,0.1045,0.1056,0.1198,0.1266,0.1273,0.1314, 0.1328,0.1351,0.1383,0.1389,0.1393,0.1395,0.1411,0.1462,0.1491,0.1506, 0.1567,0.1576,0.1670,0.1678,0.1716,0.1718,0.1787,0.1869,0.1894,0.1983, 0.2041,0.2088,0.2096,0.2098,0.2115,0.2165,0.2188,0.2215,0.2236,0.2266, 0.2275,0.2283,0.2528,0.2560,0.2598,0.2617,0.2671,0.2678,0.2693,0.2746, 0.2904,0.2929,0.2985,0.2994,0.2997,0.3007,0.3026,0.3081,0.3106,0.3136, 0.3142,0.3196,0.3241,0.3281,0.3309,0.3391,0.3409,0.3439,0.3493,0.3530, 0.3582,0.3583,0.3601,0.3659,0.3734,0.3748,0.3770,0.3796,0.3854,0.3875, 0.3901,0.4018,0.4037,0.4063,0.4097,0.4109,0.4183,0.4200,0.4201,0.4201, 0.4222,0.4240,0.4256,0.4256,0.4296,0.4302,0.4363,0.4445,0.4466,0.4514, 0.4578,0.4588,0.4595,0.4597,0.4631,0.4648,0.4760,0.4864,0.4885,0.4990, 0.5019,0.5052,0.5080,0.5090,0.5138,0.5182,0.5243,0.5322,0.5392,0.5409, 0.5425,0.5545,0.5594,0.5602,0.5679,0.5733,0.5736,0.5791,0.5799,0.5871, 0.5903,0.5947,0.5951,0.5952,0.5965,0.5972,0.5986,0.5986,0.6039,0.6043, 0.6109,0.6166,0.6246,0.6254,0.6270,0.6290,0.6329,0.6419,0.6489,0.6501, 0.6526,0.6576,0.6605,0.6633,0.6670,0.6841,0.6879,0.6882,0.6978,0.6989, 0.7003,0.7095,0.7251,0.7280,0.7315,0.7400,0.7464,0.7490,0.7507,0.7526, 0.7540,0.7552,0.7566,0.7699,0.7716,0.7729,0.7791,0.7798,0.7897,0.7944, 0.7961,0.7986,0.8015,0.8079,0.8106,0.8112,0.8134,0.8169,0.8174,0.8194, 0.8254,0.8282,0.8289,0.8302,0.8361,0.8381,0.8417,0.8441,0.8488,0.8550, 0.8584,0.8592,0.8603,0.8651,0.8673,0.8720,0.8790,0.8794,0.8822,0.8840, 0.8851,0.8859,0.8970,0.9004,0.9042,0.9073,0.9073,0.9176,0.9198,0.9269, 0.9284,0.9332,0.9438,0.9494,0.9511,0.9536,0.9615,0.9620,0.9653,0.9691, 0.9715,0.9762,0.9762,0.9815,0.9822,0.9832,0.9907,0.9947,0.9951, Overall p-value after applying KStest on 269 p-values = 0.689733 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.