RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-03-28_06:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.76 18.4223 0.637322 2 to 25 16.05 15.1841 0.417777 3 to 26 16.04 15.7025 0.454985 4 to 27 15.81 11.9591 0.197392 5 to 28 15.52 28.3530 0.959021 6 to 29 16.01 23.4352 0.864390 7 to 30 15.83 4.7583 0.001625 8 to 31 15.56 17.1802 0.557779 9 to 32 15.89 9.0231 0.060466 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.634381 Tough bday spacings test for dh-ranFile-2016-03-28_06:31: 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 8 41 78 85 102 70 58 32 15 8 3 (O-E)^2/E 0.1 0.5 0.3 1.6 0.2 0.8 0.7 0.2 0.0 0.3 0.3 Birthday Spacings: Sum(O-E)^2/E= 5.066, p= 0.113 RESULTS OF GCD FOR dh-ranFile-2016-03-28_06:31 Euclid's algorithm: p-value, steps to gcd: 0.249588 p-value, dist. of gcd's: 0.403400 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-03-28_06:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.690 0.336 0.108 0.198 0.192 0.368 0.508 0.426 Bits 8 to 15---> 0.715 0.835 0.323 0.357 0.802 0.474 0.657 0.341 Bits 16 to 23---> 0.513 0.695 0.488 0.096 0.242 0.713 0.814 0.447 Bits 24 to 31---> 0.590 0.516 0.561 0.802 0.833 0.531 0.495 0.160 KS test for the above 32 p values: 0.793 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-03-28_06:31, p-values for 5 runs: 0.9022, 0.4927, 0.5446, 0.4614, 0.8849 Rank test for binary matrices (31x31) for dh-ranFile-2016-03-28_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 209 211.4 0.028 0.028 r= 29 5114 5134.0 0.078 0.106 r= 30 23145 23103.0 0.076 0.182 r= 31 11532 11551.5 0.033 0.215 chi-square = 0.215 with df = 3; p-value = 0.025 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2016-03-28_06:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 238 211.4 3.342 3.342 r= 30 5138 5134.0 0.003 3.345 r= 31 23194 23103.0 0.358 3.703 r= 32 11430 11551.5 1.278 4.982 chi-square = 4.982 with df = 3; p-value = 0.827 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2016-03-28_06:31 b-rank test for bits 1 to 8, p=0.69892 b-rank test for bits 2 to 9, p=0.62721 b-rank test for bits 3 to 10, p=0.34689 b-rank test for bits 4 to 11, p=0.17362 b-rank test for bits 5 to 12, p=0.18954 b-rank test for bits 6 to 13, p=0.43681 b-rank test for bits 7 to 14, p=0.40447 b-rank test for bits 8 to 15, p=0.17209 b-rank test for bits 9 to 16, p=0.93989 b-rank test for bits 10 to 17, p=0.52066 b-rank test for bits 11 to 18, p=0.67183 b-rank test for bits 12 to 19, p=0.55093 b-rank test for bits 13 to 20, p=0.33143 b-rank test for bits 14 to 21, p=0.79764 b-rank test for bits 15 to 22, p=0.52159 b-rank test for bits 16 to 23, p=0.29448 b-rank test for bits 17 to 24, p=0.09575 b-rank test for bits 18 to 25, p=0.34811 b-rank test for bits 19 to 26, p=0.10492 b-rank test for bits 20 to 27, p=0.68177 b-rank test for bits 21 to 28, p=0.66955 b-rank test for bits 22 to 29, p=0.76688 b-rank test for bits 23 to 30, p=0.05449 b-rank test for bits 24 to 31, p=0.42982 b-rank test for bits 25 to 32, p=0.77937 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 = 0.576214 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-03-28_06:31 (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 141781 -0.30 0.382151 2 142683 1.81 0.964669 3 142364 1.06 0.855953 4 141780 -0.30 0.381260 5 141464 -1.04 0.149056 6 141912 0.01 0.502489 7 141471 -1.02 0.152886 8 141866 -0.10 0.459681 9 142040 0.31 0.619933 10 141622 -0.67 0.251005 11 141937 0.06 0.525774 12 141789 -0.28 0.389300 13 141541 -0.86 0.194734 14 142110 0.47 0.680413 15 142107 0.46 0.677904 16 142120 0.49 0.688718 17 142114 0.48 0.683746 18 142014 0.24 0.596600 19 142152 0.57 0.714638 20 141609 -0.70 0.241431 ---------------------------------------------------------------- OPSO test for dh-ranFile-2016-03-28_06:31 Bits used No. missing words z-score p-value 23 to 32 141877 -0.1115 0.455617 22 to 31 142172 0.9058 0.817468 21 to 30 141714 -0.6736 0.250298 20 to 29 141525 -1.3253 0.092540 19 to 28 142204 1.0161 0.845210 18 to 27 142508 2.0644 0.980509 17 to 26 142209 1.0333 0.849279 16 to 25 142156 0.8506 0.802500 15 to 24 142418 1.7540 0.960288 14 to 23 141623 -0.9873 0.161737 13 to 22 142038 0.4437 0.671367 12 to 21 142264 1.2230 0.889335 11 to 20 141618 -1.0046 0.157548 10 to 19 141639 -0.9322 0.175624 9 to 18 141730 -0.6184 0.268163 8 to 17 142257 1.1989 0.884709 7 to 16 142088 0.6161 0.731087 6 to 15 141545 -1.2563 0.104502 5 to 14 141943 0.1161 0.546215 4 to 13 141780 -0.4460 0.327811 3 to 12 141906 -0.0115 0.495419 2 to 11 141995 0.2954 0.616161 1 to 10 142372 1.5954 0.944690 ----------------------------------------------------------------- OQSO test for dh-ranFile-2016-03-28_06:31 Bits used No. missing words z-score p-value 28 to 32 141460 -1.5232 0.063860 27 to 31 141727 -0.6181 0.268265 26 to 30 141710 -0.6757 0.249617 25 to 29 141875 -0.1164 0.453679 24 to 28 141883 -0.0893 0.464440 23 to 27 141802 -0.3638 0.357992 22 to 26 141858 -0.1740 0.430933 21 to 25 141815 -0.3198 0.374574 20 to 24 141918 0.0294 0.511723 19 to 23 142045 0.4599 0.677205 18 to 22 142000 0.3074 0.620714 17 to 21 142436 1.7853 0.962895 16 to 20 141526 -1.2994 0.096899 15 to 19 141905 -0.0147 0.494145 14 to 18 142017 0.3650 0.642438 13 to 17 141845 -0.2181 0.413688 12 to 16 141894 -0.0520 0.479278 11 to 15 141525 -1.3028 0.096319 10 to 14 141883 -0.0893 0.464440 9 to 13 141684 -0.7638 0.222484 8 to 12 141629 -0.9503 0.170987 7 to 11 142046 0.4633 0.678421 6 to 10 142300 1.3243 0.907299 5 to 9 141959 0.1684 0.566855 4 to 8 142342 1.4667 0.928768 3 to 7 142165 0.8667 0.806941 2 to 6 142522 2.0768 0.981092 1 to 5 141843 -0.2248 0.411049 ----------------------------------------------------------------- DNA test for dh-ranFile-2016-03-28_06:31 Bits used No. missing words z-score p-value 31 to 32 142178 0.7925 0.785976 30 to 31 142295 1.1377 0.872371 29 to 30 142315 1.1967 0.884282 28 to 29 142074 0.4858 0.686429 27 to 28 142377 1.3796 0.916139 26 to 27 141755 -0.4553 0.324464 25 to 26 141446 -1.3668 0.085851 24 to 25 141939 0.0875 0.534872 23 to 24 141889 -0.0600 0.476090 22 to 23 141663 -0.7266 0.233724 21 to 22 141734 -0.5172 0.302509 20 to 21 141644 -0.7827 0.216906 19 to 20 141649 -0.7679 0.221263 18 to 19 141664 -0.7237 0.234629 17 to 18 141838 -0.2104 0.416673 16 to 17 141478 -1.2724 0.101623 15 to 16 142142 0.6863 0.753751 14 to 15 142018 0.3206 0.625728 13 to 14 141881 -0.0836 0.466699 12 to 13 141919 0.0285 0.511378 11 to 12 141681 -0.6735 0.250302 10 to 11 141819 -0.2665 0.394942 9 to 10 141133 -2.2901 0.011009 8 to 9 142297 1.1436 0.873599 7 to 8 142430 1.5359 0.937719 6 to 7 141678 -0.6824 0.247496 5 to 6 142282 1.0993 0.864186 4 to 5 141528 -1.1249 0.130323 3 to 4 141785 -0.3668 0.356901 2 to 3 141832 -0.2281 0.409780 1 to 2 141302 -1.7915 0.036604 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2016-03-28_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2451.01 -0.693 0.244192 Test results for specific bytes for dh-ranFile-2016-03-28_06:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2494.92 -0.072 0.471380 2 to 9 2462.94 -0.524 0.300124 3 to 10 2419.74 -1.135 0.128167 4 to 11 2422.04 -1.103 0.135122 5 to 12 2433.88 -0.935 0.174891 6 to 13 2346.43 -2.172 0.014937 7 to 14 2462.92 -0.524 0.299998 8 to 15 2564.51 0.912 0.819192 9 to 16 2473.87 -0.370 0.355850 10 to 17 2535.12 0.497 0.690265 11 to 18 2569.65 0.985 0.837702 12 to 19 2554.51 0.771 0.779627 13 to 20 2487.12 -0.182 0.427713 14 to 21 2572.54 1.026 0.847536 15 to 22 2518.87 0.267 0.605189 16 to 23 2390.39 -1.550 0.060560 17 to 24 2549.58 0.701 0.758412 18 to 25 2442.07 -0.819 0.206335 19 to 26 2523.50 0.332 0.630171 20 to 27 2527.93 0.395 0.653573 21 to 28 2438.52 -0.869 0.192308 22 to 29 2430.90 -0.977 0.164236 23 to 30 2363.54 -1.930 0.026815 24 to 31 2452.73 -0.669 0.251888 25 to 32 2518.56 0.262 0.603517 CDPARK for dh-ranFile-2016-03-28_06:31: 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 3470 -2.4201 0.007758 3539 0.7306 0.767486 3502 -0.9589 0.168804 3532 0.4110 0.659449 3530 0.3196 0.625377 3509 -0.6393 0.261324 3512 -0.5023 0.307734 3534 0.5023 0.692266 3540 0.7763 0.781201 3513 -0.4566 0.323972 Square side=100, avg. no. parked=3518.10 sample std.=20.55 p-value of the KSTEST for those 10 p-values: 0.679620 Results for the MINIMUM DISTANCE test for dh-ranFile-2016-03-28_06:31 0.0286,0.3689,0.0490,0.2371,0.4091,0.7901,0.4314,0.5343,0.5075,0.2446, The KS test for those 10 p-values: 0.177522 The 3DSPHERES test for dh-ranFile-2016-03-28_06:31 sample no r^3 equiv. uni. 1 32.587 0.662513 2 105.475 0.970277 3 0.964 0.031608 4 136.982 0.989601 5 49.196 0.805994 6 9.823 0.279222 7 19.673 0.480957 8 158.521 0.994928 9 2.210 0.071030 10 13.760 0.367881 11 48.433 0.800996 12 19.480 0.477613 13 120.979 0.982272 14 20.950 0.502592 15 16.014 0.413636 16 33.786 0.675737 17 3.408 0.107374 18 117.838 0.980316 19 18.412 0.458667 20 6.566 0.196569 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.105117 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-03-28_06:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -2.0 0.1 1.5 1.4 0.7 1.9 -0.4 0.1 0.9 -0.6 1.3 -0.1 -0.1 -1.0 -1.4 1.2 -0.1 0.8 0.2 -0.0 0.2 -0.1 -0.7 -0.2 -1.6 1.4 -0.3 0.6 0.6 -0.7 0.3 -2.4 0.3 -1.7 -1.7 -1.6 -1.0 -1.2 -0.7 0.1 -1.0 -0.1 Chi-square with 42 degrees of freedom:45.737322 z-score=0.407775, p-value=0.680311 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2016-03-28_06:31 Test no p-value 1 0.767534 2 0.371011 3 0.399728 4 0.478725 5 0.494132 6 0.007395 7 0.481979 8 0.091776 9 0.514712 10 0.774445 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.396560 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-03-28_06:31: (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 66623 0.03 66699 0.02 3 25000.00 25061 0.15 25107 0.46 4 6666.67 6613 0.43 6607 0.53 5 1388.89 1399 0.07 1349 1.15 6 238.10 255 1.20 213 2.65 7 34.72 39 0.53 17 9.04 8 4.96 9 3.29 7 0.84 p=0.54257 p=0.97711 Number of rngs required: 687402, p-value: 0.122 RESULTS OF CRAPS TEST for dh-ranFile-2016-03-28_06:31 No. of wins: Observed Expected 98971 98585.9 z-score= 1.723, pvalue=0.95752 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66700 66666.7 0.017 0.017 2 37620 37654.3 0.031 0.048 3 26893 26954.7 0.141 0.189 4 19463 19313.5 1.158 1.347 5 13895 13851.4 0.137 1.484 6 9971 9943.5 0.076 1.560 7 7169 7145.0 0.080 1.641 8 5189 5139.1 0.485 2.126 9 3627 3699.9 1.435 3.561 10 2588 2666.3 2.299 5.860 11 1891 1923.3 0.543 6.403 12 1401 1388.7 0.108 6.511 13 979 1003.7 0.609 7.120 14 704 726.1 0.675 7.795 15 539 525.8 0.330 8.125 16 354 381.2 1.934 10.059 17 263 276.5 0.663 10.722 18 222 200.8 2.232 12.953 19 152 146.0 0.248 13.201 20 98 106.2 0.635 13.837 21 282 287.1 0.091 13.928 Chisq= 13.93 for 20 degrees of freedom, p= 0.16585 SUMMARY of craptest p-value for no. of wins: 0.957517 p-value for throws/game: 0.165853 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2016-03-28_06:31 No. of wins: Observed Expected 98830 98585.9 z-score= 1.092, pvalue=0.86257 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66934 66666.7 1.072 1.072 2 37594 37654.3 0.097 1.169 3 26940 26954.7 0.008 1.177 4 19294 19313.5 0.020 1.196 5 13820 13851.4 0.071 1.268 6 9760 9943.5 3.388 4.656 7 7149 7145.0 0.002 4.658 8 5073 5139.1 0.849 5.507 9 3728 3699.9 0.214 5.721 10 2689 2666.3 0.193 5.914 11 1915 1923.3 0.036 5.951 12 1365 1388.7 0.406 6.356 13 1022 1003.7 0.333 6.689 14 717 726.1 0.115 6.805 15 533 525.8 0.098 6.902 16 389 381.2 0.162 7.064 17 295 276.5 1.232 8.296 18 234 200.8 5.479 13.775 19 134 146.0 0.984 14.759 20 112 106.2 0.315 15.074 21 303 287.1 0.879 15.953 Chisq= 15.95 for 20 degrees of freedom, p= 0.28044 SUMMARY of craptest p-value for no. of wins: 0.862571 p-value for throws/game: 0.280435 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0016,0.0074,0.0078,0.0110,0.0149,0.0248,0.0268,0.0286,0.0316,0.0366, 0.0490,0.0545,0.0605,0.0606,0.0639,0.0710,0.0859,0.0918,0.0925,0.0958, 0.0963,0.0965,0.0969,0.1016,0.1045,0.1049,0.1051,0.1074,0.1080,0.1133, 0.1225,0.1282,0.1303,0.1351,0.1491,0.1529,0.1575,0.1601,0.1617,0.1642, 0.1659,0.1688,0.1710,0.1721,0.1736,0.1749,0.1756,0.1775,0.1895,0.1918, 0.1923,0.1947,0.1966,0.1974,0.1977,0.2063,0.2169,0.2213,0.2225,0.2337, 0.2346,0.2371,0.2414,0.2417,0.2442,0.2446,0.2475,0.2496,0.2496,0.2503, 0.2503,0.2510,0.2519,0.2613,0.2682,0.2683,0.2792,0.2804,0.2945,0.3000, 0.3001,0.3025,0.3077,0.3230,0.3240,0.3245,0.3278,0.3314,0.3361,0.3408, 0.3469,0.3481,0.3558,0.3567,0.3569,0.3580,0.3675,0.3679,0.3689,0.3710, 0.3746,0.3813,0.3822,0.3893,0.3949,0.3966,0.3997,0.4034,0.4045,0.4091, 0.4098,0.4110,0.4136,0.4137,0.4167,0.4178,0.4257,0.4277,0.4298,0.4309, 0.4314,0.4368,0.4470,0.4537,0.4550,0.4556,0.4587,0.4597,0.4614,0.4644, 0.4644,0.4667,0.4714,0.4744,0.4761,0.4776,0.4787,0.4793,0.4810,0.4820, 0.4879,0.4927,0.4941,0.4941,0.4945,0.4954,0.5025,0.5026,0.5075,0.5080, 0.5114,0.5117,0.5131,0.5147,0.5163,0.5207,0.5216,0.5258,0.5312,0.5343, 0.5349,0.5426,0.5446,0.5462,0.5509,0.5578,0.5611,0.5669,0.5762,0.5905, 0.5966,0.6035,0.6052,0.6162,0.6199,0.6207,0.6254,0.6257,0.6272,0.6302, 0.6344,0.6373,0.6424,0.6536,0.6572,0.6594,0.6625,0.6695,0.6714,0.6718, 0.6757,0.6772,0.6779,0.6784,0.6796,0.6803,0.6804,0.6818,0.6837,0.6864, 0.6887,0.6903,0.6903,0.6923,0.6946,0.6989,0.7126,0.7146,0.7152,0.7311, 0.7538,0.7584,0.7669,0.7675,0.7675,0.7744,0.7794,0.7796,0.7812,0.7860, 0.7901,0.7928,0.7976,0.8010,0.8015,0.8016,0.8025,0.8060,0.8069,0.8145, 0.8175,0.8192,0.8269,0.8327,0.8349,0.8377,0.8452,0.8475,0.8493,0.8560, 0.8626,0.8642,0.8644,0.8724,0.8736,0.8843,0.8847,0.8849,0.8893,0.9022, 0.9073,0.9161,0.9288,0.9377,0.9399,0.9447,0.9575,0.9590,0.9603,0.9629, 0.9647,0.9703,0.9771,0.9803,0.9805,0.9811,0.9823,0.9896,0.9949, Overall p-value after applying KStest on 269 p-values = 0.257692 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.