diff --git a/include/boost/math/special_functions/beta.hpp b/include/boost/math/special_functions/beta.hpp index 27901a113..2e7245d93 100644 --- a/include/boost/math/special_functions/beta.hpp +++ b/include/boost/math/special_functions/beta.hpp @@ -240,21 +240,25 @@ BOOST_MATH_GPU_ENABLED T ibeta_power_terms(T a, T c = a + b; // combine power terms with Lanczos approximation: - T agh = static_cast(a + Lanczos::g() - 0.5f); - T bgh = static_cast(b + Lanczos::g() - 0.5f); - T cgh = static_cast(c + Lanczos::g() - 0.5f); + T gh = Lanczos::g() - 0.5f; + T agh = static_cast(a + gh); + T bgh = static_cast(b + gh); + T cgh = static_cast(c + gh); if ((a < tools::min_value()) || (b < tools::min_value())) result = 0; // denominator overflows in this case else result = Lanczos::lanczos_sum_expG_scaled(c) / (Lanczos::lanczos_sum_expG_scaled(a) * Lanczos::lanczos_sum_expG_scaled(b)); + BOOST_MATH_INSTRUMENT_VARIABLE(result); result *= prefix; + BOOST_MATH_INSTRUMENT_VARIABLE(result); // combine with the leftover terms from the Lanczos approximation: result *= sqrt(bgh / boost::math::constants::e()); result *= sqrt(agh / cgh); + BOOST_MATH_INSTRUMENT_VARIABLE(result); // l1 and l2 are the base of the exponents minus one: - T l1 = (x * b - y * agh) / agh; - T l2 = (y * a - x * bgh) / bgh; + T l1 = ((x * b - y * a) - y * gh) / agh; + T l2 = ((y * a - x * b) - x * gh) / bgh; if((BOOST_MATH_GPU_SAFE_MIN(fabs(l1), fabs(l2)) < 0.2)) { // when the base of the exponent is very near 1 we get really @@ -809,9 +813,8 @@ struct ibeta_fraction2_t BOOST_MATH_GPU_ENABLED result_type operator()() { - T aN = (a + m - 1) * (a + b + m - 1) * m * (b - m) * x * x; T denom = (a + 2 * m - 1); - aN /= denom * denom; + T aN = (m * (a + m - 1) / denom) * ((a + b + m - 1) / denom) * (b - m) * x * x; T bN = static_cast(m); bN += (m * (b - m) * x) / (a + 2*m - 1); @@ -844,7 +847,9 @@ BOOST_MATH_GPU_ENABLED inline T ibeta_fraction2(T a, T b, T x, T y, const Policy return result; ibeta_fraction2_t f(a, b, x, y); - T fract = boost::math::tools::continued_fraction_b(f, boost::math::policies::get_epsilon()); + boost::uintmax_t max_terms = boost::math::policies::get_max_series_iterations(); + T fract = boost::math::tools::continued_fraction_b(f, boost::math::policies::get_epsilon(), max_terms); + boost::math::policies::check_series_iterations("boost::math::ibeta", max_terms, pol); BOOST_MATH_INSTRUMENT_VARIABLE(fract); BOOST_MATH_INSTRUMENT_VARIABLE(result); return result / fract; @@ -1118,6 +1123,60 @@ BOOST_MATH_GPU_ENABLED T binomial_ccdf(T n, T k, T x, T y, const Policy& pol) return result; } +template +T ibeta_large_ab(T a, T b, T x, T y, bool invert, bool normalised, const Policy& pol) +{ + // + // Large arguments, symetric case, see https://dlmf.nist.gov/8.18 + // + BOOST_MATH_STD_USING + + T x0 = a / (a + b); + T y0 = b / (a + b); + T nu = x0 * log(x / x0) + y0 * log(y / y0); + // + // Above compution is unstable, force nu to zero if + // something went wrong: + // + if ((nu > 0) || (x == x0) || (y == y0)) + nu = 0; + nu = sqrt(-2 * nu); + // + // As per https://dlmf.nist.gov/8.18#E10 we need to make sure we have the correct root: + // + if ((nu != 0) && (nu / (x - x0) < 0)) + nu = -nu; + // + // The correction term in https://dlmf.nist.gov/8.18#E9 is badly unstable, and often + // makes the compution worse not better, we exclude it for now: + /* + T c0 = 0; + + if (nu != 0) + { + c0 = 1 / nu; + T lim = fabs(10 * tools::epsilon() * c0); + c0 -= sqrt(x0 * y0) / (x - x0); + if(fabs(c0) < lim) + c0 = (1 - 2 * x0) / (3 * sqrt(x0 * y0)); + else + c0 *= exp(a * log(x / x0) + b * log(y / y0)); + c0 /= sqrt(constants::two_pi() * (a + b)); + } + else + { + c0 = (1 - 2 * x0) / (3 * sqrt(x0 * y0)); + c0 /= sqrt(constants::two_pi() * (a + b)); + } + */ + T mul = 1; + if (!normalised) + mul = beta(a, b, pol); + + return mul * ((invert ? (1 + boost::math::erf(-nu * sqrt((a + b) / 2), pol)) / 2 : boost::math::erfc(-nu * sqrt((a + b) / 2), pol) / 2)); +} + + // // The incomplete beta function implementation: @@ -1502,7 +1561,37 @@ BOOST_MATH_GPU_ENABLED T ibeta_imp(T a, T b, T x, const Policy& pol, bool inv, b } else { - fract = ibeta_fraction2(a, b, x, y, pol, normalised, p_derivative); + // a and b both large: + bool use_asym = false; + T ma = (std::max)(a, b); + T xa = ma == a ? x : y; + T saddle = ma / (a + b); + T powers = 0; + if ((ma > 1e-5f / tools::epsilon()) && (ma / (std::min)(a, b) < (xa < saddle ? 2 : 15))) + { + if (a == b) + use_asym = true; + else + { + powers = exp(log(x / (a / (a + b))) * a + log(y / (b / (a + b))) * b); + if (powers < tools::epsilon()) + use_asym = true; + } + } + if(use_asym) + { + fract = ibeta_large_ab(a, b, x, y, invert, normalised, pol); + if (fract * tools::epsilon() < powers) + { + // Erf approximation failed, correction term is too large, fall back: + fract = ibeta_fraction2(a, b, x, y, pol, normalised, p_derivative); + } + else + invert = false; + } + else + fract = ibeta_fraction2(a, b, x, y, pol, normalised, p_derivative); + BOOST_MATH_INSTRUMENT_VARIABLE(fract); } } diff --git a/test/Jamfile.v2 b/test/Jamfile.v2 index 4adb29d16..5a07a5344 100644 --- a/test/Jamfile.v2 +++ b/test/Jamfile.v2 @@ -260,6 +260,7 @@ test-suite special_fun : : # requirements TEST_FLOAT intel:off + gcc:-Wno-overflow : test_ibeta_float ] [ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework : # command line @@ -267,6 +268,7 @@ test-suite special_fun : : # requirements TEST_DOUBLE intel:off + gcc:-Wno-overflow : test_ibeta_double ] [ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework : # command line @@ -274,6 +276,7 @@ test-suite special_fun : : # requirements TEST_LDOUBLE intel:off + gcc:-Wno-overflow : test_ibeta_long_double ] [ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework : # command line @@ -282,6 +285,7 @@ test-suite special_fun : TEST_REAL_CONCEPT TEST_DATA=1 intel:off + gcc:-Wno-overflow : test_ibeta_real_concept1 ] [ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework : # command line @@ -290,6 +294,7 @@ test-suite special_fun : TEST_REAL_CONCEPT TEST_DATA=2 intel:off + gcc:-Wno-overflow : test_ibeta_real_concept2 ] [ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework : # command line @@ -298,6 +303,7 @@ test-suite special_fun : TEST_REAL_CONCEPT TEST_DATA=3 intel:off + gcc:-Wno-overflow : test_ibeta_real_concept3 ] [ run test_ibeta.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework : # command line @@ -306,6 +312,7 @@ test-suite special_fun : TEST_REAL_CONCEPT TEST_DATA=4 intel:off + gcc:-Wno-overflow : test_ibeta_real_concept4 ] [ run test_ibeta_derivative.cpp 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SC_(5.8391785318011288791248765287286587015835e-01), SC_(4.1608214681988711208751234712713412984165e-01) }, + { SC_(1.0000000037683200000000000000000000000000e+14), SC_(1.0043945438412800000000000000000000000000e+14), SC_(4.9914738535881042480468750000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.0000000000000000000000000000000000000000e+00), SC_(3.3725767201098864079571539530740542062052e-10332262) }, + { SC_(1.0000000037683200000000000000000000000000e+14), SC_(1.0043945438412800000000000000000000000000e+14), SC_(4.9939098954200744628906250000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.0000000000000000000000000000000000000000e+00), SC_(2.6001277949704053752299775322548093477099e-41327720) }, + { SC_(1.0000000037683200000000000000000000000000e+14), SC_(1.0043945438412800000000000000000000000000e+14), 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SC_(3.4690874676360331196400484194307104811619e-258305643) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(9.9511718631178240000000000000000000000000e+15), SC_(5.0122374296188354492187500000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.9999999999999999999999999999999999987697e-01), SC_(1.2302666016759449711870058233366459796960e-37) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(9.9560552409333760000000000000000000000000e+15), SC_(5.0110107660293579101562500000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.9999999999999999976545013709598875539400e-01), SC_(2.3454986290401124460599880352760930729250e-19) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(9.9609375450071040000000000000000000000000e+15), SC_(5.0097846984863281250000000000000000000000e-01), 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SC_(1.0000000272564224000000000000000000000000e+16), SC_(9.9755866047119360000000000000000000000000e+15), SC_(5.0061106681823730468750000000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.0363068846773661692843822127551858585241e-09), SC_(9.9999999796369311532263383071561778724481e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(9.9804689087856640000000000000000000000000e+15), SC_(5.0048875808715820312500000000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.7522423632716591948192694598633130149782e-01), SC_(8.2477576367283408051807305401366869850218e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(9.9853522866012160000000000000000000000000e+15), SC_(5.0036644935607910156250000000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(6.3652791991551795147216462542835659809785e-08), SC_(9.9999993634720800844820485278353745716434e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(9.9902345906749440000000000000000000000000e+15), SC_(5.0024425983428955078125000000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(3.3828547471369519837468982173176403958851e-01), SC_(6.6171452528630480162531017826823596041149e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(9.9951179684904960000000000000000000000000e+15), SC_(5.0012212991714477539062500000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.9999999999999999999999999999999866555398e-01), SC_(1.3344460183197995360536892964659708589971e-33) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0000000272564224000000000000000000000000e+16), SC_(5.0000000000000000000000000000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.0000000000000000000000000000000000000000e-01), SC_(5.0000000000000000000000000000000000000000e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0004882576637952000000000000000000000000e+16), SC_(4.9987795948982238769531250000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(1.6364494216375254857808433208671045206023e-04), SC_(9.9983635505783624745142191566791328954794e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0009765954453504000000000000000000000000e+16), SC_(4.9975594878196716308593750000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(5.5124021708439874198863467060757438977578e-16), SC_(9.9999999999999944875978291560125801136533e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0014648258527232000000000000000000000000e+16), SC_(4.9963405728340148925781250000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(8.5453527341249121800789383994577476189109e-04), SC_(9.9914546472658750878199210616005422523811e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0019531636342784000000000000000000000000e+16), SC_(4.9951219558715820312500000000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(8.2413660614659781256881921247356587954404e-01), SC_(1.7586339385340218743118078752643412045596e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0024413940416512000000000000000000000000e+16), SC_(4.9939042329788208007812500000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.9999999819816685089564579570950050641769e-01), SC_(1.8018331491043542042904994935823064033111e-09) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0029297318232064000000000000000000000000e+16), SC_(4.9926868081092834472656250000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.9999999999999999999999655346226949501499e-01), SC_(3.4465377305049850103766836582355539425439e-24) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0034179622305792000000000000000000000000e+16), SC_(4.9914696812629699707031250000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(4.6139019895710894972876657976032041346712e-02), SC_(9.5386098010428910502712334202396795865329e-01) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0039063000121344000000000000000000000000e+16), SC_(4.9902534484863281250000000000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(9.9596958743115699762055064903293314550541e-01), SC_(4.0304125688430023794493509670668544945940e-03) }, + { SC_(1.0000000272564224000000000000000000000000e+16), SC_(1.0043945304195072000000000000000000000000e+16), SC_(4.9890375137329101562500000000000000000000e-01), SC_(0.0000000000000000000000000000000000000000e+00), SC_(0.0000000000000000000000000000000000000000e+00), SC_(2.1688105044138971856553460331015977667304e-19), SC_(9.9999999999999999978311894955861028143447e-01) } + }}; +//#undef SC_ diff --git a/test/ibeta_large_asym_data.ipp b/test/ibeta_large_asym_data.ipp new file mode 100644 index 000000000..58282397a --- /dev/null +++ b/test/ibeta_large_asym_data.ipp @@ -0,0 +1,223 @@ +#ifndef SC_ +# define SC_(x) static_cast(BOOST_JOIN(x, L)) +#endif + static const std::array, 216> ibeta_large_asym_data = {{ + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.9028755000000000000000000000000000000000e+06), SC_(4.4999998807907104492187500000000000000000e-01), SC_(6.7345257302164224681015863169909954819429e-1153957), SC_(1.5954073231380415067243088463626848362274e-1145648), SC_(4.2211951973306332397251065526138530932813e-8309), SC_(1.0000000000000000000000000000000000000000e+00) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(2.3812680000000000000000000000000000000000e+06), SC_(4.3972539901733398437500000000000000000000e-01), SC_(6.8182153543183326515176359239213424241007e-1278111), SC_(8.7872964934870212072663237910183403621465e-1278035), SC_(7.7591729826936709829482073357324976283268e-77), SC_(1.0000000000000000000000000000000000000000e+00) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(7.9934700000000000000000000000000000000000e+06), SC_(1.9226138293743133544921875000000000000000e-01), SC_(9.9067809076337205020226204324704297621190e-2103896), SC_(1.2658599881338445200823176947439963560657e-2103895), SC_(4.3902564730816430949562878362500765540572e-01), SC_(5.6097435269183569050437121637499234459428e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.5393168000000000000000000000000000000000e+07), SC_(1.1001686006784439086914062500000000000000e-01), SC_(3.0709384592321328069793224227070303132484e-2603162), SC_(3.1427207567895459654869249145913055789048e-2603162), SC_(4.9422383051098736680545332614875134887372e-01), SC_(5.0577616948901263319454667385124865112628e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.8907696000000000000000000000000000000000e+07), SC_(9.1437831521034240722656250000000000000000e-02), SC_(2.0420460469102022545138913384686152410490e-2764269), SC_(2.0462559304440475118318579715281013896173e-2764269), SC_(4.9948513055577052930631242831720019446330e-01), SC_(5.0051486944422947069368757168279980553670e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(6.6064240000000000000000000000000000000000e+07), SC_(2.7997003868222236633300781250000000000000e-02), SC_(1.5774679601689457701293713337946112843357e-3769687), SC_(1.5767088254989601689348312809270469665752e-3769687), SC_(5.0012033800284039124664276046170731990251e-01), SC_(4.9987966199715960875335723953829268009749e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.2840448000000000000000000000000000000000e+08), SC_(1.4617582783102989196777343750000000000000e-02), SC_(1.2272989543515196592379719361127742228658e-4313187), SC_(1.1011430443339915966266513371237709561213e-4313188), SC_(9.1766620847363110463334708486842706468688e-01), SC_(8.2333791526368895366652915131572935313120e-02) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.6388441600000000000000000000000000000000e+08), SC_(1.2625593692064285278320312500000000000000e-02), SC_(2.2379905591363438077718248053802504138894e-4513497), SC_(1.2306617078599706585561478539321573698236e-4517423), SC_(1.0000000000000000000000000000000000000000e+00), SC_(5.4989584421432573401578165749458187966298e-3927) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(4.3818304000000000000000000000000000000000e+08), SC_(4.3239160440862178802490234375000000000000e-03), SC_(2.1351052162080738377752158329364831082938e-5323262), SC_(2.0876657782441229043598198786249387838491e-5323262), SC_(5.0561709811238592429363082896628831418203e-01), SC_(4.9438290188761407570636917103371168581797e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(7.0231680000000000000000000000000000000000e+08), SC_(2.7021053247153759002685546875000000000000e-03), SC_(1.7171753658340205536597508835090813960451e-5712445), SC_(1.7160489432345209932774457020612746553550e-5712445), SC_(5.0016404733540482924881125749617034624668e-01), SC_(4.9983595266459517075118874250382965375332e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.1784750080000000000000000000000000000000e+09), SC_(1.6120901564136147499084472656250000000000e-03), SC_(4.4528130280243712434575052875990444930800e-6139736), SC_(4.4507560572119092841812213188918101812581e-6139736), SC_(5.0011551383455162868187758358483146394170e-01), SC_(4.9988448616544837131812241641516853605830e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(3.3226301440000000000000000000000000000000e+09), SC_(5.1513640210032463073730468750000000000000e-04), SC_(6.1227243528801362601263162508127393370932e-7000342), SC_(4.6306591220351569534527518404998617242648e-6995907), SC_(1.3222144389218661275155255990656824473730e-4435), SC_(1.0000000000000000000000000000000000000000e+00) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(5.4911078400000000000000000000000000000000e+09), SC_(3.4295339719392359256744384765625000000000e-04), SC_(2.6149108484367269736237820382089470752852e-7411022), SC_(3.7248296633465956938312661632485346466848e-7410979), SC_(7.0202159152892498671644211451960469438267e-44), SC_(1.0000000000000000000000000000000000000000e+00) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.0208120832000000000000000000000000000000e+10), SC_(1.8635463493410497903823852539062500000000e-04), SC_(9.2748555649264491893525898280981783335603e-7923331), SC_(1.1556342762635367611762646503508689369005e-7923330), SC_(4.4523869530130975886731984520101623889977e-01), SC_(5.5476130469869024113268015479898376110023e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(2.6575216640000000000000000000000000000000e+10), SC_(7.1597540227230638265609741210937500000000e-05), SC_(4.6276736624195611675530268686084230968335e-8713987), SC_(4.7293318011006872829167186573859413979977e-8713987), SC_(4.9456780595686000753719434572816230736847e-01), SC_(5.0543219404313999246280565427183769263153e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(6.8474880000000000000000000000000000000000e+10), SC_(2.7788595616584643721580505371093750000000e-05), SC_(1.9961080344733652118397772544625551064161e-9496154), SC_(1.9996632325188685070655211837751330538841e-9496154), SC_(4.9955512993513021760290705811696850552580e-01), SC_(5.0044487006486978239709294188303149447420e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.3451883315200000000000000000000000000000e+11), SC_(1.4145593013381585478782653808593750000000e-05), SC_(1.7802207917710567492358760459317641530120e-10054170), SC_(1.7793621662538154355941990724670419045647e-10054170), SC_(5.0012060760029564593906902888483559886994e-01), SC_(4.9987939239970435406093097111516440113006e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(2.7439156428800000000000000000000000000000e+11), SC_(6.9417778831848409026861190795898437500000e-06), SC_(5.1498173848455335180334842326780925784369e-10643274), SC_(4.7162291027388222554886517100796076759608e-10643275), SC_(9.1610283387989561791260098861862134587185e-01), SC_(8.3897166120104382087399011381378654128150e-02) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(5.4010445824000000000000000000000000000000e+11), SC_(3.8754646993766073137521743774414062500000e-06), SC_(1.3881076254193924371200087146474294833952e-11202921), SC_(7.5711059271845288998190054758937238577325e-11206800), SC_(1.0000000000000000000000000000000000000000e+00), SC_(5.4542643441621118418855248447818265689195e-3879) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.0817516339200000000000000000000000000000e+12), SC_(1.7590832612768281251192092895507812500000e-06), SC_(3.6772333809533645557755250995091540910167e-11776923), SC_(3.5957399673152117619500596891305185785393e-11776923), SC_(5.0560248262545560791996817742161318129120e-01), SC_(4.9439751737454439208003182257838681870880e-01) }, + { SC_(1.9028755000000000000000000000000000000000e+06), SC_(1.2728087347200000000000000000000000000000e+12), SC_(1.4950186368878348730504512786865234375000e-06), SC_(8.7426884581369101298023785104687130896670e-11911334), SC_(8.7380599673087001814241395987917522701361e-11911334), SC_(5.0013238823406074964018234911849650065137e-01), SC_(4.9986761176593925035981765088150349934863e-01) }, + { SC_(2.3812680000000000000000000000000000000000e+06), SC_(1.9028755000000000000000000000000000000000e+06), SC_(5.5583292245864868164062500000000000000000e-01), SC_(4.3935276310388312510238078544989597454643e-1278035), SC_(4.3937688624481899562425159365193806166822e-1278035), SC_(4.9998627385513067065623722003879892278745e-01), SC_(5.0001372614486932934376277996120107721255e-01) }, + { SC_(2.3812680000000000000000000000000000000000e+06), SC_(2.3812680000000000000000000000000000000000e+06), SC_(4.4999998807907104492187500000000000000000e-01), 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SC_(1.7982567628805513164721163082264438987906e-82380117), SC_(5.5538018339724802981269582109648165246413e-20002), SC_(1.0000000000000000000000000000000000000000e+00) }, + { SC_(1.2728087347200000000000000000000000000000e+12), SC_(1.8907696000000000000000000000000000000000e+07), SC_(9.9998515844345092773437500000000000000000e-01), SC_(5.6911712371451191546793733229095185848466e-99500284), SC_(2.7398036679964406630476792082766168887765e-99500288), SC_(9.9995186102012250980477933663466132120549e-01), SC_(4.8138979877490195220663365338678794509716e-05) } + }}; +//#undef SC_ + diff --git a/test/test_ibeta.cpp b/test/test_ibeta.cpp index 987b36110..6d814b87d 100644 --- a/test/test_ibeta.cpp +++ b/test/test_ibeta.cpp @@ -97,6 +97,23 @@ void expected_results() largest_type, // test type(s) "(?i).*medium.*", // test data group ".*", 300, 80); // test function + if (std::numeric_limits::max_exponent < std::numeric_limits::max_exponent) + { + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + largest_type, // test type(s) + "(?i).*Very Large.*", // test data group + ".*", 2000000, 200000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + ".*", // platform + largest_type, // test type(s) + "(?i).*Asymptotically.*", // test data group + ".*", 900000000, 90000000); // test function + } // // Deficiencies in pow function really kick in here for // large arguments. Note also that the tests here get @@ -110,15 +127,25 @@ void expected_results() largest_type, // test type(s) "(?i).*large.*", // test data group ".*", 200000, 10000); // test function -#ifndef BOOST_MATH_NO_REAL_CONCEPT_TESTS - add_expected_result( - "[^|]*", // compiler - "[^|]*", // stdlib - "linux|Mac OS|Sun.*", // platform - "double", // test type(s) - "(?i).*large.*", // test data group - ".*", 40, 20); // test function -#endif + if (std::numeric_limits::digits == 64) + { + // 80-bit long double, errors spill over: + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + ".*", // platform + "double", // test type(s) + "(?i).*Asymptotically.*", // test data group + ".*", 500000, 50000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + ".*", // platform + "double", // test type(s) + "(?i).*large.*", // test data group + ".*", 200, 20); // test function + } + add_expected_result( "[^|]*", // compiler "[^|]*", // stdlib @@ -267,6 +294,20 @@ void expected_results() largest_type, // test type(s) "(?i).*medium.*", // test data group ".*", 350, 50); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + largest_type, // test type(s) + "(?i).*Very Large.*", // test data group + ".*", 200000, 20000); // test function + add_expected_result( + "[^|]*", // compiler + "[^|]*", // stdlib + "[^|]*", // platform + largest_type, // test type(s) + "(?i).*Asymptotically Large.*", // test data group + ".*", 900000000, 80000000); // test function add_expected_result( "[^|]*", // compiler "[^|]*", // stdlib diff --git a/test/test_ibeta.hpp b/test/test_ibeta.hpp index cfd5d78cd..e2c47955a 100644 --- a/test/test_ibeta.hpp +++ b/test/test_ibeta.hpp @@ -131,6 +131,19 @@ void test_beta(T, const char* name) do_test_beta(ibeta_int_data, name, "Incomplete Beta Function: Small Integer Values"); #endif + +#if !defined(TEST_DATA) || (TEST_DATA == 5) + if (std::numeric_limits::is_specialized) + { +# include "ibeta_large_asym_data.ipp" + + do_test_beta(ibeta_large_asym_data, name, "Incomplete Beta Function: Very Large a,b Values"); + +# include "ibeta_asym.ipp" + + do_test_beta(ibeta_asym, name, "Incomplete Beta Function: Asymptotically Large a,b Values"); + } +#endif } template diff --git a/tools/ibeta_data.cpp b/tools/ibeta_data.cpp index 357422b4a..8d24f9927 100644 --- a/tools/ibeta_data.cpp +++ b/tools/ibeta_data.cpp @@ -79,16 +79,22 @@ T get_beta(T a, T b) // compute the continued fraction: // template -T get_ibeta_fraction1(T a, T b, T x) +T get_ibeta_fraction1(T a, T b, T x, T log_scaling = 0) { + using std::isnormal; ibeta_fraction1_t f(a, b, x); T fract = boost::math::tools::continued_fraction_a(f, boost::math::policies::digits >()); T denom = (a * (fract + 1)); T num = pow(x, a) * pow(1 - x, b); - if(num == 0) - return 0; - else if(denom == 0) + if(denom == 0) return -1; + else if (!isnormal(num) || log_scaling) + { + return exp(a * log(x) + b * log(1 - x) - log(denom) - log_scaling); + } + else if (num == 0) + return 0; + return num / denom; } // @@ -100,7 +106,7 @@ std::pair ibeta_fraction1(T a, T b, T x) T bet = get_beta(a, b); if(x > ((a+1)/(a+b+2))) { - T fract = get_ibeta_fraction1(b, a, 1-x); + T fract = get_ibeta_fraction1(b, a, T(1-x)); if(fract/bet > 0.75) { fract = get_ibeta_fraction1(a, b, x); @@ -111,7 +117,7 @@ std::pair ibeta_fraction1(T a, T b, T x) T fract = get_ibeta_fraction1(a, b, x); if(fract/bet > 0.75) { - fract = get_ibeta_fraction1(b, a, 1-x); + fract = get_ibeta_fraction1(b, a, T(1-x)); return std::make_pair(bet - fract, fract); } return std::make_pair(fract, bet - fract); @@ -124,24 +130,30 @@ template std::pair ibeta_fraction1_regular(T a, T b, T x) { T bet = get_beta(a, b); + T log_scaling = 0; + if (bet == 0) + { + log_scaling = boost::math::lgamma(a) + boost::math::lgamma(b) - boost::math::lgamma(a + b); + bet = 1; + } if(x > ((a+1)/(a+b+2))) { - T fract = get_ibeta_fraction1(b, a, 1-x); + T fract = get_ibeta_fraction1(b, a, T(1-x), log_scaling); if(fract == 0) bet = 1; // normalise so we don't get 0/0 else if(bet == 0) return std::make_pair(T(-1), T(-1)); // Yikes!! if(fract / bet > 0.75) { - fract = get_ibeta_fraction1(a, b, x); + fract = get_ibeta_fraction1(a, b, x, log_scaling); return std::make_pair(fract / bet, 1 - (fract / bet)); } return std::make_pair(1 - (fract / bet), fract / bet); } - T fract = get_ibeta_fraction1(a, b, x); + T fract = get_ibeta_fraction1(a, b, x, log_scaling); if(fract / bet > 0.75) { - fract = get_ibeta_fraction1(b, a, 1-x); + fract = get_ibeta_fraction1(b, a, T(1-x), log_scaling); return std::make_pair(1 - (fract / bet), fract / bet); } return std::make_pair(fract / bet, 1 - (fract / bet)); @@ -237,9 +249,70 @@ struct beta_data_generator_int } }; +template +bool is_01(const T& x) +{ + return (x >= 0) && (x <= 1); +} + +template +bool is_interesting(const T& x) +{ + return (x > 0) && (x < 1); +} + +struct beta_data_generator_asym +{ + boost::math::tuple operator()(mp_t a_, mp_t b_) + { + float a = truncate_to_float(a_); + float b = truncate_to_float(b_); + float x0 = a / (a + b); + static const float mul[] = { 0.9, 0.99, 0.9999, 0.99999, 0.999999, 0.99999999, 1.001, 1.1, 1.00001, 1.0000001, 1.000000001 }; + static int index = 0; + float x = truncate_to_float(real_cast(x0 * mul[index])); + if (x >= 1) + throw std::domain_error(""); + index = index == 10 ? 0 : ++index; + std::pair ib_full = ibeta_fraction1(mp_t(a), mp_t(b), mp_t(x)); + std::pair ib_reg = ibeta_fraction1_regular(mp_t(a), mp_t(b), mp_t(x)); + if (!isnormal(ib_full.first) || !isnormal(ib_reg.first) || !isnormal(ib_reg.second) || !isnormal(ib_full.second) || !is_01(ib_reg.first) || !is_01(ib_reg.second)) + throw std::domain_error(""); + std::cout << a << " " << b << " " << x << " " << ib_full.first << " " << ib_reg.first << " " << ib_reg.second << std::endl; + return boost::math::make_tuple(a, b, x, ib_full.first, ib_full.second, ib_reg.first, ib_reg.second); + } +}; + +struct beta_data_generator_asym2 +{ + boost::math::tuple operator()(mp_t a_power, mp_t _b_mul, mp_t _x_mul) + { + float b_mul = truncate_to_float(_b_mul); + float x_mul = truncate_to_float(_x_mul); + float a = truncate_to_float(pow(mp_t(10), a_power)); + float b = truncate_to_float(a * b_mul); + float x0 = a / (a + b); + + std::cout << a << " " << b_mul << " " << x_mul << std::endl; + + float x = truncate_to_float(x0 * x_mul); + if (x >= 1) + throw std::domain_error(""); + if(std::isinf(a)) + throw std::domain_error(""); + + std::pair ib_full = ibeta_fraction1(mp_t(a), mp_t(b), mp_t(x)); + std::pair ib_reg = ibeta_fraction1_regular(mp_t(a), mp_t(b), mp_t(x)); + if (isnan(ib_full.first) || !isnormal(ib_reg.first) || !isnormal(ib_reg.second) || isnan(ib_full.second) || !is_01(ib_reg.first) || !is_01(ib_reg.second) || !(is_interesting(ib_reg.first) || is_interesting(ib_reg.second))) + throw std::domain_error(""); + std::cout << a << " " << b << " " << x << " " << ib_full.first << " " << ib_reg.first << " " << ib_reg.second << std::endl; + return boost::math::make_tuple(a, b, x, ib_full.first, ib_full.second, ib_reg.first, ib_reg.second); + } +}; + int main(int, char* []) { - parameter_info arg1, arg2, arg3, arg4, arg5; + parameter_info arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9, arg10, arg11, arg12; test_data data; std::cout << "Welcome.\n" @@ -252,19 +325,36 @@ int main(int, char* []) arg3 = make_random_param(mp_t(0.0001), mp_t(1), 10); arg4 = make_random_param(mp_t(0.0001), mp_t(1), 100 /*500*/); arg5 = make_periodic_param(mp_t(1), mp_t(41), 10); + arg6 = make_power_param(mp_t(0), 20, 40); + arg7 = make_power_param(mp_t(0), 20, 40); + arg8 = make_power_param(mp_t(0), 50, 70); + arg9 = make_power_param(mp_t(0), 50, 70); + arg10 = make_periodic_param(mp_t(10), mp_t(18), 4); + arg11 = make_periodic_param(mp_t(1) - 10 * mp_t(1)/2048, mp_t(1) + 10 * mp_t(1) / 2048, 20); + arg12 = make_periodic_param(mp_t(1) - 10 * mp_t(1)/2048, mp_t(1) + 10 * mp_t(1) / 2048, 20); arg1.type |= dummy_param; arg2.type |= dummy_param; arg3.type |= dummy_param; arg4.type |= dummy_param; arg5.type |= dummy_param; + arg6.type |= dummy_param; + arg7.type |= dummy_param; + arg8.type |= dummy_param; + arg9.type |= dummy_param; + arg10.type |= dummy_param; + arg11.type |= dummy_param; + arg12.type |= dummy_param; // comment out all but one of the following when running // or this program will take forever to complete! //data.insert(beta_data_generator(), arg1, arg2, arg3); //data.insert(beta_data_generator_medium(), arg4); //data.insert(beta_data_generator_small(), arg4); - data.insert(beta_data_generator_int(), arg5, arg5, arg3); + //data.insert(beta_data_generator_int(), arg5, arg5, arg3); + //data.insert(beta_data_generator_asym(), arg6, arg7); + //data.insert(beta_data_generator_asym(), arg8, arg9); + data.insert(beta_data_generator_asym2(), arg10, arg11, arg12); test_data::const_iterator i, j; i = data.begin();