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diff --git a/src/third_party/boost-1.60.0/boost/math/special_functions/detail/lgamma_small.hpp b/src/third_party/boost-1.60.0/boost/math/special_functions/detail/lgamma_small.hpp new file mode 100644 index 00000000000..e65f8b7e98e --- /dev/null +++ b/src/third_party/boost-1.60.0/boost/math/special_functions/detail/lgamma_small.hpp @@ -0,0 +1,522 @@ +// (C) Copyright John Maddock 2006. +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifndef BOOST_MATH_SPECIAL_FUNCTIONS_DETAIL_LGAMMA_SMALL +#define BOOST_MATH_SPECIAL_FUNCTIONS_DETAIL_LGAMMA_SMALL + +#ifdef _MSC_VER +#pragma once +#endif + +#include <boost/math/tools/big_constant.hpp> + +namespace boost{ namespace math{ namespace detail{ + +// +// These need forward declaring to keep GCC happy: +// +template <class T, class Policy, class Lanczos> +T gamma_imp(T z, const Policy& pol, const Lanczos& l); +template <class T, class Policy> +T gamma_imp(T z, const Policy& pol, const lanczos::undefined_lanczos& l); + +// +// lgamma for small arguments: +// +template <class T, class Policy, class Lanczos> +T lgamma_small_imp(T z, T zm1, T zm2, const mpl::int_<64>&, const Policy& /* l */, const Lanczos&) +{ + // This version uses rational approximations for small + // values of z accurate enough for 64-bit mantissas + // (80-bit long doubles), works well for 53-bit doubles as well. + // Lanczos is only used to select the Lanczos function. + + BOOST_MATH_STD_USING // for ADL of std names + T result = 0; + if(z < tools::epsilon<T>()) + { + result = -log(z); + } + else if((zm1 == 0) || (zm2 == 0)) + { + // nothing to do, result is zero.... + } + else if(z > 2) + { + // + // Begin by performing argument reduction until + // z is in [2,3): + // + if(z >= 3) + { + do + { + z -= 1; + zm2 -= 1; + result += log(z); + }while(z >= 3); + // Update zm2, we need it below: + zm2 = z - 2; + } + + // + // Use the following form: + // + // lgamma(z) = (z-2)(z+1)(Y + R(z-2)) + // + // where R(z-2) is a rational approximation optimised for + // low absolute error - as long as it's absolute error + // is small compared to the constant Y - then any rounding + // error in it's computation will get wiped out. + // + // R(z-2) has the following properties: + // + // At double: Max error found: 4.231e-18 + // At long double: Max error found: 1.987e-21 + // Maximum Deviation Found (approximation error): 5.900e-24 + // + static const T P[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.180355685678449379109e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.25126649619989678683e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.494103151567532234274e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.172491608709613993966e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.259453563205438108893e-3)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.541009869215204396339e-3)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.324588649825948492091e-4)) + }; + static const T Q[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.1e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.196202987197795200688e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.148019669424231326694e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.541391432071720958364e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.988504251128010129477e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.82130967464889339326e-2)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.224936291922115757597e-3)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.223352763208617092964e-6)) + }; + + static const float Y = 0.158963680267333984375e0f; + + T r = zm2 * (z + 1); + T R = tools::evaluate_polynomial(P, zm2); + R /= tools::evaluate_polynomial(Q, zm2); + + result += r * Y + r * R; + } + else + { + // + // If z is less than 1 use recurrance to shift to + // z in the interval [1,2]: + // + if(z < 1) + { + result += -log(z); + zm2 = zm1; + zm1 = z; + z += 1; + } + // + // Two approximations, on for z in [1,1.5] and + // one for z in [1.5,2]: + // + if(z <= 1.5) + { + // + // Use the following form: + // + // lgamma(z) = (z-1)(z-2)(Y + R(z-1)) + // + // where R(z-1) is a rational approximation optimised for + // low absolute error - as long as it's absolute error + // is small compared to the constant Y - then any rounding + // error in it's computation will get wiped out. + // + // R(z-1) has the following properties: + // + // At double precision: Max error found: 1.230011e-17 + // At 80-bit long double precision: Max error found: 5.631355e-21 + // Maximum Deviation Found: 3.139e-021 + // Expected Error Term: 3.139e-021 + + // + static const float Y = 0.52815341949462890625f; + + static const T P[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.490622454069039543534e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.969117530159521214579e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.414983358359495381969e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.406567124211938417342e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.158413586390692192217e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.240149820648571559892e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.100346687696279557415e-2)) + }; + static const T Q[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.1e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.302349829846463038743e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.348739585360723852576e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.191415588274426679201e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.507137738614363510846e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.577039722690451849648e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.195768102601107189171e-2)) + }; + + T r = tools::evaluate_polynomial(P, zm1) / tools::evaluate_polynomial(Q, zm1); + T prefix = zm1 * zm2; + + result += prefix * Y + prefix * r; + } + else + { + // + // Use the following form: + // + // lgamma(z) = (2-z)(1-z)(Y + R(2-z)) + // + // where R(2-z) is a rational approximation optimised for + // low absolute error - as long as it's absolute error + // is small compared to the constant Y - then any rounding + // error in it's computation will get wiped out. + // + // R(2-z) has the following properties: + // + // At double precision, max error found: 1.797565e-17 + // At 80-bit long double precision, max error found: 9.306419e-21 + // Maximum Deviation Found: 2.151e-021 + // Expected Error Term: 2.150e-021 + // + static const float Y = 0.452017307281494140625f; + + static const T P[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.292329721830270012337e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.144216267757192309184e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.142440390738631274135e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.542809694055053558157e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.850535976868336437746e-2)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.431171342679297331241e-3)) + }; + static const T Q[] = { + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.1e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.150169356054485044494e1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.846973248876495016101e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.220095151814995745555e0)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.25582797155975869989e-1)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.100666795539143372762e-2)), + static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.827193521891290553639e-6)) + }; + T r = zm2 * zm1; + T R = tools::evaluate_polynomial(P, T(-zm2)) / tools::evaluate_polynomial(Q, T(-zm2)); + + result += r * Y + r * R; + } + } + return result; +} +template <class T, class Policy, class Lanczos> +T lgamma_small_imp(T z, T zm1, T zm2, const mpl::int_<113>&, const Policy& /* l */, const Lanczos&) +{ + // + // This version uses rational approximations for small + // values of z accurate enough for 113-bit mantissas + // (128-bit long doubles). + // + BOOST_MATH_STD_USING // for ADL of std names + T result = 0; + if(z < tools::epsilon<T>()) + { + result = -log(z); + BOOST_MATH_INSTRUMENT_CODE(result); + } + else if((zm1 == 0) || (zm2 == 0)) + { + // nothing to do, result is zero.... + } + else if(z > 2) + { + // + // Begin by performing argument reduction until + // z is in [2,3): + // + if(z >= 3) + { + do + { + z -= 1; + result += log(z); + }while(z >= 3); + zm2 = z - 2; + } + BOOST_MATH_INSTRUMENT_CODE(zm2); + BOOST_MATH_INSTRUMENT_CODE(z); + BOOST_MATH_INSTRUMENT_CODE(result); + + // + // Use the following form: + // + // lgamma(z) = (z-2)(z+1)(Y + R(z-2)) + // + // where R(z-2) is a rational approximation optimised for + // low absolute error - as long as it's absolute error + // is small compared to the constant Y - then any rounding + // error in it's computation will get wiped out. + // + // Maximum Deviation Found (approximation error) 3.73e-37 + + static const T P[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, -0.018035568567844937910504030027467476655), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.013841458273109517271750705401202404195), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.062031842739486600078866923383017722399), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.052518418329052161202007865149435256093), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.01881718142472784129191838493267755758), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.0025104830367021839316463675028524702846), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.00021043176101831873281848891452678568311), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.00010249622350908722793327719494037981166), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.11381479670982006841716879074288176994e-4), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.49999811718089980992888533630523892389e-6), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.70529798686542184668416911331718963364e-8) + }; + static const T Q[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), + BOOST_MATH_BIG_CONSTANT(T, 113, 2.5877485070422317542808137697939233685), + BOOST_MATH_BIG_CONSTANT(T, 113, 2.8797959228352591788629602533153837126), + BOOST_MATH_BIG_CONSTANT(T, 113, 1.8030885955284082026405495275461180977), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.69774331297747390169238306148355428436), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.17261566063277623942044077039756583802), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.02729301254544230229429621192443000121), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.0026776425891195270663133581960016620433), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.00015244249160486584591370355730402168106), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.43997034032479866020546814475414346627e-5), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.46295080708455613044541885534408170934e-7), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.93326638207459533682980757982834180952e-11), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.42316456553164995177177407325292867513e-13) + }; + + T R = tools::evaluate_polynomial(P, zm2); + R /= tools::evaluate_polynomial(Q, zm2); + + static const float Y = 0.158963680267333984375F; + + T r = zm2 * (z + 1); + + result += r * Y + r * R; + BOOST_MATH_INSTRUMENT_CODE(result); + } + else + { + // + // If z is less than 1 use recurrance to shift to + // z in the interval [1,2]: + // + if(z < 1) + { + result += -log(z); + zm2 = zm1; + zm1 = z; + z += 1; + } + BOOST_MATH_INSTRUMENT_CODE(result); + BOOST_MATH_INSTRUMENT_CODE(z); + BOOST_MATH_INSTRUMENT_CODE(zm2); + // + // Three approximations, on for z in [1,1.35], [1.35,1.625] and [1.625,1] + // + if(z <= 1.35) + { + // + // Use the following form: + // + // lgamma(z) = (z-1)(z-2)(Y + R(z-1)) + // + // where R(z-1) is a rational approximation optimised for + // low absolute error - as long as it's absolute error + // is small compared to the constant Y - then any rounding + // error in it's computation will get wiped out. + // + // R(z-1) has the following properties: + // + // Maximum Deviation Found (approximation error) 1.659e-36 + // Expected Error Term (theoretical error) 1.343e-36 + // Max error found at 128-bit long double precision 1.007e-35 + // + static const float Y = 0.54076099395751953125f; + + static const T P[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, 0.036454670944013329356512090082402429697), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.066235835556476033710068679907798799959), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.67492399795577182387312206593595565371), + BOOST_MATH_BIG_CONSTANT(T, 113, -1.4345555263962411429855341651960000166), + BOOST_MATH_BIG_CONSTANT(T, 113, -1.4894319559821365820516771951249649563), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.87210277668067964629483299712322411566), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.29602090537771744401524080430529369136), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.0561832587517836908929331992218879676), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.0053236785487328044334381502530383140443), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.00018629360291358130461736386077971890789), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.10164985672213178500790406939467614498e-6), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.13680157145361387405588201461036338274e-8) + }; + static const T Q[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), + BOOST_MATH_BIG_CONSTANT(T, 113, 4.9106336261005990534095838574132225599), + BOOST_MATH_BIG_CONSTANT(T, 113, 10.258804800866438510889341082793078432), + BOOST_MATH_BIG_CONSTANT(T, 113, 11.88588976846826108836629960537466889), + BOOST_MATH_BIG_CONSTANT(T, 113, 8.3455000546999704314454891036700998428), + BOOST_MATH_BIG_CONSTANT(T, 113, 3.6428823682421746343233362007194282703), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.97465989807254572142266753052776132252), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.15121052897097822172763084966793352524), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.012017363555383555123769849654484594893), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.0003583032812720649835431669893011257277) + }; + + T r = tools::evaluate_polynomial(P, zm1) / tools::evaluate_polynomial(Q, zm1); + T prefix = zm1 * zm2; + + result += prefix * Y + prefix * r; + BOOST_MATH_INSTRUMENT_CODE(result); + } + else if(z <= 1.625) + { + // + // Use the following form: + // + // lgamma(z) = (2-z)(1-z)(Y + R(2-z)) + // + // where R(2-z) is a rational approximation optimised for + // low absolute error - as long as it's absolute error + // is small compared to the constant Y - then any rounding + // error in it's computation will get wiped out. + // + // R(2-z) has the following properties: + // + // Max error found at 128-bit long double precision 9.634e-36 + // Maximum Deviation Found (approximation error) 1.538e-37 + // Expected Error Term (theoretical error) 2.350e-38 + // + static const float Y = 0.483787059783935546875f; + + static const T P[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, -0.017977422421608624353488126610933005432), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.18484528905298309555089509029244135703), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.40401251514859546989565001431430884082), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.40277179799147356461954182877921388182), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.21993421441282936476709677700477598816), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.069595742223850248095697771331107571011), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.012681481427699686635516772923547347328), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.0012489322866834830413292771335113136034), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.57058739515423112045108068834668269608e-4), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.8207548771933585614380644961342925976e-6) + }; + static const T Q[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), + BOOST_MATH_BIG_CONSTANT(T, 113, -2.9629552288944259229543137757200262073), + BOOST_MATH_BIG_CONSTANT(T, 113, 3.7118380799042118987185957298964772755), + BOOST_MATH_BIG_CONSTANT(T, 113, -2.5569815272165399297600586376727357187), + BOOST_MATH_BIG_CONSTANT(T, 113, 1.0546764918220835097855665680632153367), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.26574021300894401276478730940980810831), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.03996289731752081380552901986471233462), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.0033398680924544836817826046380586480873), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.00013288854760548251757651556792598235735), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.17194794958274081373243161848194745111e-5) + }; + T r = zm2 * zm1; + T R = tools::evaluate_polynomial(P, T(0.625 - zm1)) / tools::evaluate_polynomial(Q, T(0.625 - zm1)); + + result += r * Y + r * R; + BOOST_MATH_INSTRUMENT_CODE(result); + } + else + { + // + // Same form as above. + // + // Max error found (at 128-bit long double precision) 1.831e-35 + // Maximum Deviation Found (approximation error) 8.588e-36 + // Expected Error Term (theoretical error) 1.458e-36 + // + static const float Y = 0.443811893463134765625f; + + static const T P[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, -0.021027558364667626231512090082402429494), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.15128811104498736604523586803722368377), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.26249631480066246699388544451126410278), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.21148748610533489823742352180628489742), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.093964130697489071999873506148104370633), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.024292059227009051652542804957550866827), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.0036284453226534839926304745756906117066), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.0002939230129315195346843036254392485984), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.11088589183158123733132268042570710338e-4), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.13240510580220763969511741896361984162e-6) + }; + static const T Q[] = { + BOOST_MATH_BIG_CONSTANT(T, 113, 1.0), + BOOST_MATH_BIG_CONSTANT(T, 113, -2.4240003754444040525462170802796471996), + BOOST_MATH_BIG_CONSTANT(T, 113, 2.4868383476933178722203278602342786002), + BOOST_MATH_BIG_CONSTANT(T, 113, -1.4047068395206343375520721509193698547), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.47583809087867443858344765659065773369), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.09865724264554556400463655444270700132), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.012238223514176587501074150988445109735), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.00084625068418239194670614419707491797097), + BOOST_MATH_BIG_CONSTANT(T, 113, 0.2796574430456237061420839429225710602e-4), + BOOST_MATH_BIG_CONSTANT(T, 113, -0.30202973883316730694433702165188835331e-6) + }; + // (2 - x) * (1 - x) * (c + R(2 - x)) + T r = zm2 * zm1; + T R = tools::evaluate_polynomial(P, T(-zm2)) / tools::evaluate_polynomial(Q, T(-zm2)); + + result += r * Y + r * R; + BOOST_MATH_INSTRUMENT_CODE(result); + } + } + BOOST_MATH_INSTRUMENT_CODE(result); + return result; +} +template <class T, class Policy, class Lanczos> +T lgamma_small_imp(T z, T zm1, T zm2, const mpl::int_<0>&, const Policy& pol, const Lanczos&) +{ + // + // No rational approximations are available because either + // T has no numeric_limits support (so we can't tell how + // many digits it has), or T has more digits than we know + // what to do with.... we do have a Lanczos approximation + // though, and that can be used to keep errors under control. + // + BOOST_MATH_STD_USING // for ADL of std names + T result = 0; + if(z < tools::epsilon<T>()) + { + result = -log(z); + } + else if(z < 0.5) + { + // taking the log of tgamma reduces the error, no danger of overflow here: + result = log(gamma_imp(z, pol, Lanczos())); + } + else if(z >= 3) + { + // taking the log of tgamma reduces the error, no danger of overflow here: + result = log(gamma_imp(z, pol, Lanczos())); + } + else if(z >= 1.5) + { + // special case near 2: + T dz = zm2; + result = dz * log((z + Lanczos::g() - T(0.5)) / boost::math::constants::e<T>()); + result += boost::math::log1p(dz / (Lanczos::g() + T(1.5)), pol) * T(1.5); + result += boost::math::log1p(Lanczos::lanczos_sum_near_2(dz), pol); + } + else + { + // special case near 1: + T dz = zm1; + result = dz * log((z + Lanczos::g() - T(0.5)) / boost::math::constants::e<T>()); + result += boost::math::log1p(dz / (Lanczos::g() + T(0.5)), pol) / 2; + result += boost::math::log1p(Lanczos::lanczos_sum_near_1(dz), pol); + } + return result; +} + +}}} // namespaces + +#endif // BOOST_MATH_SPECIAL_FUNCTIONS_DETAIL_LGAMMA_SMALL + |