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Diffstat (limited to 'inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/lgamma_small.hpp')
| -rw-r--r-- | inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/lgamma_small.hpp | 522 |
1 files changed, 0 insertions, 522 deletions
diff --git a/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/lgamma_small.hpp b/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/lgamma_small.hpp deleted file mode 100644 index e65f8b7e9..000000000 --- a/inference-engine/thirdparty/clDNN/common/boost/1.64.0/include/boost-1_64/boost/math/special_functions/detail/lgamma_small.hpp +++ /dev/null @@ -1,522 +0,0 @@ -// (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 - |