Back to home page

EIC code displayed by LXR
 
 

    

File indexing completed on 2026-08-29 08:49:27 

0001 //  Copyright John Maddock 2007.
0002 //  Copyright Matt Borland 2024.
0003 //  Use, modification and distribution are subject to the
0004 //  Boost Software License, Version 1.0. (See accompanying file
0005 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0006 
0007 #ifndef BOOST_MATH_EXPINT_HPP
0008 #define BOOST_MATH_EXPINT_HPP
0009 
0010 #ifdef _MSC_VER
0011 #pragma once
0012 #pragma warning(push)
0013 #pragma warning(disable:4702) // Unreachable code (release mode only warning)
0014 #endif
0015 
0016 #include <boost/math/tools/config.hpp>
0017 #include <boost/math/tools/cstdint.hpp>
0018 #include <boost/math/tools/type_traits.hpp>
0019 #include <boost/math/tools/tuple.hpp>
0020 #include <boost/math/tools/precision.hpp>
0021 #include <boost/math/tools/promotion.hpp>
0022 #include <boost/math/tools/fraction.hpp>
0023 #include <boost/math/tools/series.hpp>
0024 #include <boost/math/policies/error_handling.hpp>
0025 #include <boost/math/special_functions/math_fwd.hpp>
0026 #include <boost/math/special_functions/digamma.hpp>
0027 #include <boost/math/special_functions/log1p.hpp>
0028 
0029 #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
0030 //
0031 // This is the only way we can avoid
0032 // warning: non-standard suffix on floating constant [-Wpedantic]
0033 // when building with -Wall -pedantic.  Neither __extension__
0034 // nor #pragma diagnostic ignored work :(
0035 //
0036 #pragma GCC system_header
0037 #endif
0038 
0039 namespace boost{ namespace math{
0040 
0041 template <class T, class Policy>
0042 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type
0043    expint(unsigned n, T z, const Policy& /*pol*/);
0044 
0045 namespace detail{
0046 
0047 template <class T>
0048 BOOST_MATH_GPU_ENABLED inline T expint_1_rational(const T& z, const boost::math::integral_constant<int, 0>&)
0049 {
0050    // this function is never actually called
0051    BOOST_MATH_ASSERT(0);
0052    return z;
0053 }
0054 
0055 template <class T>
0056 BOOST_MATH_GPU_ENABLED T expint_1_rational(const T& z, const boost::math::integral_constant<int, 53>&)
0057 {
0058    BOOST_MATH_STD_USING
0059    T result;
0060    if(z <= 1)
0061    {
0062       // Maximum Deviation Found:                     2.006e-18
0063       // Expected Error Term:                         2.006e-18
0064       // Max error found at double precision:         2.760e-17
0065       // LCOV_EXCL_START
0066       static const T Y = 0.66373538970947265625F;
0067       static const T P[6] = {
0068          BOOST_MATH_BIG_CONSTANT(T, 53, 0.0865197248079397976498),
0069          BOOST_MATH_BIG_CONSTANT(T, 53, 0.0320913665303559189999),
0070          BOOST_MATH_BIG_CONSTANT(T, 53, -0.245088216639761496153),
0071          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0368031736257943745142),
0072          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00399167106081113256961),
0073          BOOST_MATH_BIG_CONSTANT(T, 53, -0.000111507792921197858394)
0074       };
0075       static const T Q[6] = {
0076          BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
0077          BOOST_MATH_BIG_CONSTANT(T, 53, 0.37091387659397013215),
0078          BOOST_MATH_BIG_CONSTANT(T, 53, 0.056770677104207528384),
0079          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00427347600017103698101),
0080          BOOST_MATH_BIG_CONSTANT(T, 53, 0.000131049900798434683324),
0081          BOOST_MATH_BIG_CONSTANT(T, 53, -0.528611029520217142048e-6)
0082       };
0083       // LCOV_EXCL_STOP
0084       result = tools::evaluate_polynomial(P, z)
0085          / tools::evaluate_polynomial(Q, z);
0086       result += z - log(z) - Y;
0087    }
0088    else if(z < -boost::math::tools::log_min_value<T>())
0089    {
0090       // Maximum Deviation Found (interpolated):      1.444e-17
0091       // Max error found at double precision:         3.119e-17
0092       // LCOV_EXCL_START
0093       static const T P[11] = {
0094          BOOST_MATH_BIG_CONSTANT(T, 53, -0.121013190657725568138e-18),
0095          BOOST_MATH_BIG_CONSTANT(T, 53, -0.999999999999998811143),
0096          BOOST_MATH_BIG_CONSTANT(T, 53, -43.3058660811817946037),
0097          BOOST_MATH_BIG_CONSTANT(T, 53, -724.581482791462469795),
0098          BOOST_MATH_BIG_CONSTANT(T, 53, -6046.8250112711035463),
0099          BOOST_MATH_BIG_CONSTANT(T, 53, -27182.6254466733970467),
0100          BOOST_MATH_BIG_CONSTANT(T, 53, -66598.2652345418633509),
0101          BOOST_MATH_BIG_CONSTANT(T, 53, -86273.1567711649528784),
0102          BOOST_MATH_BIG_CONSTANT(T, 53, -54844.4587226402067411),
0103          BOOST_MATH_BIG_CONSTANT(T, 53, -14751.4895786128450662),
0104          BOOST_MATH_BIG_CONSTANT(T, 53, -1185.45720315201027667)
0105       };
0106       static const T Q[12] = {
0107          BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
0108          BOOST_MATH_BIG_CONSTANT(T, 53, 45.3058660811801465927),
0109          BOOST_MATH_BIG_CONSTANT(T, 53, 809.193214954550328455),
0110          BOOST_MATH_BIG_CONSTANT(T, 53, 7417.37624454689546708),
0111          BOOST_MATH_BIG_CONSTANT(T, 53, 38129.5594484818471461),
0112          BOOST_MATH_BIG_CONSTANT(T, 53, 113057.05869159631492),
0113          BOOST_MATH_BIG_CONSTANT(T, 53, 192104.047790227984431),
0114          BOOST_MATH_BIG_CONSTANT(T, 53, 180329.498380501819718),
0115          BOOST_MATH_BIG_CONSTANT(T, 53, 86722.3403467334749201),
0116          BOOST_MATH_BIG_CONSTANT(T, 53, 18455.4124737722049515),
0117          BOOST_MATH_BIG_CONSTANT(T, 53, 1229.20784182403048905),
0118          BOOST_MATH_BIG_CONSTANT(T, 53, -0.776491285282330997549)
0119       };
0120       // LCOV_EXCL_STOP
0121       T recip = 1 / z;
0122       result = 1 + tools::evaluate_polynomial(P, recip)
0123          / tools::evaluate_polynomial(Q, recip);
0124       result *= exp(-z) * recip;
0125    }
0126    else
0127    {
0128       result = 0;
0129    }
0130    return result;
0131 }
0132 
0133 template <class T>
0134 BOOST_MATH_GPU_ENABLED T expint_1_rational(const T& z, const boost::math::integral_constant<int, 64>&)
0135 {
0136    BOOST_MATH_STD_USING
0137    T result;
0138    if(z <= 1)
0139    {
0140       // Maximum Deviation Found:                     3.807e-20
0141       // Expected Error Term:                         3.807e-20
0142       // Max error found at long double precision:    6.249e-20
0143       // LCOV_EXCL_START
0144       static const T Y = 0.66373538970947265625F;
0145       static const T P[6] = {
0146          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0865197248079397956816),
0147          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0275114007037026844633),
0148          BOOST_MATH_BIG_CONSTANT(T, 64, -0.246594388074877139824),
0149          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0237624819878732642231),
0150          BOOST_MATH_BIG_CONSTANT(T, 64, -0.00259113319641673986276),
0151          BOOST_MATH_BIG_CONSTANT(T, 64, 0.30853660894346057053e-4)
0152       };
0153       static const T Q[7] = {
0154          BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
0155          BOOST_MATH_BIG_CONSTANT(T, 64, 0.317978365797784100273),
0156          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0393622602554758722511),
0157          BOOST_MATH_BIG_CONSTANT(T, 64, 0.00204062029115966323229),
0158          BOOST_MATH_BIG_CONSTANT(T, 64, 0.732512107100088047854e-5),
0159          BOOST_MATH_BIG_CONSTANT(T, 64, -0.202872781770207871975e-5),
0160          BOOST_MATH_BIG_CONSTANT(T, 64, 0.52779248094603709945e-7)
0161       };
0162       // LCOV_EXCL_STOP
0163       result = tools::evaluate_polynomial(P, z)
0164          / tools::evaluate_polynomial(Q, z);
0165       result += z - log(z) - Y;
0166    }
0167    else if(z < -boost::math::tools::log_min_value<T>())
0168    {
0169       // Maximum Deviation Found (interpolated):     2.220e-20
0170       // Max error found at long double precision:   1.346e-19
0171       // LCOV_EXCL_START
0172       static const T P[14] = {
0173          BOOST_MATH_BIG_CONSTANT(T, 64, -0.534401189080684443046e-23),
0174          BOOST_MATH_BIG_CONSTANT(T, 64, -0.999999999999999999905),
0175          BOOST_MATH_BIG_CONSTANT(T, 64, -62.1517806091379402505),
0176          BOOST_MATH_BIG_CONSTANT(T, 64, -1568.45688271895145277),
0177          BOOST_MATH_BIG_CONSTANT(T, 64, -21015.3431990874009619),
0178          BOOST_MATH_BIG_CONSTANT(T, 64, -164333.011755931661949),
0179          BOOST_MATH_BIG_CONSTANT(T, 64, -777917.270775426696103),
0180          BOOST_MATH_BIG_CONSTANT(T, 64, -2244188.56195255112937),
0181          BOOST_MATH_BIG_CONSTANT(T, 64, -3888702.98145335643429),
0182          BOOST_MATH_BIG_CONSTANT(T, 64, -3909822.65621952648353),
0183          BOOST_MATH_BIG_CONSTANT(T, 64, -2149033.9538897398457),
0184          BOOST_MATH_BIG_CONSTANT(T, 64, -584705.537139793925189),
0185          BOOST_MATH_BIG_CONSTANT(T, 64, -65815.2605361889477244),
0186          BOOST_MATH_BIG_CONSTANT(T, 64, -2038.82870680427258038)
0187       };
0188       static const T Q[14] = {
0189          BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
0190          BOOST_MATH_BIG_CONSTANT(T, 64, 64.1517806091379399478),
0191          BOOST_MATH_BIG_CONSTANT(T, 64, 1690.76044393722763785),
0192          BOOST_MATH_BIG_CONSTANT(T, 64, 24035.9534033068949426),
0193          BOOST_MATH_BIG_CONSTANT(T, 64, 203679.998633572361706),
0194          BOOST_MATH_BIG_CONSTANT(T, 64, 1074661.58459976978285),
0195          BOOST_MATH_BIG_CONSTANT(T, 64, 3586552.65020899358773),
0196          BOOST_MATH_BIG_CONSTANT(T, 64, 7552186.84989547621411),
0197          BOOST_MATH_BIG_CONSTANT(T, 64, 9853333.79353054111434),
0198          BOOST_MATH_BIG_CONSTANT(T, 64, 7689642.74550683631258),
0199          BOOST_MATH_BIG_CONSTANT(T, 64, 3385553.35146759180739),
0200          BOOST_MATH_BIG_CONSTANT(T, 64, 763218.072732396428725),
0201          BOOST_MATH_BIG_CONSTANT(T, 64, 73930.2995984054930821),
0202          BOOST_MATH_BIG_CONSTANT(T, 64, 2063.86994219629165937)
0203       };
0204       // LCOV_EXCL_STOP
0205       T recip = 1 / z;
0206       result = 1 + tools::evaluate_polynomial(P, recip)
0207          / tools::evaluate_polynomial(Q, recip);
0208       result *= exp(-z) * recip;
0209    }
0210    else
0211    {
0212       result = 0;
0213    }
0214    return result;
0215 }
0216 
0217 template <class T>
0218 BOOST_MATH_GPU_ENABLED T expint_1_rational(const T& z, const boost::math::integral_constant<int, 113>&)
0219 {
0220    BOOST_MATH_STD_USING
0221    T result;
0222    if(z <= 1)
0223    {
0224       // Maximum Deviation Found:                     2.477e-35
0225       // Expected Error Term:                         2.477e-35
0226       // Max error found at long double precision:    6.810e-35
0227       // LCOV_EXCL_START
0228       static const T Y = 0.66373538970947265625F;
0229       static const T P[10] = {
0230          BOOST_MATH_BIG_CONSTANT(T, 113, 0.0865197248079397956434879099175975937),
0231          BOOST_MATH_BIG_CONSTANT(T, 113, 0.0369066175910795772830865304506087759),
0232          BOOST_MATH_BIG_CONSTANT(T, 113, -0.24272036838415474665971599314725545),
0233          BOOST_MATH_BIG_CONSTANT(T, 113, -0.0502166331248948515282379137550178307),
0234          BOOST_MATH_BIG_CONSTANT(T, 113, -0.00768384138547489410285101483730424919),
0235          BOOST_MATH_BIG_CONSTANT(T, 113, -0.000612574337702109683505224915484717162),
0236          BOOST_MATH_BIG_CONSTANT(T, 113, -0.380207107950635046971492617061708534e-4),
0237          BOOST_MATH_BIG_CONSTANT(T, 113, -0.136528159460768830763009294683628406e-5),
0238          BOOST_MATH_BIG_CONSTANT(T, 113, -0.346839106212658259681029388908658618e-7),
0239          BOOST_MATH_BIG_CONSTANT(T, 113, -0.340500302777838063940402160594523429e-9)
0240       };
0241       static const T Q[10] = {
0242          BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
0243          BOOST_MATH_BIG_CONSTANT(T, 113, 0.426568827778942588160423015589537302),
0244          BOOST_MATH_BIG_CONSTANT(T, 113, 0.0841384046470893490592450881447510148),
0245          BOOST_MATH_BIG_CONSTANT(T, 113, 0.0100557215850668029618957359471132995),
0246          BOOST_MATH_BIG_CONSTANT(T, 113, 0.000799334870474627021737357294799839363),
0247          BOOST_MATH_BIG_CONSTANT(T, 113, 0.434452090903862735242423068552687688e-4),
0248          BOOST_MATH_BIG_CONSTANT(T, 113, 0.15829674748799079874182885081231252e-5),
0249          BOOST_MATH_BIG_CONSTANT(T, 113, 0.354406206738023762100882270033082198e-7),
0250          BOOST_MATH_BIG_CONSTANT(T, 113, 0.369373328141051577845488477377890236e-9),
0251          BOOST_MATH_BIG_CONSTANT(T, 113, -0.274149801370933606409282434677600112e-12)
0252       };
0253       // LCOV_EXCL_STOP
0254       result = tools::evaluate_polynomial(P, z)
0255          / tools::evaluate_polynomial(Q, z);
0256       result += z - log(z) - Y;
0257    }
0258    else if(z <= 4)
0259    {
0260       // Max error in interpolated form:             5.614e-35
0261       // Max error found at long double precision:   7.979e-35
0262       // LCOV_EXCL_START
0263       static const T Y = 0.70190334320068359375F;
0264 
0265       static const T P[16] = {
0266          BOOST_MATH_BIG_CONSTANT(T, 113, 0.298096656795020369955077350585959794),
0267          BOOST_MATH_BIG_CONSTANT(T, 113, 12.9314045995266142913135497455971247),
0268          BOOST_MATH_BIG_CONSTANT(T, 113, 226.144334921582637462526628217345501),
0269          BOOST_MATH_BIG_CONSTANT(T, 113, 2070.83670924261732722117682067381405),
0270          BOOST_MATH_BIG_CONSTANT(T, 113, 10715.1115684330959908244769731347186),
0271          BOOST_MATH_BIG_CONSTANT(T, 113, 30728.7876355542048019664777316053311),
0272          BOOST_MATH_BIG_CONSTANT(T, 113, 38520.6078609349855436936232610875297),
0273          BOOST_MATH_BIG_CONSTANT(T, 113, -27606.0780981527583168728339620565165),
0274          BOOST_MATH_BIG_CONSTANT(T, 113, -169026.485055785605958655247592604835),
0275          BOOST_MATH_BIG_CONSTANT(T, 113, -254361.919204983608659069868035092282),
0276          BOOST_MATH_BIG_CONSTANT(T, 113, -195765.706874132267953259272028679935),
0277          BOOST_MATH_BIG_CONSTANT(T, 113, -83352.6826013533205474990119962408675),
0278          BOOST_MATH_BIG_CONSTANT(T, 113, -19251.6828496869586415162597993050194),
0279          BOOST_MATH_BIG_CONSTANT(T, 113, -2226.64251774578542836725386936102339),
0280          BOOST_MATH_BIG_CONSTANT(T, 113, -109.009437301400845902228611986479816),
0281          BOOST_MATH_BIG_CONSTANT(T, 113, -1.51492042209561411434644938098833499)
0282       };
0283       static const T Q[16] = {
0284          BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
0285          BOOST_MATH_BIG_CONSTANT(T, 113, 46.734521442032505570517810766704587),
0286          BOOST_MATH_BIG_CONSTANT(T, 113, 908.694714348462269000247450058595655),
0287          BOOST_MATH_BIG_CONSTANT(T, 113, 9701.76053033673927362784882748513195),
0288          BOOST_MATH_BIG_CONSTANT(T, 113, 63254.2815292641314236625196594947774),
0289          BOOST_MATH_BIG_CONSTANT(T, 113, 265115.641285880437335106541757711092),
0290          BOOST_MATH_BIG_CONSTANT(T, 113, 732707.841188071900498536533086567735),
0291          BOOST_MATH_BIG_CONSTANT(T, 113, 1348514.02492635723327306628712057794),
0292          BOOST_MATH_BIG_CONSTANT(T, 113, 1649986.81455283047769673308781585991),
0293          BOOST_MATH_BIG_CONSTANT(T, 113, 1326000.828522976970116271208812099),
0294          BOOST_MATH_BIG_CONSTANT(T, 113, 683643.09490612171772350481773951341),
0295          BOOST_MATH_BIG_CONSTANT(T, 113, 217640.505137263607952365685653352229),
0296          BOOST_MATH_BIG_CONSTANT(T, 113, 40288.3467237411710881822569476155485),
0297          BOOST_MATH_BIG_CONSTANT(T, 113, 3932.89353979531632559232883283175754),
0298          BOOST_MATH_BIG_CONSTANT(T, 113, 169.845369689596739824177412096477219),
0299          BOOST_MATH_BIG_CONSTANT(T, 113, 2.17607292280092201170768401876895354)
0300       };
0301       // LCOV_EXCL_STOP
0302       T recip = 1 / z;
0303       result = Y + tools::evaluate_polynomial(P, recip)
0304          / tools::evaluate_polynomial(Q, recip);
0305       result *= exp(-z) * recip;
0306    }
0307    else if(z < -boost::math::tools::log_min_value<T>())
0308    {
0309       // Max error in interpolated form:             4.413e-35
0310       // Max error found at long double precision:   8.928e-35
0311       // LCOV_EXCL_START
0312       static const T P[19] = {
0313          BOOST_MATH_BIG_CONSTANT(T, 113, -0.559148411832951463689610809550083986e-40),
0314          BOOST_MATH_BIG_CONSTANT(T, 113, -0.999999999999999999999999999999999997),
0315          BOOST_MATH_BIG_CONSTANT(T, 113, -166.542326331163836642960118190147367),
0316          BOOST_MATH_BIG_CONSTANT(T, 113, -12204.639128796330005065904675153652),
0317          BOOST_MATH_BIG_CONSTANT(T, 113, -520807.069767086071806275022036146855),
0318          BOOST_MATH_BIG_CONSTANT(T, 113, -14435981.5242137970691490903863125326),
0319          BOOST_MATH_BIG_CONSTANT(T, 113, -274574945.737064301247496460758654196),
0320          BOOST_MATH_BIG_CONSTANT(T, 113, -3691611582.99810039356254671781473079),
0321          BOOST_MATH_BIG_CONSTANT(T, 113, -35622515944.8255047299363690814678763),
0322          BOOST_MATH_BIG_CONSTANT(T, 113, -248040014774.502043161750715548451142),
0323          BOOST_MATH_BIG_CONSTANT(T, 113, -1243190389769.53458416330946622607913),
0324          BOOST_MATH_BIG_CONSTANT(T, 113, -4441730126135.54739052731990368425339),
0325          BOOST_MATH_BIG_CONSTANT(T, 113, -11117043181899.7388524310281751971366),
0326          BOOST_MATH_BIG_CONSTANT(T, 113, -18976497615396.9717776601813519498961),
0327          BOOST_MATH_BIG_CONSTANT(T, 113, -21237496819711.1011661104761906067131),
0328          BOOST_MATH_BIG_CONSTANT(T, 113, -14695899122092.5161620333466757812848),
0329          BOOST_MATH_BIG_CONSTANT(T, 113, -5737221535080.30569711574295785864903),
0330          BOOST_MATH_BIG_CONSTANT(T, 113, -1077042281708.42654526404581272546244),
0331          BOOST_MATH_BIG_CONSTANT(T, 113, -68028222642.1941480871395695677675137)
0332       };
0333       static const T Q[20] = {
0334          BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
0335          BOOST_MATH_BIG_CONSTANT(T, 113, 168.542326331163836642960118190147311),
0336          BOOST_MATH_BIG_CONSTANT(T, 113, 12535.7237814586576783518249115343619),
0337          BOOST_MATH_BIG_CONSTANT(T, 113, 544891.263372016404143120911148640627),
0338          BOOST_MATH_BIG_CONSTANT(T, 113, 15454474.7241010258634446523045237762),
0339          BOOST_MATH_BIG_CONSTANT(T, 113, 302495899.896629522673410325891717381),
0340          BOOST_MATH_BIG_CONSTANT(T, 113, 4215565948.38886507646911672693270307),
0341          BOOST_MATH_BIG_CONSTANT(T, 113, 42552409471.7951815668506556705733344),
0342          BOOST_MATH_BIG_CONSTANT(T, 113, 313592377066.753173979584098301610186),
0343          BOOST_MATH_BIG_CONSTANT(T, 113, 1688763640223.4541980740597514904542),
0344          BOOST_MATH_BIG_CONSTANT(T, 113, 6610992294901.59589748057620192145704),
0345          BOOST_MATH_BIG_CONSTANT(T, 113, 18601637235659.6059890851321772682606),
0346          BOOST_MATH_BIG_CONSTANT(T, 113, 36944278231087.2571020964163402941583),
0347          BOOST_MATH_BIG_CONSTANT(T, 113, 50425858518481.7497071917028793820058),
0348          BOOST_MATH_BIG_CONSTANT(T, 113, 45508060902865.0899967797848815980644),
0349          BOOST_MATH_BIG_CONSTANT(T, 113, 25649955002765.3817331501988304758142),
0350          BOOST_MATH_BIG_CONSTANT(T, 113, 8259575619094.6518520988612711292331),
0351          BOOST_MATH_BIG_CONSTANT(T, 113, 1299981487496.12607474362723586264515),
0352          BOOST_MATH_BIG_CONSTANT(T, 113, 70242279152.8241187845178443118302693),
0353          BOOST_MATH_BIG_CONSTANT(T, 113, -37633302.9409263839042721539363416685)
0354       };
0355       // LCOV_EXCL_STOP
0356       T recip = 1 / z;
0357       result = 1 + tools::evaluate_polynomial(P, recip)
0358          / tools::evaluate_polynomial(Q, recip);
0359       result *= exp(-z) * recip;
0360    }
0361    else
0362    {
0363       result = 0;
0364    }
0365    return result;
0366 }
0367 
0368 
0369 template <class T>
0370 struct expint_fraction
0371 {
0372    typedef boost::math::pair<T,T> result_type;
0373    BOOST_MATH_GPU_ENABLED expint_fraction(unsigned n_, T z_) : b(n_ + z_), i(-1), n(n_){}
0374    BOOST_MATH_GPU_ENABLED boost::math::pair<T,T> operator()()
0375    {
0376       boost::math::pair<T,T> result = boost::math::make_pair(-static_cast<T>((i+1) * (n+i)), b);
0377       b += 2;
0378       ++i;
0379       return result;
0380    }
0381 private:
0382    T b;
0383    int i;
0384    unsigned n;
0385 };
0386 
0387 template <class T, class Policy>
0388 BOOST_MATH_GPU_ENABLED inline T expint_as_fraction(unsigned n, T z, const Policy& pol)
0389 {
0390    BOOST_MATH_STD_USING
0391    BOOST_MATH_INSTRUMENT_VARIABLE(z)
0392    boost::math::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
0393    expint_fraction<T> f(n, z);
0394    T result = tools::continued_fraction_b(
0395       f,
0396       boost::math::policies::get_epsilon<T, Policy>(),
0397       max_iter);
0398    policies::check_series_iterations<T>("boost::math::expint_continued_fraction<%1%>(unsigned,%1%)", max_iter, pol);
0399    BOOST_MATH_INSTRUMENT_VARIABLE(result)
0400    BOOST_MATH_INSTRUMENT_VARIABLE(max_iter)
0401    result = exp(-z) / result;
0402    BOOST_MATH_INSTRUMENT_VARIABLE(result)
0403    return result;
0404 }
0405 
0406 template <class T>
0407 struct expint_series
0408 {
0409    typedef T result_type;
0410    BOOST_MATH_GPU_ENABLED expint_series(unsigned k_, T z_, T x_k_, T denom_, T fact_)
0411       : k(k_), z(z_), x_k(x_k_), denom(denom_), fact(fact_){}
0412    BOOST_MATH_GPU_ENABLED T operator()()
0413    {
0414       x_k *= -z;
0415       denom += 1;
0416       fact *= ++k;
0417       return x_k / (denom * fact);
0418    }
0419 private:
0420    unsigned k;
0421    T z;
0422    T x_k;
0423    T denom;
0424    T fact;
0425 };
0426 
0427 template <class T, class Policy>
0428 BOOST_MATH_GPU_ENABLED inline T expint_as_series(unsigned n, T z, const Policy& pol)
0429 {
0430    BOOST_MATH_STD_USING
0431    boost::math::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
0432 
0433    BOOST_MATH_INSTRUMENT_VARIABLE(z)
0434 
0435    T result = 0;
0436    T x_k = -1;
0437    T denom = T(1) - n;
0438    T fact = 1;
0439    unsigned k = 0;
0440    for(; k < n - 1;)
0441    {
0442       result += x_k / (denom * fact);
0443       denom += 1;
0444       x_k *= -z;
0445       fact *= ++k;
0446    }
0447    BOOST_MATH_INSTRUMENT_VARIABLE(result)
0448    result += pow(-z, static_cast<T>(n - 1))
0449       * (boost::math::digamma(static_cast<T>(n), pol) - log(z)) / fact;
0450    BOOST_MATH_INSTRUMENT_VARIABLE(result)
0451 
0452    expint_series<T> s(k, z, x_k, denom, fact);
0453    result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, result);
0454    policies::check_series_iterations<T>("boost::math::expint_series<%1%>(unsigned,%1%)", max_iter, pol);
0455    BOOST_MATH_INSTRUMENT_VARIABLE(result)
0456    BOOST_MATH_INSTRUMENT_VARIABLE(max_iter)
0457    return result;
0458 }
0459 
0460 template <class T, class Policy, class Tag>
0461 BOOST_MATH_GPU_ENABLED T expint_imp(unsigned n, T z, const Policy& pol, const Tag& tag)
0462 {
0463    BOOST_MATH_STD_USING
0464    constexpr auto function = "boost::math::expint<%1%>(unsigned, %1%)";
0465    if(z < 0)
0466       return policies::raise_domain_error<T>(function, "Function requires z >= 0 but got %1%.", z, pol);
0467    if(z == 0)
0468       return n == 1 ? policies::raise_overflow_error<T>(function, nullptr, pol) : T(1 / (static_cast<T>(n - 1)));
0469 
0470    T result;
0471 
0472    bool f;
0473    if(n < 3)
0474    {
0475       f = z < T(0.5);
0476    }
0477    else
0478    {
0479       f = z < (static_cast<T>(n - 2) / static_cast<T>(n - 1));
0480    }
0481 #ifdef _MSC_VER
0482 #  pragma warning(push)
0483 #  pragma warning(disable:4127) // conditional expression is constant
0484 #endif
0485    if(n == 0)
0486    {
0487       result = exp(-z) / z;
0488    }
0489    else if((n == 1) && (Tag::value))
0490    {
0491       result = expint_1_rational(z, tag);
0492    }
0493    else if(f)
0494    {
0495       result = expint_as_series(n, z, pol);
0496    }
0497    else
0498    {
0499       result = expint_as_fraction(n, z, pol);
0500    }
0501 #ifdef _MSC_VER
0502 #  pragma warning(pop)
0503 #endif
0504 
0505    return result;
0506 }
0507 
0508 template <class T>
0509 struct expint_i_series
0510 {
0511    typedef T result_type;
0512    BOOST_MATH_GPU_ENABLED expint_i_series(T z_) : k(0), z_k(1), z(z_){}
0513    BOOST_MATH_GPU_ENABLED T operator()()
0514    {
0515       z_k *= z / ++k;
0516       return z_k / k;
0517    }
0518 private:
0519    unsigned k;
0520    T z_k;
0521    T z;
0522 };
0523 
0524 template <class T, class Policy>
0525 BOOST_MATH_GPU_ENABLED T expint_i_as_series(T z, const Policy& pol)
0526 {
0527    BOOST_MATH_STD_USING
0528    T result = log(z); // (log(z) - log(1 / z)) / 2;
0529    result += constants::euler<T>();
0530    expint_i_series<T> s(z);
0531    boost::math::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
0532    result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, result);
0533    policies::check_series_iterations<T>("boost::math::expint_i_series<%1%>(%1%)", max_iter, pol);
0534    return result;
0535 }
0536 
0537 template <class T, class Policy, class Tag>
0538 BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const Tag& tag)
0539 {
0540    constexpr auto function = "boost::math::expint<%1%>(%1%)";
0541    if(z < 0)
0542       return -expint_imp(1, T(-z), pol, tag);
0543    if(z == 0)
0544       return -policies::raise_overflow_error<T>(function, nullptr, pol);  // LCOV_EXCL_LINE confirmed covered by real_concept tests
0545    return expint_i_as_series(z, pol);
0546 }
0547 
0548 template <class T, class Policy>
0549 BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math::integral_constant<int, 53>& tag)
0550 {
0551    BOOST_MATH_STD_USING
0552    constexpr auto function = "boost::math::expint<%1%>(%1%)";
0553    if(z < 0)
0554       return -expint_imp(1, T(-z), pol, tag);
0555    if(z == 0)
0556       return -policies::raise_overflow_error<T>(function, nullptr, pol);
0557 
0558    T result;
0559 
0560    if(z <= 6)
0561    {
0562       // Maximum Deviation Found:                     2.852e-18
0563       // Expected Error Term:                         2.852e-18
0564       // Max Error found at double precision =        Poly: 2.636335e-16   Cheb: 4.187027e-16
0565       // LCOV_EXCL_START
0566       BOOST_MATH_STATIC const T P[10] = {
0567          BOOST_MATH_BIG_CONSTANT(T, 53, 2.98677224343598593013),
0568          BOOST_MATH_BIG_CONSTANT(T, 53, 0.356343618769377415068),
0569          BOOST_MATH_BIG_CONSTANT(T, 53, 0.780836076283730801839),
0570          BOOST_MATH_BIG_CONSTANT(T, 53, 0.114670926327032002811),
0571          BOOST_MATH_BIG_CONSTANT(T, 53, 0.0499434773576515260534),
0572          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00726224593341228159561),
0573          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00115478237227804306827),
0574          BOOST_MATH_BIG_CONSTANT(T, 53, 0.000116419523609765200999),
0575          BOOST_MATH_BIG_CONSTANT(T, 53, 0.798296365679269702435e-5),
0576          BOOST_MATH_BIG_CONSTANT(T, 53, 0.2777056254402008721e-6)
0577       };
0578       BOOST_MATH_STATIC const T Q[8] = {
0579          BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
0580          BOOST_MATH_BIG_CONSTANT(T, 53, -1.17090412365413911947),
0581          BOOST_MATH_BIG_CONSTANT(T, 53, 0.62215109846016746276),
0582          BOOST_MATH_BIG_CONSTANT(T, 53, -0.195114782069495403315),
0583          BOOST_MATH_BIG_CONSTANT(T, 53, 0.0391523431392967238166),
0584          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00504800158663705747345),
0585          BOOST_MATH_BIG_CONSTANT(T, 53, 0.000389034007436065401822),
0586          BOOST_MATH_BIG_CONSTANT(T, 53, -0.138972589601781706598e-4)
0587       };
0588 
0589       BOOST_MATH_STATIC_LOCAL_VARIABLE const T c1 = BOOST_MATH_BIG_CONSTANT(T, 53, 1677624236387711.0);
0590       BOOST_MATH_STATIC_LOCAL_VARIABLE const T c2 = BOOST_MATH_BIG_CONSTANT(T, 53, 4503599627370496.0);
0591       BOOST_MATH_STATIC_LOCAL_VARIABLE const T r1 = static_cast<T>(c1 / c2);
0592       BOOST_MATH_STATIC_LOCAL_VARIABLE const T r2 = BOOST_MATH_BIG_CONSTANT(T, 53, 0.131401834143860282009280387409357165515556574352422001206362e-16);
0593       BOOST_MATH_STATIC_LOCAL_VARIABLE const T r = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 53, 0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392));
0594       // LCOV_EXCL_STOP
0595       T t = (z / 3) - 1;
0596       result = tools::evaluate_polynomial(P, t)
0597          / tools::evaluate_polynomial(Q, t);
0598       t = (z - r1) - r2;
0599       result *= t;
0600       if(fabs(t) < T(0.1))
0601       {
0602          result += boost::math::log1p(t / r, pol);
0603       }
0604       else
0605       {
0606          result += log(z / r);
0607       }
0608    }
0609    else if (z <= 10)
0610    {
0611       // Maximum Deviation Found:                     6.546e-17
0612       // Expected Error Term:                         6.546e-17
0613       // Max Error found at double precision =        Poly: 6.890169e-17   Cheb: 6.772128e-17
0614       // LCOV_EXCL_START
0615       BOOST_MATH_STATIC_LOCAL_VARIABLE const T Y = 1.158985137939453125F;
0616       BOOST_MATH_STATIC const T P[8] = {
0617          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00139324086199402804173),
0618          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0349921221823888744966),
0619          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0264095520754134848538),
0620          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00761224003005476438412),
0621          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00247496209592143627977),
0622          BOOST_MATH_BIG_CONSTANT(T, 53, -0.000374885917942100256775),
0623          BOOST_MATH_BIG_CONSTANT(T, 53, -0.554086272024881826253e-4),
0624          BOOST_MATH_BIG_CONSTANT(T, 53, -0.396487648924804510056e-5)
0625       };
0626       BOOST_MATH_STATIC const T Q[8] = {
0627          BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
0628          BOOST_MATH_BIG_CONSTANT(T, 53, 0.744625566823272107711),
0629          BOOST_MATH_BIG_CONSTANT(T, 53, 0.329061095011767059236),
0630          BOOST_MATH_BIG_CONSTANT(T, 53, 0.100128624977313872323),
0631          BOOST_MATH_BIG_CONSTANT(T, 53, 0.0223851099128506347278),
0632          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00365334190742316650106),
0633          BOOST_MATH_BIG_CONSTANT(T, 53, 0.000402453408512476836472),
0634          BOOST_MATH_BIG_CONSTANT(T, 53, 0.263649630720255691787e-4)
0635       };
0636       // LCOV_EXCL_STOP
0637       T t = z / 2 - 4;
0638       result = Y + tools::evaluate_polynomial(P, t)
0639          / tools::evaluate_polynomial(Q, t);
0640       result *= exp(z) / z;
0641       result += z;
0642    }
0643    else if(z <= 20)
0644    {
0645       // Maximum Deviation Found:                     1.843e-17
0646       // Expected Error Term:                         -1.842e-17
0647       // Max Error found at double precision =        Poly: 4.375868e-17   Cheb: 5.860967e-17
0648       // LCOV_EXCL_START
0649       BOOST_MATH_STATIC_LOCAL_VARIABLE const T Y = 1.0869731903076171875F;
0650       BOOST_MATH_STATIC const T P[9] = {
0651          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00893891094356945667451),
0652          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0484607730127134045806),
0653          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0652810444222236895772),
0654          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0478447572647309671455),
0655          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0226059218923777094596),
0656          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00720603636917482065907),
0657          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00155941947035972031334),
0658          BOOST_MATH_BIG_CONSTANT(T, 53, -0.000209750022660200888349),
0659          BOOST_MATH_BIG_CONSTANT(T, 53, -0.138652200349182596186e-4)
0660       };
0661       BOOST_MATH_STATIC const T Q[9] = {
0662          BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
0663          BOOST_MATH_BIG_CONSTANT(T, 53, 1.97017214039061194971),
0664          BOOST_MATH_BIG_CONSTANT(T, 53, 1.86232465043073157508),
0665          BOOST_MATH_BIG_CONSTANT(T, 53, 1.09601437090337519977),
0666          BOOST_MATH_BIG_CONSTANT(T, 53, 0.438873285773088870812),
0667          BOOST_MATH_BIG_CONSTANT(T, 53, 0.122537731979686102756),
0668          BOOST_MATH_BIG_CONSTANT(T, 53, 0.0233458478275769288159),
0669          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00278170769163303669021),
0670          BOOST_MATH_BIG_CONSTANT(T, 53, 0.000159150281166108755531)
0671       };
0672       // LCOV_EXCL_STOP
0673       T t = z / 5 - 3;
0674       result = Y + tools::evaluate_polynomial(P, t)
0675          / tools::evaluate_polynomial(Q, t);
0676       result *= exp(z) / z;
0677       result += z;
0678    }
0679    else if(z <= 40)
0680    {
0681       // Maximum Deviation Found:                     5.102e-18
0682       // Expected Error Term:                         5.101e-18
0683       // Max Error found at double precision =        Poly: 1.441088e-16   Cheb: 1.864792e-16
0684       // LCOV_EXCL_START
0685       BOOST_MATH_STATIC_LOCAL_VARIABLE const T Y = 1.03937530517578125F;
0686       BOOST_MATH_STATIC const T P[9] = {
0687          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00356165148914447597995),
0688          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0229930320357982333406),
0689          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0449814350482277917716),
0690          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0453759383048193402336),
0691          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0272050837209380717069),
0692          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00994403059883350813295),
0693          BOOST_MATH_BIG_CONSTANT(T, 53, -0.00207592267812291726961),
0694          BOOST_MATH_BIG_CONSTANT(T, 53, -0.000192178045857733706044),
0695          BOOST_MATH_BIG_CONSTANT(T, 53, -0.113161784705911400295e-9)
0696       };
0697       BOOST_MATH_STATIC const T Q[9] = {
0698          BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
0699          BOOST_MATH_BIG_CONSTANT(T, 53, 2.84354408840148561131),
0700          BOOST_MATH_BIG_CONSTANT(T, 53, 3.6599610090072393012),
0701          BOOST_MATH_BIG_CONSTANT(T, 53, 2.75088464344293083595),
0702          BOOST_MATH_BIG_CONSTANT(T, 53, 1.2985244073998398643),
0703          BOOST_MATH_BIG_CONSTANT(T, 53, 0.383213198510794507409),
0704          BOOST_MATH_BIG_CONSTANT(T, 53, 0.0651165455496281337831),
0705          BOOST_MATH_BIG_CONSTANT(T, 53, 0.00488071077519227853585)
0706       };
0707       // LCOV_EXCL_STOP
0708       T t = z / 10 - 3;
0709       result = Y + tools::evaluate_polynomial(P, t)
0710          / tools::evaluate_polynomial(Q, t);
0711       result *= exp(z) / z;
0712       result += z;
0713    }
0714    else
0715    {
0716       // Max Error found at double precision =        3.381886e-17
0717       // LCOV_EXCL_START
0718       BOOST_MATH_STATIC_LOCAL_VARIABLE const T exp40 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 53, 2.35385266837019985407899910749034804508871617254555467236651e17));
0719       BOOST_MATH_STATIC_LOCAL_VARIABLE const T Y= 1.013065338134765625F;
0720       BOOST_MATH_STATIC const T P[6] = {
0721          BOOST_MATH_BIG_CONSTANT(T, 53, -0.0130653381347656243849),
0722          BOOST_MATH_BIG_CONSTANT(T, 53, 0.19029710559486576682),
0723          BOOST_MATH_BIG_CONSTANT(T, 53, 94.7365094537197236011),
0724          BOOST_MATH_BIG_CONSTANT(T, 53, -2516.35323679844256203),
0725          BOOST_MATH_BIG_CONSTANT(T, 53, 18932.0850014925993025),
0726          BOOST_MATH_BIG_CONSTANT(T, 53, -38703.1431362056714134)
0727       };
0728       BOOST_MATH_STATIC const T Q[7] = {
0729          BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
0730          BOOST_MATH_BIG_CONSTANT(T, 53, 61.9733592849439884145),
0731          BOOST_MATH_BIG_CONSTANT(T, 53, -2354.56211323420194283),
0732          BOOST_MATH_BIG_CONSTANT(T, 53, 22329.1459489893079041),
0733          BOOST_MATH_BIG_CONSTANT(T, 53, -70126.245140396567133),
0734          BOOST_MATH_BIG_CONSTANT(T, 53, 54738.2833147775537106),
0735          BOOST_MATH_BIG_CONSTANT(T, 53, 8297.16296356518409347)
0736       };
0737       // LCOV_EXCL_STOP
0738       T t = 1 / z;
0739       result = Y + tools::evaluate_polynomial(P, t)
0740          / tools::evaluate_polynomial(Q, t);
0741       if(z < 41)
0742          result *= exp(z) / z;
0743       else
0744       {
0745          // Avoid premature overflow if we can:
0746          t = z - 40;
0747          if(t > tools::log_max_value<T>())
0748          {
0749             result = policies::raise_overflow_error<T>(function, nullptr, pol);
0750          }
0751          else
0752          {
0753             result *= exp(z - 40) / z;
0754             if(result > tools::max_value<T>() / exp40)
0755             {
0756                result = policies::raise_overflow_error<T>(function, nullptr, pol);
0757             }
0758             else
0759             {
0760                result *= exp40;
0761             }
0762          }
0763       }
0764       result += z;
0765    }
0766    return result;
0767 }
0768 
0769 template <class T, class Policy>
0770 BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math::integral_constant<int, 64>& tag)
0771 {
0772    BOOST_MATH_STD_USING
0773    constexpr auto function = "boost::math::expint<%1%>(%1%)";
0774    if(z < 0)
0775       return -expint_imp(1, T(-z), pol, tag);
0776    if(z == 0)
0777       return -policies::raise_overflow_error<T>(function, nullptr, pol);
0778 
0779    T result;
0780 
0781    if(z <= 6)
0782    {
0783       // Maximum Deviation Found:                     3.883e-21
0784       // Expected Error Term:                         3.883e-21
0785       // Max Error found at long double precision =   Poly: 3.344801e-19   Cheb: 4.989937e-19
0786 
0787       // LCOV_EXCL_START
0788       static const T P[11] = {
0789          BOOST_MATH_BIG_CONSTANT(T, 64, 2.98677224343598593764),
0790          BOOST_MATH_BIG_CONSTANT(T, 64, 0.25891613550886736592),
0791          BOOST_MATH_BIG_CONSTANT(T, 64, 0.789323584998672832285),
0792          BOOST_MATH_BIG_CONSTANT(T, 64, 0.092432587824602399339),
0793          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0514236978728625906656),
0794          BOOST_MATH_BIG_CONSTANT(T, 64, 0.00658477469745132977921),
0795          BOOST_MATH_BIG_CONSTANT(T, 64, 0.00124914538197086254233),
0796          BOOST_MATH_BIG_CONSTANT(T, 64, 0.000131429679565472408551),
0797          BOOST_MATH_BIG_CONSTANT(T, 64, 0.11293331317982763165e-4),
0798          BOOST_MATH_BIG_CONSTANT(T, 64, 0.629499283139417444244e-6),
0799          BOOST_MATH_BIG_CONSTANT(T, 64, 0.177833045143692498221e-7)
0800       };
0801       static const T Q[9] = {
0802          BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
0803          BOOST_MATH_BIG_CONSTANT(T, 64, -1.20352377969742325748),
0804          BOOST_MATH_BIG_CONSTANT(T, 64, 0.66707904942606479811),
0805          BOOST_MATH_BIG_CONSTANT(T, 64, -0.223014531629140771914),
0806          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0493340022262908008636),
0807          BOOST_MATH_BIG_CONSTANT(T, 64, -0.00741934273050807310677),
0808          BOOST_MATH_BIG_CONSTANT(T, 64, 0.00074353567782087939294),
0809          BOOST_MATH_BIG_CONSTANT(T, 64, -0.455861727069603367656e-4),
0810          BOOST_MATH_BIG_CONSTANT(T, 64, 0.131515429329812837701e-5)
0811       };
0812 
0813       static const T c1 = BOOST_MATH_BIG_CONSTANT(T, 64, 1677624236387711.0);
0814       static const T c2 = BOOST_MATH_BIG_CONSTANT(T, 64, 4503599627370496.0);
0815       static const T r1 = c1 / c2;
0816       static const T r2 = BOOST_MATH_BIG_CONSTANT(T, 64, 0.131401834143860282009280387409357165515556574352422001206362e-16);
0817       static const T r = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392));
0818       // LCOV_EXCL_STOP
0819 
0820       T t = (z / 3) - 1;
0821       result = tools::evaluate_polynomial(P, t)
0822          / tools::evaluate_polynomial(Q, t);
0823       t = (z - r1) - r2;
0824       result *= t;
0825       if(fabs(t) < T(0.1))
0826       {
0827          result += boost::math::log1p(t / r, pol);
0828       }
0829       else
0830       {
0831          result += log(z / r);
0832       }
0833    }
0834    else if (z <= 10)
0835    {
0836       // Maximum Deviation Found:                     2.622e-21
0837       // Expected Error Term:                         -2.622e-21
0838       // Max Error found at long double precision =   Poly: 1.208328e-20   Cheb: 1.073723e-20
0839       // LCOV_EXCL_START
0840       static const T Y = 1.158985137939453125F;
0841       static const T P[9] = {
0842          BOOST_MATH_BIG_CONSTANT(T, 64, 0.00139324086199409049399),
0843          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0345238388952337563247),
0844          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0382065278072592940767),
0845          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0156117003070560727392),
0846          BOOST_MATH_BIG_CONSTANT(T, 64, -0.00383276012430495387102),
0847          BOOST_MATH_BIG_CONSTANT(T, 64, -0.000697070540945496497992),
0848          BOOST_MATH_BIG_CONSTANT(T, 64, -0.877310384591205930343e-4),
0849          BOOST_MATH_BIG_CONSTANT(T, 64, -0.623067256376494930067e-5),
0850          BOOST_MATH_BIG_CONSTANT(T, 64, -0.377246883283337141444e-6)
0851       };
0852       static const T Q[10] = {
0853          BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
0854          BOOST_MATH_BIG_CONSTANT(T, 64, 1.08073635708902053767),
0855          BOOST_MATH_BIG_CONSTANT(T, 64, 0.553681133533942532909),
0856          BOOST_MATH_BIG_CONSTANT(T, 64, 0.176763647137553797451),
0857          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0387891748253869928121),
0858          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0060603004848394727017),
0859          BOOST_MATH_BIG_CONSTANT(T, 64, 0.000670519492939992806051),
0860          BOOST_MATH_BIG_CONSTANT(T, 64, 0.4947357050100855646e-4),
0861          BOOST_MATH_BIG_CONSTANT(T, 64, 0.204339282037446434827e-5),
0862          BOOST_MATH_BIG_CONSTANT(T, 64, 0.146951181174930425744e-7)
0863       };
0864       // LCOV_EXCL_STOP
0865       T t = z / 2 - 4;
0866       result = Y + tools::evaluate_polynomial(P, t)
0867          / tools::evaluate_polynomial(Q, t);
0868       result *= exp(z) / z;
0869       result += z;
0870    }
0871    else if(z <= 20)
0872    {
0873       // Maximum Deviation Found:                     3.220e-20
0874       // Expected Error Term:                         3.220e-20
0875       // Max Error found at long double precision =   Poly: 7.696841e-20   Cheb: 6.205163e-20
0876 
0877       // LCOV_EXCL_START
0878       static const T Y = 1.0869731903076171875F;
0879       static const T P[10] = {
0880          BOOST_MATH_BIG_CONSTANT(T, 64, -0.00893891094356946995368),
0881          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0487562980088748775943),
0882          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0670568657950041926085),
0883          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0509577352851442932713),
0884          BOOST_MATH_BIG_CONSTANT(T, 64, -0.02551800927409034206),
0885          BOOST_MATH_BIG_CONSTANT(T, 64, -0.00892913759760086687083),
0886          BOOST_MATH_BIG_CONSTANT(T, 64, -0.00224469630207344379888),
0887          BOOST_MATH_BIG_CONSTANT(T, 64, -0.000392477245911296982776),
0888          BOOST_MATH_BIG_CONSTANT(T, 64, -0.44424044184395578775e-4),
0889          BOOST_MATH_BIG_CONSTANT(T, 64, -0.252788029251437017959e-5)
0890       };
0891       static const T Q[10] = {
0892          BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
0893          BOOST_MATH_BIG_CONSTANT(T, 64, 2.00323265503572414261),
0894          BOOST_MATH_BIG_CONSTANT(T, 64, 1.94688958187256383178),
0895          BOOST_MATH_BIG_CONSTANT(T, 64, 1.19733638134417472296),
0896          BOOST_MATH_BIG_CONSTANT(T, 64, 0.513137726038353385661),
0897          BOOST_MATH_BIG_CONSTANT(T, 64, 0.159135395578007264547),
0898          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0358233587351620919881),
0899          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0056716655597009417875),
0900          BOOST_MATH_BIG_CONSTANT(T, 64, 0.000577048986213535829925),
0901          BOOST_MATH_BIG_CONSTANT(T, 64, 0.290976943033493216793e-4)
0902       };
0903       // LCOV_EXCL_STOP
0904       T t = z / 5 - 3;
0905       result = Y + tools::evaluate_polynomial(P, t)
0906          / tools::evaluate_polynomial(Q, t);
0907       result *= exp(z) / z;
0908       result += z;
0909    }
0910    else if(z <= 40)
0911    {
0912       // Maximum Deviation Found:                     2.940e-21
0913       // Expected Error Term:                         -2.938e-21
0914       // Max Error found at long double precision =   Poly: 3.419893e-19   Cheb: 3.359874e-19
0915       // LCOV_EXCL_START
0916       static const T Y = 1.03937530517578125F;
0917       static const T P[12] = {
0918          BOOST_MATH_BIG_CONSTANT(T, 64, -0.00356165148914447278177),
0919          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0240235006148610849678),
0920          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0516699967278057976119),
0921          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0586603078706856245674),
0922          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0409960120868776180825),
0923          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0185485073689590665153),
0924          BOOST_MATH_BIG_CONSTANT(T, 64, -0.00537842101034123222417),
0925          BOOST_MATH_BIG_CONSTANT(T, 64, -0.000920988084778273760609),
0926          BOOST_MATH_BIG_CONSTANT(T, 64, -0.716742618812210980263e-4),
0927          BOOST_MATH_BIG_CONSTANT(T, 64, -0.504623302166487346677e-9),
0928          BOOST_MATH_BIG_CONSTANT(T, 64, 0.712662196671896837736e-10),
0929          BOOST_MATH_BIG_CONSTANT(T, 64, -0.533769629702262072175e-11)
0930       };
0931       static const T Q[9] = {
0932          BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
0933          BOOST_MATH_BIG_CONSTANT(T, 64, 3.13286733695729715455),
0934          BOOST_MATH_BIG_CONSTANT(T, 64, 4.49281223045653491929),
0935          BOOST_MATH_BIG_CONSTANT(T, 64, 3.84900294427622911374),
0936          BOOST_MATH_BIG_CONSTANT(T, 64, 2.15205199043580378211),
0937          BOOST_MATH_BIG_CONSTANT(T, 64, 0.802912186540269232424),
0938          BOOST_MATH_BIG_CONSTANT(T, 64, 0.194793170017818925388),
0939          BOOST_MATH_BIG_CONSTANT(T, 64, 0.0280128013584653182994),
0940          BOOST_MATH_BIG_CONSTANT(T, 64, 0.00182034930799902922549)
0941       };
0942       // LCOV_EXCL_STOP
0943       T t = z / 10 - 3;
0944       result = Y + tools::evaluate_polynomial(P, t)
0945          / tools::evaluate_polynomial(Q, t);
0946       BOOST_MATH_INSTRUMENT_VARIABLE(result)
0947       result *= exp(z) / z;
0948       BOOST_MATH_INSTRUMENT_VARIABLE(result)
0949       result += z;
0950       BOOST_MATH_INSTRUMENT_VARIABLE(result)
0951    }
0952    else
0953    {
0954       // Maximum Deviation Found:                     3.536e-20
0955       // Max Error found at long double precision =   Poly: 1.310671e-19   Cheb: 8.630943e-11
0956       // LCOV_EXCL_START
0957       static const T exp40 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.35385266837019985407899910749034804508871617254555467236651e17));
0958       static const T Y= 1.013065338134765625F;
0959       static const T P[9] = {
0960          BOOST_MATH_BIG_CONSTANT(T, 64, -0.0130653381347656250004),
0961          BOOST_MATH_BIG_CONSTANT(T, 64, 0.644487780349757303739),
0962          BOOST_MATH_BIG_CONSTANT(T, 64, 143.995670348227433964),
0963          BOOST_MATH_BIG_CONSTANT(T, 64, -13918.9322758014173709),
0964          BOOST_MATH_BIG_CONSTANT(T, 64, 476260.975133624194484),
0965          BOOST_MATH_BIG_CONSTANT(T, 64, -7437102.15135982802122),
0966          BOOST_MATH_BIG_CONSTANT(T, 64, 53732298.8764767916542),
0967          BOOST_MATH_BIG_CONSTANT(T, 64, -160695051.957997452509),
0968          BOOST_MATH_BIG_CONSTANT(T, 64, 137839271.592778020028)
0969       };
0970       static const T Q[9] = {
0971          BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
0972          BOOST_MATH_BIG_CONSTANT(T, 64, 27.2103343964943718802),
0973          BOOST_MATH_BIG_CONSTANT(T, 64, -8785.48528692879413676),
0974          BOOST_MATH_BIG_CONSTANT(T, 64, 397530.290000322626766),
0975          BOOST_MATH_BIG_CONSTANT(T, 64, -7356441.34957799368252),
0976          BOOST_MATH_BIG_CONSTANT(T, 64, 63050914.5343400957524),
0977          BOOST_MATH_BIG_CONSTANT(T, 64, -246143779.638307701369),
0978          BOOST_MATH_BIG_CONSTANT(T, 64, 384647824.678554961174),
0979          BOOST_MATH_BIG_CONSTANT(T, 64, -166288297.874583961493)
0980       };
0981       // LCOV_EXCL_STOP
0982       T t = 1 / z;
0983       result = Y + tools::evaluate_polynomial(P, t)
0984          / tools::evaluate_polynomial(Q, t);
0985       if(z < 41)
0986          result *= exp(z) / z;
0987       else
0988       {
0989          // Avoid premature overflow if we can:
0990          t = z - 40;
0991          if(t > tools::log_max_value<T>())
0992          {
0993             result = policies::raise_overflow_error<T>(function, nullptr, pol);
0994          }
0995          else
0996          {
0997             result *= exp(z - 40) / z;
0998             if(result > tools::max_value<T>() / exp40)
0999             {
1000                result = policies::raise_overflow_error<T>(function, nullptr, pol);
1001             }
1002             else
1003             {
1004                result *= exp40;
1005             }
1006          }
1007       }
1008       result += z;
1009    }
1010    return result;
1011 }
1012 
1013 template <class T, class Policy>
1014 BOOST_MATH_GPU_ENABLED void expint_i_imp_113a(T& result, const T& z, const Policy& pol)
1015 {
1016    BOOST_MATH_STD_USING
1017    // Maximum Deviation Found:                     1.230e-36
1018    // Expected Error Term:                         -1.230e-36
1019    // Max Error found at long double precision =   Poly: 4.355299e-34   Cheb: 7.512581e-34
1020 
1021    // LCOV_EXCL_START
1022    static const T P[15] = {
1023       BOOST_MATH_BIG_CONSTANT(T, 113, 2.98677224343598593765287235997328555),
1024       BOOST_MATH_BIG_CONSTANT(T, 113, -0.333256034674702967028780537349334037),
1025       BOOST_MATH_BIG_CONSTANT(T, 113, 0.851831522798101228384971644036708463),
1026       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0657854833494646206186773614110374948),
1027       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0630065662557284456000060708977935073),
1028       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00311759191425309373327784154659649232),
1029       BOOST_MATH_BIG_CONSTANT(T, 113, 0.00176213568201493949664478471656026771),
1030       BOOST_MATH_BIG_CONSTANT(T, 113, -0.491548660404172089488535218163952295e-4),
1031       BOOST_MATH_BIG_CONSTANT(T, 113, 0.207764227621061706075562107748176592e-4),
1032       BOOST_MATH_BIG_CONSTANT(T, 113, -0.225445398156913584846374273379402765e-6),
1033       BOOST_MATH_BIG_CONSTANT(T, 113, 0.996939977231410319761273881672601592e-7),
1034       BOOST_MATH_BIG_CONSTANT(T, 113, 0.212546902052178643330520878928100847e-9),
1035       BOOST_MATH_BIG_CONSTANT(T, 113, 0.154646053060262871360159325115980023e-9),
1036       BOOST_MATH_BIG_CONSTANT(T, 113, 0.143971277122049197323415503594302307e-11),
1037       BOOST_MATH_BIG_CONSTANT(T, 113, 0.306243138978114692252817805327426657e-13)
1038    };
1039    static const T Q[15] = {
1040       BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1041       BOOST_MATH_BIG_CONSTANT(T, 113, -1.40178870313943798705491944989231793),
1042       BOOST_MATH_BIG_CONSTANT(T, 113, 0.943810968269701047641218856758605284),
1043       BOOST_MATH_BIG_CONSTANT(T, 113, -0.405026631534345064600850391026113165),
1044       BOOST_MATH_BIG_CONSTANT(T, 113, 0.123924153524614086482627660399122762),
1045       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0286364505373369439591132549624317707),
1046       BOOST_MATH_BIG_CONSTANT(T, 113, 0.00516148845910606985396596845494015963),
1047       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000738330799456364820380739850924783649),
1048       BOOST_MATH_BIG_CONSTANT(T, 113, 0.843737760991856114061953265870882637e-4),
1049       BOOST_MATH_BIG_CONSTANT(T, 113, -0.767957673431982543213661388914587589e-5),
1050       BOOST_MATH_BIG_CONSTANT(T, 113, 0.549136847313854595809952100614840031e-6),
1051       BOOST_MATH_BIG_CONSTANT(T, 113, -0.299801381513743676764008325949325404e-7),
1052       BOOST_MATH_BIG_CONSTANT(T, 113, 0.118419479055346106118129130945423483e-8),
1053       BOOST_MATH_BIG_CONSTANT(T, 113, -0.30372295663095470359211949045344607e-10),
1054       BOOST_MATH_BIG_CONSTANT(T, 113, 0.382742953753485333207877784720070523e-12)
1055    };
1056 
1057    static const T c1 = BOOST_MATH_BIG_CONSTANT(T, 113, 1677624236387711.0);
1058    static const T c2 = BOOST_MATH_BIG_CONSTANT(T, 113, 4503599627370496.0);
1059    static const T c3 = BOOST_MATH_BIG_CONSTANT(T, 113, 266514582277687.0);
1060    static const T c4 = BOOST_MATH_BIG_CONSTANT(T, 113, 4503599627370496.0);
1061    static const T c5 = BOOST_MATH_BIG_CONSTANT(T, 113, 4503599627370496.0);
1062    static const T r1 = c1 / c2;
1063    static const T r2 = c3 / c4 / c5;
1064    static const T r3 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.283806480836357377069325311780969887585024578164571984232357e-31));
1065    static const T r = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392));
1066    // LCOV_EXCL_STOP
1067    T t = (z / 3) - 1;
1068    result = tools::evaluate_polynomial(P, t)
1069       / tools::evaluate_polynomial(Q, t);
1070    t = ((z - r1) - r2) - r3;
1071    result *= t;
1072    if(fabs(t) < 0.1)
1073    {
1074       result += boost::math::log1p(t / r, pol);
1075    }
1076    else
1077    {
1078       result += log(z / r);
1079    }
1080 }
1081 
1082 template <class T>
1083 BOOST_MATH_GPU_ENABLED void expint_i_113b(T& result, const T& z)
1084 {
1085    BOOST_MATH_STD_USING
1086    // Maximum Deviation Found:                     7.779e-36
1087    // Expected Error Term:                         -7.779e-36
1088    // Max Error found at long double precision =   Poly: 2.576723e-35   Cheb: 1.236001e-34
1089    // LCOV_EXCL_START
1090    static const T Y = 1.158985137939453125F;
1091    static const T P[15] = {
1092       BOOST_MATH_BIG_CONSTANT(T, 113, 0.00139324086199409049282472239613554817),
1093       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0338173111691991289178779840307998955),
1094       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0555972290794371306259684845277620556),
1095       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0378677976003456171563136909186202177),
1096       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0152221583517528358782902783914356667),
1097       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00428283334203873035104248217403126905),
1098       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000922782631491644846511553601323435286),
1099       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000155513428088853161562660696055496696),
1100       BOOST_MATH_BIG_CONSTANT(T, 113, -0.205756580255359882813545261519317096e-4),
1101       BOOST_MATH_BIG_CONSTANT(T, 113, -0.220327406578552089820753181821115181e-5),
1102       BOOST_MATH_BIG_CONSTANT(T, 113, -0.189483157545587592043421445645377439e-6),
1103       BOOST_MATH_BIG_CONSTANT(T, 113, -0.122426571518570587750898968123803867e-7),
1104       BOOST_MATH_BIG_CONSTANT(T, 113, -0.635187358949437991465353268374523944e-9),
1105       BOOST_MATH_BIG_CONSTANT(T, 113, -0.203015132965870311935118337194860863e-10),
1106       BOOST_MATH_BIG_CONSTANT(T, 113, -0.384276705503357655108096065452950822e-12)
1107    };
1108    static const T Q[15] = {
1109       BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1110       BOOST_MATH_BIG_CONSTANT(T, 113, 1.58784732785354597996617046880946257),
1111       BOOST_MATH_BIG_CONSTANT(T, 113, 1.18550755302279446339364262338114098),
1112       BOOST_MATH_BIG_CONSTANT(T, 113, 0.55598993549661368604527040349702836),
1113       BOOST_MATH_BIG_CONSTANT(T, 113, 0.184290888380564236919107835030984453),
1114       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0459658051803613282360464632326866113),
1115       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0089505064268613225167835599456014705),
1116       BOOST_MATH_BIG_CONSTANT(T, 113, 0.00139042673882987693424772855926289077),
1117       BOOST_MATH_BIG_CONSTANT(T, 113, 0.000174210708041584097450805790176479012),
1118       BOOST_MATH_BIG_CONSTANT(T, 113, 0.176324034009707558089086875136647376e-4),
1119       BOOST_MATH_BIG_CONSTANT(T, 113, 0.142935845999505649273084545313710581e-5),
1120       BOOST_MATH_BIG_CONSTANT(T, 113, 0.907502324487057260675816233312747784e-7),
1121       BOOST_MATH_BIG_CONSTANT(T, 113, 0.431044337808893270797934621235918418e-8),
1122       BOOST_MATH_BIG_CONSTANT(T, 113, 0.139007266881450521776529705677086902e-9),
1123       BOOST_MATH_BIG_CONSTANT(T, 113, 0.234715286125516430792452741830364672e-11)
1124    };
1125    // LCOV_EXCL_STOP
1126    T t = z / 2 - 4;
1127    result = Y + tools::evaluate_polynomial(P, t)
1128       / tools::evaluate_polynomial(Q, t);
1129    result *= exp(z) / z;
1130    result += z;
1131 }
1132 
1133 template <class T>
1134 BOOST_MATH_GPU_ENABLED void expint_i_113c(T& result, const T& z)
1135 {
1136    BOOST_MATH_STD_USING
1137    // Maximum Deviation Found:                     1.082e-34
1138    // Expected Error Term:                         1.080e-34
1139    // Max Error found at long double precision =   Poly: 1.958294e-34   Cheb: 2.472261e-34
1140 
1141    // LCOV_EXCL_START
1142    static const T Y = 1.091579437255859375F;
1143    static const T P[17] = {
1144       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00685089599550151282724924894258520532),
1145       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0443313550253580053324487059748497467),
1146       BOOST_MATH_BIG_CONSTANT(T, 113, -0.071538561252424027443296958795814874),
1147       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0622923153354102682285444067843300583),
1148       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0361631270264607478205393775461208794),
1149       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0153192826839624850298106509601033261),
1150       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00496967904961260031539602977748408242),
1151       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00126989079663425780800919171538920589),
1152       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000258933143097125199914724875206326698),
1153       BOOST_MATH_BIG_CONSTANT(T, 113, -0.422110326689204794443002330541441956e-4),
1154       BOOST_MATH_BIG_CONSTANT(T, 113, -0.546004547590412661451073996127115221e-5),
1155       BOOST_MATH_BIG_CONSTANT(T, 113, -0.546775260262202177131068692199272241e-6),
1156       BOOST_MATH_BIG_CONSTANT(T, 113, -0.404157632825805803833379568956559215e-7),
1157       BOOST_MATH_BIG_CONSTANT(T, 113, -0.200612596196561323832327013027419284e-8),
1158       BOOST_MATH_BIG_CONSTANT(T, 113, -0.502538501472133913417609379765434153e-10),
1159       BOOST_MATH_BIG_CONSTANT(T, 113, -0.326283053716799774936661568391296584e-13),
1160       BOOST_MATH_BIG_CONSTANT(T, 113, 0.869226483473172853557775877908693647e-15)
1161    };
1162    static const T Q[15] = {
1163       BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1164       BOOST_MATH_BIG_CONSTANT(T, 113, 2.23227220874479061894038229141871087),
1165       BOOST_MATH_BIG_CONSTANT(T, 113, 2.40221000361027971895657505660959863),
1166       BOOST_MATH_BIG_CONSTANT(T, 113, 1.65476320985936174728238416007084214),
1167       BOOST_MATH_BIG_CONSTANT(T, 113, 0.816828602963895720369875535001248227),
1168       BOOST_MATH_BIG_CONSTANT(T, 113, 0.306337922909446903672123418670921066),
1169       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0902400121654409267774593230720600752),
1170       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0212708882169429206498765100993228086),
1171       BOOST_MATH_BIG_CONSTANT(T, 113, 0.00404442626252467471957713495828165491),
1172       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0006195601618842253612635241404054589),
1173       BOOST_MATH_BIG_CONSTANT(T, 113, 0.755930932686543009521454653994321843e-4),
1174       BOOST_MATH_BIG_CONSTANT(T, 113, 0.716004532773778954193609582677482803e-5),
1175       BOOST_MATH_BIG_CONSTANT(T, 113, 0.500881663076471627699290821742924233e-6),
1176       BOOST_MATH_BIG_CONSTANT(T, 113, 0.233593219218823384508105943657387644e-7),
1177       BOOST_MATH_BIG_CONSTANT(T, 113, 0.554900353169148897444104962034267682e-9)
1178    };
1179    // LCOV_EXCL_STOP
1180    T t = z / 4 - 3.5;
1181    result = Y + tools::evaluate_polynomial(P, t)
1182       / tools::evaluate_polynomial(Q, t);
1183    result *= exp(z) / z;
1184    result += z;
1185 }
1186 
1187 template <class T>
1188 BOOST_MATH_GPU_ENABLED void expint_i_113d(T& result, const T& z)
1189 {
1190    BOOST_MATH_STD_USING
1191    // Maximum Deviation Found:                     3.163e-35
1192    // Expected Error Term:                         3.163e-35
1193    // Max Error found at long double precision =   Poly: 4.158110e-35   Cheb: 5.385532e-35
1194    // LCOV_EXCL_START
1195    static const T Y = 1.051731109619140625F;
1196    static const T P[14] = {
1197       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00144552494420652573815404828020593565),
1198       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0126747451594545338365684731262912741),
1199       BOOST_MATH_BIG_CONSTANT(T, 113, -0.01757394877502366717526779263438073),
1200       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0126838952395506921945756139424722588),
1201       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0060045057928894974954756789352443522),
1202       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00205349237147226126653803455793107903),
1203       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000532606040579654887676082220195624207),
1204       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000107344687098019891474772069139014662),
1205       BOOST_MATH_BIG_CONSTANT(T, 113, -0.169536802705805811859089949943435152e-4),
1206       BOOST_MATH_BIG_CONSTANT(T, 113, -0.20863311729206543881826553010120078e-5),
1207       BOOST_MATH_BIG_CONSTANT(T, 113, -0.195670358542116256713560296776654385e-6),
1208       BOOST_MATH_BIG_CONSTANT(T, 113, -0.133291168587253145439184028259772437e-7),
1209       BOOST_MATH_BIG_CONSTANT(T, 113, -0.595500337089495614285777067722823397e-9),
1210       BOOST_MATH_BIG_CONSTANT(T, 113, -0.133141358866324100955927979606981328e-10)
1211    };
1212    static const T Q[14] = {
1213       BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1214       BOOST_MATH_BIG_CONSTANT(T, 113, 1.72490783907582654629537013560044682),
1215       BOOST_MATH_BIG_CONSTANT(T, 113, 1.44524329516800613088375685659759765),
1216       BOOST_MATH_BIG_CONSTANT(T, 113, 0.778241785539308257585068744978050181),
1217       BOOST_MATH_BIG_CONSTANT(T, 113, 0.300520486589206605184097270225725584),
1218       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0879346899691339661394537806057953957),
1219       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0200802415843802892793583043470125006),
1220       BOOST_MATH_BIG_CONSTANT(T, 113, 0.00362842049172586254520256100538273214),
1221       BOOST_MATH_BIG_CONSTANT(T, 113, 0.000519731362862955132062751246769469957),
1222       BOOST_MATH_BIG_CONSTANT(T, 113, 0.584092147914050999895178697392282665e-4),
1223       BOOST_MATH_BIG_CONSTANT(T, 113, 0.501851497707855358002773398333542337e-5),
1224       BOOST_MATH_BIG_CONSTANT(T, 113, 0.313085677467921096644895738538865537e-6),
1225       BOOST_MATH_BIG_CONSTANT(T, 113, 0.127552010539733113371132321521204458e-7),
1226       BOOST_MATH_BIG_CONSTANT(T, 113, 0.25737310826983451144405899970774587e-9)
1227    };
1228    // LCOV_EXCL_STOP
1229    T t = z / 4 - 5.5;
1230    result = Y + tools::evaluate_polynomial(P, t)
1231       / tools::evaluate_polynomial(Q, t);
1232    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1233    result *= exp(z) / z;
1234    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1235    result += z;
1236    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1237 }
1238 
1239 template <class T>
1240 BOOST_MATH_GPU_ENABLED void expint_i_113e(T& result, const T& z)
1241 {
1242    BOOST_MATH_STD_USING
1243    // Maximum Deviation Found:                     7.972e-36
1244    // Expected Error Term:                         7.962e-36
1245    // Max Error found at long double precision =   Poly: 1.711721e-34   Cheb: 3.100018e-34
1246    // LCOV_EXCL_START
1247    static const T Y = 1.032726287841796875F;
1248    static const T P[15] = {
1249       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00141056919297307534690895009969373233),
1250       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0123384175302540291339020257071411437),
1251       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0298127270706864057791526083667396115),
1252       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0390686759471630584626293670260768098),
1253       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0338226792912607409822059922949035589),
1254       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0211659736179834946452561197559654582),
1255       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0100428887460879377373158821400070313),
1256       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00370717396015165148484022792801682932),
1257       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0010768667551001624764329000496561659),
1258       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000246127328761027039347584096573123531),
1259       BOOST_MATH_BIG_CONSTANT(T, 113, -0.437318110527818613580613051861991198e-4),
1260       BOOST_MATH_BIG_CONSTANT(T, 113, -0.587532682329299591501065482317771497e-5),
1261       BOOST_MATH_BIG_CONSTANT(T, 113, -0.565697065670893984610852937110819467e-6),
1262       BOOST_MATH_BIG_CONSTANT(T, 113, -0.350233957364028523971768887437839573e-7),
1263       BOOST_MATH_BIG_CONSTANT(T, 113, -0.105428907085424234504608142258423505e-8)
1264    };
1265    static const T Q[16] = {
1266       BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1267       BOOST_MATH_BIG_CONSTANT(T, 113, 3.17261315255467581204685605414005525),
1268       BOOST_MATH_BIG_CONSTANT(T, 113, 4.85267952971640525245338392887217426),
1269       BOOST_MATH_BIG_CONSTANT(T, 113, 4.74341914912439861451492872946725151),
1270       BOOST_MATH_BIG_CONSTANT(T, 113, 3.31108463283559911602405970817931801),
1271       BOOST_MATH_BIG_CONSTANT(T, 113, 1.74657006336994649386607925179848899),
1272       BOOST_MATH_BIG_CONSTANT(T, 113, 0.718255607416072737965933040353653244),
1273       BOOST_MATH_BIG_CONSTANT(T, 113, 0.234037553177354542791975767960643864),
1274       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0607470145906491602476833515412605389),
1275       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0125048143774226921434854172947548724),
1276       BOOST_MATH_BIG_CONSTANT(T, 113, 0.00201034366420433762935768458656609163),
1277       BOOST_MATH_BIG_CONSTANT(T, 113, 0.000244823338417452367656368849303165721),
1278       BOOST_MATH_BIG_CONSTANT(T, 113, 0.213511655166983177960471085462540807e-4),
1279       BOOST_MATH_BIG_CONSTANT(T, 113, 0.119323998465870686327170541547982932e-5),
1280       BOOST_MATH_BIG_CONSTANT(T, 113, 0.322153582559488797803027773591727565e-7),
1281       BOOST_MATH_BIG_CONSTANT(T, 113, -0.161635525318683508633792845159942312e-16)
1282    };
1283    // LCOV_EXCL_STOP
1284    T t = z / 8 - 4.25;
1285    result = Y + tools::evaluate_polynomial(P, t)
1286       / tools::evaluate_polynomial(Q, t);
1287    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1288    result *= exp(z) / z;
1289    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1290    result += z;
1291    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1292 }
1293 
1294 template <class T>
1295 BOOST_MATH_GPU_ENABLED void expint_i_113f(T& result, const T& z)
1296 {
1297    BOOST_MATH_STD_USING
1298    // Maximum Deviation Found:                     4.469e-36
1299    // Expected Error Term:                         4.468e-36
1300    // Max Error found at long double precision =   Poly: 1.288958e-35   Cheb: 2.304586e-35
1301    // LCOV_EXCL_START
1302    static const T Y = 1.0216197967529296875F;
1303    static const T P[12] = {
1304       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000322999116096627043476023926572650045),
1305       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00385606067447365187909164609294113346),
1306       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00686514524727568176735949971985244415),
1307       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00606260649593050194602676772589601799),
1308       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00334382362017147544335054575436194357),
1309       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00126108534260253075708625583630318043),
1310       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000337881489347846058951220431209276776),
1311       BOOST_MATH_BIG_CONSTANT(T, 113, -0.648480902304640018785370650254018022e-4),
1312       BOOST_MATH_BIG_CONSTANT(T, 113, -0.87652644082970492211455290209092766e-5),
1313       BOOST_MATH_BIG_CONSTANT(T, 113, -0.794712243338068631557849449519994144e-6),
1314       BOOST_MATH_BIG_CONSTANT(T, 113, -0.434084023639508143975983454830954835e-7),
1315       BOOST_MATH_BIG_CONSTANT(T, 113, -0.107839681938752337160494412638656696e-8)
1316    };
1317    static const T Q[12] = {
1318       BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1319       BOOST_MATH_BIG_CONSTANT(T, 113, 2.09913805456661084097134805151524958),
1320       BOOST_MATH_BIG_CONSTANT(T, 113, 2.07041755535439919593503171320431849),
1321       BOOST_MATH_BIG_CONSTANT(T, 113, 1.26406517226052371320416108604874734),
1322       BOOST_MATH_BIG_CONSTANT(T, 113, 0.529689923703770353961553223973435569),
1323       BOOST_MATH_BIG_CONSTANT(T, 113, 0.159578150879536711042269658656115746),
1324       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0351720877642000691155202082629857131),
1325       BOOST_MATH_BIG_CONSTANT(T, 113, 0.00565313621289648752407123620997063122),
1326       BOOST_MATH_BIG_CONSTANT(T, 113, 0.000646920278540515480093843570291218295),
1327       BOOST_MATH_BIG_CONSTANT(T, 113, 0.499904084850091676776993523323213591e-4),
1328       BOOST_MATH_BIG_CONSTANT(T, 113, 0.233740058688179614344680531486267142e-5),
1329       BOOST_MATH_BIG_CONSTANT(T, 113, 0.498800627828842754845418576305379469e-7)
1330    };
1331    // LCOV_EXCL_STOP
1332    T t = z / 7 - 7;
1333    result = Y + tools::evaluate_polynomial(P, t)
1334       / tools::evaluate_polynomial(Q, t);
1335    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1336    result *= exp(z) / z;
1337    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1338    result += z;
1339    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1340 }
1341 
1342 template <class T>
1343 BOOST_MATH_GPU_ENABLED void expint_i_113g(T& result, const T& z)
1344 {
1345    BOOST_MATH_STD_USING
1346    // Maximum Deviation Found:                     5.588e-35
1347    // Expected Error Term:                         -5.566e-35
1348    // Max Error found at long double precision =   Poly: 9.976345e-35   Cheb: 8.358865e-35
1349    // LCOV_EXCL_START
1350    static const T Y = 1.015148162841796875F;
1351    static const T P[11] = {
1352       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000435714784725086961464589957142615216),
1353       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00432114324353830636009453048419094314),
1354       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0100740363285526177522819204820582424),
1355       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0116744115827059174392383504427640362),
1356       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00816145387784261141360062395898644652),
1357       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00371380272673500791322744465394211508),
1358       BOOST_MATH_BIG_CONSTANT(T, 113, -0.00112958263488611536502153195005736563),
1359       BOOST_MATH_BIG_CONSTANT(T, 113, -0.000228316462389404645183269923754256664),
1360       BOOST_MATH_BIG_CONSTANT(T, 113, -0.29462181955852860250359064291292577e-4),
1361       BOOST_MATH_BIG_CONSTANT(T, 113, -0.21972450610957417963227028788460299e-5),
1362       BOOST_MATH_BIG_CONSTANT(T, 113, -0.720558173805289167524715527536874694e-7)
1363    };
1364    static const T Q[11] = {
1365       BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1366       BOOST_MATH_BIG_CONSTANT(T, 113, 2.95918362458402597039366979529287095),
1367       BOOST_MATH_BIG_CONSTANT(T, 113, 3.96472247520659077944638411856748924),
1368       BOOST_MATH_BIG_CONSTANT(T, 113, 3.15563251550528513747923714884142131),
1369       BOOST_MATH_BIG_CONSTANT(T, 113, 1.64674612007093983894215359287448334),
1370       BOOST_MATH_BIG_CONSTANT(T, 113, 0.58695020129846594405856226787156424),
1371       BOOST_MATH_BIG_CONSTANT(T, 113, 0.144358385319329396231755457772362793),
1372       BOOST_MATH_BIG_CONSTANT(T, 113, 0.024146911506411684815134916238348063),
1373       BOOST_MATH_BIG_CONSTANT(T, 113, 0.0026257132337460784266874572001650153),
1374       BOOST_MATH_BIG_CONSTANT(T, 113, 0.000167479843750859222348869769094711093),
1375       BOOST_MATH_BIG_CONSTANT(T, 113, 0.475673638665358075556452220192497036e-5)
1376    };
1377    // LCOV_EXCL_STOP
1378    T t = z / 14 - 5;
1379    result = Y + tools::evaluate_polynomial(P, t)
1380       / tools::evaluate_polynomial(Q, t);
1381    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1382    result *= exp(z) / z;
1383    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1384    result += z;
1385    BOOST_MATH_INSTRUMENT_VARIABLE(result)
1386 }
1387 
1388 template <class T>
1389 BOOST_MATH_GPU_ENABLED void expint_i_113h(T& result, const T& z)
1390 {
1391    BOOST_MATH_STD_USING
1392    // Maximum Deviation Found:                     4.448e-36
1393    // Expected Error Term:                         4.445e-36
1394    // Max Error found at long double precision =   Poly: 2.058532e-35   Cheb: 2.165465e-27
1395    // LCOV_EXCL_START
1396    static const T Y= 1.00849151611328125F;
1397    static const T P[9] = {
1398       BOOST_MATH_BIG_CONSTANT(T, 113, -0.0084915161132812500000001440233607358),
1399       BOOST_MATH_BIG_CONSTANT(T, 113, 1.84479378737716028341394223076147872),
1400       BOOST_MATH_BIG_CONSTANT(T, 113, -130.431146923726715674081563022115568),
1401       BOOST_MATH_BIG_CONSTANT(T, 113, 4336.26945491571504885214176203512015),
1402       BOOST_MATH_BIG_CONSTANT(T, 113, -76279.0031974974730095170437591004177),
1403       BOOST_MATH_BIG_CONSTANT(T, 113, 729577.956271997673695191455111727774),
1404       BOOST_MATH_BIG_CONSTANT(T, 113, -3661928.69330208734947103004900349266),
1405       BOOST_MATH_BIG_CONSTANT(T, 113, 8570600.041606912735872059184527855),
1406       BOOST_MATH_BIG_CONSTANT(T, 113, -6758379.93672362080947905580906028645)
1407    };
1408    static const T Q[10] = {
1409       BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1410       BOOST_MATH_BIG_CONSTANT(T, 113, -99.4868026047611434569541483506091713),
1411       BOOST_MATH_BIG_CONSTANT(T, 113, 3879.67753690517114249705089803055473),
1412       BOOST_MATH_BIG_CONSTANT(T, 113, -76495.82413252517165830203774900806),
1413       BOOST_MATH_BIG_CONSTANT(T, 113, 820773.726408311894342553758526282667),
1414       BOOST_MATH_BIG_CONSTANT(T, 113, -4803087.64956923577571031564909646579),
1415       BOOST_MATH_BIG_CONSTANT(T, 113, 14521246.227703545012713173740895477),
1416       BOOST_MATH_BIG_CONSTANT(T, 113, -19762752.0196769712258527849159393044),
1417       BOOST_MATH_BIG_CONSTANT(T, 113, 8354144.67882768405803322344185185517),
1418       BOOST_MATH_BIG_CONSTANT(T, 113, 355076.853106511136734454134915432571)
1419    };
1420    // LCOV_EXCL_STOP
1421    T t = 1 / z;
1422    result = Y + tools::evaluate_polynomial(P, t)
1423       / tools::evaluate_polynomial(Q, t);
1424    result *= exp(z) / z;
1425    result += z;
1426 }
1427 
1428 template <class T, class Policy>
1429 BOOST_MATH_GPU_ENABLED T expint_i_imp(T z, const Policy& pol, const boost::math::integral_constant<int, 113>& tag)
1430 {
1431    BOOST_MATH_STD_USING
1432    constexpr auto function = "boost::math::expint<%1%>(%1%)";
1433    if(z < 0)
1434       return -expint_imp(1, T(-z), pol, tag);
1435    if(z == 0)
1436       return -policies::raise_overflow_error<T>(function, nullptr, pol);
1437 
1438    T result;
1439 
1440    if(z <= 6)
1441    {
1442       expint_i_imp_113a(result, z, pol);
1443    }
1444    else if (z <= 10)
1445    {
1446       expint_i_113b(result, z);
1447    }
1448    else if(z <= 18)
1449    {
1450       expint_i_113c(result, z);
1451    }
1452    else if(z <= 26)
1453    {
1454       expint_i_113d(result, z);
1455    }
1456    else if(z <= 42)
1457    {
1458       expint_i_113e(result, z);
1459    }
1460    else if(z <= 56)
1461    {
1462       expint_i_113f(result, z);
1463    }
1464    else if(z <= 84)
1465    {
1466       expint_i_113g(result, z);
1467    }
1468    else if(z <= 210)
1469    {
1470       expint_i_113h(result, z);
1471    }
1472    else // z > 210
1473    {
1474       // Maximum Deviation Found:                     3.963e-37
1475       // Expected Error Term:                         3.963e-37
1476       // Max Error found at long double precision =   Poly: 1.248049e-36   Cheb: 2.843486e-29
1477 
1478       static const T exp40 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2.35385266837019985407899910749034804508871617254555467236651e17));
1479       static const T Y= 1.00252532958984375F;
1480       static const T P[8] = {
1481          BOOST_MATH_BIG_CONSTANT(T, 113, -0.00252532958984375000000000000000000085),
1482          BOOST_MATH_BIG_CONSTANT(T, 113, 1.16591386866059087390621952073890359),
1483          BOOST_MATH_BIG_CONSTANT(T, 113, -67.8483431314018462417456828499277579),
1484          BOOST_MATH_BIG_CONSTANT(T, 113, 1567.68688154683822956359536287575892),
1485          BOOST_MATH_BIG_CONSTANT(T, 113, -17335.4683325819116482498725687644986),
1486          BOOST_MATH_BIG_CONSTANT(T, 113, 93632.6567462673524739954389166550069),
1487          BOOST_MATH_BIG_CONSTANT(T, 113, -225025.189335919133214440347510936787),
1488          BOOST_MATH_BIG_CONSTANT(T, 113, 175864.614717440010942804684741336853)
1489       };
1490       static const T Q[9] = {
1491          BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
1492          BOOST_MATH_BIG_CONSTANT(T, 113, -65.6998869881600212224652719706425129),
1493          BOOST_MATH_BIG_CONSTANT(T, 113, 1642.73850032324014781607859416890077),
1494          BOOST_MATH_BIG_CONSTANT(T, 113, -19937.2610222467322481947237312818575),
1495          BOOST_MATH_BIG_CONSTANT(T, 113, 124136.267326632742667972126625064538),
1496          BOOST_MATH_BIG_CONSTANT(T, 113, -384614.251466704550678760562965502293),
1497          BOOST_MATH_BIG_CONSTANT(T, 113, 523355.035910385688578278384032026998),
1498          BOOST_MATH_BIG_CONSTANT(T, 113, -217809.552260834025885677791936351294),
1499          BOOST_MATH_BIG_CONSTANT(T, 113, -8555.81719551123640677261226549550872)
1500       };
1501       T t = 1 / z;
1502       result = Y + tools::evaluate_polynomial(P, t)
1503          / tools::evaluate_polynomial(Q, t);
1504       if(z < 41)
1505          result *= exp(z) / z;
1506       else
1507       {
1508          // Avoid premature overflow if we can:
1509          t = z - 40;
1510          if(t > tools::log_max_value<T>())
1511          {
1512             result = policies::raise_overflow_error<T>(function, nullptr, pol);
1513          }
1514          else
1515          {
1516             result *= exp(z - 40) / z;
1517             if(result > tools::max_value<T>() / exp40)
1518             {
1519                result = policies::raise_overflow_error<T>(function, nullptr, pol);
1520             }
1521             else
1522             {
1523                result *= exp40;
1524             }
1525          }
1526       }
1527       result += z;
1528    }
1529    return result;
1530 }
1531 
1532 template <class T, class Policy>
1533 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type
1534    expint_forwarder(T z, const Policy& /*pol*/, boost::math::true_type const&)
1535 {
1536    typedef typename tools::promote_args<T>::type result_type;
1537    typedef typename policies::evaluation<result_type, Policy>::type value_type;
1538    typedef typename policies::precision<result_type, Policy>::type precision_type;
1539    typedef typename policies::normalise<
1540       Policy,
1541       policies::promote_float<false>,
1542       policies::promote_double<false>,
1543       policies::discrete_quantile<>,
1544       policies::assert_undefined<> >::type forwarding_policy;
1545    typedef boost::math::integral_constant<int,
1546       precision_type::value <= 0 ? 0 :
1547       precision_type::value <= 53 ? 53 :
1548       precision_type::value <= 64 ? 64 :
1549       precision_type::value <= 113 ? 113 : 0
1550    > tag_type;
1551 
1552    return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expint_i_imp(static_cast<value_type>(z), forwarding_policy(), tag_type()), "boost::math::expint<%1%>(%1%)");
1553 }
1554 
1555 template <class T>
1556 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type
1557 expint_forwarder(unsigned n, T z, const boost::math::false_type&)
1558 {
1559    return boost::math::expint(n, z, policies::policy<>());
1560 }
1561 
1562 } // namespace detail
1563 
1564 template <class T, class Policy>
1565 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type
1566    expint(unsigned n, T z, const Policy& /*pol*/)
1567 {
1568    typedef typename tools::promote_args<T>::type result_type;
1569    typedef typename policies::evaluation<result_type, Policy>::type value_type;
1570    typedef typename policies::precision<result_type, Policy>::type precision_type;
1571    typedef typename policies::normalise<
1572       Policy,
1573       policies::promote_float<false>,
1574       policies::promote_double<false>,
1575       policies::discrete_quantile<>,
1576       policies::assert_undefined<> >::type forwarding_policy;
1577    typedef boost::math::integral_constant<int,
1578       precision_type::value <= 0 ? 0 :
1579       precision_type::value <= 53 ? 53 :
1580       precision_type::value <= 64 ? 64 :
1581       precision_type::value <= 113 ? 113 : 0
1582    > tag_type;
1583 
1584    return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expint_imp(
1585       n,
1586       static_cast<value_type>(z),
1587       forwarding_policy(),
1588       tag_type()), "boost::math::expint<%1%>(unsigned, %1%)");
1589 }
1590 
1591 template <class T, class U>
1592 BOOST_MATH_GPU_ENABLED inline typename detail::expint_result<T, U>::type
1593    expint(T const z, U const u)
1594 {
1595    typedef typename policies::is_policy<U>::type tag_type;
1596    return detail::expint_forwarder(z, u, tag_type());
1597 }
1598 
1599 template <class T>
1600 BOOST_MATH_GPU_ENABLED inline typename tools::promote_args<T>::type
1601    expint(T z)
1602 {
1603    return expint(z, policies::policy<>());
1604 }
1605 
1606 }} // namespaces
1607 
1608 #ifdef _MSC_VER
1609 #pragma warning(pop)
1610 #endif
1611 
1612 #endif // BOOST_MATH_EXPINT_HPP
1613 
1614
[ Source navigation ] [ Diff markup ] [ Identifier search ] [ general search ]

This page was automatically generated by the 2.3.7 LXR engine.

The LXR team
Valid CSS 2.1! Valid HTML 4.01!