FM / special_functions

/usr/include/boost/math/special_functions/

/usr/include/boost/math/special_functions

Name	Size	Mode	Actions
detail/	-	0755	rm
acosh.hpp	3693	0644	edit dl rm
airy.hpp	16270	0644	edit dl rm
asinh.hpp	3935	0644	edit dl rm
atanh.hpp	4104	0644	edit dl rm
bernoulli.hpp	5389	0644	edit dl rm
bessel.hpp	28405	0644	edit dl rm
bessel_iterators.hpp	6893	0644	edit dl rm
bessel_prime.hpp	13238	0644	edit dl rm
beta.hpp	52594	0644	edit dl rm
binomial.hpp	2508	0644	edit dl rm
cardinal_b_spline.hpp	4796	0644	edit dl rm
cbrt.hpp	5200	0644	edit dl rm
chebyshev.hpp	4760	0644	edit dl rm
chebyshev_transform.hpp	6209	0644	edit dl rm
cos_pi.hpp	2328	0644	edit dl rm
daubechies_scaling.hpp	15036	0644	edit dl rm
daubechies_wavelet.hpp	9671	0644	edit dl rm
digamma.hpp	22318	0644	edit dl rm
ellint_1.hpp	6700	0644	edit dl rm
ellint_2.hpp	6377	0644	edit dl rm
ellint_3.hpp	12048	0644	edit dl rm
ellint_d.hpp	5965	0644	edit dl rm
ellint_rc.hpp	3135	0644	edit dl rm
ellint_rd.hpp	6280	0644	edit dl rm
ellint_rf.hpp	5255	0644	edit dl rm
ellint_rg.hpp	4125	0644	edit dl rm
ellint_rj.hpp	8862	0644	edit dl rm
erf.hpp	56660	0644	edit dl rm
expint.hpp	75066	0644	edit dl rm
expm1.hpp	11335	0644	edit dl rm
factorials.hpp	8054	0644	edit dl rm
fpclassify.hpp	19871	0644	edit dl rm
gamma.hpp	70488	0644	edit dl rm
gegenbauer.hpp	2015	0644	edit dl rm
hankel.hpp	6994	0644	edit dl rm
hermite.hpp	1778	0644	edit dl rm
heuman_lambda.hpp	2891	0644	edit dl rm
hypergeometric_0F1.hpp	4283	0644	edit dl rm
hypergeometric_1F0.hpp	2383	0644	edit dl rm
hypergeometric_1F1.hpp	31854	0644	edit dl rm
hypergeometric_2F0.hpp	6127	0644	edit dl rm
hypergeometric_pFq.hpp	8518	0644	edit dl rm
hypot.hpp	2246	0644	edit dl rm
jacobi.hpp	1884	0644	edit dl rm
jacobi_elliptic.hpp	10190	0644	edit dl rm
jacobi_zeta.hpp	2273	0644	edit dl rm
laguerre.hpp	3651	0644	edit dl rm
lambert_w.hpp	95998	0644	edit dl rm
lanczos.hpp	312974	0644	edit dl rm
legendre.hpp	11275	0644	edit dl rm
legendre_stieltjes.hpp	6901	0644	edit dl rm
log1p.hpp	16271	0644	edit dl rm
math_fwd.hpp	73671	0644	edit dl rm
modf.hpp	1628	0644	edit dl rm
next.hpp	28961	0644	edit dl rm
nonfinite_num_facets.hpp	18572	0644	edit dl rm
owens_t.hpp	49887	0644	edit dl rm
polygamma.hpp	3209	0644	edit dl rm
pow.hpp	3426	0644	edit dl rm
powm1.hpp	2442	0644	edit dl rm
prime.hpp	91594	0644	edit dl rm
relative_difference.hpp	5455	0644	edit dl rm
round.hpp	4361	0644	edit dl rm
sign.hpp	5648	0644	edit dl rm
sinc.hpp	3409	0644	edit dl rm
sinhc.hpp	4643	0644	edit dl rm
sin_pi.hpp	2311	0644	edit dl rm
spherical_harmonic.hpp	6358	0644	edit dl rm
sqrt1pm1.hpp	1149	0644	edit dl rm
trigamma.hpp	21411	0644	edit dl rm
trunc.hpp	5450	0644	edit dl rm
ulp.hpp	3324	0644	edit dl rm
zeta.hpp	53776	0644	edit dl rm

Edit: /usr/include/boost/math/special_functions/expint.hpp (75066B)

//  Copyright John Maddock 2007.
//  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_EXPINT_HPP
#define BOOST_MATH_EXPINT_HPP

#ifdef _MSC_VER
#pragma once
#pragma warning(push)
#pragma warning(disable:4702) // Unreachable code (release mode only warning)
#endif

#include <boost/math/tools/precision.hpp>
#include <boost/math/tools/promotion.hpp>
#include <boost/math/tools/fraction.hpp>
#include <boost/math/tools/series.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/special_functions/digamma.hpp>
#include <boost/math/special_functions/log1p.hpp>
#include <boost/math/special_functions/pow.hpp>

#if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
//
// This is the only way we can avoid
// warning: non-standard suffix on floating constant [-Wpedantic]
// when building with -Wall -pedantic.  Neither __extension__
// nor #pragma diagnostic ignored work :(
//
#pragma GCC system_header
#endif

namespace boost{ namespace math{

template <class T, class Policy>
inline typename tools::promote_args<T>::type
   expint(unsigned n, T z, const Policy& /*pol*/);
   
namespace detail{

template <class T>
inline T expint_1_rational(const T& z, const boost::integral_constant<int, 0>&)
{
   // this function is never actually called
   BOOST_ASSERT(0);
   return z;
}

template <class T>
T expint_1_rational(const T& z, const boost::integral_constant<int, 53>&)
{
   BOOST_MATH_STD_USING
   T result;
   if(z <= 1)
   {
      // Maximum Deviation Found:                     2.006e-18
      // Expected Error Term:                         2.006e-18
      // Max error found at double precision:         2.760e-17
      static const T Y = 0.66373538970947265625F;
      static const T P[6] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.0865197248079397976498),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.0320913665303559189999),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.245088216639761496153),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0368031736257943745142),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00399167106081113256961),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.000111507792921197858394)
      };
      static const T Q[6] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.37091387659397013215),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.056770677104207528384),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.00427347600017103698101),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.000131049900798434683324),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.528611029520217142048e-6)
      };
      result = tools::evaluate_polynomial(P, z) 
         / tools::evaluate_polynomial(Q, z);
      result += z - log(z) - Y;
   }
   else if(z < -boost::math::tools::log_min_value<T>())
   {
      // Maximum Deviation Found (interpolated):      1.444e-17
      // Max error found at double precision:         3.119e-17
      static const T P[11] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.121013190657725568138e-18),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.999999999999998811143),
         BOOST_MATH_BIG_CONSTANT(T, 53, -43.3058660811817946037),
         BOOST_MATH_BIG_CONSTANT(T, 53, -724.581482791462469795),
         BOOST_MATH_BIG_CONSTANT(T, 53, -6046.8250112711035463),
         BOOST_MATH_BIG_CONSTANT(T, 53, -27182.6254466733970467),
         BOOST_MATH_BIG_CONSTANT(T, 53, -66598.2652345418633509),
         BOOST_MATH_BIG_CONSTANT(T, 53, -86273.1567711649528784),
         BOOST_MATH_BIG_CONSTANT(T, 53, -54844.4587226402067411),
         BOOST_MATH_BIG_CONSTANT(T, 53, -14751.4895786128450662),
         BOOST_MATH_BIG_CONSTANT(T, 53, -1185.45720315201027667)
      };
      static const T Q[12] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 53, 45.3058660811801465927),
         BOOST_MATH_BIG_CONSTANT(T, 53, 809.193214954550328455),
         BOOST_MATH_BIG_CONSTANT(T, 53, 7417.37624454689546708),
         BOOST_MATH_BIG_CONSTANT(T, 53, 38129.5594484818471461),
         BOOST_MATH_BIG_CONSTANT(T, 53, 113057.05869159631492),
         BOOST_MATH_BIG_CONSTANT(T, 53, 192104.047790227984431),
         BOOST_MATH_BIG_CONSTANT(T, 53, 180329.498380501819718),
         BOOST_MATH_BIG_CONSTANT(T, 53, 86722.3403467334749201),
         BOOST_MATH_BIG_CONSTANT(T, 53, 18455.4124737722049515),
         BOOST_MATH_BIG_CONSTANT(T, 53, 1229.20784182403048905),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.776491285282330997549)
      };
      T recip = 1 / z;
      result = 1 + tools::evaluate_polynomial(P, recip)
         / tools::evaluate_polynomial(Q, recip);
      result *= exp(-z) * recip;
   }
   else
   {
      result = 0;
   }
   return result;
}

template <class T>
T expint_1_rational(const T& z, const boost::integral_constant<int, 64>&)
{
   BOOST_MATH_STD_USING
   T result;
   if(z <= 1)
   {
      // Maximum Deviation Found:                     3.807e-20
      // Expected Error Term:                         3.807e-20
      // Max error found at long double precision:    6.249e-20

static const T Y = 0.66373538970947265625F;
      static const T P[6] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0865197248079397956816),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0275114007037026844633),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.246594388074877139824),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0237624819878732642231),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.00259113319641673986276),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.30853660894346057053e-4)
      };
      static const T Q[7] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.317978365797784100273),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0393622602554758722511),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.00204062029115966323229),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.732512107100088047854e-5),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.202872781770207871975e-5),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.52779248094603709945e-7)
      };
      result = tools::evaluate_polynomial(P, z) 
         / tools::evaluate_polynomial(Q, z);
      result += z - log(z) - Y;
   }
   else if(z < -boost::math::tools::log_min_value<T>())
   {
      // Maximum Deviation Found (interpolated):     2.220e-20
      // Max error found at long double precision:   1.346e-19
      static const T P[14] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.534401189080684443046e-23),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.999999999999999999905),
         BOOST_MATH_BIG_CONSTANT(T, 64, -62.1517806091379402505),
         BOOST_MATH_BIG_CONSTANT(T, 64, -1568.45688271895145277),
         BOOST_MATH_BIG_CONSTANT(T, 64, -21015.3431990874009619),
         BOOST_MATH_BIG_CONSTANT(T, 64, -164333.011755931661949),
         BOOST_MATH_BIG_CONSTANT(T, 64, -777917.270775426696103),
         BOOST_MATH_BIG_CONSTANT(T, 64, -2244188.56195255112937),
         BOOST_MATH_BIG_CONSTANT(T, 64, -3888702.98145335643429),
         BOOST_MATH_BIG_CONSTANT(T, 64, -3909822.65621952648353),
         BOOST_MATH_BIG_CONSTANT(T, 64, -2149033.9538897398457),
         BOOST_MATH_BIG_CONSTANT(T, 64, -584705.537139793925189),
         BOOST_MATH_BIG_CONSTANT(T, 64, -65815.2605361889477244),
         BOOST_MATH_BIG_CONSTANT(T, 64, -2038.82870680427258038)
      };
      static const T Q[14] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 64, 64.1517806091379399478),
         BOOST_MATH_BIG_CONSTANT(T, 64, 1690.76044393722763785),
         BOOST_MATH_BIG_CONSTANT(T, 64, 24035.9534033068949426),
         BOOST_MATH_BIG_CONSTANT(T, 64, 203679.998633572361706),
         BOOST_MATH_BIG_CONSTANT(T, 64, 1074661.58459976978285),
         BOOST_MATH_BIG_CONSTANT(T, 64, 3586552.65020899358773),
         BOOST_MATH_BIG_CONSTANT(T, 64, 7552186.84989547621411),
         BOOST_MATH_BIG_CONSTANT(T, 64, 9853333.79353054111434),
         BOOST_MATH_BIG_CONSTANT(T, 64, 7689642.74550683631258),
         BOOST_MATH_BIG_CONSTANT(T, 64, 3385553.35146759180739),
         BOOST_MATH_BIG_CONSTANT(T, 64, 763218.072732396428725),
         BOOST_MATH_BIG_CONSTANT(T, 64, 73930.2995984054930821),
         BOOST_MATH_BIG_CONSTANT(T, 64, 2063.86994219629165937)
      };
      T recip = 1 / z;
      result = 1 + tools::evaluate_polynomial(P, recip)
         / tools::evaluate_polynomial(Q, recip);
      result *= exp(-z) * recip;
   }
   else
   {
      result = 0;
   }
   return result;
}

template <class T>
T expint_1_rational(const T& z, const boost::integral_constant<int, 113>&)
{
   BOOST_MATH_STD_USING
   T result;
   if(z <= 1)
   {
      // Maximum Deviation Found:                     2.477e-35
      // Expected Error Term:                         2.477e-35
      // Max error found at long double precision:    6.810e-35

static const T Y = 0.66373538970947265625F;
      static const T P[10] = {    
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.0865197248079397956434879099175975937),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.0369066175910795772830865304506087759),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.24272036838415474665971599314725545),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.0502166331248948515282379137550178307),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.00768384138547489410285101483730424919),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.000612574337702109683505224915484717162),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.380207107950635046971492617061708534e-4),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.136528159460768830763009294683628406e-5),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.346839106212658259681029388908658618e-7),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.340500302777838063940402160594523429e-9)
      };
      static const T Q[10] = {    
         BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.426568827778942588160423015589537302),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.0841384046470893490592450881447510148),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.0100557215850668029618957359471132995),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.000799334870474627021737357294799839363),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.434452090903862735242423068552687688e-4),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.15829674748799079874182885081231252e-5),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.354406206738023762100882270033082198e-7),
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.369373328141051577845488477377890236e-9),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.274149801370933606409282434677600112e-12)
      };
      result = tools::evaluate_polynomial(P, z) 
         / tools::evaluate_polynomial(Q, z);
      result += z - log(z) - Y;
   }
   else if(z <= 4)
   {
      // Max error in interpolated form:             5.614e-35
      // Max error found at long double precision:   7.979e-35

static const T Y = 0.70190334320068359375F;

static const T P[16] = {    
         BOOST_MATH_BIG_CONSTANT(T, 113, 0.298096656795020369955077350585959794),
         BOOST_MATH_BIG_CONSTANT(T, 113, 12.9314045995266142913135497455971247),
         BOOST_MATH_BIG_CONSTANT(T, 113, 226.144334921582637462526628217345501),
         BOOST_MATH_BIG_CONSTANT(T, 113, 2070.83670924261732722117682067381405),
         BOOST_MATH_BIG_CONSTANT(T, 113, 10715.1115684330959908244769731347186),
         BOOST_MATH_BIG_CONSTANT(T, 113, 30728.7876355542048019664777316053311),
         BOOST_MATH_BIG_CONSTANT(T, 113, 38520.6078609349855436936232610875297),
         BOOST_MATH_BIG_CONSTANT(T, 113, -27606.0780981527583168728339620565165),
         BOOST_MATH_BIG_CONSTANT(T, 113, -169026.485055785605958655247592604835),
         BOOST_MATH_BIG_CONSTANT(T, 113, -254361.919204983608659069868035092282),
         BOOST_MATH_BIG_CONSTANT(T, 113, -195765.706874132267953259272028679935),
         BOOST_MATH_BIG_CONSTANT(T, 113, -83352.6826013533205474990119962408675),
         BOOST_MATH_BIG_CONSTANT(T, 113, -19251.6828496869586415162597993050194),
         BOOST_MATH_BIG_CONSTANT(T, 113, -2226.64251774578542836725386936102339),
         BOOST_MATH_BIG_CONSTANT(T, 113, -109.009437301400845902228611986479816),
         BOOST_MATH_BIG_CONSTANT(T, 113, -1.51492042209561411434644938098833499)
      };
      static const T Q[16] = {    
         BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 113, 46.734521442032505570517810766704587),
         BOOST_MATH_BIG_CONSTANT(T, 113, 908.694714348462269000247450058595655),
         BOOST_MATH_BIG_CONSTANT(T, 113, 9701.76053033673927362784882748513195),
         BOOST_MATH_BIG_CONSTANT(T, 113, 63254.2815292641314236625196594947774),
         BOOST_MATH_BIG_CONSTANT(T, 113, 265115.641285880437335106541757711092),
         BOOST_MATH_BIG_CONSTANT(T, 113, 732707.841188071900498536533086567735),
         BOOST_MATH_BIG_CONSTANT(T, 113, 1348514.02492635723327306628712057794),
         BOOST_MATH_BIG_CONSTANT(T, 113, 1649986.81455283047769673308781585991),
         BOOST_MATH_BIG_CONSTANT(T, 113, 1326000.828522976970116271208812099),
         BOOST_MATH_BIG_CONSTANT(T, 113, 683643.09490612171772350481773951341),
         BOOST_MATH_BIG_CONSTANT(T, 113, 217640.505137263607952365685653352229),
         BOOST_MATH_BIG_CONSTANT(T, 113, 40288.3467237411710881822569476155485),
         BOOST_MATH_BIG_CONSTANT(T, 113, 3932.89353979531632559232883283175754),
         BOOST_MATH_BIG_CONSTANT(T, 113, 169.845369689596739824177412096477219),
         BOOST_MATH_BIG_CONSTANT(T, 113, 2.17607292280092201170768401876895354)
      };
      T recip = 1 / z;
      result = Y + tools::evaluate_polynomial(P, recip)
         / tools::evaluate_polynomial(Q, recip);
      result *= exp(-z) * recip;
   }
   else if(z < -boost::math::tools::log_min_value<T>())
   {
      // Max error in interpolated form:             4.413e-35
      // Max error found at long double precision:   8.928e-35

static const T P[19] = {    
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.559148411832951463689610809550083986e-40),
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.999999999999999999999999999999999997),
         BOOST_MATH_BIG_CONSTANT(T, 113, -166.542326331163836642960118190147367),
         BOOST_MATH_BIG_CONSTANT(T, 113, -12204.639128796330005065904675153652),
         BOOST_MATH_BIG_CONSTANT(T, 113, -520807.069767086071806275022036146855),
         BOOST_MATH_BIG_CONSTANT(T, 113, -14435981.5242137970691490903863125326),
         BOOST_MATH_BIG_CONSTANT(T, 113, -274574945.737064301247496460758654196),
         BOOST_MATH_BIG_CONSTANT(T, 113, -3691611582.99810039356254671781473079),
         BOOST_MATH_BIG_CONSTANT(T, 113, -35622515944.8255047299363690814678763),
         BOOST_MATH_BIG_CONSTANT(T, 113, -248040014774.502043161750715548451142),
         BOOST_MATH_BIG_CONSTANT(T, 113, -1243190389769.53458416330946622607913),
         BOOST_MATH_BIG_CONSTANT(T, 113, -4441730126135.54739052731990368425339),
         BOOST_MATH_BIG_CONSTANT(T, 113, -11117043181899.7388524310281751971366),
         BOOST_MATH_BIG_CONSTANT(T, 113, -18976497615396.9717776601813519498961),
         BOOST_MATH_BIG_CONSTANT(T, 113, -21237496819711.1011661104761906067131),
         BOOST_MATH_BIG_CONSTANT(T, 113, -14695899122092.5161620333466757812848),
         BOOST_MATH_BIG_CONSTANT(T, 113, -5737221535080.30569711574295785864903),
         BOOST_MATH_BIG_CONSTANT(T, 113, -1077042281708.42654526404581272546244),
         BOOST_MATH_BIG_CONSTANT(T, 113, -68028222642.1941480871395695677675137)
      };
      static const T Q[20] = {    
         BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 113, 168.542326331163836642960118190147311),
         BOOST_MATH_BIG_CONSTANT(T, 113, 12535.7237814586576783518249115343619),
         BOOST_MATH_BIG_CONSTANT(T, 113, 544891.263372016404143120911148640627),
         BOOST_MATH_BIG_CONSTANT(T, 113, 15454474.7241010258634446523045237762),
         BOOST_MATH_BIG_CONSTANT(T, 113, 302495899.896629522673410325891717381),
         BOOST_MATH_BIG_CONSTANT(T, 113, 4215565948.38886507646911672693270307),
         BOOST_MATH_BIG_CONSTANT(T, 113, 42552409471.7951815668506556705733344),
         BOOST_MATH_BIG_CONSTANT(T, 113, 313592377066.753173979584098301610186),
         BOOST_MATH_BIG_CONSTANT(T, 113, 1688763640223.4541980740597514904542),
         BOOST_MATH_BIG_CONSTANT(T, 113, 6610992294901.59589748057620192145704),
         BOOST_MATH_BIG_CONSTANT(T, 113, 18601637235659.6059890851321772682606),
         BOOST_MATH_BIG_CONSTANT(T, 113, 36944278231087.2571020964163402941583),
         BOOST_MATH_BIG_CONSTANT(T, 113, 50425858518481.7497071917028793820058),
         BOOST_MATH_BIG_CONSTANT(T, 113, 45508060902865.0899967797848815980644),
         BOOST_MATH_BIG_CONSTANT(T, 113, 25649955002765.3817331501988304758142),
         BOOST_MATH_BIG_CONSTANT(T, 113, 8259575619094.6518520988612711292331),
         BOOST_MATH_BIG_CONSTANT(T, 113, 1299981487496.12607474362723586264515),
         BOOST_MATH_BIG_CONSTANT(T, 113, 70242279152.8241187845178443118302693),
         BOOST_MATH_BIG_CONSTANT(T, 113, -37633302.9409263839042721539363416685)
      };
      T recip = 1 / z;
      result = 1 + tools::evaluate_polynomial(P, recip)
         / tools::evaluate_polynomial(Q, recip);
      result *= exp(-z) * recip;
   }
   else
   {
      result = 0;
   }
   return result;
}

template <class T>
struct expint_fraction
{
   typedef std::pair<T,T> result_type;
   expint_fraction(unsigned n_, T z_) : b(n_ + z_), i(-1), n(n_){}
   std::pair<T,T> operator()()
   {
      std::pair<T,T> result = std::make_pair(-static_cast<T>((i+1) * (n+i)), b);
      b += 2;
      ++i;
      return result;
   }
private:
   T b;
   int i;
   unsigned n;
};

template <class T, class Policy>
inline T expint_as_fraction(unsigned n, T z, const Policy& pol)
{
   BOOST_MATH_STD_USING
   BOOST_MATH_INSTRUMENT_VARIABLE(z)
   boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
   expint_fraction<T> f(n, z);
   T result = tools::continued_fraction_b(
      f, 
      boost::math::policies::get_epsilon<T, Policy>(),
      max_iter);
   policies::check_series_iterations<T>("boost::math::expint_continued_fraction<%1%>(unsigned,%1%)", max_iter, pol);
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   BOOST_MATH_INSTRUMENT_VARIABLE(max_iter)
   result = exp(-z) / result;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   return result;
}

template <class T>
struct expint_series
{
   typedef T result_type;
   expint_series(unsigned k_, T z_, T x_k_, T denom_, T fact_) 
      : k(k_), z(z_), x_k(x_k_), denom(denom_), fact(fact_){}
   T operator()()
   {
      x_k *= -z;
      denom += 1;
      fact *= ++k;
      return x_k / (denom * fact);
   }
private:
   unsigned k;
   T z;
   T x_k;
   T denom;
   T fact;
};

template <class T, class Policy>
inline T expint_as_series(unsigned n, T z, const Policy& pol)
{
   BOOST_MATH_STD_USING
   boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();

BOOST_MATH_INSTRUMENT_VARIABLE(z)

T result = 0;
   T x_k = -1;
   T denom = T(1) - n;
   T fact = 1;
   unsigned k = 0;
   for(; k < n - 1;)
   {
      result += x_k / (denom * fact);
      denom += 1;
      x_k *= -z;
      fact *= ++k;
   }
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result += pow(-z, static_cast<T>(n - 1)) 
      * (boost::math::digamma(static_cast<T>(n)) - log(z)) / fact;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)

expint_series<T> s(k, z, x_k, denom, fact);
   result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, result);
   policies::check_series_iterations<T>("boost::math::expint_series<%1%>(unsigned,%1%)", max_iter, pol);
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   BOOST_MATH_INSTRUMENT_VARIABLE(max_iter)
   return result;
}

template <class T, class Policy, class Tag>
T expint_imp(unsigned n, T z, const Policy& pol, const Tag& tag)
{
   BOOST_MATH_STD_USING
   static const char* function = "boost::math::expint<%1%>(unsigned, %1%)";
   if(z < 0)
      return policies::raise_domain_error<T>(function, "Function requires z >= 0 but got %1%.", z, pol);
   if(z == 0)
      return n == 1 ? policies::raise_overflow_error<T>(function, 0, pol) : T(1 / (static_cast<T>(n - 1)));

T result;

bool f;
   if(n < 3)
   {
      f = z < 0.5;
   }
   else
   {
      f = z < (static_cast<T>(n - 2) / static_cast<T>(n - 1));
   }
#ifdef BOOST_MSVC
#  pragma warning(push)
#  pragma warning(disable:4127) // conditional expression is constant
#endif
   if(n == 0)
      result = exp(-z) / z;
   else if((n == 1) && (Tag::value))
   {
      result = expint_1_rational(z, tag);
   }
   else if(f)
      result = expint_as_series(n, z, pol);
   else
      result = expint_as_fraction(n, z, pol);
#ifdef BOOST_MSVC
#  pragma warning(pop)
#endif

return result;
}

template <class T>
struct expint_i_series
{
   typedef T result_type;
   expint_i_series(T z_) : k(0), z_k(1), z(z_){}
   T operator()()
   {
      z_k *= z / ++k;
      return z_k / k;
   }
private:
   unsigned k;
   T z_k;
   T z;
};

template <class T, class Policy>
T expint_i_as_series(T z, const Policy& pol)
{
   BOOST_MATH_STD_USING
   T result = log(z); // (log(z) - log(1 / z)) / 2;
   result += constants::euler<T>();
   expint_i_series<T> s(z);
   boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
   result = tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, result);
   policies::check_series_iterations<T>("boost::math::expint_i_series<%1%>(%1%)", max_iter, pol);
   return result;
}

template <class T, class Policy, class Tag>
T expint_i_imp(T z, const Policy& pol, const Tag& tag)
{
   static const char* function = "boost::math::expint<%1%>(%1%)";
   if(z < 0)
      return -expint_imp(1, T(-z), pol, tag);
   if(z == 0)
      return -policies::raise_overflow_error<T>(function, 0, pol);
   return expint_i_as_series(z, pol);
}

template <class T, class Policy>
T expint_i_imp(T z, const Policy& pol, const boost::integral_constant<int, 53>& tag)
{
   BOOST_MATH_STD_USING
   static const char* function = "boost::math::expint<%1%>(%1%)";
   if(z < 0)
      return -expint_imp(1, T(-z), pol, tag);
   if(z == 0)
      return -policies::raise_overflow_error<T>(function, 0, pol);

T result;

if(z <= 6)
   {
      // Maximum Deviation Found:                     2.852e-18
      // Expected Error Term:                         2.852e-18
      // Max Error found at double precision =        Poly: 2.636335e-16   Cheb: 4.187027e-16
      static const T P[10] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 2.98677224343598593013),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.356343618769377415068),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.780836076283730801839),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.114670926327032002811),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.0499434773576515260534),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.00726224593341228159561),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.00115478237227804306827),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.000116419523609765200999),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.798296365679269702435e-5),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.2777056254402008721e-6)
      };
      static const T Q[8] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 53, -1.17090412365413911947),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.62215109846016746276),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.195114782069495403315),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.0391523431392967238166),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00504800158663705747345),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.000389034007436065401822),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.138972589601781706598e-4)
      };

static const T c1 = BOOST_MATH_BIG_CONSTANT(T, 53, 1677624236387711.0);
      static const T c2 = BOOST_MATH_BIG_CONSTANT(T, 53, 4503599627370496.0);
      static const T r1 = static_cast<T>(c1 / c2);
      static const T r2 = BOOST_MATH_BIG_CONSTANT(T, 53, 0.131401834143860282009280387409357165515556574352422001206362e-16);
      static const T r = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 53, 0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392));
      T t = (z / 3) - 1;
      result = tools::evaluate_polynomial(P, t) 
         / tools::evaluate_polynomial(Q, t);
      t = (z - r1) - r2;
      result *= t;
      if(fabs(t) < 0.1)
      {
         result += boost::math::log1p(t / r, pol);
      }
      else
      {
         result += log(z / r);
      }
   }
   else if (z <= 10)
   {
      // Maximum Deviation Found:                     6.546e-17
      // Expected Error Term:                         6.546e-17
      // Max Error found at double precision =        Poly: 6.890169e-17   Cheb: 6.772128e-17
      static const T Y = 1.158985137939453125F;
      static const T P[8] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.00139324086199402804173),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0349921221823888744966),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0264095520754134848538),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00761224003005476438412),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00247496209592143627977),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.000374885917942100256775),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.554086272024881826253e-4),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.396487648924804510056e-5)
      };
      static const T Q[8] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.744625566823272107711),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.329061095011767059236),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.100128624977313872323),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.0223851099128506347278),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.00365334190742316650106),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.000402453408512476836472),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.263649630720255691787e-4)
      };
      T t = z / 2 - 4;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      result *= exp(z) / z;
      result += z;
   }
   else if(z <= 20)
   {
      // Maximum Deviation Found:                     1.843e-17
      // Expected Error Term:                         -1.842e-17
      // Max Error found at double precision =        Poly: 4.375868e-17   Cheb: 5.860967e-17

static const T Y = 1.0869731903076171875F;
      static const T P[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00893891094356945667451),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0484607730127134045806),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0652810444222236895772),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0478447572647309671455),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0226059218923777094596),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00720603636917482065907),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00155941947035972031334),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.000209750022660200888349),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.138652200349182596186e-4)
      };
      static const T Q[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.97017214039061194971),
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.86232465043073157508),
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.09601437090337519977),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.438873285773088870812),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.122537731979686102756),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.0233458478275769288159),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.00278170769163303669021),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.000159150281166108755531)
      };
      T t = z / 5 - 3;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      result *= exp(z) / z;
      result += z;
   }
   else if(z <= 40)
   {
      // Maximum Deviation Found:                     5.102e-18
      // Expected Error Term:                         5.101e-18
      // Max Error found at double precision =        Poly: 1.441088e-16   Cheb: 1.864792e-16

static const T Y = 1.03937530517578125F;
      static const T P[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00356165148914447597995),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0229930320357982333406),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0449814350482277917716),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0453759383048193402336),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0272050837209380717069),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00994403059883350813295),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.00207592267812291726961),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.000192178045857733706044),
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.113161784705911400295e-9)
      };
      static const T Q[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 53, 2.84354408840148561131),
         BOOST_MATH_BIG_CONSTANT(T, 53, 3.6599610090072393012),
         BOOST_MATH_BIG_CONSTANT(T, 53, 2.75088464344293083595),
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.2985244073998398643),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.383213198510794507409),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.0651165455496281337831),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.00488071077519227853585)
      };
      T t = z / 10 - 3;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      result *= exp(z) / z;
      result += z;
   }
   else
   {
      // Max Error found at double precision =        3.381886e-17
      static const T exp40 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 53, 2.35385266837019985407899910749034804508871617254555467236651e17));
      static const T Y= 1.013065338134765625F;
      static const T P[6] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, -0.0130653381347656243849),
         BOOST_MATH_BIG_CONSTANT(T, 53, 0.19029710559486576682),
         BOOST_MATH_BIG_CONSTANT(T, 53, 94.7365094537197236011),
         BOOST_MATH_BIG_CONSTANT(T, 53, -2516.35323679844256203),
         BOOST_MATH_BIG_CONSTANT(T, 53, 18932.0850014925993025),
         BOOST_MATH_BIG_CONSTANT(T, 53, -38703.1431362056714134)
      };
      static const T Q[7] = {    
         BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 53, 61.9733592849439884145),
         BOOST_MATH_BIG_CONSTANT(T, 53, -2354.56211323420194283),
         BOOST_MATH_BIG_CONSTANT(T, 53, 22329.1459489893079041),
         BOOST_MATH_BIG_CONSTANT(T, 53, -70126.245140396567133),
         BOOST_MATH_BIG_CONSTANT(T, 53, 54738.2833147775537106),
         BOOST_MATH_BIG_CONSTANT(T, 53, 8297.16296356518409347)
      };
      T t = 1 / z;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      if(z < 41)
         result *= exp(z) / z;
      else
      {
         // Avoid premature overflow if we can:
         t = z - 40;
         if(t > tools::log_max_value<T>())
         {
            result = policies::raise_overflow_error<T>(function, 0, pol);
         }
         else
         {
            result *= exp(z - 40) / z;
            if(result > tools::max_value<T>() / exp40)
            {
               result = policies::raise_overflow_error<T>(function, 0, pol);
            }
            else
            {
               result *= exp40;
            }
         }
      }
      result += z;
   }
   return result;
}

template <class T, class Policy>
T expint_i_imp(T z, const Policy& pol, const boost::integral_constant<int, 64>& tag)
{
   BOOST_MATH_STD_USING
   static const char* function = "boost::math::expint<%1%>(%1%)";
   if(z < 0)
      return -expint_imp(1, T(-z), pol, tag);
   if(z == 0)
      return -policies::raise_overflow_error<T>(function, 0, pol);

T result;

if(z <= 6)
   {
      // Maximum Deviation Found:                     3.883e-21
      // Expected Error Term:                         3.883e-21
      // Max Error found at long double precision =   Poly: 3.344801e-19   Cheb: 4.989937e-19

static const T P[11] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 2.98677224343598593764),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.25891613550886736592),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.789323584998672832285),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.092432587824602399339),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0514236978728625906656),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.00658477469745132977921),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.00124914538197086254233),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.000131429679565472408551),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.11293331317982763165e-4),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.629499283139417444244e-6),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.177833045143692498221e-7)
      };
      static const T Q[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 64, -1.20352377969742325748),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.66707904942606479811),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.223014531629140771914),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0493340022262908008636),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.00741934273050807310677),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.00074353567782087939294),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.455861727069603367656e-4),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.131515429329812837701e-5)
      };

static const T c1 = BOOST_MATH_BIG_CONSTANT(T, 64, 1677624236387711.0);
      static const T c2 = BOOST_MATH_BIG_CONSTANT(T, 64, 4503599627370496.0);
      static const T r1 = c1 / c2;
      static const T r2 = BOOST_MATH_BIG_CONSTANT(T, 64, 0.131401834143860282009280387409357165515556574352422001206362e-16);
      static const T r = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392));
      T t = (z / 3) - 1;
      result = tools::evaluate_polynomial(P, t) 
         / tools::evaluate_polynomial(Q, t);
      t = (z - r1) - r2;
      result *= t;
      if(fabs(t) < 0.1)
      {
         result += boost::math::log1p(t / r, pol);
      }
      else
      {
         result += log(z / r);
      }
   }
   else if (z <= 10)
   {
      // Maximum Deviation Found:                     2.622e-21
      // Expected Error Term:                         -2.622e-21
      // Max Error found at long double precision =   Poly: 1.208328e-20   Cheb: 1.073723e-20

static const T Y = 1.158985137939453125F;
      static const T P[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.00139324086199409049399),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0345238388952337563247),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0382065278072592940767),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0156117003070560727392),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.00383276012430495387102),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.000697070540945496497992),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.877310384591205930343e-4),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.623067256376494930067e-5),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.377246883283337141444e-6)
      };
      static const T Q[10] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.08073635708902053767),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.553681133533942532909),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.176763647137553797451),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0387891748253869928121),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0060603004848394727017),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.000670519492939992806051),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.4947357050100855646e-4),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.204339282037446434827e-5),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.146951181174930425744e-7)
      };
      T t = z / 2 - 4;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      result *= exp(z) / z;
      result += z;
   }
   else if(z <= 20)
   {
      // Maximum Deviation Found:                     3.220e-20
      // Expected Error Term:                         3.220e-20
      // Max Error found at long double precision =   Poly: 7.696841e-20   Cheb: 6.205163e-20

static const T Y = 1.0869731903076171875F;
      static const T P[10] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.00893891094356946995368),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0487562980088748775943),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0670568657950041926085),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0509577352851442932713),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.02551800927409034206),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.00892913759760086687083),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.00224469630207344379888),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.000392477245911296982776),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.44424044184395578775e-4),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.252788029251437017959e-5)
      };
      static const T Q[10] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 64, 2.00323265503572414261),
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.94688958187256383178),
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.19733638134417472296),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.513137726038353385661),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.159135395578007264547),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0358233587351620919881),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0056716655597009417875),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.000577048986213535829925),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.290976943033493216793e-4)
      };
      T t = z / 5 - 3;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      result *= exp(z) / z;
      result += z;
   }
   else if(z <= 40)
   {
      // Maximum Deviation Found:                     2.940e-21
      // Expected Error Term:                         -2.938e-21
      // Max Error found at long double precision =   Poly: 3.419893e-19   Cheb: 3.359874e-19

static const T Y = 1.03937530517578125F;
      static const T P[12] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.00356165148914447278177),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0240235006148610849678),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0516699967278057976119),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0586603078706856245674),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0409960120868776180825),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0185485073689590665153),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.00537842101034123222417),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.000920988084778273760609),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.716742618812210980263e-4),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.504623302166487346677e-9),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.712662196671896837736e-10),
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.533769629702262072175e-11)
      };
      static const T Q[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 64, 3.13286733695729715455),
         BOOST_MATH_BIG_CONSTANT(T, 64, 4.49281223045653491929),
         BOOST_MATH_BIG_CONSTANT(T, 64, 3.84900294427622911374),
         BOOST_MATH_BIG_CONSTANT(T, 64, 2.15205199043580378211),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.802912186540269232424),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.194793170017818925388),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.0280128013584653182994),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.00182034930799902922549)
      };
      T t = z / 10 - 3;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      BOOST_MATH_INSTRUMENT_VARIABLE(result)
      result *= exp(z) / z;
      BOOST_MATH_INSTRUMENT_VARIABLE(result)
      result += z;
      BOOST_MATH_INSTRUMENT_VARIABLE(result)
   }
   else
   {
      // Maximum Deviation Found:                     3.536e-20
      // Max Error found at long double precision =   Poly: 1.310671e-19   Cheb: 8.630943e-11

static const T exp40 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.35385266837019985407899910749034804508871617254555467236651e17));
      static const T Y= 1.013065338134765625F;
      static const T P[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, -0.0130653381347656250004),
         BOOST_MATH_BIG_CONSTANT(T, 64, 0.644487780349757303739),
         BOOST_MATH_BIG_CONSTANT(T, 64, 143.995670348227433964),
         BOOST_MATH_BIG_CONSTANT(T, 64, -13918.9322758014173709),
         BOOST_MATH_BIG_CONSTANT(T, 64, 476260.975133624194484),
         BOOST_MATH_BIG_CONSTANT(T, 64, -7437102.15135982802122),
         BOOST_MATH_BIG_CONSTANT(T, 64, 53732298.8764767916542),
         BOOST_MATH_BIG_CONSTANT(T, 64, -160695051.957997452509),
         BOOST_MATH_BIG_CONSTANT(T, 64, 137839271.592778020028)
      };
      static const T Q[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 64, 27.2103343964943718802),
         BOOST_MATH_BIG_CONSTANT(T, 64, -8785.48528692879413676),
         BOOST_MATH_BIG_CONSTANT(T, 64, 397530.290000322626766),
         BOOST_MATH_BIG_CONSTANT(T, 64, -7356441.34957799368252),
         BOOST_MATH_BIG_CONSTANT(T, 64, 63050914.5343400957524),
         BOOST_MATH_BIG_CONSTANT(T, 64, -246143779.638307701369),
         BOOST_MATH_BIG_CONSTANT(T, 64, 384647824.678554961174),
         BOOST_MATH_BIG_CONSTANT(T, 64, -166288297.874583961493)
      };
      T t = 1 / z;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      if(z < 41)
         result *= exp(z) / z;
      else
      {
         // Avoid premature overflow if we can:
         t = z - 40;
         if(t > tools::log_max_value<T>())
         {
            result = policies::raise_overflow_error<T>(function, 0, pol);
         }
         else
         {
            result *= exp(z - 40) / z;
            if(result > tools::max_value<T>() / exp40)
            {
               result = policies::raise_overflow_error<T>(function, 0, pol);
            }
            else
            {
               result *= exp40;
            }
         }
      }
      result += z;
   }
   return result;
}

template <class T, class Policy>
void expint_i_imp_113a(T& result, const T& z, const Policy& pol)
{
   BOOST_MATH_STD_USING
   // Maximum Deviation Found:                     1.230e-36
   // Expected Error Term:                         -1.230e-36
   // Max Error found at long double precision =   Poly: 4.355299e-34   Cheb: 7.512581e-34

static const T P[15] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 2.98677224343598593765287235997328555),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.333256034674702967028780537349334037),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.851831522798101228384971644036708463),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0657854833494646206186773614110374948),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0630065662557284456000060708977935073),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00311759191425309373327784154659649232),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.00176213568201493949664478471656026771),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.491548660404172089488535218163952295e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.207764227621061706075562107748176592e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.225445398156913584846374273379402765e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.996939977231410319761273881672601592e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.212546902052178643330520878928100847e-9),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.154646053060262871360159325115980023e-9),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.143971277122049197323415503594302307e-11),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.306243138978114692252817805327426657e-13)
   };
   static const T Q[15] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 113, -1.40178870313943798705491944989231793),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.943810968269701047641218856758605284),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.405026631534345064600850391026113165),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.123924153524614086482627660399122762),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0286364505373369439591132549624317707),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.00516148845910606985396596845494015963),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000738330799456364820380739850924783649),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.843737760991856114061953265870882637e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.767957673431982543213661388914587589e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.549136847313854595809952100614840031e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.299801381513743676764008325949325404e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.118419479055346106118129130945423483e-8),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.30372295663095470359211949045344607e-10),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.382742953753485333207877784720070523e-12)
   };

static const T c1 = BOOST_MATH_BIG_CONSTANT(T, 113, 1677624236387711.0);
   static const T c2 = BOOST_MATH_BIG_CONSTANT(T, 113, 4503599627370496.0);
   static const T c3 = BOOST_MATH_BIG_CONSTANT(T, 113, 266514582277687.0);
   static const T c4 = BOOST_MATH_BIG_CONSTANT(T, 113, 4503599627370496.0);
   static const T c5 = BOOST_MATH_BIG_CONSTANT(T, 113, 4503599627370496.0);
   static const T r1 = c1 / c2;
   static const T r2 = c3 / c4 / c5;
   static const T r3 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.283806480836357377069325311780969887585024578164571984232357e-31));
   static const T r = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392));
   T t = (z / 3) - 1;
   result = tools::evaluate_polynomial(P, t) 
      / tools::evaluate_polynomial(Q, t);
   t = ((z - r1) - r2) - r3;
   result *= t;
   if(fabs(t) < 0.1)
   {
      result += boost::math::log1p(t / r, pol);
   }
   else
   {
      result += log(z / r);
   }
}

template <class T>
void expint_i_113b(T& result, const T& z)
{
   BOOST_MATH_STD_USING
   // Maximum Deviation Found:                     7.779e-36
   // Expected Error Term:                         -7.779e-36
   // Max Error found at long double precision =   Poly: 2.576723e-35   Cheb: 1.236001e-34

static const T Y = 1.158985137939453125F;
   static const T P[15] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.00139324086199409049282472239613554817),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0338173111691991289178779840307998955),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0555972290794371306259684845277620556),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0378677976003456171563136909186202177),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0152221583517528358782902783914356667),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00428283334203873035104248217403126905),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000922782631491644846511553601323435286),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000155513428088853161562660696055496696),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.205756580255359882813545261519317096e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.220327406578552089820753181821115181e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.189483157545587592043421445645377439e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.122426571518570587750898968123803867e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.635187358949437991465353268374523944e-9),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.203015132965870311935118337194860863e-10),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.384276705503357655108096065452950822e-12)
   };
   static const T Q[15] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.58784732785354597996617046880946257),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.18550755302279446339364262338114098),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.55598993549661368604527040349702836),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.184290888380564236919107835030984453),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0459658051803613282360464632326866113),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0089505064268613225167835599456014705),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.00139042673882987693424772855926289077),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.000174210708041584097450805790176479012),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.176324034009707558089086875136647376e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.142935845999505649273084545313710581e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.907502324487057260675816233312747784e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.431044337808893270797934621235918418e-8),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.139007266881450521776529705677086902e-9),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.234715286125516430792452741830364672e-11)
   };
   T t = z / 2 - 4;
   result = Y + tools::evaluate_polynomial(P, t)
      / tools::evaluate_polynomial(Q, t);
   result *= exp(z) / z;
   result += z;
}

template <class T>
void expint_i_113c(T& result, const T& z)
{
   BOOST_MATH_STD_USING
   // Maximum Deviation Found:                     1.082e-34
   // Expected Error Term:                         1.080e-34
   // Max Error found at long double precision =   Poly: 1.958294e-34   Cheb: 2.472261e-34

static const T Y = 1.091579437255859375F;
   static const T P[17] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00685089599550151282724924894258520532),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0443313550253580053324487059748497467),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.071538561252424027443296958795814874),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0622923153354102682285444067843300583),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0361631270264607478205393775461208794),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0153192826839624850298106509601033261),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00496967904961260031539602977748408242),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00126989079663425780800919171538920589),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000258933143097125199914724875206326698),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.422110326689204794443002330541441956e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.546004547590412661451073996127115221e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.546775260262202177131068692199272241e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.404157632825805803833379568956559215e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.200612596196561323832327013027419284e-8),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.502538501472133913417609379765434153e-10),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.326283053716799774936661568391296584e-13),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.869226483473172853557775877908693647e-15)
   };
   static const T Q[15] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 113, 2.23227220874479061894038229141871087),
      BOOST_MATH_BIG_CONSTANT(T, 113, 2.40221000361027971895657505660959863),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.65476320985936174728238416007084214),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.816828602963895720369875535001248227),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.306337922909446903672123418670921066),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0902400121654409267774593230720600752),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0212708882169429206498765100993228086),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.00404442626252467471957713495828165491),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0006195601618842253612635241404054589),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.755930932686543009521454653994321843e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.716004532773778954193609582677482803e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.500881663076471627699290821742924233e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.233593219218823384508105943657387644e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.554900353169148897444104962034267682e-9)
   };
   T t = z / 4 - 3.5;
   result = Y + tools::evaluate_polynomial(P, t)
      / tools::evaluate_polynomial(Q, t);
   result *= exp(z) / z;
   result += z;
}

template <class T>
void expint_i_113d(T& result, const T& z)
{
   BOOST_MATH_STD_USING
   // Maximum Deviation Found:                     3.163e-35
   // Expected Error Term:                         3.163e-35
   // Max Error found at long double precision =   Poly: 4.158110e-35   Cheb: 5.385532e-35

static const T Y = 1.051731109619140625F;
   static const T P[14] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00144552494420652573815404828020593565),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0126747451594545338365684731262912741),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.01757394877502366717526779263438073),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0126838952395506921945756139424722588),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0060045057928894974954756789352443522),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00205349237147226126653803455793107903),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000532606040579654887676082220195624207),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000107344687098019891474772069139014662),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.169536802705805811859089949943435152e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.20863311729206543881826553010120078e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.195670358542116256713560296776654385e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.133291168587253145439184028259772437e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.595500337089495614285777067722823397e-9),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.133141358866324100955927979606981328e-10)
   };
   static const T Q[14] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.72490783907582654629537013560044682),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.44524329516800613088375685659759765),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.778241785539308257585068744978050181),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.300520486589206605184097270225725584),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0879346899691339661394537806057953957),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0200802415843802892793583043470125006),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.00362842049172586254520256100538273214),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.000519731362862955132062751246769469957),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.584092147914050999895178697392282665e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.501851497707855358002773398333542337e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.313085677467921096644895738538865537e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.127552010539733113371132321521204458e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.25737310826983451144405899970774587e-9)
   };
   T t = z / 4 - 5.5;
   result = Y + tools::evaluate_polynomial(P, t)
      / tools::evaluate_polynomial(Q, t);
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result *= exp(z) / z;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result += z;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
}

template <class T>
void expint_i_113e(T& result, const T& z)
{
   BOOST_MATH_STD_USING
   // Maximum Deviation Found:                     7.972e-36
   // Expected Error Term:                         7.962e-36
   // Max Error found at long double precision =   Poly: 1.711721e-34   Cheb: 3.100018e-34

static const T Y = 1.032726287841796875F;
   static const T P[15] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00141056919297307534690895009969373233),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0123384175302540291339020257071411437),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0298127270706864057791526083667396115),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0390686759471630584626293670260768098),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0338226792912607409822059922949035589),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0211659736179834946452561197559654582),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0100428887460879377373158821400070313),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00370717396015165148484022792801682932),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0010768667551001624764329000496561659),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000246127328761027039347584096573123531),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.437318110527818613580613051861991198e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.587532682329299591501065482317771497e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.565697065670893984610852937110819467e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.350233957364028523971768887437839573e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.105428907085424234504608142258423505e-8)
   };
   static const T Q[16] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 113, 3.17261315255467581204685605414005525),
      BOOST_MATH_BIG_CONSTANT(T, 113, 4.85267952971640525245338392887217426),
      BOOST_MATH_BIG_CONSTANT(T, 113, 4.74341914912439861451492872946725151),
      BOOST_MATH_BIG_CONSTANT(T, 113, 3.31108463283559911602405970817931801),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.74657006336994649386607925179848899),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.718255607416072737965933040353653244),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.234037553177354542791975767960643864),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0607470145906491602476833515412605389),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0125048143774226921434854172947548724),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.00201034366420433762935768458656609163),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.000244823338417452367656368849303165721),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.213511655166983177960471085462540807e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.119323998465870686327170541547982932e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.322153582559488797803027773591727565e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.161635525318683508633792845159942312e-16)
   };
   T t = z / 8 - 4.25;
   result = Y + tools::evaluate_polynomial(P, t)
      / tools::evaluate_polynomial(Q, t);
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result *= exp(z) / z;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result += z;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
}

template <class T>
void expint_i_113f(T& result, const T& z)
{
   BOOST_MATH_STD_USING
   // Maximum Deviation Found:                     4.469e-36
   // Expected Error Term:                         4.468e-36
   // Max Error found at long double precision =   Poly: 1.288958e-35   Cheb: 2.304586e-35

static const T Y = 1.0216197967529296875F;
   static const T P[12] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000322999116096627043476023926572650045),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00385606067447365187909164609294113346),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00686514524727568176735949971985244415),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00606260649593050194602676772589601799),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00334382362017147544335054575436194357),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00126108534260253075708625583630318043),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000337881489347846058951220431209276776),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.648480902304640018785370650254018022e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.87652644082970492211455290209092766e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.794712243338068631557849449519994144e-6),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.434084023639508143975983454830954835e-7),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.107839681938752337160494412638656696e-8)
   };
   static const T Q[12] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 113, 2.09913805456661084097134805151524958),
      BOOST_MATH_BIG_CONSTANT(T, 113, 2.07041755535439919593503171320431849),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.26406517226052371320416108604874734),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.529689923703770353961553223973435569),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.159578150879536711042269658656115746),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0351720877642000691155202082629857131),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.00565313621289648752407123620997063122),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.000646920278540515480093843570291218295),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.499904084850091676776993523323213591e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.233740058688179614344680531486267142e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.498800627828842754845418576305379469e-7)
   };
   T t = z / 7 - 7;
   result = Y + tools::evaluate_polynomial(P, t)
      / tools::evaluate_polynomial(Q, t);
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result *= exp(z) / z;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result += z;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
}

template <class T>
void expint_i_113g(T& result, const T& z)
{
   BOOST_MATH_STD_USING
   // Maximum Deviation Found:                     5.588e-35
   // Expected Error Term:                         -5.566e-35
   // Max Error found at long double precision =   Poly: 9.976345e-35   Cheb: 8.358865e-35

static const T Y = 1.015148162841796875F;
   static const T P[11] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000435714784725086961464589957142615216),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00432114324353830636009453048419094314),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0100740363285526177522819204820582424),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0116744115827059174392383504427640362),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00816145387784261141360062395898644652),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00371380272673500791322744465394211508),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.00112958263488611536502153195005736563),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.000228316462389404645183269923754256664),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.29462181955852860250359064291292577e-4),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.21972450610957417963227028788460299e-5),
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.720558173805289167524715527536874694e-7)
   };
   static const T Q[11] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 113, 2.95918362458402597039366979529287095),
      BOOST_MATH_BIG_CONSTANT(T, 113, 3.96472247520659077944638411856748924),
      BOOST_MATH_BIG_CONSTANT(T, 113, 3.15563251550528513747923714884142131),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.64674612007093983894215359287448334),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.58695020129846594405856226787156424),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.144358385319329396231755457772362793),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.024146911506411684815134916238348063),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.0026257132337460784266874572001650153),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.000167479843750859222348869769094711093),
      BOOST_MATH_BIG_CONSTANT(T, 113, 0.475673638665358075556452220192497036e-5)
   };
   T t = z / 14 - 5;
   result = Y + tools::evaluate_polynomial(P, t)
      / tools::evaluate_polynomial(Q, t);
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result *= exp(z) / z;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
   result += z;
   BOOST_MATH_INSTRUMENT_VARIABLE(result)
}

template <class T>
void expint_i_113h(T& result, const T& z)
{
   BOOST_MATH_STD_USING
   // Maximum Deviation Found:                     4.448e-36
   // Expected Error Term:                         4.445e-36
   // Max Error found at long double precision =   Poly: 2.058532e-35   Cheb: 2.165465e-27

static const T Y= 1.00849151611328125F;
   static const T P[9] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, -0.0084915161132812500000001440233607358),
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.84479378737716028341394223076147872),
      BOOST_MATH_BIG_CONSTANT(T, 113, -130.431146923726715674081563022115568),
      BOOST_MATH_BIG_CONSTANT(T, 113, 4336.26945491571504885214176203512015),
      BOOST_MATH_BIG_CONSTANT(T, 113, -76279.0031974974730095170437591004177),
      BOOST_MATH_BIG_CONSTANT(T, 113, 729577.956271997673695191455111727774),
      BOOST_MATH_BIG_CONSTANT(T, 113, -3661928.69330208734947103004900349266),
      BOOST_MATH_BIG_CONSTANT(T, 113, 8570600.041606912735872059184527855),
      BOOST_MATH_BIG_CONSTANT(T, 113, -6758379.93672362080947905580906028645)
   };
   static const T Q[10] = {    
      BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
      BOOST_MATH_BIG_CONSTANT(T, 113, -99.4868026047611434569541483506091713),
      BOOST_MATH_BIG_CONSTANT(T, 113, 3879.67753690517114249705089803055473),
      BOOST_MATH_BIG_CONSTANT(T, 113, -76495.82413252517165830203774900806),
      BOOST_MATH_BIG_CONSTANT(T, 113, 820773.726408311894342553758526282667),
      BOOST_MATH_BIG_CONSTANT(T, 113, -4803087.64956923577571031564909646579),
      BOOST_MATH_BIG_CONSTANT(T, 113, 14521246.227703545012713173740895477),
      BOOST_MATH_BIG_CONSTANT(T, 113, -19762752.0196769712258527849159393044),
      BOOST_MATH_BIG_CONSTANT(T, 113, 8354144.67882768405803322344185185517),
      BOOST_MATH_BIG_CONSTANT(T, 113, 355076.853106511136734454134915432571)
   };
   T t = 1 / z;
   result = Y + tools::evaluate_polynomial(P, t)
      / tools::evaluate_polynomial(Q, t);
   result *= exp(z) / z;
   result += z;
}

template <class T, class Policy>
T expint_i_imp(T z, const Policy& pol, const boost::integral_constant<int, 113>& tag)
{
   BOOST_MATH_STD_USING
   static const char* function = "boost::math::expint<%1%>(%1%)";
   if(z < 0)
      return -expint_imp(1, T(-z), pol, tag);
   if(z == 0)
      return -policies::raise_overflow_error<T>(function, 0, pol);

T result;

if(z <= 6)
   {
      expint_i_imp_113a(result, z, pol);
   }
   else if (z <= 10)
   {
      expint_i_113b(result, z);
   }
   else if(z <= 18)
   {
      expint_i_113c(result, z);
   }
   else if(z <= 26)
   {
      expint_i_113d(result, z);
   }
   else if(z <= 42)
   {
      expint_i_113e(result, z);
   }
   else if(z <= 56)
   {
      expint_i_113f(result, z);
   }
   else if(z <= 84)
   {
      expint_i_113g(result, z);
   }
   else if(z <= 210)
   {
      expint_i_113h(result, z);
   }
   else // z > 210
   {
      // Maximum Deviation Found:                     3.963e-37
      // Expected Error Term:                         3.963e-37
      // Max Error found at long double precision =   Poly: 1.248049e-36   Cheb: 2.843486e-29

static const T exp40 = static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2.35385266837019985407899910749034804508871617254555467236651e17));
      static const T Y= 1.00252532958984375F;
      static const T P[8] = {    
         BOOST_MATH_BIG_CONSTANT(T, 113, -0.00252532958984375000000000000000000085),
         BOOST_MATH_BIG_CONSTANT(T, 113, 1.16591386866059087390621952073890359),
         BOOST_MATH_BIG_CONSTANT(T, 113, -67.8483431314018462417456828499277579),
         BOOST_MATH_BIG_CONSTANT(T, 113, 1567.68688154683822956359536287575892),
         BOOST_MATH_BIG_CONSTANT(T, 113, -17335.4683325819116482498725687644986),
         BOOST_MATH_BIG_CONSTANT(T, 113, 93632.6567462673524739954389166550069),
         BOOST_MATH_BIG_CONSTANT(T, 113, -225025.189335919133214440347510936787),
         BOOST_MATH_BIG_CONSTANT(T, 113, 175864.614717440010942804684741336853)
      };
      static const T Q[9] = {    
         BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
         BOOST_MATH_BIG_CONSTANT(T, 113, -65.6998869881600212224652719706425129),
         BOOST_MATH_BIG_CONSTANT(T, 113, 1642.73850032324014781607859416890077),
         BOOST_MATH_BIG_CONSTANT(T, 113, -19937.2610222467322481947237312818575),
         BOOST_MATH_BIG_CONSTANT(T, 113, 124136.267326632742667972126625064538),
         BOOST_MATH_BIG_CONSTANT(T, 113, -384614.251466704550678760562965502293),
         BOOST_MATH_BIG_CONSTANT(T, 113, 523355.035910385688578278384032026998),
         BOOST_MATH_BIG_CONSTANT(T, 113, -217809.552260834025885677791936351294),
         BOOST_MATH_BIG_CONSTANT(T, 113, -8555.81719551123640677261226549550872)
      };
      T t = 1 / z;
      result = Y + tools::evaluate_polynomial(P, t)
         / tools::evaluate_polynomial(Q, t);
      if(z < 41)
         result *= exp(z) / z;
      else
      {
         // Avoid premature overflow if we can:
         t = z - 40;
         if(t > tools::log_max_value<T>())
         {
            result = policies::raise_overflow_error<T>(function, 0, pol);
         }
         else
         {
            result *= exp(z - 40) / z;
            if(result > tools::max_value<T>() / exp40)
            {
               result = policies::raise_overflow_error<T>(function, 0, pol);
            }
            else
            {
               result *= exp40;
            }
         }
      }
      result += z;
   }
   return result;
}

template <class T, class Policy, class tag>
struct expint_i_initializer
{
   struct init
   {
      init()
      {
         do_init(tag());
      }
      static void do_init(const boost::integral_constant<int, 0>&){}
      static void do_init(const boost::integral_constant<int, 53>&)
      {
         boost::math::expint(T(5));
         boost::math::expint(T(7));
         boost::math::expint(T(18));
         boost::math::expint(T(38));
         boost::math::expint(T(45));
      }
      static void do_init(const boost::integral_constant<int, 64>&)
      {
         boost::math::expint(T(5));
         boost::math::expint(T(7));
         boost::math::expint(T(18));
         boost::math::expint(T(38));
         boost::math::expint(T(45));
      }
      static void do_init(const boost::integral_constant<int, 113>&)
      {
         boost::math::expint(T(5));
         boost::math::expint(T(7));
         boost::math::expint(T(17));
         boost::math::expint(T(25));
         boost::math::expint(T(40));
         boost::math::expint(T(50));
         boost::math::expint(T(80));
         boost::math::expint(T(200));
         boost::math::expint(T(220));
      }
      void force_instantiate()const{}
   };
   static const init initializer;
   static void force_instantiate()
   {
      initializer.force_instantiate();
   }
};

template <class T, class Policy, class tag>
const typename expint_i_initializer<T, Policy, tag>::init expint_i_initializer<T, Policy, tag>::initializer;

template <class T, class Policy, class tag>
struct expint_1_initializer
{
   struct init
   {
      init()
      {
         do_init(tag());
      }
      static void do_init(const boost::integral_constant<int, 0>&){}
      static void do_init(const boost::integral_constant<int, 53>&)
      {
         boost::math::expint(1, T(0.5));
         boost::math::expint(1, T(2));
      }
      static void do_init(const boost::integral_constant<int, 64>&)
      {
         boost::math::expint(1, T(0.5));
         boost::math::expint(1, T(2));
      }
      static void do_init(const boost::integral_constant<int, 113>&)
      {
         boost::math::expint(1, T(0.5));
         boost::math::expint(1, T(2));
         boost::math::expint(1, T(6));
      }
      void force_instantiate()const{}
   };
   static const init initializer;
   static void force_instantiate()
   {
      initializer.force_instantiate();
   }
};

template <class T, class Policy, class tag>
const typename expint_1_initializer<T, Policy, tag>::init expint_1_initializer<T, Policy, tag>::initializer;

template <class T, class Policy>
inline typename tools::promote_args<T>::type
   expint_forwarder(T z, const Policy& /*pol*/, boost::true_type const&)
{
   typedef typename tools::promote_args<T>::type result_type;
   typedef typename policies::evaluation<result_type, Policy>::type value_type;
   typedef typename policies::precision<result_type, Policy>::type precision_type;
   typedef typename policies::normalise<
      Policy, 
      policies::promote_float<false>, 
      policies::promote_double<false>, 
      policies::discrete_quantile<>,
      policies::assert_undefined<> >::type forwarding_policy;
   typedef boost::integral_constant<int,
      precision_type::value <= 0 ? 0 :
      precision_type::value <= 53 ? 53 :
      precision_type::value <= 64 ? 64 :
      precision_type::value <= 113 ? 113 : 0
   > tag_type;

expint_i_initializer<value_type, forwarding_policy, tag_type>::force_instantiate();

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%)");
}

template <class T>
inline typename tools::promote_args<T>::type
expint_forwarder(unsigned n, T z, const boost::false_type&)
{
   return boost::math::expint(n, z, policies::policy<>());
}

} // namespace detail

template <class T, class Policy>
inline typename tools::promote_args<T>::type
   expint(unsigned n, T z, const Policy& /*pol*/)
{
   typedef typename tools::promote_args<T>::type result_type;
   typedef typename policies::evaluation<result_type, Policy>::type value_type;
   typedef typename policies::precision<result_type, Policy>::type precision_type;
   typedef typename policies::normalise<
      Policy, 
      policies::promote_float<false>, 
      policies::promote_double<false>, 
      policies::discrete_quantile<>,
      policies::assert_undefined<> >::type forwarding_policy;
   typedef boost::integral_constant<int,
      precision_type::value <= 0 ? 0 :
      precision_type::value <= 53 ? 53 :
      precision_type::value <= 64 ? 64 :
      precision_type::value <= 113 ? 113 : 0
   > tag_type;

detail::expint_1_initializer<value_type, forwarding_policy, tag_type>::force_instantiate();

return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::expint_imp(
      n,
      static_cast<value_type>(z),
      forwarding_policy(),
      tag_type()), "boost::math::expint<%1%>(unsigned, %1%)");
}

template <class T, class U>
inline typename detail::expint_result<T, U>::type
   expint(T const z, U const u)
{
   typedef typename policies::is_policy<U>::type tag_type;
   return detail::expint_forwarder(z, u, tag_type());
}

template <class T>
inline typename tools::promote_args<T>::type
   expint(T z)
{
   return expint(z, policies::policy<>());
}

}} // namespaces

#ifdef _MSC_VER
#pragma warning(pop)
#endif

#endif // BOOST_MATH_EXPINT_HPP

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