code:
//  (C) Copyright John Maddock 2006.
//  Use, modification and distribution are subject to the
//  Boost Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_MATH_SPECIAL_ERF_HPP
#define BOOST_MATH_SPECIAL_ERF_HPP

#ifdef _MSC_VER
#pragma once
#endif

#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/tools/config.hpp>
#include <boost/math/special_functions/gamma.hpp>
#include <boost/math/tools/roots.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/math/tools/big_constant.hpp>

namespace boost{ namespace math{

namespace detail
{

//
// Asymptotic series for large z:
//
template <class T>
struct erf_asympt_series_t
{
   erf_asympt_series_t(T z) : xx(2 * -z * z), tk(1)
   {
      BOOST_MATH_STD_USING
      result = -exp(-z * z) / sqrt(boost::math::constants::pi<T>());
      result /= z;
   }

   typedef T result_type;

   T operator()()
   {
      BOOST_MATH_STD_USING
      T r = result;
      result *= tk / xx;
      tk += 2;
      if( fabs(r) < fabs(result))
         result = 0;
      return r;
   }
private:
   T result;
   T xx;
   int tk;
};
//
// How large z has to be in order to ensure that the series converges:
//
template <class T>
inline float erf_asymptotic_limit_N(const T&)
{
   return (std::numeric_limits<float>::max)();
}
inline float erf_asymptotic_limit_N(const mpl::int_<24>&)
{
   return 2.8F;
}
inline float erf_asymptotic_limit_N(const mpl::int_<53>&)
{
   return 4.3F;
}
inline float erf_asymptotic_limit_N(const mpl::int_<64>&)
{
   return 4.8F;
}
inline float erf_asymptotic_limit_N(const mpl::int_<106>&)
{
   return 6.5F;
}
inline float erf_asymptotic_limit_N(const mpl::int_<113>&)
{
   return 6.8F;
}

template <class T, class Policy>
inline T erf_asymptotic_limit()
{
   typedef typename policies::precision<T, Policy>::type precision_type;
   typedef typename mpl::if_<
      mpl::less_equal<precision_type, mpl::int_<24> >,
      typename mpl::if_<
         mpl::less_equal<precision_type, mpl::int_<0> >,
         mpl::int_<0>,
         mpl::int_<24>
      >::type,
      typename mpl::if_<
         mpl::less_equal<precision_type, mpl::int_<53> >,
         mpl::int_<53>,
         typename mpl::if_<
            mpl::less_equal<precision_type, mpl::int_<64> >,
            mpl::int_<64>,
            typename mpl::if_<
               mpl::less_equal<precision_type, mpl::int_<106> >,
               mpl::int_<106>,
               typename mpl::if_<
                  mpl::less_equal<precision_type, mpl::int_<113> >,
                  mpl::int_<113>,
                  mpl::int_<0>
               >::type
            >::type
         >::type
      >::type
   >::type tag_type;
   return erf_asymptotic_limit_N(tag_type());
}

template <class T, class Policy, class Tag>
T erf_imp(T z, bool invert, const Policy& pol, const Tag& t)
{
   BOOST_MATH_STD_USING

   BOOST_MATH_INSTRUMENT_CODE("Generic erf_imp called");

   if(z < 0)
   {
      if(!invert)
         return -erf_imp(T(-z), invert, pol, t);
      else
         return 1 + erf_imp(T(-z), false, pol, t);
   }

   T result;

   if(!invert && (z > detail::erf_asymptotic_limit<T, Policy>()))
   {
      detail::erf_asympt_series_t<T> s(z);
      boost::uintmax_t max_iter = policies::get_max_series_iterations<Policy>();
      result = boost::math::tools::sum_series(s, policies::get_epsilon<T, Policy>(), max_iter, 1);
      policies::check_series_iterations<T>("boost::math::erf<%1%>(%1%, %1%)", max_iter, pol);
   }
   else
   {
      T x = z * z;
      if(x < 0.6)
      {
         // Compute P:
         result = z * exp(-x);
         result /= sqrt(boost::math::constants::pi<T>());
         if(result != 0)
            result *= 2 * detail::lower_gamma_series(T(0.5f), x, pol);
      }
      else if(x < 1.1f)
      {
         // Compute Q:
         invert = !invert;
         result = tgamma_small_upper_part(T(0.5f), x, pol);
         result /= sqrt(boost::math::constants::pi<T>());
      }
      else
      {
         // Compute Q:
         invert = !invert;
         result = z * exp(-x);
         result /= sqrt(boost::math::constants::pi<T>());
         result *= upper_gamma_fraction(T(0.5f), x, policies::get_epsilon<T, Policy>());
      }
   }
   if(invert)
      result = 1 - result;
   return result;
}

template <class T, class Policy>
T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<53>& t)
{
   BOOST_MATH_STD_USING

   BOOST_MATH_INSTRUMENT_CODE("53-bit precision erf_imp called");

   if(z < 0)
   {
      if(!invert)
         return -erf_imp(T(-z), invert, pol, t);
      else if(z < -0.5)
         return 2 - erf_imp(T(-z), invert, pol, t);
      else
         return 1 + erf_imp(T(-z), false, pol, t);
   }

   T result;

   //
   // Big bunch of selection statements now to pick
   // which implementation to use,
   // try to put most likely options first:
   //
   if(z < 0.5)
   {
      //
      // We're going to calculate erf:
      //
      if(z < 1e-10)
      {
         if(z == 0)
         {
            result = T(0);
         }
         else
         {
            static const T c = BOOST_MATH_BIG_CONSTANT(T, 53, 0.003379167095512573896158903121545171688);
            result = static_cast<T>(z * 1.125f + z * c);
         }
      }
      else
      {
         // Maximum Deviation Found:                     1.561e-17
         // Expected Error Term:                         1.561e-17
         // Maximum Relative Change in Control Points:   1.155e-04
         // Max Error found at double precision =        2.961182e-17

         static const T Y = 1.044948577880859375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0834305892146531832907),
            BOOST_MATH_BIG_CONSTANT(T, 53, -0.338165134459360935041),
            BOOST_MATH_BIG_CONSTANT(T, 53, -0.0509990735146777432841),
            BOOST_MATH_BIG_CONSTANT(T, 53, -0.00772758345802133288487),
            BOOST_MATH_BIG_CONSTANT(T, 53, -0.000322780120964605683831),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.455004033050794024546),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0875222600142252549554),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.00858571925074406212772),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.000370900071787748000569),
         };
         T zz = z * z;
         result = z * (Y + tools::evaluate_polynomial(P, zz) / tools::evaluate_polynomial(Q, zz));
      }
   }
   else if(invert ? (z < 28) : (z < 5.8f))
   {
      //
      // We'll be calculating erfc:
      //
      invert = !invert;
      if(z < 1.5f)
      {
         // Maximum Deviation Found:                     3.702e-17
         // Expected Error Term:                         3.702e-17
         // Maximum Relative Change in Control Points:   2.845e-04
         // Max Error found at double precision =        4.841816e-17
         static const T Y = 0.405935764312744140625f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, -0.098090592216281240205),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.178114665841120341155),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.191003695796775433986),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0888900368967884466578),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0195049001251218801359),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.00180424538297014223957),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.84759070983002217845),
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.42628004845511324508),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.578052804889902404909),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.12385097467900864233),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0113385233577001411017),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.337511472483094676155e-5),
         };
         BOOST_MATH_INSTRUMENT_VARIABLE(Y);
         BOOST_MATH_INSTRUMENT_VARIABLE(P[0]);
         BOOST_MATH_INSTRUMENT_VARIABLE(Q[0]);
         BOOST_MATH_INSTRUMENT_VARIABLE(z);
         result = Y + tools::evaluate_polynomial(P, T(z - 0.5)) / tools::evaluate_polynomial(Q, T(z - 0.5));
         BOOST_MATH_INSTRUMENT_VARIABLE(result);
         result *= exp(-z * z) / z;
         BOOST_MATH_INSTRUMENT_VARIABLE(result);
      }
      else if(z < 2.5f)
      {
         // Max Error found at double precision =        6.599585e-18
         // Maximum Deviation Found:                     3.909e-18
         // Expected Error Term:                         3.909e-18
         // Maximum Relative Change in Control Points:   9.886e-05
         static const T Y = 0.50672817230224609375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, -0.0243500476207698441272),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0386540375035707201728),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.04394818964209516296),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0175679436311802092299),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.00323962406290842133584),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.000235839115596880717416),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.53991494948552447182),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.982403709157920235114),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.325732924782444448493),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0563921837420478160373),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.00410369723978904575884),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 1.5)) / tools::evaluate_polynomial(Q, T(z - 1.5));
         result *= exp(-z * z) / z;
      }
      else if(z < 4.5f)
      {
         // Maximum Deviation Found:                     1.512e-17
         // Expected Error Term:                         1.512e-17
         // Maximum Relative Change in Control Points:   2.222e-04
         // Max Error found at double precision =        2.062515e-17
         static const T Y = 0.5405750274658203125f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.00295276716530971662634),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0137384425896355332126),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.00840807615555585383007),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.00212825620914618649141),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.000250269961544794627958),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.113212406648847561139e-4),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.04217814166938418171),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.442597659481563127003),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0958492726301061423444),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0105982906484876531489),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.000479411269521714493907),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 3.5)) / tools::evaluate_polynomial(Q, T(z - 3.5));
         result *= exp(-z * z) / z;
      }
      else
      {
         // Max Error found at double precision =        2.997958e-17
         // Maximum Deviation Found:                     2.860e-17
         // Expected Error Term:                         2.859e-17
         // Maximum Relative Change in Control Points:   1.357e-05
         static const T Y = 0.5579090118408203125f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.00628057170626964891937),
            BOOST_MATH_BIG_CONSTANT(T, 53, 0.0175389834052493308818),
            BOOST_MATH_BIG_CONSTANT(T, 53, -0.212652252872804219852),
            BOOST_MATH_BIG_CONSTANT(T, 53, -0.687717681153649930619),
            BOOST_MATH_BIG_CONSTANT(T, 53, -2.5518551727311523996),
            BOOST_MATH_BIG_CONSTANT(T, 53, -3.22729451764143718517),
            BOOST_MATH_BIG_CONSTANT(T, 53, -2.8175401114513378771),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 53, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 53, 2.79257750980575282228),
            BOOST_MATH_BIG_CONSTANT(T, 53, 11.0567237927800161565),
            BOOST_MATH_BIG_CONSTANT(T, 53, 15.930646027911794143),
            BOOST_MATH_BIG_CONSTANT(T, 53, 22.9367376522880577224),
            BOOST_MATH_BIG_CONSTANT(T, 53, 13.5064170191802889145),
            BOOST_MATH_BIG_CONSTANT(T, 53, 5.48409182238641741584),
         };
         result = Y + tools::evaluate_polynomial(P, T(1 / z)) / tools::evaluate_polynomial(Q, T(1 / z));
         result *= exp(-z * z) / z;
      }
   }
   else
   {
      //
      // Any value of z larger than 28 will underflow to zero:
      //
      result = 0;
      invert = !invert;
   }

   if(invert)
   {
      result = 1 - result;
   }

   return result;
} // template <class T, class Lanczos>T erf_imp(T z, bool invert, const Lanczos& l, const mpl::int_<53>& t)

template <class T, class Policy>
T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<64>& t)
{
   BOOST_MATH_STD_USING

   BOOST_MATH_INSTRUMENT_CODE("64-bit precision erf_imp called");

   if(z < 0)
   {
      if(!invert)
         return -erf_imp(T(-z), invert, pol, t);
      else if(z < -0.5)
         return 2 - erf_imp(T(-z), invert, pol, t);
      else
         return 1 + erf_imp(T(-z), false, pol, t);
   }

   T result;

   //
   // Big bunch of selection statements now to pick which
   // implementation to use, try to put most likely options
   // first:
   //
   if(z < 0.5)
   {
      //
      // We're going to calculate erf:
      //
      if(z == 0)
      {
         result = 0;
      }
      else if(z < 1e-10)
      {
         static const T c = BOOST_MATH_BIG_CONSTANT(T, 64, 0.003379167095512573896158903121545171688);
         result = z * 1.125 + z * c;
      }
      else
      {
         // Max Error found at long double precision =   1.623299e-20
         // Maximum Deviation Found:                     4.326e-22
         // Expected Error Term:                         -4.326e-22
         // Maximum Relative Change in Control Points:   1.474e-04
         static const T Y = 1.044948577880859375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0834305892146531988966),
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.338097283075565413695),
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.0509602734406067204596),
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.00904906346158537794396),
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.000489468651464798669181),
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.200305626366151877759e-4),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.455817300515875172439),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0916537354356241792007),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0102722652675910031202),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.000650511752687851548735),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.189532519105655496778e-4),
         };
         result = z * (Y + tools::evaluate_polynomial(P, T(z * z)) / tools::evaluate_polynomial(Q, T(z * z)));
      }
   }
   else if(invert ? (z < 110) : (z < 6.4f))
   {
      //
      // We'll be calculating erfc:
      //
      invert = !invert;
      if(z < 1.5)
      {
         // Max Error found at long double precision =   3.239590e-20
         // Maximum Deviation Found:                     2.241e-20
         // Expected Error Term:                         -2.241e-20
         // Maximum Relative Change in Control Points:   5.110e-03
         static const T Y = 0.405935764312744140625f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.0980905922162812031672),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.159989089922969141329),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.222359821619935712378),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.127303921703577362312),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0384057530342762400273),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.00628431160851156719325),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.000441266654514391746428),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.266689068336295642561e-7),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 64, 2.03237474985469469291),
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.78355454954969405222),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.867940326293760578231),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.248025606990021698392),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0396649631833002269861),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.00279220237309449026796),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 0.5f)) / tools::evaluate_polynomial(Q, T(z - 0.5f));
         result *= exp(-z * z) / z;
      }
      else if(z < 2.5)
      {
         // Max Error found at long double precision =   3.686211e-21
         // Maximum Deviation Found:                     1.495e-21
         // Expected Error Term:                         -1.494e-21
         // Maximum Relative Change in Control Points:   1.793e-04
         static const T Y = 0.50672817230224609375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.024350047620769840217),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0343522687935671451309),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0505420824305544949541),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0257479325917757388209),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.00669349844190354356118),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.00090807914416099524444),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.515917266698050027934e-4),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.71657861671930336344),
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.26409634824280366218),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.512371437838969015941),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.120902623051120950935),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0158027197831887485261),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.000897871370778031611439),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 1.5f)) / tools::evaluate_polynomial(Q, T(z - 1.5f));
         result *= exp(-z * z) / z;
      }
      else if(z < 4.5)
      {
         // Maximum Deviation Found:                     1.107e-20
         // Expected Error Term:                         -1.106e-20
         // Maximum Relative Change in Control Points:   1.709e-04
         // Max Error found at long double precision =   1.446908e-20
         static const T Y  = 0.5405750274658203125f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0029527671653097284033),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0141853245895495604051),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0104959584626432293901),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.00343963795976100077626),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.00059065441194877637899),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.523435380636174008685e-4),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.189896043050331257262e-5),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.19352160185285642574),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.603256964363454392857),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.165411142458540585835),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0259729870946203166468),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.00221657568292893699158),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.804149464190309799804e-4),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 3.5f)) / tools::evaluate_polynomial(Q, T(z - 3.5f));
         result *= exp(-z * z) / z;
      }
      else
      {
         // Max Error found at long double precision =   7.961166e-21
         // Maximum Deviation Found:                     6.677e-21
         // Expected Error Term:                         6.676e-21
         // Maximum Relative Change in Control Points:   2.319e-05
         static const T Y = 0.55825519561767578125f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.00593438793008050214106),
            BOOST_MATH_BIG_CONSTANT(T, 64, 0.0280666231009089713937),
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.141597835204583050043),
            BOOST_MATH_BIG_CONSTANT(T, 64, -0.978088201154300548842),
            BOOST_MATH_BIG_CONSTANT(T, 64, -5.47351527796012049443),
            BOOST_MATH_BIG_CONSTANT(T, 64, -13.8677304660245326627),
            BOOST_MATH_BIG_CONSTANT(T, 64, -27.1274948720539821722),
            BOOST_MATH_BIG_CONSTANT(T, 64, -29.2545152747009461519),
            BOOST_MATH_BIG_CONSTANT(T, 64, -16.8865774499799676937),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 64, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 64, 4.72948911186645394541),
            BOOST_MATH_BIG_CONSTANT(T, 64, 23.6750543147695749212),
            BOOST_MATH_BIG_CONSTANT(T, 64, 60.0021517335693186785),
            BOOST_MATH_BIG_CONSTANT(T, 64, 131.766251645149522868),
            BOOST_MATH_BIG_CONSTANT(T, 64, 178.167924971283482513),
            BOOST_MATH_BIG_CONSTANT(T, 64, 182.499390505915222699),
            BOOST_MATH_BIG_CONSTANT(T, 64, 104.365251479578577989),
            BOOST_MATH_BIG_CONSTANT(T, 64, 30.8365511891224291717),
         };
         result = Y + tools::evaluate_polynomial(P, T(1 / z)) / tools::evaluate_polynomial(Q, T(1 / z));
         result *= exp(-z * z) / z;
      }
   }
   else
   {
      //
      // Any value of z larger than 110 will underflow to zero:
      //
      result = 0;
      invert = !invert;
   }

   if(invert)
   {
      result = 1 - result;
   }

   return result;
} // template <class T, class Lanczos>T erf_imp(T z, bool invert, const Lanczos& l, const mpl::int_<64>& t)

template <class T, class Policy>
T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<113>& t)
{
   BOOST_MATH_STD_USING

   BOOST_MATH_INSTRUMENT_CODE("113-bit precision erf_imp called");

   if(z < 0)
   {
      if(!invert)
         return -erf_imp(T(-z), invert, pol, t);
      else if(z < -0.5)
         return 2 - erf_imp(T(-z), invert, pol, t);
      else
         return 1 + erf_imp(T(-z), false, pol, t);
   }

   T result;

   //
   // Big bunch of selection statements now to pick which
   // implementation to use, try to put most likely options
   // first:
   //
   if(z < 0.5)
   {
      //
      // We're going to calculate erf:
      //
      if(z == 0)
      {
         result = 0;
      }
      else if(z < 1e-20)
      {
         static const T c = BOOST_MATH_BIG_CONSTANT(T, 113, 0.003379167095512573896158903121545171688);
         result = z * 1.125 + z * c;
      }
      else
      {
         // Max Error found at long double precision =   2.342380e-35
         // Maximum Deviation Found:                     6.124e-36
         // Expected Error Term:                         -6.124e-36
         // Maximum Relative Change in Control Points:   3.492e-10
         static const T Y = 1.0841522216796875f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0442269454158250738961589031215451778),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.35549265736002144875335323556961233),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.0582179564566667896225454670863270393),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.0112694696904802304229950538453123925),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.000805730648981801146251825329609079099),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.566304966591936566229702842075966273e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.169655010425186987820201021510002265e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.344448249920445916714548295433198544e-7),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.466542092785657604666906909196052522),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.100005087012526447295176964142107611),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0128341535890117646540050072234142603),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00107150448466867929159660677016658186),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.586168368028999183607733369248338474e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.196230608502104324965623171516808796e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.313388521582925207734229967907890146e-7),
         };
         result = z * (Y + tools::evaluate_polynomial(P, T(z * z)) / tools::evaluate_polynomial(Q, T(z * z)));
      }
   }
   else if(invert ? (z < 110) : (z < 8.65f))
   {
      //
      // We'll be calculating erfc:
      //
      invert = !invert;
      if(z < 1)
      {
         // Max Error found at long double precision =   3.246278e-35
         // Maximum Deviation Found:                     1.388e-35
         // Expected Error Term:                         1.387e-35
         // Maximum Relative Change in Control Points:   6.127e-05
         static const T Y = 0.371877193450927734375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.0640320213544647969396032886581290455),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.200769874440155895637857443946706731),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.378447199873537170666487408805779826),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.30521399466465939450398642044975127),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.146890026406815277906781824723458196),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0464837937749539978247589252732769567),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00987895759019540115099100165904822903),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00137507575429025512038051025154301132),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0001144764551085935580772512359680516),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.436544865032836914773944382339900079e-5),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 2.47651182872457465043733800302427977),
            BOOST_MATH_BIG_CONSTANT(T, 113, 2.78706486002517996428836400245547955),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.87295924621659627926365005293130693),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.829375825174365625428280908787261065),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.251334771307848291593780143950311514),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0522110268876176186719436765734722473),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00718332151250963182233267040106902368),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000595279058621482041084986219276392459),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.226988669466501655990637599399326874e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.270666232259029102353426738909226413e-10),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 0.5f)) / tools::evaluate_polynomial(Q, T(z - 0.5f));
         result *= exp(-z * z) / z;
      }
      else if(z < 1.5)
      {
         // Max Error found at long double precision =   2.215785e-35
         // Maximum Deviation Found:                     1.539e-35
         // Expected Error Term:                         1.538e-35
         // Maximum Relative Change in Control Points:   6.104e-05
         static const T Y = 0.45658016204833984375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.0289965858925328393392496555094848345),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0868181194868601184627743162571779226),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.169373435121178901746317404936356745),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.13350446515949251201104889028133486),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0617447837290183627136837688446313313),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0185618495228251406703152962489700468),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00371949406491883508764162050169531013),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000485121708792921297742105775823900772),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.376494706741453489892108068231400061e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.133166058052466262415271732172490045e-5),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 2.32970330146503867261275580968135126),
            BOOST_MATH_BIG_CONSTANT(T, 113, 2.46325715420422771961250513514928746),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.55307882560757679068505047390857842),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.644274289865972449441174485441409076),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.182609091063258208068606847453955649),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0354171651271241474946129665801606795),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00454060370165285246451879969534083997),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000349871943711566546821198612518656486),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.123749319840299552925421880481085392e-4),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 1.0f)) / tools::evaluate_polynomial(Q, T(z - 1.0f));
         result *= exp(-z * z) / z;
      }
      else if(z < 2.25)
      {
         // Maximum Deviation Found:                     1.418e-35
         // Expected Error Term:                         1.418e-35
         // Maximum Relative Change in Control Points:   1.316e-04
         // Max Error found at long double precision =   1.998462e-35
         static const T Y = 0.50250148773193359375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.0201233630504573402185161184151016606),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0331864357574860196516686996302305002),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0716562720864787193337475444413405461),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0545835322082103985114927569724880658),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0236692635189696678976549720784989593),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00656970902163248872837262539337601845),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00120282643299089441390490459256235021),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000142123229065182650020762792081622986),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.991531438367015135346716277792989347e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.312857043762117596999398067153076051e-6),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 2.13506082409097783827103424943508554),
            BOOST_MATH_BIG_CONSTANT(T, 113, 2.06399257267556230937723190496806215),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.18678481279932541314830499880691109),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.447733186643051752513538142316799562),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.11505680005657879437196953047542148),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.020163993632192726170219663831914034),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00232708971840141388847728782209730585),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000160733201627963528519726484608224112),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.507158721790721802724402992033269266e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.18647774409821470950544212696270639e-12),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 1.5f)) / tools::evaluate_polynomial(Q, T(z - 1.5f));
         result *= exp(-z * z) / z;
      }
      else if (z < 3)
      {
         // Maximum Deviation Found:                     3.575e-36
         // Expected Error Term:                         3.575e-36
         // Maximum Relative Change in Control Points:   7.103e-05
         // Max Error found at long double precision =   5.794737e-36
         static const T Y = 0.52896785736083984375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.00902152521745813634562524098263360074),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0145207142776691539346923710537580927),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0301681239582193983824211995978678571),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0215548540823305814379020678660434461),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00864683476267958365678294164340749949),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00219693096885585491739823283511049902),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000364961639163319762492184502159894371),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.388174251026723752769264051548703059e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.241918026931789436000532513553594321e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.676586625472423508158937481943649258e-7),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.93669171363907292305550231764920001),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.69468476144051356810672506101377494),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.880023580986436640372794392579985511),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.299099106711315090710836273697708402),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0690593962363545715997445583603382337),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0108427016361318921960863149875360222),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00111747247208044534520499324234317695),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.686843205749767250666787987163701209e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.192093541425429248675532015101904262e-5),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 2.25f)) / tools::evaluate_polynomial(Q, T(z - 2.25f));
         result *= exp(-z * z) / z;
      }
      else if(z < 3.5)
      {
         // Maximum Deviation Found:                     8.126e-37
         // Expected Error Term:                         -8.126e-37
         // Maximum Relative Change in Control Points:   1.363e-04
         // Max Error found at long double precision =   1.747062e-36
         static const T Y = 0.54037380218505859375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.0033703486408887424921155540591370375),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0104948043110005245215286678898115811),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0148530118504000311502310457390417795),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00816693029245443090102738825536188916),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00249716579989140882491939681805594585),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0004655591010047353023978045800916647),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.531129557920045295895085236636025323e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.343526765122727069515775194111741049e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.971120407556888763695313774578711839e-7),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.59911256167540354915906501335919317),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.136006830764025173864831382946934),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.468565867990030871678574840738423023),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.122821824954470343413956476900662236),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0209670914950115943338996513330141633),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00227845718243186165620199012883547257),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000144243326443913171313947613547085553),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.407763415954267700941230249989140046e-5),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 3.0f)) / tools::evaluate_polynomial(Q, T(z - 3.0f));
         result *= exp(-z * z) / z;
      }
      else if(z < 5.5)
      {
         // Maximum Deviation Found:                     5.804e-36
         // Expected Error Term:                         -5.803e-36
         // Maximum Relative Change in Control Points:   2.475e-05
         // Max Error found at long double precision =   1.349545e-35
         static const T Y = 0.55000019073486328125f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00118142849742309772151454518093813615),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0072201822885703318172366893469382745),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0078782276276860110721875733778481505),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00418229166204362376187593976656261146),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00134198400587769200074194304298642705),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000283210387078004063264777611497435572),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.405687064094911866569295610914844928e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.39348283801568113807887364414008292e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.248798540917787001526976889284624449e-6),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.929502490223452372919607105387474751e-8),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.156161469668275442569286723236274457e-9),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.52955245103668419479878456656709381),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.06263944820093830054635017117417064),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.441684612681607364321013134378316463),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.121665258426166960049773715928906382),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0232134512374747691424978642874321434),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00310778180686296328582860464875562636),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000288361770756174705123674838640161693),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.177529187194133944622193191942300132e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.655068544833064069223029299070876623e-6),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.11005507545746069573608988651927452e-7),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 4.5f)) / tools::evaluate_polynomial(Q, T(z - 4.5f));
         result *= exp(-z * z) / z;
      }
      else if(z < 7.5)
      {
         // Maximum Deviation Found:                     1.007e-36
         // Expected Error Term:                         1.007e-36
         // Maximum Relative Change in Control Points:   1.027e-03
         // Max Error found at long double precision =   2.646420e-36
         static const T Y = 0.5574436187744140625f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000293236907400849056269309713064107674),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00225110719535060642692275221961480162),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00190984458121502831421717207849429799),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000747757733460111743833929141001680706),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000170663175280949889583158597373928096),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.246441188958013822253071608197514058e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.229818000860544644974205957895688106e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.134886977703388748488480980637704864e-6),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.454764611880548962757125070106650958e-8),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.673002744115866600294723141176820155e-10),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.12843690320861239631195353379313367),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.569900657061622955362493442186537259),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.169094404206844928112348730277514273),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0324887449084220415058158657252147063),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00419252877436825753042680842608219552),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00036344133176118603523976748563178578),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.204123895931375107397698245752850347e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.674128352521481412232785122943508729e-6),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.997637501418963696542159244436245077e-8),
         };
         result = Y + tools::evaluate_polynomial(P, T(z - 6.5f)) / tools::evaluate_polynomial(Q, T(z - 6.5f));
         result *= exp(-z * z) / z;
      }
      else if(z < 11.5)
      {
         // Maximum Deviation Found:                     8.380e-36
         // Expected Error Term:                         8.380e-36
         // Maximum Relative Change in Control Points:   2.632e-06
         // Max Error found at long double precision =   9.849522e-36
         static const T Y = 0.56083202362060546875f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000282420728751494363613829834891390121),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00175387065018002823433704079355125161),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0021344978564889819420775336322920375),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00124151356560137532655039683963075661),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000423600733566948018555157026862139644),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.914030340865175237133613697319509698e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.126999927156823363353809747017945494e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.110610959842869849776179749369376402e-5),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.55075079477173482096725348704634529e-7),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.119735694018906705225870691331543806e-8),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.69889613396167354566098060039549882),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.28824647372749624464956031163282674),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.572297795434934493541628008224078717),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.164157697425571712377043857240773164),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.0315311145224594430281219516531649562),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00405588922155632380812945849777127458),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000336929033691445666232029762868642417),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.164033049810404773469413526427932109e-4),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.356615210500531410114914617294694857e-6),
         };
         result = Y + tools::evaluate_polynomial(P, T(z / 2 - 4.75f)) / tools::evaluate_polynomial(Q, T(z / 2 - 4.75f));
         result *= exp(-z * z) / z;
      }
      else
      {
         // Maximum Deviation Found:                     1.132e-35
         // Expected Error Term:                         -1.132e-35
         // Maximum Relative Change in Control Points:   4.674e-04
         // Max Error found at long double precision =   1.162590e-35
         static const T Y = 0.5632686614990234375f;
         static const T P[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.000920922048732849448079451574171836943),
            BOOST_MATH_BIG_CONSTANT(T, 113, 0.00321439044532288750501700028748922439),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.250455263029390118657884864261823431),
            BOOST_MATH_BIG_CONSTANT(T, 113, -0.906807635364090342031792404764598142),
            BOOST_MATH_BIG_CONSTANT(T, 113, -8.92233572835991735876688745989985565),
            BOOST_MATH_BIG_CONSTANT(T, 113, -21.7797433494422564811782116907878495),
            BOOST_MATH_BIG_CONSTANT(T, 113, -91.1451915251976354349734589601171659),
            BOOST_MATH_BIG_CONSTANT(T, 113, -144.1279109655993927069052125017673),
            BOOST_MATH_BIG_CONSTANT(T, 113, -313.845076581796338665519022313775589),
            BOOST_MATH_BIG_CONSTANT(T, 113, -273.11378811923343424081101235736475),
            BOOST_MATH_BIG_CONSTANT(T, 113, -271.651566205951067025696102600443452),
            BOOST_MATH_BIG_CONSTANT(T, 113, -60.0530577077238079968843307523245547),
         };
         static const T Q[] = {
            BOOST_MATH_BIG_CONSTANT(T, 113, 1.0),
            BOOST_MATH_BIG_CONSTANT(T, 113, 3.49040448075464744191022350947892036),
            BOOST_MATH_BIG_CONSTANT(T, 113, 34.3563592467165971295915749548313227),
            BOOST_MATH_BIG_CONSTANT(T, 113, 84.4993232033879023178285731843850461),
            BOOST_MATH_BIG_CONSTANT(T, 113, 376.005865281206894120659401340373818),
            BOOST_MATH_BIG_CONSTANT(T, 113, 629.95369438888946233003926191755125),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1568.35771983533158591604513304269098),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1646.02452040831961063640827116581021),
            BOOST_MATH_BIG_CONSTANT(T, 113, 2299.96860633240298708910425594484895),
            BOOST_MATH_BIG_CONSTANT(T, 113, 1222.73204392037452750381340219906374),
            BOOST_MATH_BIG_CONSTANT(T, 113, 799.359797306084372350264298361110448),
            BOOST_MATH_BIG_CONSTANT(T, 113, 72.7415265778588087243442792401576737),
         };
         result = Y + tools::evaluate_polynomial(P, T(1 / z)) / tools::evaluate_polynomial(Q, T(1 / z));
         result *= exp(-z * z) / z;
      }
   }
   else
   {
      //
      // Any value of z larger than 110 will underflow to zero:
      //
      result = 0;
      invert = !invert;
   }

   if(invert)
   {
      result = 1 - result;
   }

   return result;
} // template <class T, class Lanczos>T erf_imp(T z, bool invert, const Lanczos& l, const mpl::int_<113>& t)

template <class T, class Policy, class tag>
struct erf_initializer
{
   struct init
   {
      init()
      {
         do_init(tag());
      }
      static void do_init(const mpl::int_<0>&){}
      static void do_init(const mpl::int_<53>&)
      {
         boost::math::erf(static_cast<T>(1e-12), Policy());
         boost::math::erf(static_cast<T>(0.25), Policy());
         boost::math::erf(static_cast<T>(1.25), Policy());
         boost::math::erf(static_cast<T>(2.25), Policy());
         boost::math::erf(static_cast<T>(4.25), Policy());
         boost::math::erf(static_cast<T>(5.25), Policy());
      }
      static void do_init(const mpl::int_<64>&)
      {
         boost::math::erf(static_cast<T>(1e-12), Policy());
         boost::math::erf(static_cast<T>(0.25), Policy());
         boost::math::erf(static_cast<T>(1.25), Policy());
         boost::math::erf(static_cast<T>(2.25), Policy());
         boost::math::erf(static_cast<T>(4.25), Policy());
         boost::math::erf(static_cast<T>(5.25), Policy());
      }
      static void do_init(const mpl::int_<113>&)
      {
         boost::math::erf(static_cast<T>(1e-22), Policy());
         boost::math::erf(static_cast<T>(0.25), Policy());
         boost::math::erf(static_cast<T>(1.25), Policy());
         boost::math::erf(static_cast<T>(2.125), Policy());
         boost::math::erf(static_cast<T>(2.75), Policy());
         boost::math::erf(static_cast<T>(3.25), Policy());
         boost::math::erf(static_cast<T>(5.25), Policy());
         boost::math::erf(static_cast<T>(7.25), Policy());
         boost::math::erf(static_cast<T>(11.25), Policy());
         boost::math::erf(static_cast<T>(12.5), Policy());
      }
      void force_instantiate()const{}
   };
   static const init initializer;
   static void force_instantiate()
   {
      initializer.force_instantiate();
   }
};

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

} // namespace detail

template <class T, class Policy>
inline typename tools::promote_args<T>::type erf(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;

   BOOST_MATH_INSTRUMENT_CODE("result_type = " << typeid(result_type).name());
   BOOST_MATH_INSTRUMENT_CODE("value_type = " << typeid(value_type).name());
   BOOST_MATH_INSTRUMENT_CODE("precision_type = " << typeid(precision_type).name());

   typedef typename mpl::if_<
      mpl::less_equal<precision_type, mpl::int_<0> >,
      mpl::int_<0>,
      typename mpl::if_<
         mpl::less_equal<precision_type, mpl::int_<53> >,
         mpl::int_<53>,  // double
         typename mpl::if_<
            mpl::less_equal<precision_type, mpl::int_<64> >,
            mpl::int_<64>, // 80-bit long double
            typename mpl::if_<
               mpl::less_equal<precision_type, mpl::int_<113> >,
               mpl::int_<113>, // 128-bit long double
               mpl::int_<0> // too many bits, use generic version.
            >::type
         >::type
      >::type
   >::type tag_type;

   BOOST_MATH_INSTRUMENT_CODE("tag_type = " << typeid(tag_type).name());

   detail::erf_initializer<value_type, forwarding_policy, tag_type>::force_instantiate(); // Force constants to be initialized before main

   return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::erf_imp(
      static_cast<value_type>(z),
      false,
      forwarding_policy(),
      tag_type()), "boost::math::erf<%1%>(%1%, %1%)");
}

template <class T, class Policy>
inline typename tools::promote_args<T>::type erfc(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;

   BOOST_MATH_INSTRUMENT_CODE("result_type = " << typeid(result_type).name());
   BOOST_MATH_INSTRUMENT_CODE("value_type = " << typeid(value_type).name());
   BOOST_MATH_INSTRUMENT_CODE("precision_type = " << typeid(precision_type).name());

   typedef typename mpl::if_<
      mpl::less_equal<precision_type, mpl::int_<0> >,
      mpl::int_<0>,
      typename mpl::if_<
         mpl::less_equal<precision_type, mpl::int_<53> >,
         mpl::int_<53>,  // double
         typename mpl::if_<
            mpl::less_equal<precision_type, mpl::int_<64> >,
            mpl::int_<64>, // 80-bit long double
            typename mpl::if_<
               mpl::less_equal<precision_type, mpl::int_<113> >,
               mpl::int_<113>, // 128-bit long double
               mpl::int_<0> // too many bits, use generic version.
            >::type
         >::type
      >::type
   >::type tag_type;

   BOOST_MATH_INSTRUMENT_CODE("tag_type = " << typeid(tag_type).name());

   detail::erf_initializer<value_type, forwarding_policy, tag_type>::force_instantiate(); // Force constants to be initialized before main

   return policies::checked_narrowing_cast<result_type, forwarding_policy>(detail::erf_imp(
      static_cast<value_type>(z),
      true,
      forwarding_policy(),
      tag_type()), "boost::math::erfc<%1%>(%1%, %1%)");
}

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

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

} // namespace math
} // namespace boost

#include <boost/math/special_functions/detail/erf_inv.hpp>

#endif // BOOST_MATH_SPECIAL_ERF_HPP


code:
//  boost/chrono/process_cpu_clocks.hpp  -----------------------------------------------------------//

//  Copyright 2009-2011 Vicente J. Botet Escriba
//  Copyright (c) Microsoft Corporation 2014

//  Distributed under the Boost Software License, Version 1.0.
//  See http://www.boost.org/LICENSE_1_0.txt

//  See http://www.boost.org/libs/system for documentation.

#ifndef BOOST_CHRONO_PROCESS_CPU_CLOCKS_HPP
#define BOOST_CHRONO_PROCESS_CPU_CLOCKS_HPP

#include <boost/chrono/config.hpp>

#if defined(BOOST_CHRONO_HAS_PROCESS_CLOCKS)

#include <boost/chrono/duration.hpp>
#include <boost/chrono/time_point.hpp>
#include <boost/operators.hpp>
#include <boost/chrono/detail/system.hpp>
#include <iostream>
#include <boost/type_traits/common_type.hpp>
#include <boost/chrono/clock_string.hpp>

#ifndef BOOST_CHRONO_HEADER_ONLY
#include <boost/config/abi_prefix.hpp> // must be the last #include
#endif

namespace boost { namespace chrono {

    class BOOST_CHRONO_DECL process_real_cpu_clock {
    public:
        typedef nanoseconds                          duration;
        typedef duration::rep                        rep;
        typedef duration::period                     period;
        typedef chrono::time_point<process_real_cpu_clock>    time_point;
        BOOST_STATIC_CONSTEXPR bool is_steady =             true;

        static BOOST_CHRONO_INLINE time_point now() BOOST_NOEXCEPT;
#if !defined BOOST_CHRONO_DONT_PROVIDE_HYBRID_ERROR_HANDLING
        static BOOST_CHRONO_INLINE time_point now(system::error_code & ec );
#endif
    };

#if ! BOOST_OS_WINDOWS || BOOST_PLAT_WINDOWS_DESKTOP
    class BOOST_CHRONO_DECL process_user_cpu_clock {
    public:
        typedef nanoseconds                          duration;
        typedef duration::rep                        rep;
        typedef duration::period                     period;
        typedef chrono::time_point<process_user_cpu_clock>    time_point;
        BOOST_STATIC_CONSTEXPR bool is_steady =             true;

        static BOOST_CHRONO_INLINE time_point now() BOOST_NOEXCEPT;
#if !defined BOOST_CHRONO_DONT_PROVIDE_HYBRID_ERROR_HANDLING
        static BOOST_CHRONO_INLINE time_point now(system::error_code & ec );
#endif
    };

    class BOOST_CHRONO_DECL process_system_cpu_clock {
    public:
        typedef nanoseconds                          duration;
        typedef duration::rep                        rep;
        typedef duration::period                     period;
        typedef chrono::time_point<process_system_cpu_clock>    time_point;
        BOOST_STATIC_CONSTEXPR bool is_steady =             true;

        static BOOST_CHRONO_INLINE time_point now() BOOST_NOEXCEPT;
#if !defined BOOST_CHRONO_DONT_PROVIDE_HYBRID_ERROR_HANDLING
        static BOOST_CHRONO_INLINE time_point now(system::error_code & ec );
#endif
    };
#endif

        template <typename Rep>
        struct process_times
            : arithmetic<process_times<Rep>,
            multiplicative<process_times<Rep>, Rep,
            less_than_comparable<process_times<Rep> > > >
        {
              //typedef process_real_cpu_clock::rep rep;
              typedef Rep rep;
            process_times()
                : real(0)
                , user(0)
                , system(0){}

#if ! defined BOOST_CHRONO_DONT_PROVIDES_DEPRECATED_IO_SINCE_V2_0_0
            template <typename Rep2>
            explicit process_times(
                Rep2 r)
                : real(r)
                , user(r)
                , system(r){}
#endif
            template <typename Rep2>
            explicit process_times(
                process_times<Rep2> const& rhs)
                : real(rhs.real)
                , user(rhs.user)
                , system(rhs.system){}
            process_times(
                rep r,
                rep u,
                rep s)
                : real(r)
                , user(u)
                , system(s){}

            rep   real;    // real (i.e wall clock) time
            rep   user;    // user cpu time
            rep system;  // system cpu time

#if ! defined BOOST_CHRONO_DONT_PROVIDES_DEPRECATED_IO_SINCE_V2_0_0
            operator rep() const
            {
              return real;
            }
#endif
            template <typename Rep2>
            bool operator==(process_times<Rep2> const& rhs) {
                return (real==rhs.real &&
                        user==rhs.user &&
                        system==rhs.system);
            }

            process_times& operator+=(
                process_times const& rhs)
            {
                real+=rhs.real;
                user+=rhs.user;
                system+=rhs.system;
                return *this;
            }
            process_times& operator-=(
                process_times const& rhs)
            {
                real-=rhs.real;
                user-=rhs.user;
                system-=rhs.system;
                return *this;
            }
            process_times& operator*=(
                process_times const& rhs)
            {
                real*=rhs.real;
                user*=rhs.user;
                system*=rhs.system;
                return *this;
            }
            process_times& operator*=(rep const& rhs)
            {
                real*=rhs;
                user*=rhs;
                system*=rhs;
                return *this;
            }
            process_times& operator/=(process_times const& rhs)
            {
                real/=rhs.real;
                user/=rhs.user;
                system/=rhs.system;
                return *this;
            }
            process_times& operator/=(rep const& rhs)
            {
                real/=rhs;
                user/=rhs;
                system/=rhs;
                return *this;
            }
            bool operator<(process_times const & rhs) const
            {
                if (real < rhs.real) return true;
                if (real > rhs.real) return false;
                if (user < rhs.user) return true;
                if (user > rhs.user) return false;
                if (system < rhs.system) return true;
                else return false;
            }

            template <class CharT, class Traits>
            void print(std::basic_ostream<CharT, Traits>& os) const
            {
                os <<  "{"<< real <<";"<< user <<";"<< system << "}";
            }

            template <class CharT, class Traits>
            void read(std::basic_istream<CharT, Traits>& is)
            {
                typedef std::istreambuf_iterator<CharT, Traits> in_iterator;
                in_iterator i(is);
                in_iterator e;
                if (i == e || *i++ != '{')  // mandatory '{'
                {
                    is.setstate(is.failbit | is.eofbit);
                    return;
                }
                CharT x,y,z;
                is >> real >> x >> user >> y >> system >> z;
                if (!is.good() || (x != ';')|| (y != ';')|| (z != '}'))
                {
                    is.setstate(is.failbit);
                }
            }
        };
}
template <class Rep1, class Rep2>
struct common_type<
  chrono::process_times<Rep1>,
  chrono::process_times<Rep2>
>
{
  typedef chrono::process_times<typename common_type<Rep1, Rep2>::type> type;
};

template <class Rep1, class Rep2>
struct common_type<
  chrono::process_times<Rep1>,
  Rep2
>
{
  typedef chrono::process_times<typename common_type<Rep1, Rep2>::type> type;
};

template <class Rep1, class Rep2>
struct common_type<
  Rep1,
  chrono::process_times<Rep2>
>
{
  typedef chrono::process_times<typename common_type<Rep1, Rep2>::type> type;
};

namespace chrono
{
  template <class Rep1, class Period1, class Rep2, class Period2>
  inline BOOST_CONSTEXPR
  bool
  operator==(const duration<process_times<Rep1>, Period1>& lhs,
        const duration<process_times<Rep2>, Period2>& rhs)
  {
      return boost::chrono::detail::duration_eq<
          duration<Rep1, Period1>, duration<Rep2, Period2>
        >()(duration<Rep1, Period1>(lhs.count().real), duration<Rep2, Period2>(rhs.count().real));
  }

  template <class Rep1, class Period1, class Rep2, class Period2>
  inline BOOST_CONSTEXPR
  bool
  operator==(const duration<process_times<Rep1>, Period1>& lhs,
        const duration<Rep2, Period2>& rhs)
  {
      return boost::chrono::detail::duration_eq<
          duration<Rep1, Period1>, duration<Rep2, Period2> >()(duration<Rep1, Period1>(lhs.count().real), rhs);
  }

  template <class Rep1, class Period1, class Rep2, class Period2>
  inline BOOST_CONSTEXPR
  bool
  operator==(const duration<Rep1, Period1>& lhs,
        const duration<process_times<Rep2>, Period2>& rhs)
  {
      return rhs == lhs;
  }

  // Duration <

  template <class Rep1, class Period1, class Rep2, class Period2>
  inline BOOST_CONSTEXPR
  bool
  operator< (const duration<process_times<Rep1>, Period1>& lhs,
        const duration<Rep2, Period2>& rhs)
  {
      return boost::chrono::detail::duration_lt<
        duration<Rep1, Period1>, duration<Rep2, Period2> >()(duration<Rep1, Period1>(lhs.count().real), rhs);
  }

  template <class Rep1, class Period1, class Rep2, class Period2>
  inline BOOST_CONSTEXPR
  bool
  operator< (const duration<Rep1, Period1>& lhs,
        const duration<process_times<Rep2>, Period2>& rhs)
  {
      return boost::chrono::detail::duration_lt<
        duration<Rep1, Period1>, duration<Rep2, Period2> >()(lhs, duration<Rep2, Period2>(rhs.count().real));
  }

  template <class Rep1, class Period1, class Rep2, class Period2>
  inline BOOST_CONSTEXPR
  bool
  operator< (const duration<process_times<Rep1>, Period1>& lhs,
        const duration<process_times<Rep2>, Period2>& rhs)
  {
    return boost::chrono::detail::duration_lt<
        duration<Rep1, Period1>, duration<Rep2, Period2>
      >()(duration<Rep1, Period1>(lhs.count().real), duration<Rep2, Period2>(rhs.count().real));
  }

  typedef process_times<nanoseconds::rep> process_cpu_clock_times;
#if ! BOOST_OS_WINDOWS || BOOST_PLAT_WINDOWS_DESKTOP
    class BOOST_CHRONO_DECL process_cpu_clock
    {
    public:

        typedef process_cpu_clock_times times;
        typedef boost::chrono::duration<times,  nano>                duration;
        typedef duration::rep                       rep;
        typedef duration::period                    period;
        typedef chrono::time_point<process_cpu_clock>  time_point;
        BOOST_STATIC_CONSTEXPR bool is_steady =           true;

        static BOOST_CHRONO_INLINE time_point now() BOOST_NOEXCEPT;
#if !defined BOOST_CHRONO_DONT_PROVIDE_HYBRID_ERROR_HANDLING
        static BOOST_CHRONO_INLINE time_point now(system::error_code & ec );
#endif
    };
#endif

    template <class CharT, class Traits, typename Rep>
    std::basic_ostream<CharT, Traits>&
    operator<<(std::basic_ostream<CharT, Traits>& os,
        process_times<Rep> const& rhs)
    {
        rhs.print(os);
        return os;
    }

    template <class CharT, class Traits, typename Rep>
    std::basic_istream<CharT, Traits>&
    operator>>(std::basic_istream<CharT, Traits>& is,
        process_times<Rep>& rhs)
    {
        rhs.read(is);
        return is;
    }

    template <typename Rep>
    struct duration_values<process_times<Rep> >
    {
        typedef process_times<Rep> Res;
    public:
        static Res zero()
        {
            return Res();
        }
        static Res max BOOST_PREVENT_MACRO_SUBSTITUTION ()
        {
          return Res((std::numeric_limits<Rep>::max)(),
                      (std::numeric_limits<Rep>::max)(),
                      (std::numeric_limits<Rep>::max)());
        }
        static Res min BOOST_PREVENT_MACRO_SUBSTITUTION ()
        {
          return Res((std::numeric_limits<Rep>::min)(),
                      (std::numeric_limits<Rep>::min)(),
                      (std::numeric_limits<Rep>::min)());
        }
    };

    template<class CharT>
    struct clock_string<process_real_cpu_clock, CharT>
    {
      static std::basic_string<CharT> name()
      {
        static const CharT
            u[] =
                { 'p', 'r', 'o', 'c', 'e', 's', 's', '_', 'r', 'e', 'a', 'l', '_', 'c', 'l', 'o', 'c', 'k' };
        static const std::basic_string<CharT> str(u, u + sizeof(u)
            / sizeof(u[0]));
        return str;
      }
      static std::basic_string<CharT> since()
      {
        const CharT
            u[] =
                { ' ', 's', 'i', 'n', 'c', 'e', ' ', 'p', 'r', 'o', 'c', 'e', 's', 's', ' ', 's', 't', 'a', 'r', 't', '-', 'u', 'p' };
        const std::basic_string<CharT> str(u, u + sizeof(u) / sizeof(u[0]));
        return str;
      }
    };

#if ! BOOST_OS_WINDOWS || BOOST_PLAT_WINDOWS_DESKTOP
    template<class CharT>
    struct clock_string<process_user_cpu_clock, CharT>
    {
      static std::basic_string<CharT> name()
      {
        static const CharT
            u[] =
                { 'p', 'r', 'o', 'c', 'e', 's', 's', '_', 'u', 's', 'e', 'r', '_', 'c', 'l', 'o', 'c', 'k' };
        static const std::basic_string<CharT> str(u, u + sizeof(u)
            / sizeof(u[0]));
        return str;
      }
      static std::basic_string<CharT> since()
      {
        const CharT
            u[] =
                { ' ', 's', 'i', 'n', 'c', 'e', ' ', 'p', 'r', 'o', 'c', 'e', 's', 's', ' ', 's', 't', 'a', 'r', 't', '-', 'u', 'p' };
        const std::basic_string<CharT> str(u, u + sizeof(u) / sizeof(u[0]));
        return str;
      }
    };

    template<class CharT>
    struct clock_string<process_system_cpu_clock, CharT>
    {
      static std::basic_string<CharT> name()
      {
        static const CharT
            u[] =
                { 'p', 'r', 'o', 'c', 'e', 's', 's', '_', 's', 'y', 's', 't', 'e', 'm', '_', 'c', 'l', 'o', 'c', 'k' };
        static const std::basic_string<CharT> str(u, u + sizeof(u)
            / sizeof(u[0]));
        return str;
      }
      static std::basic_string<CharT> since()
      {
        const CharT
            u[] =
                { ' ', 's', 'i', 'n', 'c', 'e', ' ', 'p', 'r', 'o', 'c', 'e', 's', 's', ' ', 's', 't', 'a', 'r', 't', '-', 'u', 'p' };
        const std::basic_string<CharT> str(u, u + sizeof(u) / sizeof(u[0]));
        return str;
      }
    };

    template<class CharT>
    struct clock_string<process_cpu_clock, CharT>
    {
      static std::basic_string<CharT> name()
      {
        static const CharT u[] =
        { 'p', 'r', 'o', 'c', 'e', 's', 's', '_', 'c', 'l', 'o', 'c', 'k' };
        static const std::basic_string<CharT> str(u, u + sizeof(u)
            / sizeof(u[0]));
        return str;
      }
      static std::basic_string<CharT> since()
      {
        const CharT
            u[] =
                { ' ', 's', 'i', 'n', 'c', 'e', ' ', 'p', 'r', 'o', 'c', 'e', 's', 's', ' ', 's', 't', 'a', 'r', 't', '-', 'u', 'p' };
        const std::basic_string<CharT> str(u, u + sizeof(u) / sizeof(u[0]));
        return str;
      }
    };
#endif

} // namespace chrono
} // namespace boost

namespace std {

    template <typename Rep>
    struct numeric_limits<boost::chrono::process_times<Rep> >
    {
        typedef boost::chrono::process_times<Rep> Res;

        public:
        static const bool is_specialized = true;
        static Res min BOOST_PREVENT_MACRO_SUBSTITUTION ()
        {
          return Res((std::numeric_limits<Rep>::min)(),
                      (std::numeric_limits<Rep>::min)(),
                      (std::numeric_limits<Rep>::min)());
        }
        static Res max BOOST_PREVENT_MACRO_SUBSTITUTION ()
        {
          return Res((std::numeric_limits<Rep>::max)(),
                      (std::numeric_limits<Rep>::max)(),
                      (std::numeric_limits<Rep>::max)());
        }
        static Res lowest() throw()
        {
            return (min)();
        }
        static const int digits = std::numeric_limits<Rep>::digits+
                        std::numeric_limits<Rep>::digits+
                        std::numeric_limits<Rep>::digits;
        static const int digits10 = std::numeric_limits<Rep>::digits10+
                        std::numeric_limits<Rep>::digits10+
                        std::numeric_limits<Rep>::digits10;
        static const bool is_signed = Rep::is_signed;
        static const bool is_integer = Rep::is_integer;
        static const bool is_exact = Rep::is_exact;
        static const int radix = 0;
        //~ static Res epsilon() throw() { return 0; }
        //~ static Res round_error() throw() { return 0; }
        //~ static const int min_exponent = 0;
        //~ static const int min_exponent10 = 0;
        //~ static const int max_exponent = 0;
        //~ static const int max_exponent10 = 0;
        //~ static const bool has_infinity = false;
        //~ static const bool has_quiet_NaN = false;
        //~ static const bool has_signaling_NaN = false;
        //~ static const float_denorm_style has_denorm = denorm_absent;
        //~ static const bool has_denorm_loss = false;
        //~ static Res infinity() throw() { return 0; }
        //~ static Res quiet_NaN() throw() { return 0; }
        //~ static Res signaling_NaN() throw() { return 0; }
        //~ static Res denorm_min() throw() { return 0; }
        //~ static const bool is_iec559 = false;
        //~ static const bool is_bounded = true;
        //~ static const bool is_modulo = false;
        //~ static const bool traps = false;
        //~ static const bool tinyness_before = false;
        //~ static const float_round_style round_style = round_toward_zero;

    };
}

#ifndef BOOST_CHRONO_HEADER_ONLY
#include <boost/config/abi_suffix.hpp> // pops abi_prefix.hpp pragmas
#else
#include <boost/chrono/detail/inlined/process_cpu_clocks.hpp>
#endif
#endif

#endif  // BOOST_CHRONO_PROCESS_CPU_CLOCKS_HPP

license: mit


code:
#ifndef BOOST_MPL_AUX_LAMBDA_SUPPORT_HPP_INCLUDED
#define BOOST_MPL_AUX_LAMBDA_SUPPORT_HPP_INCLUDED

// Copyright Aleksey Gurtovoy 2001-2004
//
// Distributed under 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)
//
// See http://www.boost.org/libs/mpl for documentation.

// $Id$
// $Date$
// $Revision$

#include <boost/mpl/aux_/config/lambda.hpp>

#if !defined(BOOST_MPL_CFG_NO_FULL_LAMBDA_SUPPORT)

#   define BOOST_MPL_AUX_LAMBDA_SUPPORT_SPEC(i, name, params) /**/
#   define BOOST_MPL_AUX_LAMBDA_SUPPORT(i,name,params) /**/

#else

#   include <boost/mpl/int_fwd.hpp>
#   include <boost/mpl/aux_/yes_no.hpp>
#   include <boost/mpl/aux_/na_fwd.hpp>
#   include <boost/mpl/aux_/preprocessor/params.hpp>
#   include <boost/mpl/aux_/preprocessor/enum.hpp>
#   include <boost/mpl/aux_/config/msvc.hpp>
#   include <boost/mpl/aux_/config/workaround.hpp>

#   include <boost/preprocessor/tuple/to_list.hpp>
#   include <boost/preprocessor/list/for_each_i.hpp>
#   include <boost/preprocessor/inc.hpp>
#   include <boost/preprocessor/cat.hpp>

#   define BOOST_MPL_AUX_LAMBDA_SUPPORT_ARG_TYPEDEF_FUNC(R,typedef_,i,param) \
    typedef_ param BOOST_PP_CAT(arg,BOOST_PP_INC(i)); \
    /**/

// agurt, 07/mar/03: restore an old revision for the sake of SGI MIPSpro C++
#if BOOST_WORKAROUND(__EDG_VERSION__, <= 238)

#   define BOOST_MPL_AUX_LAMBDA_SUPPORT(i, name, params) \
    typedef BOOST_MPL_AUX_ADL_BARRIER_NAMESPACE::int_<i> arity; \
    BOOST_PP_LIST_FOR_EACH_I_R( \
          1 \
        , BOOST_MPL_AUX_LAMBDA_SUPPORT_ARG_TYPEDEF_FUNC \
        , typedef \
        , BOOST_PP_TUPLE_TO_LIST(i,params) \
        ) \
    struct rebind \
    { \
        template< BOOST_MPL_PP_PARAMS(i,typename U) > struct apply \
            : name< BOOST_MPL_PP_PARAMS(i,U) > \
        { \
        }; \
    }; \
    /**/

#   define BOOST_MPL_AUX_LAMBDA_SUPPORT_SPEC(i, name, params) \
    BOOST_MPL_AUX_LAMBDA_SUPPORT(i, name, params) \
    /**/

#elif BOOST_WORKAROUND(__EDG_VERSION__, <= 244) && !defined(BOOST_INTEL_CXX_VERSION)
// agurt, 18/jan/03: old EDG-based compilers actually enforce 11.4 para 9
// (in strict mode), so we have to provide an alternative to the
// MSVC-optimized implementation

#   define BOOST_MPL_AUX_LAMBDA_SUPPORT_SPEC(i, name, params) \
    typedef BOOST_MPL_AUX_ADL_BARRIER_NAMESPACE::int_<i> arity; \
    BOOST_PP_LIST_FOR_EACH_I_R( \
          1 \
        , BOOST_MPL_AUX_LAMBDA_SUPPORT_ARG_TYPEDEF_FUNC \
        , typedef \
        , BOOST_PP_TUPLE_TO_LIST(i,params) \
        ) \
    struct rebind; \
/**/

#   define BOOST_MPL_AUX_LAMBDA_SUPPORT(i, name, params) \
    BOOST_MPL_AUX_LAMBDA_SUPPORT_SPEC(i, name, params) \
}; \
template< BOOST_MPL_PP_PARAMS(i,typename T) > \
struct name<BOOST_MPL_PP_PARAMS(i,T)>::rebind \
{ \
    template< BOOST_MPL_PP_PARAMS(i,typename U) > struct apply \
        : name< BOOST_MPL_PP_PARAMS(i,U) > \
    { \
    }; \
/**/

#else // __EDG_VERSION__

namespace boost { namespace mpl { namespace aux {
template< typename T > struct has_rebind_tag;
}}}

#   define BOOST_MPL_AUX_LAMBDA_SUPPORT_SPEC(i, name, params) \
    typedef BOOST_MPL_AUX_ADL_BARRIER_NAMESPACE::int_<i> arity; \
    BOOST_PP_LIST_FOR_EACH_I_R( \
          1 \
        , BOOST_MPL_AUX_LAMBDA_SUPPORT_ARG_TYPEDEF_FUNC \
        , typedef \
        , BOOST_PP_TUPLE_TO_LIST(i,params) \
        ) \
    friend class BOOST_PP_CAT(name,_rebind); \
    typedef BOOST_PP_CAT(name,_rebind) rebind; \
/**/

#if BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x610))
#   define BOOST_MPL_AUX_LAMBDA_SUPPORT_HAS_REBIND(i, name, params) \
template< BOOST_MPL_PP_PARAMS(i,typename T) > \
::boost::mpl::aux::yes_tag operator|( \
      ::boost::mpl::aux::has_rebind_tag<int> \
    , name<BOOST_MPL_PP_PARAMS(i,T)>* \
    ); \
::boost::mpl::aux::no_tag operator|( \
      ::boost::mpl::aux::has_rebind_tag<int> \
    , name< BOOST_MPL_PP_ENUM(i,::boost::mpl::na) >* \
    ); \
/**/
#elif !BOOST_WORKAROUND(BOOST_MSVC, < 1300)
#   define BOOST_MPL_AUX_LAMBDA_SUPPORT_HAS_REBIND(i, name, params) \
template< BOOST_MPL_PP_PARAMS(i,typename T) > \
::boost::mpl::aux::yes_tag operator|( \
      ::boost::mpl::aux::has_rebind_tag<int> \
    , ::boost::mpl::aux::has_rebind_tag< name<BOOST_MPL_PP_PARAMS(i,T)> >* \
    ); \
/**/
#else
#   define BOOST_MPL_AUX_LAMBDA_SUPPORT_HAS_REBIND(i, name, params) /**/
#endif

#   if !defined(__BORLANDC__)
#   define BOOST_MPL_AUX_LAMBDA_SUPPORT(i, name, params) \
    BOOST_MPL_AUX_LAMBDA_SUPPORT_SPEC(i, name, params) \
}; \
BOOST_MPL_AUX_LAMBDA_SUPPORT_HAS_REBIND(i, name, params) \
class BOOST_PP_CAT(name,_rebind) \
{ \
 public: \
    template< BOOST_MPL_PP_PARAMS(i,typename U) > struct apply \
        : name< BOOST_MPL_PP_PARAMS(i,U) > \
    { \
    }; \
/**/
#   else
#   define BOOST_MPL_AUX_LAMBDA_SUPPORT(i, name, params) \
    BOOST_MPL_AUX_LAMBDA_SUPPORT_SPEC(i, name, params) \
}; \
BOOST_MPL_AUX_LAMBDA_SUPPORT_HAS_REBIND(i, name, params) \
class BOOST_PP_CAT(name,_rebind) \
{ \
 public: \
    template< BOOST_MPL_PP_PARAMS(i,typename U) > struct apply \
    { \
        typedef typename name< BOOST_MPL_PP_PARAMS(i,U) >::type type; \
    }; \
/**/
#   endif // __BORLANDC__

#endif // __EDG_VERSION__

#endif // BOOST_MPL_CFG_NO_FULL_LAMBDA_SUPPORT

#endif // BOOST_MPL_AUX_LAMBDA_SUPPORT_HPP_INCLUDED


code:
/////////1/////////2/////////3/////////4/////////5/////////6/////////7/////////8
// basic_binary_iprimitive.ipp:

// (C) Copyright 2002 Robert Ramey - http://www.rrsd.com .
// Use, modification and distribution is 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)

//  See http://www.boost.org for updates, documentation, and revision history.

#include <boost/assert.hpp>
#include <cstddef> // size_t, NULL
#include <cstring> // memcpy

#include <boost/config.hpp>
#if defined(BOOST_NO_STDC_NAMESPACE)
namespace std{
    using ::size_t;
    using ::memcpy;
} // namespace std
#endif

#include <boost/serialization/throw_exception.hpp>
#include <boost/core/no_exceptions_support.hpp>
#include <boost/archive/archive_exception.hpp>
#include <boost/archive/basic_binary_iprimitive.hpp>

namespace boost {
namespace archive {

//////////////////////////////////////////////////////////////////////
// implementation of basic_binary_iprimitive

template<class Archive, class Elem, class Tr>
BOOST_ARCHIVE_OR_WARCHIVE_DECL void
basic_binary_iprimitive<Archive, Elem, Tr>::init()
{
    // Detect  attempts to pass native binary archives across
    // incompatible platforms. This is not fool proof but its
    // better than nothing.
    unsigned char size;
    this->This()->load(size);
    if(sizeof(int) != size)
        boost::serialization::throw_exception(
            archive_exception(
                archive_exception::incompatible_native_format,
                "size of int"
            )
        );
    this->This()->load(size);
    if(sizeof(long) != size)
        boost::serialization::throw_exception(
            archive_exception(
                archive_exception::incompatible_native_format,
                "size of long"
            )
        );
    this->This()->load(size);
    if(sizeof(float) != size)
        boost::serialization::throw_exception(
            archive_exception(
                archive_exception::incompatible_native_format,
                "size of float"
            )
        );
    this->This()->load(size);
    if(sizeof(double) != size)
        boost::serialization::throw_exception(
            archive_exception(
                archive_exception::incompatible_native_format,
                "size of double"
            )
        );

    // for checking endian
    int i;
    this->This()->load(i);
    if(1 != i)
        boost::serialization::throw_exception(
            archive_exception(
                archive_exception::incompatible_native_format,
                "endian setting"
            )
        );
}

template<class Archive, class Elem, class Tr>
BOOST_ARCHIVE_OR_WARCHIVE_DECL void
basic_binary_iprimitive<Archive, Elem, Tr>::load(wchar_t * ws)
{
    std::size_t l; // number of wchar_t !!!
    this->This()->load(l);
    load_binary(ws, l * sizeof(wchar_t) / sizeof(char));
    ws[l] = L'\0';
}

template<class Archive, class Elem, class Tr>
BOOST_ARCHIVE_OR_WARCHIVE_DECL void
basic_binary_iprimitive<Archive, Elem, Tr>::load(std::string & s)
{
    std::size_t l;
    this->This()->load(l);
    // borland de-allocator fixup
    #if BOOST_WORKAROUND(_RWSTD_VER, BOOST_TESTED_AT(20101))
    if(NULL != s.data())
    #endif
        s.resize(l);
    // note breaking a rule here - could be a problem on some platform
    if(0 < l)
        load_binary(&(*s.begin()), l);
}

#ifndef BOOST_NO_CWCHAR
template<class Archive, class Elem, class Tr>
BOOST_ARCHIVE_OR_WARCHIVE_DECL void
basic_binary_iprimitive<Archive, Elem, Tr>::load(char * s)
{
    std::size_t l;
    this->This()->load(l);
    load_binary(s, l);
    s[l] = '\0';
}
#endif

#ifndef BOOST_NO_STD_WSTRING
template<class Archive, class Elem, class Tr>
BOOST_ARCHIVE_OR_WARCHIVE_DECL void
basic_binary_iprimitive<Archive, Elem, Tr>::load(std::wstring & ws)
{
    std::size_t l;
    this->This()->load(l);
    // borland de-allocator fixup
    #if BOOST_WORKAROUND(_RWSTD_VER, BOOST_TESTED_AT(20101))
    if(NULL != ws.data())
    #endif
        ws.resize(l);
    // note breaking a rule here - is could be a problem on some platform
    load_binary(const_cast<wchar_t *>(ws.data()), l * sizeof(wchar_t) / sizeof(char));
}
#endif

template<class Archive, class Elem, class Tr>
BOOST_ARCHIVE_OR_WARCHIVE_DECL
basic_binary_iprimitive<Archive, Elem, Tr>::basic_binary_iprimitive(
    std::basic_streambuf<Elem, Tr> & sb,
    bool no_codecvt
) :
#ifndef BOOST_NO_STD_LOCALE
    m_sb(sb),
    codecvt_null_facet(1),
    locale_saver(m_sb),
    archive_locale(sb.getloc(), & codecvt_null_facet)
{
    if(! no_codecvt){
        m_sb.pubsync();
        m_sb.pubimbue(archive_locale);
    }
}
#else
    m_sb(sb)
{}
#endif

// scoped_ptr requires that g be a complete type at time of
// destruction so define destructor here rather than in the header
template<class Archive, class Elem, class Tr>
BOOST_ARCHIVE_OR_WARCHIVE_DECL
basic_binary_iprimitive<Archive, Elem, Tr>::~basic_binary_iprimitive(){}

} // namespace archive
} // namespace boost