boost/multiprecision/float128.hpp

///////////////////////////////////////////////////////////////
//  Copyright 2013 John Maddock. 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_

#ifndef BOOST_MP_FLOAT128_HPP
#define BOOST_MP_FLOAT128_HPP

#include <boost/config.hpp>
#include <boost/scoped_array.hpp>
#include <boost/functional/hash.hpp>
#include <boost/multiprecision/number.hpp>

#if defined(BOOST_INTEL) && !defined(BOOST_MP_USE_FLOAT128) && !defined(BOOST_MP_USE_QUAD)
#  if defined(BOOST_INTEL_CXX_VERSION) && (BOOST_INTEL_CXX_VERSION >= 1310) && defined(__GNUC__)
#    if (__GNUC__ > 4) || ((__GNUC__ == 4) && (__GNUC_MINOR__ >= 6))
#      define BOOST_MP_USE_FLOAT128
#    endif
#  endif

#  ifndef BOOST_MP_USE_FLOAT128
#    define BOOST_MP_USE_QUAD
#  endif
#endif

#if defined(__GNUC__) && !defined(BOOST_MP_USE_FLOAT128) && !defined(BOOST_MP_USE_QUAD)
#  define BOOST_MP_USE_FLOAT128
#endif

#if !defined(BOOST_MP_USE_FLOAT128) && !defined(BOOST_MP_USE_QUAD)
#  error "Sorry compiler is neither GCC, not Intel, don't know how to configure this header."
#endif
#if defined(BOOST_MP_USE_FLOAT128) && defined(BOOST_MP_USE_QUAD)
#  error "Oh dear, both BOOST_MP_USE_FLOAT128 and BOOST_MP_USE_QUAD are defined, which one should I be using?"
#endif

#if defined(BOOST_MP_USE_FLOAT128)

extern "C" {
#include <quadmath.h>
}

typedef __float128 float128_type;

#elif defined(BOOST_MP_USE_QUAD)

#include <boost/multiprecision/detail/float_string_cvt.hpp>

typedef _Quad float128_type;

extern "C" {
_Quad __ldexpq(_Quad, int);
_Quad __frexpq(_Quad, int*);
_Quad __fabsq(_Quad);
_Quad __floorq(_Quad);
_Quad __ceilq(_Quad);
_Quad __sqrtq(_Quad);
_Quad __truncq(_Quad);
_Quad __expq(_Quad);
_Quad __powq(_Quad, _Quad);
_Quad __logq(_Quad);
_Quad __log10q(_Quad);
_Quad __sinq(_Quad);
_Quad __cosq(_Quad);
_Quad __tanq(_Quad);
_Quad __asinq(_Quad);
_Quad __acosq(_Quad);
_Quad __atanq(_Quad);
_Quad __sinhq(_Quad);
_Quad __coshq(_Quad);
_Quad __tanhq(_Quad);
_Quad __fmodq(_Quad, _Quad);
_Quad __atan2q(_Quad, _Quad);

#define ldexpq __ldexpq
#define frexpq __frexpq
#define fabsq __fabsq
#define floorq __floorq
#define ceilq __ceilq
#define sqrtq __sqrtq
#define truncq __truncq
#define expq __expq
#define powq __powq
#define logq __logq
#define log10q __log10q
#define sinq __sinq
#define cosq __cosq
#define tanq __tanq
#define asinq __asinq
#define acosq __acosq
#define atanq __atanq
#define sinhq __sinhq
#define coshq __coshq
#define tanhq __tanhq
#define fmodq __fmodq
#define atan2q __atan2q
}

inline _Quad isnanq(_Quad v)
{
   return v != v;
}
inline _Quad isinfq(_Quad v)
{
   return __fabsq(v) > 1.18973149535723176508575932662800702e4932Q;
}

#endif

namespace boost{
namespace multiprecision{
namespace backends{

struct float128_backend;

}

using backends::float128_backend;

template<>
struct number_category<backends::float128_backend> : public mpl::int_<number_kind_floating_point> {};
template<>
struct number_category<float128_type> : public mpl::int_<number_kind_floating_point> {};

typedef number<float128_backend, et_off> float128;

namespace backends{

struct float128_backend
{
   typedef mpl::list<signed char, short, int, long, boost::long_long_type>   signed_types;
   typedef mpl::list<unsigned char, unsigned short,
      unsigned int, unsigned long, boost::ulong_long_type>           unsigned_types;
   typedef mpl::list<float, double, long double>                 float_types;
   typedef int                                                   exponent_type;

private:
   float128_type m_value;
public:
   BOOST_CONSTEXPR float128_backend() BOOST_NOEXCEPT : m_value(0) {}
   BOOST_CONSTEXPR float128_backend(const float128_backend& o) BOOST_NOEXCEPT : m_value(o.m_value) {}
   float128_backend& operator = (const float128_backend& o) BOOST_NOEXCEPT
   {
      m_value = o.m_value;
      return *this;
   }
   template <class T>
   BOOST_CONSTEXPR float128_backend(const T& i, const typename enable_if_c<is_convertible<T, float128_type>::value>::type* = 0) BOOST_NOEXCEPT_IF(noexcept(std::declval<float128_type&>() = std::declval<const T&>()))
      : m_value(i) {}
   template <class T>
   typename enable_if_c<is_arithmetic<T>::value || is_convertible<T, float128_type>::value, float128_backend&>::type operator = (const T& i) BOOST_NOEXCEPT_IF(noexcept(std::declval<float128_type&>() = std::declval<const T&>()))
   {
      m_value = i;
      return *this;
   }
   float128_backend(long double const& f)
   {
      if(boost::math::isinf(f))
         m_value = (f < 0) ? -1.0Q / 0.0Q : 1.0Q / 0.0Q;
      else
         m_value = f;
   }
   float128_backend& operator=(long double const& f)
   {
      if(boost::math::isinf(f))
         m_value = (f < 0) ? -1.0Q / 0.0Q : 1.0Q / 0.0Q;
      else
         m_value = f;
      return *this;
   }
   float128_backend& operator = (const char* s)
   {
#ifndef BOOST_MP_USE_QUAD
      char* p_end;
      m_value = strtoflt128(s, &p_end);
      if(p_end - s != (std::ptrdiff_t)std::strlen(s))
      {
         BOOST_THROW_EXCEPTION(std::runtime_error("Unable to interpret input string as a floating point value"));
      }
#else
      boost::multiprecision::detail::convert_from_string(*this, s);
#endif
      return *this;
   }
   void swap(float128_backend& o) BOOST_NOEXCEPT
   {
      std::swap(m_value, o.value());
   }
   std::string str(std::streamsize digits, std::ios_base::fmtflags f)const
   {
#ifndef BOOST_MP_USE_QUAD
      char buf[100];
      boost::scoped_array<char> buf2;
      std::string format = "%";
      if(f & std::ios_base::showpos)
         format += "+";
      if(f & std::ios_base::showpoint)
         format += "#";
      format += ".*";
      if(digits == 0)
         digits = 36;
      format += "Q";
      if(f & std::ios_base::scientific)
         format += "e";
      else if(f & std::ios_base::fixed)
         format += "f";
      else
         format += "g";

      int v = quadmath_snprintf (buf, 100, format.c_str(), digits, m_value);

      if((v < 0) || (v >= 99))
      {
         int v_max = v;
         buf2.reset(new char[v+3]);
         v = quadmath_snprintf (&buf2[0], v_max + 3, format.c_str(), digits, m_value);
         if(v >= v_max + 3)
         {
            BOOST_THROW_EXCEPTION(std::runtime_error("Formatting of float128_type failed."));
         }
         return &buf2[0];
      }
      return buf;
#else
      return boost::multiprecision::detail::convert_to_string(*this, digits ? digits : 37, f);
#endif
   }
   void negate() BOOST_NOEXCEPT
   {
      m_value = -m_value;
   }
   int compare(const float128_backend& o)const
   {
      return m_value == o.m_value ? 0 : m_value < o.m_value ? -1 : 1;
   }
   template <class T>
   int compare(const T& i)const
   {
      return m_value == i ? 0 : m_value < i ? -1 : 1;
   }
   float128_type& value()
   {
      return m_value;
   }
   const float128_type& value()const
   {
      return m_value;
   }
};

inline void eval_add(float128_backend& result, const float128_backend& a)
{
   result.value() += a.value();
}
template <class A>
inline void eval_add(float128_backend& result, const A& a)
{
   result.value() += a;
}
inline void eval_subtract(float128_backend& result, const float128_backend& a)
{
   result.value() -= a.value();
}
template <class A>
inline void eval_subtract(float128_backend& result, const A& a)
{
   result.value() -= a;
}
inline void eval_multiply(float128_backend& result, const float128_backend& a)
{
   result.value() *= a.value();
}
template <class A>
inline void eval_multiply(float128_backend& result, const A& a)
{
   result.value() *= a;
}
inline void eval_divide(float128_backend& result, const float128_backend& a)
{
   result.value() /= a.value();
}
template <class A>
inline void eval_divide(float128_backend& result, const A& a)
{
   result.value() /= a;
}

inline void eval_add(float128_backend& result, const float128_backend& a, const float128_backend& b)
{
   result.value() = a.value() + b.value();
}
template <class A>
inline void eval_add(float128_backend& result, const float128_backend& a, const A& b)
{
   result.value() = a.value() + b;
}
inline void eval_subtract(float128_backend& result, const float128_backend& a, const float128_backend& b)
{
   result.value() = a.value() - b.value();
}
template <class A>
inline void eval_subtract(float128_backend& result, const float128_backend& a, const A& b)
{
   result.value() = a.value() - b;
}
template <class A>
inline void eval_subtract(float128_backend& result, const A& a, const float128_backend& b)
{
   result.value() = a - b.value();
}
inline void eval_multiply(float128_backend& result, const float128_backend& a, const float128_backend& b)
{
   result.value() = a.value() * b.value();
}
template <class A>
inline void eval_multiply(float128_backend& result, const float128_backend& a, const A& b)
{
   result.value() = a.value() * b;
}
inline void eval_divide(float128_backend& result, const float128_backend& a, const float128_backend& b)
{
   result.value() = a.value() / b.value();
}

template <class R>
inline void eval_convert_to(R* result, const float128_backend& val)
{
   *result = static_cast<R>(val.value());
}

inline void eval_frexp(float128_backend& result, const float128_backend& arg, int* exp)
{
   result.value() = frexpq(arg.value(), exp);
}

inline void eval_ldexp(float128_backend& result, const float128_backend& arg, int exp)
{
   result.value() = ldexpq(arg.value(), exp);
}

inline void eval_floor(float128_backend& result, const float128_backend& arg)
{
   result.value() = floorq(arg.value());
}
inline void eval_ceil(float128_backend& result, const float128_backend& arg)
{
   result.value() = ceilq(arg.value());
}
inline void eval_sqrt(float128_backend& result, const float128_backend& arg)
{
   result.value() = sqrtq(arg.value());
}
inline int eval_fpclassify(const float128_backend& arg)
{
   if(isnanq(arg.value()))
      return FP_NAN;
   else if(isinfq(arg.value()))
      return FP_INFINITE;
   else if(arg.value() == 0)
      return FP_ZERO;

   float128_backend t(arg);
   if(t.value() < 0)
      t.negate();
   if(t.value() < 3.36210314311209350626267781732175260e-4932Q)
      return FP_SUBNORMAL;
   return FP_NORMAL;
}

inline void eval_increment(float128_backend& arg)
{
   ++arg.value();
}
inline void eval_decrement(float128_backend& arg)
{
   --arg.value();
}

/*********************************************************************
*
* abs/fabs:
*
*********************************************************************/

inline void eval_abs(float128_backend& result, const float128_backend& arg)
{
   result.value() = fabsq(arg.value());
}
inline void eval_fabs(float128_backend& result, const float128_backend& arg)
{
   result.value() = fabsq(arg.value());
}

/*********************************************************************
*
* Floating point functions:
*
*********************************************************************/

inline void eval_trunc(float128_backend& result, const float128_backend& arg)
{
   if(isnanq(arg.value()) || isinfq(arg.value()))
   {
      result = boost::math::policies::raise_rounding_error(
            "boost::multiprecision::trunc<%1%>(%1%)", 0,
            number<float128_backend, et_off>(arg),
            number<float128_backend, et_off>(arg),
            boost::math::policies::policy<>()).backend();
      return;
   }
   result.value() = truncq(arg.value());
}
/*
//
// This doesn't actually work... rely on our own default version instead.
//
inline void eval_round(float128_backend& result, const float128_backend& arg)
{
   if(isnanq(arg.value()) || isinf(arg.value()))
   {
      result = boost::math::policies::raise_rounding_error(
            "boost::multiprecision::trunc<%1%>(%1%)", 0,
            number<float128_backend, et_off>(arg),
            number<float128_backend, et_off>(arg),
            boost::math::policies::policy<>()).backend();
      return;
   }
   result.value() = roundq(arg.value());
}
*/

inline void eval_exp(float128_backend& result, const float128_backend& arg)
{
   result.value() = expq(arg.value());
}
inline void eval_log(float128_backend& result, const float128_backend& arg)
{
   result.value() = logq(arg.value());
}
inline void eval_log10(float128_backend& result, const float128_backend& arg)
{
   result.value() = log10q(arg.value());
}
inline void eval_sin(float128_backend& result, const float128_backend& arg)
{
   result.value() = sinq(arg.value());
}
inline void eval_cos(float128_backend& result, const float128_backend& arg)
{
   result.value() = cosq(arg.value());
}
inline void eval_tan(float128_backend& result, const float128_backend& arg)
{
   result.value() = tanq(arg.value());
}
inline void eval_asin(float128_backend& result, const float128_backend& arg)
{
   result.value() = asinq(arg.value());
}
inline void eval_acos(float128_backend& result, const float128_backend& arg)
{
   result.value() = acosq(arg.value());
}
inline void eval_atan(float128_backend& result, const float128_backend& arg)
{
   result.value() = atanq(arg.value());
}
inline void eval_sinh(float128_backend& result, const float128_backend& arg)
{
   result.value() = sinhq(arg.value());
}
inline void eval_cosh(float128_backend& result, const float128_backend& arg)
{
   result.value() = coshq(arg.value());
}
inline void eval_tanh(float128_backend& result, const float128_backend& arg)
{
   result.value() = tanhq(arg.value());
}
inline void eval_fmod(float128_backend& result, const float128_backend& a, const float128_backend& b)
{
   result.value() = fmodq(a.value(), b.value());
}
inline void eval_pow(float128_backend& result, const float128_backend& a, const float128_backend& b)
{
   result.value() = powq(a.value(), b.value());
}
inline void eval_atan2(float128_backend& result, const float128_backend& a, const float128_backend& b)
{
   result.value() = atan2q(a.value(), b.value());
}
inline void eval_multiply_add(float128_backend& result, const float128_backend& a, const float128_backend& b, const float128_backend& c)
{
   result.value() = fmaq(a.value(), b.value(), c.value());
}

inline std::size_t hash_value(const float128_backend& val)
{
   return  boost::hash_value(static_cast<double>(val.value()));
}

} // namespace backends

   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> asinh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return asinhq(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> acosh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return acoshq(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> atanh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return atanhq(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> cbrt BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return cbrtq(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> erf BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return erfq(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> erfc BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return erfcq(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> expm1 BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return expm1q(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> lgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return lgammaq(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> tgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return tgammaq(arg.backend().value());
   }
   template<boost::multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<float128_backend, ExpressionTemplates> log1p BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<float128_backend, ExpressionTemplates>& arg)
   {
      return log1pq(arg.backend().value());
   }

   template <multiprecision::expression_template_option ExpressionTemplates>
   inline int signbit BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates>& arg)
   {
      return ::signbitq(arg.backend().value());
   }

   template <multiprecision::expression_template_option ExpressionTemplates>
   inline boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates>& a, const boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates>& b)
   {
      return ::copysignq(a.backend().value(), b.backend().value());
   }

   inline void eval_remainder(float128_backend& result, const float128_backend& a, const float128_backend& b)
   {
      result.value() = remainderq(a.value(), b.value());
   }
   inline void eval_remainder(float128_backend& result, const float128_backend& a, const float128_backend& b, int* pi)
   {
      result.value() = remquoq(a.value(), b.value(), pi);
   }

} // namespace multiprecision

namespace math {

   using boost::multiprecision::signbit;
   using boost::multiprecision::copysign;

} // namespace math

} // namespace boost

namespace boost{
namespace archive{

class binary_oarchive;
class binary_iarchive;

}

namespace serialization{ namespace float128_detail{

template <class Archive>
void do_serialize(Archive& ar, boost::multiprecision::backends::float128_backend& val, const mpl::false_&, const mpl::false_&)
{
   // saving
   // non-binary
   std::string s(val.str(0, std::ios_base::scientific));
   ar & s;
}
template <class Archive>
void do_serialize(Archive& ar, boost::multiprecision::backends::float128_backend& val, const mpl::true_&, const mpl::false_&)
{
   // loading
   // non-binary
   std::string s;
   ar & s;
   val = s.c_str();
}

template <class Archive>
void do_serialize(Archive& ar, boost::multiprecision::backends::float128_backend& val, const mpl::false_&, const mpl::true_&)
{
   // saving
   // binary
   ar.save_binary(&val, sizeof(val));
}
template <class Archive>
void do_serialize(Archive& ar, boost::multiprecision::backends::float128_backend& val, const mpl::true_&, const mpl::true_&)
{
   // loading
   // binary
   ar.load_binary(&val, sizeof(val));
}

} // detail

template <class Archive>
void serialize(Archive& ar, boost::multiprecision::backends::float128_backend& val, unsigned int /*version*/)
{
   typedef typename Archive::is_loading load_tag;
   typedef typename mpl::bool_<boost::is_same<Archive, boost::archive::binary_oarchive>::value || boost::is_same<Archive, boost::archive::binary_iarchive>::value> binary_tag;

   float128_detail::do_serialize(ar, val, load_tag(), binary_tag());
}

} // namepsace archive

} // namespace boost

namespace std{

template <boost::multiprecision::expression_template_option ExpressionTemplates>
class numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >
{
   typedef boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> number_type;
public:
   BOOST_STATIC_CONSTEXPR bool is_specialized = true;
   static number_type (min)() BOOST_NOEXCEPT { return 3.36210314311209350626267781732175260e-4932Q; }
   static number_type (max)() BOOST_NOEXCEPT { return 1.18973149535723176508575932662800702e4932Q; }
   static number_type lowest() BOOST_NOEXCEPT { return -(max)(); }
   BOOST_STATIC_CONSTEXPR int digits = 113;
   BOOST_STATIC_CONSTEXPR int digits10 = 33;
   BOOST_STATIC_CONSTEXPR int max_digits10 = 36;
   BOOST_STATIC_CONSTEXPR bool is_signed = true;
   BOOST_STATIC_CONSTEXPR bool is_integer = false;
   BOOST_STATIC_CONSTEXPR bool is_exact = false;
   BOOST_STATIC_CONSTEXPR int radix = 2;
   static number_type epsilon() { return 1.92592994438723585305597794258492732e-34Q; }
   static number_type round_error() { return 0.5; }
   BOOST_STATIC_CONSTEXPR int min_exponent = -16381;
   BOOST_STATIC_CONSTEXPR int min_exponent10 = min_exponent * 301L / 1000L;
   BOOST_STATIC_CONSTEXPR int max_exponent = 16384;
   BOOST_STATIC_CONSTEXPR int max_exponent10 = max_exponent * 301L / 1000L;
   BOOST_STATIC_CONSTEXPR bool has_infinity = true;
   BOOST_STATIC_CONSTEXPR bool has_quiet_NaN = true;
   BOOST_STATIC_CONSTEXPR bool has_signaling_NaN = false;
   BOOST_STATIC_CONSTEXPR float_denorm_style has_denorm = denorm_present;
   BOOST_STATIC_CONSTEXPR bool has_denorm_loss = true;
   static number_type infinity() { return 1.0q / 0.0q; }
   static number_type quiet_NaN() { return number_type("nan"); }
   static number_type signaling_NaN() { return 0; }
   static number_type denorm_min() { return 6.475175119438025110924438958227646552e-4966Q; }
   BOOST_STATIC_CONSTEXPR bool is_iec559 = true;
   BOOST_STATIC_CONSTEXPR bool is_bounded = false;
   BOOST_STATIC_CONSTEXPR bool is_modulo = false;
   BOOST_STATIC_CONSTEXPR bool traps = false;
   BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
   BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest;
};

template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::is_specialized;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::digits;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::digits10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::max_digits10;

template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::is_signed;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::is_integer;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::is_exact;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::radix;


template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::min_exponent;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::max_exponent;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::min_exponent10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::max_exponent10;

template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::has_infinity;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::has_quiet_NaN;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::has_signaling_NaN;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::has_denorm_loss;

template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::is_iec559;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::is_bounded;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::is_modulo;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::traps;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::tinyness_before;

template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::round_style;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::backends::float128_backend, ExpressionTemplates> >::has_denorm;

} // namespace std


#endif