EVOLUTION-MANAGER

Edit File: cpp_bin_float.hpp

///////////////////////////////////////////////////////////////
//  Copyright 2013 John Maddock. Distributed under the Boost
//  Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at https://www.boost.org/LICENSE_1_0.txt

#ifndef BOOST_MATH_CPP_BIN_FLOAT_HPP
#define BOOST_MATH_CPP_BIN_FLOAT_HPP

#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/integer.hpp>
#include <boost/math/special_functions/trunc.hpp>
#include <boost/multiprecision/detail/float_string_cvt.hpp>

//
// Some includes we need from Boost.Math, since we rely on that library to provide these functions:
//
#include <boost/math/special_functions/asinh.hpp>
#include <boost/math/special_functions/acosh.hpp>
#include <boost/math/special_functions/atanh.hpp>
#include <boost/math/special_functions/cbrt.hpp>
#include <boost/math/special_functions/expm1.hpp>
#include <boost/math/special_functions/gamma.hpp>

#ifdef BOOST_HAS_FLOAT128
#include <quadmath.h>
#endif

namespace boost {
namespace multiprecision {
namespace backends {

enum digit_base_type
{
   digit_base_2  = 2,
   digit_base_10 = 10
};

#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable : 4522 6326) // multiple assignment operators specified, comparison of two constants
#endif

namespace detail {

template <class U>
inline typename enable_if_c<is_unsigned::value, bool>::type is_negative(U) { return false; }
template <class S>
inline typename disable_if_c<is_unsigned<S>::value, bool>::type is_negative(S s) { return s < 0; }

template <class Float, int, bool = number_category<Float>::value == number_kind_floating_point>
struct is_cpp_bin_float_implicitly_constructible_from_type
{
 static const bool value = false;
};

template <class Float, int bit_count>
struct is_cpp_bin_float_implicitly_constructible_from_type<Float, bit_count, true>
{
 static const bool value = (std::numeric_limits<Float>::digits <= (int)bit_count) && (std::numeric_limits<Float>::radix == 2) && std::numeric_limits<Float>::is_specialized
#ifdef BOOST_HAS_FLOAT128
 && !boost::is_same<Float, __float128>::value
#endif
 && (is_floating_point<Float>::value || is_number<Float>::value);
};

template <class Float, int, bool = number_category<Float>::value == number_kind_floating_point>
struct is_cpp_bin_float_explicitly_constructible_from_type
{
 static const bool value = false;
};

template <class Float, int bit_count>
struct is_cpp_bin_float_explicitly_constructible_from_type<Float, bit_count, true>
{
 static const bool value = (std::numeric_limits<Float>::digits > (int)bit_count) && (std::numeric_limits<Float>::radix == 2) && std::numeric_limits<Float>::is_specialized
#ifdef BOOST_HAS_FLOAT128
 && !boost::is_same<Float, __float128>::value
#endif
 ;
};

} // namespace detail

template <unsigned Digits, digit_base_type DigitBase = digit_base_10, class Allocator = void, class Exponent = int, Exponent MinExponent = 0, Exponent MaxExponent = 0>
class cpp_bin_float
{
 public:
 static const unsigned bit_count = DigitBase == digit_base_2 ? Digits : (Digits * 1000uL) / 301uL + (((Digits * 1000uL) % 301) ? 2u : 1u);
 typedef cpp_int_backend<is_void<Allocator>::value ? bit_count : 0, bit_count, is_void<Allocator>::value ? unsigned_magnitude : signed_magnitude, unchecked, Allocator> rep_type;
 typedef cpp_int_backend<is_void<Allocator>::value ? 2 * bit_count : 0, 2 * bit_count, is_void<Allocator>::value ? unsigned_magnitude : signed_magnitude, unchecked, Allocator> double_rep_type;

typedef typename rep_type::signed_types signed_types;
 typedef typename rep_type::unsigned_types unsigned_types;
 typedef boost::mpl::list<float, double, long double> float_types;
 typedef Exponent exponent_type;

static const exponent_type max_exponent_limit = boost::integer_traits<exponent_type>::const_max - 2 * static_cast<exponent_type>(bit_count);
 static const exponent_type min_exponent_limit = boost::integer_traits<exponent_type>::const_min + 2 * static_cast<exponent_type>(bit_count);

BOOST_STATIC_ASSERT_MSG(MinExponent >= min_exponent_limit, "Template parameter MinExponent is too negative for our internal logic to function correctly, sorry!");
 BOOST_STATIC_ASSERT_MSG(MaxExponent <= max_exponent_limit, "Template parameter MaxExponent is too large for our internal logic to function correctly, sorry!");
 BOOST_STATIC_ASSERT_MSG(MinExponent <= 0, "Template parameter MinExponent can not be positive!");
 BOOST_STATIC_ASSERT_MSG(MaxExponent >= 0, "Template parameter MaxExponent can not be negative!");

static const exponent_type max_exponent = MaxExponent == 0 ? max_exponent_limit : MaxExponent;
   static const exponent_type min_exponent = MinExponent == 0 ? min_exponent_limit : MinExponent;

static const exponent_type exponent_zero     = max_exponent + 1;
   static const exponent_type exponent_infinity = max_exponent + 2;
   static const exponent_type exponent_nan      = max_exponent + 3;

private:
   rep_type      m_data;
   exponent_type m_exponent;
   bool          m_sign;

public:
   cpp_bin_float() BOOST_MP_NOEXCEPT_IF(noexcept(rep_type())) : m_data(), m_exponent(exponent_zero), m_sign(false) {}

cpp_bin_float(const cpp_bin_float& o) BOOST_MP_NOEXCEPT_IF(noexcept(rep_type(std::declval<const rep_type&>())))
 : m_data(o.m_data), m_exponent(o.m_exponent), m_sign(o.m_sign) {}

template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
 cpp_bin_float(const cpp_bin_float<D, B, A, E, MinE, MaxE>& o, typename boost::enable_if_c<(bit_count >= cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count)>::type const* = 0)
 {
 *this = o;
 }
 template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
 explicit cpp_bin_float(const cpp_bin_float<D, B, A, E, MinE, MaxE>& o, typename boost::disable_if_c<(bit_count >= cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count)>::type const* = 0)
 : m_exponent(o.exponent()), m_sign(o.sign())
 {
 *this = o;
 }
 template <class Float>
 cpp_bin_float(const Float& f,
 typename boost::enable_if_c<detail::is_cpp_bin_float_implicitly_constructible_from_type<Float, bit_count>::value>::type const* = 0)
 : m_data(), m_exponent(0), m_sign(false)
 {
 this->assign_float(f);
 }

template <class Float>
 explicit cpp_bin_float(const Float& f,
 typename boost::enable_if_c<detail::is_cpp_bin_float_explicitly_constructible_from_type<Float, bit_count>::value>::type const* = 0)
 : m_data(), m_exponent(0), m_sign(false)
 {
 this->assign_float(f);
 }
#ifdef BOOST_HAS_FLOAT128
 template <class Float>
 cpp_bin_float(const Float& f,
 typename boost::enable_if_c<
 boost::is_same<Float, __float128>::value && ((int)bit_count >= 113)>::type const* = 0)
 : m_data(), m_exponent(0), m_sign(false)
 {
 this->assign_float(f);
 }
 template <class Float>
 explicit cpp_bin_float(const Float& f,
 typename boost::enable_if_c<
 boost::is_same<Float, __float128>::value && ((int)bit_count < 113)>::type const* = 0)
 : m_data(), m_exponent(0), m_sign(false)
 {
 this->assign_float(f);
 }
#endif
 cpp_bin_float& operator=(const cpp_bin_float& o) BOOST_MP_NOEXCEPT_IF(noexcept(std::declval<rep_type&>() = std::declval<const rep_type&>()))
 {
 m_data = o.m_data;
 m_exponent = o.m_exponent;
 m_sign = o.m_sign;
 return *this;
 }

template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
 cpp_bin_float& operator=(const cpp_bin_float<D, B, A, E, MinE, MaxE>& f)
 {
 switch (eval_fpclassify(f))
 {
 case FP_ZERO:
 m_data = limb_type(0);
 m_sign = f.sign();
 m_exponent = exponent_zero;
 break;
 case FP_NAN:
 m_data = limb_type(0);
 m_sign = false;
 m_exponent = exponent_nan;
 break;
 ;
 case FP_INFINITE:
 m_data = limb_type(0);
 m_sign = f.sign();
 m_exponent = exponent_infinity;
 break;
 default:
 typename cpp_bin_float<D, B, A, E, MinE, MaxE>::rep_type b(f.bits());
 this->exponent() = f.exponent() + (E)bit_count - (E)cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count;
 this->sign() = f.sign();
 copy_and_round(*this, b);
 }
 return *this;
 }
#ifdef BOOST_HAS_FLOAT128
 template <class Float>
 typename boost::enable_if_c<
 (number_category<Float>::value == number_kind_floating_point)
 //&& (std::numeric_limits<Float>::digits <= (int)bit_count)
 && ((std::numeric_limits<Float>::radix == 2) || (boost::is_same<Float, __float128>::value)),
 cpp_bin_float&>::type
 operator=(const Float& f)
#else
 template <class Float>
 typename boost::enable_if_c<
 (number_category<Float>::value == number_kind_floating_point)
 //&& (std::numeric_limits<Float>::digits <= (int)bit_count)
 && (std::numeric_limits<Float>::radix == 2),
 cpp_bin_float&>::type
 operator=(const Float& f)
#endif
 {
 return assign_float(f);
 }

#ifdef BOOST_HAS_FLOAT128
 template <class Float>
 typename boost::enable_if_c<boost::is_same<Float, __float128>::value, cpp_bin_float&>::type assign_float(Float f)
 {
 using default_ops::eval_add;
 typedef typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type bf_int_type;
 if (f == 0)
 {
 m_data = limb_type(0);
 m_sign = (signbitq(f) > 0);
 m_exponent = exponent_zero;
 return *this;
 }
 else if (isnanq(f))
 {
 m_data = limb_type(0);
 m_sign = false;
 m_exponent = exponent_nan;
 return *this;
 }
 else if (isinfq(f))
 {
 m_data = limb_type(0);
 m_sign = (f < 0);
 m_exponent = exponent_infinity;
 return *this;
 }
 if (f < 0)
 {
 *this = -f;
 this->negate();
 return *this;
 }

typedef typename mpl::front<unsigned_types>::type ui_type;
 m_data = static_cast<ui_type>(0u);
 m_sign = false;
 m_exponent = 0;

static const int bits = sizeof(int) * CHAR_BIT - 1;
 int e;
 f = frexpq(f, &e);
 while (f)
 {
 f = ldexpq(f, bits);
 e -= bits;
 int ipart = (int)truncq(f);
 f -= ipart;
 m_exponent += bits;
 cpp_bin_float t;
 t = static_cast<bf_int_type>(ipart);
 eval_add(*this, t);
 }
 m_exponent += static_cast<Exponent>(e);
 return *this;
 }
#endif
#ifdef BOOST_HAS_FLOAT128
 template <class Float>
 typename boost::enable_if_c<is_floating_point<Float>::value && !is_same<Float, __float128>::value, cpp_bin_float&>::type assign_float(Float f)
#else
 template <class Float>
 typename boost::enable_if_c<is_floating_point<Float>::value, cpp_bin_float&>::type assign_float(Float f)
#endif
 {
 BOOST_MATH_STD_USING
 using default_ops::eval_add;
 typedef typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type bf_int_type;

switch ((boost::math::fpclassify)(f))
 {
 case FP_ZERO:
 m_data = limb_type(0);
 m_sign = ((boost::math::signbit)(f) > 0);
 m_exponent = exponent_zero;
 return *this;
 case FP_NAN:
 m_data = limb_type(0);
 m_sign = false;
 m_exponent = exponent_nan;
 return *this;
 case FP_INFINITE:
 m_data = limb_type(0);
 m_sign = (f < 0);
 m_exponent = exponent_infinity;
 return *this;
 }
 if (f < 0)
 {
 *this = -f;
 this->negate();
 return *this;
 }

typedef typename mpl::front<unsigned_types>::type ui_type;
 m_data = static_cast<ui_type>(0u);
 m_sign = false;
 m_exponent = 0;

static const int bits = sizeof(int) * CHAR_BIT - 1;
 int e;
 f = frexp(f, &e);
 while (f)
 {
 f = ldexp(f, bits);
 e -= bits;
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 int ipart = itrunc(f);
#else
 int ipart = static_cast<int>(f);
#endif
 f -= ipart;
 m_exponent += bits;
 cpp_bin_float t;
 t = static_cast<bf_int_type>(ipart);
 eval_add(*this, t);
 }
 m_exponent += static_cast<Exponent>(e);
 return *this;
 }

template <class Float>
 typename boost::enable_if_c<
 (number_category<Float>::value == number_kind_floating_point) && !boost::is_floating_point<Float>::value && (number_category<Float>::value == number_kind_floating_point),
 cpp_bin_float&>::type
 assign_float(Float f)
 {
 BOOST_MATH_STD_USING
 using default_ops::eval_add;
 using default_ops::eval_convert_to;
 using default_ops::eval_get_sign;
 using default_ops::eval_subtract;

typedef typename boost::multiprecision::detail::canonical<int, Float>::type f_int_type;
 typedef typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type bf_int_type;

switch (eval_fpclassify(f))
 {
 case FP_ZERO:
 m_data = limb_type(0);
 m_sign = (eval_get_sign(f) > 0);
 m_exponent = exponent_zero;
 return *this;
 case FP_NAN:
 m_data = limb_type(0);
 m_sign = false;
 m_exponent = exponent_nan;
 return *this;
 case FP_INFINITE:
 m_data = limb_type(0);
 m_sign = eval_get_sign(f) < 0;
 m_exponent = exponent_infinity;
 return *this;
 }
 if (eval_get_sign(f) < 0)
 {
 f.negate();
 *this = f;
 this->negate();
 return *this;
 }

typedef typename mpl::front<unsigned_types>::type ui_type;
 m_data = static_cast<ui_type>(0u);
 m_sign = false;
 m_exponent = 0;

static const int bits = sizeof(int) * CHAR_BIT - 1;
 int e;
 eval_frexp(f, f, &e);
 while (eval_get_sign(f) != 0)
 {
 eval_ldexp(f, f, bits);
 e -= bits;
 int ipart;
 eval_convert_to(&ipart, f);
 eval_subtract(f, static_cast<f_int_type>(ipart));
 m_exponent += bits;
 eval_add(*this, static_cast<bf_int_type>(ipart));
 }
 m_exponent += e;
 if (m_exponent > max_exponent)
 m_exponent = exponent_infinity;
 if (m_exponent < min_exponent)
 {
 m_data = limb_type(0u);
 m_exponent = exponent_zero;
 m_sign = (eval_get_sign(f) > 0);
 }
 else if (eval_get_sign(m_data) == 0)
 {
 m_exponent = exponent_zero;
 m_sign = (eval_get_sign(f) > 0);
 }
 return *this;
 }
 template <class B, expression_template_option et>
 cpp_bin_float& assign_float(const number<B, et>& f)
 {
 return assign_float(f.backend());
 }
 
 template <class I>
 typename boost::enable_if<is_integral, cpp_bin_float&>::type operator=(const I& i)
 {
 using default_ops::eval_bit_test;
 if (!i)
 {
 m_data = static_cast<limb_type>(0);
 m_exponent = exponent_zero;
 m_sign = false;
 }
 else
 {
 typedef typename make_unsigned::type ui_type;
 ui_type fi = static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(i));
 typedef typename boost::multiprecision::detail::canonical<ui_type, rep_type>::type ar_type;
 m_data = static_cast<ar_type>(fi);
 unsigned shift = msb(fi);
 if (shift >= bit_count)
 {
 m_exponent = static_cast<Exponent>(shift);
 m_data = static_cast<ar_type>(fi >> (shift + 1 - bit_count));
 }
 else
 {
 m_exponent = static_cast<Exponent>(shift);
 eval_left_shift(m_data, bit_count - shift - 1);
 }
 BOOST_ASSERT(eval_bit_test(m_data, bit_count - 1));
 m_sign = detail::is_negative(i);
 }
 return *this;
 }

cpp_bin_float& operator=(const char* s);

void swap(cpp_bin_float& o) BOOST_NOEXCEPT
   {
      m_data.swap(o.m_data);
      std::swap(m_exponent, o.m_exponent);
      std::swap(m_sign, o.m_sign);
   }

std::string str(std::streamsize dig, std::ios_base::fmtflags f) const;

void negate()
   {
      if (m_exponent != exponent_nan)
         m_sign = !m_sign;
   }

int compare(const cpp_bin_float& o) const BOOST_NOEXCEPT
 {
 if (m_sign != o.m_sign)
 return (m_exponent == exponent_zero) && (m_exponent == o.m_exponent) ? 0 : m_sign ? -1 : 1;
 int result;
 if (m_exponent == exponent_nan)
 return -1;
 else if (m_exponent != o.m_exponent)
 {
 if (m_exponent == exponent_zero)
 result = -1;
 else if (o.m_exponent == exponent_zero)
 result = 1;
 else
 result = m_exponent > o.m_exponent ? 1 : -1;
 }
 else
 result = m_data.compare(o.m_data);
 if (m_sign)
 result = -result;
 return result;
 }
 template <class A>
 int compare(const A& o) const BOOST_NOEXCEPT
 {
 cpp_bin_float b;
 b = o;
 return compare(b);
 }

rep_type& bits() { return m_data; }
 const rep_type& bits() const { return m_data; }
 exponent_type& exponent() { return m_exponent; }
 const exponent_type& exponent() const { return m_exponent; }
 bool& sign() { return m_sign; }
 const bool& sign() const { return m_sign; }
 void check_invariants()
 {
 using default_ops::eval_bit_test;
 using default_ops::eval_is_zero;
 if ((m_exponent <= max_exponent) && (m_exponent >= min_exponent))
 {
 BOOST_ASSERT(eval_bit_test(m_data, bit_count - 1));
 }
 else
 {
 BOOST_ASSERT(m_exponent > max_exponent);
 BOOST_ASSERT(m_exponent <= exponent_nan);
 BOOST_ASSERT(eval_is_zero(m_data));
 }
 }
 template <class Archive>
 void serialize(Archive& ar, const unsigned int /*version*/)
 {
 ar& boost::make_nvp("data", m_data);
 ar& boost::make_nvp("exponent", m_exponent);
 ar& boost::make_nvp("sign", m_sign);
 }
};

#ifdef BOOST_MSVC
#pragma warning(pop)
#endif

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class Int>
inline void copy_and_round(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, Int& arg, int bits_to_keep = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
{
 // Precondition: exponent of res must have been set before this function is called
 // as we may need to adjust it based on how many bits_to_keep in arg are set.
 using default_ops::eval_bit_test;
 using default_ops::eval_get_sign;
 using default_ops::eval_increment;
 using default_ops::eval_left_shift;
 using default_ops::eval_lsb;
 using default_ops::eval_msb;
 using default_ops::eval_right_shift;

// cancellation may have resulted in arg being all zeros:
 if (eval_get_sign(arg) == 0)
 {
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
 res.sign() = false;
 res.bits() = static_cast<limb_type>(0u);
 return;
 }
 int msb = eval_msb(arg);
 if (static_cast<int>(bits_to_keep) > msb + 1)
 {
 // Must have had cancellation in subtraction,
 // or be converting from a narrower type, so shift left:
 res.bits() = arg;
 eval_left_shift(res.bits(), bits_to_keep - msb - 1);
 res.exponent() -= static_cast<Exponent>(bits_to_keep - msb - 1);
 }
 else if (static_cast<int>(bits_to_keep) < msb + 1)
 {
 // We have more bits_to_keep than we need, so round as required,
 // first get the rounding bit:
 bool roundup = eval_bit_test(arg, msb - bits_to_keep);
 // Then check for a tie:
 if (roundup && (msb - bits_to_keep == (int)eval_lsb(arg)))
 {
 // Ties round towards even:
 if (!eval_bit_test(arg, msb - bits_to_keep + 1))
 roundup = false;
 }
 // Shift off the bits_to_keep we don't need:
 eval_right_shift(arg, msb - bits_to_keep + 1);
 res.exponent() += static_cast<Exponent>(msb - bits_to_keep + 1);
 if (roundup)
 {
 eval_increment(arg);
 if (bits_to_keep)
 {
 if (eval_bit_test(arg, bits_to_keep))
 {
 // This happens very very rairly, all the bits left after
 // truncation must be 1's and we're rounding up an order of magnitude:
 eval_right_shift(arg, 1u);
 ++res.exponent();
 }
 }
 else
 {
 // We get here when bits_to_keep is zero but we're rounding up,
 // as a result we end up with a single digit that is a 1:
 ++bits_to_keep;
 }
 }
 if (bits_to_keep != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
 {
 // Normalize result when we're rounding to fewer bits than we can hold, only happens in conversions
 // to narrower types:
 eval_left_shift(arg, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - bits_to_keep);
 res.exponent() -= static_cast<Exponent>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - bits_to_keep);
 }
 res.bits() = arg;
 }
 else
 {
 res.bits() = arg;
 }
 if (!bits_to_keep && !res.bits().limbs()[0])
 {
 // We're keeping zero bits and did not round up, so result is zero:
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
 return;
 }
 // Result must be normalized:
 BOOST_ASSERT(((int)eval_msb(res.bits()) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1));

if (res.exponent() > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent)
 {
 // Overflow:
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
 res.bits() = static_cast<limb_type>(0u);
 }
 else if (res.exponent() < cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent)
 {
 // Underflow:
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
 res.bits() = static_cast<limb_type>(0u);
 }
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void do_eval_add(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& b)
{
 if (a.exponent() < b.exponent())
 {
 bool s = a.sign();
 do_eval_add(res, b, a);
 if (res.sign() != s)
 res.negate();
 return;
 }

using default_ops::eval_add;
   using default_ops::eval_bit_test;

typedef typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type exponent_type;

typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;

// Special cases first:
 switch (a.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 {
 bool s = a.sign();
 res = b;
 res.sign() = s;
 return;
 }
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 if (b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan)
 res = b;
 else
 res = a;
 return; // result is still infinite.
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = a;
 return; // result is still a NaN.
 }
 switch (b.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 res = a;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 res = b;
 if (res.sign())
 res.negate();
 return; // result is infinite.
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = b;
 return; // result is a NaN.
 }

BOOST_STATIC_ASSERT(boost::integer_traits<exponent_type>::const_max - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent);

bool s = a.sign();
 dt = a.bits();
 if (a.exponent() > (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + b.exponent())
 {
 res.exponent() = a.exponent();
 }
 else
 {
 exponent_type e_diff = a.exponent() - b.exponent();
 BOOST_ASSERT(e_diff >= 0);
 eval_left_shift(dt, e_diff);
 res.exponent() = a.exponent() - e_diff;
 eval_add(dt, b.bits());
 }

copy_and_round(res, dt);
   res.check_invariants();
   if (res.sign() != s)
      res.negate();
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void do_eval_subtract(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& b)
{
 using default_ops::eval_bit_test;
 using default_ops::eval_decrement;
 using default_ops::eval_subtract;

typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;

// Special cases first:
 switch (a.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 if (b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan)
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 else
 {
 bool s = a.sign();
 res = b;
 if (res.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero)
 res.sign() = false;
 else if (res.sign() == s)
 res.negate();
 }
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 if ((b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan) || (b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity))
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 else
 res = a;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = a;
 return; // result is still a NaN.
 }
 switch (b.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 res = a;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
 res.sign() = !a.sign();
 res.bits() = static_cast<limb_type>(0u);
 return; // result is a NaN.
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = b;
 return; // result is still a NaN.
 }

bool s = a.sign();
 if ((a.exponent() > b.exponent()) || ((a.exponent() == b.exponent()) && a.bits().compare(b.bits()) >= 0))
 {
 dt = a.bits();
 if (a.exponent() <= (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + b.exponent())
 {
 typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e_diff = a.exponent() - b.exponent();
 eval_left_shift(dt, e_diff);
 res.exponent() = a.exponent() - e_diff;
 eval_subtract(dt, b.bits());
 }
 else if (a.exponent() == (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + b.exponent() + 1)
 {
 if (eval_lsb(b.bits()) != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)
 {
 eval_left_shift(dt, 1);
 eval_decrement(dt);
 res.exponent() = a.exponent() - 1;
 }
 else
 res.exponent() = a.exponent();
 }
 else
 res.exponent() = a.exponent();
 }
 else
 {
 dt = b.bits();
 if (b.exponent() <= (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + a.exponent())
 {
 typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type e_diff = a.exponent() - b.exponent();
 eval_left_shift(dt, -e_diff);
 res.exponent() = b.exponent() + e_diff;
 eval_subtract(dt, a.bits());
 }
 else if (b.exponent() == (int)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + a.exponent() + 1)
 {
 if (eval_lsb(a.bits()) != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)
 {
 eval_left_shift(dt, 1);
 eval_decrement(dt);
 res.exponent() = b.exponent() - 1;
 }
 else
 res.exponent() = b.exponent();
 }
 else
 res.exponent() = b.exponent();
 s = !s;
 }

copy_and_round(res, dt);
 if (res.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero)
 res.sign() = false;
 else if (res.sign() != s)
 res.negate();
 res.check_invariants();
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_add(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& b)
{
 if (a.sign() == b.sign())
 do_eval_add(res, a, b);
 else
 do_eval_subtract(res, a, b);
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_subtract(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& b)
{
 if (a.sign() != b.sign())
 do_eval_add(res, a, b);
 else
 do_eval_subtract(res, a, b);
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& a, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& b)
{
 using default_ops::eval_bit_test;
 using default_ops::eval_multiply;

// Special cases first:
 switch (a.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 {
 if (b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan)
 res = b;
 else if (b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity)
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 else
 {
 bool s = a.sign() != b.sign();
 res = a;
 res.sign() = s;
 }
 return;
 }
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 switch (b.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 break;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = b;
 break;
 default:
 bool s = a.sign() != b.sign();
 res = a;
 res.sign() = s;
 break;
 }
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = a;
 return;
 }
 if (b.exponent() > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent)
 {
 bool s = a.sign() != b.sign();
 res = b;
 res.sign() = s;
 return;
 }
 if ((a.exponent() > 0) && (b.exponent() > 0))
 {
 if (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent + 2 - a.exponent() < b.exponent())
 {
 // We will certainly overflow:
 bool s = a.sign() != b.sign();
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
 res.sign() = s;
 res.bits() = static_cast<limb_type>(0u);
 return;
 }
 }
 if ((a.exponent() < 0) && (b.exponent() < 0))
 {
 if (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent - 2 - a.exponent() > b.exponent())
 {
 // We will certainly underflow:
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
 res.sign() = a.sign() != b.sign();
 res.bits() = static_cast<limb_type>(0u);
 return;
 }
 }

typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;
 eval_multiply(dt, a.bits(), b.bits());
 res.exponent() = a.exponent() + b.exponent() - (Exponent)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count + 1;
 copy_and_round(res, dt);
 res.check_invariants();
 res.sign() = a.sign() != b.sign();
}

// Special cases first:
 switch (a.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 {
 bool s = a.sign();
 res = a;
 res.sign() = s;
 return;
 }
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 if (b == 0)
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 else
 res = a;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = a;
 return;
 }

typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;
 typedef typename boost::multiprecision::detail::canonical<U, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::type canon_ui_type;
 eval_multiply(dt, a.bits(), static_cast<canon_ui_type>(b));
 res.exponent() = a.exponent();
 copy_and_round(res, dt);
 res.check_invariants();
 res.sign() = a.sign();
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S>
inline typename enable_if_c<is_signed<S>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& a, const S& b)
{
 typedef typename make_unsigned<S>::type ui_type;
 eval_multiply(res, a, static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(b)));
 if (b < 0)
 res.negate();
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& u, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& v)
{
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable : 6326) // comparison of two constants
#endif
 using default_ops::eval_bit_test;
 using default_ops::eval_get_sign;
 using default_ops::eval_increment;
 using default_ops::eval_qr;
 using default_ops::eval_subtract;

//
 // Special cases first:
 //
 switch (u.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 {
 switch (v.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 return;
 }
 bool s = u.sign() != v.sign();
 res = u;
 res.sign() = s;
 return;
 }
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 {
 switch (v.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 return;
 }
 bool s = u.sign() != v.sign();
 res = u;
 res.sign() = s;
 return;
 }
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 return;
 }
 switch (v.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 {
 bool s = u.sign() != v.sign();
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
 res.sign() = s;
 return;
 }
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
 res.bits() = limb_type(0);
 res.sign() = u.sign() != v.sign();
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 return;
 }

// We can scale u and v so that both are integers, then perform integer
 // division to obtain quotient q and remainder r, such that:
 //
 // q * v + r = u
 //
 // and hense:
 //
 // q + r/v = u/v
 //
 // From this, assuming q has cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count
 // bits we only need to determine whether
 // r/v is less than, equal to, or greater than 0.5 to determine rounding -
 // this we can do with a shift and comparison.
 //
 // We can set the exponent and sign of the result up front:
 //
 if ((v.exponent() < 0) && (u.exponent() > 0))
 {
 // Check for overflow:
 if (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent + v.exponent() < u.exponent() - 1)
 {
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
 res.sign() = u.sign() != v.sign();
 res.bits() = static_cast<limb_type>(0u);
 return;
 }
 }
 else if ((v.exponent() > 0) && (u.exponent() < 0))
 {
 // Check for underflow:
 if (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent + v.exponent() > u.exponent())
 {
 // We will certainly underflow:
 res.exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
 res.sign() = u.sign() != v.sign();
 res.bits() = static_cast<limb_type>(0u);
 return;
 }
 }
 res.exponent() = u.exponent() - v.exponent() - 1;
 res.sign() = u.sign() != v.sign();
 //
 // Now get the quotient and remainder:
 //
 typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(u.bits()), t2(v.bits()), q, r;
 eval_left_shift(t, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count);
 eval_qr(t, t2, q, r);
 //
 // We now have either "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count"
 // or "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1" significant
 // bits in q.
 //
 static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
 if (eval_bit_test(q, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count))
 {
 //
 // OK we have cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1 bits,
 // so we already have rounding info,
 // we just need to changes things if the last bit is 1 and either the
 // remainder is non-zero (ie we do not have a tie) or the quotient would
 // be odd if it were shifted to the correct number of bits (ie a tiebreak).
 //
 BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count));
 if ((q.limbs()[0] & 1u) && (eval_get_sign(r) || (q.limbs()[0] & 2u)))
 {
 eval_increment(q);
 }
 }
 else
 {
 //
 // We have exactly "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" bits in q.
 // Get rounding info, which we can get by comparing 2r with v.
 // We want to call copy_and_round to handle rounding and general cleanup,
 // so we'll left shift q and add some fake digits on the end to represent
 // how we'll be rounding.
 //
 BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1));
 static const unsigned lshift = (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count < limb_bits) ? 2 : limb_bits;
 eval_left_shift(q, lshift);
 res.exponent() -= lshift;
 eval_left_shift(r, 1u);
 int c = r.compare(v.bits());
 if (c == 0)
 q.limbs()[0] |= static_cast<limb_type>(1u) << (lshift - 1);
 else if (c > 0)
 q.limbs()[0] |= (static_cast<limb_type>(1u) << (lshift - 1)) + static_cast<limb_type>(1u);
 }
 copy_and_round(res, q);
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U>
inline typename enable_if_c<is_unsigned::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& u, const U& v)
{
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable : 6326) // comparison of two constants
#endif
 using default_ops::eval_bit_test;
 using default_ops::eval_get_sign;
 using default_ops::eval_increment;
 using default_ops::eval_qr;
 using default_ops::eval_subtract;

//
 // Special cases first:
 //
 switch (u.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 {
 if (v == 0)
 {
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 return;
 }
 bool s = u.sign() != (v < 0);
 res = u;
 res.sign() = s;
 return;
 }
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 res = u;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 return;
 }
 if (v == 0)
 {
 bool s = u.sign();
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
 res.sign() = s;
 return;
 }

// We can scale u and v so that both are integers, then perform integer
 // division to obtain quotient q and remainder r, such that:
 //
 // q * v + r = u
 //
 // and hense:
 //
 // q + r/v = u/v
 //
 // From this, assuming q has "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count, we only need to determine whether
 // r/v is less than, equal to, or greater than 0.5 to determine rounding -
 // this we can do with a shift and comparison.
 //
 // We can set the exponent and sign of the result up front:
 //
 int gb = msb(v);
 res.exponent() = u.exponent() - static_cast<Exponent>(gb) - static_cast<Exponent>(1);
 res.sign() = u.sign();
 //
 // Now get the quotient and remainder:
 //
 typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(u.bits()), q, r;
 eval_left_shift(t, gb + 1);
 eval_qr(t, number<typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::canonical_value(v), q, r);
 //
 // We now have either "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" or "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1" significant cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count in q.
 //
 static const unsigned limb_bits = sizeof(limb_type) * CHAR_BIT;
 if (eval_bit_test(q, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count))
 {
 //
 // OK we have cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count+1 cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count, so we already have rounding info,
 // we just need to changes things if the last bit is 1 and the
 // remainder is non-zero (ie we do not have a tie).
 //
 BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count));
 if ((q.limbs()[0] & 1u) && eval_get_sign(r))
 {
 eval_increment(q);
 }
 }
 else
 {
 //
 // We have exactly "cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count" cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count in q.
 // Get rounding info, which we can get by comparing 2r with v.
 // We want to call copy_and_round to handle rounding and general cleanup,
 // so we'll left shift q and add some fake cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count on the end to represent
 // how we'll be rounding.
 //
 BOOST_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1));
 static const unsigned lshift = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count < limb_bits ? 2 : limb_bits;
 eval_left_shift(q, lshift);
 res.exponent() -= lshift;
 eval_left_shift(r, 1u);
 int c = r.compare(number<typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::canonical_value(v));
 if (c == 0)
 q.limbs()[0] |= static_cast<limb_type>(1u) << (lshift - 1);
 else if (c > 0)
 q.limbs()[0] |= (static_cast<limb_type>(1u) << (lshift - 1)) + static_cast<limb_type>(1u);
 }
 copy_and_round(res, q);
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class S>
inline typename enable_if_c<is_signed<S>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& u, const S& v)
{
 typedef typename make_unsigned<S>::type ui_type;
 eval_divide(res, u, static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(v)));
 if (v < 0)
 res.negate();
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline int eval_get_sign(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 return arg.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero ? 0 : arg.sign() ? -1 : 1;
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline bool eval_is_zero(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 return arg.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline bool eval_eq(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& a, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& b)
{
 if (a.exponent() == b.exponent())
 {
 if (a.exponent() == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero)
 return true;
 return (a.sign() == b.sign()) && (a.bits().compare(b.bits()) == 0) && (a.exponent() != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan);
 }
 return false;
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_convert_to(boost::long_long_type* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 switch (arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 *res = 0;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer."));
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 *res = (std::numeric_limits<boost::long_long_type>::max)();
 if (arg.sign())
 *res = -*res;
 return;
 }
 typedef typename mpl::if_c<sizeof(typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type) < sizeof(int), int, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type>::type shift_type;
 typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::rep_type man(arg.bits());
 shift_type shift = (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - arg.exponent();
 if (shift > (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)
 {
 *res = 0;
 return;
 }
 if (arg.sign() && (arg.compare((std::numeric_limits<boost::long_long_type>::min)()) <= 0))
 {
 *res = (std::numeric_limits<boost::long_long_type>::min)();
 return;
 }
 else if (!arg.sign() && (arg.compare((std::numeric_limits<boost::long_long_type>::max)()) >= 0))
 {
 *res = (std::numeric_limits<boost::long_long_type>::max)();
 return;
 }

if (shift < 0)
 {
 if (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - shift <= std::numeric_limits<boost::long_long_type>::digits)
 {
 // We have more bits in long_long_type than the float, so it's OK to left shift:
 eval_convert_to(res, man);
 *res <<= -shift;
 }
 else
 {
 *res = (std::numeric_limits<boost::long_long_type>::max)();
 return;
 }
 }
 else
 {
 eval_right_shift(man, shift);
 eval_convert_to(res, man);
 }
 if (arg.sign())
 {
 *res = -*res;
 }
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_convert_to(boost::ulong_long_type* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 switch (arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 *res = 0;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 BOOST_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer."));
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 *res = (std::numeric_limits<boost::ulong_long_type>::max)();
 return;
 }
 typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::rep_type man(arg.bits());
 typedef typename mpl::if_c<sizeof(typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type) < sizeof(int), int, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type>::type shift_type;
 shift_type shift = (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - arg.exponent();
 if (shift > (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1)
 {
 *res = 0;
 return;
 }
 else if (shift < 0)
 {
 if (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - shift <= std::numeric_limits<boost::ulong_long_type>::digits)
 {
 // We have more bits in ulong_long_type than the float, so it's OK to left shift:
 eval_convert_to(res, man);
 *res <<= -shift;
 return;
 }
 *res = (std::numeric_limits<boost::ulong_long_type>::max)();
 return;
 }
 eval_right_shift(man, shift);
 eval_convert_to(res, man);
}

template <class Float, unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline typename boost::enable_if_c<boost::is_float<Float>::value>::type eval_convert_to(Float* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& original_arg)
{
 typedef cpp_bin_float<std::numeric_limits<Float>::digits, digit_base_2, void, Exponent, MinE, MaxE> conv_type;
 typedef typename common_type<typename conv_type::exponent_type, int>::type common_exp_type;
 //
 // Special cases first:
 //
 switch (original_arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 *res = 0;
 if (original_arg.sign())
 *res = -*res;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 *res = std::numeric_limits<Float>::quiet_NaN();
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 *res = (std::numeric_limits<Float>::infinity)();
 if (original_arg.sign())
 *res = -*res;
 return;
 }
 //
 // Check for super large exponent that must be converted to infinity:
 //
 if (original_arg.exponent() > std::numeric_limits<Float>::max_exponent)
 {
 *res = std::numeric_limits<Float>::has_infinity ? std::numeric_limits<Float>::infinity() : (std::numeric_limits<Float>::max)();
 if (original_arg.sign())
 *res = -*res;
 return;
 }
 //
 // Figure out how many digits we will have in our result,
 // allowing for a possibly denormalized result:
 //
 common_exp_type digits_to_round_to = std::numeric_limits<Float>::digits;
 if (original_arg.exponent() < std::numeric_limits<Float>::min_exponent - 1)
 {
 common_exp_type diff = original_arg.exponent();
 diff -= std::numeric_limits<Float>::min_exponent - 1;
 digits_to_round_to += diff;
 }
 if (digits_to_round_to < 0)
 {
 // Result must be zero:
 *res = 0;
 if (original_arg.sign())
 *res = -*res;
 return;
 }
 //
 // Perform rounding first, then afterwards extract the digits:
 //
 cpp_bin_float<std::numeric_limits<Float>::digits, digit_base_2, Allocator, Exponent, MinE, MaxE> arg;
 typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::rep_type bits(original_arg.bits());
 arg.exponent() = original_arg.exponent();
 copy_and_round(arg, bits, (int)digits_to_round_to);
 common_exp_type e = arg.exponent();
 e -= cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1;
 static const unsigned limbs_needed = std::numeric_limits<Float>::digits / (sizeof(*arg.bits().limbs()) * CHAR_BIT) + (std::numeric_limits<Float>::digits % (sizeof(*arg.bits().limbs()) * CHAR_BIT) ? 1 : 0);
 unsigned first_limb_needed = arg.bits().size() - limbs_needed;
 *res = 0;
 e += first_limb_needed * sizeof(*arg.bits().limbs()) * CHAR_BIT;
 while (first_limb_needed < arg.bits().size())
 {
 *res += std::ldexp(static_cast<Float>(arg.bits().limbs()[first_limb_needed]), static_cast<int>(e));
 ++first_limb_needed;
 e += sizeof(*arg.bits().limbs()) * CHAR_BIT;
 }
 if (original_arg.sign())
 *res = -*res;
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_frexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg, Exponent* e)
{
 switch (arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 *e = 0;
 res = arg;
 return;
 }
 res = arg;
 *e = arg.exponent() + 1;
 res.exponent() = -1;
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I>
inline void eval_frexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg, I* pe)
{
 Exponent e;
 eval_frexp(res, arg, &e);
 if ((e > (std::numeric_limits::max)()) || (e < (std::numeric_limits::min)()))
 {
 BOOST_THROW_EXCEPTION(std::runtime_error("Exponent was outside of the range of the argument type to frexp."));
 }
 *pe = static_cast(e);
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_ldexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg, Exponent e)
{
 switch (arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 res = arg;
 return;
 }
 if ((e > 0) && (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent - e < arg.exponent()))
 {
 // Overflow:
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
 res.sign() = arg.sign();
 }
 else if ((e < 0) && (cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent - e > arg.exponent()))
 {
 // Underflow:
 res = limb_type(0);
 }
 else
 {
 res = arg;
 res.exponent() += e;
 }
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I>
inline typename enable_if_c<is_unsigned::value>::type eval_ldexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg, I e)
{
 typedef typename make_signed::type si_type;
 if (e > static_cast((std::numeric_limits<si_type>::max)()))
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
 else
 eval_ldexp(res, arg, static_cast<si_type>(e));
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class I>
inline typename enable_if_c<is_signed::value>::type eval_ldexp(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg, I e)
{
 if ((e > (std::numeric_limits<Exponent>::max)()) || (e < (std::numeric_limits<Exponent>::min)()))
 {
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity().backend();
 if (e < 0)
 res.negate();
 }
 else
 eval_ldexp(res, arg, static_cast<Exponent>(e));
}

/*
* Sign manipulation
*/

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_abs(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 res = arg;
 res.sign() = false;
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_fabs(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 res = arg;
 res.sign() = false;
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline int eval_fpclassify(const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 switch (arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 return FP_ZERO;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 return FP_INFINITE;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 return FP_NAN;
 }
 return FP_NORMAL;
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_sqrt(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 using default_ops::eval_bit_test;
 using default_ops::eval_increment;
 using default_ops::eval_integer_sqrt;
 switch (arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 errno = EDOM;
 // fallthrough...
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 res = arg;
 return;
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 if (arg.sign())
 {
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 errno = EDOM;
 }
 else
 res = arg;
 return;
 }
 if (arg.sign())
 {
 res = std::numeric_limits<number<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN().backend();
 errno = EDOM;
 return;
 }

typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type t(arg.bits()), r, s;
 eval_left_shift(t, arg.exponent() & 1 ? cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count : cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1);
 eval_integer_sqrt(s, r, t);

if (!eval_bit_test(s, cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count))
 {
 // We have exactly the right number of cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count in the result, round as required:
 if (s.compare(r) < 0)
 {
 eval_increment(s);
 }
 }
 typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type ae = arg.exponent();
 res.exponent() = ae / 2;
 if ((ae & 1) && (ae < 0))
 --res.exponent();
 copy_and_round(res, s);
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_floor(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 using default_ops::eval_increment;
 switch (arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 errno = EDOM;
 // fallthrough...
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 res = arg;
 return;
 }
 typedef typename mpl::if_c<sizeof(typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type) < sizeof(int), int, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type>::type shift_type;
 shift_type shift =
 (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - arg.exponent() - 1;
 if ((arg.exponent() > (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent) || (shift <= 0))
 {
 // Either arg is already an integer, or a special value:
 res = arg;
 return;
 }
 if (shift >= (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
 {
 res = static_cast<signed_limb_type>(arg.sign() ? -1 : 0);
 return;
 }
 bool fractional = (shift_type)eval_lsb(arg.bits()) < shift;
 res = arg;
 eval_right_shift(res.bits(), shift);
 if (fractional && res.sign())
 {
 eval_increment(res.bits());
 if (eval_msb(res.bits()) != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - shift)
 {
 // Must have extended result by one bit in the increment:
 --shift;
 ++res.exponent();
 }
 }
 eval_left_shift(res.bits(), shift);
}

template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_ceil(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
 using default_ops::eval_increment;
 switch (arg.exponent())
 {
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
 errno = EDOM;
 // fallthrough...
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero:
 case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan:
 res = arg;
 return;
 }
 typedef typename mpl::if_c<sizeof(typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type) < sizeof(int), int, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type>::type shift_type;
 shift_type shift = (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - arg.exponent() - 1;
 if ((arg.exponent() > (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent) || (shift <= 0))
 {
 // Either arg is already an integer, or a special value:
 res = arg;
 return;
 }
 if (shift >= (shift_type)cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count)
 {
 bool s = arg.sign(); // takes care of signed zeros
 res = static_cast<signed_limb_type>(arg.sign() ? 0 : 1);
 res.sign() = s;
 return;
 }
 bool fractional = (shift_type)eval_lsb(arg.bits()) < shift;
 res = arg;
 eval_right_shift(res.bits(), shift);
 if (fractional && !res.sign())
 {
 eval_increment(res.bits());
 if (eval_msb(res.bits()) != cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1 - shift)
 {
 // Must have extended result by one bit in the increment:
 --shift;
 ++res.exponent();
 }
 }
 eval_left_shift(res.bits(), shift);
}

template <unsigned D1, backends::digit_base_type B1, class A1, class E1, E1 M1, E1 M2>
int eval_signbit(const cpp_bin_float<D1, B1, A1, E1, M1, M2>& val)
{
 return val.sign();
}

template <unsigned D1, backends::digit_base_type B1, class A1, class E1, E1 M1, E1 M2>
inline std::size_t hash_value(const cpp_bin_float<D1, B1, A1, E1, M1, M2>& val)
{
 std::size_t result = hash_value(val.bits());
 boost::hash_combine(result, val.exponent());
 boost::hash_combine(result, val.sign());
 return result;
}

} // namespace backends

#ifdef BOOST_NO_SFINAE_EXPR

namespace detail {

template <unsigned D1, backends::digit_base_type B1, class A1, class E1, E1 M1, E1 M2, unsigned D2, backends::digit_base_type B2, class A2, class E2, E2 M3, E2 M4>
struct is_explicitly_convertible<backends::cpp_bin_float<D1, B1, A1, E1, M1, M2>, backends::cpp_bin_float<D2, B2, A2, E2, M3, M4> > : public mpl::true_
{};
template <class FloatT, unsigned D2, backends::digit_base_type B2, class A2, class E2, E2 M3, E2 M4>
struct is_explicitly_convertible<FloatT, backends::cpp_bin_float<D2, B2, A2, E2, M3, M4> > : public boost::is_floating_point<FloatT>
{};

} // namespace detail
#endif

template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Exponent, Exponent MinE, Exponent MaxE, class Allocator, boost::multiprecision::expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates>
 copysign BOOST_PREVENT_MACRO_SUBSTITUTION(
 const boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates>& a,
 const boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates>& b)
{
 boost::multiprecision::number<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> res(a);
 res.backend().sign() = b.backend().sign();
 return res;
}

using backends::cpp_bin_float;
using backends::digit_base_10;
using backends::digit_base_2;

template <unsigned Digits, backends::digit_base_type DigitBase, class Exponent, Exponent MinE, Exponent MaxE, class Allocator>
struct number_category<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > : public boost::mpl::int_<boost::multiprecision::number_kind_floating_point>
{};

template <unsigned Digits, backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
struct expression_template_default<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> >
{
 static const expression_template_option value = is_void<Allocator>::value ? et_off : et_on;
};

typedef number<backends::cpp_bin_float<50> > cpp_bin_float_50;
typedef number<backends::cpp_bin_float<100> > cpp_bin_float_100;

typedef number<backends::cpp_bin_float<24, backends::digit_base_2, void, boost::int16_t, -126, 127>, et_off> cpp_bin_float_single;
typedef number<backends::cpp_bin_float<53, backends::digit_base_2, void, boost::int16_t, -1022, 1023>, et_off> cpp_bin_float_double;
typedef number<backends::cpp_bin_float<64, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_double_extended;
typedef number<backends::cpp_bin_float<113, backends::digit_base_2, void, boost::int16_t, -16382, 16383>, et_off> cpp_bin_float_quad;
typedef number<backends::cpp_bin_float<237, backends::digit_base_2, void, boost::int32_t, -262142, 262143>, et_off> cpp_bin_float_oct;

} // namespace multiprecision

namespace math {

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

} // namespace math

} // namespace boost

#include <boost/multiprecision/cpp_bin_float/io.hpp>
#include <boost/multiprecision/cpp_bin_float/transcendental.hpp>

namespace std {

//
// numeric_limits [partial] specializations for the types declared in this header:
//
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
class numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >
{
 typedef boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> number_type;

public:
 BOOST_STATIC_CONSTEXPR bool is_specialized = true;
 static number_type(min)()
 {
 initializer.do_nothing();
 static std::pair<bool, number_type> value;
 if (!value.first)
 {
 value.first = true;
 typedef typename boost::mpl::front<typename number_type::backend_type::unsigned_types>::type ui_type;
 value.second.backend() = ui_type(1u);
 value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent;
 }
 return value.second;
 }
 static number_type(max)()
 {
 initializer.do_nothing();
 static std::pair<bool, number_type> value;
 if (!value.first)
 {
 value.first = true;
 if (boost::is_void<Allocator>::value)
 eval_complement(value.second.backend().bits(), value.second.backend().bits());
 else
 {
 // We jump through hoops here using the backend type directly just to keep VC12 happy
 // (ie compiler workaround, for very strange compiler bug):
 using boost::multiprecision::default_ops::eval_add;
 using boost::multiprecision::default_ops::eval_decrement;
 using boost::multiprecision::default_ops::eval_left_shift;
 typedef typename number_type::backend_type::rep_type int_backend_type;
 typedef typename boost::mpl::front<typename int_backend_type::unsigned_types>::type ui_type;
 int_backend_type i;
 i = ui_type(1u);
 eval_left_shift(i, boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1);
 int_backend_type j(i);
 eval_decrement(i);
 eval_add(j, i);
 value.second.backend().bits() = j;
 }
 value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent;
 }
 return value.second;
 }
 BOOST_STATIC_CONSTEXPR number_type lowest()
 {
 return -(max)();
 }
 BOOST_STATIC_CONSTEXPR int digits = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count;
 BOOST_STATIC_CONSTEXPR int digits10 = (digits - 1) * 301 / 1000;
 // Is this really correct???
 BOOST_STATIC_CONSTEXPR int max_digits10 = (digits * 301 / 1000) + 3;
 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()
 {
 initializer.do_nothing();
 static std::pair<bool, number_type> value;
 if (!value.first)
 {
 // We jump through hoops here just to keep VC12 happy (ie compiler workaround, for very strange compiler bug):
 typedef typename boost::mpl::front<typename number_type::backend_type::unsigned_types>::type ui_type;
 value.first = true;
 value.second.backend() = ui_type(1u);
 value.second = ldexp(value.second, 1 - (int)digits);
 }
 return value.second;
 }
 // What value should this be????
 static number_type round_error()
 {
 // returns 0.5
 initializer.do_nothing();
 static std::pair<bool, number_type> value;
 if (!value.first)
 {
 value.first = true;
 // We jump through hoops here just to keep VC12 happy (ie compiler workaround, for very strange compiler bug):
 typedef typename boost::mpl::front<typename number_type::backend_type::unsigned_types>::type ui_type;
 value.second.backend() = ui_type(1u);
 value.second = ldexp(value.second, -1);
 }
 return value.second;
 }
 BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type min_exponent = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent;
 BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type min_exponent10 = (min_exponent / 1000) * 301L;
 BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type max_exponent = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent;
 BOOST_STATIC_CONSTEXPR typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type max_exponent10 = (max_exponent / 1000) * 301L;
 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_absent;
 BOOST_STATIC_CONSTEXPR bool has_denorm_loss = false;
 static number_type infinity()
 {
 initializer.do_nothing();
 static std::pair<bool, number_type> value;
 if (!value.first)
 {
 value.first = true;
 value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
 }
 return value.second;
 }
 static number_type quiet_NaN()
 {
 initializer.do_nothing();
 static std::pair<bool, number_type> value;
 if (!value.first)
 {
 value.first = true;
 value.second.backend().exponent() = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_nan;
 }
 return value.second;
 }
 BOOST_STATIC_CONSTEXPR number_type signaling_NaN()
 {
 return number_type(0);
 }
 BOOST_STATIC_CONSTEXPR number_type denorm_min() { return number_type(0); }
 BOOST_STATIC_CONSTEXPR bool is_iec559 = false;
 BOOST_STATIC_CONSTEXPR bool is_bounded = true;
 BOOST_STATIC_CONSTEXPR bool is_modulo = false;
 BOOST_STATIC_CONSTEXPR bool traps = true;
 BOOST_STATIC_CONSTEXPR bool tinyness_before = false;
 BOOST_STATIC_CONSTEXPR float_round_style round_style = round_to_nearest;

private:
 struct data_initializer
 {
 data_initializer()
 {
 std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::epsilon();
 std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::round_error();
 (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::min)();
 (std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::max)();
 std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::infinity();
 std::numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE> > >::quiet_NaN();
 }
 void do_nothing() const {}
 };
 static const data_initializer initializer;
};

#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION

template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::digits;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::digits10;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::max_digits10;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_signed;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_integer;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_exact;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST int numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::radix;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::min_exponent;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::min_exponent10;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::max_exponent;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::max_exponent10;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_infinity;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_quiet_NaN;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_signaling_NaN;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_denorm;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::has_denorm_loss;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_iec559;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_bounded;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::is_modulo;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::traps;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST bool numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::tinyness_before;
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
BOOST_CONSTEXPR_OR_CONST float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::round_style;

#endif

} // namespace std

#endif