////////////////////////////////////////////////////////////////
// Copyright 2013 - 2022 John Maddock.
// Copyright 2022 Christopher Kormanyos.
// 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_MP_CPP_BIN_FLOAT_HPP
#define BOOST_MP_CPP_BIN_FLOAT_HPP
#include <cmath>
#include <cstdint>
#include <limits>
#include <type_traits>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/integer.hpp>
#include <boost/multiprecision/detail/standalone_config.hpp>
#include <boost/multiprecision/detail/fpclassify.hpp>
#include <boost/multiprecision/detail/float_string_cvt.hpp>
#include <boost/multiprecision/traits/max_digits10.hpp>
#include <boost/multiprecision/detail/hash.hpp>
#include <boost/multiprecision/detail/no_exceptions_support.hpp>
#include <boost/multiprecision/detail/assert.hpp>
#include <boost/multiprecision/detail/float128_functions.hpp>
#include <boost/multiprecision/detail/functions/trunc.hpp>
//
// Some includes we need from Boost.Math, since we rely on that library to provide these functions:
//
#ifdef BOOST_MP_MATH_AVAILABLE
#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>
#endif
#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 std::enable_if<boost::multiprecision::detail::is_unsigned<U>::value, bool>::type is_negative(U) { return false; }
template <class S>
inline typename std::enable_if< !boost::multiprecision::detail::is_unsigned<S>::value, bool>::type is_negative(S s) { return s < 0; }
template <class Float, std::ptrdiff_t, bool = number_category<Float>::value == number_kind_floating_point>
struct is_cpp_bin_float_implicitly_constructible_from_type
{
static constexpr bool value = false;
};
template <class Float, std::ptrdiff_t bit_count>
struct is_cpp_bin_float_implicitly_constructible_from_type<Float, bit_count, true>
{
static constexpr bool value = (std::numeric_limits<Float>::digits <= static_cast<int>(bit_count)) && (std::numeric_limits<Float>::radix == 2) && std::numeric_limits<Float>::is_specialized
#ifdef BOOST_HAS_FLOAT128
&& !std::is_same<Float, float128_type>::value
#endif
&& (std::is_floating_point<Float>::value || is_number<Float>::value);
};
template <class Float, std::ptrdiff_t, bool = number_category<Float>::value == number_kind_floating_point>
struct is_cpp_bin_float_explicitly_constructible_from_type
{
static constexpr bool value = false;
};
template <class Float, std::ptrdiff_t bit_count>
struct is_cpp_bin_float_explicitly_constructible_from_type<Float, bit_count, true>
{
static constexpr bool value = (std::numeric_limits<Float>::digits > static_cast<int>(bit_count)) && (std::numeric_limits<Float>::radix == 2) && std::numeric_limits<Float>::is_specialized
#ifdef BOOST_HAS_FLOAT128
&& !std::is_same<Float, float128_type>::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 constexpr unsigned bit_count = DigitBase == digit_base_2 ? Digits : (Digits * 1000uL) / 301uL + (((Digits * 1000uL) % 301) ? 2u : 1u);
using rep_type = cpp_int_backend<std::is_void<Allocator>::value ? bit_count : 0, bit_count, std::is_void<Allocator>::value ? unsigned_magnitude : signed_magnitude, unchecked, Allocator>;
using double_rep_type = cpp_int_backend<std::is_void<Allocator>::value ? 2 * bit_count : 0, 2 * bit_count, std::is_void<Allocator>::value ? unsigned_magnitude : signed_magnitude, unchecked, Allocator>;
using signed_types = typename rep_type::signed_types;
using unsigned_types = typename rep_type::unsigned_types;
using float_types = std::tuple<float, double, long double>;
using exponent_type = Exponent;
static constexpr exponent_type max_exponent_limit = (std::numeric_limits<exponent_type>::max)()- 2 * static_cast<exponent_type>(bit_count);
static constexpr exponent_type min_exponent_limit = (std::numeric_limits<exponent_type>::min)() + 2 * static_cast<exponent_type>(bit_count);
static_assert(MinExponent >= min_exponent_limit, "Template parameter MinExponent is too negative for our internal logic to function correctly, sorry!");
static_assert(MaxExponent <= max_exponent_limit, "Template parameter MaxExponent is too large for our internal logic to function correctly, sorry!");
static_assert(MinExponent <= 0, "Template parameter MinExponent can not be positive!");
static_assert(MaxExponent >= 0, "Template parameter MaxExponent can not be negative!");
static constexpr exponent_type max_exponent = MaxExponent == 0 ? max_exponent_limit : MaxExponent;
static constexpr exponent_type min_exponent = MinExponent == 0 ? min_exponent_limit : MinExponent;
static constexpr exponent_type exponent_zero = max_exponent + 1;
static constexpr exponent_type exponent_infinity = max_exponent + 2;
static constexpr exponent_type exponent_nan = max_exponent + 3;
private:
rep_type m_data;
exponent_type m_exponent;
bool m_sign;
public:
cpp_bin_float() noexcept(noexcept(rep_type())) : m_data(), m_exponent(exponent_zero), m_sign(false) {}
cpp_bin_float(const cpp_bin_float& o) noexcept(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 std::enable_if<(bit_count >= cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count)>::type const* = nullptr)
{
*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 std::enable_if< !(bit_count >= cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count)>::type const* = nullptr)
: m_exponent(o.exponent()), m_sign(o.sign())
{
*this = o;
}
// rvalue copy:
template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
cpp_bin_float(cpp_bin_float<D, B, A, E, MinE, MaxE>&& o, typename std::enable_if<(bit_count >= cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count)>::type const* = nullptr)noexcept(noexcept(rep_type(std::declval<rep_type&&>())))
{
*this = std::move(o);
}
template <unsigned D, digit_base_type B, class A, class E, E MinE, E MaxE>
explicit cpp_bin_float(cpp_bin_float<D, B, A, E, MinE, MaxE>&& o, typename std::enable_if< !(bit_count >= cpp_bin_float<D, B, A, E, MinE, MaxE>::bit_count)>::type const* = nullptr) noexcept(noexcept(rep_type(std::declval<rep_type&&>())))
: m_exponent(o.exponent()), m_sign(o.sign())
{
*this = std::move(o);
}
template <class Float>
cpp_bin_float(const Float& f,
typename std::enable_if<detail::is_cpp_bin_float_implicitly_constructible_from_type<Float, static_cast<std::ptrdiff_t>(bit_count)>::value>::type const* = nullptr)
: m_data(), m_exponent(0), m_sign(false)
{
this->assign_float(f);
}
template <class Float>
explicit cpp_bin_float(const Float& f,
typename std::enable_if<detail::is_cpp_bin_float_explicitly_constructible_from_type<Float, static_cast<std::ptrdiff_t>(bit_count)>::value>::type const* = nullptr)
: 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 std::enable_if<
std::is_same<Float, float128_type>::value && (static_cast<int>(bit_count) >= 113)>::type const* = nullptr)
: m_data(), m_exponent(0), m_sign(false)
{
this->assign_float(f);
}
template <class Float>
explicit cpp_bin_float(const Float& f,
typename std::enable_if<
std::is_same<Float, float128_type>::value && (static_cast<int>(bit_count) < 113)>::type const* = nullptr)
: m_data(), m_exponent(0), m_sign(false)
{
this->assign_float(f);
}
#endif
cpp_bin_float& operator=(const cpp_bin_float& o) noexcept(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 <class A, class E, E MinE, E MaxE>
cpp_bin_float& operator=(const cpp_bin_float<Digits, DigitBase, A, E, MinE, MaxE>& o) noexcept(noexcept(std::declval<rep_type&>() = std::declval<const rep_type&>()))
{
m_data = o.bits();
m_sign = o.sign();
if (o.exponent() == cpp_bin_float<Digits, DigitBase, A, E, MinE, MaxE>::exponent_zero)
m_exponent = exponent_zero;
else if (o.exponent() == cpp_bin_float<Digits, DigitBase, A, E, MinE, MaxE>::exponent_nan)
m_exponent = exponent_nan;
else if (o.exponent() == cpp_bin_float<Digits, DigitBase, A, E, MinE, MaxE>::exponent_infinity)
m_exponent = exponent_infinity;
else if (o.exponent() > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent)
{
// Overflow:
exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
bits() = static_cast<limb_type>(0u);
}
else if (o.exponent() < cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent)
{
// Underflow:
exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
bits() = static_cast<limb_type>(0u);
}
else
m_exponent = o.exponent();
return *this;
}
// rvalue copy:
template <class A, class E, E MinE, E MaxE>
cpp_bin_float& operator=(cpp_bin_float<Digits, DigitBase, A, E, MinE, MaxE>&& o) noexcept(noexcept(std::declval<rep_type&>() = std::declval<rep_type&&>()))
{
m_data = std::move(o.bits());
m_sign = o.sign();
if (o.exponent() == cpp_bin_float<Digits, DigitBase, A, E, MinE, MaxE>::exponent_zero)
m_exponent = exponent_zero;
else if (o.exponent() == cpp_bin_float<Digits, DigitBase, A, E, MinE, MaxE>::exponent_nan)
m_exponent = exponent_nan;
else if (o.exponent() == cpp_bin_float<Digits, DigitBase, A, E, MinE, MaxE>::exponent_infinity)
m_exponent = exponent_infinity;
else if (o.exponent() > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent)
{
// Overflow:
exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity;
bits() = static_cast<limb_type>(0u);
}
else if (o.exponent() < cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::min_exponent)
{
// Underflow:
exponent() = cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_zero;
bits() = static_cast<limb_type>(0u);
}
else
m_exponent = o.exponent();
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 std::enable_if<
(number_category<Float>::value == number_kind_floating_point)
//&& (std::numeric_limits<Float>::digits <= static_cast<int>(bit_count))
&& ((std::numeric_limits<Float>::radix == 2) || (std::is_same<Float, float128_type>::value)),
cpp_bin_float&>::type
operator=(const Float& f)
#else
template <class Float>
typename std::enable_if<
(number_category<Float>::value == number_kind_floating_point)
//&& (std::numeric_limits<Float>::digits <= static_cast<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 std::enable_if<std::is_same<Float, float128_type>::value, cpp_bin_float&>::type assign_float(Float f)
{
using default_ops::eval_add;
using bf_int_type = typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::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;
}
using ui_type = typename std::tuple_element<0, unsigned_types>::type;
m_data = static_cast<ui_type>(0u);
m_sign = false;
m_exponent = 0;
constexpr std::ptrdiff_t bits = sizeof(int) * CHAR_BIT - 1;
int e;
f = frexpq(f, &e);
while (f)
{
f = ldexpq(f, bits);
e -= bits;
int ipart = static_cast<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 std::enable_if<std::is_floating_point<Float>::value && !std::is_same<Float, float128_type>::value, cpp_bin_float&>::type assign_float(Float f)
#else
template <class Float>
typename std::enable_if<std::is_floating_point<Float>::value, cpp_bin_float&>::type assign_float(Float f)
#endif
{
using std::frexp;
using std::ldexp;
using std::signbit;
using default_ops::eval_add;
using bf_int_type = typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::type;
switch (BOOST_MP_FPCLASSIFY(f))
{
case FP_ZERO:
m_data = limb_type(0);
m_sign = ((signbit)(f));
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;
}
using ui_type = typename std::tuple_element<0, unsigned_types>::type;
m_data = static_cast<ui_type>(0u);
m_sign = false;
m_exponent = 0;
constexpr std::ptrdiff_t bits = sizeof(int) * CHAR_BIT - 1;
int e;
f = frexp(f, &e);
while (f != static_cast<Float>(0.0F))
{
f = ldexp(f, bits);
e -= static_cast<int>(bits);
int ipart = boost::multiprecision::detail::itrunc(f);
f -= static_cast<Float>(ipart);
m_exponent += static_cast<exponent_type>(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 std::enable_if<
(number_category<Float>::value == number_kind_floating_point) && !std::is_floating_point<Float>::value && (number_category<Float>::value == number_kind_floating_point),
cpp_bin_float&>::type
assign_float(Float f)
{
using default_ops::eval_add;
using default_ops::eval_convert_to;
using default_ops::eval_get_sign;
using default_ops::eval_subtract;
using f_int_type = typename boost::multiprecision::detail::canonical<int, Float>::type ;
using bf_int_type = typename boost::multiprecision::detail::canonical<int, cpp_bin_float>::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();
assign_float(f);
this->negate();
return *this;
}
using ui_type = typename std::tuple_element<0, unsigned_types>::type;
m_data = static_cast<ui_type>(0u);
m_sign = false;
m_exponent = 0;
constexpr std::ptrdiff_t 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 std::enable_if<boost::multiprecision::detail::is_integral<I>::value, 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
{
using ui_type = typename boost::multiprecision::detail::make_unsigned<I>::type ;
ui_type fi = static_cast<ui_type>(boost::multiprecision::detail::unsigned_abs(i));
using ar_type = typename boost::multiprecision::detail::canonical<ui_type, rep_type>::type;
m_data = static_cast<ar_type>(fi);
std::size_t 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_MP_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) 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 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 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_MP_ASSERT(eval_bit_test(m_data, bit_count - 1));
}
else
{
BOOST_MP_ASSERT(m_exponent > max_exponent);
BOOST_MP_ASSERT(m_exponent <= exponent_nan);
BOOST_MP_ASSERT(eval_is_zero(m_data));
}
}
#ifndef BOOST_MP_STANDALONE
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);
}
#endif
};
#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, std::ptrdiff_t 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;
}
std::ptrdiff_t msb = static_cast<std::ptrdiff_t>(eval_msb(arg));
if (static_cast<std::ptrdiff_t >(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(), static_cast<double_limb_type>(bits_to_keep - msb - 1));
res.exponent() -= static_cast<Exponent>(bits_to_keep - msb - 1);
}
else if (static_cast<std::ptrdiff_t >(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, static_cast<std::size_t>(msb - bits_to_keep));
// Then check for a tie:
if (roundup && (msb - bits_to_keep == static_cast<std::ptrdiff_t>(eval_lsb(arg))))
{
// Ties round towards even:
if (!eval_bit_test(arg, static_cast<std::size_t>(msb - bits_to_keep + 1)))
roundup = false;
}
// Shift off the bits_to_keep we don't need:
eval_right_shift(arg, static_cast<double_limb_type>(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, static_cast<std::size_t>(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, static_cast<double_limb_type>(static_cast<std::ptrdiff_t>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) - bits_to_keep));
res.exponent() -= static_cast<Exponent>(static_cast<std::ptrdiff_t>(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_MP_ASSERT(((std::ptrdiff_t )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, class BinFloat2, class BinFloat3>
inline void do_eval_add(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const BinFloat2& a, const BinFloat3& 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;
using exponent_type = typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type;
typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;
// Special cases first:
switch (a.exponent())
{
case BinFloat2::exponent_zero:
{
bool s = a.sign();
res = b;
res.sign() = s;
return;
}
case BinFloat2::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 BinFloat3::exponent_zero:
res = a;
return;
case BinFloat3::exponent_infinity:
res = b;
if (res.sign())
res.negate();
return; // result is infinite.
case BinFloat3::exponent_nan:
res = b;
return; // result is a NaN.
}
static_assert((std::numeric_limits<exponent_type>::max)() - cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count > cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::max_exponent, "Exponent range check failed");
bool s = a.sign();
dt = a.bits();
if (a.exponent() > (std::ptrdiff_t )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_MP_ASSERT(e_diff >= 0);
eval_left_shift(dt, static_cast<double_limb_type>(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 <class BinFloat1, class BinFloat2, class BinFloat3>
inline void do_eval_subtract(BinFloat1& res, const BinFloat2& a, const BinFloat3& b)
{
using default_ops::eval_bit_test;
using default_ops::eval_decrement;
using default_ops::eval_subtract;
typename BinFloat1::double_rep_type dt;
// Special cases first:
switch (a.exponent())
{
case BinFloat2::exponent_zero:
if (b.exponent() == BinFloat3::exponent_nan)
res = std::numeric_limits<number<BinFloat1> >::quiet_NaN().backend();
else
{
bool s = a.sign();
res = b;
if (res.exponent() == BinFloat1::exponent_zero)
res.sign() = false;
else if (res.sign() == s)
res.negate();
}
return;
case BinFloat2::exponent_infinity:
if ((b.exponent() == BinFloat3::exponent_nan) || (b.exponent() == BinFloat3::exponent_infinity))
res = std::numeric_limits<number<BinFloat1> >::quiet_NaN().backend();
else
res = a;
return;
case BinFloat2::exponent_nan:
res = a;
return; // result is still a NaN.
}
switch (b.exponent())
{
case BinFloat3::exponent_zero:
res = a;
return;
case BinFloat3::exponent_infinity:
res.exponent() = BinFloat1::exponent_infinity;
res.sign() = !a.sign();
res.bits() = static_cast<limb_type>(0u);
return; // result is a NaN.
case BinFloat3::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() <= (std::ptrdiff_t )BinFloat1::bit_count + b.exponent())
{
typename BinFloat1::exponent_type e_diff = a.exponent() - b.exponent();
eval_left_shift(dt, static_cast<double_limb_type>(e_diff));
res.exponent() = a.exponent() - e_diff;
eval_subtract(dt, b.bits());
}
else if (a.exponent() == (std::ptrdiff_t )BinFloat1::bit_count + b.exponent() + 1)
{
if ((eval_lsb(a.bits()) == BinFloat1::bit_count - 1)
&& (eval_lsb(b.bits()) != BinFloat1::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() <= (std::ptrdiff_t )BinFloat1::bit_count + a.exponent())
{
typename BinFloat1::exponent_type e_diff = a.exponent() - b.exponent();
eval_left_shift(dt, static_cast<double_limb_type>(-e_diff));
res.exponent() = b.exponent() + e_diff;
eval_subtract(dt, a.bits());
}
else if (b.exponent() == (std::ptrdiff_t )BinFloat1::bit_count + a.exponent() + 1)
{
if ((eval_lsb(a.bits()) != BinFloat1::bit_count - 1)
&& eval_lsb(b.bits()))
{
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() == BinFloat1::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,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2,
class Allocator3, class Exponent3, Exponent MinE3, Exponent MaxE3>
inline void eval_add(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& a,
const cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>& 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,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2>
inline void eval_add(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& a)
{
return eval_add(res, res, a);
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2,
class Allocator3, class Exponent3, Exponent MinE3, Exponent MaxE3>
inline void eval_subtract(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& a,
const cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>& 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,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2>
inline void eval_subtract(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& a)
{
return eval_subtract(res, res, a);
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2,
class Allocator3, class Exponent3, Exponent MinE3, Exponent MaxE3>
inline void eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& a,
const cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>& b)
{
using default_ops::eval_bit_test;
using default_ops::eval_multiply;
// Special cases first:
switch (a.exponent())
{
case cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>::exponent_zero:
{
if (b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>::exponent_nan)
res = b;
else if (b.exponent() == cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>::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, Allocator2, Exponent2, MinE2, MaxE2>::exponent_infinity:
switch (b.exponent())
{
case cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>::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, Allocator3, Exponent3, MinE3, MaxE3>::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, Allocator2, Exponent2, MinE2, MaxE2>::exponent_nan:
res = a;
return;
}
if (b.exponent() > cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>::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();
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2>
inline void eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& a)
{
eval_multiply(res, res, a);
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2, class U>
inline typename std::enable_if<boost::multiprecision::detail::is_unsigned<U>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& a, const U& b)
{
using default_ops::eval_bit_test;
using default_ops::eval_multiply;
bool s = a.sign(); // saved for later in case a and res are the same object.
// Special cases first:
switch (a.exponent())
{
case cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>::exponent_zero:
{
res = a;
res.sign() = s;
return;
}
case cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>::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, Allocator2, Exponent2, MinE2, MaxE2>::exponent_nan:
res = a;
return;
}
typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type dt;
using canon_ui_type = typename boost::multiprecision::detail::canonical<U, typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::double_rep_type>::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() = s;
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class U>
inline typename std::enable_if<boost::multiprecision::detail::is_unsigned<U>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const U& b)
{
eval_multiply(res, res, b);
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2, class S>
inline typename std::enable_if<boost::multiprecision::detail::is_signed<S>::value && boost::multiprecision::detail::is_integral<S>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& a, const S& b)
{
using ui_type = typename boost::multiprecision::detail::make_unsigned<S>::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, class S>
inline typename std::enable_if<boost::multiprecision::detail::is_signed<S>::value && boost::multiprecision::detail::is_integral<S>::value>::type eval_multiply(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const S& b)
{
eval_multiply(res, res, b);
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2,
class Allocator3, class Exponent3, Exponent MinE3, Exponent MaxE3>
inline void eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& u,
const cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>& 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, Allocator2, Exponent2, MinE2, MaxE2>::exponent_zero:
{
switch (v.exponent())
{
case cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>::exponent_zero:
case cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>::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, Allocator2, Exponent2, MinE2, MaxE2>::exponent_infinity:
{
switch (v.exponent())
{
case cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>::exponent_infinity:
case cpp_bin_float<Digits, DigitBase, Allocator3, Exponent3, MinE3, MaxE3>::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, Allocator2, Exponent2, MinE2, MaxE2>::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, Allocator3, Exponent3, MinE3, MaxE3>::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, Allocator3, Exponent3, MinE3, MaxE3>::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, Allocator3, Exponent3, MinE3, MaxE3>::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.
//
constexpr 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_MP_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.
//
using local_exponent_type = typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type;
BOOST_MP_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1));
constexpr 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() -= static_cast<local_exponent_type>(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 Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2>
inline void eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& arg)
{
eval_divide(res, res, arg);
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2, class U>
inline typename std::enable_if<boost::multiprecision::detail::is_unsigned<U>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& 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, Allocator2, Exponent2, MinE2, MaxE2>::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, Allocator2, Exponent2, MinE2, MaxE2>::exponent_infinity:
res = u;
return;
case cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>::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:
//
std::ptrdiff_t gb = static_cast<std::ptrdiff_t>(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, static_cast<double_limb_type>(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.
//
constexpr 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_MP_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.
//
using local_exponent_type = typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type;
BOOST_MP_ASSERT((eval_msb(q) == cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count - 1));
constexpr 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() -= static_cast<local_exponent_type>(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 U>
inline typename std::enable_if<boost::multiprecision::detail::is_unsigned<U>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const U& v)
{
eval_divide(res, res, v);
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE,
class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2, class S>
inline typename std::enable_if<boost::multiprecision::detail::is_signed<S>::value && boost::multiprecision::detail::is_integral<S>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res,
const cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2>& u, const S& v)
{
using ui_type = typename boost::multiprecision::detail::make_unsigned<S>::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, class S>
inline typename std::enable_if<boost::multiprecision::detail::is_signed<S>::value && boost::multiprecision::detail::is_integral<S>::value>::type eval_divide(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const S& v)
{
eval_divide(res, res, v);
}
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 <class I, unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void convert_to_signed_int(I* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
static constexpr int digits = std::numeric_limits<I>::is_specialized ? std::numeric_limits<I>::digits : sizeof(I) * CHAR_BIT - 1;
static constexpr I max_val = std::numeric_limits<I>::is_specialized ? (std::numeric_limits<I>::max)() : (((I(1) << (sizeof(I) * CHAR_BIT - 2)) - 1) << 1) + 1;
static constexpr I min_val = std::numeric_limits<I>::is_specialized ? (std::numeric_limits<I>::min)() : -max_val - 1;
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_MP_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer."));
return;
case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
*res = max_val;
if (arg.sign())
*res = -*res;
return;
}
using shift_type = typename std::conditional<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;
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(min_val) <= 0))
{
*res = min_val;
return;
}
else if (!arg.sign() && (arg.compare(max_val) >= 0))
{
*res = max_val;
return;
}
if (shift < 0)
{
if (static_cast<int>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) - static_cast<int>(shift) <= 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<I>::max)();
return;
}
}
else
{
eval_right_shift(man, static_cast<double_limb_type>(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(long long* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
convert_to_signed_int(res, arg);
}
#ifdef BOOST_HAS_INT128
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_convert_to(int128_type* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
convert_to_signed_int(res, arg);
}
#endif
template <class I, unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void convert_to_unsigned_int(I* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
static constexpr int digits = std::numeric_limits<I>::is_specialized ? std::numeric_limits<I>::digits : sizeof(I) * CHAR_BIT;
static constexpr I max_val = std::numeric_limits<I>::is_specialized ? (std::numeric_limits<I>::max)() : ~static_cast<I>(0);
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_MP_THROW_EXCEPTION(std::runtime_error("Could not convert NaN to integer."));
case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
*res = max_val;
return;
}
typename cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::rep_type man(arg.bits());
using shift_type = typename std::conditional<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 = (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 <= 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 = max_val;
return;
}
eval_right_shift(man, shift);
eval_convert_to(res, man);
}
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_convert_to(unsigned long long* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
convert_to_unsigned_int(res, arg);
}
#ifdef BOOST_HAS_INT128
template <unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline void eval_convert_to(uint128_type* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& arg)
{
convert_to_unsigned_int(res, arg);
}
#endif
template <class Float, unsigned Digits, digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE>
inline typename std::enable_if<std::is_floating_point<Float>::value>::type eval_convert_to(Float* res, const cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& original_arg)
{
using conv_type = cpp_bin_float<std::numeric_limits<Float>::digits, digit_base_2, void, Exponent, MinE, MaxE>;
using common_exp_type = typename std::common_type<typename conv_type::exponent_type, int>::type;
static constexpr int float_digits = boost::multiprecision::detail::is_float128<Float>::value ? 113 : std::numeric_limits<Float>::digits;
BOOST_MP_FLOAT128_USING using std::ldexp;
//
// 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:
BOOST_IF_CONSTEXPR(boost::multiprecision::detail::is_float128<Float>::value)
{
*res = static_cast<Float>(std::numeric_limits<double>::quiet_NaN());
}
else
{
*res = std::numeric_limits<Float>::quiet_NaN();
}
return;
case cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_infinity:
BOOST_IF_CONSTEXPR(boost::multiprecision::detail::is_float128<Float>::value)
{
*res = static_cast<Float>((std::numeric_limits<double>::infinity)());
}
else
{
*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() > (boost::multiprecision::detail::is_float128<Float>::value ? 16384 : std::numeric_limits<Float>::max_exponent))
{
BOOST_IF_CONSTEXPR(boost::multiprecision::detail::is_float128<Float>::value)
{
*res = static_cast<Float>(std::numeric_limits<double>::infinity());
}
else
{
*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 = float_digits;
if (original_arg.exponent() < std::numeric_limits<Float>::min_exponent - 1)
{
common_exp_type diff = original_arg.exponent();
diff -= boost::multiprecision::detail::is_float128<Float>::value ? -16382 : 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<static_cast<unsigned>(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, (std::ptrdiff_t)digits_to_round_to);
common_exp_type e = arg.exponent();
e -= static_cast<common_exp_type>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) - 1;
constexpr std::size_t limbs_needed = static_cast<std::size_t>(float_digits) / (sizeof(*arg.bits().limbs()) * CHAR_BIT) + (static_cast<std::size_t>(float_digits) % (sizeof(*arg.bits().limbs()) * CHAR_BIT) ? 1 : 0);
std::size_t first_limb_needed = arg.bits().size() - limbs_needed;
*res = 0;
e += static_cast<common_exp_type>(first_limb_needed * sizeof(*arg.bits().limbs()) * CHAR_BIT);
while (first_limb_needed < arg.bits().size())
{
*res += ldexp(static_cast<Float>(arg.bits().limbs()[first_limb_needed]), static_cast<int>(e));
++first_limb_needed;
e += static_cast<common_exp_type>(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<I>::max)()) || (e < (std::numeric_limits<I>::min)()))
{
BOOST_MP_THROW_EXCEPTION(std::runtime_error("Exponent was outside of the range of the argument type to frexp."));
}
*pe = static_cast<I>(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 std::enable_if<boost::multiprecision::detail::is_unsigned<I>::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)
{
using si_type = typename boost::multiprecision::detail::make_signed<I>::type;
if (e > static_cast<I>((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 std::enable_if<boost::multiprecision::detail::is_signed<I>::value && boost::multiprecision::detail::is_integral<I>::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,
unsigned Digits2, digit_base_type DigitBase2, class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2>
inline void eval_abs(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits2, DigitBase2, Allocator2, Exponent2, MinE2, MaxE2>& arg)
{
res = arg;
res.sign() = false;
}
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,
unsigned Digits2, digit_base_type DigitBase2, class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2>
inline void eval_fabs(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>& res, const cpp_bin_float<Digits2, DigitBase2, Allocator2, Exponent2, MinE2, MaxE2>& 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;
res.sign() = false;
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;
}
using shift_type = typename std::conditional<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 =
(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(), static_cast<double_limb_type>(shift));
if (fractional && res.sign())
{
eval_increment(res.bits());
const std::ptrdiff_t shift_check =
static_cast<std::ptrdiff_t>(static_cast<std::ptrdiff_t>(cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count) - 1 - static_cast<std::ptrdiff_t>(shift));
if (static_cast<std::ptrdiff_t>(eval_msb(res.bits())) != shift_check)
{
// Must have extended result by one bit in the increment:
--shift;
++res.exponent();
}
}
eval_left_shift(res.bits(), static_cast<double_limb_type>(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;
}
using shift_type = typename std::conditional<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 = (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 ((std::ptrdiff_t)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::multiprecision::detail::hash_combine(result, val.exponent(), val.sign());
return result;
}
} // namespace backends
namespace detail {
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinExponent, Exponent MaxExponent>
struct transcendental_reduction_type<boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent> >
{
//
// The type used for trigonometric reduction needs 3 times the precision of the base type.
// This is double the precision of the original type, plus the largest exponent supported.
// As a practical measure the largest argument supported is 1/eps, as supporting larger
// arguments requires the division of argument by PI/2 to also be done at higher precision,
// otherwise the result (an integer) can not be represented exactly.
//
// See ARGUMENT REDUCTION FOR HUGE ARGUMENTS. K C Ng.
//
using type = boost::multiprecision::backends::cpp_bin_float<
boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent>::bit_count * 3,
boost::multiprecision::backends::digit_base_2,
Allocator, Exponent, MinExponent, MaxExponent>;
};
#ifdef BOOST_HAS_INT128
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinExponent, Exponent MaxExponent>
struct is_convertible_arithmetic<int128_type, boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent> > : public std::true_type
{};
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinExponent, Exponent MaxExponent>
struct is_convertible_arithmetic<uint128_type, boost::multiprecision::backends::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinExponent, MaxExponent> > : public std::true_type
{};
#endif
} // namespace detail
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 std::integral_constant<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 constexpr expression_template_option value = std::is_void<Allocator>::value ? et_off : et_on;
};
template <unsigned Digits, backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, class Allocator2, class Exponent2, Exponent MinE2, Exponent MaxE2>
struct is_equivalent_number_type<cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, cpp_bin_float<Digits, DigitBase, Allocator2, Exponent2, MinE2, MaxE2> >
: public std::integral_constant<bool, true> {};
using cpp_bin_float_50 = number<backends::cpp_bin_float<50> > ;
using cpp_bin_float_100 = number<backends::cpp_bin_float<100> >;
using cpp_bin_float_single = number<backends::cpp_bin_float<24, backends::digit_base_2, void, std::int16_t, -126, 127>, et_off> ;
using cpp_bin_float_double = number<backends::cpp_bin_float<53, backends::digit_base_2, void, std::int16_t, -1022, 1023>, et_off> ;
using cpp_bin_float_double_extended = number<backends::cpp_bin_float<64, backends::digit_base_2, void, std::int16_t, -16382, 16383>, et_off> ;
using cpp_bin_float_quad = number<backends::cpp_bin_float<113, backends::digit_base_2, void, std::int16_t, -16382, 16383>, et_off> ;
using cpp_bin_float_oct = number<backends::cpp_bin_float<237, backends::digit_base_2, void, std::int32_t, -262142, 262143>, et_off>;
} // 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> >
{
using number_type = boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates>;
public:
static constexpr bool is_specialized = true;
static number_type(min)()
{
static std::pair<bool, number_type> value;
if (!value.first)
{
value.first = true;
using ui_type = typename std::tuple_element<0, typename number_type::backend_type::unsigned_types>::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;
}
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable : 4127) // conditional expression is constant
#endif
static number_type(max)()
{
static std::pair<bool, number_type> value;
if (!value.first)
{
value.first = true;
BOOST_IF_CONSTEXPR(std::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;
using int_backend_type = typename number_type::backend_type::rep_type ;
using ui_type = typename std::tuple_element<0, typename int_backend_type::unsigned_types>::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;
}
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
static constexpr number_type lowest()
{
return -(max)();
}
static constexpr int digits = boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::bit_count;
static constexpr int digits10 = boost::multiprecision::detail::calc_digits10<static_cast<unsigned>(digits)>::value;
// Is this really correct???
static constexpr int max_digits10 = boost::multiprecision::detail::calc_max_digits10<static_cast<unsigned>(digits)>::value;
static constexpr bool is_signed = true;
static constexpr bool is_integer = false;
static constexpr bool is_exact = false;
static constexpr int radix = 2;
static number_type epsilon()
{
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):
using ui_type = typename std::tuple_element<0, typename number_type::backend_type::unsigned_types>::type;
value.first = true;
value.second.backend() = ui_type(1u);
value.second = ldexp(value.second, 1 - static_cast<int>(digits));
}
return value.second;
}
// What value should this be????
static number_type round_error()
{
// returns 0.5
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):
using ui_type = typename std::tuple_element<0, typename number_type::backend_type::unsigned_types>::type;
value.second.backend() = ui_type(1u);
value.second = ldexp(value.second, -1);
}
return value.second;
}
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;
static constexpr typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type min_exponent10 = (min_exponent / 1000) * 301L;
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;
static constexpr typename boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>::exponent_type max_exponent10 = (max_exponent / 1000) * 301L;
static constexpr bool has_infinity = true;
static constexpr bool has_quiet_NaN = true;
static constexpr bool has_signaling_NaN = false;
static constexpr float_denorm_style has_denorm = denorm_absent;
static constexpr bool has_denorm_loss = false;
static number_type infinity()
{
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()
{
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;
}
static constexpr number_type signaling_NaN()
{
return number_type(0);
}
static constexpr number_type denorm_min() { return number_type(0); }
static constexpr bool is_iec559 = false;
static constexpr bool is_bounded = true;
static constexpr bool is_modulo = false;
static constexpr bool traps = true;
static constexpr bool tinyness_before = false;
static constexpr float_round_style round_style = round_to_nearest;
};
template <unsigned Digits, boost::multiprecision::backends::digit_base_type DigitBase, class Allocator, class Exponent, Exponent MinE, Exponent MaxE, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::cpp_bin_float<Digits, DigitBase, Allocator, Exponent, MinE, MaxE>, ExpressionTemplates> >::round_style;
} // namespace std
#endif