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///////////////////////////////////////////////////////////////////////////////
// Copyright 2011 John Maddock. Distributed under the Boost
// Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_BN_MPFI_HPP
#define BOOST_MATH_BN_MPFI_HPP
#include <algorithm>
#include <cmath>
#include <cstdint>
#include <type_traits>
#include <boost/multiprecision/number.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
#include <boost/multiprecision/detail/big_lanczos.hpp>
#include <boost/multiprecision/detail/digits.hpp>
#include <boost/multiprecision/detail/atomic.hpp>
#include <boost/multiprecision/traits/max_digits10.hpp>
#include <boost/multiprecision/mpfr.hpp>
#include <boost/multiprecision/logged_adaptor.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/functional/hash_fwd.hpp>
#include <mpfi.h>
#ifndef BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION
#define BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION 20
#endif
namespace boost {
namespace multiprecision {
namespace backends {
template <unsigned digits10>
struct mpfi_float_backend;
} // namespace backends
template <unsigned digits10>
struct number_category<backends::mpfi_float_backend<digits10> > : public std::integral_constant<int, number_kind_floating_point>
{};
struct interval_error : public std::runtime_error
{
interval_error(const std::string& s) : std::runtime_error(s) {}
};
namespace backends {
namespace detail {
inline int mpfi_sgn(mpfi_srcptr p)
{
if (mpfi_is_zero(p))
return 0;
if (mpfi_is_strictly_pos(p))
return 1;
if (mpfi_is_strictly_neg(p))
return -1;
BOOST_THROW_EXCEPTION(interval_error("Sign of interval is ambiguous."));
}
template <unsigned digits10>
struct mpfi_float_imp;
template <unsigned digits10>
struct mpfi_float_imp
{
#ifdef BOOST_HAS_LONG_LONG
using signed_types = std::tuple<long, boost::long_long_type> ;
using unsigned_types = std::tuple<unsigned long, boost::ulong_long_type>;
#else
using signed_types = std::tuple<long> ;
using unsigned_types = std::tuple<unsigned long>;
#endif
using float_types = std::tuple<double, long double>;
using exponent_type = long ;
mpfi_float_imp()
{
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
mpfi_set_ui(m_data, 0u);
}
mpfi_float_imp(unsigned prec)
{
mpfi_init2(m_data, prec);
mpfi_set_ui(m_data, 0u);
}
mpfi_float_imp(const mpfi_float_imp& o)
{
mpfi_init2(m_data, mpfi_get_prec(o.data()));
if (o.m_data[0].left._mpfr_d)
mpfi_set(m_data, o.m_data);
}
// rvalue copy
mpfi_float_imp(mpfi_float_imp&& o) noexcept
{
m_data[0] = o.m_data[0];
o.m_data[0].left._mpfr_d = 0;
}
mpfi_float_imp& operator=(const mpfi_float_imp& o)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, mpfi_get_prec(o.data()));
if (mpfi_get_prec(o.data()) != mpfi_get_prec(data()))
{
mpfi_float_imp t(mpfi_get_prec(o.data()));
t = o;
t.swap(*this);
}
else
{
if (o.m_data[0].left._mpfr_d)
mpfi_set(m_data, o.m_data);
}
return *this;
}
// rvalue assign
mpfi_float_imp& operator=(mpfi_float_imp&& o) noexcept
{
mpfi_swap(m_data, o.m_data);
return *this;
}
#ifdef BOOST_HAS_LONG_LONG
#ifdef _MPFR_H_HAVE_INTMAX_T
mpfi_float_imp& operator=(boost::ulong_long_type i)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
mpfr_set_uj(left_data(), i, GMP_RNDD);
mpfr_set_uj(right_data(), i, GMP_RNDU);
return *this;
}
mpfi_float_imp& operator=(boost::long_long_type i)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
mpfr_set_sj(left_data(), i, GMP_RNDD);
mpfr_set_sj(right_data(), i, GMP_RNDU);
return *this;
}
#else
mpfi_float_imp& operator=(boost::ulong_long_type i)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
boost::ulong_long_type mask = ((((1uLL << (std::numeric_limits<unsigned long>::digits - 1)) - 1) << 1) | 1u);
unsigned shift = 0;
mpfi_t t;
mpfi_init2(t, (std::max)(static_cast<mpfr_prec_t>(std::numeric_limits<boost::ulong_long_type>::digits), static_cast<mpfr_prec_t>(multiprecision::detail::digits10_2_2(digits10))));
mpfi_set_ui(m_data, 0);
while (i)
{
mpfi_set_ui(t, static_cast<unsigned long>(i & mask));
if (shift)
mpfi_mul_2exp(t, t, shift);
mpfi_add(m_data, m_data, t);
shift += std::numeric_limits<unsigned long>::digits;
i >>= std::numeric_limits<unsigned long>::digits;
}
mpfi_clear(t);
return *this;
}
mpfi_float_imp& operator=(boost::long_long_type i)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
bool neg = i < 0;
*this = boost::multiprecision::detail::unsigned_abs(i);
if (neg)
mpfi_neg(m_data, m_data);
return *this;
}
#endif
#endif
mpfi_float_imp& operator=(unsigned long i)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
mpfi_set_ui(m_data, i);
return *this;
}
mpfi_float_imp& operator=(long i)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
mpfi_set_si(m_data, i);
return *this;
}
mpfi_float_imp& operator=(double d)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
mpfi_set_d(m_data, d);
return *this;
}
mpfi_float_imp& operator=(long double a)
{
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
mpfr_set_ld(left_data(), a, GMP_RNDD);
mpfr_set_ld(right_data(), a, GMP_RNDU);
return *this;
}
mpfi_float_imp& operator=(const char* s)
{
using default_ops::eval_fpclassify;
if (m_data[0].left._mpfr_d == 0)
mpfi_init2(m_data, multiprecision::detail::digits10_2_2(digits10 ? digits10 : (unsigned)get_default_precision()));
if (s && (*s == '{'))
{
mpfr_float_backend<digits10> a, b;
std::string part;
const char* p = ++s;
while (*p && (*p != ',') && (*p != '}'))
++p;
part.assign(s + 1, p);
a = part.c_str();
s = p;
if (*p && (*p != '}'))
{
++p;
while (*p && (*p != ',') && (*p != '}'))
++p;
part.assign(s + 1, p);
}
else
part.erase();
b = part.c_str();
if (eval_fpclassify(a) == (int)FP_NAN)
{
mpfi_set_fr(this->data(), a.data());
}
else if (eval_fpclassify(b) == (int)FP_NAN)
{
mpfi_set_fr(this->data(), b.data());
}
else
{
if (a.compare(b) > 0)
{
BOOST_THROW_EXCEPTION(std::runtime_error("Attempt to create interval with invalid range (start is greater than end)."));
}
mpfi_interv_fr(m_data, a.data(), b.data());
}
}
else if (mpfi_set_str(m_data, s, 10) != 0)
{
BOOST_THROW_EXCEPTION(std::runtime_error(std::string("Unable to parse string \"") + s + std::string("\"as a valid floating point number.")));
}
return *this;
}
void swap(mpfi_float_imp& o) noexcept
{
mpfi_swap(m_data, o.m_data);
}
std::string str(std::streamsize digits, std::ios_base::fmtflags f) const
{
BOOST_ASSERT(m_data[0].left._mpfr_d);
mpfr_float_backend<digits10> a, b;
mpfi_get_left(a.data(), m_data);
mpfi_get_right(b.data(), m_data);
if (a.compare(b) == 0)
return a.str(digits, f);
return "{" + a.str(digits, f) + "," + b.str(digits, f) + "}";
}
~mpfi_float_imp() noexcept
{
if (m_data[0].left._mpfr_d)
mpfi_clear(m_data);
}
void negate() noexcept
{
BOOST_ASSERT(m_data[0].left._mpfr_d);
mpfi_neg(m_data, m_data);
}
int compare(const mpfi_float_imp& o) const noexcept
{
BOOST_ASSERT(m_data[0].left._mpfr_d && o.m_data[0].left._mpfr_d);
if (mpfr_cmp(right_data(), o.left_data()) < 0)
return -1;
if (mpfr_cmp(left_data(), o.right_data()) > 0)
return 1;
if ((mpfr_cmp(left_data(), o.left_data()) == 0) && (mpfr_cmp(right_data(), o.right_data()) == 0))
return 0;
BOOST_THROW_EXCEPTION(interval_error("Ambiguous comparison between two values."));
return 0;
}
template <class V>
int compare(V v) const noexcept
{
mpfi_float_imp d;
d = v;
return compare(d);
}
mpfi_t& data() noexcept
{
BOOST_ASSERT(m_data[0].left._mpfr_d);
return m_data;
}
const mpfi_t& data() const noexcept
{
BOOST_ASSERT(m_data[0].left._mpfr_d);
return m_data;
}
mpfr_ptr left_data() noexcept
{
BOOST_ASSERT(m_data[0].left._mpfr_d);
return &(m_data[0].left);
}
mpfr_srcptr left_data() const noexcept
{
BOOST_ASSERT(m_data[0].left._mpfr_d);
return &(m_data[0].left);
}
mpfr_ptr right_data() noexcept
{
BOOST_ASSERT(m_data[0].left._mpfr_d);
return &(m_data[0].right);
}
mpfr_srcptr right_data() const noexcept
{
BOOST_ASSERT(m_data[0].left._mpfr_d);
return &(m_data[0].right);
}
protected:
mpfi_t m_data;
static boost::multiprecision::detail::precision_type& get_default_precision() noexcept
{
static boost::multiprecision::detail::precision_type val(BOOST_MULTIPRECISION_MPFI_DEFAULT_PRECISION);
return val;
}
};
} // namespace detail
template <unsigned digits10>
struct mpfi_float_backend : public detail::mpfi_float_imp<digits10>
{
mpfi_float_backend() : detail::mpfi_float_imp<digits10>() {}
mpfi_float_backend(const mpfi_float_backend& o) : detail::mpfi_float_imp<digits10>(o) {}
// rvalue copy
mpfi_float_backend(mpfi_float_backend&& o) : detail::mpfi_float_imp<digits10>(static_cast<detail::mpfi_float_imp<digits10>&&>(o))
{}
template <unsigned D>
mpfi_float_backend(const mpfi_float_backend<D>& val, typename std::enable_if<D <= digits10>::type* = 0)
: detail::mpfi_float_imp<digits10>()
{
mpfi_set(this->m_data, val.data());
}
template <unsigned D>
explicit mpfi_float_backend(const mpfi_float_backend<D>& val, typename std::enable_if<!(D <= digits10)>::type* = 0)
: detail::mpfi_float_imp<digits10>()
{
mpfi_set(this->m_data, val.data());
}
mpfi_float_backend(const mpfi_t val)
: detail::mpfi_float_imp<digits10>()
{
mpfi_set(this->m_data, val);
}
mpfi_float_backend& operator=(const mpfi_float_backend& o)
{
*static_cast<detail::mpfi_float_imp<digits10>*>(this) = static_cast<detail::mpfi_float_imp<digits10> const&>(o);
return *this;
}
template <unsigned D>
mpfi_float_backend(const mpfr_float_backend<D>& val, typename std::enable_if<D <= digits10>::type* = 0)
: detail::mpfi_float_imp<digits10>()
{
mpfi_set_fr(this->m_data, val.data());
}
template <unsigned D>
mpfi_float_backend& operator=(const mpfr_float_backend<D>& val)
{
mpfi_set_fr(this->m_data, val.data());
return *this;
}
template <unsigned D>
explicit mpfi_float_backend(const mpfr_float_backend<D>& val, typename std::enable_if<!(D <= digits10)>::type* = 0)
: detail::mpfi_float_imp<digits10>()
{
mpfi_set_fr(this->m_data, val.data());
}
// rvalue copy
mpfi_float_backend& operator=(mpfi_float_backend&& o) noexcept
{
*static_cast<detail::mpfi_float_imp<digits10>*>(this) = static_cast<detail::mpfi_float_imp<digits10>&&>(o);
return *this;
}
template <class V>
mpfi_float_backend& operator=(const V& v)
{
*static_cast<detail::mpfi_float_imp<digits10>*>(this) = v;
return *this;
}
mpfi_float_backend& operator=(const mpfi_t val)
{
mpfi_set(this->m_data, val);
return *this;
}
// We don't change our precision here, this is a fixed precision type:
template <unsigned D>
mpfi_float_backend& operator=(const mpfi_float_backend<D>& val)
{
mpfi_set(this->m_data, val.data());
return *this;
}
};
template <unsigned D1, unsigned D2, mpfr_allocation_type AllocationType>
void assign_components(mpfi_float_backend<D1>& result, const mpfr_float_backend<D2, AllocationType>& a, const mpfr_float_backend<D2, AllocationType>& b);
template <unsigned Digits10, class V>
typename std::enable_if<std::is_constructible<number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on>, V>::value || std::is_convertible<V, const char*>::value>::type
assign_components(mpfi_float_backend<Digits10>& result, const V& a, const V& b);
template <>
struct mpfi_float_backend<0> : public detail::mpfi_float_imp<0>
{
mpfi_float_backend() : detail::mpfi_float_imp<0>() {}
mpfi_float_backend(const mpfi_t val)
: detail::mpfi_float_imp<0>(mpfi_get_prec(val))
{
mpfi_set(this->m_data, val);
}
mpfi_float_backend(const mpfi_float_backend& o) : detail::mpfi_float_imp<0>(o) {}
// rvalue copy
mpfi_float_backend(mpfi_float_backend&& o) noexcept : detail::mpfi_float_imp<0>(static_cast<detail::mpfi_float_imp<0>&&>(o))
{}
mpfi_float_backend(const mpfi_float_backend& o, unsigned digits10)
: detail::mpfi_float_imp<0>(multiprecision::detail::digits10_2_2(digits10))
{
mpfi_set(this->m_data, o.data());
}
template <class V>
mpfi_float_backend(const V& a, const V& b, unsigned digits10)
: detail::mpfi_float_imp<0>(multiprecision::detail::digits10_2_2(digits10))
{
assign_components(*this, a, b);
}
template <unsigned D>
mpfi_float_backend(const mpfi_float_backend<D>& val)
: detail::mpfi_float_imp<0>(mpfi_get_prec(val.data()))
{
mpfi_set(this->m_data, val.data());
}
mpfi_float_backend& operator=(const mpfi_float_backend& o)
{
mpfi_set_prec(this->m_data, mpfi_get_prec(o.data()));
mpfi_set(this->m_data, o.data());
return *this;
}
// rvalue assign
mpfi_float_backend& operator=(mpfi_float_backend&& o) noexcept
{
*static_cast<detail::mpfi_float_imp<0>*>(this) = static_cast<detail::mpfi_float_imp<0>&&>(o);
return *this;
}
template <class V>
mpfi_float_backend& operator=(const V& v)
{
*static_cast<detail::mpfi_float_imp<0>*>(this) = v;
return *this;
}
mpfi_float_backend& operator=(const mpfi_t val)
{
mpfi_set_prec(this->m_data, mpfi_get_prec(val));
mpfi_set(this->m_data, val);
return *this;
}
template <unsigned D>
mpfi_float_backend& operator=(const mpfi_float_backend<D>& val)
{
mpfi_set_prec(this->m_data, mpfi_get_prec(val.data()));
mpfi_set(this->m_data, val.data());
return *this;
}
static unsigned default_precision() noexcept
{
return get_default_precision();
}
static void default_precision(unsigned v) noexcept
{
get_default_precision() = v;
}
unsigned precision() const noexcept
{
return multiprecision::detail::digits2_2_10(mpfi_get_prec(this->m_data));
}
void precision(unsigned digits10) noexcept
{
mpfi_float_backend t(*this, digits10);
this->swap(t);
}
};
template <unsigned digits10, class T>
inline typename std::enable_if<boost::multiprecision::detail::is_arithmetic<T>::value, bool>::type eval_eq(const mpfi_float_backend<digits10>& a, const T& b) noexcept
{
return a.compare(b) == 0;
}
template <unsigned digits10, class T>
inline typename std::enable_if<boost::multiprecision::detail::is_arithmetic<T>::value, bool>::type eval_lt(const mpfi_float_backend<digits10>& a, const T& b) noexcept
{
return a.compare(b) < 0;
}
template <unsigned digits10, class T>
inline typename std::enable_if<boost::multiprecision::detail::is_arithmetic<T>::value, bool>::type eval_gt(const mpfi_float_backend<digits10>& a, const T& b) noexcept
{
return a.compare(b) > 0;
}
template <unsigned D1, unsigned D2>
inline void eval_add(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
{
mpfi_add(result.data(), result.data(), o.data());
}
template <unsigned D1, unsigned D2>
inline void eval_subtract(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
{
mpfi_sub(result.data(), result.data(), o.data());
}
template <unsigned D1, unsigned D2>
inline void eval_multiply(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
{
if ((void*)&result == (void*)&o)
mpfi_sqr(result.data(), o.data());
else
mpfi_mul(result.data(), result.data(), o.data());
}
template <unsigned D1, unsigned D2>
inline void eval_divide(mpfi_float_backend<D1>& result, const mpfi_float_backend<D2>& o)
{
mpfi_div(result.data(), result.data(), o.data());
}
template <unsigned digits10>
inline void eval_add(mpfi_float_backend<digits10>& result, unsigned long i)
{
mpfi_add_ui(result.data(), result.data(), i);
}
template <unsigned digits10>
inline void eval_subtract(mpfi_float_backend<digits10>& result, unsigned long i)
{
mpfi_sub_ui(result.data(), result.data(), i);
}
template <unsigned digits10>
inline void eval_multiply(mpfi_float_backend<digits10>& result, unsigned long i)
{
mpfi_mul_ui(result.data(), result.data(), i);
}
template <unsigned digits10>
inline void eval_divide(mpfi_float_backend<digits10>& result, unsigned long i)
{
mpfi_div_ui(result.data(), result.data(), i);
}
template <unsigned digits10>
inline void eval_add(mpfi_float_backend<digits10>& result, long i)
{
if (i > 0)
mpfi_add_ui(result.data(), result.data(), i);
else
mpfi_sub_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i));
}
template <unsigned digits10>
inline void eval_subtract(mpfi_float_backend<digits10>& result, long i)
{
if (i > 0)
mpfi_sub_ui(result.data(), result.data(), i);
else
mpfi_add_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i));
}
template <unsigned digits10>
inline void eval_multiply(mpfi_float_backend<digits10>& result, long i)
{
mpfi_mul_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i));
if (i < 0)
mpfi_neg(result.data(), result.data());
}
template <unsigned digits10>
inline void eval_divide(mpfi_float_backend<digits10>& result, long i)
{
mpfi_div_ui(result.data(), result.data(), boost::multiprecision::detail::unsigned_abs(i));
if (i < 0)
mpfi_neg(result.data(), result.data());
}
//
// Specialised 3 arg versions of the basic operators:
//
template <unsigned D1, unsigned D2, unsigned D3>
inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
{
mpfi_add(a.data(), x.data(), y.data());
}
template <unsigned D1, unsigned D2>
inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
{
mpfi_add_ui(a.data(), x.data(), y);
}
template <unsigned D1, unsigned D2>
inline void eval_add(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
{
if (y < 0)
mpfi_sub_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
else
mpfi_add_ui(a.data(), x.data(), y);
}
template <unsigned D1, unsigned D2>
inline void eval_add(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
{
mpfi_add_ui(a.data(), y.data(), x);
}
template <unsigned D1, unsigned D2>
inline void eval_add(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
{
if (x < 0)
{
mpfi_ui_sub(a.data(), boost::multiprecision::detail::unsigned_abs(x), y.data());
mpfi_neg(a.data(), a.data());
}
else
mpfi_add_ui(a.data(), y.data(), x);
}
template <unsigned D1, unsigned D2, unsigned D3>
inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
{
mpfi_sub(a.data(), x.data(), y.data());
}
template <unsigned D1, unsigned D2>
inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
{
mpfi_sub_ui(a.data(), x.data(), y);
}
template <unsigned D1, unsigned D2>
inline void eval_subtract(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
{
if (y < 0)
mpfi_add_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
else
mpfi_sub_ui(a.data(), x.data(), y);
}
template <unsigned D1, unsigned D2>
inline void eval_subtract(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
{
mpfi_ui_sub(a.data(), x, y.data());
}
template <unsigned D1, unsigned D2>
inline void eval_subtract(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
{
if (x < 0)
{
mpfi_add_ui(a.data(), y.data(), boost::multiprecision::detail::unsigned_abs(x));
mpfi_neg(a.data(), a.data());
}
else
mpfi_ui_sub(a.data(), x, y.data());
}
template <unsigned D1, unsigned D2, unsigned D3>
inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
{
if ((void*)&x == (void*)&y)
mpfi_sqr(a.data(), x.data());
else
mpfi_mul(a.data(), x.data(), y.data());
}
template <unsigned D1, unsigned D2>
inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
{
mpfi_mul_ui(a.data(), x.data(), y);
}
template <unsigned D1, unsigned D2>
inline void eval_multiply(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
{
if (y < 0)
{
mpfi_mul_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
a.negate();
}
else
mpfi_mul_ui(a.data(), x.data(), y);
}
template <unsigned D1, unsigned D2>
inline void eval_multiply(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
{
mpfi_mul_ui(a.data(), y.data(), x);
}
template <unsigned D1, unsigned D2>
inline void eval_multiply(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
{
if (x < 0)
{
mpfi_mul_ui(a.data(), y.data(), boost::multiprecision::detail::unsigned_abs(x));
mpfi_neg(a.data(), a.data());
}
else
mpfi_mul_ui(a.data(), y.data(), x);
}
template <unsigned D1, unsigned D2, unsigned D3>
inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, const mpfi_float_backend<D3>& y)
{
mpfi_div(a.data(), x.data(), y.data());
}
template <unsigned D1, unsigned D2>
inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, unsigned long y)
{
mpfi_div_ui(a.data(), x.data(), y);
}
template <unsigned D1, unsigned D2>
inline void eval_divide(mpfi_float_backend<D1>& a, const mpfi_float_backend<D2>& x, long y)
{
if (y < 0)
{
mpfi_div_ui(a.data(), x.data(), boost::multiprecision::detail::unsigned_abs(y));
a.negate();
}
else
mpfi_div_ui(a.data(), x.data(), y);
}
template <unsigned D1, unsigned D2>
inline void eval_divide(mpfi_float_backend<D1>& a, unsigned long x, const mpfi_float_backend<D2>& y)
{
mpfi_ui_div(a.data(), x, y.data());
}
template <unsigned D1, unsigned D2>
inline void eval_divide(mpfi_float_backend<D1>& a, long x, const mpfi_float_backend<D2>& y)
{
if (x < 0)
{
mpfi_ui_div(a.data(), boost::multiprecision::detail::unsigned_abs(x), y.data());
mpfi_neg(a.data(), a.data());
}
else
mpfi_ui_div(a.data(), x, y.data());
}
template <unsigned digits10>
inline bool eval_is_zero(const mpfi_float_backend<digits10>& val) noexcept
{
return 0 != mpfi_is_zero(val.data());
}
template <unsigned digits10>
inline int eval_get_sign(const mpfi_float_backend<digits10>& val)
{
return detail::mpfi_sgn(val.data());
}
template <unsigned digits10>
inline void eval_convert_to(unsigned long* result, const mpfi_float_backend<digits10>& val)
{
mpfr_float_backend<digits10> t;
mpfi_mid(t.data(), val.data());
eval_convert_to(result, t);
}
template <unsigned digits10>
inline void eval_convert_to(long* result, const mpfi_float_backend<digits10>& val)
{
mpfr_float_backend<digits10> t;
mpfi_mid(t.data(), val.data());
eval_convert_to(result, t);
}
#ifdef _MPFR_H_HAVE_INTMAX_T
template <unsigned digits10>
inline void eval_convert_to(boost::ulong_long_type* result, const mpfi_float_backend<digits10>& val)
{
mpfr_float_backend<digits10> t;
mpfi_mid(t.data(), val.data());
eval_convert_to(result, t);
}
template <unsigned digits10>
inline void eval_convert_to(boost::long_long_type* result, const mpfi_float_backend<digits10>& val)
{
mpfr_float_backend<digits10> t;
mpfi_mid(t.data(), val.data());
eval_convert_to(result, t);
}
#endif
template <unsigned digits10>
inline void eval_convert_to(double* result, const mpfi_float_backend<digits10>& val) noexcept
{
*result = mpfi_get_d(val.data());
}
template <unsigned digits10>
inline void eval_convert_to(long double* result, const mpfi_float_backend<digits10>& val) noexcept
{
mpfr_float_backend<digits10> t;
mpfi_mid(t.data(), val.data());
eval_convert_to(result, t);
}
template <unsigned D1, unsigned D2, mpfr_allocation_type AllocationType>
inline void assign_components(mpfi_float_backend<D1>& result, const mpfr_float_backend<D2, AllocationType>& a, const mpfr_float_backend<D2, AllocationType>& b)
{
using default_ops::eval_fpclassify;
if (eval_fpclassify(a) == (int)FP_NAN)
{
mpfi_set_fr(result.data(), a.data());
}
else if (eval_fpclassify(b) == (int)FP_NAN)
{
mpfi_set_fr(result.data(), b.data());
}
else
{
if (a.compare(b) > 0)
{
BOOST_THROW_EXCEPTION(std::runtime_error("Attempt to create interval with invalid range (start is greater than end)."));
}
mpfi_interv_fr(result.data(), a.data(), b.data());
}
}
template <unsigned Digits10, class V>
inline typename std::enable_if<std::is_constructible<number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on>, V>::value || std::is_convertible<V, const char*>::value>::type
assign_components(mpfi_float_backend<Digits10>& result, const V& a, const V& b)
{
number<mpfr_float_backend<Digits10, allocate_dynamic>, et_on> x(a), y(b);
assign_components(result, x.backend(), y.backend());
}
//
// Native non-member operations:
//
template <unsigned Digits10>
inline void eval_sqrt(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
{
mpfi_sqrt(result.data(), val.data());
}
template <unsigned Digits10>
inline void eval_abs(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
{
mpfi_abs(result.data(), val.data());
}
template <unsigned Digits10>
inline void eval_fabs(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
{
mpfi_abs(result.data(), val.data());
}
template <unsigned Digits10>
inline void eval_ceil(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
{
mpfr_float_backend<Digits10> a, b;
mpfr_set(a.data(), val.left_data(), GMP_RNDN);
mpfr_set(b.data(), val.right_data(), GMP_RNDN);
eval_ceil(a, a);
eval_ceil(b, b);
if (a.compare(b) != 0)
{
BOOST_THROW_EXCEPTION(interval_error("Attempt to take the ceil of a value that straddles an integer boundary."));
}
mpfi_set_fr(result.data(), a.data());
}
template <unsigned Digits10>
inline void eval_floor(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val)
{
mpfr_float_backend<Digits10> a, b;
mpfr_set(a.data(), val.left_data(), GMP_RNDN);
mpfr_set(b.data(), val.right_data(), GMP_RNDN);
eval_floor(a, a);
eval_floor(b, b);
if (a.compare(b) != 0)
{
BOOST_THROW_EXCEPTION(interval_error("Attempt to take the floor of a value that straddles an integer boundary."));
}
mpfi_set_fr(result.data(), a.data());
}
template <unsigned Digits10>
inline void eval_ldexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, long e)
{
if (e > 0)
mpfi_mul_2exp(result.data(), val.data(), e);
else if (e < 0)
mpfi_div_2exp(result.data(), val.data(), -e);
else
result = val;
}
template <unsigned Digits10>
inline void eval_frexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, int* e)
{
mpfr_float_backend<Digits10> t, rt;
mpfi_mid(t.data(), val.data());
eval_frexp(rt, t, e);
eval_ldexp(result, val, -*e);
}
template <unsigned Digits10>
inline void eval_frexp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& val, long* e)
{
mpfr_float_backend<Digits10> t, rt;
mpfi_mid(t.data(), val.data());
eval_frexp(rt, t, e);
eval_ldexp(result, val, -*e);
}
template <unsigned Digits10>
inline int eval_fpclassify(const mpfi_float_backend<Digits10>& val) noexcept
{
return mpfi_inf_p(val.data()) ? FP_INFINITE : mpfi_nan_p(val.data()) ? FP_NAN : mpfi_is_zero(val.data()) ? FP_ZERO : FP_NORMAL;
}
template <unsigned Digits10>
inline void eval_pow(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& b, const mpfi_float_backend<Digits10>& e)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, mpfi_float_backend<Digits10> >::type;
using default_ops::eval_get_sign;
int s = eval_get_sign(b);
if (s == 0)
{
if (eval_get_sign(e) == 0)
{
result = ui_type(1);
}
else
{
result = ui_type(0);
}
return;
}
if (s < 0)
{
if (eval_get_sign(e) < 0)
{
mpfi_float_backend<Digits10> t1, t2;
t1 = e;
t1.negate();
eval_pow(t2, b, t1);
t1 = ui_type(1);
eval_divide(result, t1, t2);
return;
}
typename boost::multiprecision::detail::canonical<std::uintmax_t, mpfi_float_backend<Digits10> >::type an;
#ifndef BOOST_NO_EXCEPTIONS
try
{
#endif
using default_ops::eval_convert_to;
eval_convert_to(&an, e);
if (e.compare(an) == 0)
{
mpfi_float_backend<Digits10> pb(b);
pb.negate();
eval_pow(result, pb, e);
if (an & 1u)
result.negate();
return;
}
#ifndef BOOST_NO_EXCEPTIONS
}
catch (const std::exception&)
{
// conversion failed, just fall through, value is not an integer.
}
#endif
result = std::numeric_limits<number<mpfi_float_backend<Digits10>, et_on> >::quiet_NaN().backend();
return;
}
mpfi_log(result.data(), b.data());
mpfi_mul(result.data(), result.data(), e.data());
mpfi_exp(result.data(), result.data());
}
template <unsigned Digits10>
inline void eval_exp(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_exp(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_exp2(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_exp2(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_log(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_log(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_log10(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_log10(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_sin(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_sin(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_cos(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_cos(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_tan(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_tan(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_asin(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_asin(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_acos(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_acos(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_atan(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_atan(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_atan2(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg1, const mpfi_float_backend<Digits10>& arg2)
{
mpfi_atan2(result.data(), arg1.data(), arg2.data());
}
template <unsigned Digits10>
inline void eval_sinh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_sinh(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_cosh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_cosh(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_tanh(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_tanh(result.data(), arg.data());
}
template <unsigned Digits10>
inline void eval_log2(mpfi_float_backend<Digits10>& result, const mpfi_float_backend<Digits10>& arg)
{
mpfi_log2(result.data(), arg.data());
}
template <unsigned Digits10>
inline std::size_t hash_value(const mpfi_float_backend<Digits10>& val)
{
std::size_t result = 0;
std::size_t len = val.left_data()[0]._mpfr_prec / mp_bits_per_limb;
if (val.left_data()[0]._mpfr_prec % mp_bits_per_limb)
++len;
for (std::size_t i = 0; i < len; ++i)
boost::hash_combine(result, val.left_data()[0]._mpfr_d[i]);
boost::hash_combine(result, val.left_data()[0]._mpfr_exp);
boost::hash_combine(result, val.left_data()[0]._mpfr_sign);
len = val.right_data()[0]._mpfr_prec / mp_bits_per_limb;
if (val.right_data()[0]._mpfr_prec % mp_bits_per_limb)
++len;
for (std::size_t i = 0; i < len; ++i)
boost::hash_combine(result, val.right_data()[0]._mpfr_d[i]);
boost::hash_combine(result, val.right_data()[0]._mpfr_exp);
boost::hash_combine(result, val.right_data()[0]._mpfr_sign);
return result;
}
template <class To, unsigned D>
void generic_interconvert(To& to, const mpfi_float_backend<D>& from, const std::integral_constant<int, number_kind_integer>& to_type, const std::integral_constant<int, number_kind_floating_point>& from_type)
{
using boost::multiprecision::detail::generic_interconvert;
mpfr_float_backend<D> t;
mpfi_mid(t.data(), from.data());
generic_interconvert(to, t, to_type, from_type);
}
template <class To, unsigned D>
void generic_interconvert(To& to, const mpfi_float_backend<D>& from, const std::integral_constant<int, number_kind_rational>& to_type, const std::integral_constant<int, number_kind_floating_point>& from_type)
{
using boost::multiprecision::detail::generic_interconvert;
mpfr_float_backend<D> t;
mpfi_mid(t.data(), from.data());
generic_interconvert(to, t, to_type, from_type);
}
template <class To, unsigned D>
void generic_interconvert(To& to, const mpfi_float_backend<D>& from, const std::integral_constant<int, number_kind_floating_point>& to_type, const std::integral_constant<int, number_kind_floating_point>& from_type)
{
using boost::multiprecision::detail::generic_interconvert;
mpfr_float_backend<D> t;
mpfi_mid(t.data(), from.data());
generic_interconvert(to, t, to_type, from_type);
}
} // namespace backends
namespace detail {
template <>
struct is_variable_precision<backends::mpfi_float_backend<0> > : public std::integral_constant<bool, true>
{};
} // namespace detail
template <>
struct number_category<detail::canonical<mpfi_t, backends::mpfi_float_backend<0> >::type> : public std::integral_constant<int, number_kind_floating_point>
{};
template <unsigned Digits10>
struct is_interval_number<backends::mpfi_float_backend<Digits10> > : public std::integral_constant<bool, true>
{};
using boost::multiprecision::backends::mpfi_float_backend;
using mpfi_float_50 = number<mpfi_float_backend<50> > ;
using mpfi_float_100 = number<mpfi_float_backend<100> > ;
using mpfi_float_500 = number<mpfi_float_backend<500> > ;
using mpfi_float_1000 = number<mpfi_float_backend<1000> >;
using mpfi_float = number<mpfi_float_backend<0> > ;
//
// Special interval specific functions:
//
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> lower(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfr_float_backend<Digits10>, ExpressionTemplates> > precision_guard(val);
number<mpfr_float_backend<Digits10> > result;
mpfr_set(result.backend().data(), val.backend().left_data(), GMP_RNDN);
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> upper(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfr_float_backend<Digits10>, ExpressionTemplates> > precision_guard(val);
number<mpfr_float_backend<Digits10> > result;
mpfr_set(result.backend().data(), val.backend().right_data(), GMP_RNDN);
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> median(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfr_float_backend<Digits10>, ExpressionTemplates> > precision_guard(val);
number<mpfr_float_backend<Digits10> > result;
mpfi_mid(result.backend().data(), val.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline number<mpfr_float_backend<Digits10>, ExpressionTemplates> width(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& val)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfr_float_backend<Digits10>, ExpressionTemplates> > precision_guard(val);
number<mpfr_float_backend<Digits10> > result;
mpfi_diam_abs(result.backend().data(), val.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline number<mpfi_float_backend<Digits10>, ExpressionTemplates> intersect(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(a, b);
number<mpfi_float_backend<Digits10>, ExpressionTemplates> result;
mpfi_intersect(result.backend().data(), a.backend().data(), b.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline number<mpfi_float_backend<Digits10>, ExpressionTemplates> hull(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(a, b);
number<mpfi_float_backend<Digits10>, ExpressionTemplates> result;
mpfi_union(result.backend().data(), a.backend().data(), b.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline bool overlap(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b)
{
return (lower(a) <= lower(b) && lower(b) <= upper(a)) ||
(lower(b) <= lower(a) && lower(a) <= upper(b));
}
template <unsigned Digits10, expression_template_option ExpressionTemplates1, expression_template_option ExpressionTemplates2>
inline bool in(const number<mpfr_float_backend<Digits10>, ExpressionTemplates1>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates2>& b)
{
return mpfi_is_inside_fr(a.backend().data(), b.backend().data()) != 0;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline bool zero_in(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a)
{
return mpfi_has_zero(a.backend().data()) != 0;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline bool subset(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b)
{
return mpfi_is_inside(a.backend().data(), b.backend().data()) != 0;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline bool proper_subset(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a, const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& b)
{
return mpfi_is_strictly_inside(a.backend().data(), b.backend().data()) != 0;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline bool empty(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a)
{
return mpfi_is_empty(a.backend().data()) != 0;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline bool singleton(const number<mpfi_float_backend<Digits10>, ExpressionTemplates>& a)
{
return mpfr_cmp(a.backend().left_data(), a.backend().right_data()) == 0;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
struct component_type<number<mpfi_float_backend<Digits10>, ExpressionTemplates> >
{
using type = number<mpfr_float_backend<Digits10>, ExpressionTemplates>;
};
//
// Overloaded special functions which call native mpfr routines:
//
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> asinh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);
boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
mpfi_asinh(result.backend().data(), arg.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> acosh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);
boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
mpfi_acosh(result.backend().data(), arg.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> atanh BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);
boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
mpfi_atanh(result.backend().data(), arg.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> cbrt BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);
boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
mpfi_cbrt(result.backend().data(), arg.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> expm1 BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);
boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
mpfi_expm1(result.backend().data(), arg.backend().data());
return result;
}
template <unsigned Digits10, expression_template_option ExpressionTemplates>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> log1p BOOST_PREVENT_MACRO_SUBSTITUTION(const boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>& arg)
{
boost::multiprecision::detail::scoped_default_precision<number<mpfi_float_backend<Digits10>, ExpressionTemplates> > precision_guard(arg);
boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> result;
mpfi_log1p(result.backend().data(), arg.backend().data());
return result;
}
} // namespace multiprecision
namespace math {
namespace tools {
inline void set_output_precision(const boost::multiprecision::mpfi_float& val, std::ostream& os)
{
os << std::setprecision(val.precision());
}
template <>
inline int digits<boost::multiprecision::mpfi_float>()
#ifdef BOOST_MATH_NOEXCEPT
noexcept
#endif
{
return multiprecision::detail::digits10_2_2(boost::multiprecision::mpfi_float::default_precision());
}
template <>
inline int digits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> >()
#ifdef BOOST_MATH_NOEXCEPT
noexcept
#endif
{
return multiprecision::detail::digits10_2_2(boost::multiprecision::mpfi_float::default_precision());
}
template <>
inline boost::multiprecision::mpfi_float
max_value<boost::multiprecision::mpfi_float>()
{
boost::multiprecision::mpfi_float result(0.5);
mpfi_mul_2exp(result.backend().data(), result.backend().data(), mpfr_get_emax());
//BOOST_ASSERT(mpfi_number_p(result.backend().data()));
return result;
}
template <>
inline boost::multiprecision::mpfi_float
min_value<boost::multiprecision::mpfi_float>()
{
boost::multiprecision::mpfi_float result(0.5);
mpfi_div_2exp(result.backend().data(), result.backend().data(), -mpfr_get_emin());
//BOOST_ASSERT(mpfi_number_p(result.backend().data()));
return result;
}
template <>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off>
max_value<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> >()
{
boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> result(0.5);
mpfi_mul_2exp(result.backend().data(), result.backend().data(), mpfr_get_emax());
//BOOST_ASSERT(mpfi_number_p(result.backend().data()));
return result;
}
template <>
inline boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off>
min_value<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> >()
{
boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, boost::multiprecision::et_off> result(0.5);
mpfi_div_2exp(result.backend().data(), result.backend().data(), -mpfr_get_emin());
//BOOST_ASSERT(mpfi_number_p(result.backend().data()));
return result;
}
// mpfi gets used with logged_adaptor fairly often, so specialize for that use case as well:
using logged_type1 = boost::multiprecision::number<boost::multiprecision::backends::logged_adaptor<boost::multiprecision::mpfi_float::backend_type>, boost::multiprecision::et_on> ;
using logged_type2 = boost::multiprecision::number<boost::multiprecision::backends::logged_adaptor<boost::multiprecision::mpfi_float::backend_type>, boost::multiprecision::et_off>;
template <>
inline int digits<logged_type1>()
#ifdef BOOST_MATH_NOEXCEPT
noexcept
#endif
{
return multiprecision::detail::digits10_2_2(logged_type1::default_precision());
}
template <>
inline int digits<logged_type2>()
#ifdef BOOST_MATH_NOEXCEPT
noexcept
#endif
{
return multiprecision::detail::digits10_2_2(logged_type1::default_precision());
}
template <>
inline logged_type1
max_value<logged_type1>()
{
logged_type1 result(0.5);
mpfi_mul_2exp(result.backend().value().data(), result.backend().value().data(), mpfr_get_emax());
//BOOST_ASSERT(mpfi_number_p(result.backend().data()));
return result;
}
template <>
inline logged_type1
min_value<logged_type1>()
{
logged_type1 result(0.5);
mpfi_div_2exp(result.backend().value().data(), result.backend().value().data(), -mpfr_get_emin());
//BOOST_ASSERT(mpfi_number_p(result.backend().data()));
return result;
}
template <>
inline logged_type2
max_value<logged_type2>()
{
logged_type2 result(0.5);
mpfi_mul_2exp(result.backend().value().data(), result.backend().value().data(), mpfr_get_emax());
//BOOST_ASSERT(mpfi_number_p(result.backend().data()));
return result;
}
template <>
inline logged_type2
min_value<logged_type2>()
{
logged_type2 result(0.5);
mpfi_div_2exp(result.backend().value().data(), result.backend().value().data(), -mpfr_get_emin());
//BOOST_ASSERT(mpfi_number_p(result.backend().data()));
return result;
}
} // namespace tools
namespace constants { namespace detail {
template <class T>
struct constant_pi;
template <class T>
struct constant_ln_two;
template <class T>
struct constant_euler;
template <class T>
struct constant_catalan;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
struct constant_pi<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
{
using result_type = boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>;
template <int N>
static inline const result_type& get(const std::integral_constant<int, N>&)
{
static result_type result;
static bool has_init = false;
if (!has_init)
{
has_init = true;
mpfi_const_pi(result.backend().data());
}
return result;
}
static inline result_type get(const std::integral_constant<int, 0>&)
{
result_type result;
mpfi_const_pi(result.backend().data());
return result;
}
};
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
struct constant_ln_two<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
{
using result_type = boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>;
template <int N>
static inline const result_type& get(const std::integral_constant<int, N>&)
{
static result_type result;
static bool has_init = false;
if (!has_init)
{
has_init = true;
mpfi_const_log2(result.backend().data());
}
return result;
}
static inline result_type get(const std::integral_constant<int, 0>&)
{
result_type result;
mpfi_const_log2(result.backend().data());
return result;
}
};
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
struct constant_euler<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
{
using result_type = boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>;
template <int N>
static inline const result_type& get(const std::integral_constant<int, N>&)
{
static result_type result;
static bool has_init = false;
if (!has_init)
{
has_init = true;
mpfi_const_euler(result.backend().data());
}
return result;
}
static inline result_type get(const std::integral_constant<int, 0>&)
{
result_type result;
mpfi_const_euler(result.backend().data());
return result;
}
};
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
struct constant_catalan<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
{
using result_type = boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates>;
template <int N>
static inline const result_type& get(const std::integral_constant<int, N>&)
{
static result_type result;
static bool has_init = false;
if (!has_init)
{
has_init = true;
mpfi_const_catalan(result.backend().data());
}
return result;
}
static inline result_type get(const std::integral_constant<int, 0>&)
{
result_type result;
mpfi_const_catalan(result.backend().data());
return result;
}
};
}} // namespace constants::detail
} // namespace math
} // namespace boost
namespace std {
//
// numeric_limits [partial] specializations for the types declared in this header:
//
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
class numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >
{
using number_type = boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, 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;
value.second = 0.5;
mpfi_div_2exp(value.second.backend().data(), value.second.backend().data(), -mpfr_get_emin());
}
return value.second;
}
static number_type(max)()
{
static std::pair<bool, number_type> value;
if (!value.first)
{
value.first = true;
value.second = 0.5;
mpfi_mul_2exp(value.second.backend().data(), value.second.backend().data(), mpfr_get_emax());
}
return value.second;
}
static constexpr number_type lowest()
{
return -(max)();
}
static constexpr int digits = static_cast<int>((Digits10 * 1000L) / 301L + ((Digits10 * 1000L) % 301 ? 2 : 1));
static constexpr int digits10 = Digits10;
// Is this really correct???
static constexpr int max_digits10 = boost::multiprecision::detail::calc_max_digits10<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)
{
value.first = true;
value.second = 1;
mpfi_div_2exp(value.second.backend().data(), value.second.backend().data(), std::numeric_limits<number_type>::digits - 1);
}
return value.second;
}
// What value should this be????
static number_type round_error()
{
// returns epsilon/2
static std::pair<bool, number_type> value;
if (!value.first)
{
value.first = true;
value.second = 1;
mpfi_div_2exp(value.second.backend().data(), value.second.backend().data(), 1);
}
return value.second;
}
static constexpr long min_exponent = MPFR_EMIN_DEFAULT;
static constexpr long min_exponent10 = (MPFR_EMIN_DEFAULT / 1000) * 301L;
static constexpr long max_exponent = MPFR_EMAX_DEFAULT;
static constexpr long max_exponent10 = (MPFR_EMAX_DEFAULT / 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)
{
boost::multiprecision::mpfr_float_backend<Digits10> t;
mpfr_set_inf(t.data(), 1);
value.first = true;
mpfi_set_fr(value.second.backend().data(), t.data());
}
return value.second;
}
static number_type quiet_NaN()
{
static std::pair<bool, number_type> value;
if (!value.first)
{
boost::multiprecision::mpfr_float_backend<Digits10> t;
mpfr_set_nan(t.data());
value.first = true;
mpfi_set_fr(value.second.backend().data(), t.data());
}
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 Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::digits;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::digits10;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_digits10;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_signed;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_integer;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_exact;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::radix;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::min_exponent;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::min_exponent10;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_exponent;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr long numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::max_exponent10;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_infinity;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_quiet_NaN;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_signaling_NaN;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_denorm;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::has_denorm_loss;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_iec559;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_bounded;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::is_modulo;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::traps;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::tinyness_before;
template <unsigned Digits10, boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<Digits10>, ExpressionTemplates> >::round_style;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
class numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >
{
using number_type = boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates>;
public:
static constexpr bool is_specialized = false;
static number_type(min)() { return number_type(0); }
static number_type(max)() { return number_type(0); }
static number_type lowest() { return number_type(0); }
static constexpr int digits = 0;
static constexpr int digits10 = 0;
static constexpr int max_digits10 = 0;
static constexpr bool is_signed = false;
static constexpr bool is_integer = false;
static constexpr bool is_exact = false;
static constexpr int radix = 0;
static number_type epsilon() { return number_type(0); }
static number_type round_error() { return number_type(0); }
static constexpr int min_exponent = 0;
static constexpr int min_exponent10 = 0;
static constexpr int max_exponent = 0;
static constexpr int max_exponent10 = 0;
static constexpr bool has_infinity = false;
static constexpr bool has_quiet_NaN = false;
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() { return number_type(0); }
static number_type quiet_NaN() { return number_type(0); }
static number_type signaling_NaN() { return number_type(0); }
static number_type denorm_min() { return number_type(0); }
static constexpr bool is_iec559 = false;
static constexpr bool is_bounded = false;
static constexpr bool is_modulo = false;
static constexpr bool traps = false;
static constexpr bool tinyness_before = false;
static constexpr float_round_style round_style = round_toward_zero;
};
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::digits;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::digits10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_digits10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_signed;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_integer;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_exact;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::radix;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::min_exponent;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::min_exponent10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_exponent;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr int numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::max_exponent10;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_infinity;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_quiet_NaN;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_signaling_NaN;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr float_denorm_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_denorm;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::has_denorm_loss;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_iec559;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_bounded;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::is_modulo;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::traps;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr bool numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::tinyness_before;
template <boost::multiprecision::expression_template_option ExpressionTemplates>
constexpr float_round_style numeric_limits<boost::multiprecision::number<boost::multiprecision::mpfi_float_backend<0>, ExpressionTemplates> >::round_style;
} // namespace std
#endif
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