boost/multiprecision/detail/default_ops.hpp
///////////////////////////////////////////////////////////////////////////////
// Copyright 2011-21 John Maddock.
// Copyright 2021 Iskandarov Lev. 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_MP_DEFAULT_OPS
#define BOOST_MP_DEFAULT_OPS
#include <boost/multiprecision/detail/standalone_config.hpp>
#include <boost/multiprecision/detail/no_exceptions_support.hpp>
#include <boost/multiprecision/detail/number_base.hpp>
#include <boost/multiprecision/detail/assert.hpp>
#include <boost/multiprecision/traits/is_backend.hpp>
#include <boost/multiprecision/detail/fpclassify.hpp>
#include <cstdint>
#include <complex>
#ifndef BOOST_NO_CXX17_HDR_STRING_VIEW
#include <string_view>
#endif
#ifdef BOOST_MP_MATH_AVAILABLE
#include <boost/math/special_functions/fpclassify.hpp>
#include <boost/math/special_functions/next.hpp>
#include <boost/math/special_functions/hypot.hpp>
#include <boost/math/policies/error_handling.hpp>
#endif
#ifndef INSTRUMENT_BACKEND
#ifndef BOOST_MP_INSTRUMENT
#define INSTRUMENT_BACKEND(x)
#else
#define INSTRUMENT_BACKEND(x) \
std::cout << BOOST_STRINGIZE(x) << " = " << x.str(0, std::ios_base::scientific) << std::endl;
#endif
#endif
namespace boost {
namespace multiprecision {
namespace detail {
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_floating_point>& /*to_type*/, const std::integral_constant<int, number_kind_integer>& /*from_type*/);
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_integer>& /*to_type*/, const std::integral_constant<int, number_kind_integer>& /*from_type*/);
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_floating_point>& /*to_type*/, const std::integral_constant<int, number_kind_floating_point>& /*from_type*/);
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_rational>& /*to_type*/, const std::integral_constant<int, number_kind_rational>& /*from_type*/);
template <class To, class From>
void generic_interconvert(To& to, const From& from, const std::integral_constant<int, number_kind_rational>& /*to_type*/, const std::integral_constant<int, number_kind_integer>& /*from_type*/);
template <class Integer>
BOOST_MP_CXX14_CONSTEXPR Integer karatsuba_sqrt(const Integer& x, Integer& r, size_t bits);
} // namespace detail
namespace default_ops {
template <class T>
BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_backend<T>::value, int>::type eval_signbit(const T& val);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!boost::multiprecision::detail::is_backend<T>::value, int>::type eval_signbit(const T& val) { return val < 0; }
inline int eval_signbit(float val) { return (std::signbit)(val); }
inline int eval_signbit(double val) { return (std::signbit)(val); }
inline int eval_signbit(long double val) { return (std::signbit)(val); }
#ifdef BOOST_HAS_FLOAT128
extern "C" int signbitq(float128_type) throw();
inline int eval_signbit(float128_type val) { return signbitq(val); }
#endif
template <class T>
BOOST_MP_CXX14_CONSTEXPR bool eval_is_zero(const T& val);
#ifdef BOOST_MSVC
// warning C4127: conditional expression is constant
// warning C4146: unary minus operator applied to unsigned type, result still unsigned
#pragma warning(push)
#pragma warning(disable : 4127 4146)
#endif
//
// Default versions of mixed arithmetic, these just construct a temporary
// from the arithmetic value and then do the arithmetic on that, two versions
// of each depending on whether the backend can be directly constructed from type V.
//
// Note that we have to provide *all* the template parameters to class number when used in
// enable_if as MSVC-10 won't compile the code if we rely on a computed-default parameter.
// Since the result of the test doesn't depend on whether expression templates are on or off
// we just use et_on everywhere. We could use a BOOST_WORKAROUND but that just obfuscates the
// code even more....
//
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< !std::is_convertible<V, T>::value>::type
eval_add(T& result, V const& v)
{
T t;
t = v;
eval_add(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, T>::value>::type
eval_add(T& result, V const& v)
{
T t(v);
eval_add(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< !std::is_convertible<V, T>::value>::type
eval_subtract(T& result, V const& v)
{
T t;
t = v;
eval_subtract(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, T>::value>::type
eval_subtract(T& result, V const& v)
{
T t(v);
eval_subtract(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< !std::is_convertible<V, T>::value>::type
eval_multiply(T& result, V const& v)
{
T t;
t = v;
eval_multiply(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, T>::value>::type
eval_multiply(T& result, V const& v)
{
T t(v);
eval_multiply(result, t);
}
template <class T, class U, class V>
BOOST_MP_CXX14_CONSTEXPR void eval_multiply(T& t, const U& u, const V& v);
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!(!std::is_same<T, U>::value && std::is_same<T, V>::value)>::type eval_multiply_add(T& t, const U& u, const V& v)
{
T z;
eval_multiply(z, u, v);
eval_add(t, z);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!std::is_same<T, U>::value && std::is_same<T, V>::value>::type eval_multiply_add(T& t, const U& u, const V& v)
{
eval_multiply_add(t, v, u);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!(!std::is_same<T, U>::value && std::is_same<T, V>::value)>::type eval_multiply_subtract(T& t, const U& u, const V& v)
{
T z;
eval_multiply(z, u, v);
eval_subtract(t, z);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!std::is_same<T, U>::value && std::is_same<T, V>::value>::type eval_multiply_subtract(T& t, const U& u, const V& v)
{
eval_multiply_subtract(t, v, u);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && !std::is_convertible<V, T>::value>::type
eval_divide(T& result, V const& v)
{
T t;
t = v;
eval_divide(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && std::is_convertible<V, T>::value>::type
eval_divide(T& result, V const& v)
{
T t(v);
eval_divide(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && !std::is_convertible<V, T>::value>::type
eval_modulus(T& result, V const& v)
{
T t;
t = v;
eval_modulus(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && std::is_convertible<V, T>::value>::type
eval_modulus(T& result, V const& v)
{
T t(v);
eval_modulus(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && !std::is_convertible<V, T>::value>::type
eval_bitwise_and(T& result, V const& v)
{
T t;
t = v;
eval_bitwise_and(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && std::is_convertible<V, T>::value>::type
eval_bitwise_and(T& result, V const& v)
{
T t(v);
eval_bitwise_and(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && !std::is_convertible<V, T>::value>::type
eval_bitwise_or(T& result, V const& v)
{
T t;
t = v;
eval_bitwise_or(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && std::is_convertible<V, T>::value>::type
eval_bitwise_or(T& result, V const& v)
{
T t(v);
eval_bitwise_or(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && !std::is_convertible<V, T>::value>::type
eval_bitwise_xor(T& result, V const& v)
{
T t;
t = v;
eval_bitwise_xor(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && std::is_convertible<V, T>::value>::type
eval_bitwise_xor(T& result, V const& v)
{
T t(v);
eval_bitwise_xor(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && !std::is_convertible<V, T>::value>::type
eval_complement(T& result, V const& v)
{
T t;
t = v;
eval_complement(result, t);
}
template <class T, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<V, number<T, et_on> >::value && std::is_convertible<V, T>::value>::type
eval_complement(T& result, V const& v)
{
T t(v);
eval_complement(result, t);
}
//
// Default versions of 3-arg arithmetic functions, these mostly just forward to the 2 arg versions:
//
template <class T, class U, class V>
BOOST_MP_CXX14_CONSTEXPR void eval_add(T& t, const U& u, const V& v);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_add_default(T& t, const T& u, const T& v)
{
if (&t == &v)
{
eval_add(t, u);
}
else if (&t == &u)
{
eval_add(t, v);
}
else
{
t = u;
eval_add(t, v);
}
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_add_default(T& t, const T& u, const U& v)
{
T vv;
vv = v;
eval_add(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_add_default(T& t, const T& u, const U& v)
{
T vv(v);
eval_add(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value>::type eval_add_default(T& t, const U& u, const T& v)
{
eval_add(t, v, u);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_add_default(T& t, const U& u, const V& v)
{
BOOST_IF_CONSTEXPR(std::is_same<T, V>::value)
{
if ((void*)&t == (void*)&v)
{
eval_add(t, u);
}
else
{
t = u;
eval_add(t, v);
}
}
else
{
t = u;
eval_add(t, v);
}
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_add(T& t, const U& u, const V& v)
{
eval_add_default(t, u, v);
}
template <class T, class U, class V>
void BOOST_MP_CXX14_CONSTEXPR eval_subtract(T& t, const U& u, const V& v);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_subtract_default(T& t, const T& u, const T& v)
{
if ((&t == &v) && is_signed_number<T>::value)
{
eval_subtract(t, u);
t.negate();
}
else if (&t == &u)
{
eval_subtract(t, v);
}
else
{
t = u;
eval_subtract(t, v);
}
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_subtract_default(T& t, const T& u, const U& v)
{
T vv;
vv = v;
eval_subtract(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_subtract_default(T& t, const T& u, const U& v)
{
T vv(v);
eval_subtract(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && is_signed_number<T>::value && (number_category<T>::value != number_kind_complex)>::type eval_subtract_default(T& t, const U& u, const T& v)
{
eval_subtract(t, v, u);
if(!eval_is_zero(t) || (eval_signbit(u) != eval_signbit(v)))
t.negate();
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && is_signed_number<T>::value && (number_category<T>::value == number_kind_complex)>::type eval_subtract_default(T& t, const U& u, const T& v)
{
eval_subtract(t, v, u);
t.negate();
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value && is_unsigned_number<T>::value>::type eval_subtract_default(T& t, const U& u, const T& v)
{
T temp;
temp = u;
eval_subtract(t, temp, v);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value && is_unsigned_number<T>::value>::type eval_subtract_default(T& t, const U& u, const T& v)
{
T temp(u);
eval_subtract(t, temp, v);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_subtract_default(T& t, const U& u, const V& v)
{
BOOST_IF_CONSTEXPR(std::is_same<T, V>::value)
{
if ((void*)&t == (void*)&v)
{
eval_subtract(t, u);
t.negate();
}
else
{
t = u;
eval_subtract(t, v);
}
}
else
{
t = u;
eval_subtract(t, v);
}
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_subtract(T& t, const U& u, const V& v)
{
eval_subtract_default(t, u, v);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_multiply_default(T& t, const T& u, const T& v)
{
if (&t == &v)
{
eval_multiply(t, u);
}
else if (&t == &u)
{
eval_multiply(t, v);
}
else
{
t = u;
eval_multiply(t, v);
}
}
#if !BOOST_WORKAROUND(BOOST_MSVC, < 1900)
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_multiply_default(T& t, const T& u, const U& v)
{
T vv;
vv = v;
eval_multiply(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_multiply_default(T& t, const T& u, const U& v)
{
T vv(v);
eval_multiply(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value>::type eval_multiply_default(T& t, const U& u, const T& v)
{
eval_multiply(t, v, u);
}
#endif
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_multiply_default(T& t, const U& u, const V& v)
{
BOOST_IF_CONSTEXPR(std::is_same<T, V>::value)
{
if ((void*)&t == (void*)&v)
{
eval_multiply(t, u);
}
else
{
t = number<T>::canonical_value(u);
eval_multiply(t, v);
}
}
else
{
t = number<T>::canonical_value(u);
eval_multiply(t, v);
}
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_multiply(T& t, const U& u, const V& v)
{
eval_multiply_default(t, u, v);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_multiply_add(T& t, const T& u, const T& v, const T& x)
{
if ((void*)&x == (void*)&t)
{
T z;
z = number<T>::canonical_value(x);
eval_multiply_add(t, u, v, z);
}
else
{
eval_multiply(t, u, v);
eval_add(t, x);
}
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< !std::is_same<T, U>::value, T>::type make_T(const U& u)
{
T t;
t = number<T>::canonical_value(u);
return t;
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR const T& make_T(const T& t)
{
return t;
}
template <class T, class U, class V, class X>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!(!std::is_same<T, U>::value && std::is_same<T, V>::value)>::type eval_multiply_add(T& t, const U& u, const V& v, const X& x)
{
eval_multiply_add(t, make_T<T>(u), make_T<T>(v), make_T<T>(x));
}
template <class T, class U, class V, class X>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!std::is_same<T, U>::value && std::is_same<T, V>::value>::type eval_multiply_add(T& t, const U& u, const V& v, const X& x)
{
eval_multiply_add(t, v, u, x);
}
template <class T, class U, class V, class X>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!(!std::is_same<T, U>::value && std::is_same<T, V>::value)>::type eval_multiply_subtract(T& t, const U& u, const V& v, const X& x)
{
if ((void*)&x == (void*)&t)
{
T z;
z = x;
eval_multiply_subtract(t, u, v, z);
}
else
{
eval_multiply(t, u, v);
eval_subtract(t, x);
}
}
template <class T, class U, class V, class X>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!std::is_same<T, U>::value && std::is_same<T, V>::value>::type eval_multiply_subtract(T& t, const U& u, const V& v, const X& x)
{
eval_multiply_subtract(t, v, u, x);
}
template <class T, class U, class V>
BOOST_MP_CXX14_CONSTEXPR void eval_divide(T& t, const U& u, const V& v);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_divide_default(T& t, const T& u, const T& v)
{
if (&t == &u)
eval_divide(t, v);
else if (&t == &v)
{
T temp;
eval_divide(temp, u, v);
temp.swap(t);
}
else
{
t = u;
eval_divide(t, v);
}
}
#if !BOOST_WORKAROUND(BOOST_MSVC, < 1900)
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_divide_default(T& t, const T& u, const U& v)
{
T vv;
vv = v;
eval_divide(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_divide_default(T& t, const T& u, const U& v)
{
T vv(v);
eval_divide(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_divide_default(T& t, const U& u, const T& v)
{
T uu;
uu = u;
eval_divide(t, uu, v);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_divide_default(T& t, const U& u, const T& v)
{
T uu(u);
eval_divide(t, uu, v);
}
#endif
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_divide_default(T& t, const U& u, const V& v)
{
BOOST_IF_CONSTEXPR(std::is_same<T, V>::value)
{
if ((void*)&t == (void*)&v)
{
T temp;
temp = u;
eval_divide(temp, v);
t = temp;
}
else
{
t = u;
eval_divide(t, v);
}
}
else
{
t = u;
eval_divide(t, v);
}
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_divide(T& t, const U& u, const V& v)
{
eval_divide_default(t, u, v);
}
template <class T, class U, class V>
BOOST_MP_CXX14_CONSTEXPR void eval_modulus(T& t, const U& u, const V& v);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_modulus_default(T& t, const T& u, const T& v)
{
if (&t == &u)
eval_modulus(t, v);
else if (&t == &v)
{
T temp;
eval_modulus(temp, u, v);
temp.swap(t);
}
else
{
t = u;
eval_modulus(t, v);
}
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_modulus_default(T& t, const T& u, const U& v)
{
T vv;
vv = v;
eval_modulus(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_modulus_default(T& t, const T& u, const U& v)
{
T vv(v);
eval_modulus(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_modulus_default(T& t, const U& u, const T& v)
{
T uu;
uu = u;
eval_modulus(t, uu, v);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_modulus_default(T& t, const U& u, const T& v)
{
T uu(u);
eval_modulus(t, uu, v);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_modulus_default(T& t, const U& u, const V& v)
{
BOOST_IF_CONSTEXPR(std::is_same<T, V>::value)
{
if ((void*)&t == (void*)&v)
{
T temp(u);
eval_modulus(temp, v);
t = temp;
}
else
{
t = u;
eval_modulus(t, v);
}
}
else
{
t = u;
eval_modulus(t, v);
}
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_modulus(T& t, const U& u, const V& v)
{
eval_modulus_default(t, u, v);
}
template <class T, class U, class V>
BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_and(T& t, const U& u, const V& v);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_and_default(T& t, const T& u, const T& v)
{
if (&t == &v)
{
eval_bitwise_and(t, u);
}
else if (&t == &u)
{
eval_bitwise_and(t, v);
}
else
{
t = u;
eval_bitwise_and(t, v);
}
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< !std::is_convertible<U, T>::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v)
{
T vv;
vv = v;
eval_bitwise_and(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, T>::value>::type eval_bitwise_and_default(T& t, const T& u, const U& v)
{
T vv(v);
eval_bitwise_and(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value>::type eval_bitwise_and_default(T& t, const U& u, const T& v)
{
eval_bitwise_and(t, v, u);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<!std::is_same<T, U>::value || std::is_same<T, V>::value>::type eval_bitwise_and_default(T& t, const U& u, const V& v)
{
t = u;
eval_bitwise_and(t, v);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_and(T& t, const U& u, const V& v)
{
eval_bitwise_and_default(t, u, v);
}
template <class T, class U, class V>
BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_or(T& t, const U& u, const V& v);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_or_default(T& t, const T& u, const T& v)
{
if (&t == &v)
{
eval_bitwise_or(t, u);
}
else if (&t == &u)
{
eval_bitwise_or(t, v);
}
else
{
t = u;
eval_bitwise_or(t, v);
}
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v)
{
T vv;
vv = v;
eval_bitwise_or(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_bitwise_or_default(T& t, const T& u, const U& v)
{
T vv(v);
eval_bitwise_or(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value>::type eval_bitwise_or_default(T& t, const U& u, const T& v)
{
eval_bitwise_or(t, v, u);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_or_default(T& t, const U& u, const V& v)
{
BOOST_IF_CONSTEXPR(std::is_same<T, V>::value)
{
if ((void*)&t == (void*)&v)
{
eval_bitwise_or(t, u);
}
else
{
t = u;
eval_bitwise_or(t, v);
}
}
else
{
t = u;
eval_bitwise_or(t, v);
}
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_or(T& t, const U& u, const V& v)
{
eval_bitwise_or_default(t, u, v);
}
template <class T, class U, class V>
BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_xor(T& t, const U& u, const V& v);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_xor_default(T& t, const T& u, const T& v)
{
if (&t == &v)
{
eval_bitwise_xor(t, u);
}
else if (&t == &u)
{
eval_bitwise_xor(t, v);
}
else
{
t = u;
eval_bitwise_xor(t, v);
}
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && !std::is_convertible<U, T>::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v)
{
T vv;
vv = v;
eval_bitwise_xor(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value && std::is_convertible<U, T>::value>::type eval_bitwise_xor_default(T& t, const T& u, const U& v)
{
T vv(v);
eval_bitwise_xor(t, u, vv);
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_convertible<U, number<T, et_on> >::value>::type eval_bitwise_xor_default(T& t, const U& u, const T& v)
{
eval_bitwise_xor(t, v, u);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_xor_default(T& t, const U& u, const V& v)
{
BOOST_IF_CONSTEXPR(std::is_same<T, V>::value)
{
if ((void*)&t == (void*)&v)
{
eval_bitwise_xor(t, u);
}
else
{
t = u;
eval_bitwise_xor(t, v);
}
}
else
{
t = u;
eval_bitwise_xor(t, v);
}
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bitwise_xor(T& t, const U& u, const V& v)
{
eval_bitwise_xor_default(t, u, v);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_increment(T& val)
{
using ui_type = typename std::tuple_element<0, typename T::unsigned_types>::type;
eval_add(val, static_cast<ui_type>(1u));
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_decrement(T& val)
{
using ui_type = typename std::tuple_element<0, typename T::unsigned_types>::type;
eval_subtract(val, static_cast<ui_type>(1u));
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_left_shift(T& result, const U& arg, const V val)
{
result = arg;
eval_left_shift(result, val);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_right_shift(T& result, const U& arg, const V val)
{
result = arg;
eval_right_shift(result, val);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR bool eval_is_zero(const T& val)
{
using ui_type = typename std::tuple_element<0, typename T::unsigned_types>::type;
return val.compare(static_cast<ui_type>(0)) == 0;
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR int eval_get_sign(const T& val)
{
using ui_type = typename std::tuple_element<0, typename T::unsigned_types>::type;
return val.compare(static_cast<ui_type>(0));
}
template <class T, class V, class U>
inline BOOST_MP_CXX14_CONSTEXPR void assign_components_imp2(T& result, const V& v1, const U& v2, const std::false_type&, const std::false_type&)
{
using component_number_type = typename component_type<number<T> >::type;
boost::multiprecision::detail::scoped_precision_options<component_number_type> sp(result);
(void)sp;
component_number_type x(v1), y(v2);
assign_components(result, x.backend(), y.backend());
}
template <class T, class V, class U>
inline BOOST_MP_CXX14_CONSTEXPR void assign_components_imp2(T& result, const V& v1, const U& v2, const std::true_type&, const std::false_type&)
{
boost::multiprecision::detail::scoped_source_precision<number<V>> scope;
(void)scope;
assign_components_imp2(result, number<V>(v1), v2, std::false_type(), std::false_type());
}
template <class T, class V, class U>
inline BOOST_MP_CXX14_CONSTEXPR void assign_components_imp2(T& result, const V& v1, const U& v2, const std::true_type&, const std::true_type&)
{
boost::multiprecision::detail::scoped_source_precision<number<V>> scope1;
boost::multiprecision::detail::scoped_source_precision<number<U>> scope2;
(void)scope1;
(void)scope2;
assign_components_imp2(result, number<V>(v1), number<U>(v2), std::false_type(), std::false_type());
}
template <class T, class V, class U>
inline BOOST_MP_CXX14_CONSTEXPR void assign_components_imp2(T& result, const V& v1, const U& v2, const std::false_type&, const std::true_type&)
{
boost::multiprecision::detail::scoped_source_precision<number<U>> scope;
(void)scope;
assign_components_imp2(result, v1, number<U>(v2), std::false_type(), std::false_type());
}
template <class T, class V, class U>
inline BOOST_MP_CXX14_CONSTEXPR void assign_components_imp(T& result, const V& v1, const U& v2, const std::integral_constant<int, number_kind_rational>&)
{
result = v1;
T t;
t = v2;
eval_divide(result, t);
}
template <class T, class V, class U, int N>
inline BOOST_MP_CXX14_CONSTEXPR void assign_components_imp(T& result, const V& v1, const U& v2, const std::integral_constant<int, N>&)
{
assign_components_imp2(result, v1, v2, boost::multiprecision::detail::is_backend<V>(), boost::multiprecision::detail::is_backend<U>());
}
template <class T, class V, class U>
inline BOOST_MP_CXX14_CONSTEXPR void assign_components(T& result, const V& v1, const U& v2)
{
return assign_components_imp(result, v1, v2, typename number_category<T>::type());
}
#ifndef BOOST_NO_CXX17_HDR_STRING_VIEW
template <class Result, class Traits>
inline void assign_from_string_view(Result& result, const std::basic_string_view<char, Traits>& view)
{
// since most (all?) backends require a const char* to construct from, we just
// convert to that:
std::string s(view);
result = s.c_str();
}
template <class Result, class Traits>
inline void assign_from_string_view(Result& result, const std::basic_string_view<char, Traits>& view_x, const std::basic_string_view<char, Traits>& view_y)
{
// since most (all?) backends require a const char* to construct from, we just
// convert to that:
std::string x(view_x), y(view_y);
assign_components(result, x.c_str(), y.c_str());
}
#endif
template <class R, int b>
struct has_enough_bits
{
template <class T>
struct type : public std::integral_constant<bool, !std::is_same<R, T>::value && (std::numeric_limits<T>::digits >= b)>
{};
};
template <class R>
struct terminal
{
BOOST_MP_CXX14_CONSTEXPR terminal(const R& v) : value(v) {}
BOOST_MP_CXX14_CONSTEXPR terminal() {}
BOOST_MP_CXX14_CONSTEXPR terminal& operator=(R val)
{
value = val;
return *this;
}
R value;
BOOST_MP_CXX14_CONSTEXPR operator R() const { return value; }
};
template <class Tuple, int i, class T, bool = (i == std::tuple_size<Tuple>::value)>
struct find_index_of_type
{
static constexpr int value =
std::is_same<T, typename std::tuple_element<static_cast<std::size_t>(i), Tuple>::type>::value
? i
: find_index_of_type<Tuple, i + 1, T>::value;
};
template <class Tuple, int i, class T>
struct find_index_of_type<Tuple, i, T, true>
{
static constexpr int value = -1;
};
template <class R, class B>
struct calculate_next_larger_type
{
// Find which list we're looking through:
using list_type = typename std::conditional<
boost::multiprecision::detail::is_signed<R>::value && boost::multiprecision::detail::is_integral<R>::value,
typename B::signed_types,
typename std::conditional<
boost::multiprecision::detail::is_unsigned<R>::value,
typename B::unsigned_types,
typename B::float_types>::type>::type;
static constexpr int start = find_index_of_type<list_type, 0, R>::value;
static constexpr int index_of_type = boost::multiprecision::detail::find_index_of_large_enough_type<list_type, start == INT_MAX ? 0 : start + 1, boost::multiprecision::detail::bits_of<R>::value> ::value;
using type = typename boost::multiprecision::detail::dereference_tuple<index_of_type, list_type, terminal<R> >::type;
};
template <class R, class T>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<R>::value, bool>::type check_in_range(const T& t)
{
// Can t fit in an R?
if ((t > 0) && std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::is_bounded && (t > (std::numeric_limits<R>::max)()))
return true;
else
return false;
}
template <class R, class B>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<R>::value>::type eval_convert_to(R* result, const B& backend)
{
using next_type = typename calculate_next_larger_type<R, B>::type;
next_type n = next_type();
eval_convert_to(&n, backend);
BOOST_IF_CONSTEXPR(!boost::multiprecision::detail::is_unsigned<R>::value && std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::is_bounded)
{
if(n > static_cast<next_type>((std::numeric_limits<R>::max)()))
{
*result = (std::numeric_limits<R>::max)();
return;
}
}
BOOST_IF_CONSTEXPR(std::numeric_limits<R>::is_specialized&& std::numeric_limits<R>::is_bounded)
{
if (n < static_cast<next_type>((std::numeric_limits<R>::min)()))
{
*result = (std::numeric_limits<R>::min)();
return;
}
}
*result = static_cast<R>(n);
}
template <class R, class B>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< !boost::multiprecision::detail::is_integral<R>::value && !std::is_enum<R>::value>::type eval_convert_to(R* result, const B& backend)
{
using next_type = typename calculate_next_larger_type<R, B>::type;
next_type n = next_type();
eval_convert_to(&n, backend);
BOOST_IF_CONSTEXPR(std::numeric_limits<R>::is_specialized && std::numeric_limits<R>::is_bounded)
{
if ((n > (next_type)(std::numeric_limits<R>::max)() || (n < (next_type) - (std::numeric_limits<R>::max)())))
{
*result = n > 0 ? (std::numeric_limits<R>::max)() : -(std::numeric_limits<R>::max)();
}
else
*result = static_cast<R>(n);
}
else
*result = static_cast<R>(n);
}
template <class R, class B>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_enum<R>::value>::type eval_convert_to(R* result, const B& backend)
{
typename std::underlying_type<R>::type t{};
eval_convert_to(&t, backend);
*result = static_cast<R>(t);
}
#ifndef BOOST_MP_STANDALONE
template <class R, class B>
inline void last_chance_eval_convert_to(terminal<R>* result, const B& backend, const std::integral_constant<bool, false>&)
{
//
// We ran out of types to try for the conversion, try
// a lexical_cast and hope for the best:
//
BOOST_IF_CONSTEXPR (std::numeric_limits<R>::is_integer && !std::numeric_limits<R>::is_signed)
if (eval_get_sign(backend) < 0)
BOOST_MP_THROW_EXCEPTION(std::range_error("Attempt to convert negative value to an unsigned integer results in undefined behaviour"));
BOOST_MP_TRY {
result->value = boost::lexical_cast<R>(backend.str(0, std::ios_base::fmtflags(0)));
}
BOOST_MP_CATCH (const bad_lexical_cast&)
{
if (eval_get_sign(backend) < 0)
{
BOOST_IF_CONSTEXPR(std::numeric_limits<R>::is_integer && !std::numeric_limits<R>::is_signed)
*result = (std::numeric_limits<R>::max)(); // we should never get here, exception above will be raised.
else BOOST_IF_CONSTEXPR(std::numeric_limits<R>::is_integer)
*result = (std::numeric_limits<R>::min)();
else
*result = -(std::numeric_limits<R>::max)();
}
else
*result = (std::numeric_limits<R>::max)();
}
BOOST_MP_CATCH_END
}
template <class R, class B>
inline void last_chance_eval_convert_to(terminal<R>* result, const B& backend, const std::integral_constant<bool, true>&)
{
//
// Last chance conversion to an unsigned integer.
// We ran out of types to try for the conversion, try
// a lexical_cast and hope for the best:
//
if (eval_get_sign(backend) < 0)
BOOST_MP_THROW_EXCEPTION(std::range_error("Attempt to convert negative value to an unsigned integer results in undefined behaviour"));
BOOST_MP_TRY {
B t(backend);
R mask = ~static_cast<R>(0u);
eval_bitwise_and(t, mask);
result->value = boost::lexical_cast<R>(t.str(0, std::ios_base::fmtflags(0)));
}
BOOST_MP_CATCH (const bad_lexical_cast&)
{
// We should never really get here...
*result = (std::numeric_limits<R>::max)();
}
BOOST_MP_CATCH_END
}
#else // Using standalone mode
template <class R, class B>
inline void last_chance_eval_convert_to(terminal<R>*, const B&, const std::integral_constant<bool, false>&)
{
static_assert(sizeof(R) == 1, "This type can not be used in standalone mode. Please de-activate and file a bug at https://github.com/boostorg/multiprecision/");
}
template <class R, class B>
inline void last_chance_eval_convert_to(terminal<R>* result, const B& backend, const std::integral_constant<bool, true>&)
{
static_cast<void>(result);
static_cast<void>(backend);
static_assert(sizeof(R) == 1, "This type can not be used in standalone mode. Please de-activate and file a bug at https://github.com/boostorg/multiprecision/");
}
#endif
template <class R, class B>
inline BOOST_MP_CXX14_CONSTEXPR void eval_convert_to(terminal<R>* result, const B& backend)
{
using tag_type = std::integral_constant<bool, boost::multiprecision::detail::is_unsigned<R>::value && number_category<B>::value == number_kind_integer>;
last_chance_eval_convert_to(result, backend, tag_type());
}
template <class B1, class B2, expression_template_option et>
inline BOOST_MP_CXX14_CONSTEXPR void eval_convert_to(terminal<number<B1, et> >* result, const B2& backend)
{
//
// We ran out of types to try for the conversion, try
// a generic conversion and hope for the best:
//
boost::multiprecision::detail::generic_interconvert(result->value.backend(), backend, number_category<B1>(), number_category<B2>());
}
template <class B>
inline BOOST_MP_CXX14_CONSTEXPR void eval_convert_to(std::string* result, const B& backend)
{
*result = backend.str(0, std::ios_base::fmtflags(0));
}
template <class B>
inline BOOST_MP_CXX14_CONSTEXPR void eval_convert_to(std::complex<float>* result, const B& backend)
{
using scalar_type = typename scalar_result_from_possible_complex<multiprecision::number<B> >::type;
scalar_type re, im;
eval_real(re.backend(), backend);
eval_imag(im.backend(), backend);
*result = std::complex<float>(re.template convert_to<float>(), im.template convert_to<float>());
}
template <class B>
inline BOOST_MP_CXX14_CONSTEXPR void eval_convert_to(std::complex<double>* result, const B& backend)
{
using scalar_type = typename scalar_result_from_possible_complex<multiprecision::number<B> >::type;
scalar_type re, im;
eval_real(re.backend(), backend);
eval_imag(im.backend(), backend);
*result = std::complex<double>(re.template convert_to<double>(), im.template convert_to<double>());
}
template <class B>
inline BOOST_MP_CXX14_CONSTEXPR void eval_convert_to(std::complex<long double>* result, const B& backend)
{
using scalar_type = typename scalar_result_from_possible_complex<multiprecision::number<B> >::type;
scalar_type re, im;
eval_real(re.backend(), backend);
eval_imag(im.backend(), backend);
*result = std::complex<long double>(re.template convert_to<long double>(), im.template convert_to<long double>());
}
//
// Functions:
//
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR void eval_abs(T& result, const U& arg)
{
using type_list = typename U::signed_types ;
using front = typename std::tuple_element<0, type_list>::type;
result = arg;
if (arg.compare(front(0)) < 0)
result.negate();
}
template <class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR void eval_fabs(T& result, const U& arg)
{
static_assert(number_category<T>::value == number_kind_floating_point, "The fabs function is only valid for floating point types.");
using type_list = typename U::signed_types ;
using front = typename std::tuple_element<0, type_list>::type;
result = arg;
if (arg.compare(front(0)) < 0)
result.negate();
}
template <class Backend>
inline BOOST_MP_CXX14_CONSTEXPR int eval_fpclassify(const Backend& arg)
{
static_assert(number_category<Backend>::value == number_kind_floating_point, "The fpclassify function is only valid for floating point types.");
return eval_is_zero(arg) ? FP_ZERO : FP_NORMAL;
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_fmod(T& result, const T& a, const T& b)
{
static_assert(number_category<T>::value == number_kind_floating_point, "The fmod function is only valid for floating point types.");
if ((&result == &a) || (&result == &b))
{
T temp;
eval_fmod(temp, a, b);
result = temp;
return;
}
switch (eval_fpclassify(a))
{
case FP_ZERO:
result = a;
return;
case FP_INFINITE:
case FP_NAN:
result = std::numeric_limits<number<T> >::quiet_NaN().backend();
errno = EDOM;
return;
}
switch (eval_fpclassify(b))
{
case FP_ZERO:
case FP_NAN:
result = std::numeric_limits<number<T> >::quiet_NaN().backend();
errno = EDOM;
return;
}
T n;
eval_divide(result, a, b);
if (eval_get_sign(result) < 0)
eval_ceil(n, result);
else
eval_floor(n, result);
eval_multiply(n, b);
eval_subtract(result, a, n);
}
template <class T, class A>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_arithmetic<A>::value, void>::type eval_fmod(T& result, const T& x, const A& a)
{
using canonical_type = typename boost::multiprecision::detail::canonical<A, T>::type ;
using cast_type = typename std::conditional<std::is_same<A, canonical_type>::value, T, canonical_type>::type;
cast_type c;
c = a;
eval_fmod(result, x, c);
}
template <class T, class A>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_arithmetic<A>::value, void>::type eval_fmod(T& result, const A& x, const T& a)
{
using canonical_type = typename boost::multiprecision::detail::canonical<A, T>::type ;
using cast_type = typename std::conditional<std::is_same<A, canonical_type>::value, T, canonical_type>::type;
cast_type c;
c = x;
eval_fmod(result, c, a);
}
template <class T>
BOOST_MP_CXX14_CONSTEXPR void eval_round(T& result, const T& a);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_remquo(T& result, const T& a, const T& b, int* pi)
{
static_assert(number_category<T>::value == number_kind_floating_point, "The remquo function is only valid for floating point types.");
if ((&result == &a) || (&result == &b))
{
T temp;
eval_remquo(temp, a, b, pi);
result = temp;
return;
}
T n;
eval_divide(result, a, b);
eval_round(n, result);
eval_convert_to(pi, n);
eval_multiply(n, b);
eval_subtract(result, a, n);
if (eval_is_zero(result))
{
if (eval_signbit(a))
result.negate();
}
}
template <class T, class A>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_arithmetic<A>::value, void>::type eval_remquo(T& result, const T& x, const A& a, int* pi)
{
using canonical_type = typename boost::multiprecision::detail::canonical<A, T>::type ;
using cast_type = typename std::conditional<std::is_same<A, canonical_type>::value, T, canonical_type>::type;
cast_type c = cast_type();
c = a;
eval_remquo(result, x, c, pi);
}
template <class T, class A>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_arithmetic<A>::value, void>::type eval_remquo(T& result, const A& x, const T& a, int* pi)
{
using canonical_type = typename boost::multiprecision::detail::canonical<A, T>::type ;
using cast_type = typename std::conditional<std::is_same<A, canonical_type>::value, T, canonical_type>::type;
cast_type c = cast_type();
c = x;
eval_remquo(result, c, a, pi);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_remainder(T& result, const U& a, const V& b)
{
int i(0);
eval_remquo(result, a, b, &i);
}
template <class B>
BOOST_MP_CXX14_CONSTEXPR bool eval_gt(const B& a, const B& b);
template <class T, class U>
BOOST_MP_CXX14_CONSTEXPR bool eval_gt(const T& a, const U& b);
template <class B>
BOOST_MP_CXX14_CONSTEXPR bool eval_lt(const B& a, const B& b);
template <class T, class U>
BOOST_MP_CXX14_CONSTEXPR bool eval_lt(const T& a, const U& b);
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_fdim(T& result, const T& a, const T& b)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
const ui_type zero = 0u;
switch (eval_fpclassify(b))
{
case FP_NAN:
case FP_INFINITE:
result = zero;
return;
}
switch (eval_fpclassify(a))
{
case FP_NAN:
result = zero;
return;
case FP_INFINITE:
result = a;
return;
}
if (eval_gt(a, b))
{
eval_subtract(result, a, b);
}
else
result = zero;
}
template <class T, class A>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_arithmetic<A>::value>::type eval_fdim(T& result, const T& a, const A& b)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
using arithmetic_type = typename boost::multiprecision::detail::canonical<A, T>::type ;
const ui_type zero = 0u;
arithmetic_type canonical_b = b;
switch (BOOST_MP_FPCLASSIFY(b))
{
case FP_NAN:
case FP_INFINITE:
result = zero;
return;
}
switch (eval_fpclassify(a))
{
case FP_NAN:
result = zero;
return;
case FP_INFINITE:
result = a;
return;
}
if (eval_gt(a, canonical_b))
{
eval_subtract(result, a, canonical_b);
}
else
result = zero;
}
template <class T, class A>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_arithmetic<A>::value>::type eval_fdim(T& result, const A& a, const T& b)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
using arithmetic_type = typename boost::multiprecision::detail::canonical<A, T>::type ;
const ui_type zero = 0u;
arithmetic_type canonical_a = a;
switch (eval_fpclassify(b))
{
case FP_NAN:
case FP_INFINITE:
result = zero;
return;
}
switch (BOOST_MP_FPCLASSIFY(a))
{
case FP_NAN:
result = zero;
return;
case FP_INFINITE:
result = std::numeric_limits<number<T> >::infinity().backend();
return;
}
if (eval_gt(canonical_a, b))
{
eval_subtract(result, canonical_a, b);
}
else
result = zero;
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_trunc(T& result, const T& a)
{
static_assert(number_category<T>::value == number_kind_floating_point, "The trunc function is only valid for floating point types.");
switch (eval_fpclassify(a))
{
case FP_NAN:
errno = EDOM;
// fallthrough...
case FP_ZERO:
case FP_INFINITE:
result = a;
return;
}
if (eval_get_sign(a) < 0)
eval_ceil(result, a);
else
eval_floor(result, a);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_modf(T& result, T const& arg, T* pipart)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
int c = eval_fpclassify(arg);
if (c == static_cast<int>(FP_NAN))
{
if (pipart)
*pipart = arg;
result = arg;
return;
}
else if (c == static_cast<int>(FP_INFINITE))
{
if (pipart)
*pipart = arg;
result = ui_type(0u);
return;
}
if (pipart)
{
eval_trunc(*pipart, arg);
eval_subtract(result, arg, *pipart);
}
else
{
T ipart;
eval_trunc(ipart, arg);
eval_subtract(result, arg, ipart);
}
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_round(T& result, const T& a)
{
static_assert(number_category<T>::value == number_kind_floating_point, "The round function is only valid for floating point types.");
using fp_type = typename boost::multiprecision::detail::canonical<float, T>::type;
int c = eval_fpclassify(a);
if (c == static_cast<int>(FP_NAN))
{
result = a;
errno = EDOM;
return;
}
if ((c == FP_ZERO) || (c == static_cast<int>(FP_INFINITE)))
{
result = a;
}
else if (eval_get_sign(a) < 0)
{
eval_subtract(result, a, fp_type(0.5f));
eval_ceil(result, result);
}
else
{
eval_add(result, a, fp_type(0.5f));
eval_floor(result, result);
}
}
template <class B>
BOOST_MP_CXX14_CONSTEXPR void eval_lcm(B& result, const B& a, const B& b);
template <class B>
BOOST_MP_CXX14_CONSTEXPR void eval_gcd(B& result, const B& a, const B& b);
template <class T, class Arithmetic>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Arithmetic>::value >::type eval_gcd(T& result, const T& a, const Arithmetic& b)
{
using si_type = typename boost::multiprecision::detail::canonical<Arithmetic, T>::type;
using default_ops::eval_gcd;
T t;
t = static_cast<si_type>(b);
eval_gcd(result, a, t);
}
template <class T, class Arithmetic>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Arithmetic>::value >::type eval_gcd(T& result, const Arithmetic& a, const T& b)
{
eval_gcd(result, b, a);
}
template <class T, class Arithmetic>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Arithmetic>::value >::type eval_lcm(T& result, const T& a, const Arithmetic& b)
{
using si_type = typename boost::multiprecision::detail::canonical<Arithmetic, T>::type;
using default_ops::eval_lcm;
T t;
t = static_cast<si_type>(b);
eval_lcm(result, a, t);
}
template <class T, class Arithmetic>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<Arithmetic>::value >::type eval_lcm(T& result, const Arithmetic& a, const T& b)
{
eval_lcm(result, b, a);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR std::size_t eval_lsb(const T& val)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
int c = eval_get_sign(val);
if (c == 0)
{
BOOST_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
}
if (c < 0)
{
BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
}
std::size_t result = 0;
T mask, t;
mask = ui_type(1);
do
{
eval_bitwise_and(t, mask, val);
++result;
eval_left_shift(mask, 1);
} while (eval_is_zero(t));
return --result;
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR std::ptrdiff_t eval_msb(const T& val)
{
int c = eval_get_sign(val);
if (c == 0)
{
BOOST_MP_THROW_EXCEPTION(std::domain_error("No bits were set in the operand."));
}
if (c < 0)
{
BOOST_MP_THROW_EXCEPTION(std::domain_error("Testing individual bits in negative values is not supported - results are undefined."));
}
//
// This implementation is really really rubbish - it does
// a linear scan for the most-significant-bit. We should really
// do a binary search, but as none of our backends actually needs
// this implementation, we'll leave it for now. In fact for most
// backends it's likely that there will always be a more efficient
// native implementation possible.
//
std::size_t result = 0;
T t(val);
while (!eval_is_zero(t))
{
eval_right_shift(t, 1);
++result;
}
--result;
return static_cast<std::ptrdiff_t>(result);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR bool eval_bit_test(const T& val, std::size_t index)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
T mask, t;
mask = ui_type(1);
eval_left_shift(mask, index);
eval_bitwise_and(t, mask, val);
return !eval_is_zero(t);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bit_set(T& val, std::size_t index)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
T mask;
mask = ui_type(1);
eval_left_shift(mask, index);
eval_bitwise_or(val, mask);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bit_flip(T& val, std::size_t index)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
T mask;
mask = ui_type(1);
eval_left_shift(mask, index);
eval_bitwise_xor(val, mask);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_bit_unset(T& val, std::size_t index)
{
using ui_type = typename boost::multiprecision::detail::canonical<unsigned, T>::type;
T mask, t;
mask = ui_type(1);
eval_left_shift(mask, index);
eval_bitwise_and(t, mask, val);
if (!eval_is_zero(t))
eval_bitwise_xor(val, mask);
}
template <class Backend>
BOOST_MP_CXX14_CONSTEXPR void eval_qr(const Backend& x, const Backend& y, Backend& q, Backend& r);
template <class Backend>
BOOST_MP_CXX14_CONSTEXPR void eval_karatsuba_sqrt(Backend& result, const Backend& x, Backend& r, Backend& t, size_t bits)
{
using default_ops::eval_is_zero;
using default_ops::eval_subtract;
using default_ops::eval_right_shift;
using default_ops::eval_left_shift;
using default_ops::eval_bit_set;
using default_ops::eval_decrement;
using default_ops::eval_bitwise_and;
using default_ops::eval_add;
using default_ops::eval_qr;
using small_uint = typename std::tuple_element<0, typename Backend::unsigned_types>::type;
constexpr small_uint zero = 0u;
// we can calculate it faster with std::sqrt
#ifdef BOOST_HAS_INT128
if (bits <= 128)
{
uint128_type a{}, b{}, c{};
eval_convert_to(&a, x);
c = boost::multiprecision::detail::karatsuba_sqrt(a, b, bits);
r = number<Backend>::canonical_value(b);
result = number<Backend>::canonical_value(c);
return;
}
#else
if (bits <= std::numeric_limits<std::uintmax_t>::digits)
{
std::uintmax_t a{ 0 }, b{ 0 }, c{ 0 };
eval_convert_to(&a, x);
c = boost::multiprecision::detail::karatsuba_sqrt(a, b, bits);
r = number<Backend>::canonical_value(b);
result = number<Backend>::canonical_value(c);
return;
}
#endif
// https://hal.inria.fr/file/index/docid/72854/filename/RR-3805.pdf
std::size_t b = bits / 4;
Backend q(x);
eval_right_shift(q, b * 2);
Backend s;
eval_karatsuba_sqrt(s, q, r, t, bits - b * 2);
t = zero;
eval_bit_set(t, static_cast<unsigned>(b * 2));
eval_left_shift(r, b);
eval_decrement(t);
eval_bitwise_and(t, x);
eval_right_shift(t, b);
eval_add(t, r);
eval_left_shift(s, 1u);
eval_qr(t, s, q, r);
eval_left_shift(r, b);
t = zero;
eval_bit_set(t, static_cast<unsigned>(b));
eval_decrement(t);
eval_bitwise_and(t, x);
eval_add(r, t);
eval_left_shift(s, b - 1);
eval_add(s, q);
eval_multiply(q, q);
// we substract after, so it works for unsigned integers too
if (r.compare(q) < 0)
{
t = s;
eval_left_shift(t, 1u);
eval_decrement(t);
eval_add(r, t);
eval_decrement(s);
}
eval_subtract(r, q);
result = s;
}
template <class B>
void BOOST_MP_CXX14_CONSTEXPR eval_integer_sqrt_bitwise(B& s, B& r, const B& x)
{
//
// This is slow bit-by-bit integer square root, see for example
// http://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_.28base_2.29
// There are better methods such as http://hal.inria.fr/docs/00/07/28/54/PDF/RR-3805.pdf
// and http://hal.inria.fr/docs/00/07/21/13/PDF/RR-4475.pdf which should be implemented
// at some point.
//
using ui_type = typename boost::multiprecision::detail::canonical<unsigned char, B>::type;
s = ui_type(0u);
if (eval_get_sign(x) == 0)
{
r = ui_type(0u);
return;
}
std::ptrdiff_t g = static_cast<std::ptrdiff_t>(eval_msb(x));
if (g <= 1)
{
s = ui_type(1);
eval_subtract(r, x, s);
return;
}
B t;
r = x;
g /= 2;
std::ptrdiff_t org_g = g;
eval_bit_set(s, static_cast<std::size_t>(g));
eval_bit_set(t, static_cast<std::size_t>(2 * g));
eval_subtract(r, x, t);
--g;
if (eval_get_sign(r) == 0)
return;
std::ptrdiff_t msbr = static_cast<std::ptrdiff_t>(eval_msb(r));
do
{
if (msbr >= org_g + g + 1)
{
t = s;
eval_left_shift(t, static_cast<std::size_t>(g + 1));
eval_bit_set(t, static_cast<std::size_t>(2 * g));
if (t.compare(r) <= 0)
{
BOOST_MP_ASSERT(g >= 0);
eval_bit_set(s, static_cast<std::size_t>(g));
eval_subtract(r, t);
if (eval_get_sign(r) == 0)
return;
msbr = static_cast<std::ptrdiff_t>(eval_msb(r));
}
}
--g;
} while (g >= 0);
}
template <class Backend>
BOOST_MP_CXX14_CONSTEXPR void eval_integer_sqrt(Backend& result, Backend& r, const Backend& x)
{
#ifndef BOOST_MP_NO_CONSTEXPR_DETECTION
// recursive Karatsuba sqrt can cause issues in constexpr context:
if (BOOST_MP_IS_CONST_EVALUATED(result.size()))
return eval_integer_sqrt_bitwise(result, r, x);
#endif
using small_uint = typename std::tuple_element<0, typename Backend::unsigned_types>::type;
constexpr small_uint zero = 0u;
if (eval_is_zero(x))
{
r = zero;
result = zero;
return;
}
Backend t;
eval_karatsuba_sqrt(result, x, r, t, eval_msb(x) + 1);
}
template <class B>
inline BOOST_MP_CXX14_CONSTEXPR void eval_conj(B& result, const B& val)
{
result = val; // assume non-complex result.
}
template <class B>
inline BOOST_MP_CXX14_CONSTEXPR void eval_proj(B& result, const B& val)
{
result = val; // assume non-complex result.
}
//
// These have to implemented by the backend, declared here so that our macro generated code compiles OK.
//
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_floor();
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_ceil();
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_trunc();
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_sqrt();
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_ldexp();
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_frexp();
// TODO implement default versions of these:
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_asinh();
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_acosh();
template <class T>
typename std::enable_if<sizeof(T) == 0>::type eval_atanh();
//
// eval_logb and eval_scalbn simply assume base 2 and forward to
// eval_ldexp and eval_frexp:
//
template <class B>
inline BOOST_MP_CXX14_CONSTEXPR typename B::exponent_type eval_ilogb(const B& val)
{
static_assert(!std::numeric_limits<number<B> >::is_specialized || (std::numeric_limits<number<B> >::radix == 2), "The default implementation of ilogb requires a base 2 number type");
typename B::exponent_type e(0);
switch (eval_fpclassify(val))
{
case FP_NAN:
#ifdef FP_ILOGBNAN
return FP_ILOGBNAN > 0 ? (std::numeric_limits<typename B::exponent_type>::max)() : (std::numeric_limits<typename B::exponent_type>::min)();
#else
return (std::numeric_limits<typename B::exponent_type>::max)();
#endif
case FP_INFINITE:
return (std::numeric_limits<typename B::exponent_type>::max)();
case FP_ZERO:
return (std::numeric_limits<typename B::exponent_type>::min)();
}
B result;
eval_frexp(result, val, &e);
return e - 1;
}
template <class B>
inline BOOST_MP_CXX14_CONSTEXPR void eval_logb(B& result, const B& val)
{
switch (eval_fpclassify(val))
{
case FP_NAN:
result = val;
errno = EDOM;
return;
case FP_ZERO:
result = std::numeric_limits<number<B> >::infinity().backend();
result.negate();
errno = ERANGE;
return;
case FP_INFINITE:
result = val;
if (eval_signbit(val))
result.negate();
return;
}
using max_t = typename std::conditional<std::is_same<std::intmax_t, long>::value, long long, std::intmax_t>::type;
result = static_cast<max_t>(eval_ilogb(val));
}
template <class B, class A>
inline BOOST_MP_CXX14_CONSTEXPR void eval_scalbn(B& result, const B& val, A e)
{
static_assert(!std::numeric_limits<number<B> >::is_specialized || (std::numeric_limits<number<B> >::radix == 2), "The default implementation of scalbn requires a base 2 number type");
eval_ldexp(result, val, static_cast<typename B::exponent_type>(e));
}
template <class B, class A>
inline BOOST_MP_CXX14_CONSTEXPR void eval_scalbln(B& result, const B& val, A e)
{
eval_scalbn(result, val, e);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR bool is_arg_nan(const T& val, std::integral_constant<bool, true> const&, const std::integral_constant<bool, false>&)
{
return eval_fpclassify(val) == FP_NAN;
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR bool is_arg_nan(const T& val, std::integral_constant<bool, false> const&, const std::integral_constant<bool, true>&)
{
return BOOST_MP_ISNAN(val);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR bool is_arg_nan(const T&, std::integral_constant<bool, false> const&, const std::integral_constant<bool, false>&)
{
return false;
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR bool is_arg_nan(const T& val)
{
return is_arg_nan(val, std::integral_constant<bool, boost::multiprecision::detail::is_backend<T>::value>(), std::is_floating_point<T>());
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_fmax(T& result, const U& a, const V& b)
{
if (is_arg_nan(a))
result = number<T>::canonical_value(b);
else if (is_arg_nan(b))
result = number<T>::canonical_value(a);
else if (eval_lt(number<T>::canonical_value(a), number<T>::canonical_value(b)))
result = number<T>::canonical_value(b);
else
result = number<T>::canonical_value(a);
}
template <class T, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR void eval_fmin(T& result, const U& a, const V& b)
{
if (is_arg_nan(a))
result = number<T>::canonical_value(b);
else if (is_arg_nan(b))
result = number<T>::canonical_value(a);
else if (eval_lt(number<T>::canonical_value(a), number<T>::canonical_value(b)))
result = number<T>::canonical_value(a);
else
result = number<T>::canonical_value(b);
}
template <class R, class T, class U>
inline BOOST_MP_CXX14_CONSTEXPR void eval_hypot(R& result, const T& a, const U& b)
{
//
// Normalize x and y, so that both are positive and x >= y:
//
R x, y;
x = number<R>::canonical_value(a);
y = number<R>::canonical_value(b);
if (eval_get_sign(x) < 0)
x.negate();
if (eval_get_sign(y) < 0)
y.negate();
// Special case, see C99 Annex F.
// The order of the if's is important: do not change!
int c1 = eval_fpclassify(x);
int c2 = eval_fpclassify(y);
if (c1 == FP_ZERO)
{
result = y;
return;
}
if (c2 == FP_ZERO)
{
result = x;
return;
}
if (c1 == FP_INFINITE)
{
result = x;
return;
}
if ((c2 == FP_INFINITE) || (c2 == FP_NAN))
{
result = y;
return;
}
if (c1 == FP_NAN)
{
result = x;
return;
}
if (eval_gt(y, x))
x.swap(y);
eval_multiply(result, x, std::numeric_limits<number<R> >::epsilon().backend());
if (eval_gt(result, y))
{
result = x;
return;
}
R rat;
eval_divide(rat, y, x);
eval_multiply(result, rat, rat);
eval_increment(result);
eval_sqrt(rat, result);
eval_multiply(result, rat, x);
}
template <class R, class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_nearbyint(R& result, const T& a)
{
eval_round(result, a);
}
template <class R, class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_rint(R& result, const T& a)
{
eval_nearbyint(result, a);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_backend<T>::value, int>::type eval_signbit(const T& val)
{
return eval_get_sign(val) < 0 ? 1 : 0;
}
//
// Real and imaginary parts:
//
template <class To, class From>
inline BOOST_MP_CXX14_CONSTEXPR void eval_real(To& to, const From& from)
{
to = from;
}
template <class To, class From>
inline BOOST_MP_CXX14_CONSTEXPR void eval_imag(To& to, const From&)
{
using ui_type = typename std::tuple_element<0, typename To::unsigned_types>::type;
to = ui_type(0);
}
} // namespace default_ops
namespace default_ops_adl {
template <class To, class From>
inline BOOST_MP_CXX14_CONSTEXPR void eval_set_real_imp(To& to, const From& from)
{
using to_component_type = typename component_type<number<To> >::type;
typename to_component_type::backend_type to_component;
to_component = from;
eval_set_real(to, to_component);
}
template <class To, class From>
inline BOOST_MP_CXX14_CONSTEXPR void eval_set_imag_imp(To& to, const From& from)
{
using to_component_type = typename component_type<number<To> >::type;
typename to_component_type::backend_type to_component;
to_component = from;
eval_set_imag(to, to_component);
}
} // namespace default_ops_adl
namespace default_ops {
template <class To, class From>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<To>::value == number_kind_complex>::type eval_set_real(To& to, const From& from)
{
default_ops_adl::eval_set_real_imp(to, from);
}
template <class To, class From>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<To>::value != number_kind_complex>::type eval_set_real(To& to, const From& from)
{
to = from;
}
template <class To, class From>
inline BOOST_MP_CXX14_CONSTEXPR void eval_set_imag(To& to, const From& from)
{
default_ops_adl::eval_set_imag_imp(to, from);
}
template <class T>
inline BOOST_MP_CXX14_CONSTEXPR void eval_set_real(T& to, const T& from)
{
to = from;
}
template <class T>
void BOOST_MP_CXX14_CONSTEXPR eval_set_imag(T&, const T&)
{
static_assert(sizeof(T) == INT_MAX, "eval_set_imag needs to be specialised for each specific backend");
}
//
// These functions are implemented in separate files, but expanded inline here,
// DO NOT CHANGE THE ORDER OF THESE INCLUDES:
//
#include <boost/multiprecision/detail/functions/constants.hpp>
#include <boost/multiprecision/detail/functions/pow.hpp>
#include <boost/multiprecision/detail/functions/trig.hpp>
} // namespace default_ops
//
// Default versions of floating point classification routines:
//
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
using multiprecision::default_ops::eval_fpclassify;
return eval_fpclassify(arg.backend());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR int fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
int v = fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(arg);
return (v != static_cast<int>(FP_INFINITE)) && (v != static_cast<int>(FP_NAN));
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR bool isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return isfinite BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(arg) == static_cast<int>(FP_NAN);
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR bool isnan BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return isnan BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(arg) == static_cast<int>(FP_INFINITE);
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR bool isinf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return isinf BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
return fpclassify BOOST_PREVENT_MACRO_SUBSTITUTION(arg) == static_cast<int>(FP_NORMAL);
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR bool isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return isnormal BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
// Default versions of sign manipulation functions, if individual backends can do better than this
// (for example with signed zero), then they should overload these functions further:
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR int sign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
return arg.sign();
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR int sign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return sign BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR bool signbit BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
using default_ops::eval_signbit;
return static_cast<bool>(eval_signbit(arg.backend()));
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR bool signbit BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return static_cast<bool>(signbit BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg)));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> changesign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
return -arg;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type changesign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return changesign BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
{
return (boost::multiprecision::signbit)(a) != (boost::multiprecision::signbit)(b) ? (boost::multiprecision::changesign)(a) : a;
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::detail::expression<tag, A1, A2, A3, A4>& b)
{
return copysign BOOST_PREVENT_MACRO_SUBSTITUTION(a, multiprecision::number<Backend, ExpressionTemplates>(b));
}
template <class tag, class A1, class A2, class A3, class A4, class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
{
return copysign BOOST_PREVENT_MACRO_SUBSTITUTION(multiprecision::number<Backend, ExpressionTemplates>(a), b);
}
template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type copysign BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::detail::expression<tagb, A1b, A2b, A3b, A4b>& b)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
return copysign BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(a), value_type(b));
}
//
// real and imag:
//
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename scalar_result_from_possible_complex<multiprecision::number<Backend, ExpressionTemplates> >::type
real(const multiprecision::number<Backend, ExpressionTemplates>& a)
{
using default_ops::eval_real;
using result_type = typename scalar_result_from_possible_complex<multiprecision::number<Backend, ExpressionTemplates> >::type;
boost::multiprecision::detail::scoped_default_precision<result_type> precision_guard(a);
result_type result;
eval_real(result.backend(), a.backend());
return result;
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename scalar_result_from_possible_complex<multiprecision::number<Backend, ExpressionTemplates> >::type
imag(const multiprecision::number<Backend, ExpressionTemplates>& a)
{
using default_ops::eval_imag;
using result_type = typename scalar_result_from_possible_complex<multiprecision::number<Backend, ExpressionTemplates> >::type;
boost::multiprecision::detail::scoped_default_precision<result_type> precision_guard(a);
result_type result;
eval_imag(result.backend(), a.backend());
return result;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename scalar_result_from_possible_complex<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
real(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return real(value_type(arg));
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename scalar_result_from_possible_complex<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
imag(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return imag(value_type(arg));
}
//
// Complex number functions, these are overloaded at the Backend level, we just provide the
// expression template versions here, plus overloads for non-complex types:
//
#ifdef BOOST_MP_MATH_AVAILABLE
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_complex, component_type<number<T, ExpressionTemplates>>>::type::type
abs(const number<T, ExpressionTemplates>& v)
{
return std::move(boost::math::hypot(real(v), imag(v)));
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_complex, component_type<typename detail::expression<tag, A1, A2, A3, A4>::result_type>>::type::type
abs(const detail::expression<tag, A1, A2, A3, A4>& v)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(abs(static_cast<number_type>(v)));
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_complex, typename scalar_result_from_possible_complex<number<T, ExpressionTemplates> >::type>::type
arg(const number<T, ExpressionTemplates>& v)
{
return std::move(atan2(imag(v), real(v)));
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_floating_point, typename scalar_result_from_possible_complex<number<T, ExpressionTemplates> >::type>::type
arg(const number<T, ExpressionTemplates>&)
{
return 0;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_complex || number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename scalar_result_from_possible_complex<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type>::type
arg(const detail::expression<tag, A1, A2, A3, A4>& v)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(arg(static_cast<number_type>(v)));
}
#endif // BOOST_MP_MATH_AVAILABLE
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_complex, component_type<number<T, ExpressionTemplates>>>::type::type
norm(const number<T, ExpressionTemplates>& v)
{
typename component_type<number<T, ExpressionTemplates> >::type a(real(v)), b(imag(v));
return std::move(a * a + b * b);
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value != number_kind_complex, typename scalar_result_from_possible_complex<number<T, ExpressionTemplates> >::type>::type
norm(const number<T, ExpressionTemplates>& v)
{
return v * v;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename scalar_result_from_possible_complex<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
norm(const detail::expression<tag, A1, A2, A3, A4>& v)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(norm(static_cast<number_type>(v)));
}
template <class Backend, expression_template_option ExpressionTemplates>
BOOST_MP_CXX14_CONSTEXPR typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type polar(number<Backend, ExpressionTemplates> const& r, number<Backend, ExpressionTemplates> const& theta)
{
return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(number<Backend, ExpressionTemplates>(r * cos(theta)), number<Backend, ExpressionTemplates>(r * sin(theta)));
}
template <class tag, class A1, class A2, class A3, class A4, class Backend, expression_template_option ExpressionTemplates>
BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_same<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, ExpressionTemplates> >::value,
typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type>::type
polar(detail::expression<tag, A1, A2, A3, A4> const& r, number<Backend, ExpressionTemplates> const& theta)
{
return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(number<Backend, ExpressionTemplates>(r * cos(theta)), number<Backend, ExpressionTemplates>(r * sin(theta)));
}
template <class Backend, expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_same<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, ExpressionTemplates> >::value,
typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type>::type
polar(number<Backend, ExpressionTemplates> const& r, detail::expression<tag, A1, A2, A3, A4> const& theta)
{
return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(number<Backend, ExpressionTemplates>(r * cos(theta)), number<Backend, ExpressionTemplates>(r * sin(theta)));
}
template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b>
BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_same<typename detail::expression<tag, A1, A2, A3, A4>::result_type, typename detail::expression<tagb, A1b, A2b, A3b, A4b>::result_type>::value,
typename complex_result_from_scalar<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type>::type
polar(detail::expression<tag, A1, A2, A3, A4> const& r, detail::expression<tagb, A1b, A2b, A3b, A4b> const& theta)
{
using scalar_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return typename complex_result_from_scalar<scalar_type>::type(scalar_type(r * cos(theta)), scalar_type(r * sin(theta)));
}
//
// We also allow the first argument to polar to be an arithmetic type (probably a literal):
//
template <class Scalar, class Backend, expression_template_option ExpressionTemplates>
BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_arithmetic<Scalar>::value, typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type>::type
polar(Scalar const& r, number<Backend, ExpressionTemplates> const& theta)
{
return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(number<Backend, ExpressionTemplates>(r * cos(theta)), number<Backend, ExpressionTemplates>(r * sin(theta)));
}
template <class tag, class A1, class A2, class A3, class A4, class Scalar>
BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_arithmetic<Scalar>::value,
typename complex_result_from_scalar<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type>::type
polar(Scalar const& r, detail::expression<tag, A1, A2, A3, A4> const& theta)
{
using scalar_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return typename complex_result_from_scalar<scalar_type>::type(scalar_type(r * cos(theta)), scalar_type(r * sin(theta)));
}
//
// Single argument overloads:
//
template <class Backend, expression_template_option ExpressionTemplates>
BOOST_MP_CXX14_CONSTEXPR typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type polar(number<Backend, ExpressionTemplates> const& r)
{
return typename complex_result_from_scalar<number<Backend, ExpressionTemplates> >::type(r);
}
template <class tag, class A1, class A2, class A3, class A4>
BOOST_MP_CXX14_CONSTEXPR typename complex_result_from_scalar<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
polar(detail::expression<tag, A1, A2, A3, A4> const& r)
{
return typename complex_result_from_scalar<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type(r);
}
} // namespace multiprecision
namespace math {
//
// Import Math functions here, so they can be found by Boost.Math:
//
using boost::multiprecision::changesign;
using boost::multiprecision::copysign;
using boost::multiprecision::fpclassify;
using boost::multiprecision::isfinite;
using boost::multiprecision::isinf;
using boost::multiprecision::isnan;
using boost::multiprecision::isnormal;
using boost::multiprecision::sign;
using boost::multiprecision::signbit;
#ifndef BOOST_MP_MATH_AVAILABLE
namespace policies {
template <typename... Args>
class policy {};
template <typename T1, typename T2, typename T3, typename T4, typename T5>
void raise_rounding_error(T1, T2, T3, T4, T5)
{
BOOST_MP_THROW_EXCEPTION(std::runtime_error("Rounding error"));
}
template <typename T1, typename T2, typename T3, typename T4, typename T5>
void raise_overflow_error(T1, T2, T3, T4, T5)
{
BOOST_MP_THROW_EXCEPTION(std::runtime_error("Overflow error"));
}
template <typename T1, typename T2, typename T3, typename T4, typename T5>
void raise_evaluation_error(T1, T2, T3, T4, T5)
{
BOOST_MP_THROW_EXCEPTION(std::runtime_error("Evaluation error"));
}
template <typename T, typename... Args>
struct is_policy
{
static constexpr bool value = false;
};
template <typename... Args>
struct is_policy<policy<Args...>>
{
static constexpr bool value = true;
};
} // namespace policies
#endif
} // namespace math
namespace multiprecision {
#ifdef BOOST_MP_MATH_AVAILABLE
using c99_error_policy = ::boost::math::policies::policy<
::boost::math::policies::domain_error< ::boost::math::policies::errno_on_error>,
::boost::math::policies::pole_error< ::boost::math::policies::errno_on_error>,
::boost::math::policies::overflow_error< ::boost::math::policies::errno_on_error>,
::boost::math::policies::evaluation_error< ::boost::math::policies::errno_on_error>,
::boost::math::policies::rounding_error< ::boost::math::policies::errno_on_error> >;
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value != number_kind_complex, multiprecision::number<Backend, ExpressionTemplates> >::type
asinh
BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
return boost::math::asinh(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value != number_kind_complex, typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
asinh
BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return asinh(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value != number_kind_complex, multiprecision::number<Backend, ExpressionTemplates> >::type
acosh
BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
return boost::math::acosh(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value != number_kind_complex, typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
acosh
BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return acosh(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value != number_kind_complex, multiprecision::number<Backend, ExpressionTemplates> >::type
atanh
BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
return boost::math::atanh(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::value != number_kind_complex, typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type>::type
atanh
BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return atanh(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> cbrt BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
return boost::math::cbrt(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type cbrt BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return cbrt(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> erf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
return boost::math::erf(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type erf BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return erf(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> erfc BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
return boost::math::erfc(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type erfc BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return erfc(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> expm1 BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
return boost::math::expm1(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type expm1 BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return expm1(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> lgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
multiprecision::number<Backend, ExpressionTemplates> result;
result = boost::math::lgamma(arg, c99_error_policy());
if ((boost::multiprecision::isnan)(result) && !(boost::multiprecision::isnan)(arg))
{
result = std::numeric_limits<multiprecision::number<Backend, ExpressionTemplates> >::infinity();
errno = ERANGE;
}
return result;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type lgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return lgamma(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> tgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
if ((arg == 0) && std::numeric_limits<multiprecision::number<Backend, ExpressionTemplates> >::has_infinity)
{
errno = ERANGE;
return 1 / arg;
}
return boost::math::tgamma(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type tgamma BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return tgamma(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR long lrint BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
return lround(arg);
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR long lrint BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
return lround(arg);
}
#ifndef BOOST_NO_LONG_LONG
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR long long llrint BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
return llround(arg);
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR long long llrint BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
return llround(arg);
}
#endif
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> log1p BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(arg);
return boost::math::log1p(arg, c99_error_policy());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type log1p BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& arg)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(arg);
return log1p(value_type(arg));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
return boost::math::nextafter(a, b, c99_error_policy());
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::detail::expression<tag, A1, A2, A3, A4>& b)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
return nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(a, multiprecision::number<Backend, ExpressionTemplates>(b));
}
template <class tag, class A1, class A2, class A3, class A4, class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
return nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(multiprecision::number<Backend, ExpressionTemplates>(a), b);
}
template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::detail::expression<tagb, A1b, A2b, A3b, A4b>& b)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(a, b);
return nextafter BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(a), value_type(b));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
return boost::math::nextafter(a, b, c99_error_policy());
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::number<Backend, ExpressionTemplates>& a, const multiprecision::detail::expression<tag, A1, A2, A3, A4>& b)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
return nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(a, multiprecision::number<Backend, ExpressionTemplates>(b));
}
template <class tag, class A1, class A2, class A3, class A4, class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR multiprecision::number<Backend, ExpressionTemplates> nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::number<Backend, ExpressionTemplates>& b)
{
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(a, b);
return nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(multiprecision::number<Backend, ExpressionTemplates>(a), b);
}
template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b>
inline BOOST_MP_CXX14_CONSTEXPR typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(const multiprecision::detail::expression<tag, A1, A2, A3, A4>& a, const multiprecision::detail::expression<tagb, A1b, A2b, A3b, A4b>& b)
{
using value_type = typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<value_type> precision_guard(a, b);
return nexttoward BOOST_PREVENT_MACRO_SUBSTITUTION(value_type(a), value_type(b));
}
#endif // BOOST_MP_MATH_AVAILABLE
template <class B1, class B2, class B3, expression_template_option ET1, expression_template_option ET2, expression_template_option ET3>
inline BOOST_MP_CXX14_CONSTEXPR number<B1, ET1>& add(number<B1, ET1>& result, const number<B2, ET2>& a, const number<B3, ET3>& b)
{
static_assert((std::is_convertible<B2, B1>::value), "No conversion to the target of a mixed precision addition exists");
static_assert((std::is_convertible<B3, B1>::value), "No conversion to the target of a mixed precision addition exists");
using default_ops::eval_add;
eval_add(result.backend(), a.backend(), b.backend());
return result;
}
template <class B1, class B2, class B3, expression_template_option ET1, expression_template_option ET2, expression_template_option ET3>
inline BOOST_MP_CXX14_CONSTEXPR number<B1, ET1>& subtract(number<B1, ET1>& result, const number<B2, ET2>& a, const number<B3, ET3>& b)
{
static_assert((std::is_convertible<B2, B1>::value), "No conversion to the target of a mixed precision addition exists");
static_assert((std::is_convertible<B3, B1>::value), "No conversion to the target of a mixed precision addition exists");
using default_ops::eval_subtract;
eval_subtract(result.backend(), a.backend(), b.backend());
return result;
}
template <class B1, class B2, class B3, expression_template_option ET1, expression_template_option ET2, expression_template_option ET3>
inline BOOST_MP_CXX14_CONSTEXPR number<B1, ET1>& multiply(number<B1, ET1>& result, const number<B2, ET2>& a, const number<B3, ET3>& b)
{
static_assert((std::is_convertible<B2, B1>::value), "No conversion to the target of a mixed precision addition exists");
static_assert((std::is_convertible<B3, B1>::value), "No conversion to the target of a mixed precision addition exists");
using default_ops::eval_multiply;
eval_multiply(result.backend(), a.backend(), b.backend());
return result;
}
template <class B, expression_template_option ET, class I>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<I>::value, number<B, ET>&>::type
add(number<B, ET>& result, const I& a, const I& b)
{
using default_ops::eval_add;
using canonical_type = typename detail::canonical<I, B>::type;
eval_add(result.backend(), static_cast<canonical_type>(a), static_cast<canonical_type>(b));
return result;
}
template <class B, expression_template_option ET, class I>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<I>::value, number<B, ET>&>::type
subtract(number<B, ET>& result, const I& a, const I& b)
{
using default_ops::eval_subtract;
using canonical_type = typename detail::canonical<I, B>::type;
eval_subtract(result.backend(), static_cast<canonical_type>(a), static_cast<canonical_type>(b));
return result;
}
template <class B, expression_template_option ET, class I>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<boost::multiprecision::detail::is_integral<I>::value, number<B, ET>&>::type
multiply(number<B, ET>& result, const I& a, const I& b)
{
using default_ops::eval_multiply;
using canonical_type = typename detail::canonical<I, B>::type;
eval_multiply(result.backend(), static_cast<canonical_type>(a), static_cast<canonical_type>(b));
return result;
}
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR typename detail::expression<tag, A1, A2, A3, A4>::result_type trunc(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(trunc(number_type(v), pol));
}
template <class Backend, expression_template_option ExpressionTemplates, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR number<Backend, ExpressionTemplates> trunc(const number<Backend, ExpressionTemplates>& v, const Policy&)
{
using default_ops::eval_trunc;
detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(v);
number<Backend, ExpressionTemplates> result;
eval_trunc(result.backend(), v.backend());
return result;
}
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR int itrunc(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
number_type r(trunc(v, pol));
if ((r > (std::numeric_limits<int>::max)()) || r < (std::numeric_limits<int>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", nullptr, number_type(v), 0, pol);
return r.template convert_to<int>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR int itrunc(const detail::expression<tag, A1, A2, A3, A4>& v)
{
return itrunc(v, boost::math::policies::policy<>());
}
template <class Backend, expression_template_option ExpressionTemplates, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR int itrunc(const number<Backend, ExpressionTemplates>& v, const Policy& pol)
{
number<Backend, ExpressionTemplates> r(trunc(v, pol));
if ((r > (std::numeric_limits<int>::max)()) || r < (std::numeric_limits<int>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::itrunc<%1%>(%1%)", nullptr, v, 0, pol);
return r.template convert_to<int>();
}
template <class Backend, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR int itrunc(const number<Backend, ExpressionTemplates>& v)
{
return itrunc(v, boost::math::policies::policy<>());
}
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR long ltrunc(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
number_type r(trunc(v, pol));
if ((r > (std::numeric_limits<long>::max)()) || r < (std::numeric_limits<long>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", nullptr, number_type(v), 0L, pol);
return r.template convert_to<long>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR long ltrunc(const detail::expression<tag, A1, A2, A3, A4>& v)
{
return ltrunc(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR long ltrunc(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
number<T, ExpressionTemplates> r(trunc(v, pol));
if ((r > (std::numeric_limits<long>::max)()) || r < (std::numeric_limits<long>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::ltrunc<%1%>(%1%)", nullptr, v, 0L, pol);
return r.template convert_to<long>();
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR long ltrunc(const number<T, ExpressionTemplates>& v)
{
return ltrunc(v, boost::math::policies::policy<>());
}
#ifndef BOOST_NO_LONG_LONG
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR long long lltrunc(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
number_type r(trunc(v, pol));
if ((r > (std::numeric_limits<long long>::max)()) || r < (std::numeric_limits<long long>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", nullptr, number_type(v), 0LL, pol);
return r.template convert_to<long long>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR long long lltrunc(const detail::expression<tag, A1, A2, A3, A4>& v)
{
return lltrunc(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR long long lltrunc(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
number<T, ExpressionTemplates> r(trunc(v, pol));
if ((r > (std::numeric_limits<long long>::max)()) || r < (std::numeric_limits<long long>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::lltrunc<%1%>(%1%)", nullptr, v, 0LL, pol);
return r.template convert_to<long long>();
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR long long lltrunc(const number<T, ExpressionTemplates>& v)
{
return lltrunc(v, boost::math::policies::policy<>());
}
#endif
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR typename detail::expression<tag, A1, A2, A3, A4>::result_type round(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(round(static_cast<number_type>(v), pol));
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR number<T, ExpressionTemplates> round(const number<T, ExpressionTemplates>& v, const Policy&)
{
using default_ops::eval_round;
detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
number<T, ExpressionTemplates> result;
eval_round(result.backend(), v.backend());
return result;
}
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR int iround(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
number_type r(round(v, pol));
if ((r > (std::numeric_limits<int>::max)()) || r < (std::numeric_limits<int>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", nullptr, number_type(v), 0, pol);
return r.template convert_to<int>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR int iround(const detail::expression<tag, A1, A2, A3, A4>& v)
{
return iround(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR int iround(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
number<T, ExpressionTemplates> r(round(v, pol));
if ((r > (std::numeric_limits<int>::max)()) || r < (std::numeric_limits<int>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", nullptr, v, 0, pol);
return r.template convert_to<int>();
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR int iround(const number<T, ExpressionTemplates>& v)
{
return iround(v, boost::math::policies::policy<>());
}
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR long lround(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
number_type r(round(v, pol));
if ((r > (std::numeric_limits<long>::max)()) || r < (std::numeric_limits<long>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", nullptr, number_type(v), 0L, pol);
return r.template convert_to<long>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR long lround(const detail::expression<tag, A1, A2, A3, A4>& v)
{
return lround(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR long lround(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
number<T, ExpressionTemplates> r(round(v, pol));
if ((r > (std::numeric_limits<long>::max)()) || r < (std::numeric_limits<long>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::lround<%1%>(%1%)", nullptr, v, 0L, pol);
return r.template convert_to<long>();
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR long lround(const number<T, ExpressionTemplates>& v)
{
return lround(v, boost::math::policies::policy<>());
}
#ifndef BOOST_NO_LONG_LONG
template <class tag, class A1, class A2, class A3, class A4, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR long long llround(const detail::expression<tag, A1, A2, A3, A4>& v, const Policy& pol)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
number_type r(round(v, pol));
if ((r > (std::numeric_limits<long long>::max)()) || r < (std::numeric_limits<long long>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", nullptr, number_type(v), 0LL, pol);
return r.template convert_to<long long>();
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR long long llround(const detail::expression<tag, A1, A2, A3, A4>& v)
{
return llround(v, boost::math::policies::policy<>());
}
template <class T, expression_template_option ExpressionTemplates, class Policy>
inline BOOST_MP_CXX14_CONSTEXPR long long llround(const number<T, ExpressionTemplates>& v, const Policy& pol)
{
number<T, ExpressionTemplates> r(round(v, pol));
if ((r > (std::numeric_limits<long long>::max)()) || r < (std::numeric_limits<long long>::min)() || !BOOST_MP_ISFINITE(v))
return boost::math::policies::raise_rounding_error("boost::multiprecision::iround<%1%>(%1%)", nullptr, v, 0LL, pol);
return r.template convert_to<long long>();
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR long long llround(const number<T, ExpressionTemplates>& v)
{
return llround(v, boost::math::policies::policy<>());
}
#endif
//
// frexp does not return an expression template since we require the
// integer argument to be evaluated even if the returned value is
// not assigned to anything...
//
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type frexp(const number<T, ExpressionTemplates>& v, short* pint)
{
using default_ops::eval_frexp;
detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
number<T, ExpressionTemplates> result;
eval_frexp(result.backend(), v.backend(), pint);
return result;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
frexp(const detail::expression<tag, A1, A2, A3, A4>& v, short* pint)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(frexp(static_cast<number_type>(v), pint));
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type frexp(const number<T, ExpressionTemplates>& v, int* pint)
{
using default_ops::eval_frexp;
detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
number<T, ExpressionTemplates> result;
eval_frexp(result.backend(), v.backend(), pint);
return result;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
frexp(const detail::expression<tag, A1, A2, A3, A4>& v, int* pint)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(frexp(static_cast<number_type>(v), pint));
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type frexp(const number<T, ExpressionTemplates>& v, long* pint)
{
using default_ops::eval_frexp;
detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
number<T, ExpressionTemplates> result;
eval_frexp(result.backend(), v.backend(), pint);
return result;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
frexp(const detail::expression<tag, A1, A2, A3, A4>& v, long* pint)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(frexp(static_cast<number_type>(v), pint));
}
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type frexp(const number<T, ExpressionTemplates>& v, long long* pint)
{
using default_ops::eval_frexp;
detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
number<T, ExpressionTemplates> result;
eval_frexp(result.backend(), v.backend(), pint);
return result;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_floating_point, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
frexp(const detail::expression<tag, A1, A2, A3, A4>& v, long long* pint)
{
using number_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
return std::move(frexp(static_cast<number_type>(v), pint));
}
//
// modf does not return an expression template since we require the
// second argument to be evaluated even if the returned value is
// not assigned to anything...
//
template <class T, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type modf(const number<T, ExpressionTemplates>& v, number<T, ExpressionTemplates>* pipart)
{
using default_ops::eval_modf;
detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
number<T, ExpressionTemplates> result;
eval_modf(result.backend(), v.backend(), pipart ? &pipart->backend() : nullptr);
return result;
}
template <class T, expression_template_option ExpressionTemplates, class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<T>::value == number_kind_floating_point, number<T, ExpressionTemplates> >::type modf(const detail::expression<tag, A1, A2, A3, A4>& v, number<T, ExpressionTemplates>* pipart)
{
using default_ops::eval_modf;
detail::scoped_default_precision<multiprecision::number<T, ExpressionTemplates> > precision_guard(v);
number<T, ExpressionTemplates> result, arg(v);
eval_modf(result.backend(), arg.backend(), pipart ? &pipart->backend() : nullptr);
return result;
}
//
// Integer square root:
//
template <class B, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<B>::value == number_kind_integer, number<B, ExpressionTemplates> >::type
sqrt(const number<B, ExpressionTemplates>& x)
{
using default_ops::eval_integer_sqrt;
number<B, ExpressionTemplates> s, r;
eval_integer_sqrt(s.backend(), r.backend(), x.backend());
return s;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value == number_kind_integer, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::type
sqrt(const detail::expression<tag, A1, A2, A3, A4>& arg)
{
using default_ops::eval_integer_sqrt;
using result_type = typename detail::expression<tag, A1, A2, A3, A4>::result_type;
detail::scoped_default_precision<result_type> precision_guard(arg);
result_type result, v(arg), r;
eval_integer_sqrt(result.backend(), r.backend(), v.backend());
return result;
}
//
// fma:
//
namespace default_ops {
struct fma_func
{
template <class B, class T, class U, class V>
BOOST_MP_CXX14_CONSTEXPR void operator()(B& result, const T& a, const U& b, const V& c) const
{
eval_multiply_add(result, a, b, c);
}
};
} // namespace default_ops
template <class Backend, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<number<Backend, et_on> >::value == number_kind_floating_point) &&
(is_number<U>::value || is_number_expression<U>::value || boost::multiprecision::detail::is_arithmetic<U>::value) &&
(is_number<V>::value || is_number_expression<V>::value || boost::multiprecision::detail::is_arithmetic<V>::value),
detail::expression<detail::function, default_ops::fma_func, number<Backend, et_on>, U, V> >::type
fma(const number<Backend, et_on>& a, const U& b, const V& c)
{
return detail::expression<detail::function, default_ops::fma_func, number<Backend, et_on>, U, V>(
default_ops::fma_func(), a, b, c);
}
template <class tag, class Arg1, class Arg2, class Arg3, class Arg4, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type>::value == number_kind_floating_point) &&
(is_number<U>::value || is_number_expression<U>::value || boost::multiprecision::detail::is_arithmetic<U>::value) &&
(is_number<V>::value || is_number_expression<V>::value || boost::multiprecision::detail::is_arithmetic<V>::value),
detail::expression<detail::function, default_ops::fma_func, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, U, V> >::type
fma(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& a, const U& b, const V& c)
{
return detail::expression<detail::function, default_ops::fma_func, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, U, V>(
default_ops::fma_func(), a, b, c);
}
template <class Backend, class U, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<number<Backend, et_off> >::value == number_kind_floating_point) &&
(is_number<U>::value || is_number_expression<U>::value || boost::multiprecision::detail::is_arithmetic<U>::value) &&
(is_number<V>::value || is_number_expression<V>::value || boost::multiprecision::detail::is_arithmetic<V>::value),
number<Backend, et_off> >::type
fma(const number<Backend, et_off>& a, const U& b, const V& c)
{
using default_ops::eval_multiply_add;
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b, c);
number<Backend, et_off> result;
eval_multiply_add(result.backend(), number<Backend, et_off>::canonical_value(a), number<Backend, et_off>::canonical_value(b), number<Backend, et_off>::canonical_value(c));
return result;
}
template <class U, class Backend, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<number<Backend, et_on> >::value == number_kind_floating_point) &&
boost::multiprecision::detail::is_arithmetic<U>::value &&
(is_number<V>::value || is_number_expression<V>::value || boost::multiprecision::detail::is_arithmetic<V>::value),
detail::expression<detail::function, default_ops::fma_func, U, number<Backend, et_on>, V> >::type
fma(const U& a, const number<Backend, et_on>& b, const V& c)
{
return detail::expression<detail::function, default_ops::fma_func, U, number<Backend, et_on>, V>(
default_ops::fma_func(), a, b, c);
}
template <class U, class tag, class Arg1, class Arg2, class Arg3, class Arg4, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type>::value == number_kind_floating_point) &&
boost::multiprecision::detail::is_arithmetic<U>::value &&
(is_number<V>::value || is_number_expression<V>::value || boost::multiprecision::detail::is_arithmetic<V>::value),
detail::expression<detail::function, default_ops::fma_func, U, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, V> >::type
fma(const U& a, const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& b, const V& c)
{
return detail::expression<detail::function, default_ops::fma_func, U, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, V>(
default_ops::fma_func(), a, b, c);
}
template <class U, class Backend, class V>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<number<Backend, et_off> >::value == number_kind_floating_point) &&
boost::multiprecision::detail::is_arithmetic<U>::value &&
(is_number<V>::value || is_number_expression<V>::value || boost::multiprecision::detail::is_arithmetic<V>::value),
number<Backend, et_off> >::type
fma(const U& a, const number<Backend, et_off>& b, const V& c)
{
using default_ops::eval_multiply_add;
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b, c);
number<Backend, et_off> result;
eval_multiply_add(result.backend(), number<Backend, et_off>::canonical_value(a), number<Backend, et_off>::canonical_value(b), number<Backend, et_off>::canonical_value(c));
return result;
}
template <class U, class V, class Backend>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<number<Backend, et_on> >::value == number_kind_floating_point) &&
boost::multiprecision::detail::is_arithmetic<U>::value &&
boost::multiprecision::detail::is_arithmetic<V>::value,
detail::expression<detail::function, default_ops::fma_func, U, V, number<Backend, et_on> > >::type
fma(const U& a, const V& b, const number<Backend, et_on>& c)
{
return detail::expression<detail::function, default_ops::fma_func, U, V, number<Backend, et_on> >(
default_ops::fma_func(), a, b, c);
}
template <class U, class V, class tag, class Arg1, class Arg2, class Arg3, class Arg4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type>::value == number_kind_floating_point) &&
boost::multiprecision::detail::is_arithmetic<U>::value &&
boost::multiprecision::detail::is_arithmetic<V>::value,
detail::expression<detail::function, default_ops::fma_func, U, V, detail::expression<tag, Arg1, Arg2, Arg3, Arg4> > >::type
fma(const U& a, const V& b, const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& c)
{
return detail::expression<detail::function, default_ops::fma_func, U, V, detail::expression<tag, Arg1, Arg2, Arg3, Arg4> >(
default_ops::fma_func(), a, b, c);
}
template <class U, class V, class Backend>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<number<Backend, et_off> >::value == number_kind_floating_point) &&
boost::multiprecision::detail::is_arithmetic<U>::value &&
boost::multiprecision::detail::is_arithmetic<V>::value,
number<Backend, et_off> >::type
fma(const U& a, const V& b, const number<Backend, et_off>& c)
{
using default_ops::eval_multiply_add;
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b, c);
number<Backend, et_off> result;
eval_multiply_add(result.backend(), number<Backend, et_off>::canonical_value(a), number<Backend, et_off>::canonical_value(b), number<Backend, et_off>::canonical_value(c));
return result;
}
namespace default_ops {
struct remquo_func
{
template <class B, class T, class U>
BOOST_MP_CXX14_CONSTEXPR void operator()(B& result, const T& a, const U& b, int* pi) const
{
eval_remquo(result, a, b, pi);
}
};
} // namespace default_ops
template <class Backend, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
number_category<number<Backend, et_on> >::value == number_kind_floating_point,
detail::expression<detail::function, default_ops::remquo_func, number<Backend, et_on>, U, int*> >::type
remquo(const number<Backend, et_on>& a, const U& b, int* pi)
{
return detail::expression<detail::function, default_ops::remquo_func, number<Backend, et_on>, U, int*>(
default_ops::remquo_func(), a, b, pi);
}
template <class tag, class Arg1, class Arg2, class Arg3, class Arg4, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type>::value == number_kind_floating_point,
detail::expression<detail::function, default_ops::remquo_func, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, U, int*> >::type
remquo(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& a, const U& b, int* pi)
{
return detail::expression<detail::function, default_ops::remquo_func, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, U, int*>(
default_ops::remquo_func(), a, b, pi);
}
template <class U, class Backend>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<number<Backend, et_on> >::value == number_kind_floating_point) && !is_number<U>::value && !is_number_expression<U>::value,
detail::expression<detail::function, default_ops::remquo_func, U, number<Backend, et_on>, int*> >::type
remquo(const U& a, const number<Backend, et_on>& b, int* pi)
{
return detail::expression<detail::function, default_ops::remquo_func, U, number<Backend, et_on>, int*>(
default_ops::remquo_func(), a, b, pi);
}
template <class U, class tag, class Arg1, class Arg2, class Arg3, class Arg4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<typename detail::expression<tag, Arg1, Arg2, Arg3, Arg4>::result_type>::value == number_kind_floating_point) && !is_number<U>::value && !is_number_expression<U>::value,
detail::expression<detail::function, default_ops::remquo_func, U, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, int*> >::type
remquo(const U& a, const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& b, int* pi)
{
return detail::expression<detail::function, default_ops::remquo_func, U, detail::expression<tag, Arg1, Arg2, Arg3, Arg4>, int*>(
default_ops::remquo_func(), a, b, pi);
}
template <class Backend, class U>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
number_category<number<Backend, et_on> >::value == number_kind_floating_point,
number<Backend, et_off> >::type
remquo(const number<Backend, et_off>& a, const U& b, int* pi)
{
using default_ops::eval_remquo;
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b);
number<Backend, et_off> result;
eval_remquo(result.backend(), a.backend(), number<Backend, et_off>::canonical_value(b), pi);
return result;
}
template <class U, class Backend>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<
(number_category<number<Backend, et_on> >::value == number_kind_floating_point) && !is_number<U>::value && !is_number_expression<U>::value,
number<Backend, et_off> >::type
remquo(const U& a, const number<Backend, et_off>& b, int* pi)
{
using default_ops::eval_remquo;
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(a, b);
number<Backend, et_off> result;
eval_remquo(result.backend(), number<Backend, et_off>::canonical_value(a), b.backend(), pi);
return result;
}
template <class B, expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<B>::value == number_kind_integer, number<B, ExpressionTemplates> >::type
sqrt(const number<B, ExpressionTemplates>& x, number<B, ExpressionTemplates>& r)
{
using default_ops::eval_integer_sqrt;
detail::scoped_default_precision<multiprecision::number<B, ExpressionTemplates> > precision_guard(x, r);
number<B, ExpressionTemplates> s;
eval_integer_sqrt(s.backend(), r.backend(), x.backend());
return s;
}
template <class B, expression_template_option ExpressionTemplates, class tag, class Arg1, class Arg2, class Arg3, class Arg4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<B>::value == number_kind_integer, number<B, ExpressionTemplates> >::type
sqrt(const detail::expression<tag, Arg1, Arg2, Arg3, Arg4>& arg, number<B, ExpressionTemplates>& r)
{
using default_ops::eval_integer_sqrt;
detail::scoped_default_precision<multiprecision::number<B, ExpressionTemplates> > precision_guard(r);
number<B, ExpressionTemplates> s;
number<B, ExpressionTemplates> x(arg);
eval_integer_sqrt(s.backend(), r.backend(), x.backend());
return s;
}
// clang-format off
//
// Regrettably, when the argument to a function is an rvalue we must return by value, and not return an
// expression template, otherwise we can end up with dangling references.
// See https://github.com/boostorg/multiprecision/issues/175.
//
#define UNARY_OP_FUNCTOR_CXX11_RVALUE(func, category)\
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value == category, number<Backend, et_on> > ::type \
func(number<Backend, et_on>&& arg) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_on> > precision_guard(arg); \
number<Backend, et_on> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func)(result.backend(), arg.backend()); \
return result; \
} \
#define BINARY_OP_FUNCTOR_CXX11_RVALUE(func, category)\
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value == category, number<Backend, et_on> >::type func(number<Backend, et_on>&& arg, const number<Backend, et_on>& a) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_on> > precision_guard(arg, a); \
number<Backend, et_on> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func)(result.backend(), arg.backend(), a.backend()); \
return result; \
} \
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value == category, number<Backend, et_on> >::type func(const number<Backend, et_on>& arg, number<Backend, et_on>&& a) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_on> > precision_guard(arg, a); \
number<Backend, et_on> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func)(result.backend(), arg.backend(), a.backend()); \
return result; \
} \
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value == category, number<Backend, et_on> >::type func(number<Backend, et_on>&& arg, number<Backend, et_on>&& a) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_on> > precision_guard(arg, a); \
number<Backend, et_on> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func)(result.backend(), arg.backend(), a.backend()); \
return result; \
} \
template <class Backend, class tag, class A1, class A2, class A3, class A4> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<(number_category<Backend>::value == category) && (std::is_convertible<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, et_on> >::value), \
number<Backend, et_on> > ::type \
func(number<Backend, et_on>&& arg, const detail::expression<tag, A1, A2, A3, A4>& a) \
{ \
return detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
number<Backend, et_on>, detail::expression<tag, A1, A2, A3, A4> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>(), arg, a); \
} \
template <class tag, class A1, class A2, class A3, class A4, class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<(number_category<Backend>::value == category) && (std::is_convertible<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, et_on> >::value), \
number<Backend, et_on> > ::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, number<Backend, et_on>&& a) \
{ \
return detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
detail::expression<tag, A1, A2, A3, A4>, number<Backend, et_on> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>(), arg, a); \
} \
template <class Backend, class Arithmetic> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
is_compatible_arithmetic_type<Arithmetic, number<Backend, et_on> >::value && (number_category<Backend>::value == category), \
number<Backend, et_on> >::type \
func(number<Backend, et_on>&& arg, const Arithmetic& a) \
{ \
return detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>, \
number<Backend, et_on>, Arithmetic > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>(), arg, a); \
} \
template <class Backend, class Arithmetic> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
is_compatible_arithmetic_type<Arithmetic, number<Backend, et_on> >::value && (number_category<Backend>::value == category), \
number<Backend, et_on> > ::type \
func(const Arithmetic& arg, number<Backend, et_on>&& a) \
{ \
return detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
Arithmetic, number<Backend, et_on> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend > (), arg, a); \
} \
#define UNARY_OP_FUNCTOR(func, category) \
namespace detail { \
template <class Backend> \
struct BOOST_JOIN(category, BOOST_JOIN(func, _funct)) \
{ \
BOOST_MP_CXX14_CONSTEXPR void operator()(Backend& result, const Backend& arg) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func) \
(result, arg); \
} \
template <class U> \
BOOST_MP_CXX14_CONSTEXPR void operator()(U& result, const Backend& arg) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
Backend temp; \
BOOST_JOIN(eval_, func) \
(temp, arg); \
result = std::move(temp); \
} \
}; \
} \
\
template <class tag, class A1, class A2, class A3, class A4> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category, \
detail::expression<detail::function, \
detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
detail::expression<tag, A1, A2, A3, A4> > > ::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg) \
{ \
return detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
detail::expression<tag, A1, A2, A3, A4> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type > (), arg); \
} \
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value == category, \
detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, number<Backend, et_on> > > ::type \
func(const number<Backend, et_on>& arg) \
{ \
return detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
number<Backend, et_on> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend > (), arg); \
} \
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
boost::multiprecision::number_category<Backend>::value == category, \
number<Backend, et_off> >::type \
func(const number<Backend, et_off>& arg) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg); \
number<Backend, et_off> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func)(result.backend(), arg.backend()); \
return result; \
}\
UNARY_OP_FUNCTOR_CXX11_RVALUE(func, category)\
#define BINARY_OP_FUNCTOR(func, category) \
namespace detail { \
template <class Backend> \
struct BOOST_JOIN(category, BOOST_JOIN(func, _funct)) \
{ \
BOOST_MP_CXX14_CONSTEXPR void operator()(Backend& result, const Backend& arg, const Backend& a) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func) \
(result, arg, a); \
} \
template <class Arithmetic> \
BOOST_MP_CXX14_CONSTEXPR void operator()(Backend& result, const Backend& arg, const Arithmetic& a) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func) \
(result, arg, number<Backend>::canonical_value(a)); \
} \
template <class Arithmetic> \
BOOST_MP_CXX14_CONSTEXPR void operator()(Backend& result, const Arithmetic& arg, const Backend& a) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func) \
(result, number<Backend>::canonical_value(arg), a); \
} \
template <class U> \
BOOST_MP_CXX14_CONSTEXPR void operator()(U& result, const Backend& arg, const Backend& a) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
Backend r; \
BOOST_JOIN(eval_, func) \
(r, arg, a); \
result = std::move(r); \
} \
template <class U, class Arithmetic> \
BOOST_MP_CXX14_CONSTEXPR void operator()(U& result, const Backend& arg, const Arithmetic& a) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
Backend r; \
BOOST_JOIN(eval_, func) \
(r, arg, number<Backend>::canonical_value(a)); \
result = std::move(r); \
} \
template <class U, class Arithmetic> \
BOOST_MP_CXX14_CONSTEXPR void operator()(U& result, const Arithmetic& arg, const Backend& a) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
Backend r; \
BOOST_JOIN(eval_, func) \
(r, number<Backend>::canonical_value(arg), a); \
result = std::move(r); \
} \
}; \
} \
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value == category, detail::expression<detail::function, \
detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>, number<Backend, et_on>, number<Backend, et_on> > > ::type \
func(const number<Backend, et_on>& arg, const number<Backend, et_on>& a) \
{ \
return detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
number<Backend, et_on>, number<Backend, et_on> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>(), arg, a); \
} \
template <class Backend, class tag, class A1, class A2, class A3, class A4> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<(number_category<Backend>::value == category) && (std::is_convertible<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, et_on> >::value), \
detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>, number<Backend, et_on>, detail::expression<tag, A1, A2, A3, A4> > > ::type \
func(const number<Backend, et_on>& arg, const detail::expression<tag, A1, A2, A3, A4>& a) \
{ \
return detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
number<Backend, et_on>, detail::expression<tag, A1, A2, A3, A4> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>(), arg, a); \
} \
template <class tag, class A1, class A2, class A3, class A4, class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<(number_category<Backend>::value == category) && (std::is_convertible<typename detail::expression<tag, A1, A2, A3, A4>::result_type, number<Backend, et_on> >::value), \
detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>, detail::expression<tag, A1, A2, A3, A4>, number<Backend, et_on> > > ::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, const number<Backend, et_on>& a) \
{ \
return detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
detail::expression<tag, A1, A2, A3, A4>, number<Backend, et_on> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>(), arg, a); \
} \
template <class tag, class A1, class A2, class A3, class A4, class tagb, class A1b, class A2b, class A3b, class A4b> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<(number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category) && (number_category<detail::expression<tagb, A1b, A2b, A3b, A4b> >::value == category), \
detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
detail::expression<tag, A1, A2, A3, A4>, detail::expression<tagb, A1b, A2b, A3b, A4b> > > ::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, const detail::expression<tagb, A1b, A2b, A3b, A4b>& a) \
{ \
return detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
detail::expression<tag, A1, A2, A3, A4>, detail::expression<tagb, A1b, A2b, A3b, A4b> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>(), arg, a); \
} \
template <class Backend, class Arithmetic> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
is_compatible_arithmetic_type<Arithmetic, number<Backend, et_on> >::value && (number_category<Backend>::value == category), \
detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
number<Backend, et_on>, Arithmetic> > ::type \
func(const number<Backend, et_on>& arg, const Arithmetic& a) \
{ \
return detail::expression<detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>, \
number<Backend, et_on>, Arithmetic > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct))<Backend>(), arg, a); \
} \
template <class tag, class A1, class A2, class A3, class A4, class Arithmetic> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
is_compatible_arithmetic_type<Arithmetic, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value && (number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category), \
detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
detail::expression<tag, A1, A2, A3, A4>, Arithmetic> > ::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, const Arithmetic& a) \
{ \
return detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
detail::expression<tag, A1, A2, A3, A4>, Arithmetic > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type > (), arg, a); \
} \
template <class Backend, class Arithmetic> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
is_compatible_arithmetic_type<Arithmetic, number<Backend, et_on> >::value && (number_category<Backend>::value == category), \
detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
Arithmetic, number<Backend, et_on> > > ::type \
func(const Arithmetic& arg, const number<Backend, et_on>& a) \
{ \
return detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
Arithmetic, number<Backend, et_on> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend > (), arg, a); \
} \
template <class tag, class A1, class A2, class A3, class A4, class Arithmetic> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
is_compatible_arithmetic_type<Arithmetic, typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value && (number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category), \
detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
Arithmetic, detail::expression<tag, A1, A2, A3, A4> > > ::type \
func(const Arithmetic& arg, const detail::expression<tag, A1, A2, A3, A4>& a) \
{ \
return detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
Arithmetic, detail::expression<tag, A1, A2, A3, A4> > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type > (), arg, a); \
} \
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<(number_category<Backend>::value == category), number<Backend, et_off> >::type \
func(const number<Backend, et_off>& arg, const number<Backend, et_off>& a) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg, a); \
number<Backend, et_off> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func)(result.backend(), arg.backend(), a.backend()); \
return result; \
} \
template <class Backend, class Arithmetic> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
is_compatible_arithmetic_type<Arithmetic, number<Backend, et_off> >::value && (number_category<Backend>::value == category), \
number<Backend, et_off> >::type \
func(const number<Backend, et_off>& arg, const Arithmetic& a) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg); \
number<Backend, et_off> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func) \
(result.backend(), arg.backend(), number<Backend, et_off>::canonical_value(a)); \
return result; \
} \
template <class Backend, class Arithmetic> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
is_compatible_arithmetic_type<Arithmetic, number<Backend, et_off> >::value && (number_category<Backend>::value == category), \
number<Backend, et_off> >::type \
func(const Arithmetic& a, const number<Backend, et_off>& arg) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg); \
number<Backend, et_off> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func) \
(result.backend(), number<Backend, et_off>::canonical_value(a), arg.backend()); \
return result; \
}\
BINARY_OP_FUNCTOR_CXX11_RVALUE(func, category)
#define HETERO_BINARY_OP_FUNCTOR_B(func, Arg2, category) \
template <class tag, class A1, class A2, class A3, class A4> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
(number_category<detail::expression<tag, A1, A2, A3, A4> >::value == category), \
detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
detail::expression<tag, A1, A2, A3, A4>, Arg2> > ::type \
func(const detail::expression<tag, A1, A2, A3, A4>& arg, Arg2 const& a) \
{ \
return detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, \
detail::expression<tag, A1, A2, A3, A4>, Arg2 > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type > (), arg, a); \
} \
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
(number_category<Backend>::value == category), \
detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
number<Backend, et_on>, Arg2> > ::type \
func(const number<Backend, et_on>& arg, Arg2 const& a) \
{ \
return detail::expression< \
detail::function, detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend>, \
number<Backend, et_on>, Arg2 > (detail::BOOST_JOIN(category, BOOST_JOIN(func, _funct)) < Backend > (), arg, a); \
} \
template <class Backend> \
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if< \
(number_category<Backend>::value == category), \
number<Backend, et_off> >::type \
func(const number<Backend, et_off>& arg, Arg2 const& a) \
{ \
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg, a); \
number<Backend, et_off> result; \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func) \
(result.backend(), arg.backend(), a); \
return result; \
}
#define HETERO_BINARY_OP_FUNCTOR(func, Arg2, category) \
namespace detail { \
template <class Backend> \
struct BOOST_JOIN(category, BOOST_JOIN(func, _funct)) \
{ \
template <class Arg> \
BOOST_MP_CXX14_CONSTEXPR void operator()(Backend& result, Backend const& arg, Arg a) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
BOOST_JOIN(eval_, func) \
(result, arg, a); \
} \
template <class U, class Arg> \
BOOST_MP_CXX14_CONSTEXPR void operator()(U& result, Backend const& arg, Arg a) const \
{ \
using default_ops::BOOST_JOIN(eval_, func); \
Backend temp; \
BOOST_JOIN(eval_, func) \
(temp, arg, a); \
result = std::move(temp); \
} \
}; \
} \
\
HETERO_BINARY_OP_FUNCTOR_B(func, Arg2, category)
// clang-format on
namespace detail {
template <class Backend>
struct abs_funct
{
BOOST_MP_CXX14_CONSTEXPR void operator()(Backend& result, const Backend& arg) const
{
using default_ops::eval_abs;
eval_abs(result, arg);
}
};
template <class Backend>
struct conj_funct
{
BOOST_MP_CXX14_CONSTEXPR void operator()(Backend& result, const Backend& arg) const
{
using default_ops::eval_conj;
eval_conj(result, arg);
}
//
// To allow for mixed complex/scalar arithmetic where conj is called on the scalar type (as in Eigen)
// we provide an overload that will promote the arg to the distination type:
//
template <class Other>
BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<std::is_constructible<Other, Backend>::value>::type operator()(Other& result, const Backend& arg) const
{
using default_ops::eval_conj;
Other t(arg);
eval_conj(result, t);
}
};
template <class Backend>
struct proj_funct
{
BOOST_MP_CXX14_CONSTEXPR void operator()(Backend& result, const Backend& arg) const
{
using default_ops::eval_proj;
eval_proj(result, arg);
}
};
} // namespace detail
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<typename detail::expression<tag, A1, A2, A3, A4>::result_type>::value != number_kind_complex,
detail::expression<
detail::function, detail::abs_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, detail::expression<tag, A1, A2, A3, A4> > >::type
abs(const detail::expression<tag, A1, A2, A3, A4>& arg)
{
return detail::expression<
detail::function, detail::abs_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, detail::expression<tag, A1, A2, A3, A4> >(
detail::abs_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>(), arg);
}
template <class Backend>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value != number_kind_complex,
detail::expression<
detail::function, detail::abs_funct<Backend>, number<Backend, et_on> > >::type
abs(const number<Backend, et_on>& arg)
{
return detail::expression<
detail::function, detail::abs_funct<Backend>, number<Backend, et_on> >(
detail::abs_funct<Backend>(), arg);
}
template <class Backend>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value != number_kind_complex, number<Backend, et_off> >::type
abs(const number<Backend, et_off>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);
number<Backend, et_off> result;
using default_ops::eval_abs;
eval_abs(result.backend(), arg.backend());
return result;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR detail::expression<
detail::function, detail::conj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, detail::expression<tag, A1, A2, A3, A4> >
conj(const detail::expression<tag, A1, A2, A3, A4>& arg)
{
return detail::expression<
detail::function, detail::conj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, detail::expression<tag, A1, A2, A3, A4> >(
detail::conj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>(), arg);
}
template <class Backend>
inline BOOST_MP_CXX14_CONSTEXPR detail::expression<
detail::function, detail::conj_funct<Backend>, number<Backend, et_on> >
conj(const number<Backend, et_on>& arg)
{
return detail::expression<
detail::function, detail::conj_funct<Backend>, number<Backend, et_on> >(
detail::conj_funct<Backend>(), arg);
}
template <class Backend>
inline BOOST_MP_CXX14_CONSTEXPR number<Backend, et_off>
conj(const number<Backend, et_off>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);
number<Backend, et_off> result;
using default_ops::eval_conj;
eval_conj(result.backend(), arg.backend());
return result;
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR detail::expression<
detail::function, detail::proj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, detail::expression<tag, A1, A2, A3, A4> >
proj(const detail::expression<tag, A1, A2, A3, A4>& arg)
{
return detail::expression<
detail::function, detail::proj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>, detail::expression<tag, A1, A2, A3, A4> >(
detail::proj_funct<typename detail::backend_type<detail::expression<tag, A1, A2, A3, A4> >::type>(), arg);
}
template <class Backend>
inline BOOST_MP_CXX14_CONSTEXPR detail::expression<
detail::function, detail::proj_funct<Backend>, number<Backend, et_on> >
proj(const number<Backend, et_on>& arg)
{
return detail::expression<
detail::function, detail::proj_funct<Backend>, number<Backend, et_on> >(
detail::proj_funct<Backend>(), arg);
}
template <class Backend>
inline BOOST_MP_CXX14_CONSTEXPR number<Backend, et_off>
proj(const number<Backend, et_off>& arg)
{
detail::scoped_default_precision<multiprecision::number<Backend, et_off> > precision_guard(arg);
number<Backend, et_off> result;
using default_ops::eval_proj;
eval_proj(result.backend(), arg.backend());
return result;
}
UNARY_OP_FUNCTOR(fabs, number_kind_floating_point)
UNARY_OP_FUNCTOR(sqrt, number_kind_floating_point)
UNARY_OP_FUNCTOR(floor, number_kind_floating_point)
UNARY_OP_FUNCTOR(ceil, number_kind_floating_point)
UNARY_OP_FUNCTOR(trunc, number_kind_floating_point)
UNARY_OP_FUNCTOR(round, number_kind_floating_point)
UNARY_OP_FUNCTOR(exp, number_kind_floating_point)
UNARY_OP_FUNCTOR(exp2, number_kind_floating_point)
UNARY_OP_FUNCTOR(log, number_kind_floating_point)
UNARY_OP_FUNCTOR(log10, number_kind_floating_point)
UNARY_OP_FUNCTOR(cos, number_kind_floating_point)
UNARY_OP_FUNCTOR(sin, number_kind_floating_point)
UNARY_OP_FUNCTOR(tan, number_kind_floating_point)
UNARY_OP_FUNCTOR(asin, number_kind_floating_point)
UNARY_OP_FUNCTOR(acos, number_kind_floating_point)
UNARY_OP_FUNCTOR(atan, number_kind_floating_point)
UNARY_OP_FUNCTOR(cosh, number_kind_floating_point)
UNARY_OP_FUNCTOR(sinh, number_kind_floating_point)
UNARY_OP_FUNCTOR(tanh, number_kind_floating_point)
UNARY_OP_FUNCTOR(log2, number_kind_floating_point)
UNARY_OP_FUNCTOR(nearbyint, number_kind_floating_point)
UNARY_OP_FUNCTOR(rint, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR(ldexp, short, number_kind_floating_point)
//HETERO_BINARY_OP_FUNCTOR(frexp, short*, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(ldexp, int, number_kind_floating_point)
//HETERO_BINARY_OP_FUNCTOR_B(frexp, int*, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(ldexp, long, number_kind_floating_point)
//HETERO_BINARY_OP_FUNCTOR_B(frexp, long*, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(ldexp, long long, number_kind_floating_point)
//HETERO_BINARY_OP_FUNCTOR_B(frexp, long long*, number_kind_floating_point)
BINARY_OP_FUNCTOR(pow, number_kind_floating_point)
BINARY_OP_FUNCTOR(fmod, number_kind_floating_point)
BINARY_OP_FUNCTOR(fmax, number_kind_floating_point)
BINARY_OP_FUNCTOR(fmin, number_kind_floating_point)
BINARY_OP_FUNCTOR(atan2, number_kind_floating_point)
BINARY_OP_FUNCTOR(fdim, number_kind_floating_point)
BINARY_OP_FUNCTOR(hypot, number_kind_floating_point)
BINARY_OP_FUNCTOR(remainder, number_kind_floating_point)
UNARY_OP_FUNCTOR(logb, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR(scalbn, short, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR(scalbln, short, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbn, int, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbln, int, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbn, long, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbln, long, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbn, long long, number_kind_floating_point)
HETERO_BINARY_OP_FUNCTOR_B(scalbln, long long, number_kind_floating_point)
//
// Complex functions:
//
UNARY_OP_FUNCTOR(exp, number_kind_complex)
UNARY_OP_FUNCTOR(log, number_kind_complex)
UNARY_OP_FUNCTOR(log10, number_kind_complex)
BINARY_OP_FUNCTOR(pow, number_kind_complex)
UNARY_OP_FUNCTOR(sqrt, number_kind_complex)
UNARY_OP_FUNCTOR(sin, number_kind_complex)
UNARY_OP_FUNCTOR(cos, number_kind_complex)
UNARY_OP_FUNCTOR(tan, number_kind_complex)
UNARY_OP_FUNCTOR(asin, number_kind_complex)
UNARY_OP_FUNCTOR(acos, number_kind_complex)
UNARY_OP_FUNCTOR(atan, number_kind_complex)
UNARY_OP_FUNCTOR(sinh, number_kind_complex)
UNARY_OP_FUNCTOR(cosh, number_kind_complex)
UNARY_OP_FUNCTOR(tanh, number_kind_complex)
UNARY_OP_FUNCTOR(asinh, number_kind_complex)
UNARY_OP_FUNCTOR(acosh, number_kind_complex)
UNARY_OP_FUNCTOR(atanh, number_kind_complex)
//
// Integer functions:
//
BINARY_OP_FUNCTOR(gcd, number_kind_integer)
BINARY_OP_FUNCTOR(lcm, number_kind_integer)
HETERO_BINARY_OP_FUNCTOR(pow, unsigned, number_kind_integer)
#undef BINARY_OP_FUNCTOR
#undef UNARY_OP_FUNCTOR
//
// ilogb:
//
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<Backend>::value == number_kind_floating_point, typename Backend::exponent_type>::type
ilogb(const multiprecision::number<Backend, ExpressionTemplates>& val)
{
using default_ops::eval_ilogb;
return eval_ilogb(val.backend());
}
template <class tag, class A1, class A2, class A3, class A4>
inline BOOST_MP_CXX14_CONSTEXPR typename std::enable_if<number_category<detail::expression<tag, A1, A2, A3, A4> >::value == number_kind_floating_point, typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type::backend_type::exponent_type>::type
ilogb(const detail::expression<tag, A1, A2, A3, A4>& val)
{
using default_ops::eval_ilogb;
typename multiprecision::detail::expression<tag, A1, A2, A3, A4>::result_type arg(val);
return eval_ilogb(arg.backend());
}
} //namespace multiprecision
namespace math {
//
// Overload of Boost.Math functions that find the wrong overload when used with number:
//
namespace detail {
template <class T>
T sinc_pi_imp(T);
template <class T>
T sinhc_pi_imp(T);
} // namespace detail
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline multiprecision::number<Backend, ExpressionTemplates> sinc_pi(const multiprecision::number<Backend, ExpressionTemplates>& x)
{
boost::multiprecision::detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(x);
return std::move(detail::sinc_pi_imp(x));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class Policy>
inline multiprecision::number<Backend, ExpressionTemplates> sinc_pi(const multiprecision::number<Backend, ExpressionTemplates>& x, const Policy&)
{
boost::multiprecision::detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(x);
return std::move(detail::sinc_pi_imp(x));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates>
inline multiprecision::number<Backend, ExpressionTemplates> sinhc_pi(const multiprecision::number<Backend, ExpressionTemplates>& x)
{
boost::multiprecision::detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(x);
return std::move(detail::sinhc_pi_imp(x));
}
template <class Backend, multiprecision::expression_template_option ExpressionTemplates, class Policy>
inline multiprecision::number<Backend, ExpressionTemplates> sinhc_pi(const multiprecision::number<Backend, ExpressionTemplates>& x, const Policy&)
{
boost::multiprecision::detail::scoped_default_precision<multiprecision::number<Backend, ExpressionTemplates> > precision_guard(x);
return std::move(boost::math::sinhc_pi(x));
}
using boost::multiprecision::gcd;
using boost::multiprecision::lcm;
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
} // namespace math
namespace integer {
using boost::multiprecision::gcd;
using boost::multiprecision::lcm;
} // namespace integer
} // namespace boost
//
// This has to come last of all:
//
#include <boost/multiprecision/detail/no_et_ops.hpp>
#include <boost/multiprecision/detail/et_ops.hpp>
//
// min/max overloads:
//
#include <boost/multiprecision/detail/min_max.hpp>
#endif