fma.hpp
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// (C) Copyright Matt Borland 2022.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_CCMATH_FMA_HPP
#define BOOST_MATH_CCMATH_FMA_HPP
#include <cmath>
#include <limits>
#include <type_traits>
#include <boost/math/tools/is_constant_evaluated.hpp>
#include <boost/math/ccmath/isinf.hpp>
#include <boost/math/ccmath/isnan.hpp>
namespace boost::math::ccmath {
namespace detail {
template <typename T>
constexpr T fma_imp(const T x, const T y, const T z) noexcept
{
#if defined(__GNUC__) && !defined(__clang__) && !defined(__INTEL_COMPILER) && !defined(__INTEL_LLVM_COMPILER)
if constexpr (std::is_same_v<T, float>)
{
return __builtin_fmaf(x, y, z);
}
else if constexpr (std::is_same_v<T, double>)
{
return __builtin_fma(x, y, z);
}
else if constexpr (std::is_same_v<T, long double>)
{
return __builtin_fmal(x, y, z);
}
#endif
// If we can't use compiler intrinsics hope that -fma flag optimizes this call to fma instruction
return (x * y) + z;
}
} // Namespace detail
template <typename Real, std::enable_if_t<!std::is_integral_v<Real>, bool> = true>
constexpr Real fma(Real x, Real y, Real z) noexcept
{
if (BOOST_MATH_IS_CONSTANT_EVALUATED(x))
{
if (x == 0 && boost::math::ccmath::isinf(y))
{
return std::numeric_limits<Real>::quiet_NaN();
}
else if (y == 0 && boost::math::ccmath::isinf(x))
{
return std::numeric_limits<Real>::quiet_NaN();
}
else if (boost::math::ccmath::isnan(x))
{
return std::numeric_limits<Real>::quiet_NaN();
}
else if (boost::math::ccmath::isnan(y))
{
return std::numeric_limits<Real>::quiet_NaN();
}
else if (boost::math::ccmath::isnan(z))
{
return std::numeric_limits<Real>::quiet_NaN();
}
return boost::math::ccmath::detail::fma_imp(x, y, z);
}
else
{
using std::fma;
return fma(x, y, z);
}
}
template <typename T1, typename T2, typename T3>
constexpr auto fma(T1 x, T2 y, T3 z) noexcept
{
if (BOOST_MATH_IS_CONSTANT_EVALUATED(x))
{
// If the type is an integer (e.g. epsilon == 0) then set the epsilon value to 1 so that type is at a minimum
// cast to double
constexpr auto T1p = std::numeric_limits<T1>::epsilon() > 0 ? std::numeric_limits<T1>::epsilon() : 1;
constexpr auto T2p = std::numeric_limits<T2>::epsilon() > 0 ? std::numeric_limits<T2>::epsilon() : 1;
constexpr auto T3p = std::numeric_limits<T3>::epsilon() > 0 ? std::numeric_limits<T3>::epsilon() : 1;
using promoted_type =
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
std::conditional_t<T1p <= LDBL_EPSILON && T1p <= T2p, T1,
std::conditional_t<T2p <= LDBL_EPSILON && T2p <= T1p, T2,
std::conditional_t<T3p <= LDBL_EPSILON && T3p <= T2p, T3,
#endif
std::conditional_t<T1p <= DBL_EPSILON && T1p <= T2p, T1,
std::conditional_t<T2p <= DBL_EPSILON && T2p <= T1p, T2,
std::conditional_t<T3p <= DBL_EPSILON && T3p <= T2p, T3, double
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
>>>>>>;
#else
>>>;
#endif
return boost::math::ccmath::fma(promoted_type(x), promoted_type(y), promoted_type(z));
}
else
{
using std::fma;
return fma(x, y, z);
}
}
constexpr float fmaf(float x, float y, float z) noexcept
{
return boost::math::ccmath::fma(x, y, z);
}
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
constexpr long double fmal(long double x, long double y, long double z) noexcept
{
return boost::math::ccmath::fma(x, y, z);
}
#endif
} // Namespace boost::math::ccmath
#endif // BOOST_MATH_CCMATH_FMA_HPP