Constexpr fma (#734)

* constexpr fma

* Improve use of intrinsics for calculation

* Changes to intrinsics and address sonarlint comments

doc/sf/ccmath.qbk

@@ -182,6 +182,13 @@ All of the following functions require C++17 or greater.
         template <typename T>
         inline constexpr bool isunordered(T x, T y) noexcept
 
+        template <typename Real>
+        inline constexpr Real fma(Real x, Real y, Real z) noexcept
+        Requires compiling with fma flag
+
+        template <typename Arithmetic1, typename Arithmetic2, typename Arithmetic3>
+        inline constepxr Promoted fma(Arithmetic1 x, Arithmetic2 y, Arithmetic3 z) noexcept
+
     } // Namespaces
 
 [endsect] [/section:ccmath Constexpr CMath]

include/boost/math/ccmath/ccmath.hpp

@@ -38,5 +38,6 @@
 #include <boost/math/ccmath/isless.hpp>
 #include <boost/math/ccmath/islessequal.hpp>
 #include <boost/math/ccmath/isunordered.hpp>
+#include <boost/math/ccmath/fma.hpp>
 
 #endif // BOOST_MATH_CCMATH_HPP

include/boost/math/ccmath/fma.hpp

@@ -0,0 +1,128 @@
+//  (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

test/Jamfile.v2

@@ -154,6 +154,7 @@ test-suite special_fun :
    [ run ccmath_isless_test.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx17_if_constexpr ] ]
    [ run ccmath_islessequal_test.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx17_if_constexpr ] ]
    [ run ccmath_isunordered_test.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx17_if_constexpr ] ]
+   [ run ccmath_fma_test.cpp ../../test/build//boost_unit_test_framework : : : [ requires cxx17_if_constexpr ] ]
    [ run log1p_expm1_test.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
    [ run powm1_sqrtp1m1_test.cpp test_instances//test_instances pch_light ../../test/build//boost_unit_test_framework  ]
    [ run git_issue_705.cpp ../../test/build//boost_unit_test_framework  ]

test/ccmath_fma_test.cpp

@@ -0,0 +1,73 @@
+//  (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)
+
+#include <cmath>
+#include <cfloat>
+#include <cstdint>
+#include <limits>
+#include <type_traits>
+#include <boost/math/ccmath/fma.hpp>
+#include <boost/math/ccmath/isnan.hpp>
+#include <boost/math/ccmath/isinf.hpp>
+#include <boost/math/ccmath/abs.hpp>
+
+#ifdef BOOST_HAS_FLOAT128
+#include <boost/multiprecision/float128.hpp>
+#endif
+
+#if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P)
+template <typename T>
+constexpr void test()
+{
+    // Error handling
+    static_assert(boost::math::ccmath::isnan(boost::math::ccmath::fma(std::numeric_limits<T>::infinity(), T(0), T(1))));
+    static_assert(boost::math::ccmath::isnan(boost::math::ccmath::fma(T(0), std::numeric_limits<T>::infinity(), T(1))));
+
+    static_assert(boost::math::ccmath::isnan(boost::math::ccmath::fma(std::numeric_limits<T>::infinity(), T(0), std::numeric_limits<T>::quiet_NaN())));
+    static_assert(boost::math::ccmath::isnan(boost::math::ccmath::fma(T(0), std::numeric_limits<T>::infinity(), std::numeric_limits<T>::quiet_NaN())));
+
+    static_assert(boost::math::ccmath::isnan(boost::math::ccmath::fma(std::numeric_limits<T>::quiet_NaN(), T(1), T(1))));
+    static_assert(boost::math::ccmath::isnan(boost::math::ccmath::fma(T(1), std::numeric_limits<T>::quiet_NaN(), T(1))));
+
+    static_assert(boost::math::ccmath::isnan(boost::math::ccmath::fma(T(1), T(1), std::numeric_limits<T>::quiet_NaN())));
+
+    // Functionality
+    static_assert(boost::math::ccmath::fma(T(1), T(2), T(3)) == T(5));
+    static_assert(boost::math::ccmath::fma(T(2), T(3), T(1)) == T(7));
+
+    // Correct promoted types
+    if constexpr (!std::is_same_v<T, float>)
+    {
+        constexpr auto test_type = boost::math::ccmath::fma(T(1), 1.0, 1.0f);
+        static_assert(std::is_same_v<T, std::remove_cv_t<decltype(test_type)>>);
+    }
+    else
+    {
+        constexpr auto test_type = boost::math::ccmath::fma(1.0f, 1, 1.0);
+        static_assert(std::is_same_v<double, std::remove_cv_t<decltype(test_type)>>);
+    }
+}
+
+int main()
+{
+    test<float>();
+    test<double>();
+
+    #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+    test<long double>();
+    #endif
+    
+    #ifdef BOOST_HAS_FLOAT128
+    test<boost::multiprecision::float128>();
+    #endif
+
+    return 0;
+}
+#else
+int main()
+{
+    return 0;
+}
+#endif

test/compile_test/ccmath_fma_incl_test.cpp

@@ -0,0 +1,16 @@
+//  (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)
+
+#include <boost/math/ccmath/fma.hpp>
+#include "test_compile_result.hpp"
+
+void compile_and_link_test()
+{
+   check_result<float>(boost::math::ccmath::fma(1.0f, 1.0f, 1.0f));
+   check_result<double>(boost::math::ccmath::fma(1.0, 1.0, 1.0));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result<long double>(boost::math::ccmath::fma(1.0l, 1.0l, 1.0l));
+#endif
+}