From 720573ad106a98e7fb1f5250b85e0c2cb7f36491 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Thu, 6 Jan 2022 23:50:12 +0200
Subject: [PATCH 1/3] constexpr fma

---
 doc/sf/ccmath.qbk                          |   6 ++
 include/boost/math/ccmath/ccmath.hpp       |   1 +
 include/boost/math/ccmath/fma.hpp          | 115 +++++++++++++++++++++
 test/Jamfile.v2                            |   1 +
 test/ccmath_fma_test.cpp                   |  73 +++++++++++++
 test/compile_test/ccmath_fma_incl_test.cpp |  16 +++
 6 files changed, 212 insertions(+)
 create mode 100644 include/boost/math/ccmath/fma.hpp
 create mode 100644 test/ccmath_fma_test.cpp
 create mode 100644 test/compile_test/ccmath_fma_incl_test.cpp

diff --git a/doc/sf/ccmath.qbk b/doc/sf/ccmath.qbk
index 0a88ce6310..f39e388ee5 100644
--- a/doc/sf/ccmath.qbk
+++ b/doc/sf/ccmath.qbk
@@ -182,6 +182,12 @@ 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
+
+        template <typename Arithmetic1, typename Arithmetic2, typename Arithmetic3>
+        inline constepxr Promoted fma(Arithmetic1 x, Arithmetic2 y, Arithmetic3 z) noexcept
+
     } // Namespaces
 
 [endsect] [/section:ccmath Constexpr CMath]
diff --git a/include/boost/math/ccmath/ccmath.hpp b/include/boost/math/ccmath/ccmath.hpp
index 72c49922f1..2749ec7b28 100644
--- a/include/boost/math/ccmath/ccmath.hpp
+++ b/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
diff --git a/include/boost/math/ccmath/fma.hpp b/include/boost/math/ccmath/fma.hpp
new file mode 100644
index 0000000000..12390953e7
--- /dev/null
+++ b/include/boost/math/ccmath/fma.hpp
@@ -0,0 +1,115 @@
+//  (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>
+inline constexpr T fma_imp(const T x, const T y, const T z) noexcept
+{
+    #if __GNUC__ < 10
+        return (x * y) + z;
+    #else
+    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);
+    }
+    else // e.g. Boost.Multiprecision types where no built-in exists
+    {
+        return (x * y) + z;
+    }
+    #endif
+}
+
+} // Namespace detail
+
+template <typename Real, std::enable_if_t<!std::is_integral_v<Real>, bool> = true>
+inline constexpr Real fma(Real x, Real y, Real z) noexcept
+{
+    if (BOOST_MATH_IS_CONSTANT_EVALUATED(x))
+    {
+        return x == 0 && boost::math::ccmath::isinf(y) ? std::numeric_limits<Real>::quiet_NaN() :
+               y == 0 && boost::math::ccmath::isinf(x) ? std::numeric_limits<Real>::quiet_NaN() :
+               boost::math::ccmath::isnan(x) ? std::numeric_limits<Real>::quiet_NaN() :
+               boost::math::ccmath::isnan(y) ? std::numeric_limits<Real>::quiet_NaN() :
+               boost::math::ccmath::isnan(z) ? std::numeric_limits<Real>::quiet_NaN() :
+               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>
+inline 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);
+    }
+}
+
+inline 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
+inline 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
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 5deced8cb0..e38665f777 100644
--- a/test/Jamfile.v2
+++ b/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  ]
diff --git a/test/ccmath_fma_test.cpp b/test/ccmath_fma_test.cpp
new file mode 100644
index 0000000000..3b7354df2e
--- /dev/null
+++ b/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
+
+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)>>);
+    }
+}
+
+#if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P)
+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
diff --git a/test/compile_test/ccmath_fma_incl_test.cpp b/test/compile_test/ccmath_fma_incl_test.cpp
new file mode 100644
index 0000000000..ef035bd8b6
--- /dev/null
+++ b/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
+}

From 49881beaf13e9b8a534152236fbbe21efb9dcde1 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Tue, 24 May 2022 19:44:19 -0700
Subject: [PATCH 2/3] Improve use of intrinsics for calculation

---
 doc/sf/ccmath.qbk                 |  1 +
 include/boost/math/ccmath/fma.hpp | 25 ++++++++++++++++++++-----
 test/ccmath_fma_test.cpp          |  2 +-
 3 files changed, 22 insertions(+), 6 deletions(-)

diff --git a/doc/sf/ccmath.qbk b/doc/sf/ccmath.qbk
index f39e388ee5..4a2b0b2fbf 100644
--- a/doc/sf/ccmath.qbk
+++ b/doc/sf/ccmath.qbk
@@ -184,6 +184,7 @@ All of the following functions require C++17 or greater.
 
         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
diff --git a/include/boost/math/ccmath/fma.hpp b/include/boost/math/ccmath/fma.hpp
index 12390953e7..0ed3cc5668 100644
--- a/include/boost/math/ccmath/fma.hpp
+++ b/include/boost/math/ccmath/fma.hpp
@@ -13,6 +13,11 @@
 #include <boost/math/ccmath/isinf.hpp>
 #include <boost/math/ccmath/isnan.hpp>
 
+#if __has_include("immintrin.h") && defined(__X86_64__) || defined(__amd64__)
+#   include "immintrin.h"
+#   define BOOST_MATH_HAS_IMMINTRIN_H
+#endif
+
 namespace boost::math::ccmath {
 
 namespace detail {
@@ -20,9 +25,7 @@ namespace detail {
 template <typename T>
 inline constexpr T fma_imp(const T x, const T y, const T z) noexcept
 {
-    #if __GNUC__ < 10
-        return (x * y) + z;
-    #else
+    #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);
@@ -35,11 +38,23 @@ inline constexpr T fma_imp(const T x, const T y, const T z) noexcept
     {
         return __builtin_fmal(x, y, z);
     }
-    else // e.g. Boost.Multiprecision types where no built-in exists
+    #elif defined(BOOST_MATH_HAS_IMMINTRIN_H)
+    if constexpr (std::is_same_v<T, float>)
+    {
+        return static_cast<float>(_mm_fmadd_ps(x, y, z));
+    }
+    else if constexpr (std::is_same_v<T, double>)
+    {
+        return static_cast<double>(_mm_fmadd_pd(x, y, z));
+    }
+    else if constexpr (std::is_same_v<T, long double>)
     {
-        return (x * y) + z;
+        return static_cast<long double>(_mm256_fmadd_pd(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
diff --git a/test/ccmath_fma_test.cpp b/test/ccmath_fma_test.cpp
index 3b7354df2e..a5aa74914d 100644
--- a/test/ccmath_fma_test.cpp
+++ b/test/ccmath_fma_test.cpp
@@ -17,6 +17,7 @@
 #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()
 {
@@ -49,7 +50,6 @@ constexpr void test()
     }
 }
 
-#if !defined(BOOST_MATH_NO_CONSTEXPR_DETECTION) && !defined(BOOST_MATH_USING_BUILTIN_CONSTANT_P)
 int main()
 {
     test<float>();

From 38aaf9d7669a4fde40bba5d590b552ac4a32a890 Mon Sep 17 00:00:00 2001
From: Matt Borland <matt@mattborland.com>
Date: Fri, 27 May 2022 11:26:52 -0700
Subject: [PATCH 3/3] Changes to intrinsics and address sonarlint comments

---
 include/boost/math/ccmath/fma.hpp | 56 +++++++++++++++----------------
 1 file changed, 27 insertions(+), 29 deletions(-)

diff --git a/include/boost/math/ccmath/fma.hpp b/include/boost/math/ccmath/fma.hpp
index 0ed3cc5668..3056f76d47 100644
--- a/include/boost/math/ccmath/fma.hpp
+++ b/include/boost/math/ccmath/fma.hpp
@@ -13,17 +13,12 @@
 #include <boost/math/ccmath/isinf.hpp>
 #include <boost/math/ccmath/isnan.hpp>
 
-#if __has_include("immintrin.h") && defined(__X86_64__) || defined(__amd64__)
-#   include "immintrin.h"
-#   define BOOST_MATH_HAS_IMMINTRIN_H
-#endif
-
 namespace boost::math::ccmath {
 
 namespace detail {
 
 template <typename T>
-inline constexpr T fma_imp(const T x, const T y, const T z) noexcept
+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>)
@@ -38,19 +33,6 @@ inline constexpr T fma_imp(const T x, const T y, const T z) noexcept
     {
         return __builtin_fmal(x, y, z);
     }
-    #elif defined(BOOST_MATH_HAS_IMMINTRIN_H)
-    if constexpr (std::is_same_v<T, float>)
-    {
-        return static_cast<float>(_mm_fmadd_ps(x, y, z));
-    }
-    else if constexpr (std::is_same_v<T, double>)
-    {
-        return static_cast<double>(_mm_fmadd_pd(x, y, z));
-    }
-    else if constexpr (std::is_same_v<T, long double>)
-    {
-        return static_cast<long double>(_mm256_fmadd_pd(x, y, z));
-    }
     #endif
     
     // If we can't use compiler intrinsics hope that -fma flag optimizes this call to fma instruction
@@ -60,16 +42,32 @@ inline constexpr T fma_imp(const T x, const T y, const T z) noexcept
 } // Namespace detail
 
 template <typename Real, std::enable_if_t<!std::is_integral_v<Real>, bool> = true>
-inline constexpr Real fma(Real x, Real y, Real z) noexcept
+constexpr Real fma(Real x, Real y, Real z) noexcept
 {
     if (BOOST_MATH_IS_CONSTANT_EVALUATED(x))
     {
-        return x == 0 && boost::math::ccmath::isinf(y) ? std::numeric_limits<Real>::quiet_NaN() :
-               y == 0 && boost::math::ccmath::isinf(x) ? std::numeric_limits<Real>::quiet_NaN() :
-               boost::math::ccmath::isnan(x) ? std::numeric_limits<Real>::quiet_NaN() :
-               boost::math::ccmath::isnan(y) ? std::numeric_limits<Real>::quiet_NaN() :
-               boost::math::ccmath::isnan(z) ? std::numeric_limits<Real>::quiet_NaN() :
-               boost::math::ccmath::detail::fma_imp(x, y, z);
+        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
     {
@@ -79,7 +77,7 @@ inline constexpr Real fma(Real x, Real y, Real z) noexcept
 }
 
 template <typename T1, typename T2, typename T3>
-inline constexpr auto fma(T1 x, T2 y, T3 z) noexcept
+constexpr auto fma(T1 x, T2 y, T3 z) noexcept
 {
     if (BOOST_MATH_IS_CONSTANT_EVALUATED(x))
     {
@@ -113,13 +111,13 @@ inline constexpr auto fma(T1 x, T2 y, T3 z) noexcept
     }
 }
 
-inline constexpr float fmaf(float x, float y, float z) noexcept
+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
-inline constexpr long double fmal(long double x, long double y, long double z) noexcept
+constexpr long double fmal(long double x, long double y, long double z) noexcept
 {
     return boost::math::ccmath::fma(x, y, z);
 }