From 6bb2d0fb87030d45f47b9eac0fc485231ca2edae Mon Sep 17 00:00:00 2001
From: bolero-MURAKAMI <bolero.murakami@gmail.com>
Date: Wed, 9 May 2012 10:15:19 +0900
Subject: [PATCH] replace implementation <cmath> functions to
 Sprout.Math.Functions

---
 sprout/complex.hpp                            | 75 +++++++++++--------
 sprout/cstdlib/str_to_float.hpp               |  1 -
 sprout/cstdlib/str_to_int.hpp                 |  7 +-
 sprout/darkroom/cameras/simple_camera.hpp     | 10 ++-
 sprout/darkroom/coords/vector.hpp             |  4 +-
 sprout/darkroom/objects/sphere.hpp            |  9 ++-
 sprout/iterator/sinusoid_iterator.hpp         |  6 +-
 sprout/math/abs.hpp                           | 42 +++++++++++
 sprout/math/acosh.hpp                         |  1 +
 sprout/math/asinh.hpp                         |  5 +-
 sprout/math/cos.hpp                           | 17 +++--
 sprout/math/fabs.hpp                          | 24 ------
 sprout/math/fma.hpp                           | 55 ++++++++++++++
 sprout/math/operations.hpp                    |  2 +
 sprout/numeric/dft/detail/dft_element_gen.hpp |  7 +-
 sprout/numeric/dft/fixed/sinusoid.hpp         |  4 +-
 sprout/numeric/dft/fixed/spectrum.hpp         | 10 +--
 sprout/random/binomial_distribution.hpp       | 20 +++--
 sprout/random/geometric_distribution.hpp      |  5 +-
 sprout/random/normal_distribution.hpp         | 13 ++--
 sprout/string/float_to_string.hpp             |  1 -
 21 files changed, 212 insertions(+), 106 deletions(-)
 create mode 100644 sprout/math/abs.hpp
 create mode 100644 sprout/math/fma.hpp

diff --git a/sprout/complex.hpp b/sprout/complex.hpp
index 41a92e40..7dbf25de 100644
--- a/sprout/complex.hpp
+++ b/sprout/complex.hpp
@@ -1,11 +1,20 @@
 #ifndef SPROUT_COMPLEX_HPP
 #define SPROUT_COMPLEX_HPP
 
-#include <cmath>
 #include <iosfwd>
 #include <ios>
 #include <sprout/config.hpp>
 #include <sprout/math/constants.hpp>
+#include <sprout/math/abs.hpp>
+#include <sprout/math/sin.hpp>
+#include <sprout/math/cos.hpp>
+#include <sprout/math/atan2.hpp>
+#include <sprout/math/sinh.hpp>
+#include <sprout/math/cosh.hpp>
+#include <sprout/math/exp.hpp>
+#include <sprout/math/log.hpp>
+#include <sprout/math/pow.hpp>
+#include <sprout/math/sqrt.hpp>
 
 namespace sprout {
 	template<typename T>
@@ -281,12 +290,12 @@ namespace sprout {
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR T abs(sprout::complex<T> const& x) {
-		using std::sqrt;
+		using sprout::sqrt;
 		return sqrt(sprout::norm(x));
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR T arg(sprout::complex<T> const& x) {
-		using std::atan2;
+		using sprout::atan2;
 		return atan2(x.imag(), x.real());
 	}
 	template<typename T>
@@ -315,8 +324,8 @@ namespace sprout {
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> polar(T const& rho, T const& theta = 0) {
-		using std::cos;
-		using std::sin;
+		using sprout::cos;
+		using sprout::sin;
 		return sprout::complex<T>(rho * cos(theta), rho * sin(theta));
 	}
 	// 26.4.8, transcendentals:
@@ -388,8 +397,8 @@ namespace sprout {
 			T const& den
 			)
 		{
-			using std::atan2;
-			using std::log;
+			using sprout::atan2;
+			using sprout::log;
 			return sprout::complex<T>(
 				T(0.5) * atan2(T(2) * x.real(), z),
 				T(0.25) * log((r2 + num * num) / (r2 + den * den))
@@ -440,8 +449,8 @@ namespace sprout {
 			T const& den
 			)
 		{
-			using std::atan2;
-			using std::log;
+			using sprout::atan2;
+			using sprout::log;
 			return sprout::complex<T>(
 				T(0.25) * (log(i2 + num * num) - log(i2 + den * den)),
 				T(0.5) * atan2(T(2) * x.imag(), z)
@@ -468,10 +477,10 @@ namespace sprout {
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> cos(sprout::complex<T> const& x) {
-		using std::cos;
-		using std::sin;
-		using std::cosh;
-		using std::sinh;
+		using sprout::cos;
+		using sprout::sin;
+		using sprout::cosh;
+		using sprout::sinh;
 		return sprout::complex<T>(
 			cos(x.real()) * cosh(x.imag()),
 			-(sin(x.real()) * sinh(x.imag()))
@@ -479,10 +488,10 @@ namespace sprout {
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> cosh(sprout::complex<T> const& x) {
-		using std::cos;
-		using std::sin;
-		using std::cosh;
-		using std::sinh;
+		using sprout::cos;
+		using sprout::sin;
+		using sprout::cosh;
+		using sprout::sinh;
 		return sprout::complex<T>(
 			cosh(x.real()) * cos(x.imag()),
 			sinh(x.real()) * sin(x.imag())
@@ -490,7 +499,7 @@ namespace sprout {
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> exp(sprout::complex<T> const& x) {
-		using std::exp;
+		using sprout::exp;
 		return sprout::polar(exp(x.real()), x.imag());
 	}
 	template<typename T>
@@ -499,19 +508,19 @@ namespace sprout {
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> log10(sprout::complex<T> const& x) {
-		using std::log;
+		using sprout::log;
 		return sprout::log(x) / log(T(10));
 	}
 	namespace detail {
 		template<typename T>
 		SPROUT_CONSTEXPR sprout::complex<T> pow_impl(sprout::complex<T> const& t, T const& y) {
-			using std::exp;
+			using sprout::exp;
 			return sprout::polar(exp(y * t.real()), y * t.imag());
 		}
 	}	// namespace detail
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> pow(sprout::complex<T> const& x, T const& y) {
-		using std::pow;
+		using sprout::pow;
 		return x == T() ? T()
 			: x.imag() == T() && x.real() > T() ? pow(x.real(), y)
 			: sprout::detail::pow_impl(sprout::log(x), y)
@@ -525,17 +534,17 @@ namespace sprout {
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> pow(T const& x, sprout::complex<T> const& y) {
-		using std::log;
+		using sprout::log;
 		return x > T() ? sprout::polar(sprout::pow(x, y.real()), y.imag() * log(x))
 			: sprout::pow(sprout::complex<T>(x), y)
 			;
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> sin(sprout::complex<T> const& x) {
-		using std::cos;
-		using std::sin;
-		using std::cosh;
-		using std::sinh;
+		using sprout::cos;
+		using sprout::sin;
+		using sprout::cosh;
+		using sprout::sinh;
 		return sprout::complex<T>(
 			sin(x.real()) * cosh(x.imag()),
 			cos(x.real()) * sinh(x.imag())
@@ -543,10 +552,10 @@ namespace sprout {
 	}
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> sinh(sprout::complex<T> const& x) {
-		using std::cos;
-		using std::sin;
-		using std::cosh;
-		using std::sinh;
+		using sprout::cos;
+		using sprout::sin;
+		using sprout::cosh;
+		using sprout::sinh;
 		return sprout::complex<T>(
 			sinh(x.real()) * cos(x.imag()),
 			cosh(x.real()) * sin(x.imag())
@@ -559,7 +568,7 @@ namespace sprout {
 		}
 		template<typename T>
 		SPROUT_CONSTEXPR sprout::complex<T> sqrt_impl_2_1(sprout::complex<T> const& x, T const& t, T const& u) {
-			using std::abs;
+			using sprout::abs;
 			return x.real() > T() ? sprout::complex<T>(u, x.imag() / t)
 				: sprout::complex<T>(abs(x.imag()) / t, x.imag() < T() ? -u : u)
 				;
@@ -571,8 +580,8 @@ namespace sprout {
 	}	// namespace detail
 	template<typename T>
 	SPROUT_CONSTEXPR sprout::complex<T> sqrt(sprout::complex<T> const& x) {
-		using std::sqrt;
-		using std::abs;
+		using sprout::sqrt;
+		using sprout::abs;
 		return x.real() == T() ? sprout::detail::sqrt_impl_1(x, sqrt(abs(x.imag()) / 2))
 			: sprout::detail::sqrt_impl_2(x, sqrt(2 * (sprout::abs(x) + abs(x.real()))))
 			;
diff --git a/sprout/cstdlib/str_to_float.hpp b/sprout/cstdlib/str_to_float.hpp
index 082f773b..31ae9880 100644
--- a/sprout/cstdlib/str_to_float.hpp
+++ b/sprout/cstdlib/str_to_float.hpp
@@ -3,7 +3,6 @@
 
 #include <cstddef>
 #include <cstdlib>
-#include <cmath>
 #include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
diff --git a/sprout/cstdlib/str_to_int.hpp b/sprout/cstdlib/str_to_int.hpp
index e057f2e5..a352c03b 100644
--- a/sprout/cstdlib/str_to_int.hpp
+++ b/sprout/cstdlib/str_to_int.hpp
@@ -3,6 +3,7 @@
 
 #include <cstddef>
 #include <cstdlib>
+#include <cinttypes>
 #include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
@@ -83,9 +84,11 @@ namespace sprout {
 			return !endptr ? sprout::detail::str_to_int<IntType>(str, base)
 				: std::is_signed<IntType>::value
 					? sizeof(IntType) <= sizeof(long) ? static_cast<IntType>(std::strtol(&*str, endptr, base))
-						: static_cast<IntType>(std::strtoll(&*str, endptr, base))
+						: sizeof(IntType) <= sizeof(long long) ? static_cast<IntType>(std::strtoll(&*str, endptr, base))
+						: static_cast<IntType>(std::strtoimax(&*str, endptr, base))
 					: sizeof(IntType) <= sizeof(unsigned long) ? static_cast<IntType>(std::strtoul(&*str, endptr, base))
-						: static_cast<IntType>(std::strtoull(&*str, endptr, base))
+						: sizeof(IntType) <= sizeof(unsigned long long) ? static_cast<IntType>(std::strtoull(&*str, endptr, base))
+						: static_cast<IntType>(std::strtoumax(&*str, endptr, base))
 				;
 		}
 	}	// namespace detail
diff --git a/sprout/darkroom/cameras/simple_camera.hpp b/sprout/darkroom/cameras/simple_camera.hpp
index b9809720..6d02512a 100644
--- a/sprout/darkroom/cameras/simple_camera.hpp
+++ b/sprout/darkroom/cameras/simple_camera.hpp
@@ -1,9 +1,11 @@
 #ifndef SPROUT_DARKROOM_CAMERAS_SIMPLE_CAMERA_HPP
 #define SPROUT_DARKROOM_CAMERAS_SIMPLE_CAMERA_HPP
 
-#include <cmath>
 #include <sprout/config.hpp>
 #include <sprout/tuple/tuple.hpp>
+#include <sprout/math/sin.hpp>
+#include <sprout/math/cos.hpp>
+#include <sprout/math/sqrt.hpp>
 #include <sprout/darkroom/coords/vector.hpp>
 #include <sprout/darkroom/cameras/angle_of_view.hpp>
 
@@ -49,9 +51,9 @@ namespace sprout {
 					unit_type const& v
 					) const
 				{
-					using std::sqrt;
-					using std::sin;
-					using std::cos;
+					using sprout::sqrt;
+					using sprout::sin;
+					using sprout::cos;
 					return transform_1(
 						c,
 						u * cos(rotate_) - v * sin(rotate_),
diff --git a/sprout/darkroom/coords/vector.hpp b/sprout/darkroom/coords/vector.hpp
index 218e03e7..54e7d6d8 100644
--- a/sprout/darkroom/coords/vector.hpp
+++ b/sprout/darkroom/coords/vector.hpp
@@ -1,11 +1,11 @@
 #ifndef SPROUT_DARKROOM_COORDS_VECTOR_HPP
 #define SPROUT_DARKROOM_COORDS_VECTOR_HPP
 
-#include <cmath>
 #include <sprout/config.hpp>
 #include <sprout/tuple/tuple.hpp>
 #include <sprout/tuple/functions.hpp>
 #include <sprout/utility/forward.hpp>
+#include <sprout/math/sqrt.hpp>
 #include <sprout/darkroom/access/access.hpp>
 
 namespace sprout {
@@ -63,7 +63,7 @@ namespace sprout {
 			template<typename Vector>
 			inline SPROUT_CONSTEXPR typename sprout::darkroom::access::unit<Vector>::type
 			length(Vector const& vec) {
-				using std::sqrt;
+				using sprout::sqrt;
 				return sqrt(sprout::darkroom::coords::length_sq(vec));
 			}
 			//
diff --git a/sprout/darkroom/objects/sphere.hpp b/sprout/darkroom/objects/sphere.hpp
index 6d9cc512..bfeec47a 100644
--- a/sprout/darkroom/objects/sphere.hpp
+++ b/sprout/darkroom/objects/sphere.hpp
@@ -2,12 +2,13 @@
 #define SPROUT_DARKROOM_OBJECTS_SPHERE_HPP
 
 #include <cstddef>
-#include <cmath>
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/tuple/tuple.hpp>
 #include <sprout/tuple/functions.hpp>
 #include <sprout/math/constants.hpp>
+#include <sprout/math/atan2.hpp>
+#include <sprout/math/sqrt.hpp>
 #include <sprout/darkroom/access/access.hpp>
 #include <sprout/darkroom/coords/vector.hpp>
 #include <sprout/darkroom/rays/ray.hpp>
@@ -142,8 +143,8 @@ namespace sprout {
 					Vec const& normal
 					) const
 				{
-					using std::atan2;
-					using std::sqrt;
+					using sprout::atan2;
+					using sprout::sqrt;
 					return typename intersection<Ray>::type(
 						sprout::tuples::get<zw::does_intersect>(zwo),
 						sprout::tuples::get<zw::distance>(zwo),
@@ -205,7 +206,7 @@ namespace sprout {
 					unit_type const& det_sq
 					) const
 				{
-					using std::sqrt;
+					using sprout::sqrt;
 					return intersect_4(
 						ray,
 						zweitens(
diff --git a/sprout/iterator/sinusoid_iterator.hpp b/sprout/iterator/sinusoid_iterator.hpp
index e73a3bb7..ba8066ac 100644
--- a/sprout/iterator/sinusoid_iterator.hpp
+++ b/sprout/iterator/sinusoid_iterator.hpp
@@ -2,7 +2,6 @@
 #define SPROUT_ITERATOR_SINUSOID_ITERATOR_HPP
 
 #include <cstddef>
-#include <cmath>
 #include <iterator>
 #include <utility>
 #include <type_traits>
@@ -11,6 +10,7 @@
 #include <sprout/iterator/prev.hpp>
 #include <sprout/iterator/distance.hpp>
 #include <sprout/math/constants.hpp>
+#include <sprout/math/sin.hpp>
 
 namespace sprout {
 	//
@@ -94,7 +94,7 @@ namespace sprout {
 			return phase_;
 		}
 		SPROUT_CONSTEXPR reference operator*() const {
-			using std::sin;
+			using sprout::sin;
 			return amplitude_ * sin(d_ * value_type(index_) + phase_);
 		}
 		SPROUT_CONSTEXPR pointer operator->() const {
@@ -135,7 +135,7 @@ namespace sprout {
 			return *this;
 		}
 		SPROUT_CONSTEXPR reference operator[](difference_type n) const {
-			using std::sin;
+			using sprout::sin;
 			return amplitude_ * sin(d_ * value_type(index_ + n) + phase_);
 		}
 		SPROUT_CONSTEXPR sinusoid_iterator next() const {
diff --git a/sprout/math/abs.hpp b/sprout/math/abs.hpp
new file mode 100644
index 00000000..8bdc5c4f
--- /dev/null
+++ b/sprout/math/abs.hpp
@@ -0,0 +1,42 @@
+#ifndef SPROUT_MATH_ABS_HPP
+#define SPROUT_MATH_ABS_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/utility/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <cmath>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			abs(FloatType x) {
+				return x < 0 ? -x : x;
+			}
+		}	// namespace detail
+
+		template<
+			typename FloatType,
+			typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+		>
+		inline SPROUT_CONSTEXPR FloatType
+		abs(FloatType x) {
+#		if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+			using std::abs;
+#		else
+			using sprout::math::detail::abs;
+#		endif
+			return abs(x);
+		}
+	}	// namespace math
+
+	using sprout::math::abs;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_ABS_HPP
diff --git a/sprout/math/acosh.hpp b/sprout/math/acosh.hpp
index d8a750a9..933ba193 100644
--- a/sprout/math/acosh.hpp
+++ b/sprout/math/acosh.hpp
@@ -21,6 +21,7 @@ namespace sprout {
 			inline SPROUT_CONSTEXPR FloatType
 			acosh(FloatType x) {
 				return x < 1 ? std::numeric_limits<FloatType>::quiet_NaN()
+					: x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
 					: sprout::math::detail::log(x + sprout::math::detail::sqrt(x * x - 1))
 					;
 			}
diff --git a/sprout/math/asinh.hpp b/sprout/math/asinh.hpp
index ef0fc6bd..228e7823 100644
--- a/sprout/math/asinh.hpp
+++ b/sprout/math/asinh.hpp
@@ -1,6 +1,7 @@
 #ifndef SPROUT_MATH_ASINH_HPP
 #define SPROUT_MATH_ASINH_HPP
 
+#include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/math/log.hpp>
@@ -19,7 +20,9 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			asinh(FloatType x) {
-				return sprout::math::detail::log(x + sprout::math::detail::sqrt(x * x + 1))
+				return x == std::numeric_limits<FloatType>::infinity() ? std::numeric_limits<FloatType>::infinity()
+					: x == -std::numeric_limits<FloatType>::infinity() ? -std::numeric_limits<FloatType>::infinity()
+					: sprout::math::detail::log(x + sprout::math::detail::sqrt(x * x + 1))
 					;
 			}
 
diff --git a/sprout/math/cos.hpp b/sprout/math/cos.hpp
index aaace216..32c0f7f0 100644
--- a/sprout/math/cos.hpp
+++ b/sprout/math/cos.hpp
@@ -2,6 +2,7 @@
 #define SPROUT_MATH_COS_HPP
 
 #include <cstddef>
+#include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/math/factorial.hpp>
@@ -33,12 +34,16 @@ namespace sprout {
 			inline SPROUT_CONSTEXPR FloatType
 			cos(FloatType x) {
 				typedef double type;
-				return static_cast<FloatType>(sprout::math::detail::cos_impl(
-					static_cast<type>(x),
-					type(1),
-					1,
-					static_cast<type>(x) * static_cast<type>(x)
-					));
+				return x == std::numeric_limits<FloatType>::infinity()
+					|| x == -std::numeric_limits<FloatType>::infinity()
+					? std::numeric_limits<FloatType>::quiet_NaN()
+					: static_cast<FloatType>(sprout::math::detail::cos_impl(
+						static_cast<type>(x),
+						type(1),
+						1,
+						static_cast<type>(x) * static_cast<type>(x)
+						))
+					;
 			}
 
 			template<
diff --git a/sprout/math/fabs.hpp b/sprout/math/fabs.hpp
index 606ed855..068f5c12 100644
--- a/sprout/math/fabs.hpp
+++ b/sprout/math/fabs.hpp
@@ -11,15 +11,6 @@
 namespace sprout {
 	namespace math {
 		namespace detail {
-			template<
-				typename FloatType,
-				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
-			>
-			inline SPROUT_CONSTEXPR FloatType
-			abs(FloatType x) {
-				return x < 0 ? -x : x;
-			}
-
 			template<
 				typename FloatType,
 				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
@@ -39,20 +30,6 @@ namespace sprout {
 			}
 		}	// namespace detail
 
-		template<
-			typename FloatType,
-			typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
-		>
-		inline SPROUT_CONSTEXPR FloatType
-		abs(FloatType x) {
-#		if SPROUT_USE_BUILTIN_CMATH_FUNCTION
-			using std::abs;
-#		else
-			using sprout::math::detail::abs;
-#		endif
-			return abs(x);
-		}
-
 #	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
 		using std::fabs;
 #	else
@@ -60,7 +37,6 @@ namespace sprout {
 #	endif
 	}	// namespace math
 
-	using sprout::math::abs;
 	using sprout::math::fabs;
 }	// namespace sprout
 
diff --git a/sprout/math/fma.hpp b/sprout/math/fma.hpp
new file mode 100644
index 00000000..69af1946
--- /dev/null
+++ b/sprout/math/fma.hpp
@@ -0,0 +1,55 @@
+#ifndef SPROUT_MATH_FMA_HPP
+#define SPROUT_MATH_FMA_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/float_promote.hpp>
+#include <sprout/utility/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <cmath>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			fma(FloatType x, FloatType y, FloatType z) {
+				return x * y + z;
+			}
+
+			template<
+				typename ArithmeticType1,
+				typename ArithmeticType2,
+				typename ArithmeticType3,
+				typename sprout::enabler_if<
+					std::is_arithmetic<ArithmeticType1>::value
+						&& std::is_arithmetic<ArithmeticType2>::value
+						&& std::is_arithmetic<ArithmeticType3>::value
+				>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR typename sprout::math::float_promote<
+				ArithmeticType1, ArithmeticType2, ArithmeticType3
+			>::type
+			fma(ArithmeticType1 x, ArithmeticType2 y, ArithmeticType3 z) {
+				typedef typename sprout::math::float_promote<
+					ArithmeticType1, ArithmeticType2, ArithmeticType3
+				>::type type;
+				return sprout::math::detail::fma(static_cast<type>(x), static_cast<type>(y), static_cast<type>(z));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::fma;
+#	else
+		using sprout::math::detail::fma;
+#	endif
+	}	// namespace math
+
+	using sprout::math::fma;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_FMA_HPP
diff --git a/sprout/math/operations.hpp b/sprout/math/operations.hpp
index df845bd9..209eb73b 100644
--- a/sprout/math/operations.hpp
+++ b/sprout/math/operations.hpp
@@ -1,7 +1,9 @@
 #ifndef SPROUT_MATH_OPERATIONS_HPP
 #define SPROUT_MATH_OPERATIONS_HPP
 
+#include <sprout/math/abs.hpp>
 #include <sprout/math/fabs.hpp>
+#include <sprout/math/fma.hpp>
 #include <sprout/math/fmax.hpp>
 #include <sprout/math/fmin.hpp>
 #include <sprout/math/fdim.hpp>
diff --git a/sprout/numeric/dft/detail/dft_element_gen.hpp b/sprout/numeric/dft/detail/dft_element_gen.hpp
index 193046e1..7957f3f6 100644
--- a/sprout/numeric/dft/detail/dft_element_gen.hpp
+++ b/sprout/numeric/dft/detail/dft_element_gen.hpp
@@ -1,11 +1,12 @@
 #ifndef SPROUT_NUMERIC_DFT_DETAIL_DFT_ELEMENT_GEN_HPP
 #define SPROUT_NUMERIC_DFT_DETAIL_DFT_ELEMENT_GEN_HPP
 
-#include <cmath>
 #include <iterator>
 #include <type_traits>
 #include <sprout/config.hpp>
 #include <sprout/iterator/operation.hpp>
+#include <sprout/math/sin.hpp>
+#include <sprout/math/cos.hpp>
 
 namespace sprout {
 	namespace detail {
@@ -20,8 +21,8 @@ namespace sprout {
 			)
 		{
 			typedef typename std::iterator_traits<InputIterator>::value_type value_type;
-			using std::cos;
-			using std::sin;
+			using sprout::cos;
+			using sprout::sin;
 			return first != last
 				? value + sprout::detail::dft_element_gen(
 					sprout::next(first),
diff --git a/sprout/numeric/dft/fixed/sinusoid.hpp b/sprout/numeric/dft/fixed/sinusoid.hpp
index 0339ef6d..a5585a82 100644
--- a/sprout/numeric/dft/fixed/sinusoid.hpp
+++ b/sprout/numeric/dft/fixed/sinusoid.hpp
@@ -1,7 +1,6 @@
 #ifndef SPROUT_NUMERIC_DFT_FIXED_SINUSOID_HPP
 #define SPROUT_NUMERIC_DFT_FIXED_SINUSOID_HPP
 
-#include <cmath>
 #include <sprout/config.hpp>
 #include <sprout/index_tuple.hpp>
 #include <sprout/container/traits.hpp>
@@ -9,6 +8,7 @@
 #include <sprout/container/indexes.hpp>
 #include <sprout/algorithm/fixed/result_of.hpp>
 #include <sprout/math/constants.hpp>
+#include <sprout/math/sin.hpp>
 
 namespace sprout {
 	namespace fixed {
@@ -26,7 +26,7 @@ namespace sprout {
 				)
 			{
 				typedef typename sprout::container_traits<Container>::value_type value_type;
-				using std::sin;
+				using sprout::sin;
 				return sprout::remake<Container>(
 					cont,
 					size,
diff --git a/sprout/numeric/dft/fixed/spectrum.hpp b/sprout/numeric/dft/fixed/spectrum.hpp
index 89c8c798..7a2324f9 100644
--- a/sprout/numeric/dft/fixed/spectrum.hpp
+++ b/sprout/numeric/dft/fixed/spectrum.hpp
@@ -1,14 +1,14 @@
 #ifndef SPROUT_NUMERIC_DFT_FIXED_SPECTRUM_HPP
 #define SPROUT_NUMERIC_DFT_FIXED_SPECTRUM_HPP
 
-#include <cmath>
-#include <complex>
 #include <sprout/config.hpp>
 #include <sprout/index_tuple.hpp>
 #include <sprout/container/traits.hpp>
 #include <sprout/container/functions.hpp>
 #include <sprout/iterator/operation.hpp>
 #include <sprout/algorithm/fixed/result_of.hpp>
+#include <sprout/complex.hpp>
+#include <sprout/math/sqrt.hpp>
 #include HDR_ITERATOR_SSCRISK_CEL_OR_SPROUT
 
 namespace sprout {
@@ -26,9 +26,9 @@ namespace sprout {
 				typename sprout::container_traits<Result>::size_type input_size
 				)
 			{
-				using std::sqrt;
-				using std::real;
-				using std::imag;
+				using sprout::sqrt;
+				using sprout::real;
+				using sprout::imag;
 				return sprout::remake<Result>(
 					result,
 					size,
diff --git a/sprout/random/binomial_distribution.hpp b/sprout/random/binomial_distribution.hpp
index f4108447..1f5b81ad 100644
--- a/sprout/random/binomial_distribution.hpp
+++ b/sprout/random/binomial_distribution.hpp
@@ -7,6 +7,10 @@
 #include <stdexcept>
 #include <sprout/config.hpp>
 #include <sprout/array.hpp>
+#include <sprout/math/abs.hpp>
+#include <sprout/math/log.hpp>
+#include <sprout/math/pow.hpp>
+#include <sprout/math/sqrt.hpp>
 #include <sprout/random/random_result.hpp>
 #include <sprout/random/uniform_01.hpp>
 
@@ -155,7 +159,7 @@ namespace sprout {
 				return init_btrd_5(t, p, r, nr, npq, sqrt_npq, RealType(1.15) + RealType(2.53) * sqrt_npq);
 			}
 			static SPROUT_CONSTEXPR btrd_type init_btrd_3(IntType t, RealType p, RealType r, RealType nr, RealType npq) {
-				using std::sqrt;
+				using sprout::sqrt;
 				return init_btrd_4(t, p, r, nr, npq, sqrt(npq));
 			}
 			static SPROUT_CONSTEXPR btrd_type init_btrd_2(IntType t, RealType p, RealType r) {
@@ -168,7 +172,7 @@ namespace sprout {
 				return init_btrd_1(init_t(t), init_p(p));
 			}
 			static SPROUT_CONSTEXPR RealType init_q_n(IntType t, RealType p) {
-				using std::pow;
+				using sprout::pow;
 				return pow(1 - init_p(p), static_cast<RealType>(init_t(t)));
 			}
 			static SPROUT_CONSTEXPR bool init_use_inversion(IntType t, RealType p) {
@@ -230,7 +234,7 @@ namespace sprout {
 			}
 			template<typename Engine>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_10(Engine const& eng, RealType v, IntType k, IntType nm, RealType h, IntType nk) const {
-				using std::log;
+				using sprout::log;
 				return v <= h + (t_ + 1) * log(static_cast<RealType>(nm) / nk) + (k + RealType(0.5)) * log(nk * btrd_.r / (k + 1))- fc(k)- fc(t_ - k)
 					? sprout::random::random_result<Engine, binomial_distribution>(k, eng, *this)
 					: generate(eng)
@@ -238,7 +242,7 @@ namespace sprout {
 			}
 			template<typename Engine>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_9(Engine const& eng, RealType v, IntType k, IntType nm) const {
-				using std::log;
+				using sprout::log;
 				return generate_10(eng, v, k, nm, (m_ + RealType(0.5)) * log((m_ + 1) / (btrd_.r * nm)) + fc(m_) + fc(t_ - m_), t_ - k + 1);
 			}
 			template<typename Engine>
@@ -278,7 +282,7 @@ namespace sprout {
 			}
 			template<typename Engine>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_6(Engine const& eng, RealType v, IntType k, RealType km) const {
-				using std::log;
+				using sprout::log;
 				return km <= 15
 					? generate_7(eng, v, k)
 					: generate_8(eng, log(v), k, (km / btrd_.npq) * (((km / RealType(3.0) + RealType(0.625)) * km + RealType(1.0) / 6) / btrd_.npq + RealType(0.5)), -km * km / (2 * btrd_.npq))
@@ -286,7 +290,7 @@ namespace sprout {
 			}
 			template<typename Engine>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_5(Engine const& eng, RealType v, RealType u, RealType us, IntType k) const {
-				using std::abs;
+				using sprout::abs;
 				return k < 0 || k > t_
 					? generate(eng)
 					: generate_6(eng, v * btrd_.alpha / (btrd_.a / (us * us) + btrd_.b), k, abs(k - m_))
@@ -299,7 +303,7 @@ namespace sprout {
 			}
 			template<typename Engine>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_3(Engine const& eng, RealType v, RealType u) const {
-				using std::abs;
+				using sprout::abs;
 				return generate_4(eng, v, u, 0.5 - abs(u));
 			}
 			template<typename Engine, typename Random>
@@ -320,7 +324,7 @@ namespace sprout {
 			template<typename Engine>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, binomial_distribution> generate_1_1(Engine const& eng, RealType u) const {
 				using std::floor;
-				using std::abs;
+				using sprout::abs;
 				return sprout::random::random_result<Engine, binomial_distribution>(
 					static_cast<IntType>(floor((2 * btrd_.a / (RealType(0.5) - abs(u)) + btrd_.b) * u + btrd_.c)),
 					eng,
diff --git a/sprout/random/geometric_distribution.hpp b/sprout/random/geometric_distribution.hpp
index 1a8d9c05..6efef849 100644
--- a/sprout/random/geometric_distribution.hpp
+++ b/sprout/random/geometric_distribution.hpp
@@ -6,6 +6,7 @@
 #include <limits>
 #include <stdexcept>
 #include <sprout/config.hpp>
+#include <sprout/math/log.hpp>
 #include <sprout/random/random_result.hpp>
 #include <sprout/random/uniform_01.hpp>
 
@@ -96,7 +97,7 @@ namespace sprout {
 		private:
 		public:
 			static SPROUT_CONSTEXPR RealType init_log_1mp(RealType p) {
-				using std::log;
+				using sprout::log;
 				return log(1 - p);
 			}
 		private:
@@ -106,7 +107,7 @@ namespace sprout {
 		private:
 			template<typename Engine, typename Random>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, geometric_distribution> generate_1(Random const& rnd) const {
-				using std::log;
+				using sprout::log;
 				using std::floor;
 				return sprout::random::random_result<Engine, geometric_distribution>(
 					static_cast<IntType>(floor(log(RealType(1) - rnd.result()) / log_1mp_)),
diff --git a/sprout/random/normal_distribution.hpp b/sprout/random/normal_distribution.hpp
index 0b6bb94c..3e403d31 100644
--- a/sprout/random/normal_distribution.hpp
+++ b/sprout/random/normal_distribution.hpp
@@ -1,13 +1,16 @@
 #ifndef SPROUT_RANDOM_NORMAL_DISTRIBUTION_HPP
 #define SPROUT_RANDOM_NORMAL_DISTRIBUTION_HPP
 
-#include <cmath>
 #include <limits>
 #include <ios>
 #include <istream>
 #include <stdexcept>
 #include <sprout/config.hpp>
 #include <sprout/math/constants.hpp>
+#include <sprout/math/sin.hpp>
+#include <sprout/math/cos.hpp>
+#include <sprout/math/log.hpp>
+#include <sprout/math/sqrt.hpp>
 #include <sprout/random/uniform_01.hpp>
 #include <sprout/random/random_result.hpp>
 
@@ -121,8 +124,8 @@ namespace sprout {
 			{}
 			template<typename Engine>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, normal_distribution> generate_2(Engine const& eng, RealType r1, RealType r2, RealType cached_rho, bool valid) const {
-				using std::sin;
-				using std::cos;
+				using sprout::sin;
+				using sprout::cos;
 				return sprout::random::random_result<Engine, normal_distribution>(
 					cached_rho
 						* (valid
@@ -144,8 +147,8 @@ namespace sprout {
 			}
 			template<typename Engine, typename Random>
 			SPROUT_CONSTEXPR sprout::random::random_result<Engine, normal_distribution> generate_1_1(RealType r1, Random const& rnd) const {
-				using std::sqrt;
-				using std::log;
+				using sprout::sqrt;
+				using sprout::log;
 				return generate_2(rnd.engine(), r1, rnd.result(), sqrt(-result_type(2) * log(result_type(1) - rnd.result())), true);
 			}
 			template<typename Engine, typename Random>
diff --git a/sprout/string/float_to_string.hpp b/sprout/string/float_to_string.hpp
index 9e7c33ad..8a1f9a6a 100644
--- a/sprout/string/float_to_string.hpp
+++ b/sprout/string/float_to_string.hpp
@@ -2,7 +2,6 @@
 #define SPROUT_STRING_FLOAT_TO_STRING_HPP
 
 #include <cstddef>
-#include <cmath>
 #include <limits>
 #include <type_traits>
 #include <sprout/config.hpp>