add sprout::sinh, cosh, tanh, sqrt

sprout/cmath.hpp

@@ -2,6 +2,6 @@
 #define SPROUT_CMATH_HPP
 
 #include <sprout/config.hpp>
-#include <sprout/math/trigonometric.hpp>
+#include <sprout/math/functions.hpp>
 
 #endif	// #ifndef SPROUT_CMATH_HPP

sprout/math/cosh.hpp

@@ -0,0 +1,64 @@
+#ifndef SPROUT_MATH_COSH_HPP
+#define SPROUT_MATH_COSH_HPP
+
+#include <cstddef>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/factorial.hpp>
+#include <sprout/utility/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <cmath>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			cosh_impl(T x, T tmp, std::size_t n, T x2n) {
+				return 2 * n > sprout::math::factorial_limit<T>() ? tmp
+					: sprout::math::detail::cosh_impl(
+						x,
+						tmp + 1 / sprout::math::factorial<T>(2 * n) * x2n,
+						n + 1,
+						x2n * x * x
+						)
+					;
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			cosh(FloatType x) {
+				typedef double type;
+				return static_cast<FloatType>(sprout::math::detail::cosh_impl(
+					static_cast<type>(x),
+					type(1),
+					1,
+					static_cast<type>(x) * static_cast<type>(x)
+					));
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			cosh(IntType x) {
+				return sprout::math::detail::cosh(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::cosh;
+#	else
+		using sprout::math::detail::cosh;
+#	endif
+	}	// namespace math
+
+	using sprout::math::cosh;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_COSH_HPP

sprout/math/functions.hpp

@@ -0,0 +1,9 @@
+#ifndef SPROUT_MATH_FUNCTIONS_HPP
+#define SPROUT_MATH_FUNCTIONS_HPP
+
+#include <sprout/config.hpp>
+#include <sprout/math/power.hpp>
+#include <sprout/math/trigonometric.hpp>
+#include <sprout/math/hyperbolic.hpp>
+
+#endif	// #ifndef SPROUT_MATH_FUNCTIONS_HPP

sprout/math/hyperbolic.hpp

@@ -0,0 +1,8 @@
+#ifndef SPROUT_MATH_HYPERBOLIC_HPP
+#define SPROUT_MATH_HYPERBOLIC_HPP
+
+#include <sprout/math/sinh.hpp>
+#include <sprout/math/cosh.hpp>
+#include <sprout/math/tanh.hpp>
+
+#endif	// #ifndef SPROUT_MATH_HYPERBOLIC_HPP

sprout/math/power.hpp

@@ -0,0 +1,6 @@
+#ifndef SPROUT_MATH_POWER_HPP
+#define SPROUT_MATH_POWER_HPP
+
+#include <sprout/math/sqrt.hpp>
+
+#endif	// #ifndef SPROUT_MATH_POWER_HPP

sprout/math/sinh.hpp

@@ -0,0 +1,64 @@
+#ifndef SPROUT_MATH_SINH_HPP
+#define SPROUT_MATH_SINH_HPP
+
+#include <cstddef>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/factorial.hpp>
+#include <sprout/utility/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <cmath>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			sinh_impl(T x, T tmp, std::size_t n, T x2n1) {
+				return 2 * n + 1 > sprout::math::factorial_limit<T>() ? tmp
+					: sprout::math::detail::sinh_impl(
+						x,
+						tmp + 1 / sprout::math::factorial<T>(2 * n + 1) * x2n1,
+						n + 1,
+						x2n1 * x * x
+						)
+					;
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			sinh(FloatType x) {
+				typedef double type;
+				return static_cast<FloatType>(sprout::math::detail::sinh_impl(
+					static_cast<type>(x),
+					static_cast<type>(x),
+					1,
+					static_cast<type>(x) * static_cast<type>(x) * static_cast<type>(x)
+					));
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			sinh(IntType x) {
+				return sprout::math::detail::sinh(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::sinh;
+#	else
+		using sprout::math::detail::sinh;
+#	endif
+	}	// namespace math
+
+	using sprout::math::sinh;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_SINH_HPP

sprout/math/sqrt.hpp

@@ -0,0 +1,72 @@
+#ifndef SPROUT_MATH_SQRT_HPP
+#define SPROUT_MATH_SQRT_HPP
+
+#include <limits>
+#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 T>
+			inline SPROUT_CONSTEXPR T
+			sqrt_impl_1(T x, T s, T s2) {
+				return !(s < s2) ? s2
+					: sprout::math::detail::sqrt_impl_1(
+						x,
+						(x / s + s) / 2,
+						s
+						)
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			sqrt_impl(T x, T s) {
+				return sprout::math::detail::sqrt_impl_1(
+						x,
+						(x / s + s) / 2,
+						s
+						)
+					;
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			sqrt(FloatType x) {
+				typedef double type;
+				return x < 0 ? std::numeric_limits<FloatType>::quiet_NaN()
+					: x == 0 ? type(0)
+					: static_cast<FloatType>(sprout::math::detail::sqrt_impl(
+						static_cast<type>(x),
+						x > 1 ? static_cast<type>(x) : type(1)
+						));
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			sqrt(IntType x) {
+				return sprout::math::detail::sqrt(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::sqrt;
+#	else
+		using sprout::math::detail::sqrt;
+#	endif
+	}	// namespace math
+
+	using sprout::math::sqrt;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_SQRT_HPP

sprout/math/tanh.hpp

@@ -0,0 +1,45 @@
+#ifndef SPROUT_MATH_TANH_HPP
+#define SPROUT_MATH_TANH_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/sinh.hpp>
+#include <sprout/math/cosh.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
+			tanh(FloatType x) {
+				return sprout::math::detail::sinh(x) / sprout::math::detail::cosh(x);
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			tanh(IntType x) {
+				return sprout::math::detail::tanh(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::tanh;
+#	else
+		using sprout::math::detail::tanh;
+#	endif
+	}	// namespace math
+
+	using sprout::math::tanh;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_TANH_HPP