From 28f22ab73dbd7e1b8820688ddf9f63f6be88ebdd Mon Sep 17 00:00:00 2001
From: bolero-MURAKAMI <bolero.murakami@gmail.com>
Date: Fri, 4 May 2012 23:23:39 +0900
Subject: [PATCH] add sprout::asin, acos, pow

---
 sprout/math/acos.hpp          | 45 ++++++++++++++++++
 sprout/math/asin.hpp          | 88 ++++++++++++++++++++++++++++++++++
 sprout/math/pow.hpp           | 89 +++++++++++++++++++++++++++++++++++
 sprout/math/power.hpp         |  1 +
 sprout/math/trigonometric.hpp |  2 +
 5 files changed, 225 insertions(+)
 create mode 100644 sprout/math/acos.hpp
 create mode 100644 sprout/math/asin.hpp
 create mode 100644 sprout/math/pow.hpp

diff --git a/sprout/math/acos.hpp b/sprout/math/acos.hpp
new file mode 100644
index 00000000..405564dc
--- /dev/null
+++ b/sprout/math/acos.hpp
@@ -0,0 +1,45 @@
+#ifndef SPROUT_MATH_ACOS_HPP
+#define SPROUT_MATH_ACOS_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/asin.hpp>
+#include <sprout/math/constants.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
+			acos(FloatType x) {
+				return sprout::math::half_pi<FloatType>() - sprout::math::detail::asin(x);
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			acos(IntType x) {
+				return sprout::math::detail::acos(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::acos;
+#	else
+		using sprout::math::detail::acos;
+#	endif
+	}	// namespace math
+
+	using sprout::math::acos;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_ACOS_HPP
diff --git a/sprout/math/asin.hpp b/sprout/math/asin.hpp
new file mode 100644
index 00000000..f97b043f
--- /dev/null
+++ b/sprout/math/asin.hpp
@@ -0,0 +1,88 @@
+#ifndef SPROUT_MATH_ASIN_HPP
+#define SPROUT_MATH_ASIN_HPP
+
+#include <cstddef>
+#include <limits>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/constants.hpp>
+#include <sprout/math/factorial.hpp>
+#include <sprout/math/sqrt.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
+			asin_impl_2(T x, T tmp, std::size_t n, T x2n1, T _4n) {
+				return 2 * n > sprout::math::factorial_limit<T>() ? tmp
+					: sprout::math::detail::asin_impl_2(
+						x,
+						tmp + sprout::math::factorial<T>(2 * n)
+							/ _4n / sprout::math::factorial<T>(n) / sprout::math::factorial<T>(n) / (2 * n + 1)
+							* x2n1
+							,
+						n + 1,
+						x2n1 * x * x,
+						_4n * 4
+						)
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			asin_impl_1(T x) {
+				return sprout::math::detail::asin_impl_2(
+					x,
+					x,
+					1,
+					x * x * x,
+					T(4)
+					);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			asin_impl(T x) {
+				return x > sprout::math::half_root_two<T>()
+						? sprout::math::half_pi<T>() - sprout::math::detail::asin_impl_1(sprout::math::detail::sqrt(1 - x * x))
+					: sprout::math::detail::asin_impl_1(x)
+					;
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			asin(FloatType x) {
+				typedef double type;
+				return x > 1 || x < -1 ? std::numeric_limits<FloatType>::quiet_NaN()
+					: x < 0 ? -static_cast<FloatType>(sprout::math::detail::asin_impl(static_cast<type>(-x)))
+					: static_cast<FloatType>(sprout::math::detail::asin_impl(static_cast<type>(x)))
+					;
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			asin(IntType x) {
+				return sprout::math::detail::asin(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::asin;
+#	else
+		using sprout::math::detail::asin;
+#	endif
+	}	// namespace math
+
+	using sprout::math::asin;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_ASIN_HPP
diff --git a/sprout/math/pow.hpp b/sprout/math/pow.hpp
new file mode 100644
index 00000000..841ec18a
--- /dev/null
+++ b/sprout/math/pow.hpp
@@ -0,0 +1,89 @@
+#ifndef SPROUT_MATH_POW_HPP
+#define SPROUT_MATH_POW_HPP
+
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/exp.hpp>
+#include <sprout/math/log.hpp>
+#include <sprout/math/constants.hpp>
+#include <sprout/utility/enabler_if.hpp>
+#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+#	include <cmath>
+#endif
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename X, typename Y, typename Enable = void>
+			struct pow_promoted {};
+			template<typename X, typename Y>
+			struct pow_promoted<
+				X,
+				Y,
+				typename std::enable_if<
+					std::is_arithmetic<X>::value && std::is_arithmetic<Y>::value
+						&& (std::is_same<X, long double>::value || std::is_same<Y, long double>::value)
+				>::type
+			> {
+			public:
+				typedef long double type;
+			};
+			template<typename X, typename Y>
+			struct pow_promoted<
+				X,
+				Y,
+				typename std::enable_if<
+					std::is_arithmetic<X>::value && std::is_arithmetic<Y>::value
+						&& !(std::is_same<X, long double>::value || std::is_same<Y, long double>::value)
+				>::type
+			> {
+			public:
+				typedef double type;
+			};
+		}	// namespace detail
+		//
+		// pow_promoted
+		//
+		template<typename X, typename Y>
+		struct pow_promoted
+			: public sprout::math::detail::pow_promoted<
+				typename std::remove_cv<X>::type,
+				typename std::remove_cv<Y>::type
+			>
+		{};
+
+		namespace detail {
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			pow(FloatType x, FloatType y) {
+				return sprout::math::detail::exp(y * sprout::math::detail::log(x));
+			}
+
+			template<
+				typename ArithmeticType1,
+				typename ArithmeticType2,
+				typename sprout::enabler_if<
+					std::is_arithmetic<ArithmeticType1>::value && std::is_arithmetic<ArithmeticType2>::value
+				>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR typename sprout::math::pow_promoted<ArithmeticType1, ArithmeticType2>::type
+			pow(ArithmeticType1 x, ArithmeticType2 y) {
+				typedef typename sprout::math::pow_promoted<ArithmeticType1, ArithmeticType2>::type type;
+				return sprout::math::detail::pow(static_cast<type>(x), static_cast<type>(y));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::pow;
+#	else
+		using sprout::math::detail::pow;
+#	endif
+	}	// namespace math
+
+	using sprout::math::pow;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_POW_HPP
diff --git a/sprout/math/power.hpp b/sprout/math/power.hpp
index ab356abd..ebcd6e55 100644
--- a/sprout/math/power.hpp
+++ b/sprout/math/power.hpp
@@ -2,5 +2,6 @@
 #define SPROUT_MATH_POWER_HPP
 
 #include <sprout/math/sqrt.hpp>
+#include <sprout/math/pow.hpp>
 
 #endif	// #ifndef SPROUT_MATH_POWER_HPP
diff --git a/sprout/math/trigonometric.hpp b/sprout/math/trigonometric.hpp
index e4203bfa..299062a1 100644
--- a/sprout/math/trigonometric.hpp
+++ b/sprout/math/trigonometric.hpp
@@ -4,6 +4,8 @@
 #include <sprout/math/sin.hpp>
 #include <sprout/math/cos.hpp>
 #include <sprout/math/tan.hpp>
+#include <sprout/math/asin.hpp>
+#include <sprout/math/acos.hpp>
 #include <sprout/math/atan.hpp>
 
 #endif	// #ifndef SPROUT_MATH_TRIGONOMETRIC_HPP