From 29a55bf31d59a83eed594c28c8682b3eccca805c Mon Sep 17 00:00:00 2001
From: bolero-MURAKAMI <bolero.murakami@gmail.com>
Date: Fri, 4 May 2012 16:40:25 +0900
Subject: [PATCH] add sprout::exp, log

---
 sprout/math/constants.hpp   |  7 ++++
 sprout/math/cos.hpp         |  2 +-
 sprout/math/cosh.hpp        |  2 +-
 sprout/math/exp.hpp         | 64 +++++++++++++++++++++++++++++
 sprout/math/exponential.hpp |  7 ++++
 sprout/math/functions.hpp   |  1 +
 sprout/math/log.hpp         | 81 +++++++++++++++++++++++++++++++++++++
 sprout/math/sinh.hpp        |  2 +-
 8 files changed, 163 insertions(+), 3 deletions(-)
 create mode 100644 sprout/math/exp.hpp
 create mode 100644 sprout/math/exponential.hpp
 create mode 100644 sprout/math/log.hpp

diff --git a/sprout/math/constants.hpp b/sprout/math/constants.hpp
index a743395c..da7de011 100644
--- a/sprout/math/constants.hpp
+++ b/sprout/math/constants.hpp
@@ -19,6 +19,13 @@ namespace sprout {
 		inline SPROUT_CONSTEXPR T pi_div_two() {
 			return 1.570796326794896619231321691639751442098584699687552910487472L;
 		}
+		//
+		// root_two
+		//
+		template<typename T>
+		inline SPROUT_CONSTEXPR T root_two() {
+			return 1.414213562373095048801688724209698078569671875376948073L;
+		}
 	}	// namespace math
 }	// namespace sprout
 
diff --git a/sprout/math/cos.hpp b/sprout/math/cos.hpp
index 3b0443b8..aaace216 100644
--- a/sprout/math/cos.hpp
+++ b/sprout/math/cos.hpp
@@ -19,7 +19,7 @@ namespace sprout {
 				return 2 * n > sprout::math::factorial_limit<T>() ? tmp
 					: sprout::math::detail::cos_impl(
 						x,
-						tmp + (n % 2 ? -1 : 1) / sprout::math::factorial<T>(2 * n) * x2n,
+						tmp + (n % 2 ? -1 : 1) * x2n / sprout::math::factorial<T>(2 * n),
 						n + 1,
 						x2n * x * x
 						)
diff --git a/sprout/math/cosh.hpp b/sprout/math/cosh.hpp
index 359a46bd..ff205d2a 100644
--- a/sprout/math/cosh.hpp
+++ b/sprout/math/cosh.hpp
@@ -19,7 +19,7 @@ namespace sprout {
 				return 2 * n > sprout::math::factorial_limit<T>() ? tmp
 					: sprout::math::detail::cosh_impl(
 						x,
-						tmp + 1 / sprout::math::factorial<T>(2 * n) * x2n,
+						tmp + x2n / sprout::math::factorial<T>(2 * n),
 						n + 1,
 						x2n * x * x
 						)
diff --git a/sprout/math/exp.hpp b/sprout/math/exp.hpp
new file mode 100644
index 00000000..78acbb01
--- /dev/null
+++ b/sprout/math/exp.hpp
@@ -0,0 +1,64 @@
+#ifndef SPROUT_MATH_EXP_HPP
+#define SPROUT_MATH_EXP_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
+			exp_impl(T x, T tmp, std::size_t n, T xn) {
+				return n > sprout::math::factorial_limit<T>() ? tmp
+					: sprout::math::detail::exp_impl(
+						x,
+						tmp + xn / sprout::math::factorial<T>(n),
+						n + 1,
+						xn * x
+						)
+					;
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			exp(FloatType x) {
+				typedef double type;
+				return static_cast<FloatType>(sprout::math::detail::exp_impl(
+					static_cast<type>(x),
+					type(1),
+					1,
+					static_cast<type>(x)
+					));
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			exp(IntType x) {
+				return sprout::math::detail::exp(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::exp;
+#	else
+		using sprout::math::detail::exp;
+#	endif
+	}	// namespace math
+
+	using sprout::math::exp;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_EXP_HPP
diff --git a/sprout/math/exponential.hpp b/sprout/math/exponential.hpp
new file mode 100644
index 00000000..b441aee3
--- /dev/null
+++ b/sprout/math/exponential.hpp
@@ -0,0 +1,7 @@
+#ifndef SPROUT_MATH_EXPONENTIAL_HPP
+#define SPROUT_MATH_EXPONENTIAL_HPP
+
+#include <sprout/math/exp.hpp>
+#include <sprout/math/log.hpp>
+
+#endif	// #ifndef SPROUT_MATH_EXPONENTIAL_HPP
diff --git a/sprout/math/functions.hpp b/sprout/math/functions.hpp
index 8e5462fe..5d984352 100644
--- a/sprout/math/functions.hpp
+++ b/sprout/math/functions.hpp
@@ -2,6 +2,7 @@
 #define SPROUT_MATH_FUNCTIONS_HPP
 
 #include <sprout/config.hpp>
+#include <sprout/math/exponential.hpp>
 #include <sprout/math/power.hpp>
 #include <sprout/math/trigonometric.hpp>
 #include <sprout/math/hyperbolic.hpp>
diff --git a/sprout/math/log.hpp b/sprout/math/log.hpp
new file mode 100644
index 00000000..a59fb3d9
--- /dev/null
+++ b/sprout/math/log.hpp
@@ -0,0 +1,81 @@
+#ifndef SPROUT_MATH_LOG_HPP
+#define SPROUT_MATH_LOG_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
+			log_impl_2(T x, T tmp, std::size_t n, T xn) {
+				return n > sprout::math::factorial_limit<T>() ? tmp
+					: sprout::math::detail::log_impl_2(
+						x,
+						tmp + (n % 2 ? 1 : -1) * xn / n,
+						n + 1,
+						xn * x
+						)
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			log_impl_1(T x) {
+				return sprout::math::detail::log_impl_2(
+					x,
+					x,
+					2,
+					x * x
+					);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			log_impl(T x) {
+				return !(x > sprout::math::root_two<T>()) ? sprout::math::detail::log_impl_1(x - 1)
+					: 2 * sprout::math::detail::log_impl(sprout::math::detail::sqrt(x))
+					;
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			log(FloatType x) {
+				typedef double type;
+				return !(x > 0) ? -std::numeric_limits<FloatType>::infinity()
+					: static_cast<FloatType>(sprout::math::detail::log_impl(x))
+					;
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			log(IntType x) {
+				return sprout::math::detail::log(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::log;
+#	else
+		using sprout::math::detail::log;
+#	endif
+	}	// namespace math
+
+	using sprout::math::log;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_LOG_HPP
diff --git a/sprout/math/sinh.hpp b/sprout/math/sinh.hpp
index b2ae1750..741a6b32 100644
--- a/sprout/math/sinh.hpp
+++ b/sprout/math/sinh.hpp
@@ -19,7 +19,7 @@ namespace sprout {
 				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,
+						tmp + x2n1 / sprout::math::factorial<T>(2 * n + 1),
 						n + 1,
 						x2n1 * x * x
 						)