add sprout::atan

sprout/complex.hpp

@@ -361,7 +361,7 @@ namespace sprout {
 	namespace detail {
 		template<typename T>
 		SPROUT_CONSTEXPR sprout::complex<T> acos_impl(sprout::complex<T> const& t) {
-			return sprout::complex<T>(sprout::math::pi_div_two<T>() - t.real(), -t.imag());
+			return sprout::complex<T>(sprout::math::half_pi<T>() - t.real(), -t.imag());
 		}
 	}	// namespace detail
 	template<typename T>

sprout/darkroom/objects/sphere.hpp

@@ -164,7 +164,7 @@ namespace sprout {
 										+ sprout::darkroom::coords::z(normal) * sprout::darkroom::coords::z(normal)
 									)
 								)
-								/ sprout::math::pi_div_two<unit_type>()
+								/ sprout::math::half_pi<unit_type>()
 							)
 						);
 				}

sprout/math/atan.hpp

@@ -0,0 +1,83 @@
+#ifndef SPROUT_MATH_ATAN_HPP
+#define SPROUT_MATH_ATAN_HPP
+
+#include <cstddef>
+#include <type_traits>
+#include <sprout/config.hpp>
+#include <sprout/math/constants.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
+			atan_impl_2(T x, T tmp, std::size_t n, T x2n1) {
+				return n > sprout::math::factorial_limit<T>() ? tmp
+					: sprout::math::detail::atan_impl_2(
+						x,
+						tmp + (n % 2 ? -1 : 1) * x2n1 / (2 * n + 1),
+						n + 1,
+						x2n1 * x * x
+						)
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			atan_impl_1(T x) {
+				return sprout::math::detail::atan_impl_2(
+					x,
+					x,
+					1,
+					x * x * x
+					);
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			atan_impl(T x) {
+				return x > sprout::math::root_two<T>() + 1
+						? sprout::math::half_pi<T>() - sprout::math::detail::atan_impl_1(1 / x)
+					: x > sprout::math::root_two<T>() - 1
+						? sprout::math::quarter_pi<T>() + sprout::math::detail::atan_impl_1((x - 1) / (x + 1))
+					: sprout::math::detail::atan_impl_1(x)
+					;
+			}
+
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			atan(FloatType x) {
+				typedef double type;
+				return static_cast<FloatType>(
+					x < 0 ? -sprout::math::detail::atan_impl(static_cast<type>(-x))
+						: sprout::math::detail::atan_impl(static_cast<type>(x))
+					);
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			atan(IntType x) {
+				return sprout::math::detail::atan(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+#	if SPROUT_USE_BUILTIN_CMATH_FUNCTION
+		using std::atan;
+#	else
+		using sprout::math::detail::atan;
+#	endif
+	}	// namespace math
+
+	using sprout::math::atan;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_ATAN_HPP

sprout/math/constants.hpp

@@ -13,13 +13,20 @@ namespace sprout {
 			return 3.141592653589793238462643383279502884197169399375105820974944L;
 		}
 		//
-		// pi_div_two
+		// half_pi
 		//
 		template<typename T>
-		inline SPROUT_CONSTEXPR T pi_div_two() {
+		inline SPROUT_CONSTEXPR T half_pi() {
 			return 1.570796326794896619231321691639751442098584699687552910487472L;
 		}
 		//
+		// quarter_pi
+		//
+		template<typename T>
+		inline SPROUT_CONSTEXPR T quarter_pi() {
+			return 0.785398163397448309615660845819875721049292349843776455243736L;
+		}
+		//
 		// root_two
 		//
 		template<typename T>

sprout/math/sin.hpp

@@ -19,7 +19,7 @@ namespace sprout {
 			>
 			inline SPROUT_CONSTEXPR FloatType
 			sin(FloatType x) {
-				return -sprout::math::detail::cos(x + sprout::math::pi_div_two<FloatType>());
+				return -sprout::math::detail::cos(x + sprout::math::half_pi<FloatType>());
 			}
 
 			template<

sprout/math/trigonometric.hpp

@@ -4,5 +4,6 @@
 #include <sprout/math/sin.hpp>
 #include <sprout/math/cos.hpp>
 #include <sprout/math/tan.hpp>
+#include <sprout/math/atan.hpp>
 
 #endif	// #ifndef SPROUT_MATH_TRIGONOMETRIC_HPP