Sprout/sprout/math/atan.hpp

#ifndef SPROUT_MATH_ATAN_HPP
#define SPROUT_MATH_ATAN_HPP

#include <cstddef>
#include <limits>
#include <type_traits>
#include <sprout/config.hpp>
#include <sprout/detail/pow.hpp>
#include <sprout/math/detail/config.hpp>
#include <sprout/math/detail/float_compute.hpp>
#include <sprout/math/constants.hpp>
#include <sprout/math/factorial.hpp>
#include <sprout/math/copysign.hpp>
#include <sprout/type_traits/enabler_if.hpp>

namespace sprout {
	namespace math {
		namespace detail {
			template<typename T>
			inline SPROUT_CONSTEXPR T
			atan_impl_1(T x, std::size_t n, std::size_t last) {
				return last - n == 1
					? (n % 2 ? -1 : 1) * sprout::detail::pow_n(x, 2 * n + 1) / (2 * n + 1)
					: sprout::math::detail::atan_impl_1(x, n, n + (last - n) / 2)
						+ sprout::math::detail::atan_impl_1(x, n + (last - n) / 2, last)
					;
			}
			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, 0, sprout::math::factorial_limit<T>() + 1)
					: x > sprout::math::root_two<T>() - 1
						? sprout::math::quarter_pi<T>() + sprout::math::detail::atan_impl_1((x - 1) / (x + 1), 0, sprout::math::factorial_limit<T>() + 1)
					: x + sprout::math::detail::atan_impl_1(x, 1, sprout::math::factorial_limit<T>() + 1)
					;
			}

			template<
				typename FloatType,
				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
			>
			inline SPROUT_CONSTEXPR FloatType
			atan(FloatType x) {
				return x == std::numeric_limits<FloatType>::infinity() ? sprout::math::half_pi<FloatType>()
					: x == -std::numeric_limits<FloatType>::infinity() ? -sprout::math::half_pi<FloatType>()
#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
					: std::atan(x)
#else
					: x == 0 ? sprout::math::copysign(FloatType(0), x)
					: static_cast<FloatType>(
						x < 0 ? -sprout::math::detail::atan_impl(static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(-x))
							: sprout::math::detail::atan_impl(static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x))
						)
#endif
					;
			}
			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

		using sprout::math::detail::atan;
	}	// namespace math

	using sprout::math::atan;
}	// namespace sprout

#endif	// #ifndef SPROUT_MATH_ATAN_HPP