fix math functions

sprout/math/erf.hpp

@@ -0,0 +1,69 @@
+#ifndef SPROUT_MATH_ERF_HPP
+#define SPROUT_MATH_ERF_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/factorial.hpp>
+#include <sprout/math/constants.hpp>
+#include <sprout/type_traits/enabler_if.hpp>
+
+namespace sprout {
+	namespace math {
+		namespace detail {
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			erf_impl_1(T x, std::size_t n, std::size_t last) {
+				return last - n == 1
+					? (n % 2 ? -1 : 1) / sprout::math::factorial<T>(n) / (2 * n + 1) * sprout::detail::pow_n(x, 2 * n + 1)
+					: sprout::math::detail::erf_impl_1(x, n, n + (last - n) / 2)
+						+ sprout::math::detail::erf_impl_1(x, n + (last - n) / 2, last)
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			erf_impl(T x) {
+				return sprout::math::two_div_root_pi<T>()
+					* (x + sprout::math::detail::erf_impl_1(x, 1, sprout::math::factorial_limit<T>() + 1))
+					;
+			}
+			template<typename T>
+			inline SPROUT_CONSTEXPR T
+			erf_impl(T x2, T a) {
+				return T(1) - sprout::math::exp(-x2 / (T(1) + a * x2) * (sprout::math::quarter_pi<T>() + a * x2));
+			}
+			template<
+				typename FloatType,
+				typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR FloatType
+			erf(FloatType x) {
+				typedef typename sprout::math::detail::float_compute<FloatType>::type type;
+				return x == 0 ? FloatType(0)
+					: x == std::numeric_limits<FloatType>::infinity() ? FloatType(1)
+					: x == -std::numeric_limits<FloatType>::infinity() ? FloatType(-1)
+					: static_cast<FloatType>(sprout::math::detail::erf_impl(static_cast<type>(x)))
+					;
+			}
+
+			template<
+				typename IntType,
+				typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
+			>
+			inline SPROUT_CONSTEXPR double
+			erf(IntType x) {
+				return sprout::math::detail::erf(static_cast<double>(x));
+			}
+		}	// namespace detail
+
+		using NS_SPROUT_MATH_DETAIL::erf;
+	}	// namespace math
+
+	using sprout::math::erf;
+}	// namespace sprout
+
+#endif	// #ifndef SPROUT_MATH_ERF_HPP