Sprout/sprout/math/asin.hpp

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#ifndef SPROUT_MATH_ASIN_HPP
#define SPROUT_MATH_ASIN_HPP
#include <cstddef>
#include <limits>
#include <type_traits>
#include <sprout/config.hpp>
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#include <sprout/math/detail/config.hpp>
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#include <sprout/math/constants.hpp>
#include <sprout/math/factorial.hpp>
#include <sprout/math/sqrt.hpp>
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#include <sprout/type_traits/enabler_if.hpp>
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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>()
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? sprout::math::half_pi<T>() - sprout::math::detail::asin_impl_1(sprout::math::sqrt(1 - x * x))
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: 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
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using NS_SPROUT_MATH_DETAIL::asin;
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} // namespace math
using sprout::math::asin;
} // namespace sprout
#endif // #ifndef SPROUT_MATH_ASIN_HPP