mirror of
https://github.com/bolero-MURAKAMI/Sprout.git
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82 lines
3 KiB
C++
82 lines
3 KiB
C++
/*=============================================================================
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Copyright (c) 2011-2013 Bolero MURAKAMI
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https://github.com/bolero-MURAKAMI/Sprout
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================*/
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#ifndef SPROUT_MATH_ATAN_HPP
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#define SPROUT_MATH_ATAN_HPP
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#include <cstddef>
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#include <type_traits>
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#include <sprout/config.hpp>
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#include <sprout/limits.hpp>
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#include <sprout/detail/pow.hpp>
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#include <sprout/math/detail/config.hpp>
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#include <sprout/math/detail/float_compute.hpp>
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#include <sprout/math/constants.hpp>
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#include <sprout/math/factorial.hpp>
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#include <sprout/math/isnan.hpp>
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#include <sprout/type_traits/enabler_if.hpp>
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namespace sprout {
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namespace math {
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR T
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atan_impl_1(T x, std::size_t n, std::size_t last) {
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return last - n == 1
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? (n % 2 ? -1 : 1) * sprout::detail::pow_n(x, 2 * n + 1) / (2 * n + 1)
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: sprout::math::detail::atan_impl_1(x, n, n + (last - n) / 2)
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+ sprout::math::detail::atan_impl_1(x, n + (last - n) / 2, last)
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;
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}
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template<typename T>
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inline SPROUT_CONSTEXPR T
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atan_impl(T x) {
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return x > sprout::math::root_two<T>() + 1
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? sprout::math::half_pi<T>() - sprout::math::detail::atan_impl_1(1 / x, 0, sprout::math::factorial_limit<T>() + 1)
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: x > sprout::math::root_two<T>() - 1
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? sprout::math::quarter_pi<T>() + sprout::math::detail::atan_impl_1((x - 1) / (x + 1), 0, sprout::math::factorial_limit<T>() + 1)
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: x + sprout::math::detail::atan_impl_1(x, 1, sprout::math::factorial_limit<T>() + 1)
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;
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}
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template<
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typename FloatType,
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typename sprout::enabler_if<std::is_floating_point<FloatType>::value>::type = sprout::enabler
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>
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inline SPROUT_CONSTEXPR FloatType
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atan(FloatType x) {
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return sprout::math::isnan(x) ? x
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: x == sprout::numeric_limits<FloatType>::infinity() ? sprout::math::half_pi<FloatType>()
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: x == -sprout::numeric_limits<FloatType>::infinity() ? -sprout::math::half_pi<FloatType>()
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#if SPROUT_USE_BUILTIN_CMATH_FUNCTION
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: std::atan(x)
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#else
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: x == 0 ? x
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: static_cast<FloatType>(
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x < 0 ? -sprout::math::detail::atan_impl(static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(-x))
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: sprout::math::detail::atan_impl(static_cast<typename sprout::math::detail::float_compute<FloatType>::type>(x))
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)
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#endif
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;
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}
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template<
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typename IntType,
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typename sprout::enabler_if<std::is_integral<IntType>::value>::type = sprout::enabler
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>
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inline SPROUT_CONSTEXPR double
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atan(IntType x) {
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return sprout::math::detail::atan(static_cast<double>(x));
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}
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} // namespace detail
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using sprout::math::detail::atan;
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} // namespace math
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using sprout::math::atan;
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} // namespace sprout
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#endif // #ifndef SPROUT_MATH_ATAN_HPP
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