Sprout/sprout/complex/acos.hpp
2016-02-25 18:48:28 +09:00

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/*=============================================================================
Copyright (c) 2011-2016 Bolero MURAKAMI
https://github.com/bolero-MURAKAMI/Sprout
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
=============================================================================*/
#ifndef SPROUT_COMPLEX_ACOS_HPP
#define SPROUT_COMPLEX_ACOS_HPP
#include <sprout/config.hpp>
#include <sprout/limits.hpp>
#include <sprout/math/constants.hpp>
#include <sprout/math/isnan.hpp>
#include <sprout/math/isinf.hpp>
#include <sprout/math/copysign.hpp>
#include <sprout/complex/complex.hpp>
#include <sprout/complex/asin.hpp>
namespace sprout {
//
// acos
//
// G.6.1.1 The cacos functions
// cacos(conj(z)) = conj(cacos(z)).
// cacos(<28>}0 + i0) returns p /2 - i0.
// cacos(<28>}0 + iNaN) returns p /2 + iNaN.
// cacos(x + i<>‡) returns p /2 - i<>‡, for finite x.
// cacos(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for nonzero finite x.
// cacos(-<2D>‡+ iy) returns p - i<>‡, for positive-signed finite y.
// cacos(+<2B>‡+ iy) returns +0 - i<>‡, for positive-signed finite y.
// cacos(-<2D>‡+ i<>‡) returns 3p /4 - i<>‡.
// cacos(+<2B>‡+ i<>‡) returns p /4 - i<>‡.
// cacos(<28>}<7D>‡+ iNaN) returns NaN <20>} i<>‡ (where the sign of the imaginary part of the result is unspecified).
// cacos(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite y.
// cacos(NaN + i<>‡) returns NaN - i<>‡.
// cacos(NaN + iNaN) returns NaN + iNaN.
//
namespace detail {
template<typename T>
inline SPROUT_CONSTEXPR sprout::complex<T>
acos_impl(sprout::complex<T> const& t) {
return sprout::complex<T>(sprout::math::half_pi<T>() - t.real(), -t.imag());
}
} // namespace detail
template<typename T>
inline SPROUT_CONSTEXPR sprout::complex<T>
acos(sprout::complex<T> const& x) {
typedef sprout::complex<T> type;
return sprout::math::isnan(x.real())
? sprout::math::isnan(x.imag()) ? x
: sprout::math::isinf(x.imag()) ? type(x.real(), -x.imag())
: type(x.real(), sprout::numeric_limits<T>::quiet_NaN())
: sprout::math::isnan(x.imag())
? sprout::math::isinf(x.real()) ? type(sprout::numeric_limits<T>::quiet_NaN(), x.real())
: x.real() == 0 ? type(sprout::math::half_pi<T>(), x.imag())
: type(sprout::numeric_limits<T>::quiet_NaN(), sprout::numeric_limits<T>::quiet_NaN())
: x.real() == sprout::numeric_limits<T>::infinity()
? sprout::math::isinf(x.imag()) ? type(sprout::math::quarter_pi<T>(), -x.imag())
: type(T(0), sprout::math::copysign(sprout::numeric_limits<T>::infinity(), -x.imag()))
: x.real() == -sprout::numeric_limits<T>::infinity()
? sprout::math::isinf(x.imag()) ? type(sprout::math::three_quarters_pi<T>(), -x.imag())
: type(sprout::math::pi<T>(), sprout::math::copysign(sprout::numeric_limits<T>::infinity(), -x.imag()))
: sprout::math::isinf(x.imag()) ? type(sprout::math::half_pi<T>(), sprout::math::copysign(sprout::numeric_limits<T>::infinity(), -x.imag()))
: x.real() == 0 && x.imag() == 0 ? type(sprout::math::half_pi<T>(), -x.imag())
: sprout::detail::acos_impl(sprout::asin(x))
;
}
} // namespace sprout
#endif // #ifndef SPROUT_COMPLEX_ACOS_HPP