2014-07-19 11:03:13 +00:00
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/*=============================================================================
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2018-12-30 08:25:21 +00:00
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Copyright (c) 2011-2018 Bolero MURAKAMI
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2014-07-19 11:03:13 +00:00
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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_COMPLEX_ACOS_HPP
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#define SPROUT_COMPLEX_ACOS_HPP
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#include <sprout/config.hpp>
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#include <sprout/limits.hpp>
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#include <sprout/math/constants.hpp>
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#include <sprout/math/isnan.hpp>
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#include <sprout/math/isinf.hpp>
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#include <sprout/math/copysign.hpp>
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#include <sprout/complex/complex.hpp>
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#include <sprout/complex/asin.hpp>
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namespace sprout {
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//
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// acos
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//
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// G.6.1.1 The cacos functions
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// cacos(conj(z)) = conj(cacos(z)).
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// cacos(<28>}0 + i0) returns p /2 - i0.
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// cacos(<28>}0 + iNaN) returns p /2 + iNaN.
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// cacos(x + i<><69>) returns p /2 - i<><69>, for finite x.
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// 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.
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// cacos(-<2D><>+ iy) returns p - i<><69>, for positive-signed finite y.
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// cacos(+<2B><>+ iy) returns +0 - i<><69>, for positive-signed finite y.
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// cacos(-<2D><>+ i<><69>) returns 3p /4 - i<><69>.
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// cacos(+<2B><>+ i<><69>) returns p /4 - i<><69>.
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// cacos(<28>}<7D><>+ iNaN) returns NaN <20>} i<><69> (where the sign of the imaginary part of the result is unspecified).
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// cacos(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite y.
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// cacos(NaN + i<><69>) returns NaN - i<><69>.
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// cacos(NaN + iNaN) returns NaN + iNaN.
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//
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namespace detail {
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::complex<T>
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acos_impl(sprout::complex<T> const& t) {
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return sprout::complex<T>(sprout::math::half_pi<T>() - t.real(), -t.imag());
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}
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} // namespace detail
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::complex<T>
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acos(sprout::complex<T> const& x) {
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typedef sprout::complex<T> type;
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return sprout::math::isnan(x.real())
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? sprout::math::isnan(x.imag()) ? x
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: sprout::math::isinf(x.imag()) ? type(x.real(), -x.imag())
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: type(x.real(), sprout::numeric_limits<T>::quiet_NaN())
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: sprout::math::isnan(x.imag())
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? sprout::math::isinf(x.real()) ? type(sprout::numeric_limits<T>::quiet_NaN(), x.real())
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: x.real() == 0 ? type(sprout::math::half_pi<T>(), x.imag())
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: type(sprout::numeric_limits<T>::quiet_NaN(), sprout::numeric_limits<T>::quiet_NaN())
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: x.real() == sprout::numeric_limits<T>::infinity()
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? sprout::math::isinf(x.imag()) ? type(sprout::math::quarter_pi<T>(), -x.imag())
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: type(T(0), sprout::math::copysign(sprout::numeric_limits<T>::infinity(), -x.imag()))
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: x.real() == -sprout::numeric_limits<T>::infinity()
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? sprout::math::isinf(x.imag()) ? type(sprout::math::three_quarters_pi<T>(), -x.imag())
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: type(sprout::math::pi<T>(), sprout::math::copysign(sprout::numeric_limits<T>::infinity(), -x.imag()))
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: sprout::math::isinf(x.imag()) ? type(sprout::math::half_pi<T>(), sprout::math::copysign(sprout::numeric_limits<T>::infinity(), -x.imag()))
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: x.real() == 0 && x.imag() == 0 ? type(sprout::math::half_pi<T>(), -x.imag())
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: sprout::detail::acos_impl(sprout::asin(x))
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;
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}
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} // namespace sprout
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#endif // #ifndef SPROUT_COMPLEX_ACOS_HPP
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