2014-07-19 11:03:13 +00:00
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/*=============================================================================
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2017-07-29 05:20:01 +00:00
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Copyright (c) 2011-2017 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_ACOSH_HPP
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#define SPROUT_COMPLEX_ACOSH_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/log.hpp>
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#include <sprout/complex/sqrt.hpp>
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namespace sprout {
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//
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// acosh
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//
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// G.6.2.1 The cacosh functions
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// cacosh(conj(z)) = conj(cacosh(z)).
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// cacosh(<28>}0 + i0) returns +0 + ip /2.
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// cacosh(x + i<><69>) returns +<2B><>+ ip /2, for finite x.
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// cacosh(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite x.
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// cacosh(-<2D><>+ iy) returns +<2B><>+ ip , for positive-signed finite y.
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// cacosh(+<2B><>+ iy) returns +<2B><>+ i0, for positive-signed finite y.
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// cacosh(-<2D><>+ i<><69>) returns +<2B><>+ i3p /4.
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// cacosh(+<2B><>+ i<><69>) returns +<2B><>+ ip /4.
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// cacosh(<28>}<7D><>+ iNaN) returns +<2B><>+ iNaN.
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// cacosh(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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// cacosh(NaN + i<><69>) returns +<2B><>+ iNaN.
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// cacosh(NaN + iNaN) returns NaN + iNaN.
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//
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template<typename T>
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inline SPROUT_CONSTEXPR sprout::complex<T>
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acosh(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(sprout::numeric_limits<T>::infinity(), x.real())
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: type(x.real(), x.real())
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: sprout::math::isnan(x.imag())
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? sprout::math::isinf(x.real()) ? type(sprout::numeric_limits<T>::infinity(), x.imag())
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: type(sprout::numeric_limits<T>::quiet_NaN(), x.imag())
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: x.real() == sprout::numeric_limits<T>::infinity()
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? sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::quarter_pi<T>(), x.imag()))
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: type(sprout::numeric_limits<T>::infinity(), (x.imag() == 0 ? x.imag() : sprout::math::copysign(T(0), x.imag())))
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: x.real() == -sprout::numeric_limits<T>::infinity()
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? sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::three_quarters_pi<T>(), x.imag()))
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: type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::pi<T>(), x.imag()))
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: sprout::math::isinf(x.imag()) ? type(sprout::numeric_limits<T>::infinity(), sprout::math::copysign(sprout::math::half_pi<T>(), x.imag()))
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: x.real() == 0 && x.imag() == 0 ? type(T(0), sprout::math::copysign(sprout::math::half_pi<T>(), x.imag()))
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: T(2) * sprout::log(sprout::sqrt(sprout::math::half<T>() * (x + T(1))) + sprout::sqrt(sprout::math::half<T>() * (x - T(1))))
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;
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}
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} // namespace sprout
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#endif // #ifndef SPROUT_COMPLEX_ACOSH_HPP
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