2014-07-19 11:03:13 +00:00
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/*=============================================================================
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2016-02-25 09:48:28 +00:00
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Copyright (c) 2011-2016 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_ASINH_HPP
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#define SPROUT_COMPLEX_ASINH_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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// asinh
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//
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// G.6.2.2 The casinh functions
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// casinh(conj(z)) = conj(casinh(z)) and casinh is odd.
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// casinh(+0 + i0) returns 0 + i0.
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// casinh(x + i<><69>) returns +<2B><>+ ip /2 for positive-signed finite x.
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// casinh(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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// casinh(+<2B><>+ iy) returns +<2B><>+ i0 for positive-signed finite y.
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// casinh(+<2B><>+ i<><69>) returns +<2B><>+ ip /4.
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// casinh(+<2B><>+ iNaN) returns +<2B><>+ iNaN.
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// casinh(NaN + i0) returns NaN + i0.
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// casinh(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite nonzero y.
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// casinh(NaN + i<><69>) returns <20>}<7D><>+ iNaN (where the sign of the real part of the result is unspecified).
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// casinh(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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asinh(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.imag(), x.real())
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: x.imag() == 0 ? x
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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()) ? x
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: type(sprout::math::copysign(sprout::numeric_limits<T>::quiet_NaN(), x.real()), x.imag())
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: sprout::math::isinf(x.real())
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? x.imag() == sprout::numeric_limits<T>::infinity() ? type(x.real(), sprout::math::quarter_pi<T>())
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: x.imag() == -sprout::numeric_limits<T>::infinity() ? type(x.real(), -sprout::math::quarter_pi<T>())
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: x.imag() == 0 ? x
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: type(x.real(), (x.imag() == 0 ? x.imag() : sprout::math::copysign(T(0), x.imag())))
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: sprout::math::isinf(x.imag()) ? type(
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sprout::math::copysign(sprout::numeric_limits<T>::infinity(), x.real()),
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sprout::math::copysign(sprout::math::half_pi<T>(), x.imag())
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)
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: x.real() == 0 && x.imag() == 0 ? x
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: sprout::log(sprout::sqrt(type((x.real() - x.imag()) * (x.real() + x.imag()) + T(1), T(2) * x.real() * x.imag())) + x)
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;
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}
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} // namespace sprout
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#endif // #ifndef SPROUT_COMPLEX_ASINH_HPP
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