2014-07-19 11:03:13 +00:00
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/*=============================================================================
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2015-01-10 10:13:57 +00:00
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Copyright (c) 2011-2015 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_ATANH_HPP
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#define SPROUT_COMPLEX_ATANH_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/math/log.hpp>
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#include <sprout/math/atan2.hpp>
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#include <sprout/complex/complex.hpp>
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2014-08-01 08:21:44 +00:00
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#include <sprout/complex/operators.hpp>
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2014-07-19 11:03:13 +00:00
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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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// atanh
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//
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// G.6.2.3 The catanh functions
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// catanh(conj(z)) = conj(catanh(z)) and catanh is odd.
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// catanh(+0 + i0) returns +0 + i0.
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// catanh(+0 + iNaN) returns +0 + iNaN.
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// catanh(+1 + i0) returns +<2B><>+ i0 and raises the <20>e<EFBFBD>edivide-by-zero<72>f<EFBFBD>f floating-point exception.
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// catanh(x + i<><69>) returns +0 + ip /2, for finite positive-signed x.
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// catanh(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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// catanh(+<2B><>+ iy) returns +0 + ip /2, for finite positive-signed y.
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// catanh(+<2B><>+ i<><69>) returns +0 + ip /2.
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// catanh(+<2B><>+ iNaN) returns +0 + iNaN.
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// catanh(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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// catanh(NaN + i<><69>) returns <20>}0 + ip /2 (where the sign of the real part of the result is unspecified).
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// catanh(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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atanh(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()) ? type(x.imag(), x.imag())
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: sprout::math::isinf(x.imag()) ? type(sprout::math::copysign(T(0), x.real()), sprout::math::copysign(sprout::math::half_pi<T>(), x.imag()))
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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::math::copysign(T(0), x.real()), x.imag())
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: x.real() == 0 ? x
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: type(x.imag(), x.imag())
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: sprout::math::isinf(x.real()) || sprout::math::isinf(x.imag())
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? type(sprout::math::copysign(T(0), x.real()), sprout::math::copysign(sprout::math::half_pi<T>(), x.imag()))
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: x.real() == 0 && x.imag() == 0 ? x
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: (x.real() == 1 || x.real() == -1) && x.imag() == 0 ? type(sprout::math::copysign(sprout::numeric_limits<T>::infinity(), x.real()), x.imag())
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: (sprout::log(T(1) + x) - sprout::log(T(1) - x)) / T(2)
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;
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}
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} // namespace sprout
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#endif // #ifndef SPROUT_COMPLEX_ATANH_HPP
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