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74 lines
4 KiB
C++
74 lines
4 KiB
C++
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/*=============================================================================
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Copyright (c) 2011-2014 Bolero MURAKAMI
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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_COSH_HPP
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#define SPROUT_COMPLEX_COSH_HPP
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#include <sprout/config.hpp>
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#include <sprout/limits.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/abs.hpp>
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#include <sprout/math/cos.hpp>
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#include <sprout/math/sin.hpp>
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#include <sprout/math/cosh.hpp>
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#include <sprout/math/sinh.hpp>
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#include <sprout/complex/complex.hpp>
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#include <sprout/complex/operators.hpp>
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#include <sprout/complex/euler.hpp>
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#include <sprout/complex/detail/copysign_mul.hpp>
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namespace sprout {
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//
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// cosh
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//
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// G.6.2.4 The ccosh functions
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// ccosh(conj(z)) = conj(ccosh(z)) and ccosh is even.
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// ccosh(+0 + i0) returns 1 + i0.
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// ccosh(+0 + i<><69>) returns NaN <20>} i0 (where the sign of the imaginary part of the result is unspecified) and raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception.
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// ccosh(+0 + iNaN) returns NaN <20>} i0 (where the sign of the imaginary part of the result is unspecified).
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// ccosh(x + i<><69>) returns NaN + iNaN and raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite nonzero x.
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// ccosh(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite nonzero x.
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// ccosh(+<2B><>+ i0) returns +<2B><>+ i0.
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// ccosh(+<2B><>+ iy) returns +<2B><> cis(y), for finite nonzero y.
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// ccosh(+<2B><>+ i<><69>) returns <20>}<7D><>+ iNaN (where the sign of the real part of the result is unspecified) and raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception.
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// ccosh(+<2B><>+ iNaN) returns +<2B><>+ iNaN.
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// ccosh(NaN + i0) returns NaN <20>} i0 (where the sign of the imaginary part of the result is unspecified).
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// ccosh(NaN + iy) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for all nonzero numbers y.
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// ccosh(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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cosh(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.real(), x.real())
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: x.imag() == 0 ? type(sprout::numeric_limits<T>::quiet_NaN(), 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::numeric_limits<T>::infinity(), sprout::numeric_limits<T>::quiet_NaN())
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: x.real() == 0 ? type(sprout::numeric_limits<T>::quiet_NaN(), x.real())
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: type(x.imag(), 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::numeric_limits<T>::quiet_NaN())
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: x.imag() == 0 ? type(sprout::numeric_limits<T>::infinity(), x.imag())
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: sprout::detail::copysign_mul(sprout::numeric_limits<T>::infinity(), sprout::euler(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::numeric_limits<T>::quiet_NaN())
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: x.imag() == 0 ? type(sprout::numeric_limits<T>::infinity(), x.imag()) // ???? GCC or Clang
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: sprout::detail::copysign_mul(sprout::numeric_limits<T>::infinity(), sprout::euler(-x.imag()))
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: sprout::math::isinf(x.imag())
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? x.real() == 0 ? type(sprout::numeric_limits<T>::quiet_NaN(), x.real())
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: type(-sprout::numeric_limits<T>::quiet_NaN(), -sprout::numeric_limits<T>::quiet_NaN())
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: x.real() == 0 && x.imag() == 0 ? type(T(1), x.imag())
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: type(sprout::math::cosh(x.real()) * sprout::math::cos(x.imag()), sprout::math::sinh(x.real()) * sprout::math::sin(x.imag()))
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;
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}
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} // namespace sprout
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#endif // #ifndef SPROUT_COMPLEX_COSH_HPP
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