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re-implementation complex transcendental functions

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bolero-MURAKAMI 2014-07-19 20:03:13 +09:00
parent c830cab086
commit 22c3f6e132
32 changed files with 1460 additions and 486 deletions
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sprout/complex/sinh.hpp Normal file
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/*=============================================================================
Copyright (c) 2011-2014 Bolero MURAKAMI
https://github.com/bolero-MURAKAMI/Sprout
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
=============================================================================*/
#ifndef SPROUT_COMPLEX_SINH_HPP
#define SPROUT_COMPLEX_SINH_HPP
#include <sprout/config.hpp>
#include <sprout/limits.hpp>
#include <sprout/math/isnan.hpp>
#include <sprout/math/isinf.hpp>
#include <sprout/math/cos.hpp>
#include <sprout/math/sin.hpp>
#include <sprout/math/cosh.hpp>
#include <sprout/math/sinh.hpp>
#include <sprout/complex/complex.hpp>
#include <sprout/complex/operators.hpp>
#include <sprout/complex/euler.hpp>
#include <sprout/complex/detail/copysign_mul.hpp>
namespace sprout {
//
// sinh
//
// G.6.2.5 The csinh functions
// csinh(conj(z)) = conj(csinh(z)) and csinh is odd.
// csinh(+0 + i0) returns +0 + i0.
// csinh(+0 + i<>‡) returns <20>}0 + 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.
// csinh(+0 + iNaN) returns <20>}0 + iNaN (where the sign of the real part of the result is unspecified).
// csinh(x + i<>‡) returns NaN + iNaN and raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for positive finite x.
// csinh(x + iNaN) returns NaN + iNaN and optionally raises the <20>e<EFBFBD>einvalid<69>f<EFBFBD>f floating-point exception, for finite nonzero x.
// csinh(+<2B>‡+ i0) returns +<2B>‡+ i0.
// csinh(+<2B>‡+ iy) returns +<2B>‡ cis(y), for positive finite y.
// csinh(+<2B>‡+ i<>‡) 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.
// csinh(+<2B>‡+ iNaN) returns <20>}<7D>‡+ iNaN (where the sign of the real part of the result is unspecified).
// csinh(NaN + i0) returns NaN + i0.
// csinh(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.
// csinh(NaN + iNaN) returns NaN + iNaN.
//
template<typename T>
inline SPROUT_CONSTEXPR sprout::complex<T>
sinh(sprout::complex<T> const& x) {
typedef sprout::complex<T> type;
return sprout::math::isnan(x.real())
? sprout::math::isnan(x.imag()) ? type(x.real(), x.real())
: sprout::math::isinf(x.imag()) ? type(x.real(), x.real())
: x.imag() == 0 ? x
: type(x.real(), x.real())
: sprout::math::isnan(x.imag())
? sprout::math::isinf(x.real()) ? type(x.real(), sprout::numeric_limits<T>::quiet_NaN())
: x.real() == 0 ? type(x.real(), sprout::numeric_limits<T>::quiet_NaN())
: type(x.imag(), x.imag())
: x.real() == sprout::numeric_limits<T>::infinity()
? sprout::math::isinf(x.imag()) ? type(x.real(), sprout::numeric_limits<T>::quiet_NaN())
: x.imag() == 0 ? x
: sprout::detail::copysign_mul(sprout::numeric_limits<T>::infinity(), sprout::euler(x.imag()))
: x.real() == -sprout::numeric_limits<T>::infinity()
? sprout::math::isinf(x.imag()) ? type(x.real(), sprout::numeric_limits<T>::quiet_NaN())
: x.imag() == 0 ? x
: -sprout::detail::copysign_mul(sprout::numeric_limits<T>::infinity(), sprout::euler(-x.imag()))
: sprout::math::isinf(x.imag())
? x.real() == 0 ? type(x.real(), sprout::numeric_limits<T>::quiet_NaN())
: type(-sprout::numeric_limits<T>::quiet_NaN(), -sprout::numeric_limits<T>::quiet_NaN())
: x.real() == 0 && x.imag() == 0 ? x
: type(sprout::math::sinh(x.real()) * sprout::math::cos(x.imag()), sprout::math::cosh(x.real()) * sprout::math::sin(x.imag()))
;
}
} // namespace sprout
#endif // #ifndef SPROUT_COMPLEX_SINH_HPP