410 lines
12 KiB
Plaintext
410 lines
12 KiB
Plaintext
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// TR1 complex -*- C++ -*-
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// Copyright (C) 2006 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the
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// terms of the GNU General Public License as published by the
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// Free Software Foundation; either version 2, or (at your option)
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// any later version.
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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// You should have received a copy of the GNU General Public License along
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// with this library; see the file COPYING. If not, write to the Free
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// Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
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// USA.
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// As a special exception, you may use this file as part of a free software
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// library without restriction. Specifically, if other files instantiate
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// templates or use macros or inline functions from this file, or you compile
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// this file and link it with other files to produce an executable, this
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// file does not by itself cause the resulting executable to be covered by
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// the GNU General Public License. This exception does not however
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// invalidate any other reasons why the executable file might be covered by
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// the GNU General Public License.
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/** @file tr1/complex
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* This is a TR1 C++ Library header.
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*/
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#ifndef _TR1_COMPLEX
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#define _TR1_COMPLEX 1
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#include "../complex"
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#include <tr1/common.h>
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// namespace std::tr1
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namespace std
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{
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_GLIBCXX_BEGIN_NAMESPACE(tr1)
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// Forward declarations.
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template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
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template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
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template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
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template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
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template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
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template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
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template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
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/// @brief acos(__z) [8.1.2].
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// Effects: Behaves the same as C99 function cacos, defined
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// in subclause 7.3.5.1.
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template<typename _Tp>
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inline std::complex<_Tp>
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__complex_acos(const std::complex<_Tp>& __z)
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{
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const std::complex<_Tp> __t = std::tr1::asin(__z);
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const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
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return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
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}
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#if _GLIBCXX_USE_C99_COMPLEX_TR1
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inline __complex__ float
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__complex_acos(__complex__ float __z)
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{ return __builtin_cacosf(__z); }
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inline __complex__ double
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__complex_acos(__complex__ double __z)
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{ return __builtin_cacos(__z); }
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inline __complex__ long double
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__complex_acos(const __complex__ long double& __z)
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{ return __builtin_cacosl(__z); }
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template<typename _Tp>
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inline std::complex<_Tp>
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acos(const std::complex<_Tp>& __z)
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{ return __complex_acos(__z.__rep()); }
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#else
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template<typename _Tp>
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inline std::complex<_Tp>
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acos(const std::complex<_Tp>& __z)
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{ return __complex_acos(__z); }
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#endif
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/// @brief asin(__z) [8.1.3].
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// Effects: Behaves the same as C99 function casin, defined
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// in subclause 7.3.5.2.
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template<typename _Tp>
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inline std::complex<_Tp>
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__complex_asin(const std::complex<_Tp>& __z)
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{
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std::complex<_Tp> __t(-__z.imag(), __z.real());
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__t = std::tr1::asinh(__t);
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return std::complex<_Tp>(__t.imag(), -__t.real());
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}
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#if _GLIBCXX_USE_C99_COMPLEX_TR1
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inline __complex__ float
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__complex_asin(__complex__ float __z)
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{ return __builtin_casinf(__z); }
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inline __complex__ double
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__complex_asin(__complex__ double __z)
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{ return __builtin_casin(__z); }
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inline __complex__ long double
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__complex_asin(const __complex__ long double& __z)
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{ return __builtin_casinl(__z); }
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template<typename _Tp>
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inline std::complex<_Tp>
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asin(const std::complex<_Tp>& __z)
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{ return __complex_asin(__z.__rep()); }
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#else
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template<typename _Tp>
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inline std::complex<_Tp>
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asin(const std::complex<_Tp>& __z)
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{ return __complex_asin(__z); }
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#endif
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/// @brief atan(__z) [8.1.4].
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// Effects: Behaves the same as C99 function catan, defined
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// in subclause 7.3.5.3.
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template<typename _Tp>
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std::complex<_Tp>
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__complex_atan(const std::complex<_Tp>& __z)
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{
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const _Tp __r2 = __z.real() * __z.real();
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const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
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_Tp __num = __z.imag() + _Tp(1.0);
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_Tp __den = __z.imag() - _Tp(1.0);
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__num = __r2 + __num * __num;
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__den = __r2 + __den * __den;
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return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
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_Tp(0.25) * log(__num / __den));
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}
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#if _GLIBCXX_USE_C99_COMPLEX_TR1
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inline __complex__ float
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__complex_atan(__complex__ float __z)
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{ return __builtin_catanf(__z); }
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inline __complex__ double
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__complex_atan(__complex__ double __z)
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{ return __builtin_catan(__z); }
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inline __complex__ long double
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__complex_atan(const __complex__ long double& __z)
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{ return __builtin_catanl(__z); }
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template<typename _Tp>
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inline std::complex<_Tp>
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atan(const std::complex<_Tp>& __z)
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{ return __complex_atan(__z.__rep()); }
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#else
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template<typename _Tp>
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inline std::complex<_Tp>
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atan(const std::complex<_Tp>& __z)
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{ return __complex_atan(__z); }
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#endif
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/// @brief acosh(__z) [8.1.5].
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// Effects: Behaves the same as C99 function cacosh, defined
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// in subclause 7.3.6.1.
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template<typename _Tp>
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std::complex<_Tp>
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__complex_acosh(const std::complex<_Tp>& __z)
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{
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std::complex<_Tp> __t((__z.real() - __z.imag())
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* (__z.real() + __z.imag()) - _Tp(1.0),
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_Tp(2.0) * __z.real() * __z.imag());
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__t = std::sqrt(__t);
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return std::log(__t + __z);
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}
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#if _GLIBCXX_USE_C99_COMPLEX_TR1
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inline __complex__ float
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__complex_acosh(__complex__ float __z)
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{ return __builtin_cacoshf(__z); }
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inline __complex__ double
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__complex_acosh(__complex__ double __z)
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{ return __builtin_cacosh(__z); }
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inline __complex__ long double
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__complex_acosh(const __complex__ long double& __z)
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{ return __builtin_cacoshl(__z); }
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template<typename _Tp>
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inline std::complex<_Tp>
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acosh(const std::complex<_Tp>& __z)
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{ return __complex_acosh(__z.__rep()); }
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#else
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template<typename _Tp>
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inline std::complex<_Tp>
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acosh(const std::complex<_Tp>& __z)
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{ return __complex_acosh(__z); }
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#endif
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/// @brief asinh(__z) [8.1.6].
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// Effects: Behaves the same as C99 function casin, defined
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// in subclause 7.3.6.2.
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template<typename _Tp>
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std::complex<_Tp>
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__complex_asinh(const std::complex<_Tp>& __z)
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{
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std::complex<_Tp> __t((__z.real() - __z.imag())
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* (__z.real() + __z.imag()) + _Tp(1.0),
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_Tp(2.0) * __z.real() * __z.imag());
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__t = std::sqrt(__t);
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return std::log(__t + __z);
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}
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#if _GLIBCXX_USE_C99_COMPLEX_TR1
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inline __complex__ float
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__complex_asinh(__complex__ float __z)
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{ return __builtin_casinhf(__z); }
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inline __complex__ double
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__complex_asinh(__complex__ double __z)
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{ return __builtin_casinh(__z); }
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inline __complex__ long double
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__complex_asinh(const __complex__ long double& __z)
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{ return __builtin_casinhl(__z); }
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template<typename _Tp>
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inline std::complex<_Tp>
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asinh(const std::complex<_Tp>& __z)
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{ return __complex_asinh(__z.__rep()); }
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#else
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template<typename _Tp>
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inline std::complex<_Tp>
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asinh(const std::complex<_Tp>& __z)
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{ return __complex_asinh(__z); }
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#endif
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/// @brief atanh(__z) [8.1.7].
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// Effects: Behaves the same as C99 function catanh, defined
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// in subclause 7.3.6.3.
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template<typename _Tp>
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std::complex<_Tp>
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__complex_atanh(const std::complex<_Tp>& __z)
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{
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const _Tp __i2 = __z.imag() * __z.imag();
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const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
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_Tp __num = _Tp(1.0) + __z.real();
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_Tp __den = _Tp(1.0) - __z.real();
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__num = __i2 + __num * __num;
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__den = __i2 + __den * __den;
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return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
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_Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
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}
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#if _GLIBCXX_USE_C99_COMPLEX_TR1
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inline __complex__ float
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__complex_atanh(__complex__ float __z)
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{ return __builtin_catanhf(__z); }
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inline __complex__ double
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__complex_atanh(__complex__ double __z)
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{ return __builtin_catanh(__z); }
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inline __complex__ long double
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__complex_atanh(const __complex__ long double& __z)
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{ return __builtin_catanhl(__z); }
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template<typename _Tp>
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inline std::complex<_Tp>
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atanh(const std::complex<_Tp>& __z)
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{ return __complex_atanh(__z.__rep()); }
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#else
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template<typename _Tp>
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inline std::complex<_Tp>
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atanh(const std::complex<_Tp>& __z)
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{ return __complex_atanh(__z); }
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#endif
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/// @brief fabs(__z) [8.1.8].
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// Effects: Behaves the same as C99 function cabs, defined
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// in subclause 7.3.8.1.
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template<typename _Tp>
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inline std::complex<_Tp>
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fabs(const std::complex<_Tp>& __z)
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{ return std::abs(__z); }
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/// @brief Additional overloads [8.1.9].
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//
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// See common.h for the primary template.
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template<typename _Tp, typename _Up>
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struct __promote_2<std::complex<_Tp>, _Up>
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{
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public:
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typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
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};
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template<typename _Tp, typename _Up>
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struct __promote_2<_Tp, std::complex<_Up> >
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{
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public:
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typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
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};
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template<typename _Tp, typename _Up>
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struct __promote_2<std::complex<_Tp>, std::complex<_Up> >
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{
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public:
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typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
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};
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using std::arg;
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template<typename _Tp>
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inline typename __promote<_Tp>::__type
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arg(_Tp __x)
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{
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typedef typename __promote<_Tp>::__type __type;
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return std::arg(std::complex<__type>(__x));
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}
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using std::conj;
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template<typename _Tp>
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inline std::complex<typename __promote<_Tp>::__type>
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conj(_Tp __x)
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{ return __x; }
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using std::imag;
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template<typename _Tp>
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inline typename __promote<_Tp>::__type
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imag(_Tp)
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{ return _Tp(); }
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using std::norm;
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template<typename _Tp>
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inline typename __promote<_Tp>::__type
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norm(_Tp __x)
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{
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typedef typename __promote<_Tp>::__type __type;
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return __type(__x) * __type(__x);
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}
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using std::polar;
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template<typename _Tp, typename _Up>
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||
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inline std::complex<typename __promote_2<_Tp, _Up>::__type>
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|
polar(const _Tp& __rho, const _Up& __theta)
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||
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{
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||
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|
typedef typename __promote_2<_Tp, _Up>::__type __type;
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||
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|
return std::polar(__type(__rho), __type(__theta));
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||
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}
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||
|
|
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||
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using std::pow;
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||
|
|
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||
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|
template<typename _Tp, typename _Up>
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||
|
|
inline std::complex<typename __promote_2<_Tp, _Up>::__type>
|
||
|
|
pow(const std::complex<_Tp>& __x, const _Up& __y)
|
||
|
|
{
|
||
|
|
typedef typename __promote_2<_Tp, _Up>::__type __type;
|
||
|
|
return std::pow(std::complex<__type>(__x), __type(__y));
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename _Tp, typename _Up>
|
||
|
|
inline std::complex<typename __promote_2<_Tp, _Up>::__type>
|
||
|
|
pow(const _Tp& __x, const std::complex<_Up>& __y)
|
||
|
|
{
|
||
|
|
typedef typename __promote_2<_Tp, _Up>::__type __type;
|
||
|
|
return std::pow(__type(__x), std::complex<__type>(__y));
|
||
|
|
}
|
||
|
|
|
||
|
|
template<typename _Tp, typename _Up>
|
||
|
|
inline std::complex<typename __promote_2<_Tp, _Up>::__type>
|
||
|
|
pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
|
||
|
|
{
|
||
|
|
typedef typename __promote_2<_Tp, _Up>::__type __type;
|
||
|
|
return std::pow(std::complex<__type>(__x),
|
||
|
|
std::complex<__type>(__y));
|
||
|
|
}
|
||
|
|
|
||
|
|
using std::real;
|
||
|
|
|
||
|
|
template<typename _Tp>
|
||
|
|
inline typename __promote<_Tp>::__type
|
||
|
|
real(_Tp __x)
|
||
|
|
{ return __x; }
|
||
|
|
|
||
|
|
_GLIBCXX_END_NAMESPACE
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif
|