371 lines
11 KiB
C++
371 lines
11 KiB
C++
// TR1 complex -*- C++ -*-
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// Copyright (C) 2007, 2008, 2009 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 3, 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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// Under Section 7 of GPL version 3, you are granted additional
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// permissions described in the GCC Runtime Library Exception, version
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// 3.1, as published by the Free Software Foundation.
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// You should have received a copy of the GNU General Public License and
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// a copy of the GCC Runtime Library Exception along with this program;
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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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// <http://www.gnu.org/licenses/>.
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/** @file tr1_impl/complex
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* This is an internal header file, included by other library headers.
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* You should not attempt to use it directly.
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*/
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namespace std
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{
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_GLIBCXX_BEGIN_NAMESPACE_TR1
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/**
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* @addtogroup complex_numbers
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* @{
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*/
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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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#ifdef _GLIBCXX_INCLUDE_AS_CXX0X
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// DR 595.
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template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
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#else
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template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&);
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#endif
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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::_GLIBCXX_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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/// 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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acos(const std::complex<_Tp>& __z)
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{ return __complex_acos(__z); }
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#endif
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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::_GLIBCXX_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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/// 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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asin(const std::complex<_Tp>& __z)
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{ return __complex_asin(__z); }
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#endif
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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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/// 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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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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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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/// 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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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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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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/// 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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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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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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/// 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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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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template<typename _Tp>
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#ifdef _GLIBCXX_INCLUDE_AS_CXX0X
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inline _Tp
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#else
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inline std::complex<_Tp>
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#endif
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/// 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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fabs(const std::complex<_Tp>& __z)
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{ return std::abs(__z); }
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/// Additional overloads [8.1.9].
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#if (defined(_GLIBCXX_INCLUDE_AS_CXX0X) \
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|| (defined(_GLIBCXX_INCLUDE_AS_TR1) \
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&& !defined(__GXX_EXPERIMENTAL_CXX0X__)))
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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arg(_Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return std::arg(std::complex<__type>(__x));
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}
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template<typename _Tp>
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inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
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conj(_Tp __x)
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{ return __x; }
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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imag(_Tp)
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{ return _Tp(); }
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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norm(_Tp __x)
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{
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
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return __type(__x) * __type(__x);
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}
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template<typename _Tp>
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inline typename __gnu_cxx::__promote<_Tp>::__type
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real(_Tp __x)
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{ return __x; }
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#endif
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template<typename _Tp, typename _Up>
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inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
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pow(const std::complex<_Tp>& __x, const _Up& __y)
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{
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typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
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return std::pow(std::complex<__type>(__x), __type(__y));
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}
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template<typename _Tp, typename _Up>
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inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
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pow(const _Tp& __x, const std::complex<_Up>& __y)
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{
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typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
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return std::pow(__type(__x), std::complex<__type>(__y));
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}
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template<typename _Tp, typename _Up>
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inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
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pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
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{
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typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
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return std::pow(std::complex<__type>(__x),
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std::complex<__type>(__y));
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}
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// @} group complex_numbers
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_GLIBCXX_END_NAMESPACE_TR1
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}
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