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// TR1 complex -*- C++ -*- |
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// Copyright (C) 2006-2021 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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|
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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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|
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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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|
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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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|
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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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|
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#ifndef _GLIBCXX_TR1_COMPLEX |
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#define _GLIBCXX_TR1_COMPLEX 1 |
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|
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#pragma GCC system_header |
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|
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#include <complex> |
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|
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namespace std _GLIBCXX_VISIBILITY(default) |
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{ |
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_GLIBCXX_BEGIN_NAMESPACE_VERSION |
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|
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namespace tr1 |
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{ |
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/** |
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* @addtogroup complex_numbers |
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* @{ |
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*/ |
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|
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#if __cplusplus >= 201103L |
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using std::acos; |
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using std::asin; |
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using std::atan; |
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using std::acosh; |
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using std::asinh; |
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using std::atanh; |
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#else |
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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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#endif |
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|
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// The std::fabs return type in C++11 mode is different (just _Tp). |
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template<typename _Tp> std::complex<_Tp> fabs(const std::complex<_Tp>&); |
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|
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#if __cplusplus < 201103L |
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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__num = __r2 + __num * __num; |
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__den = __r2 + __den * __den; |
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|
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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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|
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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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|
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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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|
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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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|
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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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|
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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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// Kahan's formula. |
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return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) |
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+ std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); |
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} |
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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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|
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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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|
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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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|
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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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|
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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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|
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return std::log(__t + __z); |
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} |
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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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|
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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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|
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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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|
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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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|
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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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|
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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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|
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__num = __i2 + __num * __num; |
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__den = __i2 + __den * __den; |
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|
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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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|
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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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|
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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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|
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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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|
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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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|
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#endif // C++11 |
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|
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template<typename _Tp> |
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inline std::complex<_Tp> |
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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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|
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/// Additional overloads [8.1.9]. |
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#if __cplusplus < 201103L |
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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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arg(_Tp __x) |
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{ |
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typedef typename __gnu_cxx::__promote<_Tp>::__type __type; |
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#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) |
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return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) |
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: __type(); |
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#else |
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return std::arg(std::complex<__type>(__x)); |
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#endif |
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} |
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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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imag(_Tp) |
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{ return _Tp(); } |
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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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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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|
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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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|
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#endif |
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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 _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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|
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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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|
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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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|
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using std::arg; |
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|
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template<typename _Tp> |
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inline std::complex<_Tp> |
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conj(const std::complex<_Tp>& __z) |
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{ return std::conj(__z); } |
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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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|
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using std::imag; |
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using std::norm; |
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using std::polar; |
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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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polar(const _Tp& __rho, const _Up& __theta) |
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{ |
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typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; |
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return std::polar(__type(__rho), __type(__theta)); |
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} |
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|
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using std::real; |
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|
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template<typename _Tp> |
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inline std::complex<_Tp> |
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pow(const std::complex<_Tp>& __x, const _Tp& __y) |
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{ return std::pow(__x, __y); } |
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|
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template<typename _Tp> |
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inline std::complex<_Tp> |
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pow(const _Tp& __x, const std::complex<_Tp>& __y) |
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{ return std::pow(__x, __y); } |
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|
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template<typename _Tp> |
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inline std::complex<_Tp> |
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pow(const std::complex<_Tp>& __x, const std::complex<_Tp>& __y) |
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{ return std::pow(__x, __y); } |
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|
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/// @} group complex_numbers |
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} |
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|
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_GLIBCXX_END_NAMESPACE_VERSION |
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} |
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|
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#endif // _GLIBCXX_TR1_COMPLEX |
