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