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Diffstat (limited to 'libstdc++-v3/include/std/complex')
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diff --git a/libstdc++-v3/include/std/complex b/libstdc++-v3/include/std/complex new file mode 100644 index 0000000..26f31f6 --- /dev/null +++ b/libstdc++-v3/include/std/complex @@ -0,0 +1,1489 @@ +// The template and inlines for the -*- C++ -*- complex number classes. + +// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005 +// 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 complex + * This is a Standard C++ Library header. + */ + +// +// ISO C++ 14882: 26.2 Complex Numbers +// Note: this is not a conforming implementation. +// Initially implemented by Ulrich Drepper <drepper@cygnus.com> +// Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr> +// + +#ifndef _GLIBCXX_COMPLEX +#define _GLIBCXX_COMPLEX 1 + +#pragma GCC system_header + +#include <bits/c++config.h> +#include <bits/cpp_type_traits.h> +#include <cmath> +#include <sstream> + +_GLIBCXX_BEGIN_NAMESPACE(std) + + // Forward declarations. + template<typename _Tp> class complex; + template<> class complex<float>; + template<> class complex<double>; + template<> class complex<long double>; + + /// Return magnitude of @a z. + template<typename _Tp> _Tp abs(const complex<_Tp>&); + /// Return phase angle of @a z. + template<typename _Tp> _Tp arg(const complex<_Tp>&); + /// Return @a z magnitude squared. + template<typename _Tp> _Tp norm(const complex<_Tp>&); + + /// Return complex conjugate of @a z. + template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&); + /// Return complex with magnitude @a rho and angle @a theta. + template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0); + + // Transcendentals: + /// Return complex cosine of @a z. + template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&); + /// Return complex hyperbolic cosine of @a z. + template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&); + /// Return complex base e exponential of @a z. + template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&); + /// Return complex natural logarithm of @a z. + template<typename _Tp> complex<_Tp> log(const complex<_Tp>&); + /// Return complex base 10 logarithm of @a z. + template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&); + /// Return complex cosine of @a z. + template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int); + /// Return @a x to the @a y'th power. + template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&); + /// Return @a x to the @a y'th power. + template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, + const complex<_Tp>&); + /// Return @a x to the @a y'th power. + template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&); + /// Return complex sine of @a z. + template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&); + /// Return complex hyperbolic sine of @a z. + template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&); + /// Return complex square root of @a z. + template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&); + /// Return complex tangent of @a z. + template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&); + /// Return complex hyperbolic tangent of @a z. + template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&); + //@} + + + // 26.2.2 Primary template class complex + /** + * Template to represent complex numbers. + * + * Specializations for float, double, and long double are part of the + * library. Results with any other type are not guaranteed. + * + * @param Tp Type of real and imaginary values. + */ + template<typename _Tp> + struct complex + { + /// Value typedef. + typedef _Tp value_type; + + /// Default constructor. First parameter is x, second parameter is y. + /// Unspecified parameters default to 0. + complex(const _Tp& = _Tp(), const _Tp & = _Tp()); + + // Lets the compiler synthesize the copy constructor + // complex (const complex<_Tp>&); + /// Copy constructor. + template<typename _Up> + complex(const complex<_Up>&); + + /// Return real part of complex number. + _Tp& real(); + /// Return real part of complex number. + const _Tp& real() const; + /// Return imaginary part of complex number. + _Tp& imag(); + /// Return imaginary part of complex number. + const _Tp& imag() const; + + /// Assign this complex number to scalar @a t. + complex<_Tp>& operator=(const _Tp&); + /// Add @a t to this complex number. + complex<_Tp>& operator+=(const _Tp&); + /// Subtract @a t from this complex number. + complex<_Tp>& operator-=(const _Tp&); + /// Multiply this complex number by @a t. + complex<_Tp>& operator*=(const _Tp&); + /// Divide this complex number by @a t. + complex<_Tp>& operator/=(const _Tp&); + + // Lets the compiler synthesize the + // copy and assignment operator + // complex<_Tp>& operator= (const complex<_Tp>&); + /// Assign this complex number to complex @a z. + template<typename _Up> + complex<_Tp>& operator=(const complex<_Up>&); + /// Add @a z to this complex number. + template<typename _Up> + complex<_Tp>& operator+=(const complex<_Up>&); + /// Subtract @a z from this complex number. + template<typename _Up> + complex<_Tp>& operator-=(const complex<_Up>&); + /// Multiply this complex number by @a z. + template<typename _Up> + complex<_Tp>& operator*=(const complex<_Up>&); + /// Divide this complex number by @a z. + template<typename _Up> + complex<_Tp>& operator/=(const complex<_Up>&); + + const complex& __rep() const; + + private: + _Tp _M_real; + _Tp _M_imag; + }; + + template<typename _Tp> + inline _Tp& + complex<_Tp>::real() { return _M_real; } + + template<typename _Tp> + inline const _Tp& + complex<_Tp>::real() const { return _M_real; } + + template<typename _Tp> + inline _Tp& + complex<_Tp>::imag() { return _M_imag; } + + template<typename _Tp> + inline const _Tp& + complex<_Tp>::imag() const { return _M_imag; } + + template<typename _Tp> + inline + complex<_Tp>::complex(const _Tp& __r, const _Tp& __i) + : _M_real(__r), _M_imag(__i) { } + + template<typename _Tp> + template<typename _Up> + inline + complex<_Tp>::complex(const complex<_Up>& __z) + : _M_real(__z.real()), _M_imag(__z.imag()) { } + + template<typename _Tp> + complex<_Tp>& + complex<_Tp>::operator=(const _Tp& __t) + { + _M_real = __t; + _M_imag = _Tp(); + return *this; + } + + // 26.2.5/1 + template<typename _Tp> + inline complex<_Tp>& + complex<_Tp>::operator+=(const _Tp& __t) + { + _M_real += __t; + return *this; + } + + // 26.2.5/3 + template<typename _Tp> + inline complex<_Tp>& + complex<_Tp>::operator-=(const _Tp& __t) + { + _M_real -= __t; + return *this; + } + + // 26.2.5/5 + template<typename _Tp> + complex<_Tp>& + complex<_Tp>::operator*=(const _Tp& __t) + { + _M_real *= __t; + _M_imag *= __t; + return *this; + } + + // 26.2.5/7 + template<typename _Tp> + complex<_Tp>& + complex<_Tp>::operator/=(const _Tp& __t) + { + _M_real /= __t; + _M_imag /= __t; + return *this; + } + + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator=(const complex<_Up>& __z) + { + _M_real = __z.real(); + _M_imag = __z.imag(); + return *this; + } + + // 26.2.5/9 + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator+=(const complex<_Up>& __z) + { + _M_real += __z.real(); + _M_imag += __z.imag(); + return *this; + } + + // 26.2.5/11 + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator-=(const complex<_Up>& __z) + { + _M_real -= __z.real(); + _M_imag -= __z.imag(); + return *this; + } + + // 26.2.5/13 + // XXX: This is a grammar school implementation. + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator*=(const complex<_Up>& __z) + { + const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag(); + _M_imag = _M_real * __z.imag() + _M_imag * __z.real(); + _M_real = __r; + return *this; + } + + // 26.2.5/15 + // XXX: This is a grammar school implementation. + template<typename _Tp> + template<typename _Up> + complex<_Tp>& + complex<_Tp>::operator/=(const complex<_Up>& __z) + { + const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag(); + const _Tp __n = std::norm(__z); + _M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n; + _M_real = __r / __n; + return *this; + } + + template<typename _Tp> + inline const complex<_Tp>& + complex<_Tp>::__rep() const { return *this; } + + // Operators: + //@{ + /// Return new complex value @a x plus @a y. + template<typename _Tp> + inline complex<_Tp> + operator+(const complex<_Tp>& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r += __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator+(const complex<_Tp>& __x, const _Tp& __y) + { + complex<_Tp> __r = __x; + __r.real() += __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator+(const _Tp& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __y; + __r.real() += __x; + return __r; + } + //@} + + //@{ + /// Return new complex value @a x minus @a y. + template<typename _Tp> + inline complex<_Tp> + operator-(const complex<_Tp>& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r -= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator-(const complex<_Tp>& __x, const _Tp& __y) + { + complex<_Tp> __r = __x; + __r.real() -= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator-(const _Tp& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r(__x, -__y.imag()); + __r.real() -= __y.real(); + return __r; + } + //@} + + //@{ + /// Return new complex value @a x times @a y. + template<typename _Tp> + inline complex<_Tp> + operator*(const complex<_Tp>& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r *= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator*(const complex<_Tp>& __x, const _Tp& __y) + { + complex<_Tp> __r = __x; + __r *= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator*(const _Tp& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __y; + __r *= __x; + return __r; + } + //@} + + //@{ + /// Return new complex value @a x divided by @a y. + template<typename _Tp> + inline complex<_Tp> + operator/(const complex<_Tp>& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r /= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator/(const complex<_Tp>& __x, const _Tp& __y) + { + complex<_Tp> __r = __x; + __r /= __y; + return __r; + } + + template<typename _Tp> + inline complex<_Tp> + operator/(const _Tp& __x, const complex<_Tp>& __y) + { + complex<_Tp> __r = __x; + __r /= __y; + return __r; + } + //@} + + /// Return @a x. + template<typename _Tp> + inline complex<_Tp> + operator+(const complex<_Tp>& __x) + { return __x; } + + /// Return complex negation of @a x. + template<typename _Tp> + inline complex<_Tp> + operator-(const complex<_Tp>& __x) + { return complex<_Tp>(-__x.real(), -__x.imag()); } + + //@{ + /// Return true if @a x is equal to @a y. + template<typename _Tp> + inline bool + operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) + { return __x.real() == __y.real() && __x.imag() == __y.imag(); } + + template<typename _Tp> + inline bool + operator==(const complex<_Tp>& __x, const _Tp& __y) + { return __x.real() == __y && __x.imag() == _Tp(); } + + template<typename _Tp> + inline bool + operator==(const _Tp& __x, const complex<_Tp>& __y) + { return __x == __y.real() && _Tp() == __y.imag(); } + //@} + + //@{ + /// Return false if @a x is equal to @a y. + template<typename _Tp> + inline bool + operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) + { return __x.real() != __y.real() || __x.imag() != __y.imag(); } + + template<typename _Tp> + inline bool + operator!=(const complex<_Tp>& __x, const _Tp& __y) + { return __x.real() != __y || __x.imag() != _Tp(); } + + template<typename _Tp> + inline bool + operator!=(const _Tp& __x, const complex<_Tp>& __y) + { return __x != __y.real() || _Tp() != __y.imag(); } + //@} + + /// Extraction operator for complex values. + template<typename _Tp, typename _CharT, class _Traits> + basic_istream<_CharT, _Traits>& + operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) + { + _Tp __re_x, __im_x; + _CharT __ch; + __is >> __ch; + if (__ch == '(') + { + __is >> __re_x >> __ch; + if (__ch == ',') + { + __is >> __im_x >> __ch; + if (__ch == ')') + __x = complex<_Tp>(__re_x, __im_x); + else + __is.setstate(ios_base::failbit); + } + else if (__ch == ')') + __x = __re_x; + else + __is.setstate(ios_base::failbit); + } + else + { + __is.putback(__ch); + __is >> __re_x; + __x = __re_x; + } + return __is; + } + + /// Insertion operator for complex values. + template<typename _Tp, typename _CharT, class _Traits> + basic_ostream<_CharT, _Traits>& + operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) + { + basic_ostringstream<_CharT, _Traits> __s; + __s.flags(__os.flags()); + __s.imbue(__os.getloc()); + __s.precision(__os.precision()); + __s << '(' << __x.real() << ',' << __x.imag() << ')'; + return __os << __s.str(); + } + + // Values + template<typename _Tp> + inline _Tp& + real(complex<_Tp>& __z) + { return __z.real(); } + + template<typename _Tp> + inline const _Tp& + real(const complex<_Tp>& __z) + { return __z.real(); } + + template<typename _Tp> + inline _Tp& + imag(complex<_Tp>& __z) + { return __z.imag(); } + + template<typename _Tp> + inline const _Tp& + imag(const complex<_Tp>& __z) + { return __z.imag(); } + + // 26.2.7/3 abs(__z): Returns the magnitude of __z. + template<typename _Tp> + inline _Tp + __complex_abs(const complex<_Tp>& __z) + { + _Tp __x = __z.real(); + _Tp __y = __z.imag(); + const _Tp __s = std::max(abs(__x), abs(__y)); + if (__s == _Tp()) // well ... + return __s; + __x /= __s; + __y /= __s; + return __s * sqrt(__x * __x + __y * __y); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline float + __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } + + inline double + __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } + + inline long double + __complex_abs(const __complex__ long double& __z) + { return __builtin_cabsl(__z); } + + template<typename _Tp> + inline _Tp + abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } +#else + template<typename _Tp> + inline _Tp + abs(const complex<_Tp>& __z) { return __complex_abs(__z); } +#endif + + + // 26.2.7/4: arg(__z): Returns the phase angle of __z. + template<typename _Tp> + inline _Tp + __complex_arg(const complex<_Tp>& __z) + { return atan2(__z.imag(), __z.real()); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline float + __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } + + inline double + __complex_arg(__complex__ double __z) { return __builtin_carg(__z); } + + inline long double + __complex_arg(const __complex__ long double& __z) + { return __builtin_cargl(__z); } + + template<typename _Tp> + inline _Tp + arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } +#else + template<typename _Tp> + inline _Tp + arg(const complex<_Tp>& __z) { return __complex_arg(__z); } +#endif + + // 26.2.7/5: norm(__z) returns the squared magintude of __z. + // As defined, norm() is -not- a norm is the common mathematical + // sens used in numerics. The helper class _Norm_helper<> tries to + // distinguish between builtin floating point and the rest, so as + // to deliver an answer as close as possible to the real value. + template<bool> + struct _Norm_helper + { + template<typename _Tp> + static inline _Tp _S_do_it(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return __x * __x + __y * __y; + } + }; + + template<> + struct _Norm_helper<true> + { + template<typename _Tp> + static inline _Tp _S_do_it(const complex<_Tp>& __z) + { + _Tp __res = std::abs(__z); + return __res * __res; + } + }; + + template<typename _Tp> + inline _Tp + norm(const complex<_Tp>& __z) + { + return _Norm_helper<__is_floating<_Tp>::__value + && !_GLIBCXX_FAST_MATH>::_S_do_it(__z); + } + + template<typename _Tp> + inline complex<_Tp> + polar(const _Tp& __rho, const _Tp& __theta) + { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } + + template<typename _Tp> + inline complex<_Tp> + conj(const complex<_Tp>& __z) + { return complex<_Tp>(__z.real(), -__z.imag()); } + + // Transcendentals + + // 26.2.8/1 cos(__z): Returns the cosine of __z. + template<typename _Tp> + inline complex<_Tp> + __complex_cos(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } + + inline __complex__ double + __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } + + inline __complex__ long double + __complex_cos(const __complex__ long double& __z) + { return __builtin_ccosl(__z); } + + template<typename _Tp> + inline complex<_Tp> + cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + cos(const complex<_Tp>& __z) { return __complex_cos(__z); } +#endif + + // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. + template<typename _Tp> + inline complex<_Tp> + __complex_cosh(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } + + inline __complex__ double + __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } + + inline __complex__ long double + __complex_cosh(const __complex__ long double& __z) + { return __builtin_ccoshl(__z); } + + template<typename _Tp> + inline complex<_Tp> + cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } +#endif + + // 26.2.8/3 exp(__z): Returns the complex base e exponential of x + template<typename _Tp> + inline complex<_Tp> + __complex_exp(const complex<_Tp>& __z) + { return std::polar(exp(__z.real()), __z.imag()); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } + + inline __complex__ double + __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } + + inline __complex__ long double + __complex_exp(const __complex__ long double& __z) + { return __builtin_cexpl(__z); } + + template<typename _Tp> + inline complex<_Tp> + exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + exp(const complex<_Tp>& __z) { return __complex_exp(__z); } +#endif + + // 26.2.8/5 log(__z): Reurns the natural complex logaritm of __z. + // The branch cut is along the negative axis. + template<typename _Tp> + inline complex<_Tp> + __complex_log(const complex<_Tp>& __z) + { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_log(__complex__ float __z) { return __builtin_clogf(__z); } + + inline __complex__ double + __complex_log(__complex__ double __z) { return __builtin_clog(__z); } + + inline __complex__ long double + __complex_log(const __complex__ long double& __z) + { return __builtin_clogl(__z); } + + template<typename _Tp> + inline complex<_Tp> + log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + log(const complex<_Tp>& __z) { return __complex_log(__z); } +#endif + + template<typename _Tp> + inline complex<_Tp> + log10(const complex<_Tp>& __z) + { return std::log(__z) / log(_Tp(10.0)); } + + // 26.2.8/10 sin(__z): Returns the sine of __z. + template<typename _Tp> + inline complex<_Tp> + __complex_sin(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } + + inline __complex__ double + __complex_sin(__complex__ double __z) { return __builtin_csin(__z); } + + inline __complex__ long double + __complex_sin(const __complex__ long double& __z) + { return __builtin_csinl(__z); } + + template<typename _Tp> + inline complex<_Tp> + sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + sin(const complex<_Tp>& __z) { return __complex_sin(__z); } +#endif + + // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. + template<typename _Tp> + inline complex<_Tp> + __complex_sinh(const complex<_Tp>& __z) + { + const _Tp __x = __z.real(); + const _Tp __y = __z.imag(); + return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } + + inline __complex__ double + __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } + + inline __complex__ long double + __complex_sinh(const __complex__ long double& __z) + { return __builtin_csinhl(__z); } + + template<typename _Tp> + inline complex<_Tp> + sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } +#endif + + // 26.2.8/13 sqrt(__z): Returns the complex square root of __z. + // The branch cut is on the negative axis. + template<typename _Tp> + complex<_Tp> + __complex_sqrt(const complex<_Tp>& __z) + { + _Tp __x = __z.real(); + _Tp __y = __z.imag(); + + if (__x == _Tp()) + { + _Tp __t = sqrt(abs(__y) / 2); + return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); + } + else + { + _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); + _Tp __u = __t / 2; + return __x > _Tp() + ? complex<_Tp>(__u, __y / __t) + : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); + } + } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } + + inline __complex__ double + __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } + + inline __complex__ long double + __complex_sqrt(const __complex__ long double& __z) + { return __builtin_csqrtl(__z); } + + template<typename _Tp> + inline complex<_Tp> + sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } +#endif + + // 26.2.8/14 tan(__z): Return the complex tangent of __z. + + template<typename _Tp> + inline complex<_Tp> + __complex_tan(const complex<_Tp>& __z) + { return std::sin(__z) / std::cos(__z); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } + + inline __complex__ double + __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } + + inline __complex__ long double + __complex_tan(const __complex__ long double& __z) + { return __builtin_ctanl(__z); } + + template<typename _Tp> + inline complex<_Tp> + tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + tan(const complex<_Tp>& __z) { return __complex_tan(__z); } +#endif + + + // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. + + template<typename _Tp> + inline complex<_Tp> + __complex_tanh(const complex<_Tp>& __z) + { return std::sinh(__z) / std::cosh(__z); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } + + inline __complex__ double + __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } + + inline __complex__ long double + __complex_tanh(const __complex__ long double& __z) + { return __builtin_ctanhl(__z); } + + template<typename _Tp> + inline complex<_Tp> + tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } +#endif + + + // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x + // raised to the __y-th power. The branch + // cut is on the negative axis. + template<typename _Tp> + inline complex<_Tp> + pow(const complex<_Tp>& __z, int __n) + { return std::__pow_helper(__z, __n); } + + template<typename _Tp> + complex<_Tp> + pow(const complex<_Tp>& __x, const _Tp& __y) + { +#ifndef _GLIBCXX_USE_C99_COMPLEX + if (__x == _Tp()) + return _Tp(); +#endif + if (__x.imag() == _Tp() && __x.real() > _Tp()) + return pow(__x.real(), __y); + + complex<_Tp> __t = std::log(__x); + return std::polar(exp(__y * __t.real()), __y * __t.imag()); + } + + template<typename _Tp> + inline complex<_Tp> + __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) + { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } + +#if _GLIBCXX_USE_C99_COMPLEX + inline __complex__ float + __complex_pow(__complex__ float __x, __complex__ float __y) + { return __builtin_cpowf(__x, __y); } + + inline __complex__ double + __complex_pow(__complex__ double __x, __complex__ double __y) + { return __builtin_cpow(__x, __y); } + + inline __complex__ long double + __complex_pow(const __complex__ long double& __x, + const __complex__ long double& __y) + { return __builtin_cpowl(__x, __y); } + + template<typename _Tp> + inline complex<_Tp> + pow(const complex<_Tp>& __x, const complex<_Tp>& __y) + { return __complex_pow(__x.__rep(), __y.__rep()); } +#else + template<typename _Tp> + inline complex<_Tp> + pow(const complex<_Tp>& __x, const complex<_Tp>& __y) + { return __complex_pow(__x, __y); } +#endif + + template<typename _Tp> + inline complex<_Tp> + pow(const _Tp& __x, const complex<_Tp>& __y) + { + return __x > _Tp() ? std::polar(pow(__x, __y.real()), + __y.imag() * log(__x)) + : std::pow(complex<_Tp>(__x, _Tp()), __y); + } + + // 26.2.3 complex specializations + // complex<float> specialization + template<> + struct complex<float> + { + typedef float value_type; + typedef __complex__ float _ComplexT; + + complex(_ComplexT __z) : _M_value(__z) { } + + complex(float = 0.0f, float = 0.0f); + + explicit complex(const complex<double>&); + explicit complex(const complex<long double>&); + + float& real(); + const float& real() const; + float& imag(); + const float& imag() const; + + complex<float>& operator=(float); + complex<float>& operator+=(float); + complex<float>& operator-=(float); + complex<float>& operator*=(float); + complex<float>& operator/=(float); + + // Let's the compiler synthetize the copy and assignment + // operator. It always does a pretty good job. + // complex& operator= (const complex&); + template<typename _Tp> + complex<float>&operator=(const complex<_Tp>&); + template<typename _Tp> + complex<float>& operator+=(const complex<_Tp>&); + template<class _Tp> + complex<float>& operator-=(const complex<_Tp>&); + template<class _Tp> + complex<float>& operator*=(const complex<_Tp>&); + template<class _Tp> + complex<float>&operator/=(const complex<_Tp>&); + + const _ComplexT& __rep() const { return _M_value; } + + private: + _ComplexT _M_value; + }; + + inline float& + complex<float>::real() + { return __real__ _M_value; } + + inline const float& + complex<float>::real() const + { return __real__ _M_value; } + + inline float& + complex<float>::imag() + { return __imag__ _M_value; } + + inline const float& + complex<float>::imag() const + { return __imag__ _M_value; } + + inline + complex<float>::complex(float r, float i) + { + __real__ _M_value = r; + __imag__ _M_value = i; + } + + inline complex<float>& + complex<float>::operator=(float __f) + { + __real__ _M_value = __f; + __imag__ _M_value = 0.0f; + return *this; + } + + inline complex<float>& + complex<float>::operator+=(float __f) + { + __real__ _M_value += __f; + return *this; + } + + inline complex<float>& + complex<float>::operator-=(float __f) + { + __real__ _M_value -= __f; + return *this; + } + + inline complex<float>& + complex<float>::operator*=(float __f) + { + _M_value *= __f; + return *this; + } + + inline complex<float>& + complex<float>::operator/=(float __f) + { + _M_value /= __f; + return *this; + } + + template<typename _Tp> + inline complex<float>& + complex<float>::operator=(const complex<_Tp>& __z) + { + __real__ _M_value = __z.real(); + __imag__ _M_value = __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<float>& + complex<float>::operator+=(const complex<_Tp>& __z) + { + __real__ _M_value += __z.real(); + __imag__ _M_value += __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<float>& + complex<float>::operator-=(const complex<_Tp>& __z) + { + __real__ _M_value -= __z.real(); + __imag__ _M_value -= __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<float>& + complex<float>::operator*=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value *= __t; + return *this; + } + + template<typename _Tp> + inline complex<float>& + complex<float>::operator/=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value /= __t; + return *this; + } + + // 26.2.3 complex specializations + // complex<double> specialization + template<> + struct complex<double> + { + typedef double value_type; + typedef __complex__ double _ComplexT; + + complex(_ComplexT __z) : _M_value(__z) { } + + complex(double = 0.0, double = 0.0); + + complex(const complex<float>&); + explicit complex(const complex<long double>&); + + double& real(); + const double& real() const; + double& imag(); + const double& imag() const; + + complex<double>& operator=(double); + complex<double>& operator+=(double); + complex<double>& operator-=(double); + complex<double>& operator*=(double); + complex<double>& operator/=(double); + + // The compiler will synthetize this, efficiently. + // complex& operator= (const complex&); + template<typename _Tp> + complex<double>& operator=(const complex<_Tp>&); + template<typename _Tp> + complex<double>& operator+=(const complex<_Tp>&); + template<typename _Tp> + complex<double>& operator-=(const complex<_Tp>&); + template<typename _Tp> + complex<double>& operator*=(const complex<_Tp>&); + template<typename _Tp> + complex<double>& operator/=(const complex<_Tp>&); + + const _ComplexT& __rep() const { return _M_value; } + + private: + _ComplexT _M_value; + }; + + inline double& + complex<double>::real() + { return __real__ _M_value; } + + inline const double& + complex<double>::real() const + { return __real__ _M_value; } + + inline double& + complex<double>::imag() + { return __imag__ _M_value; } + + inline const double& + complex<double>::imag() const + { return __imag__ _M_value; } + + inline + complex<double>::complex(double __r, double __i) + { + __real__ _M_value = __r; + __imag__ _M_value = __i; + } + + inline complex<double>& + complex<double>::operator=(double __d) + { + __real__ _M_value = __d; + __imag__ _M_value = 0.0; + return *this; + } + + inline complex<double>& + complex<double>::operator+=(double __d) + { + __real__ _M_value += __d; + return *this; + } + + inline complex<double>& + complex<double>::operator-=(double __d) + { + __real__ _M_value -= __d; + return *this; + } + + inline complex<double>& + complex<double>::operator*=(double __d) + { + _M_value *= __d; + return *this; + } + + inline complex<double>& + complex<double>::operator/=(double __d) + { + _M_value /= __d; + return *this; + } + + template<typename _Tp> + inline complex<double>& + complex<double>::operator=(const complex<_Tp>& __z) + { + __real__ _M_value = __z.real(); + __imag__ _M_value = __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<double>& + complex<double>::operator+=(const complex<_Tp>& __z) + { + __real__ _M_value += __z.real(); + __imag__ _M_value += __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<double>& + complex<double>::operator-=(const complex<_Tp>& __z) + { + __real__ _M_value -= __z.real(); + __imag__ _M_value -= __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<double>& + complex<double>::operator*=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value *= __t; + return *this; + } + + template<typename _Tp> + inline complex<double>& + complex<double>::operator/=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value /= __t; + return *this; + } + + // 26.2.3 complex specializations + // complex<long double> specialization + template<> + struct complex<long double> + { + typedef long double value_type; + typedef __complex__ long double _ComplexT; + + complex(_ComplexT __z) : _M_value(__z) { } + + complex(long double = 0.0L, long double = 0.0L); + + complex(const complex<float>&); + complex(const complex<double>&); + + long double& real(); + const long double& real() const; + long double& imag(); + const long double& imag() const; + + complex<long double>& operator= (long double); + complex<long double>& operator+= (long double); + complex<long double>& operator-= (long double); + complex<long double>& operator*= (long double); + complex<long double>& operator/= (long double); + + // The compiler knows how to do this efficiently + // complex& operator= (const complex&); + template<typename _Tp> + complex<long double>& operator=(const complex<_Tp>&); + template<typename _Tp> + complex<long double>& operator+=(const complex<_Tp>&); + template<typename _Tp> + complex<long double>& operator-=(const complex<_Tp>&); + template<typename _Tp> + complex<long double>& operator*=(const complex<_Tp>&); + template<typename _Tp> + complex<long double>& operator/=(const complex<_Tp>&); + + const _ComplexT& __rep() const { return _M_value; } + + private: + _ComplexT _M_value; + }; + + inline + complex<long double>::complex(long double __r, long double __i) + { + __real__ _M_value = __r; + __imag__ _M_value = __i; + } + + inline long double& + complex<long double>::real() + { return __real__ _M_value; } + + inline const long double& + complex<long double>::real() const + { return __real__ _M_value; } + + inline long double& + complex<long double>::imag() + { return __imag__ _M_value; } + + inline const long double& + complex<long double>::imag() const + { return __imag__ _M_value; } + + inline complex<long double>& + complex<long double>::operator=(long double __r) + { + __real__ _M_value = __r; + __imag__ _M_value = 0.0L; + return *this; + } + + inline complex<long double>& + complex<long double>::operator+=(long double __r) + { + __real__ _M_value += __r; + return *this; + } + + inline complex<long double>& + complex<long double>::operator-=(long double __r) + { + __real__ _M_value -= __r; + return *this; + } + + inline complex<long double>& + complex<long double>::operator*=(long double __r) + { + _M_value *= __r; + return *this; + } + + inline complex<long double>& + complex<long double>::operator/=(long double __r) + { + _M_value /= __r; + return *this; + } + + template<typename _Tp> + inline complex<long double>& + complex<long double>::operator=(const complex<_Tp>& __z) + { + __real__ _M_value = __z.real(); + __imag__ _M_value = __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<long double>& + complex<long double>::operator+=(const complex<_Tp>& __z) + { + __real__ _M_value += __z.real(); + __imag__ _M_value += __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<long double>& + complex<long double>::operator-=(const complex<_Tp>& __z) + { + __real__ _M_value -= __z.real(); + __imag__ _M_value -= __z.imag(); + return *this; + } + + template<typename _Tp> + inline complex<long double>& + complex<long double>::operator*=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value *= __t; + return *this; + } + + template<typename _Tp> + inline complex<long double>& + complex<long double>::operator/=(const complex<_Tp>& __z) + { + _ComplexT __t; + __real__ __t = __z.real(); + __imag__ __t = __z.imag(); + _M_value /= __t; + return *this; + } + + // These bits have to be at the end of this file, so that the + // specializations have all been defined. + // ??? No, they have to be there because of compiler limitation at + // inlining. It suffices that class specializations be defined. + inline + complex<float>::complex(const complex<double>& __z) + : _M_value(__z.__rep()) { } + + inline + complex<float>::complex(const complex<long double>& __z) + : _M_value(__z.__rep()) { } + + inline + complex<double>::complex(const complex<float>& __z) + : _M_value(__z.__rep()) { } + + inline + complex<double>::complex(const complex<long double>& __z) + : _M_value(__z.__rep()) { } + + inline + complex<long double>::complex(const complex<float>& __z) + : _M_value(__z.__rep()) { } + + inline + complex<long double>::complex(const complex<double>& __z) + : _M_value(__z.__rep()) { } + +_GLIBCXX_END_NAMESPACE + +#endif /* _GLIBCXX_COMPLEX */ |