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gcc/libstdc++-v3/include/std/std_complex.h
Jan van Dijk 9ef313e31c std_complex.h (sin(const complex<_Tp>& __z)): Make this function return a value. 
2004-06-10  Jan van Dijk  <jan@etpmod.phys.tue.nl>

	* include/std/std_complex.h (sin(const complex<_Tp>& __z)): Make
	this function return a value.

From-SVN: r82928
2004-06-10 16:54:49 +00:00

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// The template and inlines for the -*- C++ -*- complex number classes.
// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004
// 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, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
// 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.
//
// 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>
//
/** @file complex
* This is a Standard C++ Library header. You should @c #include this header
* in your programs, rather than any of the "st[dl]_*.h" implementation files.
*/
#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>
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);
}
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()); }
// 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());
}
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()); }
// 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>::_M_type && !_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));
}
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()); }
// 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));
}
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()); }
// 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()); }
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()); }
// 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)); }
/*
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); } */
// FIXME: Currently wer don't use built-ins for log() because of some
// obscure user name-space issues. So, we use the generic version
// which is why we don't use __z.__rep() in the call below.
template<typename _Tp>
inline complex<_Tp>
log(const complex<_Tp>& __z) { return __complex_log(__z); }
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));
}
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()); }
// 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));
}
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()); }
// 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);
}
}
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()); }
// 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); }
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()); }
// 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); }
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()); }
// 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)
{
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)); }
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(__complex__ long double& __x, __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, __y); }
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);
#ifdef _GLIBCXX_BUGGY_COMPLEX
complex(const complex& __z) : _M_value(__z._M_value) { }
#endif
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);
#ifdef _GLIBCXX_BUGGY_COMPLEX
complex(const complex& __z) : _M_value(__z._M_value) { }
#endif
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);
#ifdef _GLIBCXX_BUGGY_COMPLEX
complex(const complex& __z) : _M_value(__z._M_value) { }
#endif
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()) { }
} // namespace std
#endif /* _GLIBCXX_COMPLEX */
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