mirror of
git://gcc.gnu.org/git/gcc.git
synced 2024-12-20 18:50:00 +08:00
1143680eca
* include/c_std/cmath.tcc: Use _GLIBCXX_ prefix on file guard. * include/c_std/std_cctype.h: Ditto. * include/c_std/std_cerrno.h: Ditto. * include/c_std/std_cfloat.h: Ditto. * include/c_std/std_climits.h: Ditto. * include/c_std/std_clocale.h: Ditto. * include/c_std/std_cmath.h: Ditto. * include/c_std/std_csetjmp.h: Ditto. * include/c_std/std_csignal.h: Ditto. * include/c_std/std_cstdarg.h: Ditto. * include/c_std/std_cstddef.h: Ditto. * include/c_std/std_cstdio.h: Ditto. * include/c_std/std_cstdlib.h: Ditto. * include/c_std/std_cstring.h: Ditto. * include/c_std/std_ctime.h: Ditto. * include/c_std/std_cwchar.h: Ditto. * include/c_std/std_cwctype.h: Ditto. * include/std/std_algorithm.h: Ditto. * include/std/std_bitset.h: Ditto. * include/std/std_complex.h: Ditto. * include/std/std_deque.h: Ditto. * include/std/std_fstream.h: Ditto. * include/std/std_functional.h: Ditto. * include/std/std_iomanip.h: Ditto. * include/std/std_ios.h: Ditto. * include/std/std_iosfwd.h: Ditto. * include/std/std_iostream.h: Ditto. * include/std/std_istream.h: Ditto. * include/std/std_iterator.h: Ditto. * include/std/std_limits.h: Ditto. * include/std/std_list.h: Ditto. * include/std/std_locale.h: Ditto. * include/std/std_map.h: Ditto. * include/std/std_memory.h: Ditto. * include/std/std_numeric.h: Ditto. * include/std/std_ostream.h: Ditto. * include/std/std_queue.h: Ditto. * include/std/std_set.h: Ditto. * include/std/std_sstream.h: Ditto. * include/std/std_stack.h: Ditto. * include/std/std_stdexcept.h: Ditto. * include/std/std_streambuf.h: Ditto. * include/std/std_string.h: Ditto. * include/std/std_utility.h: Ditto. * include/std/std_valarray.h: Ditto. * include/std/std_vector.h: Ditto. From-SVN: r69705
1066 lines
28 KiB
C++
1066 lines
28 KiB
C++
// The template and inlines for the -*- C++ -*- complex number classes.
|
|
|
|
// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002
|
|
// 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>;
|
|
|
|
template<typename _Tp> _Tp abs(const complex<_Tp>&);
|
|
template<typename _Tp> _Tp arg(const complex<_Tp>&);
|
|
template<typename _Tp> _Tp norm(const complex<_Tp>&);
|
|
|
|
template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
|
|
|
|
// Transcendentals:
|
|
template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
|
|
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
|
|
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
|
|
const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
|
|
template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
|
|
|
|
|
|
// 26.2.2 Primary template class complex
|
|
template<typename _Tp>
|
|
class complex
|
|
{
|
|
public:
|
|
typedef _Tp value_type;
|
|
|
|
complex(const _Tp& = _Tp(), const _Tp & = _Tp());
|
|
|
|
// Let's the compiler synthetize the copy constructor
|
|
// complex (const complex<_Tp>&);
|
|
template<typename _Up>
|
|
complex(const complex<_Up>&);
|
|
|
|
_Tp real() const;
|
|
_Tp imag() const;
|
|
|
|
complex<_Tp>& operator=(const _Tp&);
|
|
complex<_Tp>& operator+=(const _Tp&);
|
|
complex<_Tp>& operator-=(const _Tp&);
|
|
complex<_Tp>& operator*=(const _Tp&);
|
|
complex<_Tp>& operator/=(const _Tp&);
|
|
|
|
// Let's the compiler synthetize the
|
|
// copy and assignment operator
|
|
// complex<_Tp>& operator= (const complex<_Tp>&);
|
|
template<typename _Up>
|
|
complex<_Tp>& operator=(const complex<_Up>&);
|
|
template<typename _Up>
|
|
complex<_Tp>& operator+=(const complex<_Up>&);
|
|
template<typename _Up>
|
|
complex<_Tp>& operator-=(const complex<_Up>&);
|
|
template<typename _Up>
|
|
complex<_Tp>& operator*=(const complex<_Up>&);
|
|
template<typename _Up>
|
|
complex<_Tp>& operator/=(const complex<_Up>&);
|
|
|
|
private:
|
|
_Tp _M_real, _M_imag;
|
|
};
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
complex<_Tp>::real() const { return _M_real; }
|
|
|
|
template<typename _Tp>
|
|
inline _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;
|
|
}
|
|
|
|
// Operators:
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return complex<_Tp> (__x) += __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator+(const complex<_Tp>& __x, const _Tp& __y)
|
|
{ return complex<_Tp> (__x) += __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator+(const _Tp& __x, const complex<_Tp>& __y)
|
|
{ return complex<_Tp> (__y) += __x; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return complex<_Tp> (__x) -= __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator-(const complex<_Tp>& __x, const _Tp& __y)
|
|
{ return complex<_Tp> (__x) -= __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator-(const _Tp& __x, const complex<_Tp>& __y)
|
|
{ return complex<_Tp> (__x) -= __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return complex<_Tp> (__x) *= __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator*(const complex<_Tp>& __x, const _Tp& __y)
|
|
{ return complex<_Tp> (__x) *= __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator*(const _Tp& __x, const complex<_Tp>& __y)
|
|
{ return complex<_Tp> (__y) *= __x; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return complex<_Tp> (__x) /= __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator/(const complex<_Tp>& __x, const _Tp& __y)
|
|
{ return complex<_Tp> (__x) /= __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator/(const _Tp& __x, const complex<_Tp>& __y)
|
|
{ return complex<_Tp> (__x) /= __y; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator+(const complex<_Tp>& __x)
|
|
{ return __x; }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
operator-(const complex<_Tp>& __x)
|
|
{ return complex<_Tp>(-__x.real(), -__x.imag()); }
|
|
|
|
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(); }
|
|
|
|
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(); }
|
|
|
|
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 = complex<_Tp>(__re_x, _Tp(0));
|
|
else
|
|
__is.setstate(ios_base::failbit);
|
|
}
|
|
else
|
|
{
|
|
__is.putback(__ch);
|
|
__is >> __re_x;
|
|
__x = complex<_Tp>(__re_x, _Tp(0));
|
|
}
|
|
return __is;
|
|
}
|
|
|
|
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(const complex<_Tp>& __z)
|
|
{ return __z.real(); }
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
imag(const complex<_Tp>& __z)
|
|
{ return __z.imag(); }
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
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);
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
arg(const complex<_Tp>& __z)
|
|
{ return atan2(__z.imag(), __z.real()); }
|
|
|
|
// 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
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
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));
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
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));
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
exp(const complex<_Tp>& __z)
|
|
{ return std::polar(exp(__z.real()), __z.imag()); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
log(const complex<_Tp>& __z)
|
|
{ return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
log10(const complex<_Tp>& __z)
|
|
{ return std::log(__z) / log(_Tp(10.0)); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
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));
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
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));
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex<_Tp>
|
|
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);
|
|
}
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tan(const complex<_Tp>& __z)
|
|
{
|
|
return std::sin(__z) / std::cos(__z);
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tanh(const complex<_Tp>& __z)
|
|
{
|
|
return std::sinh(__z) / std::cosh(__z);
|
|
}
|
|
|
|
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())
|
|
return pow(__x.real(), __y);
|
|
|
|
complex<_Tp> __t = log(__x);
|
|
return std::polar(exp(__y * __t.real()), __y * __t.imag());
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{
|
|
return __x == _Tp() ? _Tp() : exp(__y * log(__x));
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
return __x == _Tp()
|
|
? _Tp()
|
|
: std::polar(pow(__x, __y.real()), __y.imag() * log(__x));
|
|
}
|
|
|
|
// 26.2.3 complex specializations
|
|
// complex<float> specialization
|
|
template<> class complex<float>
|
|
{
|
|
public:
|
|
typedef float value_type;
|
|
|
|
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 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>&);
|
|
|
|
private:
|
|
typedef __complex__ float _ComplexT;
|
|
_ComplexT _M_value;
|
|
|
|
complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
friend class complex<double>;
|
|
friend class complex<long double>;
|
|
};
|
|
|
|
inline float
|
|
complex<float>::real() const
|
|
{ return __real__ _M_value; }
|
|
|
|
inline 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<> class complex<double>
|
|
{
|
|
public:
|
|
typedef double value_type;
|
|
|
|
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 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>&);
|
|
|
|
private:
|
|
typedef __complex__ double _ComplexT;
|
|
_ComplexT _M_value;
|
|
|
|
complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
friend class complex<float>;
|
|
friend class complex<long double>;
|
|
};
|
|
|
|
inline double
|
|
complex<double>::real() const
|
|
{ return __real__ _M_value; }
|
|
|
|
inline 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<> class complex<long double>
|
|
{
|
|
public:
|
|
typedef long double value_type;
|
|
|
|
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 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>&);
|
|
|
|
private:
|
|
typedef __complex__ long double _ComplexT;
|
|
_ComplexT _M_value;
|
|
|
|
complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
friend class complex<float>;
|
|
friend class complex<double>;
|
|
};
|
|
|
|
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() const
|
|
{ return __real__ _M_value; }
|
|
|
|
inline 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(_ComplexT(__z._M_value)) { }
|
|
|
|
inline
|
|
complex<float>::complex(const complex<long double>& __z)
|
|
: _M_value(_ComplexT(__z._M_value)) { }
|
|
|
|
inline
|
|
complex<double>::complex(const complex<float>& __z)
|
|
: _M_value(_ComplexT(__z._M_value)) { }
|
|
|
|
inline
|
|
complex<double>::complex(const complex<long double>& __z)
|
|
{
|
|
__real__ _M_value = __z.real();
|
|
__imag__ _M_value = __z.imag();
|
|
}
|
|
|
|
inline
|
|
complex<long double>::complex(const complex<float>& __z)
|
|
: _M_value(_ComplexT(__z._M_value)) { }
|
|
|
|
inline
|
|
complex<long double>::complex(const complex<double>& __z)
|
|
: _M_value(_ComplexT(__z._M_value)) { }
|
|
} // namespace std
|
|
|
|
#endif /* _GLIBCXX_COMPLEX */
|