967 lines
28 KiB
C++
967 lines
28 KiB
C++
// The template and inlines for the -*- C++ -*- complex number classes.
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// Copyright (C) 1997-1999 Free Software Foundation, Inc.
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//
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// This file is part of the GNU ISO C++ Library. This library is free
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// software; you can redistribute it and/or modify it under the
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// terms of the GNU General Public License as published by the
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// Free Software Foundation; either version 2, or (at your option)
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// any later version.
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU General Public License for more details.
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// You should have received a copy of the GNU General Public License along
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// with this library; see the file COPYING. If not, write to the Free
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// Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307,
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// USA.
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// As a special exception, you may use this file as part of a free software
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// library without restriction. Specifically, if other files instantiate
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// templates or use macros or inline functions from this file, or you compile
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// this file and link it with other files to produce an executable, this
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// file does not by itself cause the resulting executable to be covered by
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// the GNU General Public License. This exception does not however
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// invalidate any other reasons why the executable file might be covered by
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// the GNU General Public License.
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//
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// ISO 14882/26.2.1
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// Note: this is not a conforming implementation.
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// Initially implemented by Ulrich Drepper <drepper@cygnus.com>
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// Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
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//
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#ifndef _CPP_COMPLEX
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#define _CPP_COMPLEX 1
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#include <bits/c++config.h>
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#include <bits/std_iosfwd.h>
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namespace std
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{
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// Forward declarations
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template<typename _Tp> class complex;
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template<> class complex<float>;
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template<> class complex<double>;
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template<> class complex<long double>;
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template<typename _Tp> _Tp abs(const complex<_Tp>&);
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template<typename _Tp> _Tp arg(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp&);
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// Transcendentals:
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template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
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template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
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template<typename _Tp> complex<_Tp> pow (const complex<_Tp>&,
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const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
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template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
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//
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// 26.2.2 Primary template class complex
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//
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template <typename _Tp>
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class complex
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{
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public:
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typedef _Tp value_type;
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complex (const _Tp& = _Tp(), const _Tp & = _Tp());
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// Let's the compiler synthetize the copy constructor
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// complex (const complex<_Tp>&);
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template <typename _Up>
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complex (const complex<_Up>&);
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_Tp real () const;
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_Tp imag () const;
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complex<_Tp>& operator= (const _Tp&);
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complex<_Tp>& operator+= (const _Tp&);
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complex<_Tp>& operator-= (const _Tp&);
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complex<_Tp>& operator*= (const _Tp&);
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complex<_Tp>& operator/= (const _Tp&);
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// Let's the compiler synthetize the
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// copy and assignment operator
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// complex<_Tp>& operator= (const complex<_Tp>&);
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template <typename _Up>
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complex<_Tp>& operator= (const complex<_Up>&);
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template <typename _Up>
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complex<_Tp>& operator+= (const complex<_Up>&);
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template <typename _Up>
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complex<_Tp>& operator-= (const complex<_Up>&);
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template <typename _Up>
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complex<_Tp>& operator*= (const complex<_Up>&);
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template <typename _Up>
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complex<_Tp>& operator/= (const complex<_Up>&);
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private:
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_Tp _M_real, _M_imag;
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};
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template<typename _Tp>
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inline _Tp
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complex<_Tp>::real() const { return _M_real; }
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template<typename _Tp>
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inline _Tp
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complex<_Tp>::imag() const { return _M_imag; }
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//
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// 26.2.3 complex specializations
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//
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//
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// complex<float> specialization
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//
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template<> class complex<float>
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{
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public:
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typedef float value_type;
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complex(float = 0.0f, float = 0.0f);
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#ifdef _GLIBCPP_BUGGY_COMPLEX
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complex(const complex& __z) : _M_value(__z._M_value) {}
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#endif
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explicit complex(const complex<double>&);
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explicit complex(const complex<long double>&);
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float real() const;
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float imag() const;
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complex<float>& operator= (float);
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complex<float>& operator+= (float);
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complex<float>& operator-= (float);
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complex<float>& operator*= (float);
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complex<float>& operator/= (float);
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// Let's the compiler synthetize the copy and assignment
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// operator. It always does a pretty good job.
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// complex& operator= (const complex&);
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template <typename _Tp>
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complex<float>&operator= (const complex<_Tp>&);
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template <typename _Tp>
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complex<float>& operator+= (const complex<_Tp>&);
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template <class _Tp>
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complex<float>& operator-= (const complex<_Tp>&);
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template <class _Tp>
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complex<float>& operator*= (const complex<_Tp>&);
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template <class _Tp>
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complex<float>&operator/= (const complex<_Tp>&);
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private:
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typedef __complex__ float _ComplexT;
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_ComplexT _M_value;
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complex(_ComplexT __z) : _M_value(__z) {}
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friend class complex<double>;
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friend class complex<long double>;
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friend float abs<>(const complex<float>&);
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friend float arg<>(const complex<float>&);
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friend complex<float> conj<>(const complex<float>&);
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friend complex<float> cos<>(const complex<float>&);
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friend complex<float> cosh<>(const complex<float>&);
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friend complex<float> exp<>(const complex<float>&);
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friend complex<float> log<>(const complex<float>&);
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friend complex<float> log10<>(const complex<float>&);
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friend complex<float> pow<>(const complex<float>&, int);
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friend complex<float> pow<>(const complex<float>&, const float&);
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friend complex<float> pow<>(const complex<float>&,
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const complex<float>&);
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friend complex<float> pow<>(const float&, const complex<float>&);
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friend complex<float> sin<>(const complex<float>&);
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friend complex<float> sinh<>(const complex<float>&);
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friend complex<float> sqrt<>(const complex<float>&);
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friend complex<float> tan<>(const complex<float>&);
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friend complex<float> tanh<>(const complex<float>&);
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};
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inline float
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complex<float>::real() const
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{ return __real__ _M_value; }
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inline float
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complex<float>::imag() const
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{ return __imag__ _M_value; }
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//
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// complex<double> specialization
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//
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template<> class complex<double>
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{
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public:
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typedef double value_type;
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complex(double =0.0, double =0.0);
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#ifdef _GLIBCPP_BUGGY_COMPLEX
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complex(const complex& __z) : _M_value(__z._M_value) {}
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#endif
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complex(const complex<float>&);
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explicit complex(const complex<long double>&);
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double real () const;
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double imag () const;
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complex<double>& operator= (double);
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complex<double>& operator+= (double);
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complex<double>& operator-= (double);
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complex<double>& operator*= (double);
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complex<double>& operator/= (double);
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// The compiler will synthetize this, efficiently.
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// complex& operator= (const complex&);
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template <typename _Tp>
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complex<double>& operator= (const complex<_Tp>&);
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template <typename _Tp>
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complex<double>& operator+= (const complex<_Tp>&);
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template <typename _Tp>
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complex<double>& operator-= (const complex<_Tp>&);
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template <typename _Tp>
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complex<double>& operator*= (const complex<_Tp>&);
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template <typename _Tp>
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complex<double>& operator/= (const complex<_Tp>&);
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private:
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typedef __complex__ double _ComplexT;
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_ComplexT _M_value;
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complex(_ComplexT __z) : _M_value(__z) {}
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friend class complex<float>;
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friend class complex<long double>;
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friend double abs<>(const complex<double>&);
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friend double arg<>(const complex<double>&);
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friend complex<double> conj<>(const complex<double>&);
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friend complex<double> cos<>(const complex<double>&);
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friend complex<double> cosh<>(const complex<double>&);
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friend complex<double> exp<>(const complex<double>&);
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friend complex<double> log<>(const complex<double>&);
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friend complex<double> log10<>(const complex<double>&);
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friend complex<double> pow<>(const complex<double>&, int);
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friend complex<double> pow<>(const complex<double>&, const double&);
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friend complex<double> pow<>(const complex<double>&,
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const complex<double>&);
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friend complex<double> pow<>(const double&, const complex<double>&);
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friend complex<double> sin<>(const complex<double>&);
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friend complex<double> sinh<>(const complex<double>&);
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friend complex<double> sqrt<>(const complex<double>&);
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friend complex<double> tan<>(const complex<double>&);
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friend complex<double> tanh<>(const complex<double>&);
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};
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inline double
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complex<double>::real() const
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{ return __real__ _M_value; }
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inline double
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complex<double>::imag() const
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{ return __imag__ _M_value; }
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//
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// complex<long double> specialization
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//
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template<> class complex<long double>
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{
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public:
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typedef long double value_type;
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complex(long double = 0.0L, long double = 0.0L);
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#ifdef _GLIBCPP_BUGGY_COMPLEX
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complex(const complex& __z) : _M_value(__z._M_value) {}
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#endif
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complex(const complex<float>&);
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complex(const complex<double>&);
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long double real() const;
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long double imag() const;
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complex<long double>& operator= (long double);
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complex<long double>& operator+= (long double);
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complex<long double>& operator-= (long double);
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complex<long double>& operator*= (long double);
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complex<long double>& operator/= (long double);
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// The compiler knows how to do this efficiently
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// complex& operator= (const complex&);
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template<typename _Tp>
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complex<long double>& operator= (const complex<_Tp>&);
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template<typename _Tp>
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complex<long double>& operator+= (const complex<_Tp>&);
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template<typename _Tp>
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complex<long double>& operator-= (const complex<_Tp>&);
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template<typename _Tp>
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complex<long double>& operator*= (const complex<_Tp>&);
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template<typename _Tp>
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complex<long double>& operator/= (const complex<_Tp>&);
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private:
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typedef __complex__ long double _ComplexT;
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_ComplexT _M_value;
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complex(_ComplexT __z) : _M_value(__z) {}
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friend class complex<float>;
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friend class complex<double>;
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friend long double abs<>(const complex<long double>&);
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friend long double arg<>(const complex<long double>&);
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friend complex<long double> conj<>(const complex<long double>&);
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friend complex<long double> cos<>(const complex<long double>&);
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friend complex<long double> cosh<>(const complex<long double>&);
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friend complex<long double> exp<>(const complex<long double>&);
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friend complex<long double> log<>(const complex<long double>&);
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friend complex<long double> log10<>(const complex<long double>&);
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friend complex<long double> pow<>(const complex<long double>&, int);
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friend complex<long double> pow<>(const complex<long double>&,
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const long double&);
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friend complex<long double> pow<>(const complex<long double>&,
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const complex<long double>&);
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friend complex<long double> pow<>(const long double&,
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const complex<long double>&);
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friend complex<long double> sin<>(const complex<long double>&);
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friend complex<long double> sinh<>(const complex<long double>&);
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friend complex<long double> sqrt<>(const complex<long double>&);
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friend complex<long double> tan<>(const complex<long double>&);
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friend complex<long double> tanh<>(const complex<long double>&);
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};
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inline
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complex<long double>::complex(long double __r, long double __i)
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{
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__real__ _M_value = __r;
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__imag__ _M_value = __i;
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}
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inline
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complex<long double>::complex(const complex<float>& __z)
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: _M_value(_ComplexT(__z._M_value)) {}
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inline
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complex<long double>::complex(const complex<double>& __z)
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: _M_value(_ComplexT(__z._M_value)) {}
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inline long double
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complex<long double>::real() const
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{ return __real__ _M_value; }
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inline long double
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complex<long double>::imag() const
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{ return __imag__ _M_value; }
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inline complex<long double>&
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complex<long double>::operator= (long double __r)
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{
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__real__ _M_value = __r;
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__imag__ _M_value = 0.0L;
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return *this;
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}
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inline complex<long double>&
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complex<long double>::operator+= (long double __r)
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{
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__real__ _M_value += __r;
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return *this;
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}
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inline complex<long double>&
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complex<long double>::operator-= (long double __r)
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{
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__real__ _M_value -= __r;
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return *this;
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}
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inline complex<long double>&
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complex<long double>::operator*= (long double __r)
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{
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__real__ _M_value *= __r;
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return *this;
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}
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inline complex<long double>&
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complex<long double>::operator/= (long double __r)
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{
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__real__ _M_value /= __r;
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return *this;
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}
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template<typename _Tp>
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inline complex<long double>&
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complex<long double>::operator= (const complex<_Tp>& __z)
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{
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__real__ _M_value = __z.real();
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__imag__ _M_value = __z.imag();
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return *this;
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}
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template<typename _Tp>
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inline complex<long double>&
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complex<long double>::operator+= (const complex<_Tp>& __z)
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{
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__real__ _M_value += __z.real();
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__imag__ _M_value += __z.imag();
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return *this;
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}
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template<typename _Tp>
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inline complex<long double>&
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complex<long double>::operator-= (const complex<_Tp>& __z)
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{
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__real__ _M_value -= __z.real();
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__imag__ _M_value -= __z.imag();
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return *this;
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}
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template<typename _Tp>
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inline complex<long double>&
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complex<long double>::operator*= (const complex<_Tp>& __z)
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{
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_ComplexT __t;
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__real__ __t = __z.real();
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__imag__ __t = __z.imag();
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_M_value *= __t;
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return *this;
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}
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template<typename _Tp>
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inline complex<long double>&
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complex<long double>::operator/= (const complex<_Tp>& __z)
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{
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_ComplexT __t;
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__real__ __t = __z.real();
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__imag__ __t = __z.imag();
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_M_value /= __t;
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return *this;
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}
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//
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// complex<float> continued.
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//
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inline
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complex<float>::complex(float r, float i)
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{
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__real__ _M_value = r;
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__imag__ _M_value = i;
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}
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inline
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complex<float>::complex(const complex<double>& __z)
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: _M_value(_ComplexT(__z._M_value)) {}
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inline
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complex<float>::complex(const complex<long double>& __z)
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: _M_value(_ComplexT(__z._M_value)) {}
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inline complex<float>&
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complex<float>::operator= (float __f)
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{
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__real__ _M_value = __f;
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__imag__ _M_value = 0.0f;
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return *this;
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}
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inline complex<float>&
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complex<float>::operator+= (float __f)
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{
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__real__ _M_value += __f;
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return *this;
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}
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inline complex<float>&
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complex<float>::operator-= (float __f)
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{
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__real__ _M_value -= __f;
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return *this;
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}
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inline complex<float>&
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complex<float>::operator*= (float __f)
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{
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_M_value *= __f;
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return *this;
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}
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inline complex<float>&
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complex<float>::operator/= (float __f)
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{
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_M_value /= __f;
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return *this;
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}
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template<typename _Tp>
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inline complex<float>&
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complex<float>::operator= (const complex<_Tp>& __z)
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{
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__real__ _M_value = __z.real();
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__imag__ _M_value = __z.imag();
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return *this;
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}
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template<typename _Tp>
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inline complex<float>&
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complex<float>::operator+= (const complex<_Tp>& __z)
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{
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__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.real();
|
|
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;
|
|
}
|
|
|
|
|
|
//
|
|
// complex<double> continued.
|
|
//
|
|
inline
|
|
complex<double>::complex(double __r, double __i)
|
|
{
|
|
__real__ _M_value = __r;
|
|
__imag__ _M_value = __i;
|
|
}
|
|
|
|
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<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;
|
|
}
|
|
|
|
//
|
|
// Primary template class complex continued.
|
|
//
|
|
// 26.2.4
|
|
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()) {}
|
|
|
|
// 26.2.7/6
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
conj(const complex<_Tp>& __z)
|
|
{ return complex<_Tp>(__z.real(), -__z.imag()); }
|
|
|
|
// 26.2.7/4
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
norm(const complex<_Tp>& __z)
|
|
{
|
|
// XXX: Grammar school computation
|
|
return __z.real() * __z.real() + __z.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)
|
|
{
|
|
_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)
|
|
{
|
|
_Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
|
|
_Tp __n = norm(__z);
|
|
_M_imag = (_M_real * __z.imag() - _M_imag * __z.real()) / __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() == 0; }
|
|
|
|
template<typename _Tp>
|
|
inline bool
|
|
operator==(const _Tp& __x, const complex<_Tp>& __y)
|
|
{ return __x == __y.real() && 0 == __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() != 0; }
|
|
|
|
template<typename _Tp>
|
|
inline bool
|
|
operator!=(const _Tp& __x, const complex<_Tp>& __y)
|
|
{ return __x != __y.real() || 0 != __y.imag(); }
|
|
|
|
template<typename _Tp, typename _CharT, class _Traits>
|
|
basic_istream<_CharT, _Traits>&
|
|
operator>>(basic_istream<_CharT, _Traits>&, complex<_Tp>&);
|
|
|
|
template<typename _Tp, typename _CharT, class _Traits>
|
|
basic_ostream<_CharT, _Traits>&
|
|
operator<<(basic_ostream<_CharT, _Traits>&, const complex<_Tp>&);
|
|
|
|
|
|
// 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(); }
|
|
|
|
|
|
// We use here a few more specializations.
|
|
template<>
|
|
inline complex<float>
|
|
conj(const complex<float> &__x)
|
|
#ifdef _GLIBCPP_BUGGY_FLOAT_COMPLEX
|
|
{
|
|
complex<float> __tmpf(~__x._M_value);
|
|
return __tmpf;
|
|
}
|
|
#else
|
|
{ return complex<float>(~__x._M_value); }
|
|
#endif
|
|
|
|
template<>
|
|
inline complex<double>
|
|
conj(const complex<double> &__x)
|
|
{ return complex<double> (~__x._M_value); }
|
|
|
|
template<>
|
|
inline complex<long double>
|
|
conj(const complex<long double> &__x)
|
|
{
|
|
return complex<long double> (~__x._M_value);
|
|
}
|
|
|
|
} // namespace std
|
|
|
|
#endif /* _CPP_COMPLEX */
|