1934 lines
51 KiB
C++
1934 lines
51 KiB
C++
// The template and inlines for the -*- C++ -*- complex number classes.
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// Copyright (C) 1997-2013 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 3, 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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// Under Section 7 of GPL version 3, you are granted additional
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// permissions described in the GCC Runtime Library Exception, version
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// 3.1, as published by the Free Software Foundation.
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// You should have received a copy of the GNU General Public License and
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// a copy of the GCC Runtime Library Exception along with this program;
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// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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// <http://www.gnu.org/licenses/>.
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/** @file include/complex
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* This is a Standard C++ Library header.
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*/
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//
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// ISO C++ 14882: 26.2 Complex Numbers
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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 _GLIBCXX_COMPLEX
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#define _GLIBCXX_COMPLEX 1
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#pragma GCC system_header
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#include <bits/c++config.h>
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#include <bits/cpp_type_traits.h>
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#include <ext/type_traits.h>
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#include <cmath>
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#include <sstream>
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// Get rid of a macro possibly defined in <complex.h>
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#undef complex
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namespace std _GLIBCXX_VISIBILITY(default)
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{
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_GLIBCXX_BEGIN_NAMESPACE_VERSION
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/**
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* @defgroup complex_numbers Complex Numbers
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* @ingroup numerics
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*
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* Classes and functions for complex numbers.
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* @{
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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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/// Return magnitude of @a z.
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template<typename _Tp> _Tp abs(const complex<_Tp>&);
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/// Return phase angle of @a z.
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template<typename _Tp> _Tp arg(const complex<_Tp>&);
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/// Return @a z magnitude squared.
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template<typename _Tp> _Tp norm(const complex<_Tp>&);
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/// Return complex conjugate of @a z.
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template<typename _Tp> complex<_Tp> conj(const complex<_Tp>&);
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/// Return complex with magnitude @a rho and angle @a theta.
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template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
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// Transcendentals:
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/// Return complex cosine of @a z.
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template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
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/// Return complex hyperbolic cosine of @a z.
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template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
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/// Return complex base e exponential of @a z.
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template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
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/// Return complex natural logarithm of @a z.
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template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
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/// Return complex base 10 logarithm of @a z.
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template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
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#if __cplusplus < 201103L
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// DR 844.
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/// Return @a x to the @a y'th power.
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template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
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#endif
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/// Return @a x to the @a y'th power.
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template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
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/// Return @a x to the @a y'th power.
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template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
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const complex<_Tp>&);
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/// Return @a x to the @a y'th power.
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template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
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/// Return complex sine of @a z.
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template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
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/// Return complex hyperbolic sine of @a z.
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template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
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/// Return complex square root of @a z.
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template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
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/// Return complex tangent of @a z.
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template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
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/// Return complex hyperbolic tangent of @a z.
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template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
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// 26.2.2 Primary template class complex
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/**
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* Template to represent complex numbers.
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*
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* Specializations for float, double, and long double are part of the
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* library. Results with any other type are not guaranteed.
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*
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* @param Tp Type of real and imaginary values.
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*/
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template<typename _Tp>
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struct complex
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{
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/// Value typedef.
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typedef _Tp value_type;
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/// Default constructor. First parameter is x, second parameter is y.
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/// Unspecified parameters default to 0.
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_GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
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: _M_real(__r), _M_imag(__i) { }
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// Lets the compiler synthesize the copy constructor
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// complex (const complex<_Tp>&);
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/// Copy constructor.
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template<typename _Up>
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_GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
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: _M_real(__z.real()), _M_imag(__z.imag()) { }
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#if __cplusplus >= 201103L
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// _GLIBCXX_RESOLVE_LIB_DEFECTS
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// DR 387. std::complex over-encapsulated.
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_GLIBCXX_ABI_TAG_CXX11
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constexpr _Tp
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real() { return _M_real; }
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_GLIBCXX_ABI_TAG_CXX11
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constexpr _Tp
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imag() { return _M_imag; }
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#else
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/// Return real part of complex number.
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_Tp&
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real() { return _M_real; }
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/// Return real part of complex number.
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const _Tp&
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real() const { return _M_real; }
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/// Return imaginary part of complex number.
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_Tp&
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imag() { return _M_imag; }
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/// Return imaginary part of complex number.
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const _Tp&
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imag() const { return _M_imag; }
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#endif
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// _GLIBCXX_RESOLVE_LIB_DEFECTS
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// DR 387. std::complex over-encapsulated.
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void
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real(_Tp __val) { _M_real = __val; }
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void
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imag(_Tp __val) { _M_imag = __val; }
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/// Assign this complex number to scalar @a t.
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complex<_Tp>& operator=(const _Tp&);
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/// Add @a t to this complex number.
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// 26.2.5/1
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complex<_Tp>&
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operator+=(const _Tp& __t)
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{
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_M_real += __t;
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return *this;
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}
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/// Subtract @a t from this complex number.
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// 26.2.5/3
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complex<_Tp>&
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operator-=(const _Tp& __t)
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{
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_M_real -= __t;
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return *this;
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}
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/// Multiply this complex number by @a t.
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complex<_Tp>& operator*=(const _Tp&);
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/// Divide this complex number by @a t.
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complex<_Tp>& operator/=(const _Tp&);
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// Lets the compiler synthesize the
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// copy and assignment operator
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// complex<_Tp>& operator= (const complex<_Tp>&);
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/// Assign this complex number to complex @a z.
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template<typename _Up>
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complex<_Tp>& operator=(const complex<_Up>&);
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/// Add @a z to this complex number.
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template<typename _Up>
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complex<_Tp>& operator+=(const complex<_Up>&);
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/// Subtract @a z from this complex number.
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template<typename _Up>
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complex<_Tp>& operator-=(const complex<_Up>&);
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/// Multiply this complex number by @a z.
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template<typename _Up>
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complex<_Tp>& operator*=(const complex<_Up>&);
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/// Divide this complex number by @a z.
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template<typename _Up>
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complex<_Tp>& operator/=(const complex<_Up>&);
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_GLIBCXX_USE_CONSTEXPR complex __rep() const
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{ return *this; }
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private:
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_Tp _M_real;
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_Tp _M_imag;
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};
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template<typename _Tp>
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complex<_Tp>&
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complex<_Tp>::operator=(const _Tp& __t)
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{
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_M_real = __t;
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_M_imag = _Tp();
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return *this;
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}
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// 26.2.5/5
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template<typename _Tp>
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complex<_Tp>&
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complex<_Tp>::operator*=(const _Tp& __t)
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{
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_M_real *= __t;
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_M_imag *= __t;
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return *this;
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}
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// 26.2.5/7
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template<typename _Tp>
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complex<_Tp>&
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complex<_Tp>::operator/=(const _Tp& __t)
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{
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_M_real /= __t;
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_M_imag /= __t;
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return *this;
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}
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template<typename _Tp>
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template<typename _Up>
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complex<_Tp>&
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complex<_Tp>::operator=(const complex<_Up>& __z)
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{
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_M_real = __z.real();
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_M_imag = __z.imag();
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return *this;
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}
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// 26.2.5/9
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template<typename _Tp>
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template<typename _Up>
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complex<_Tp>&
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complex<_Tp>::operator+=(const complex<_Up>& __z)
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{
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_M_real += __z.real();
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_M_imag += __z.imag();
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return *this;
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}
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// 26.2.5/11
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template<typename _Tp>
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template<typename _Up>
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complex<_Tp>&
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complex<_Tp>::operator-=(const complex<_Up>& __z)
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{
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_M_real -= __z.real();
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_M_imag -= __z.imag();
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return *this;
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}
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// 26.2.5/13
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// XXX: This is a grammar school implementation.
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template<typename _Tp>
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template<typename _Up>
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complex<_Tp>&
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complex<_Tp>::operator*=(const complex<_Up>& __z)
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{
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const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
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_M_imag = _M_real * __z.imag() + _M_imag * __z.real();
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_M_real = __r;
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return *this;
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}
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// 26.2.5/15
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// XXX: This is a grammar school implementation.
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template<typename _Tp>
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template<typename _Up>
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complex<_Tp>&
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complex<_Tp>::operator/=(const complex<_Up>& __z)
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{
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const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
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const _Tp __n = std::norm(__z);
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_M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
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_M_real = __r / __n;
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return *this;
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}
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// Operators:
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//@{
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/// Return new complex value @a x plus @a y.
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template<typename _Tp>
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inline complex<_Tp>
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operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
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{
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complex<_Tp> __r = __x;
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__r += __y;
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return __r;
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}
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template<typename _Tp>
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inline complex<_Tp>
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operator+(const complex<_Tp>& __x, const _Tp& __y)
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{
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complex<_Tp> __r = __x;
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__r += __y;
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return __r;
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}
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template<typename _Tp>
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inline complex<_Tp>
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operator+(const _Tp& __x, const complex<_Tp>& __y)
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{
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complex<_Tp> __r = __y;
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__r += __x;
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return __r;
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}
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//@}
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//@{
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/// Return new complex value @a x minus @a y.
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template<typename _Tp>
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inline complex<_Tp>
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operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
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{
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complex<_Tp> __r = __x;
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__r -= __y;
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return __r;
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}
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template<typename _Tp>
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inline complex<_Tp>
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operator-(const complex<_Tp>& __x, const _Tp& __y)
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{
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complex<_Tp> __r = __x;
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__r -= __y;
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return __r;
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}
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template<typename _Tp>
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inline complex<_Tp>
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operator-(const _Tp& __x, const complex<_Tp>& __y)
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{
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complex<_Tp> __r(__x, -__y.imag());
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__r -= __y.real();
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return __r;
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}
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//@}
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//@{
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/// Return new complex value @a x times @a y.
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template<typename _Tp>
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inline complex<_Tp>
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operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
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{
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complex<_Tp> __r = __x;
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__r *= __y;
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return __r;
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}
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template<typename _Tp>
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inline complex<_Tp>
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operator*(const complex<_Tp>& __x, const _Tp& __y)
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{
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complex<_Tp> __r = __x;
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__r *= __y;
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return __r;
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}
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template<typename _Tp>
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inline complex<_Tp>
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operator*(const _Tp& __x, const complex<_Tp>& __y)
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{
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complex<_Tp> __r = __y;
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__r *= __x;
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return __r;
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}
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//@}
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//@{
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/// Return new complex value @a x divided by @a y.
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template<typename _Tp>
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inline complex<_Tp>
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operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
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{
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complex<_Tp> __r = __x;
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__r /= __y;
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return __r;
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}
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template<typename _Tp>
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inline complex<_Tp>
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operator/(const complex<_Tp>& __x, const _Tp& __y)
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{
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complex<_Tp> __r = __x;
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__r /= __y;
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return __r;
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}
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template<typename _Tp>
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inline complex<_Tp>
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operator/(const _Tp& __x, const complex<_Tp>& __y)
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{
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complex<_Tp> __r = __x;
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__r /= __y;
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return __r;
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}
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//@}
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/// Return @a x.
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template<typename _Tp>
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inline complex<_Tp>
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operator+(const complex<_Tp>& __x)
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{ return __x; }
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/// Return complex negation of @a x.
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template<typename _Tp>
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inline complex<_Tp>
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operator-(const complex<_Tp>& __x)
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{ return complex<_Tp>(-__x.real(), -__x.imag()); }
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//@{
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/// Return true if @a x is equal to @a y.
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template<typename _Tp>
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inline _GLIBCXX_CONSTEXPR bool
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operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
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{ return __x.real() == __y.real() && __x.imag() == __y.imag(); }
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template<typename _Tp>
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inline _GLIBCXX_CONSTEXPR bool
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operator==(const complex<_Tp>& __x, const _Tp& __y)
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{ return __x.real() == __y && __x.imag() == _Tp(); }
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template<typename _Tp>
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inline _GLIBCXX_CONSTEXPR bool
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operator==(const _Tp& __x, const complex<_Tp>& __y)
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{ return __x == __y.real() && _Tp() == __y.imag(); }
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//@}
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//@{
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/// Return false if @a x is equal to @a y.
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template<typename _Tp>
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inline _GLIBCXX_CONSTEXPR bool
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operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
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{ return __x.real() != __y.real() || __x.imag() != __y.imag(); }
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template<typename _Tp>
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inline _GLIBCXX_CONSTEXPR bool
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operator!=(const complex<_Tp>& __x, const _Tp& __y)
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{ return __x.real() != __y || __x.imag() != _Tp(); }
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template<typename _Tp>
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inline _GLIBCXX_CONSTEXPR bool
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operator!=(const _Tp& __x, const complex<_Tp>& __y)
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{ return __x != __y.real() || _Tp() != __y.imag(); }
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//@}
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/// Extraction operator for complex values.
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template<typename _Tp, typename _CharT, class _Traits>
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basic_istream<_CharT, _Traits>&
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operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
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{
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_Tp __re_x, __im_x;
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_CharT __ch;
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__is >> __ch;
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if (__ch == '(')
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{
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__is >> __re_x >> __ch;
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if (__ch == ',')
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{
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__is >> __im_x >> __ch;
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if (__ch == ')')
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__x = complex<_Tp>(__re_x, __im_x);
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else
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__is.setstate(ios_base::failbit);
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}
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else if (__ch == ')')
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__x = __re_x;
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else
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__is.setstate(ios_base::failbit);
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}
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else
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{
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__is.putback(__ch);
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__is >> __re_x;
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__x = __re_x;
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}
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return __is;
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}
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/// Insertion operator for complex values.
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template<typename _Tp, typename _CharT, class _Traits>
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basic_ostream<_CharT, _Traits>&
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operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
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{
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basic_ostringstream<_CharT, _Traits> __s;
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__s.flags(__os.flags());
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__s.imbue(__os.getloc());
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__s.precision(__os.precision());
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__s << '(' << __x.real() << ',' << __x.imag() << ')';
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return __os << __s.str();
|
|
}
|
|
|
|
// Values
|
|
#if __cplusplus >= 201103L
|
|
template<typename _Tp>
|
|
constexpr _Tp
|
|
real(const complex<_Tp>& __z)
|
|
{ return __z.real(); }
|
|
|
|
template<typename _Tp>
|
|
constexpr _Tp
|
|
imag(const complex<_Tp>& __z)
|
|
{ return __z.imag(); }
|
|
#else
|
|
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(); }
|
|
#endif
|
|
|
|
// 26.2.7/3 abs(__z): Returns the magnitude of __z.
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
__complex_abs(const complex<_Tp>& __z)
|
|
{
|
|
_Tp __x = __z.real();
|
|
_Tp __y = __z.imag();
|
|
const _Tp __s = std::max(abs(__x), abs(__y));
|
|
if (__s == _Tp()) // well ...
|
|
return __s;
|
|
__x /= __s;
|
|
__y /= __s;
|
|
return __s * sqrt(__x * __x + __y * __y);
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline float
|
|
__complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
|
|
|
|
inline double
|
|
__complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
|
|
|
|
inline long double
|
|
__complex_abs(const __complex__ long double& __z)
|
|
{ return __builtin_cabsl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
|
|
#endif
|
|
|
|
|
|
// 26.2.7/4: arg(__z): Returns the phase angle of __z.
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
__complex_arg(const complex<_Tp>& __z)
|
|
{ return atan2(__z.imag(), __z.real()); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline float
|
|
__complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
|
|
|
|
inline double
|
|
__complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
|
|
|
|
inline long double
|
|
__complex_arg(const __complex__ long double& __z)
|
|
{ return __builtin_cargl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
|
|
#endif
|
|
|
|
// 26.2.7/5: norm(__z) returns the squared magnitude of __z.
|
|
// As defined, norm() is -not- a norm is the common mathematical
|
|
// sens used in numerics. The helper class _Norm_helper<> tries to
|
|
// distinguish between builtin floating point and the rest, so as
|
|
// to deliver an answer as close as possible to the real value.
|
|
template<bool>
|
|
struct _Norm_helper
|
|
{
|
|
template<typename _Tp>
|
|
static inline _Tp _S_do_it(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return __x * __x + __y * __y;
|
|
}
|
|
};
|
|
|
|
template<>
|
|
struct _Norm_helper<true>
|
|
{
|
|
template<typename _Tp>
|
|
static inline _Tp _S_do_it(const complex<_Tp>& __z)
|
|
{
|
|
_Tp __res = std::abs(__z);
|
|
return __res * __res;
|
|
}
|
|
};
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
norm(const complex<_Tp>& __z)
|
|
{
|
|
return _Norm_helper<__is_floating<_Tp>::__value
|
|
&& !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
polar(const _Tp& __rho, const _Tp& __theta)
|
|
{ return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
conj(const complex<_Tp>& __z)
|
|
{ return complex<_Tp>(__z.real(), -__z.imag()); }
|
|
|
|
// Transcendentals
|
|
|
|
// 26.2.8/1 cos(__z): Returns the cosine of __z.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_cos(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_cos(const __complex__ long double& __z)
|
|
{ return __builtin_ccosl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_cosh(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_cosh(const __complex__ long double& __z)
|
|
{ return __builtin_ccoshl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/3 exp(__z): Returns the complex base e exponential of x
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_exp(const complex<_Tp>& __z)
|
|
{ return std::polar(exp(__z.real()), __z.imag()); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_exp(const __complex__ long double& __z)
|
|
{ return __builtin_cexpl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
|
|
// The branch cut is along the negative axis.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_log(const complex<_Tp>& __z)
|
|
{ return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_log(__complex__ double __z) { return __builtin_clog(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_log(const __complex__ long double& __z)
|
|
{ return __builtin_clogl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
log(const complex<_Tp>& __z) { return __complex_log(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
log10(const complex<_Tp>& __z)
|
|
{ return std::log(__z) / log(_Tp(10.0)); }
|
|
|
|
// 26.2.8/10 sin(__z): Returns the sine of __z.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_sin(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_sin(const __complex__ long double& __z)
|
|
{ return __builtin_csinl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_sinh(const complex<_Tp>& __z)
|
|
{
|
|
const _Tp __x = __z.real();
|
|
const _Tp __y = __z.imag();
|
|
return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_sinh(const __complex__ long double& __z)
|
|
{ return __builtin_csinhl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
|
|
// The branch cut is on the negative axis.
|
|
template<typename _Tp>
|
|
complex<_Tp>
|
|
__complex_sqrt(const complex<_Tp>& __z)
|
|
{
|
|
_Tp __x = __z.real();
|
|
_Tp __y = __z.imag();
|
|
|
|
if (__x == _Tp())
|
|
{
|
|
_Tp __t = sqrt(abs(__y) / 2);
|
|
return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
|
|
}
|
|
else
|
|
{
|
|
_Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
|
|
_Tp __u = __t / 2;
|
|
return __x > _Tp()
|
|
? complex<_Tp>(__u, __y / __t)
|
|
: complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
|
|
}
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_sqrt(const __complex__ long double& __z)
|
|
{ return __builtin_csqrtl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
|
|
#endif
|
|
|
|
// 26.2.8/14 tan(__z): Return the complex tangent of __z.
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_tan(const complex<_Tp>& __z)
|
|
{ return std::sin(__z) / std::cos(__z); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_tan(const __complex__ long double& __z)
|
|
{ return __builtin_ctanl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
|
|
#endif
|
|
|
|
|
|
// 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_tanh(const complex<_Tp>& __z)
|
|
{ return std::sinh(__z) / std::cosh(__z); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_tanh(const __complex__ long double& __z)
|
|
{ return __builtin_ctanhl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
|
|
#endif
|
|
|
|
|
|
// 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
|
|
// raised to the __y-th power. The branch
|
|
// cut is on the negative axis.
|
|
#if __cplusplus < 201103L
|
|
template<typename _Tp>
|
|
complex<_Tp>
|
|
__complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
|
|
{
|
|
complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
|
|
|
|
while (__n >>= 1)
|
|
{
|
|
__x *= __x;
|
|
if (__n % 2)
|
|
__y *= __x;
|
|
}
|
|
|
|
return __y;
|
|
}
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 844. complex pow return type is ambiguous.
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const complex<_Tp>& __z, int __n)
|
|
{
|
|
return __n < 0
|
|
? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
|
|
: std::__complex_pow_unsigned(__z, __n);
|
|
}
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
complex<_Tp>
|
|
pow(const complex<_Tp>& __x, const _Tp& __y)
|
|
{
|
|
#ifndef _GLIBCXX_USE_C99_COMPLEX
|
|
if (__x == _Tp())
|
|
return _Tp();
|
|
#endif
|
|
if (__x.imag() == _Tp() && __x.real() > _Tp())
|
|
return pow(__x.real(), __y);
|
|
|
|
complex<_Tp> __t = std::log(__x);
|
|
return std::polar(exp(__y * __t.real()), __y * __t.imag());
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
__complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_pow(__complex__ float __x, __complex__ float __y)
|
|
{ return __builtin_cpowf(__x, __y); }
|
|
|
|
inline __complex__ double
|
|
__complex_pow(__complex__ double __x, __complex__ double __y)
|
|
{ return __builtin_cpow(__x, __y); }
|
|
|
|
inline __complex__ long double
|
|
__complex_pow(const __complex__ long double& __x,
|
|
const __complex__ long double& __y)
|
|
{ return __builtin_cpowl(__x, __y); }
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return __complex_pow(__x.__rep(), __y.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
|
{ return __complex_pow(__x, __y); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline complex<_Tp>
|
|
pow(const _Tp& __x, const complex<_Tp>& __y)
|
|
{
|
|
return __x > _Tp() ? std::polar(pow(__x, __y.real()),
|
|
__y.imag() * log(__x))
|
|
: std::pow(complex<_Tp>(__x), __y);
|
|
}
|
|
|
|
/// 26.2.3 complex specializations
|
|
/// complex<float> specialization
|
|
template<>
|
|
struct complex<float>
|
|
{
|
|
typedef float value_type;
|
|
typedef __complex__ float _ComplexT;
|
|
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
_GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
|
|
#if __cplusplus >= 201103L
|
|
: _M_value{ __r, __i } { }
|
|
#else
|
|
{
|
|
__real__ _M_value = __r;
|
|
__imag__ _M_value = __i;
|
|
}
|
|
#endif
|
|
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
|
|
|
|
#if __cplusplus >= 201103L
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr float
|
|
real() { return __real__ _M_value; }
|
|
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr float
|
|
imag() { return __imag__ _M_value; }
|
|
#else
|
|
float&
|
|
real() { return __real__ _M_value; }
|
|
|
|
const float&
|
|
real() const { return __real__ _M_value; }
|
|
|
|
float&
|
|
imag() { return __imag__ _M_value; }
|
|
|
|
const float&
|
|
imag() const { return __imag__ _M_value; }
|
|
#endif
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
void
|
|
real(float __val) { __real__ _M_value = __val; }
|
|
|
|
void
|
|
imag(float __val) { __imag__ _M_value = __val; }
|
|
|
|
complex&
|
|
operator=(float __f)
|
|
{
|
|
_M_value = __f;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator+=(float __f)
|
|
{
|
|
_M_value += __f;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator-=(float __f)
|
|
{
|
|
_M_value -= __f;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator*=(float __f)
|
|
{
|
|
_M_value *= __f;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator/=(float __f)
|
|
{
|
|
_M_value /= __f;
|
|
return *this;
|
|
}
|
|
|
|
// Let the compiler synthesize the copy and assignment
|
|
// operator. It always does a pretty good job.
|
|
// complex& operator=(const complex&);
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value = __z.real();
|
|
__imag__ _M_value = __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator+=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value += __z.real();
|
|
__imag__ _M_value += __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<class _Tp>
|
|
complex&
|
|
operator-=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value -= __z.real();
|
|
__imag__ _M_value -= __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<class _Tp>
|
|
complex&
|
|
operator*=(const complex<_Tp>& __z)
|
|
{
|
|
_ComplexT __t;
|
|
__real__ __t = __z.real();
|
|
__imag__ __t = __z.imag();
|
|
_M_value *= __t;
|
|
return *this;
|
|
}
|
|
|
|
template<class _Tp>
|
|
complex&
|
|
operator/=(const complex<_Tp>& __z)
|
|
{
|
|
_ComplexT __t;
|
|
__real__ __t = __z.real();
|
|
__imag__ __t = __z.imag();
|
|
_M_value /= __t;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
|
|
|
private:
|
|
_ComplexT _M_value;
|
|
};
|
|
|
|
/// 26.2.3 complex specializations
|
|
/// complex<double> specialization
|
|
template<>
|
|
struct complex<double>
|
|
{
|
|
typedef double value_type;
|
|
typedef __complex__ double _ComplexT;
|
|
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
_GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
|
|
#if __cplusplus >= 201103L
|
|
: _M_value{ __r, __i } { }
|
|
#else
|
|
{
|
|
__real__ _M_value = __r;
|
|
__imag__ _M_value = __i;
|
|
}
|
|
#endif
|
|
|
|
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
|
|
|
|
#if __cplusplus >= 201103L
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr double
|
|
real() { return __real__ _M_value; }
|
|
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr double
|
|
imag() { return __imag__ _M_value; }
|
|
#else
|
|
double&
|
|
real() { return __real__ _M_value; }
|
|
|
|
const double&
|
|
real() const { return __real__ _M_value; }
|
|
|
|
double&
|
|
imag() { return __imag__ _M_value; }
|
|
|
|
const double&
|
|
imag() const { return __imag__ _M_value; }
|
|
#endif
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
void
|
|
real(double __val) { __real__ _M_value = __val; }
|
|
|
|
void
|
|
imag(double __val) { __imag__ _M_value = __val; }
|
|
|
|
complex&
|
|
operator=(double __d)
|
|
{
|
|
_M_value = __d;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator+=(double __d)
|
|
{
|
|
_M_value += __d;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator-=(double __d)
|
|
{
|
|
_M_value -= __d;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator*=(double __d)
|
|
{
|
|
_M_value *= __d;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator/=(double __d)
|
|
{
|
|
_M_value /= __d;
|
|
return *this;
|
|
}
|
|
|
|
// The compiler will synthesize this, efficiently.
|
|
// complex& operator=(const complex&);
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value = __z.real();
|
|
__imag__ _M_value = __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator+=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value += __z.real();
|
|
__imag__ _M_value += __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator-=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value -= __z.real();
|
|
__imag__ _M_value -= __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator*=(const complex<_Tp>& __z)
|
|
{
|
|
_ComplexT __t;
|
|
__real__ __t = __z.real();
|
|
__imag__ __t = __z.imag();
|
|
_M_value *= __t;
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator/=(const complex<_Tp>& __z)
|
|
{
|
|
_ComplexT __t;
|
|
__real__ __t = __z.real();
|
|
__imag__ __t = __z.imag();
|
|
_M_value /= __t;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
|
|
|
private:
|
|
_ComplexT _M_value;
|
|
};
|
|
|
|
/// 26.2.3 complex specializations
|
|
/// complex<long double> specialization
|
|
template<>
|
|
struct complex<long double>
|
|
{
|
|
typedef long double value_type;
|
|
typedef __complex__ long double _ComplexT;
|
|
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
|
|
|
_GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
|
|
long double __i = 0.0L)
|
|
#if __cplusplus >= 201103L
|
|
: _M_value{ __r, __i } { }
|
|
#else
|
|
{
|
|
__real__ _M_value = __r;
|
|
__imag__ _M_value = __i;
|
|
}
|
|
#endif
|
|
|
|
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
_GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
#if __cplusplus >= 201103L
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr long double
|
|
real() { return __real__ _M_value; }
|
|
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
|
constexpr long double
|
|
imag() { return __imag__ _M_value; }
|
|
#else
|
|
long double&
|
|
real() { return __real__ _M_value; }
|
|
|
|
const long double&
|
|
real() const { return __real__ _M_value; }
|
|
|
|
long double&
|
|
imag() { return __imag__ _M_value; }
|
|
|
|
const long double&
|
|
imag() const { return __imag__ _M_value; }
|
|
#endif
|
|
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
|
// DR 387. std::complex over-encapsulated.
|
|
void
|
|
real(long double __val) { __real__ _M_value = __val; }
|
|
|
|
void
|
|
imag(long double __val) { __imag__ _M_value = __val; }
|
|
|
|
complex&
|
|
operator=(long double __r)
|
|
{
|
|
_M_value = __r;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator+=(long double __r)
|
|
{
|
|
_M_value += __r;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator-=(long double __r)
|
|
{
|
|
_M_value -= __r;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator*=(long double __r)
|
|
{
|
|
_M_value *= __r;
|
|
return *this;
|
|
}
|
|
|
|
complex&
|
|
operator/=(long double __r)
|
|
{
|
|
_M_value /= __r;
|
|
return *this;
|
|
}
|
|
|
|
// The compiler knows how to do this efficiently
|
|
// complex& operator=(const complex&);
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value = __z.real();
|
|
__imag__ _M_value = __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator+=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value += __z.real();
|
|
__imag__ _M_value += __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator-=(const complex<_Tp>& __z)
|
|
{
|
|
__real__ _M_value -= __z.real();
|
|
__imag__ _M_value -= __z.imag();
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator*=(const complex<_Tp>& __z)
|
|
{
|
|
_ComplexT __t;
|
|
__real__ __t = __z.real();
|
|
__imag__ __t = __z.imag();
|
|
_M_value *= __t;
|
|
return *this;
|
|
}
|
|
|
|
template<typename _Tp>
|
|
complex&
|
|
operator/=(const complex<_Tp>& __z)
|
|
{
|
|
_ComplexT __t;
|
|
__real__ __t = __z.real();
|
|
__imag__ __t = __z.imag();
|
|
_M_value /= __t;
|
|
return *this;
|
|
}
|
|
|
|
_GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
|
|
|
private:
|
|
_ComplexT _M_value;
|
|
};
|
|
|
|
// These bits have to be at the end of this file, so that the
|
|
// specializations have all been defined.
|
|
inline _GLIBCXX_CONSTEXPR
|
|
complex<float>::complex(const complex<double>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
inline _GLIBCXX_CONSTEXPR
|
|
complex<float>::complex(const complex<long double>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
inline _GLIBCXX_CONSTEXPR
|
|
complex<double>::complex(const complex<long double>& __z)
|
|
: _M_value(__z.__rep()) { }
|
|
|
|
// Inhibit implicit instantiations for required instantiations,
|
|
// which are defined via explicit instantiations elsewhere.
|
|
// NB: This syntax is a GNU extension.
|
|
#if _GLIBCXX_EXTERN_TEMPLATE
|
|
extern template istream& operator>>(istream&, complex<float>&);
|
|
extern template ostream& operator<<(ostream&, const complex<float>&);
|
|
extern template istream& operator>>(istream&, complex<double>&);
|
|
extern template ostream& operator<<(ostream&, const complex<double>&);
|
|
extern template istream& operator>>(istream&, complex<long double>&);
|
|
extern template ostream& operator<<(ostream&, const complex<long double>&);
|
|
|
|
#ifdef _GLIBCXX_USE_WCHAR_T
|
|
extern template wistream& operator>>(wistream&, complex<float>&);
|
|
extern template wostream& operator<<(wostream&, const complex<float>&);
|
|
extern template wistream& operator>>(wistream&, complex<double>&);
|
|
extern template wostream& operator<<(wostream&, const complex<double>&);
|
|
extern template wistream& operator>>(wistream&, complex<long double>&);
|
|
extern template wostream& operator<<(wostream&, const complex<long double>&);
|
|
#endif
|
|
#endif
|
|
|
|
// @} group complex_numbers
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace
|
|
|
|
namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
|
|
{
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
|
|
|
// See ext/type_traits.h for the primary template.
|
|
template<typename _Tp, typename _Up>
|
|
struct __promote_2<std::complex<_Tp>, _Up>
|
|
{
|
|
public:
|
|
typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
|
|
};
|
|
|
|
template<typename _Tp, typename _Up>
|
|
struct __promote_2<_Tp, std::complex<_Up> >
|
|
{
|
|
public:
|
|
typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
|
|
};
|
|
|
|
template<typename _Tp, typename _Up>
|
|
struct __promote_2<std::complex<_Tp>, std::complex<_Up> >
|
|
{
|
|
public:
|
|
typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
|
|
};
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace
|
|
|
|
#if __cplusplus >= 201103L
|
|
|
|
namespace std _GLIBCXX_VISIBILITY(default)
|
|
{
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
|
|
|
// Forward declarations.
|
|
template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
|
|
template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
|
|
template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
|
|
|
|
template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
|
|
template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
|
|
template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
|
|
// DR 595.
|
|
template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
__complex_acos(const std::complex<_Tp>& __z)
|
|
{
|
|
const std::complex<_Tp> __t = std::asin(__z);
|
|
const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
|
|
return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
|
inline __complex__ float
|
|
__complex_acos(__complex__ float __z)
|
|
{ return __builtin_cacosf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_acos(__complex__ double __z)
|
|
{ return __builtin_cacos(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_acos(const __complex__ long double& __z)
|
|
{ return __builtin_cacosl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
acos(const std::complex<_Tp>& __z)
|
|
{ return __complex_acos(__z.__rep()); }
|
|
#else
|
|
/// acos(__z) [8.1.2].
|
|
// Effects: Behaves the same as C99 function cacos, defined
|
|
// in subclause 7.3.5.1.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
acos(const std::complex<_Tp>& __z)
|
|
{ return __complex_acos(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
__complex_asin(const std::complex<_Tp>& __z)
|
|
{
|
|
std::complex<_Tp> __t(-__z.imag(), __z.real());
|
|
__t = std::asinh(__t);
|
|
return std::complex<_Tp>(__t.imag(), -__t.real());
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
|
inline __complex__ float
|
|
__complex_asin(__complex__ float __z)
|
|
{ return __builtin_casinf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_asin(__complex__ double __z)
|
|
{ return __builtin_casin(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_asin(const __complex__ long double& __z)
|
|
{ return __builtin_casinl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
asin(const std::complex<_Tp>& __z)
|
|
{ return __complex_asin(__z.__rep()); }
|
|
#else
|
|
/// asin(__z) [8.1.3].
|
|
// Effects: Behaves the same as C99 function casin, defined
|
|
// in subclause 7.3.5.2.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
asin(const std::complex<_Tp>& __z)
|
|
{ return __complex_asin(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_atan(const std::complex<_Tp>& __z)
|
|
{
|
|
const _Tp __r2 = __z.real() * __z.real();
|
|
const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
|
|
|
|
_Tp __num = __z.imag() + _Tp(1.0);
|
|
_Tp __den = __z.imag() - _Tp(1.0);
|
|
|
|
__num = __r2 + __num * __num;
|
|
__den = __r2 + __den * __den;
|
|
|
|
return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
|
|
_Tp(0.25) * log(__num / __den));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
|
inline __complex__ float
|
|
__complex_atan(__complex__ float __z)
|
|
{ return __builtin_catanf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_atan(__complex__ double __z)
|
|
{ return __builtin_catan(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_atan(const __complex__ long double& __z)
|
|
{ return __builtin_catanl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
atan(const std::complex<_Tp>& __z)
|
|
{ return __complex_atan(__z.__rep()); }
|
|
#else
|
|
/// atan(__z) [8.1.4].
|
|
// Effects: Behaves the same as C99 function catan, defined
|
|
// in subclause 7.3.5.3.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
atan(const std::complex<_Tp>& __z)
|
|
{ return __complex_atan(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_acosh(const std::complex<_Tp>& __z)
|
|
{
|
|
// Kahan's formula.
|
|
return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
|
|
+ std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
|
inline __complex__ float
|
|
__complex_acosh(__complex__ float __z)
|
|
{ return __builtin_cacoshf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_acosh(__complex__ double __z)
|
|
{ return __builtin_cacosh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_acosh(const __complex__ long double& __z)
|
|
{ return __builtin_cacoshl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
acosh(const std::complex<_Tp>& __z)
|
|
{ return __complex_acosh(__z.__rep()); }
|
|
#else
|
|
/// acosh(__z) [8.1.5].
|
|
// Effects: Behaves the same as C99 function cacosh, defined
|
|
// in subclause 7.3.6.1.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
acosh(const std::complex<_Tp>& __z)
|
|
{ return __complex_acosh(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_asinh(const std::complex<_Tp>& __z)
|
|
{
|
|
std::complex<_Tp> __t((__z.real() - __z.imag())
|
|
* (__z.real() + __z.imag()) + _Tp(1.0),
|
|
_Tp(2.0) * __z.real() * __z.imag());
|
|
__t = std::sqrt(__t);
|
|
|
|
return std::log(__t + __z);
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
|
inline __complex__ float
|
|
__complex_asinh(__complex__ float __z)
|
|
{ return __builtin_casinhf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_asinh(__complex__ double __z)
|
|
{ return __builtin_casinh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_asinh(const __complex__ long double& __z)
|
|
{ return __builtin_casinhl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
asinh(const std::complex<_Tp>& __z)
|
|
{ return __complex_asinh(__z.__rep()); }
|
|
#else
|
|
/// asinh(__z) [8.1.6].
|
|
// Effects: Behaves the same as C99 function casin, defined
|
|
// in subclause 7.3.6.2.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
asinh(const std::complex<_Tp>& __z)
|
|
{ return __complex_asinh(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_atanh(const std::complex<_Tp>& __z)
|
|
{
|
|
const _Tp __i2 = __z.imag() * __z.imag();
|
|
const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
|
|
|
|
_Tp __num = _Tp(1.0) + __z.real();
|
|
_Tp __den = _Tp(1.0) - __z.real();
|
|
|
|
__num = __i2 + __num * __num;
|
|
__den = __i2 + __den * __den;
|
|
|
|
return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
|
|
_Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
|
inline __complex__ float
|
|
__complex_atanh(__complex__ float __z)
|
|
{ return __builtin_catanhf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_atanh(__complex__ double __z)
|
|
{ return __builtin_catanh(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_atanh(const __complex__ long double& __z)
|
|
{ return __builtin_catanhl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
atanh(const std::complex<_Tp>& __z)
|
|
{ return __complex_atanh(__z.__rep()); }
|
|
#else
|
|
/// atanh(__z) [8.1.7].
|
|
// Effects: Behaves the same as C99 function catanh, defined
|
|
// in subclause 7.3.6.3.
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
atanh(const std::complex<_Tp>& __z)
|
|
{ return __complex_atanh(__z); }
|
|
#endif
|
|
|
|
template<typename _Tp>
|
|
inline _Tp
|
|
/// fabs(__z) [8.1.8].
|
|
// Effects: Behaves the same as C99 function cabs, defined
|
|
// in subclause 7.3.8.1.
|
|
fabs(const std::complex<_Tp>& __z)
|
|
{ return std::abs(__z); }
|
|
|
|
/// Additional overloads [8.1.9].
|
|
template<typename _Tp>
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
arg(_Tp __x)
|
|
{
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
|
#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
|
|
return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
|
|
: __type();
|
|
#else
|
|
return std::arg(std::complex<__type>(__x));
|
|
#endif
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
imag(_Tp)
|
|
{ return _Tp(); }
|
|
|
|
template<typename _Tp>
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
norm(_Tp __x)
|
|
{
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
|
return __type(__x) * __type(__x);
|
|
}
|
|
|
|
template<typename _Tp>
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
real(_Tp __x)
|
|
{ return __x; }
|
|
|
|
template<typename _Tp, typename _Up>
|
|
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
|
|
pow(const std::complex<_Tp>& __x, const _Up& __y)
|
|
{
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
|
return std::pow(std::complex<__type>(__x), __type(__y));
|
|
}
|
|
|
|
template<typename _Tp, typename _Up>
|
|
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
|
|
pow(const _Tp& __x, const std::complex<_Up>& __y)
|
|
{
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
|
return std::pow(__type(__x), std::complex<__type>(__y));
|
|
}
|
|
|
|
template<typename _Tp, typename _Up>
|
|
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
|
|
pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
|
|
{
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
|
return std::pow(std::complex<__type>(__x),
|
|
std::complex<__type>(__y));
|
|
}
|
|
|
|
// Forward declarations.
|
|
// DR 781.
|
|
template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
|
|
|
|
template<typename _Tp>
|
|
std::complex<_Tp>
|
|
__complex_proj(const std::complex<_Tp>& __z)
|
|
{
|
|
const _Tp __den = (__z.real() * __z.real()
|
|
+ __z.imag() * __z.imag() + _Tp(1.0));
|
|
|
|
return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
|
|
(_Tp(2.0) * __z.imag()) / __den);
|
|
}
|
|
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
|
inline __complex__ float
|
|
__complex_proj(__complex__ float __z)
|
|
{ return __builtin_cprojf(__z); }
|
|
|
|
inline __complex__ double
|
|
__complex_proj(__complex__ double __z)
|
|
{ return __builtin_cproj(__z); }
|
|
|
|
inline __complex__ long double
|
|
__complex_proj(const __complex__ long double& __z)
|
|
{ return __builtin_cprojl(__z); }
|
|
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
proj(const std::complex<_Tp>& __z)
|
|
{ return __complex_proj(__z.__rep()); }
|
|
#else
|
|
template<typename _Tp>
|
|
inline std::complex<_Tp>
|
|
proj(const std::complex<_Tp>& __z)
|
|
{ return __complex_proj(__z); }
|
|
#endif
|
|
|
|
// DR 1137.
|
|
template<typename _Tp>
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
proj(_Tp __x)
|
|
{ return __x; }
|
|
|
|
template<typename _Tp>
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
|
conj(_Tp __x)
|
|
{ return __x; }
|
|
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
|
} // namespace
|
|
|
|
#endif // C++11
|
|
|
|
#endif /* _GLIBCXX_COMPLEX */
|