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ultra_embe |
// The template and inlines for the -*- C++ -*- complex number classes.
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// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
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// 2006, 2007, 2008, 2009, 2010, 2011
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// 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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// .
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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
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// Improved by Gabriel Dos Reis
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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
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#include
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#include
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#include
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#include
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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 class complex;
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template<> class complex;
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template<> class complex;
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template<> class complex;
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/// Return magnitude of @a z.
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template _Tp abs(const complex<_Tp>&);
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/// Return phase angle of @a z.
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template _Tp arg(const complex<_Tp>&);
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/// Return @a z magnitude squared.
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template _Tp norm(const complex<_Tp>&);
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/// Return complex conjugate of @a z.
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template 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 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 complex<_Tp> cos(const complex<_Tp>&);
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/// Return complex hyperbolic cosine of @a z.
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template complex<_Tp> cosh(const complex<_Tp>&);
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/// Return complex base e exponential of @a z.
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template complex<_Tp> exp(const complex<_Tp>&);
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/// Return complex natural logarithm of @a z.
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template complex<_Tp> log(const complex<_Tp>&);
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/// Return complex base 10 logarithm of @a z.
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template 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 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 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 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 complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
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/// Return complex sine of @a z.
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template complex<_Tp> sin(const complex<_Tp>&);
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/// Return complex hyperbolic sine of @a z.
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template complex<_Tp> sinh(const complex<_Tp>&);
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/// Return complex square root of @a z.
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template complex<_Tp> sqrt(const complex<_Tp>&);
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/// Return complex tangent of @a z.
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template complex<_Tp> tan(const complex<_Tp>&);
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/// Return complex hyperbolic tangent of @a z.
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template 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
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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
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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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__attribute ((__abi_tag__ ("cxx11")))
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constexpr _Tp
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real() { return _M_real; }
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__attribute ((__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
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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
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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
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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
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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
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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
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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
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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
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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
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template
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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
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template
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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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| 275 |
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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
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template
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| 283 |
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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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| 286 |
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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
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| 294 |
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template
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| 295 |
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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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| 298 |
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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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| 300 |
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_M_real = __r;
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| 301 |
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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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| 306 |
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template
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| 307 |
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template
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| 308 |
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complex<_Tp>&
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| 309 |
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complex<_Tp>::operator/=(const complex<_Up>& __z)
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| 310 |
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{
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| 311 |
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const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
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| 312 |
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const _Tp __n = std::norm(__z);
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| 313 |
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_M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
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| 314 |
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_M_real = __r / __n;
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| 315 |
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return *this;
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| 316 |
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}
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| 317 |
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| 318 |
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// Operators:
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| 319 |
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//@{
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| 320 |
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/// Return new complex value @a x plus @a y.
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| 321 |
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template
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| 322 |
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inline complex<_Tp>
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| 323 |
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operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
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| 324 |
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{
|
| 325 |
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complex<_Tp> __r = __x;
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| 326 |
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__r += __y;
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| 327 |
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return __r;
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| 328 |
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}
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| 329 |
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| 330 |
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template
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| 331 |
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inline complex<_Tp>
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| 332 |
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operator+(const complex<_Tp>& __x, const _Tp& __y)
|
| 333 |
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{
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| 334 |
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complex<_Tp> __r = __x;
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| 335 |
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__r += __y;
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| 336 |
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return __r;
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}
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| 338 |
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| 339 |
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template
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| 340 |
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inline complex<_Tp>
|
| 341 |
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operator+(const _Tp& __x, const complex<_Tp>& __y)
|
| 342 |
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{
|
| 343 |
|
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complex<_Tp> __r = __y;
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| 344 |
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__r += __x;
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| 345 |
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return __r;
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| 346 |
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}
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| 347 |
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//@}
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| 348 |
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| 349 |
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//@{
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| 350 |
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/// Return new complex value @a x minus @a y.
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| 351 |
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template
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| 352 |
|
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inline complex<_Tp>
|
| 353 |
|
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operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
| 354 |
|
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{
|
| 355 |
|
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complex<_Tp> __r = __x;
|
| 356 |
|
|
__r -= __y;
|
| 357 |
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return __r;
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| 358 |
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}
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| 359 |
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|
| 360 |
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template
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| 361 |
|
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inline complex<_Tp>
|
| 362 |
|
|
operator-(const complex<_Tp>& __x, const _Tp& __y)
|
| 363 |
|
|
{
|
| 364 |
|
|
complex<_Tp> __r = __x;
|
| 365 |
|
|
__r -= __y;
|
| 366 |
|
|
return __r;
|
| 367 |
|
|
}
|
| 368 |
|
|
|
| 369 |
|
|
template
|
| 370 |
|
|
inline complex<_Tp>
|
| 371 |
|
|
operator-(const _Tp& __x, const complex<_Tp>& __y)
|
| 372 |
|
|
{
|
| 373 |
|
|
complex<_Tp> __r(__x, -__y.imag());
|
| 374 |
|
|
__r -= __y.real();
|
| 375 |
|
|
return __r;
|
| 376 |
|
|
}
|
| 377 |
|
|
//@}
|
| 378 |
|
|
|
| 379 |
|
|
//@{
|
| 380 |
|
|
/// Return new complex value @a x times @a y.
|
| 381 |
|
|
template
|
| 382 |
|
|
inline complex<_Tp>
|
| 383 |
|
|
operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
| 384 |
|
|
{
|
| 385 |
|
|
complex<_Tp> __r = __x;
|
| 386 |
|
|
__r *= __y;
|
| 387 |
|
|
return __r;
|
| 388 |
|
|
}
|
| 389 |
|
|
|
| 390 |
|
|
template
|
| 391 |
|
|
inline complex<_Tp>
|
| 392 |
|
|
operator*(const complex<_Tp>& __x, const _Tp& __y)
|
| 393 |
|
|
{
|
| 394 |
|
|
complex<_Tp> __r = __x;
|
| 395 |
|
|
__r *= __y;
|
| 396 |
|
|
return __r;
|
| 397 |
|
|
}
|
| 398 |
|
|
|
| 399 |
|
|
template
|
| 400 |
|
|
inline complex<_Tp>
|
| 401 |
|
|
operator*(const _Tp& __x, const complex<_Tp>& __y)
|
| 402 |
|
|
{
|
| 403 |
|
|
complex<_Tp> __r = __y;
|
| 404 |
|
|
__r *= __x;
|
| 405 |
|
|
return __r;
|
| 406 |
|
|
}
|
| 407 |
|
|
//@}
|
| 408 |
|
|
|
| 409 |
|
|
//@{
|
| 410 |
|
|
/// Return new complex value @a x divided by @a y.
|
| 411 |
|
|
template
|
| 412 |
|
|
inline complex<_Tp>
|
| 413 |
|
|
operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
| 414 |
|
|
{
|
| 415 |
|
|
complex<_Tp> __r = __x;
|
| 416 |
|
|
__r /= __y;
|
| 417 |
|
|
return __r;
|
| 418 |
|
|
}
|
| 419 |
|
|
|
| 420 |
|
|
template
|
| 421 |
|
|
inline complex<_Tp>
|
| 422 |
|
|
operator/(const complex<_Tp>& __x, const _Tp& __y)
|
| 423 |
|
|
{
|
| 424 |
|
|
complex<_Tp> __r = __x;
|
| 425 |
|
|
__r /= __y;
|
| 426 |
|
|
return __r;
|
| 427 |
|
|
}
|
| 428 |
|
|
|
| 429 |
|
|
template
|
| 430 |
|
|
inline complex<_Tp>
|
| 431 |
|
|
operator/(const _Tp& __x, const complex<_Tp>& __y)
|
| 432 |
|
|
{
|
| 433 |
|
|
complex<_Tp> __r = __x;
|
| 434 |
|
|
__r /= __y;
|
| 435 |
|
|
return __r;
|
| 436 |
|
|
}
|
| 437 |
|
|
//@}
|
| 438 |
|
|
|
| 439 |
|
|
/// Return @a x.
|
| 440 |
|
|
template
|
| 441 |
|
|
inline complex<_Tp>
|
| 442 |
|
|
operator+(const complex<_Tp>& __x)
|
| 443 |
|
|
{ return __x; }
|
| 444 |
|
|
|
| 445 |
|
|
/// Return complex negation of @a x.
|
| 446 |
|
|
template
|
| 447 |
|
|
inline complex<_Tp>
|
| 448 |
|
|
operator-(const complex<_Tp>& __x)
|
| 449 |
|
|
{ return complex<_Tp>(-__x.real(), -__x.imag()); }
|
| 450 |
|
|
|
| 451 |
|
|
//@{
|
| 452 |
|
|
/// Return true if @a x is equal to @a y.
|
| 453 |
|
|
template
|
| 454 |
|
|
inline _GLIBCXX_CONSTEXPR bool
|
| 455 |
|
|
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
| 456 |
|
|
{ return __x.real() == __y.real() && __x.imag() == __y.imag(); }
|
| 457 |
|
|
|
| 458 |
|
|
template
|
| 459 |
|
|
inline _GLIBCXX_CONSTEXPR bool
|
| 460 |
|
|
operator==(const complex<_Tp>& __x, const _Tp& __y)
|
| 461 |
|
|
{ return __x.real() == __y && __x.imag() == _Tp(); }
|
| 462 |
|
|
|
| 463 |
|
|
template
|
| 464 |
|
|
inline _GLIBCXX_CONSTEXPR bool
|
| 465 |
|
|
operator==(const _Tp& __x, const complex<_Tp>& __y)
|
| 466 |
|
|
{ return __x == __y.real() && _Tp() == __y.imag(); }
|
| 467 |
|
|
//@}
|
| 468 |
|
|
|
| 469 |
|
|
//@{
|
| 470 |
|
|
/// Return false if @a x is equal to @a y.
|
| 471 |
|
|
template
|
| 472 |
|
|
inline _GLIBCXX_CONSTEXPR bool
|
| 473 |
|
|
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
| 474 |
|
|
{ return __x.real() != __y.real() || __x.imag() != __y.imag(); }
|
| 475 |
|
|
|
| 476 |
|
|
template
|
| 477 |
|
|
inline _GLIBCXX_CONSTEXPR bool
|
| 478 |
|
|
operator!=(const complex<_Tp>& __x, const _Tp& __y)
|
| 479 |
|
|
{ return __x.real() != __y || __x.imag() != _Tp(); }
|
| 480 |
|
|
|
| 481 |
|
|
template
|
| 482 |
|
|
inline _GLIBCXX_CONSTEXPR bool
|
| 483 |
|
|
operator!=(const _Tp& __x, const complex<_Tp>& __y)
|
| 484 |
|
|
{ return __x != __y.real() || _Tp() != __y.imag(); }
|
| 485 |
|
|
//@}
|
| 486 |
|
|
|
| 487 |
|
|
/// Extraction operator for complex values.
|
| 488 |
|
|
template
|
| 489 |
|
|
basic_istream<_CharT, _Traits>&
|
| 490 |
|
|
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
|
| 491 |
|
|
{
|
| 492 |
|
|
_Tp __re_x, __im_x;
|
| 493 |
|
|
_CharT __ch;
|
| 494 |
|
|
__is >> __ch;
|
| 495 |
|
|
if (__ch == '(')
|
| 496 |
|
|
{
|
| 497 |
|
|
__is >> __re_x >> __ch;
|
| 498 |
|
|
if (__ch == ',')
|
| 499 |
|
|
{
|
| 500 |
|
|
__is >> __im_x >> __ch;
|
| 501 |
|
|
if (__ch == ')')
|
| 502 |
|
|
__x = complex<_Tp>(__re_x, __im_x);
|
| 503 |
|
|
else
|
| 504 |
|
|
__is.setstate(ios_base::failbit);
|
| 505 |
|
|
}
|
| 506 |
|
|
else if (__ch == ')')
|
| 507 |
|
|
__x = __re_x;
|
| 508 |
|
|
else
|
| 509 |
|
|
__is.setstate(ios_base::failbit);
|
| 510 |
|
|
}
|
| 511 |
|
|
else
|
| 512 |
|
|
{
|
| 513 |
|
|
__is.putback(__ch);
|
| 514 |
|
|
__is >> __re_x;
|
| 515 |
|
|
__x = __re_x;
|
| 516 |
|
|
}
|
| 517 |
|
|
return __is;
|
| 518 |
|
|
}
|
| 519 |
|
|
|
| 520 |
|
|
/// Insertion operator for complex values.
|
| 521 |
|
|
template
|
| 522 |
|
|
basic_ostream<_CharT, _Traits>&
|
| 523 |
|
|
operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
|
| 524 |
|
|
{
|
| 525 |
|
|
basic_ostringstream<_CharT, _Traits> __s;
|
| 526 |
|
|
__s.flags(__os.flags());
|
| 527 |
|
|
__s.imbue(__os.getloc());
|
| 528 |
|
|
__s.precision(__os.precision());
|
| 529 |
|
|
__s << '(' << __x.real() << ',' << __x.imag() << ')';
|
| 530 |
|
|
return __os << __s.str();
|
| 531 |
|
|
}
|
| 532 |
|
|
|
| 533 |
|
|
// Values
|
| 534 |
|
|
#if __cplusplus >= 201103L
|
| 535 |
|
|
template
|
| 536 |
|
|
constexpr _Tp
|
| 537 |
|
|
real(const complex<_Tp>& __z)
|
| 538 |
|
|
{ return __z.real(); }
|
| 539 |
|
|
|
| 540 |
|
|
template
|
| 541 |
|
|
constexpr _Tp
|
| 542 |
|
|
imag(const complex<_Tp>& __z)
|
| 543 |
|
|
{ return __z.imag(); }
|
| 544 |
|
|
#else
|
| 545 |
|
|
template
|
| 546 |
|
|
inline _Tp&
|
| 547 |
|
|
real(complex<_Tp>& __z)
|
| 548 |
|
|
{ return __z.real(); }
|
| 549 |
|
|
|
| 550 |
|
|
template
|
| 551 |
|
|
inline const _Tp&
|
| 552 |
|
|
real(const complex<_Tp>& __z)
|
| 553 |
|
|
{ return __z.real(); }
|
| 554 |
|
|
|
| 555 |
|
|
template
|
| 556 |
|
|
inline _Tp&
|
| 557 |
|
|
imag(complex<_Tp>& __z)
|
| 558 |
|
|
{ return __z.imag(); }
|
| 559 |
|
|
|
| 560 |
|
|
template
|
| 561 |
|
|
inline const _Tp&
|
| 562 |
|
|
imag(const complex<_Tp>& __z)
|
| 563 |
|
|
{ return __z.imag(); }
|
| 564 |
|
|
#endif
|
| 565 |
|
|
|
| 566 |
|
|
// 26.2.7/3 abs(__z): Returns the magnitude of __z.
|
| 567 |
|
|
template
|
| 568 |
|
|
inline _Tp
|
| 569 |
|
|
__complex_abs(const complex<_Tp>& __z)
|
| 570 |
|
|
{
|
| 571 |
|
|
_Tp __x = __z.real();
|
| 572 |
|
|
_Tp __y = __z.imag();
|
| 573 |
|
|
const _Tp __s = std::max(abs(__x), abs(__y));
|
| 574 |
|
|
if (__s == _Tp()) // well ...
|
| 575 |
|
|
return __s;
|
| 576 |
|
|
__x /= __s;
|
| 577 |
|
|
__y /= __s;
|
| 578 |
|
|
return __s * sqrt(__x * __x + __y * __y);
|
| 579 |
|
|
}
|
| 580 |
|
|
|
| 581 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 582 |
|
|
inline float
|
| 583 |
|
|
__complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
|
| 584 |
|
|
|
| 585 |
|
|
inline double
|
| 586 |
|
|
__complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
|
| 587 |
|
|
|
| 588 |
|
|
inline long double
|
| 589 |
|
|
__complex_abs(const __complex__ long double& __z)
|
| 590 |
|
|
{ return __builtin_cabsl(__z); }
|
| 591 |
|
|
|
| 592 |
|
|
template
|
| 593 |
|
|
inline _Tp
|
| 594 |
|
|
abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
|
| 595 |
|
|
#else
|
| 596 |
|
|
template
|
| 597 |
|
|
inline _Tp
|
| 598 |
|
|
abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
|
| 599 |
|
|
#endif
|
| 600 |
|
|
|
| 601 |
|
|
|
| 602 |
|
|
// 26.2.7/4: arg(__z): Returns the phase angle of __z.
|
| 603 |
|
|
template
|
| 604 |
|
|
inline _Tp
|
| 605 |
|
|
__complex_arg(const complex<_Tp>& __z)
|
| 606 |
|
|
{ return atan2(__z.imag(), __z.real()); }
|
| 607 |
|
|
|
| 608 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 609 |
|
|
inline float
|
| 610 |
|
|
__complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
|
| 611 |
|
|
|
| 612 |
|
|
inline double
|
| 613 |
|
|
__complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
|
| 614 |
|
|
|
| 615 |
|
|
inline long double
|
| 616 |
|
|
__complex_arg(const __complex__ long double& __z)
|
| 617 |
|
|
{ return __builtin_cargl(__z); }
|
| 618 |
|
|
|
| 619 |
|
|
template
|
| 620 |
|
|
inline _Tp
|
| 621 |
|
|
arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
|
| 622 |
|
|
#else
|
| 623 |
|
|
template
|
| 624 |
|
|
inline _Tp
|
| 625 |
|
|
arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
|
| 626 |
|
|
#endif
|
| 627 |
|
|
|
| 628 |
|
|
// 26.2.7/5: norm(__z) returns the squared magnitude of __z.
|
| 629 |
|
|
// As defined, norm() is -not- a norm is the common mathematical
|
| 630 |
|
|
// sens used in numerics. The helper class _Norm_helper<> tries to
|
| 631 |
|
|
// distinguish between builtin floating point and the rest, so as
|
| 632 |
|
|
// to deliver an answer as close as possible to the real value.
|
| 633 |
|
|
template
|
| 634 |
|
|
struct _Norm_helper
|
| 635 |
|
|
{
|
| 636 |
|
|
template
|
| 637 |
|
|
static inline _Tp _S_do_it(const complex<_Tp>& __z)
|
| 638 |
|
|
{
|
| 639 |
|
|
const _Tp __x = __z.real();
|
| 640 |
|
|
const _Tp __y = __z.imag();
|
| 641 |
|
|
return __x * __x + __y * __y;
|
| 642 |
|
|
}
|
| 643 |
|
|
};
|
| 644 |
|
|
|
| 645 |
|
|
template<>
|
| 646 |
|
|
struct _Norm_helper
|
| 647 |
|
|
{
|
| 648 |
|
|
template
|
| 649 |
|
|
static inline _Tp _S_do_it(const complex<_Tp>& __z)
|
| 650 |
|
|
{
|
| 651 |
|
|
_Tp __res = std::abs(__z);
|
| 652 |
|
|
return __res * __res;
|
| 653 |
|
|
}
|
| 654 |
|
|
};
|
| 655 |
|
|
|
| 656 |
|
|
template
|
| 657 |
|
|
inline _Tp
|
| 658 |
|
|
norm(const complex<_Tp>& __z)
|
| 659 |
|
|
{
|
| 660 |
|
|
return _Norm_helper<__is_floating<_Tp>::__value
|
| 661 |
|
|
&& !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
|
| 662 |
|
|
}
|
| 663 |
|
|
|
| 664 |
|
|
template
|
| 665 |
|
|
inline complex<_Tp>
|
| 666 |
|
|
polar(const _Tp& __rho, const _Tp& __theta)
|
| 667 |
|
|
{ return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
|
| 668 |
|
|
|
| 669 |
|
|
template
|
| 670 |
|
|
inline complex<_Tp>
|
| 671 |
|
|
conj(const complex<_Tp>& __z)
|
| 672 |
|
|
{ return complex<_Tp>(__z.real(), -__z.imag()); }
|
| 673 |
|
|
|
| 674 |
|
|
// Transcendentals
|
| 675 |
|
|
|
| 676 |
|
|
// 26.2.8/1 cos(__z): Returns the cosine of __z.
|
| 677 |
|
|
template
|
| 678 |
|
|
inline complex<_Tp>
|
| 679 |
|
|
__complex_cos(const complex<_Tp>& __z)
|
| 680 |
|
|
{
|
| 681 |
|
|
const _Tp __x = __z.real();
|
| 682 |
|
|
const _Tp __y = __z.imag();
|
| 683 |
|
|
return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
|
| 684 |
|
|
}
|
| 685 |
|
|
|
| 686 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 687 |
|
|
inline __complex__ float
|
| 688 |
|
|
__complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
|
| 689 |
|
|
|
| 690 |
|
|
inline __complex__ double
|
| 691 |
|
|
__complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
|
| 692 |
|
|
|
| 693 |
|
|
inline __complex__ long double
|
| 694 |
|
|
__complex_cos(const __complex__ long double& __z)
|
| 695 |
|
|
{ return __builtin_ccosl(__z); }
|
| 696 |
|
|
|
| 697 |
|
|
template
|
| 698 |
|
|
inline complex<_Tp>
|
| 699 |
|
|
cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
|
| 700 |
|
|
#else
|
| 701 |
|
|
template
|
| 702 |
|
|
inline complex<_Tp>
|
| 703 |
|
|
cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
|
| 704 |
|
|
#endif
|
| 705 |
|
|
|
| 706 |
|
|
// 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
|
| 707 |
|
|
template
|
| 708 |
|
|
inline complex<_Tp>
|
| 709 |
|
|
__complex_cosh(const complex<_Tp>& __z)
|
| 710 |
|
|
{
|
| 711 |
|
|
const _Tp __x = __z.real();
|
| 712 |
|
|
const _Tp __y = __z.imag();
|
| 713 |
|
|
return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
|
| 714 |
|
|
}
|
| 715 |
|
|
|
| 716 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 717 |
|
|
inline __complex__ float
|
| 718 |
|
|
__complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
|
| 719 |
|
|
|
| 720 |
|
|
inline __complex__ double
|
| 721 |
|
|
__complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
|
| 722 |
|
|
|
| 723 |
|
|
inline __complex__ long double
|
| 724 |
|
|
__complex_cosh(const __complex__ long double& __z)
|
| 725 |
|
|
{ return __builtin_ccoshl(__z); }
|
| 726 |
|
|
|
| 727 |
|
|
template
|
| 728 |
|
|
inline complex<_Tp>
|
| 729 |
|
|
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
|
| 730 |
|
|
#else
|
| 731 |
|
|
template
|
| 732 |
|
|
inline complex<_Tp>
|
| 733 |
|
|
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
|
| 734 |
|
|
#endif
|
| 735 |
|
|
|
| 736 |
|
|
// 26.2.8/3 exp(__z): Returns the complex base e exponential of x
|
| 737 |
|
|
template
|
| 738 |
|
|
inline complex<_Tp>
|
| 739 |
|
|
__complex_exp(const complex<_Tp>& __z)
|
| 740 |
|
|
{ return std::polar(exp(__z.real()), __z.imag()); }
|
| 741 |
|
|
|
| 742 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 743 |
|
|
inline __complex__ float
|
| 744 |
|
|
__complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
|
| 745 |
|
|
|
| 746 |
|
|
inline __complex__ double
|
| 747 |
|
|
__complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
|
| 748 |
|
|
|
| 749 |
|
|
inline __complex__ long double
|
| 750 |
|
|
__complex_exp(const __complex__ long double& __z)
|
| 751 |
|
|
{ return __builtin_cexpl(__z); }
|
| 752 |
|
|
|
| 753 |
|
|
template
|
| 754 |
|
|
inline complex<_Tp>
|
| 755 |
|
|
exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
|
| 756 |
|
|
#else
|
| 757 |
|
|
template
|
| 758 |
|
|
inline complex<_Tp>
|
| 759 |
|
|
exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
|
| 760 |
|
|
#endif
|
| 761 |
|
|
|
| 762 |
|
|
// 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
|
| 763 |
|
|
// The branch cut is along the negative axis.
|
| 764 |
|
|
template
|
| 765 |
|
|
inline complex<_Tp>
|
| 766 |
|
|
__complex_log(const complex<_Tp>& __z)
|
| 767 |
|
|
{ return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
|
| 768 |
|
|
|
| 769 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 770 |
|
|
inline __complex__ float
|
| 771 |
|
|
__complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
|
| 772 |
|
|
|
| 773 |
|
|
inline __complex__ double
|
| 774 |
|
|
__complex_log(__complex__ double __z) { return __builtin_clog(__z); }
|
| 775 |
|
|
|
| 776 |
|
|
inline __complex__ long double
|
| 777 |
|
|
__complex_log(const __complex__ long double& __z)
|
| 778 |
|
|
{ return __builtin_clogl(__z); }
|
| 779 |
|
|
|
| 780 |
|
|
template
|
| 781 |
|
|
inline complex<_Tp>
|
| 782 |
|
|
log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
|
| 783 |
|
|
#else
|
| 784 |
|
|
template
|
| 785 |
|
|
inline complex<_Tp>
|
| 786 |
|
|
log(const complex<_Tp>& __z) { return __complex_log(__z); }
|
| 787 |
|
|
#endif
|
| 788 |
|
|
|
| 789 |
|
|
template
|
| 790 |
|
|
inline complex<_Tp>
|
| 791 |
|
|
log10(const complex<_Tp>& __z)
|
| 792 |
|
|
{ return std::log(__z) / log(_Tp(10.0)); }
|
| 793 |
|
|
|
| 794 |
|
|
// 26.2.8/10 sin(__z): Returns the sine of __z.
|
| 795 |
|
|
template
|
| 796 |
|
|
inline complex<_Tp>
|
| 797 |
|
|
__complex_sin(const complex<_Tp>& __z)
|
| 798 |
|
|
{
|
| 799 |
|
|
const _Tp __x = __z.real();
|
| 800 |
|
|
const _Tp __y = __z.imag();
|
| 801 |
|
|
return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
|
| 802 |
|
|
}
|
| 803 |
|
|
|
| 804 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 805 |
|
|
inline __complex__ float
|
| 806 |
|
|
__complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
|
| 807 |
|
|
|
| 808 |
|
|
inline __complex__ double
|
| 809 |
|
|
__complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
|
| 810 |
|
|
|
| 811 |
|
|
inline __complex__ long double
|
| 812 |
|
|
__complex_sin(const __complex__ long double& __z)
|
| 813 |
|
|
{ return __builtin_csinl(__z); }
|
| 814 |
|
|
|
| 815 |
|
|
template
|
| 816 |
|
|
inline complex<_Tp>
|
| 817 |
|
|
sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
|
| 818 |
|
|
#else
|
| 819 |
|
|
template
|
| 820 |
|
|
inline complex<_Tp>
|
| 821 |
|
|
sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
|
| 822 |
|
|
#endif
|
| 823 |
|
|
|
| 824 |
|
|
// 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
|
| 825 |
|
|
template
|
| 826 |
|
|
inline complex<_Tp>
|
| 827 |
|
|
__complex_sinh(const complex<_Tp>& __z)
|
| 828 |
|
|
{
|
| 829 |
|
|
const _Tp __x = __z.real();
|
| 830 |
|
|
const _Tp __y = __z.imag();
|
| 831 |
|
|
return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
|
| 832 |
|
|
}
|
| 833 |
|
|
|
| 834 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 835 |
|
|
inline __complex__ float
|
| 836 |
|
|
__complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
|
| 837 |
|
|
|
| 838 |
|
|
inline __complex__ double
|
| 839 |
|
|
__complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
|
| 840 |
|
|
|
| 841 |
|
|
inline __complex__ long double
|
| 842 |
|
|
__complex_sinh(const __complex__ long double& __z)
|
| 843 |
|
|
{ return __builtin_csinhl(__z); }
|
| 844 |
|
|
|
| 845 |
|
|
template
|
| 846 |
|
|
inline complex<_Tp>
|
| 847 |
|
|
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
|
| 848 |
|
|
#else
|
| 849 |
|
|
template
|
| 850 |
|
|
inline complex<_Tp>
|
| 851 |
|
|
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
|
| 852 |
|
|
#endif
|
| 853 |
|
|
|
| 854 |
|
|
// 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
|
| 855 |
|
|
// The branch cut is on the negative axis.
|
| 856 |
|
|
template
|
| 857 |
|
|
complex<_Tp>
|
| 858 |
|
|
__complex_sqrt(const complex<_Tp>& __z)
|
| 859 |
|
|
{
|
| 860 |
|
|
_Tp __x = __z.real();
|
| 861 |
|
|
_Tp __y = __z.imag();
|
| 862 |
|
|
|
| 863 |
|
|
if (__x == _Tp())
|
| 864 |
|
|
{
|
| 865 |
|
|
_Tp __t = sqrt(abs(__y) / 2);
|
| 866 |
|
|
return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
|
| 867 |
|
|
}
|
| 868 |
|
|
else
|
| 869 |
|
|
{
|
| 870 |
|
|
_Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
|
| 871 |
|
|
_Tp __u = __t / 2;
|
| 872 |
|
|
return __x > _Tp()
|
| 873 |
|
|
? complex<_Tp>(__u, __y / __t)
|
| 874 |
|
|
: complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
|
| 875 |
|
|
}
|
| 876 |
|
|
}
|
| 877 |
|
|
|
| 878 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 879 |
|
|
inline __complex__ float
|
| 880 |
|
|
__complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
|
| 881 |
|
|
|
| 882 |
|
|
inline __complex__ double
|
| 883 |
|
|
__complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
|
| 884 |
|
|
|
| 885 |
|
|
inline __complex__ long double
|
| 886 |
|
|
__complex_sqrt(const __complex__ long double& __z)
|
| 887 |
|
|
{ return __builtin_csqrtl(__z); }
|
| 888 |
|
|
|
| 889 |
|
|
template
|
| 890 |
|
|
inline complex<_Tp>
|
| 891 |
|
|
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
|
| 892 |
|
|
#else
|
| 893 |
|
|
template
|
| 894 |
|
|
inline complex<_Tp>
|
| 895 |
|
|
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
|
| 896 |
|
|
#endif
|
| 897 |
|
|
|
| 898 |
|
|
// 26.2.8/14 tan(__z): Return the complex tangent of __z.
|
| 899 |
|
|
|
| 900 |
|
|
template
|
| 901 |
|
|
inline complex<_Tp>
|
| 902 |
|
|
__complex_tan(const complex<_Tp>& __z)
|
| 903 |
|
|
{ return std::sin(__z) / std::cos(__z); }
|
| 904 |
|
|
|
| 905 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 906 |
|
|
inline __complex__ float
|
| 907 |
|
|
__complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
|
| 908 |
|
|
|
| 909 |
|
|
inline __complex__ double
|
| 910 |
|
|
__complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
|
| 911 |
|
|
|
| 912 |
|
|
inline __complex__ long double
|
| 913 |
|
|
__complex_tan(const __complex__ long double& __z)
|
| 914 |
|
|
{ return __builtin_ctanl(__z); }
|
| 915 |
|
|
|
| 916 |
|
|
template
|
| 917 |
|
|
inline complex<_Tp>
|
| 918 |
|
|
tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
|
| 919 |
|
|
#else
|
| 920 |
|
|
template
|
| 921 |
|
|
inline complex<_Tp>
|
| 922 |
|
|
tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
|
| 923 |
|
|
#endif
|
| 924 |
|
|
|
| 925 |
|
|
|
| 926 |
|
|
// 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
|
| 927 |
|
|
|
| 928 |
|
|
template
|
| 929 |
|
|
inline complex<_Tp>
|
| 930 |
|
|
__complex_tanh(const complex<_Tp>& __z)
|
| 931 |
|
|
{ return std::sinh(__z) / std::cosh(__z); }
|
| 932 |
|
|
|
| 933 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 934 |
|
|
inline __complex__ float
|
| 935 |
|
|
__complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
|
| 936 |
|
|
|
| 937 |
|
|
inline __complex__ double
|
| 938 |
|
|
__complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
|
| 939 |
|
|
|
| 940 |
|
|
inline __complex__ long double
|
| 941 |
|
|
__complex_tanh(const __complex__ long double& __z)
|
| 942 |
|
|
{ return __builtin_ctanhl(__z); }
|
| 943 |
|
|
|
| 944 |
|
|
template
|
| 945 |
|
|
inline complex<_Tp>
|
| 946 |
|
|
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
|
| 947 |
|
|
#else
|
| 948 |
|
|
template
|
| 949 |
|
|
inline complex<_Tp>
|
| 950 |
|
|
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
|
| 951 |
|
|
#endif
|
| 952 |
|
|
|
| 953 |
|
|
|
| 954 |
|
|
// 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
|
| 955 |
|
|
// raised to the __y-th power. The branch
|
| 956 |
|
|
// cut is on the negative axis.
|
| 957 |
|
|
#if __cplusplus < 201103L
|
| 958 |
|
|
template
|
| 959 |
|
|
complex<_Tp>
|
| 960 |
|
|
__complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
|
| 961 |
|
|
{
|
| 962 |
|
|
complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
|
| 963 |
|
|
|
| 964 |
|
|
while (__n >>= 1)
|
| 965 |
|
|
{
|
| 966 |
|
|
__x *= __x;
|
| 967 |
|
|
if (__n % 2)
|
| 968 |
|
|
__y *= __x;
|
| 969 |
|
|
}
|
| 970 |
|
|
|
| 971 |
|
|
return __y;
|
| 972 |
|
|
}
|
| 973 |
|
|
|
| 974 |
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
| 975 |
|
|
// DR 844. complex pow return type is ambiguous.
|
| 976 |
|
|
template
|
| 977 |
|
|
inline complex<_Tp>
|
| 978 |
|
|
pow(const complex<_Tp>& __z, int __n)
|
| 979 |
|
|
{
|
| 980 |
|
|
return __n < 0
|
| 981 |
|
|
? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -__n)
|
| 982 |
|
|
: std::__complex_pow_unsigned(__z, __n);
|
| 983 |
|
|
}
|
| 984 |
|
|
#endif
|
| 985 |
|
|
|
| 986 |
|
|
template
|
| 987 |
|
|
complex<_Tp>
|
| 988 |
|
|
pow(const complex<_Tp>& __x, const _Tp& __y)
|
| 989 |
|
|
{
|
| 990 |
|
|
#ifndef _GLIBCXX_USE_C99_COMPLEX
|
| 991 |
|
|
if (__x == _Tp())
|
| 992 |
|
|
return _Tp();
|
| 993 |
|
|
#endif
|
| 994 |
|
|
if (__x.imag() == _Tp() && __x.real() > _Tp())
|
| 995 |
|
|
return pow(__x.real(), __y);
|
| 996 |
|
|
|
| 997 |
|
|
complex<_Tp> __t = std::log(__x);
|
| 998 |
|
|
return std::polar(exp(__y * __t.real()), __y * __t.imag());
|
| 999 |
|
|
}
|
| 1000 |
|
|
|
| 1001 |
|
|
template
|
| 1002 |
|
|
inline complex<_Tp>
|
| 1003 |
|
|
__complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
| 1004 |
|
|
{ return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
|
| 1005 |
|
|
|
| 1006 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 1007 |
|
|
inline __complex__ float
|
| 1008 |
|
|
__complex_pow(__complex__ float __x, __complex__ float __y)
|
| 1009 |
|
|
{ return __builtin_cpowf(__x, __y); }
|
| 1010 |
|
|
|
| 1011 |
|
|
inline __complex__ double
|
| 1012 |
|
|
__complex_pow(__complex__ double __x, __complex__ double __y)
|
| 1013 |
|
|
{ return __builtin_cpow(__x, __y); }
|
| 1014 |
|
|
|
| 1015 |
|
|
inline __complex__ long double
|
| 1016 |
|
|
__complex_pow(const __complex__ long double& __x,
|
| 1017 |
|
|
const __complex__ long double& __y)
|
| 1018 |
|
|
{ return __builtin_cpowl(__x, __y); }
|
| 1019 |
|
|
|
| 1020 |
|
|
template
|
| 1021 |
|
|
inline complex<_Tp>
|
| 1022 |
|
|
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
| 1023 |
|
|
{ return __complex_pow(__x.__rep(), __y.__rep()); }
|
| 1024 |
|
|
#else
|
| 1025 |
|
|
template
|
| 1026 |
|
|
inline complex<_Tp>
|
| 1027 |
|
|
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
|
| 1028 |
|
|
{ return __complex_pow(__x, __y); }
|
| 1029 |
|
|
#endif
|
| 1030 |
|
|
|
| 1031 |
|
|
template
|
| 1032 |
|
|
inline complex<_Tp>
|
| 1033 |
|
|
pow(const _Tp& __x, const complex<_Tp>& __y)
|
| 1034 |
|
|
{
|
| 1035 |
|
|
return __x > _Tp() ? std::polar(pow(__x, __y.real()),
|
| 1036 |
|
|
__y.imag() * log(__x))
|
| 1037 |
|
|
: std::pow(complex<_Tp>(__x), __y);
|
| 1038 |
|
|
}
|
| 1039 |
|
|
|
| 1040 |
|
|
/// 26.2.3 complex specializations
|
| 1041 |
|
|
/// complex specialization
|
| 1042 |
|
|
template<>
|
| 1043 |
|
|
struct complex
|
| 1044 |
|
|
{
|
| 1045 |
|
|
typedef float value_type;
|
| 1046 |
|
|
typedef __complex__ float _ComplexT;
|
| 1047 |
|
|
|
| 1048 |
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
| 1049 |
|
|
|
| 1050 |
|
|
_GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
|
| 1051 |
|
|
#if __cplusplus >= 201103L
|
| 1052 |
|
|
: _M_value{ __r, __i } { }
|
| 1053 |
|
|
#else
|
| 1054 |
|
|
{
|
| 1055 |
|
|
__real__ _M_value = __r;
|
| 1056 |
|
|
__imag__ _M_value = __i;
|
| 1057 |
|
|
}
|
| 1058 |
|
|
#endif
|
| 1059 |
|
|
|
| 1060 |
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex&);
|
| 1061 |
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex&);
|
| 1062 |
|
|
|
| 1063 |
|
|
#if __cplusplus >= 201103L
|
| 1064 |
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
| 1065 |
|
|
// DR 387. std::complex over-encapsulated.
|
| 1066 |
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
| 1067 |
|
|
constexpr float
|
| 1068 |
|
|
real() { return __real__ _M_value; }
|
| 1069 |
|
|
|
| 1070 |
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
| 1071 |
|
|
constexpr float
|
| 1072 |
|
|
imag() { return __imag__ _M_value; }
|
| 1073 |
|
|
#else
|
| 1074 |
|
|
float&
|
| 1075 |
|
|
real() { return __real__ _M_value; }
|
| 1076 |
|
|
|
| 1077 |
|
|
const float&
|
| 1078 |
|
|
real() const { return __real__ _M_value; }
|
| 1079 |
|
|
|
| 1080 |
|
|
float&
|
| 1081 |
|
|
imag() { return __imag__ _M_value; }
|
| 1082 |
|
|
|
| 1083 |
|
|
const float&
|
| 1084 |
|
|
imag() const { return __imag__ _M_value; }
|
| 1085 |
|
|
#endif
|
| 1086 |
|
|
|
| 1087 |
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
| 1088 |
|
|
// DR 387. std::complex over-encapsulated.
|
| 1089 |
|
|
void
|
| 1090 |
|
|
real(float __val) { __real__ _M_value = __val; }
|
| 1091 |
|
|
|
| 1092 |
|
|
void
|
| 1093 |
|
|
imag(float __val) { __imag__ _M_value = __val; }
|
| 1094 |
|
|
|
| 1095 |
|
|
complex&
|
| 1096 |
|
|
operator=(float __f)
|
| 1097 |
|
|
{
|
| 1098 |
|
|
_M_value = __f;
|
| 1099 |
|
|
return *this;
|
| 1100 |
|
|
}
|
| 1101 |
|
|
|
| 1102 |
|
|
complex&
|
| 1103 |
|
|
operator+=(float __f)
|
| 1104 |
|
|
{
|
| 1105 |
|
|
_M_value += __f;
|
| 1106 |
|
|
return *this;
|
| 1107 |
|
|
}
|
| 1108 |
|
|
|
| 1109 |
|
|
complex&
|
| 1110 |
|
|
operator-=(float __f)
|
| 1111 |
|
|
{
|
| 1112 |
|
|
_M_value -= __f;
|
| 1113 |
|
|
return *this;
|
| 1114 |
|
|
}
|
| 1115 |
|
|
|
| 1116 |
|
|
complex&
|
| 1117 |
|
|
operator*=(float __f)
|
| 1118 |
|
|
{
|
| 1119 |
|
|
_M_value *= __f;
|
| 1120 |
|
|
return *this;
|
| 1121 |
|
|
}
|
| 1122 |
|
|
|
| 1123 |
|
|
complex&
|
| 1124 |
|
|
operator/=(float __f)
|
| 1125 |
|
|
{
|
| 1126 |
|
|
_M_value /= __f;
|
| 1127 |
|
|
return *this;
|
| 1128 |
|
|
}
|
| 1129 |
|
|
|
| 1130 |
|
|
// Let the compiler synthesize the copy and assignment
|
| 1131 |
|
|
// operator. It always does a pretty good job.
|
| 1132 |
|
|
// complex& operator=(const complex&);
|
| 1133 |
|
|
|
| 1134 |
|
|
template
|
| 1135 |
|
|
complex&
|
| 1136 |
|
|
operator=(const complex<_Tp>& __z)
|
| 1137 |
|
|
{
|
| 1138 |
|
|
__real__ _M_value = __z.real();
|
| 1139 |
|
|
__imag__ _M_value = __z.imag();
|
| 1140 |
|
|
return *this;
|
| 1141 |
|
|
}
|
| 1142 |
|
|
|
| 1143 |
|
|
template
|
| 1144 |
|
|
complex&
|
| 1145 |
|
|
operator+=(const complex<_Tp>& __z)
|
| 1146 |
|
|
{
|
| 1147 |
|
|
__real__ _M_value += __z.real();
|
| 1148 |
|
|
__imag__ _M_value += __z.imag();
|
| 1149 |
|
|
return *this;
|
| 1150 |
|
|
}
|
| 1151 |
|
|
|
| 1152 |
|
|
template
|
| 1153 |
|
|
complex&
|
| 1154 |
|
|
operator-=(const complex<_Tp>& __z)
|
| 1155 |
|
|
{
|
| 1156 |
|
|
__real__ _M_value -= __z.real();
|
| 1157 |
|
|
__imag__ _M_value -= __z.imag();
|
| 1158 |
|
|
return *this;
|
| 1159 |
|
|
}
|
| 1160 |
|
|
|
| 1161 |
|
|
template
|
| 1162 |
|
|
complex&
|
| 1163 |
|
|
operator*=(const complex<_Tp>& __z)
|
| 1164 |
|
|
{
|
| 1165 |
|
|
_ComplexT __t;
|
| 1166 |
|
|
__real__ __t = __z.real();
|
| 1167 |
|
|
__imag__ __t = __z.imag();
|
| 1168 |
|
|
_M_value *= __t;
|
| 1169 |
|
|
return *this;
|
| 1170 |
|
|
}
|
| 1171 |
|
|
|
| 1172 |
|
|
template
|
| 1173 |
|
|
complex&
|
| 1174 |
|
|
operator/=(const complex<_Tp>& __z)
|
| 1175 |
|
|
{
|
| 1176 |
|
|
_ComplexT __t;
|
| 1177 |
|
|
__real__ __t = __z.real();
|
| 1178 |
|
|
__imag__ __t = __z.imag();
|
| 1179 |
|
|
_M_value /= __t;
|
| 1180 |
|
|
return *this;
|
| 1181 |
|
|
}
|
| 1182 |
|
|
|
| 1183 |
|
|
_GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
| 1184 |
|
|
|
| 1185 |
|
|
private:
|
| 1186 |
|
|
_ComplexT _M_value;
|
| 1187 |
|
|
};
|
| 1188 |
|
|
|
| 1189 |
|
|
/// 26.2.3 complex specializations
|
| 1190 |
|
|
/// complex specialization
|
| 1191 |
|
|
template<>
|
| 1192 |
|
|
struct complex
|
| 1193 |
|
|
{
|
| 1194 |
|
|
typedef double value_type;
|
| 1195 |
|
|
typedef __complex__ double _ComplexT;
|
| 1196 |
|
|
|
| 1197 |
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
| 1198 |
|
|
|
| 1199 |
|
|
_GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
|
| 1200 |
|
|
#if __cplusplus >= 201103L
|
| 1201 |
|
|
: _M_value{ __r, __i } { }
|
| 1202 |
|
|
#else
|
| 1203 |
|
|
{
|
| 1204 |
|
|
__real__ _M_value = __r;
|
| 1205 |
|
|
__imag__ _M_value = __i;
|
| 1206 |
|
|
}
|
| 1207 |
|
|
#endif
|
| 1208 |
|
|
|
| 1209 |
|
|
_GLIBCXX_CONSTEXPR complex(const complex& __z)
|
| 1210 |
|
|
: _M_value(__z.__rep()) { }
|
| 1211 |
|
|
|
| 1212 |
|
|
explicit _GLIBCXX_CONSTEXPR complex(const complex&);
|
| 1213 |
|
|
|
| 1214 |
|
|
#if __cplusplus >= 201103L
|
| 1215 |
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
| 1216 |
|
|
// DR 387. std::complex over-encapsulated.
|
| 1217 |
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
| 1218 |
|
|
constexpr double
|
| 1219 |
|
|
real() { return __real__ _M_value; }
|
| 1220 |
|
|
|
| 1221 |
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
| 1222 |
|
|
constexpr double
|
| 1223 |
|
|
imag() { return __imag__ _M_value; }
|
| 1224 |
|
|
#else
|
| 1225 |
|
|
double&
|
| 1226 |
|
|
real() { return __real__ _M_value; }
|
| 1227 |
|
|
|
| 1228 |
|
|
const double&
|
| 1229 |
|
|
real() const { return __real__ _M_value; }
|
| 1230 |
|
|
|
| 1231 |
|
|
double&
|
| 1232 |
|
|
imag() { return __imag__ _M_value; }
|
| 1233 |
|
|
|
| 1234 |
|
|
const double&
|
| 1235 |
|
|
imag() const { return __imag__ _M_value; }
|
| 1236 |
|
|
#endif
|
| 1237 |
|
|
|
| 1238 |
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
| 1239 |
|
|
// DR 387. std::complex over-encapsulated.
|
| 1240 |
|
|
void
|
| 1241 |
|
|
real(double __val) { __real__ _M_value = __val; }
|
| 1242 |
|
|
|
| 1243 |
|
|
void
|
| 1244 |
|
|
imag(double __val) { __imag__ _M_value = __val; }
|
| 1245 |
|
|
|
| 1246 |
|
|
complex&
|
| 1247 |
|
|
operator=(double __d)
|
| 1248 |
|
|
{
|
| 1249 |
|
|
_M_value = __d;
|
| 1250 |
|
|
return *this;
|
| 1251 |
|
|
}
|
| 1252 |
|
|
|
| 1253 |
|
|
complex&
|
| 1254 |
|
|
operator+=(double __d)
|
| 1255 |
|
|
{
|
| 1256 |
|
|
_M_value += __d;
|
| 1257 |
|
|
return *this;
|
| 1258 |
|
|
}
|
| 1259 |
|
|
|
| 1260 |
|
|
complex&
|
| 1261 |
|
|
operator-=(double __d)
|
| 1262 |
|
|
{
|
| 1263 |
|
|
_M_value -= __d;
|
| 1264 |
|
|
return *this;
|
| 1265 |
|
|
}
|
| 1266 |
|
|
|
| 1267 |
|
|
complex&
|
| 1268 |
|
|
operator*=(double __d)
|
| 1269 |
|
|
{
|
| 1270 |
|
|
_M_value *= __d;
|
| 1271 |
|
|
return *this;
|
| 1272 |
|
|
}
|
| 1273 |
|
|
|
| 1274 |
|
|
complex&
|
| 1275 |
|
|
operator/=(double __d)
|
| 1276 |
|
|
{
|
| 1277 |
|
|
_M_value /= __d;
|
| 1278 |
|
|
return *this;
|
| 1279 |
|
|
}
|
| 1280 |
|
|
|
| 1281 |
|
|
// The compiler will synthesize this, efficiently.
|
| 1282 |
|
|
// complex& operator=(const complex&);
|
| 1283 |
|
|
|
| 1284 |
|
|
template
|
| 1285 |
|
|
complex&
|
| 1286 |
|
|
operator=(const complex<_Tp>& __z)
|
| 1287 |
|
|
{
|
| 1288 |
|
|
__real__ _M_value = __z.real();
|
| 1289 |
|
|
__imag__ _M_value = __z.imag();
|
| 1290 |
|
|
return *this;
|
| 1291 |
|
|
}
|
| 1292 |
|
|
|
| 1293 |
|
|
template
|
| 1294 |
|
|
complex&
|
| 1295 |
|
|
operator+=(const complex<_Tp>& __z)
|
| 1296 |
|
|
{
|
| 1297 |
|
|
__real__ _M_value += __z.real();
|
| 1298 |
|
|
__imag__ _M_value += __z.imag();
|
| 1299 |
|
|
return *this;
|
| 1300 |
|
|
}
|
| 1301 |
|
|
|
| 1302 |
|
|
template
|
| 1303 |
|
|
complex&
|
| 1304 |
|
|
operator-=(const complex<_Tp>& __z)
|
| 1305 |
|
|
{
|
| 1306 |
|
|
__real__ _M_value -= __z.real();
|
| 1307 |
|
|
__imag__ _M_value -= __z.imag();
|
| 1308 |
|
|
return *this;
|
| 1309 |
|
|
}
|
| 1310 |
|
|
|
| 1311 |
|
|
template
|
| 1312 |
|
|
complex&
|
| 1313 |
|
|
operator*=(const complex<_Tp>& __z)
|
| 1314 |
|
|
{
|
| 1315 |
|
|
_ComplexT __t;
|
| 1316 |
|
|
__real__ __t = __z.real();
|
| 1317 |
|
|
__imag__ __t = __z.imag();
|
| 1318 |
|
|
_M_value *= __t;
|
| 1319 |
|
|
return *this;
|
| 1320 |
|
|
}
|
| 1321 |
|
|
|
| 1322 |
|
|
template
|
| 1323 |
|
|
complex&
|
| 1324 |
|
|
operator/=(const complex<_Tp>& __z)
|
| 1325 |
|
|
{
|
| 1326 |
|
|
_ComplexT __t;
|
| 1327 |
|
|
__real__ __t = __z.real();
|
| 1328 |
|
|
__imag__ __t = __z.imag();
|
| 1329 |
|
|
_M_value /= __t;
|
| 1330 |
|
|
return *this;
|
| 1331 |
|
|
}
|
| 1332 |
|
|
|
| 1333 |
|
|
_GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
| 1334 |
|
|
|
| 1335 |
|
|
private:
|
| 1336 |
|
|
_ComplexT _M_value;
|
| 1337 |
|
|
};
|
| 1338 |
|
|
|
| 1339 |
|
|
/// 26.2.3 complex specializations
|
| 1340 |
|
|
/// complex specialization
|
| 1341 |
|
|
template<>
|
| 1342 |
|
|
struct complex
|
| 1343 |
|
|
{
|
| 1344 |
|
|
typedef long double value_type;
|
| 1345 |
|
|
typedef __complex__ long double _ComplexT;
|
| 1346 |
|
|
|
| 1347 |
|
|
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
|
| 1348 |
|
|
|
| 1349 |
|
|
_GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
|
| 1350 |
|
|
long double __i = 0.0L)
|
| 1351 |
|
|
#if __cplusplus >= 201103L
|
| 1352 |
|
|
: _M_value{ __r, __i } { }
|
| 1353 |
|
|
#else
|
| 1354 |
|
|
{
|
| 1355 |
|
|
__real__ _M_value = __r;
|
| 1356 |
|
|
__imag__ _M_value = __i;
|
| 1357 |
|
|
}
|
| 1358 |
|
|
#endif
|
| 1359 |
|
|
|
| 1360 |
|
|
_GLIBCXX_CONSTEXPR complex(const complex& __z)
|
| 1361 |
|
|
: _M_value(__z.__rep()) { }
|
| 1362 |
|
|
|
| 1363 |
|
|
_GLIBCXX_CONSTEXPR complex(const complex& __z)
|
| 1364 |
|
|
: _M_value(__z.__rep()) { }
|
| 1365 |
|
|
|
| 1366 |
|
|
#if __cplusplus >= 201103L
|
| 1367 |
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
| 1368 |
|
|
// DR 387. std::complex over-encapsulated.
|
| 1369 |
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
| 1370 |
|
|
constexpr long double
|
| 1371 |
|
|
real() { return __real__ _M_value; }
|
| 1372 |
|
|
|
| 1373 |
|
|
__attribute ((__abi_tag__ ("cxx11")))
|
| 1374 |
|
|
constexpr long double
|
| 1375 |
|
|
imag() { return __imag__ _M_value; }
|
| 1376 |
|
|
#else
|
| 1377 |
|
|
long double&
|
| 1378 |
|
|
real() { return __real__ _M_value; }
|
| 1379 |
|
|
|
| 1380 |
|
|
const long double&
|
| 1381 |
|
|
real() const { return __real__ _M_value; }
|
| 1382 |
|
|
|
| 1383 |
|
|
long double&
|
| 1384 |
|
|
imag() { return __imag__ _M_value; }
|
| 1385 |
|
|
|
| 1386 |
|
|
const long double&
|
| 1387 |
|
|
imag() const { return __imag__ _M_value; }
|
| 1388 |
|
|
#endif
|
| 1389 |
|
|
|
| 1390 |
|
|
// _GLIBCXX_RESOLVE_LIB_DEFECTS
|
| 1391 |
|
|
// DR 387. std::complex over-encapsulated.
|
| 1392 |
|
|
void
|
| 1393 |
|
|
real(long double __val) { __real__ _M_value = __val; }
|
| 1394 |
|
|
|
| 1395 |
|
|
void
|
| 1396 |
|
|
imag(long double __val) { __imag__ _M_value = __val; }
|
| 1397 |
|
|
|
| 1398 |
|
|
complex&
|
| 1399 |
|
|
operator=(long double __r)
|
| 1400 |
|
|
{
|
| 1401 |
|
|
_M_value = __r;
|
| 1402 |
|
|
return *this;
|
| 1403 |
|
|
}
|
| 1404 |
|
|
|
| 1405 |
|
|
complex&
|
| 1406 |
|
|
operator+=(long double __r)
|
| 1407 |
|
|
{
|
| 1408 |
|
|
_M_value += __r;
|
| 1409 |
|
|
return *this;
|
| 1410 |
|
|
}
|
| 1411 |
|
|
|
| 1412 |
|
|
complex&
|
| 1413 |
|
|
operator-=(long double __r)
|
| 1414 |
|
|
{
|
| 1415 |
|
|
_M_value -= __r;
|
| 1416 |
|
|
return *this;
|
| 1417 |
|
|
}
|
| 1418 |
|
|
|
| 1419 |
|
|
complex&
|
| 1420 |
|
|
operator*=(long double __r)
|
| 1421 |
|
|
{
|
| 1422 |
|
|
_M_value *= __r;
|
| 1423 |
|
|
return *this;
|
| 1424 |
|
|
}
|
| 1425 |
|
|
|
| 1426 |
|
|
complex&
|
| 1427 |
|
|
operator/=(long double __r)
|
| 1428 |
|
|
{
|
| 1429 |
|
|
_M_value /= __r;
|
| 1430 |
|
|
return *this;
|
| 1431 |
|
|
}
|
| 1432 |
|
|
|
| 1433 |
|
|
// The compiler knows how to do this efficiently
|
| 1434 |
|
|
// complex& operator=(const complex&);
|
| 1435 |
|
|
|
| 1436 |
|
|
template
|
| 1437 |
|
|
complex&
|
| 1438 |
|
|
operator=(const complex<_Tp>& __z)
|
| 1439 |
|
|
{
|
| 1440 |
|
|
__real__ _M_value = __z.real();
|
| 1441 |
|
|
__imag__ _M_value = __z.imag();
|
| 1442 |
|
|
return *this;
|
| 1443 |
|
|
}
|
| 1444 |
|
|
|
| 1445 |
|
|
template
|
| 1446 |
|
|
complex&
|
| 1447 |
|
|
operator+=(const complex<_Tp>& __z)
|
| 1448 |
|
|
{
|
| 1449 |
|
|
__real__ _M_value += __z.real();
|
| 1450 |
|
|
__imag__ _M_value += __z.imag();
|
| 1451 |
|
|
return *this;
|
| 1452 |
|
|
}
|
| 1453 |
|
|
|
| 1454 |
|
|
template
|
| 1455 |
|
|
complex&
|
| 1456 |
|
|
operator-=(const complex<_Tp>& __z)
|
| 1457 |
|
|
{
|
| 1458 |
|
|
__real__ _M_value -= __z.real();
|
| 1459 |
|
|
__imag__ _M_value -= __z.imag();
|
| 1460 |
|
|
return *this;
|
| 1461 |
|
|
}
|
| 1462 |
|
|
|
| 1463 |
|
|
template
|
| 1464 |
|
|
complex&
|
| 1465 |
|
|
operator*=(const complex<_Tp>& __z)
|
| 1466 |
|
|
{
|
| 1467 |
|
|
_ComplexT __t;
|
| 1468 |
|
|
__real__ __t = __z.real();
|
| 1469 |
|
|
__imag__ __t = __z.imag();
|
| 1470 |
|
|
_M_value *= __t;
|
| 1471 |
|
|
return *this;
|
| 1472 |
|
|
}
|
| 1473 |
|
|
|
| 1474 |
|
|
template
|
| 1475 |
|
|
complex&
|
| 1476 |
|
|
operator/=(const complex<_Tp>& __z)
|
| 1477 |
|
|
{
|
| 1478 |
|
|
_ComplexT __t;
|
| 1479 |
|
|
__real__ __t = __z.real();
|
| 1480 |
|
|
__imag__ __t = __z.imag();
|
| 1481 |
|
|
_M_value /= __t;
|
| 1482 |
|
|
return *this;
|
| 1483 |
|
|
}
|
| 1484 |
|
|
|
| 1485 |
|
|
_GLIBCXX_USE_CONSTEXPR _ComplexT __rep() const { return _M_value; }
|
| 1486 |
|
|
|
| 1487 |
|
|
private:
|
| 1488 |
|
|
_ComplexT _M_value;
|
| 1489 |
|
|
};
|
| 1490 |
|
|
|
| 1491 |
|
|
// These bits have to be at the end of this file, so that the
|
| 1492 |
|
|
// specializations have all been defined.
|
| 1493 |
|
|
inline _GLIBCXX_CONSTEXPR
|
| 1494 |
|
|
complex::complex(const complex& __z)
|
| 1495 |
|
|
: _M_value(__z.__rep()) { }
|
| 1496 |
|
|
|
| 1497 |
|
|
inline _GLIBCXX_CONSTEXPR
|
| 1498 |
|
|
complex::complex(const complex& __z)
|
| 1499 |
|
|
: _M_value(__z.__rep()) { }
|
| 1500 |
|
|
|
| 1501 |
|
|
inline _GLIBCXX_CONSTEXPR
|
| 1502 |
|
|
complex::complex(const complex& __z)
|
| 1503 |
|
|
: _M_value(__z.__rep()) { }
|
| 1504 |
|
|
|
| 1505 |
|
|
// Inhibit implicit instantiations for required instantiations,
|
| 1506 |
|
|
// which are defined via explicit instantiations elsewhere.
|
| 1507 |
|
|
// NB: This syntax is a GNU extension.
|
| 1508 |
|
|
#if _GLIBCXX_EXTERN_TEMPLATE
|
| 1509 |
|
|
extern template istream& operator>>(istream&, complex&);
|
| 1510 |
|
|
extern template ostream& operator<<(ostream&, const complex&);
|
| 1511 |
|
|
extern template istream& operator>>(istream&, complex&);
|
| 1512 |
|
|
extern template ostream& operator<<(ostream&, const complex&);
|
| 1513 |
|
|
extern template istream& operator>>(istream&, complex&);
|
| 1514 |
|
|
extern template ostream& operator<<(ostream&, const complex&);
|
| 1515 |
|
|
|
| 1516 |
|
|
#ifdef _GLIBCXX_USE_WCHAR_T
|
| 1517 |
|
|
extern template wistream& operator>>(wistream&, complex&);
|
| 1518 |
|
|
extern template wostream& operator<<(wostream&, const complex&);
|
| 1519 |
|
|
extern template wistream& operator>>(wistream&, complex&);
|
| 1520 |
|
|
extern template wostream& operator<<(wostream&, const complex&);
|
| 1521 |
|
|
extern template wistream& operator>>(wistream&, complex&);
|
| 1522 |
|
|
extern template wostream& operator<<(wostream&, const complex&);
|
| 1523 |
|
|
#endif
|
| 1524 |
|
|
#endif
|
| 1525 |
|
|
|
| 1526 |
|
|
// @} group complex_numbers
|
| 1527 |
|
|
|
| 1528 |
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
| 1529 |
|
|
} // namespace
|
| 1530 |
|
|
|
| 1531 |
|
|
namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
|
| 1532 |
|
|
{
|
| 1533 |
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
| 1534 |
|
|
|
| 1535 |
|
|
// See ext/type_traits.h for the primary template.
|
| 1536 |
|
|
template
|
| 1537 |
|
|
struct __promote_2, _Up>
|
| 1538 |
|
|
{
|
| 1539 |
|
|
public:
|
| 1540 |
|
|
typedef std::complex::__type> __type;
|
| 1541 |
|
|
};
|
| 1542 |
|
|
|
| 1543 |
|
|
template
|
| 1544 |
|
|
struct __promote_2<_Tp, std::complex<_Up> >
|
| 1545 |
|
|
{
|
| 1546 |
|
|
public:
|
| 1547 |
|
|
typedef std::complex::__type> __type;
|
| 1548 |
|
|
};
|
| 1549 |
|
|
|
| 1550 |
|
|
template
|
| 1551 |
|
|
struct __promote_2, std::complex<_Up> >
|
| 1552 |
|
|
{
|
| 1553 |
|
|
public:
|
| 1554 |
|
|
typedef std::complex::__type> __type;
|
| 1555 |
|
|
};
|
| 1556 |
|
|
|
| 1557 |
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
| 1558 |
|
|
} // namespace
|
| 1559 |
|
|
|
| 1560 |
|
|
#if __cplusplus >= 201103L
|
| 1561 |
|
|
|
| 1562 |
|
|
namespace std _GLIBCXX_VISIBILITY(default)
|
| 1563 |
|
|
{
|
| 1564 |
|
|
_GLIBCXX_BEGIN_NAMESPACE_VERSION
|
| 1565 |
|
|
|
| 1566 |
|
|
// Forward declarations.
|
| 1567 |
|
|
template std::complex<_Tp> acos(const std::complex<_Tp>&);
|
| 1568 |
|
|
template std::complex<_Tp> asin(const std::complex<_Tp>&);
|
| 1569 |
|
|
template std::complex<_Tp> atan(const std::complex<_Tp>&);
|
| 1570 |
|
|
|
| 1571 |
|
|
template std::complex<_Tp> acosh(const std::complex<_Tp>&);
|
| 1572 |
|
|
template std::complex<_Tp> asinh(const std::complex<_Tp>&);
|
| 1573 |
|
|
template std::complex<_Tp> atanh(const std::complex<_Tp>&);
|
| 1574 |
|
|
// DR 595.
|
| 1575 |
|
|
template _Tp fabs(const std::complex<_Tp>&);
|
| 1576 |
|
|
|
| 1577 |
|
|
template
|
| 1578 |
|
|
inline std::complex<_Tp>
|
| 1579 |
|
|
__complex_acos(const std::complex<_Tp>& __z)
|
| 1580 |
|
|
{
|
| 1581 |
|
|
const std::complex<_Tp> __t = std::asin(__z);
|
| 1582 |
|
|
const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
|
| 1583 |
|
|
return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
|
| 1584 |
|
|
}
|
| 1585 |
|
|
|
| 1586 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
| 1587 |
|
|
inline __complex__ float
|
| 1588 |
|
|
__complex_acos(__complex__ float __z)
|
| 1589 |
|
|
{ return __builtin_cacosf(__z); }
|
| 1590 |
|
|
|
| 1591 |
|
|
inline __complex__ double
|
| 1592 |
|
|
__complex_acos(__complex__ double __z)
|
| 1593 |
|
|
{ return __builtin_cacos(__z); }
|
| 1594 |
|
|
|
| 1595 |
|
|
inline __complex__ long double
|
| 1596 |
|
|
__complex_acos(const __complex__ long double& __z)
|
| 1597 |
|
|
{ return __builtin_cacosl(__z); }
|
| 1598 |
|
|
|
| 1599 |
|
|
template
|
| 1600 |
|
|
inline std::complex<_Tp>
|
| 1601 |
|
|
acos(const std::complex<_Tp>& __z)
|
| 1602 |
|
|
{ return __complex_acos(__z.__rep()); }
|
| 1603 |
|
|
#else
|
| 1604 |
|
|
/// acos(__z) [8.1.2].
|
| 1605 |
|
|
// Effects: Behaves the same as C99 function cacos, defined
|
| 1606 |
|
|
// in subclause 7.3.5.1.
|
| 1607 |
|
|
template
|
| 1608 |
|
|
inline std::complex<_Tp>
|
| 1609 |
|
|
acos(const std::complex<_Tp>& __z)
|
| 1610 |
|
|
{ return __complex_acos(__z); }
|
| 1611 |
|
|
#endif
|
| 1612 |
|
|
|
| 1613 |
|
|
template
|
| 1614 |
|
|
inline std::complex<_Tp>
|
| 1615 |
|
|
__complex_asin(const std::complex<_Tp>& __z)
|
| 1616 |
|
|
{
|
| 1617 |
|
|
std::complex<_Tp> __t(-__z.imag(), __z.real());
|
| 1618 |
|
|
__t = std::asinh(__t);
|
| 1619 |
|
|
return std::complex<_Tp>(__t.imag(), -__t.real());
|
| 1620 |
|
|
}
|
| 1621 |
|
|
|
| 1622 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
| 1623 |
|
|
inline __complex__ float
|
| 1624 |
|
|
__complex_asin(__complex__ float __z)
|
| 1625 |
|
|
{ return __builtin_casinf(__z); }
|
| 1626 |
|
|
|
| 1627 |
|
|
inline __complex__ double
|
| 1628 |
|
|
__complex_asin(__complex__ double __z)
|
| 1629 |
|
|
{ return __builtin_casin(__z); }
|
| 1630 |
|
|
|
| 1631 |
|
|
inline __complex__ long double
|
| 1632 |
|
|
__complex_asin(const __complex__ long double& __z)
|
| 1633 |
|
|
{ return __builtin_casinl(__z); }
|
| 1634 |
|
|
|
| 1635 |
|
|
template
|
| 1636 |
|
|
inline std::complex<_Tp>
|
| 1637 |
|
|
asin(const std::complex<_Tp>& __z)
|
| 1638 |
|
|
{ return __complex_asin(__z.__rep()); }
|
| 1639 |
|
|
#else
|
| 1640 |
|
|
/// asin(__z) [8.1.3].
|
| 1641 |
|
|
// Effects: Behaves the same as C99 function casin, defined
|
| 1642 |
|
|
// in subclause 7.3.5.2.
|
| 1643 |
|
|
template
|
| 1644 |
|
|
inline std::complex<_Tp>
|
| 1645 |
|
|
asin(const std::complex<_Tp>& __z)
|
| 1646 |
|
|
{ return __complex_asin(__z); }
|
| 1647 |
|
|
#endif
|
| 1648 |
|
|
|
| 1649 |
|
|
template
|
| 1650 |
|
|
std::complex<_Tp>
|
| 1651 |
|
|
__complex_atan(const std::complex<_Tp>& __z)
|
| 1652 |
|
|
{
|
| 1653 |
|
|
const _Tp __r2 = __z.real() * __z.real();
|
| 1654 |
|
|
const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
|
| 1655 |
|
|
|
| 1656 |
|
|
_Tp __num = __z.imag() + _Tp(1.0);
|
| 1657 |
|
|
_Tp __den = __z.imag() - _Tp(1.0);
|
| 1658 |
|
|
|
| 1659 |
|
|
__num = __r2 + __num * __num;
|
| 1660 |
|
|
__den = __r2 + __den * __den;
|
| 1661 |
|
|
|
| 1662 |
|
|
return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
|
| 1663 |
|
|
_Tp(0.25) * log(__num / __den));
|
| 1664 |
|
|
}
|
| 1665 |
|
|
|
| 1666 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
| 1667 |
|
|
inline __complex__ float
|
| 1668 |
|
|
__complex_atan(__complex__ float __z)
|
| 1669 |
|
|
{ return __builtin_catanf(__z); }
|
| 1670 |
|
|
|
| 1671 |
|
|
inline __complex__ double
|
| 1672 |
|
|
__complex_atan(__complex__ double __z)
|
| 1673 |
|
|
{ return __builtin_catan(__z); }
|
| 1674 |
|
|
|
| 1675 |
|
|
inline __complex__ long double
|
| 1676 |
|
|
__complex_atan(const __complex__ long double& __z)
|
| 1677 |
|
|
{ return __builtin_catanl(__z); }
|
| 1678 |
|
|
|
| 1679 |
|
|
template
|
| 1680 |
|
|
inline std::complex<_Tp>
|
| 1681 |
|
|
atan(const std::complex<_Tp>& __z)
|
| 1682 |
|
|
{ return __complex_atan(__z.__rep()); }
|
| 1683 |
|
|
#else
|
| 1684 |
|
|
/// atan(__z) [8.1.4].
|
| 1685 |
|
|
// Effects: Behaves the same as C99 function catan, defined
|
| 1686 |
|
|
// in subclause 7.3.5.3.
|
| 1687 |
|
|
template
|
| 1688 |
|
|
inline std::complex<_Tp>
|
| 1689 |
|
|
atan(const std::complex<_Tp>& __z)
|
| 1690 |
|
|
{ return __complex_atan(__z); }
|
| 1691 |
|
|
#endif
|
| 1692 |
|
|
|
| 1693 |
|
|
template
|
| 1694 |
|
|
std::complex<_Tp>
|
| 1695 |
|
|
__complex_acosh(const std::complex<_Tp>& __z)
|
| 1696 |
|
|
{
|
| 1697 |
|
|
// Kahan's formula.
|
| 1698 |
|
|
return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
|
| 1699 |
|
|
+ std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
|
| 1700 |
|
|
}
|
| 1701 |
|
|
|
| 1702 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
| 1703 |
|
|
inline __complex__ float
|
| 1704 |
|
|
__complex_acosh(__complex__ float __z)
|
| 1705 |
|
|
{ return __builtin_cacoshf(__z); }
|
| 1706 |
|
|
|
| 1707 |
|
|
inline __complex__ double
|
| 1708 |
|
|
__complex_acosh(__complex__ double __z)
|
| 1709 |
|
|
{ return __builtin_cacosh(__z); }
|
| 1710 |
|
|
|
| 1711 |
|
|
inline __complex__ long double
|
| 1712 |
|
|
__complex_acosh(const __complex__ long double& __z)
|
| 1713 |
|
|
{ return __builtin_cacoshl(__z); }
|
| 1714 |
|
|
|
| 1715 |
|
|
template
|
| 1716 |
|
|
inline std::complex<_Tp>
|
| 1717 |
|
|
acosh(const std::complex<_Tp>& __z)
|
| 1718 |
|
|
{ return __complex_acosh(__z.__rep()); }
|
| 1719 |
|
|
#else
|
| 1720 |
|
|
/// acosh(__z) [8.1.5].
|
| 1721 |
|
|
// Effects: Behaves the same as C99 function cacosh, defined
|
| 1722 |
|
|
// in subclause 7.3.6.1.
|
| 1723 |
|
|
template
|
| 1724 |
|
|
inline std::complex<_Tp>
|
| 1725 |
|
|
acosh(const std::complex<_Tp>& __z)
|
| 1726 |
|
|
{ return __complex_acosh(__z); }
|
| 1727 |
|
|
#endif
|
| 1728 |
|
|
|
| 1729 |
|
|
template
|
| 1730 |
|
|
std::complex<_Tp>
|
| 1731 |
|
|
__complex_asinh(const std::complex<_Tp>& __z)
|
| 1732 |
|
|
{
|
| 1733 |
|
|
std::complex<_Tp> __t((__z.real() - __z.imag())
|
| 1734 |
|
|
* (__z.real() + __z.imag()) + _Tp(1.0),
|
| 1735 |
|
|
_Tp(2.0) * __z.real() * __z.imag());
|
| 1736 |
|
|
__t = std::sqrt(__t);
|
| 1737 |
|
|
|
| 1738 |
|
|
return std::log(__t + __z);
|
| 1739 |
|
|
}
|
| 1740 |
|
|
|
| 1741 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
| 1742 |
|
|
inline __complex__ float
|
| 1743 |
|
|
__complex_asinh(__complex__ float __z)
|
| 1744 |
|
|
{ return __builtin_casinhf(__z); }
|
| 1745 |
|
|
|
| 1746 |
|
|
inline __complex__ double
|
| 1747 |
|
|
__complex_asinh(__complex__ double __z)
|
| 1748 |
|
|
{ return __builtin_casinh(__z); }
|
| 1749 |
|
|
|
| 1750 |
|
|
inline __complex__ long double
|
| 1751 |
|
|
__complex_asinh(const __complex__ long double& __z)
|
| 1752 |
|
|
{ return __builtin_casinhl(__z); }
|
| 1753 |
|
|
|
| 1754 |
|
|
template
|
| 1755 |
|
|
inline std::complex<_Tp>
|
| 1756 |
|
|
asinh(const std::complex<_Tp>& __z)
|
| 1757 |
|
|
{ return __complex_asinh(__z.__rep()); }
|
| 1758 |
|
|
#else
|
| 1759 |
|
|
/// asinh(__z) [8.1.6].
|
| 1760 |
|
|
// Effects: Behaves the same as C99 function casin, defined
|
| 1761 |
|
|
// in subclause 7.3.6.2.
|
| 1762 |
|
|
template
|
| 1763 |
|
|
inline std::complex<_Tp>
|
| 1764 |
|
|
asinh(const std::complex<_Tp>& __z)
|
| 1765 |
|
|
{ return __complex_asinh(__z); }
|
| 1766 |
|
|
#endif
|
| 1767 |
|
|
|
| 1768 |
|
|
template
|
| 1769 |
|
|
std::complex<_Tp>
|
| 1770 |
|
|
__complex_atanh(const std::complex<_Tp>& __z)
|
| 1771 |
|
|
{
|
| 1772 |
|
|
const _Tp __i2 = __z.imag() * __z.imag();
|
| 1773 |
|
|
const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
|
| 1774 |
|
|
|
| 1775 |
|
|
_Tp __num = _Tp(1.0) + __z.real();
|
| 1776 |
|
|
_Tp __den = _Tp(1.0) - __z.real();
|
| 1777 |
|
|
|
| 1778 |
|
|
__num = __i2 + __num * __num;
|
| 1779 |
|
|
__den = __i2 + __den * __den;
|
| 1780 |
|
|
|
| 1781 |
|
|
return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
|
| 1782 |
|
|
_Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
|
| 1783 |
|
|
}
|
| 1784 |
|
|
|
| 1785 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX_TR1
|
| 1786 |
|
|
inline __complex__ float
|
| 1787 |
|
|
__complex_atanh(__complex__ float __z)
|
| 1788 |
|
|
{ return __builtin_catanhf(__z); }
|
| 1789 |
|
|
|
| 1790 |
|
|
inline __complex__ double
|
| 1791 |
|
|
__complex_atanh(__complex__ double __z)
|
| 1792 |
|
|
{ return __builtin_catanh(__z); }
|
| 1793 |
|
|
|
| 1794 |
|
|
inline __complex__ long double
|
| 1795 |
|
|
__complex_atanh(const __complex__ long double& __z)
|
| 1796 |
|
|
{ return __builtin_catanhl(__z); }
|
| 1797 |
|
|
|
| 1798 |
|
|
template
|
| 1799 |
|
|
inline std::complex<_Tp>
|
| 1800 |
|
|
atanh(const std::complex<_Tp>& __z)
|
| 1801 |
|
|
{ return __complex_atanh(__z.__rep()); }
|
| 1802 |
|
|
#else
|
| 1803 |
|
|
/// atanh(__z) [8.1.7].
|
| 1804 |
|
|
// Effects: Behaves the same as C99 function catanh, defined
|
| 1805 |
|
|
// in subclause 7.3.6.3.
|
| 1806 |
|
|
template
|
| 1807 |
|
|
inline std::complex<_Tp>
|
| 1808 |
|
|
atanh(const std::complex<_Tp>& __z)
|
| 1809 |
|
|
{ return __complex_atanh(__z); }
|
| 1810 |
|
|
#endif
|
| 1811 |
|
|
|
| 1812 |
|
|
template
|
| 1813 |
|
|
inline _Tp
|
| 1814 |
|
|
/// fabs(__z) [8.1.8].
|
| 1815 |
|
|
// Effects: Behaves the same as C99 function cabs, defined
|
| 1816 |
|
|
// in subclause 7.3.8.1.
|
| 1817 |
|
|
fabs(const std::complex<_Tp>& __z)
|
| 1818 |
|
|
{ return std::abs(__z); }
|
| 1819 |
|
|
|
| 1820 |
|
|
/// Additional overloads [8.1.9].
|
| 1821 |
|
|
template
|
| 1822 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 1823 |
|
|
arg(_Tp __x)
|
| 1824 |
|
|
{
|
| 1825 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 1826 |
|
|
#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
|
| 1827 |
|
|
return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
|
| 1828 |
|
|
: __type();
|
| 1829 |
|
|
#else
|
| 1830 |
|
|
return std::arg(std::complex<__type>(__x));
|
| 1831 |
|
|
#endif
|
| 1832 |
|
|
}
|
| 1833 |
|
|
|
| 1834 |
|
|
template
|
| 1835 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 1836 |
|
|
imag(_Tp)
|
| 1837 |
|
|
{ return _Tp(); }
|
| 1838 |
|
|
|
| 1839 |
|
|
template
|
| 1840 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 1841 |
|
|
norm(_Tp __x)
|
| 1842 |
|
|
{
|
| 1843 |
|
|
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
|
| 1844 |
|
|
return __type(__x) * __type(__x);
|
| 1845 |
|
|
}
|
| 1846 |
|
|
|
| 1847 |
|
|
template
|
| 1848 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 1849 |
|
|
real(_Tp __x)
|
| 1850 |
|
|
{ return __x; }
|
| 1851 |
|
|
|
| 1852 |
|
|
template
|
| 1853 |
|
|
inline std::complex::__type>
|
| 1854 |
|
|
pow(const std::complex<_Tp>& __x, const _Up& __y)
|
| 1855 |
|
|
{
|
| 1856 |
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
| 1857 |
|
|
return std::pow(std::complex<__type>(__x), __type(__y));
|
| 1858 |
|
|
}
|
| 1859 |
|
|
|
| 1860 |
|
|
template
|
| 1861 |
|
|
inline std::complex::__type>
|
| 1862 |
|
|
pow(const _Tp& __x, const std::complex<_Up>& __y)
|
| 1863 |
|
|
{
|
| 1864 |
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
| 1865 |
|
|
return std::pow(__type(__x), std::complex<__type>(__y));
|
| 1866 |
|
|
}
|
| 1867 |
|
|
|
| 1868 |
|
|
template
|
| 1869 |
|
|
inline std::complex::__type>
|
| 1870 |
|
|
pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
|
| 1871 |
|
|
{
|
| 1872 |
|
|
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
|
| 1873 |
|
|
return std::pow(std::complex<__type>(__x),
|
| 1874 |
|
|
std::complex<__type>(__y));
|
| 1875 |
|
|
}
|
| 1876 |
|
|
|
| 1877 |
|
|
// Forward declarations.
|
| 1878 |
|
|
// DR 781.
|
| 1879 |
|
|
template std::complex<_Tp> proj(const std::complex<_Tp>&);
|
| 1880 |
|
|
|
| 1881 |
|
|
template
|
| 1882 |
|
|
std::complex<_Tp>
|
| 1883 |
|
|
__complex_proj(const std::complex<_Tp>& __z)
|
| 1884 |
|
|
{
|
| 1885 |
|
|
const _Tp __den = (__z.real() * __z.real()
|
| 1886 |
|
|
+ __z.imag() * __z.imag() + _Tp(1.0));
|
| 1887 |
|
|
|
| 1888 |
|
|
return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
|
| 1889 |
|
|
(_Tp(2.0) * __z.imag()) / __den);
|
| 1890 |
|
|
}
|
| 1891 |
|
|
|
| 1892 |
|
|
#if _GLIBCXX_USE_C99_COMPLEX
|
| 1893 |
|
|
inline __complex__ float
|
| 1894 |
|
|
__complex_proj(__complex__ float __z)
|
| 1895 |
|
|
{ return __builtin_cprojf(__z); }
|
| 1896 |
|
|
|
| 1897 |
|
|
inline __complex__ double
|
| 1898 |
|
|
__complex_proj(__complex__ double __z)
|
| 1899 |
|
|
{ return __builtin_cproj(__z); }
|
| 1900 |
|
|
|
| 1901 |
|
|
inline __complex__ long double
|
| 1902 |
|
|
__complex_proj(const __complex__ long double& __z)
|
| 1903 |
|
|
{ return __builtin_cprojl(__z); }
|
| 1904 |
|
|
|
| 1905 |
|
|
template
|
| 1906 |
|
|
inline std::complex<_Tp>
|
| 1907 |
|
|
proj(const std::complex<_Tp>& __z)
|
| 1908 |
|
|
{ return __complex_proj(__z.__rep()); }
|
| 1909 |
|
|
#else
|
| 1910 |
|
|
template
|
| 1911 |
|
|
inline std::complex<_Tp>
|
| 1912 |
|
|
proj(const std::complex<_Tp>& __z)
|
| 1913 |
|
|
{ return __complex_proj(__z); }
|
| 1914 |
|
|
#endif
|
| 1915 |
|
|
|
| 1916 |
|
|
// DR 1137.
|
| 1917 |
|
|
template
|
| 1918 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 1919 |
|
|
proj(_Tp __x)
|
| 1920 |
|
|
{ return __x; }
|
| 1921 |
|
|
|
| 1922 |
|
|
template
|
| 1923 |
|
|
inline typename __gnu_cxx::__promote<_Tp>::__type
|
| 1924 |
|
|
conj(_Tp __x)
|
| 1925 |
|
|
{ return __x; }
|
| 1926 |
|
|
|
| 1927 |
|
|
_GLIBCXX_END_NAMESPACE_VERSION
|
| 1928 |
|
|
} // namespace
|
| 1929 |
|
|
|
| 1930 |
|
|
#endif // C++11
|
| 1931 |
|
|
|
| 1932 |
|
|
#endif /* _GLIBCXX_COMPLEX */
|
