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// The template and inlines for the -*- C++ -*- complex number classes. |
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// Copyright (C) 1997-2015 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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// Get rid of a macro possibly defined in |
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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 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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/// 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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/// 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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// Let the compiler synthesize the copy constructor |
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#if __cplusplus >= 201103L |
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constexpr complex(const complex&) = default; |
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#endif |
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/// Converting 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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_GLIBCXX_ABI_TAG_CXX11 |
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constexpr _Tp |
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real() const { return _M_real; } |
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_GLIBCXX_ABI_TAG_CXX11 |
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constexpr _Tp |
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imag() const { 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 a scalar to this complex number. |
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complex<_Tp>& operator=(const _Tp&); |
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/// Add a scalar 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 scalar 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 scalar. |
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complex<_Tp>& operator*=(const _Tp&); |
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/// Divide this complex number by a scalar. |
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complex<_Tp>& operator/=(const _Tp&); |
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// Let the compiler synthesize the copy assignment operator |
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#if __cplusplus >= 201103L |
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complex& operator=(const complex&) = default; |
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#endif |
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/// Assign another complex number to this one. |
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template |
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complex<_Tp>& operator=(const complex<_Up>&); |
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/// Add another complex number to this one. |
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template |
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complex<_Tp>& operator+=(const complex<_Up>&); |
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/// Subtract another complex number from this one. |
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template |
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complex<_Tp>& operator-=(const complex<_Up>&); |
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/// Multiply this complex number by another. |
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template |
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complex<_Tp>& operator*=(const complex<_Up>&); |
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/// Divide this complex number by another. |
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template |
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complex<_Tp>& operator/=(const complex<_Up>&); |
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_GLIBCXX_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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_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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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 |
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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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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 |
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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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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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 |
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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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411 |
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//@{ |
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/// Return new complex value @a x divided by @a y. |
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template |
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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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|
418 |
complex<_Tp> __r = __x; |
|
|
419 |
__r /= __y; |
|
|
420 |
return __r; |
|
|
421 |
} |
|
|
422 |
|
|
|
423 |
template |
|
|
424 |
inline complex<_Tp> |
|
|
425 |
operator/(const complex<_Tp>& __x, const _Tp& __y) |
|
|
426 |
{ |
|
|
427 |
complex<_Tp> __r = __x; |
|
|
428 |
__r /= __y; |
|
|
429 |
return __r; |
|
|
430 |
} |
|
|
431 |
|
|
|
432 |
template |
|
|
433 |
inline complex<_Tp> |
|
|
434 |
operator/(const _Tp& __x, const complex<_Tp>& __y) |
|
|
435 |
{ |
|
|
436 |
complex<_Tp> __r = __x; |
|
|
437 |
__r /= __y; |
|
|
438 |
return __r; |
|
|
439 |
} |
|
|
440 |
//@} |
|
|
441 |
|
|
|
442 |
/// Return @a x. |
|
|
443 |
template |
|
|
444 |
inline complex<_Tp> |
|
|
445 |
operator+(const complex<_Tp>& __x) |
|
|
446 |
{ return __x; } |
|
|
447 |
|
|
|
448 |
/// Return complex negation of @a x. |
|
|
449 |
template |
|
|
450 |
inline complex<_Tp> |
|
|
451 |
operator-(const complex<_Tp>& __x) |
|
|
452 |
{ return complex<_Tp>(-__x.real(), -__x.imag()); } |
|
|
453 |
|
|
|
454 |
//@{ |
|
|
455 |
/// Return true if @a x is equal to @a y. |
|
|
456 |
template |
|
|
457 |
inline _GLIBCXX_CONSTEXPR bool |
|
|
458 |
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y) |
|
|
459 |
{ return __x.real() == __y.real() && __x.imag() == __y.imag(); } |
|
|
460 |
|
|
|
461 |
template |
|
|
462 |
inline _GLIBCXX_CONSTEXPR bool |
|
|
463 |
operator==(const complex<_Tp>& __x, const _Tp& __y) |
|
|
464 |
{ return __x.real() == __y && __x.imag() == _Tp(); } |
|
|
465 |
|
|
|
466 |
template |
|
|
467 |
inline _GLIBCXX_CONSTEXPR bool |
|
|
468 |
operator==(const _Tp& __x, const complex<_Tp>& __y) |
|
|
469 |
{ return __x == __y.real() && _Tp() == __y.imag(); } |
|
|
470 |
//@} |
|
|
471 |
|
|
|
472 |
//@{ |
|
|
473 |
/// Return false if @a x is equal to @a y. |
|
|
474 |
template |
|
|
475 |
inline _GLIBCXX_CONSTEXPR bool |
|
|
476 |
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y) |
|
|
477 |
{ return __x.real() != __y.real() || __x.imag() != __y.imag(); } |
|
|
478 |
|
|
|
479 |
template |
|
|
480 |
inline _GLIBCXX_CONSTEXPR bool |
|
|
481 |
operator!=(const complex<_Tp>& __x, const _Tp& __y) |
|
|
482 |
{ return __x.real() != __y || __x.imag() != _Tp(); } |
|
|
483 |
|
|
|
484 |
template |
|
|
485 |
inline _GLIBCXX_CONSTEXPR bool |
|
|
486 |
operator!=(const _Tp& __x, const complex<_Tp>& __y) |
|
|
487 |
{ return __x != __y.real() || _Tp() != __y.imag(); } |
|
|
488 |
//@} |
|
|
489 |
|
|
|
490 |
/// Extraction operator for complex values. |
|
|
491 |
template |
|
|
492 |
basic_istream<_CharT, _Traits>& |
|
|
493 |
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x) |
|
|
494 |
{ |
|
|
495 |
_Tp __re_x, __im_x; |
|
|
496 |
_CharT __ch; |
|
|
497 |
__is >> __ch; |
|
|
498 |
if (__ch == '(') |
|
|
499 |
{ |
|
|
500 |
__is >> __re_x >> __ch; |
|
|
501 |
if (__ch == ',') |
|
|
502 |
{ |
|
|
503 |
__is >> __im_x >> __ch; |
|
|
504 |
if (__ch == ')') |
|
|
505 |
__x = complex<_Tp>(__re_x, __im_x); |
|
|
506 |
else |
|
|
507 |
__is.setstate(ios_base::failbit); |
|
|
508 |
} |
|
|
509 |
else if (__ch == ')') |
|
|
510 |
__x = __re_x; |
|
|
511 |
else |
|
|
512 |
__is.setstate(ios_base::failbit); |
|
|
513 |
} |
|
|
514 |
else |
|
|
515 |
{ |
|
|
516 |
__is.putback(__ch); |
|
|
517 |
__is >> __re_x; |
|
|
518 |
__x = __re_x; |
|
|
519 |
} |
|
|
520 |
return __is; |
|
|
521 |
} |
|
|
522 |
|
|
|
523 |
/// Insertion operator for complex values. |
|
|
524 |
template |
|
|
525 |
basic_ostream<_CharT, _Traits>& |
|
|
526 |
operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x) |
|
|
527 |
{ |
|
|
528 |
basic_ostringstream<_CharT, _Traits> __s; |
|
|
529 |
__s.flags(__os.flags()); |
|
|
530 |
__s.imbue(__os.getloc()); |
|
|
531 |
__s.precision(__os.precision()); |
|
|
532 |
__s << '(' << __x.real() << ',' << __x.imag() << ')'; |
|
|
533 |
return __os << __s.str(); |
|
|
534 |
} |
|
|
535 |
|
|
|
536 |
// Values |
|
|
537 |
#if __cplusplus >= 201103L |
|
|
538 |
template |
|
|
539 |
constexpr _Tp |
|
|
540 |
real(const complex<_Tp>& __z) |
|
|
541 |
{ return __z.real(); } |
|
|
542 |
|
|
|
543 |
template |
|
|
544 |
constexpr _Tp |
|
|
545 |
imag(const complex<_Tp>& __z) |
|
|
546 |
{ return __z.imag(); } |
|
|
547 |
#else |
|
|
548 |
template |
|
|
549 |
inline _Tp& |
|
|
550 |
real(complex<_Tp>& __z) |
|
|
551 |
{ return __z.real(); } |
|
|
552 |
|
|
|
553 |
template |
|
|
554 |
inline const _Tp& |
|
|
555 |
real(const complex<_Tp>& __z) |
|
|
556 |
{ return __z.real(); } |
|
|
557 |
|
|
|
558 |
template |
|
|
559 |
inline _Tp& |
|
|
560 |
imag(complex<_Tp>& __z) |
|
|
561 |
{ return __z.imag(); } |
|
|
562 |
|
|
|
563 |
template |
|
|
564 |
inline const _Tp& |
|
|
565 |
imag(const complex<_Tp>& __z) |
|
|
566 |
{ return __z.imag(); } |
|
|
567 |
#endif |
|
|
568 |
|
|
|
569 |
// 26.2.7/3 abs(__z): Returns the magnitude of __z. |
|
|
570 |
template |
|
|
571 |
inline _Tp |
|
|
572 |
__complex_abs(const complex<_Tp>& __z) |
|
|
573 |
{ |
|
|
574 |
_Tp __x = __z.real(); |
|
|
575 |
_Tp __y = __z.imag(); |
|
|
576 |
const _Tp __s = std::max(abs(__x), abs(__y)); |
|
|
577 |
if (__s == _Tp()) // well ... |
|
|
578 |
return __s; |
|
|
579 |
__x /= __s; |
|
|
580 |
__y /= __s; |
|
|
581 |
return __s * sqrt(__x * __x + __y * __y); |
|
|
582 |
} |
|
|
583 |
|
|
|
584 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
585 |
inline float |
|
|
586 |
__complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); } |
|
|
587 |
|
|
|
588 |
inline double |
|
|
589 |
__complex_abs(__complex__ double __z) { return __builtin_cabs(__z); } |
|
|
590 |
|
|
|
591 |
inline long double |
|
|
592 |
__complex_abs(const __complex__ long double& __z) |
|
|
593 |
{ return __builtin_cabsl(__z); } |
|
|
594 |
|
|
|
595 |
template |
|
|
596 |
inline _Tp |
|
|
597 |
abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); } |
|
|
598 |
#else |
|
|
599 |
template |
|
|
600 |
inline _Tp |
|
|
601 |
abs(const complex<_Tp>& __z) { return __complex_abs(__z); } |
|
|
602 |
#endif |
|
|
603 |
|
|
|
604 |
|
|
|
605 |
// 26.2.7/4: arg(__z): Returns the phase angle of __z. |
|
|
606 |
template |
|
|
607 |
inline _Tp |
|
|
608 |
__complex_arg(const complex<_Tp>& __z) |
|
|
609 |
{ return atan2(__z.imag(), __z.real()); } |
|
|
610 |
|
|
|
611 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
612 |
inline float |
|
|
613 |
__complex_arg(__complex__ float __z) { return __builtin_cargf(__z); } |
|
|
614 |
|
|
|
615 |
inline double |
|
|
616 |
__complex_arg(__complex__ double __z) { return __builtin_carg(__z); } |
|
|
617 |
|
|
|
618 |
inline long double |
|
|
619 |
__complex_arg(const __complex__ long double& __z) |
|
|
620 |
{ return __builtin_cargl(__z); } |
|
|
621 |
|
|
|
622 |
template |
|
|
623 |
inline _Tp |
|
|
624 |
arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); } |
|
|
625 |
#else |
|
|
626 |
template |
|
|
627 |
inline _Tp |
|
|
628 |
arg(const complex<_Tp>& __z) { return __complex_arg(__z); } |
|
|
629 |
#endif |
|
|
630 |
|
|
|
631 |
// 26.2.7/5: norm(__z) returns the squared magnitude of __z. |
|
|
632 |
// As defined, norm() is -not- a norm is the common mathematical |
|
|
633 |
// sense used in numerics. The helper class _Norm_helper<> tries to |
|
|
634 |
// distinguish between builtin floating point and the rest, so as |
|
|
635 |
// to deliver an answer as close as possible to the real value. |
|
|
636 |
template |
|
|
637 |
struct _Norm_helper |
|
|
638 |
{ |
|
|
639 |
template |
|
|
640 |
static inline _Tp _S_do_it(const complex<_Tp>& __z) |
|
|
641 |
{ |
|
|
642 |
const _Tp __x = __z.real(); |
|
|
643 |
const _Tp __y = __z.imag(); |
|
|
644 |
return __x * __x + __y * __y; |
|
|
645 |
} |
|
|
646 |
}; |
|
|
647 |
|
|
|
648 |
template<> |
|
|
649 |
struct _Norm_helper |
|
|
650 |
{ |
|
|
651 |
template |
|
|
652 |
static inline _Tp _S_do_it(const complex<_Tp>& __z) |
|
|
653 |
{ |
|
|
654 |
_Tp __res = std::abs(__z); |
|
|
655 |
return __res * __res; |
|
|
656 |
} |
|
|
657 |
}; |
|
|
658 |
|
|
|
659 |
template |
|
|
660 |
inline _Tp |
|
|
661 |
norm(const complex<_Tp>& __z) |
|
|
662 |
{ |
|
|
663 |
return _Norm_helper<__is_floating<_Tp>::__value |
|
|
664 |
&& !_GLIBCXX_FAST_MATH>::_S_do_it(__z); |
|
|
665 |
} |
|
|
666 |
|
|
|
667 |
template |
|
|
668 |
inline complex<_Tp> |
|
|
669 |
polar(const _Tp& __rho, const _Tp& __theta) |
|
|
670 |
{ return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); } |
|
|
671 |
|
|
|
672 |
template |
|
|
673 |
inline complex<_Tp> |
|
|
674 |
conj(const complex<_Tp>& __z) |
|
|
675 |
{ return complex<_Tp>(__z.real(), -__z.imag()); } |
|
|
676 |
|
|
|
677 |
// Transcendentals |
|
|
678 |
|
|
|
679 |
// 26.2.8/1 cos(__z): Returns the cosine of __z. |
|
|
680 |
template |
|
|
681 |
inline complex<_Tp> |
|
|
682 |
__complex_cos(const complex<_Tp>& __z) |
|
|
683 |
{ |
|
|
684 |
const _Tp __x = __z.real(); |
|
|
685 |
const _Tp __y = __z.imag(); |
|
|
686 |
return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y)); |
|
|
687 |
} |
|
|
688 |
|
|
|
689 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
690 |
inline __complex__ float |
|
|
691 |
__complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); } |
|
|
692 |
|
|
|
693 |
inline __complex__ double |
|
|
694 |
__complex_cos(__complex__ double __z) { return __builtin_ccos(__z); } |
|
|
695 |
|
|
|
696 |
inline __complex__ long double |
|
|
697 |
__complex_cos(const __complex__ long double& __z) |
|
|
698 |
{ return __builtin_ccosl(__z); } |
|
|
699 |
|
|
|
700 |
template |
|
|
701 |
inline complex<_Tp> |
|
|
702 |
cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); } |
|
|
703 |
#else |
|
|
704 |
template |
|
|
705 |
inline complex<_Tp> |
|
|
706 |
cos(const complex<_Tp>& __z) { return __complex_cos(__z); } |
|
|
707 |
#endif |
|
|
708 |
|
|
|
709 |
// 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z. |
|
|
710 |
template |
|
|
711 |
inline complex<_Tp> |
|
|
712 |
__complex_cosh(const complex<_Tp>& __z) |
|
|
713 |
{ |
|
|
714 |
const _Tp __x = __z.real(); |
|
|
715 |
const _Tp __y = __z.imag(); |
|
|
716 |
return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y)); |
|
|
717 |
} |
|
|
718 |
|
|
|
719 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
720 |
inline __complex__ float |
|
|
721 |
__complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); } |
|
|
722 |
|
|
|
723 |
inline __complex__ double |
|
|
724 |
__complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); } |
|
|
725 |
|
|
|
726 |
inline __complex__ long double |
|
|
727 |
__complex_cosh(const __complex__ long double& __z) |
|
|
728 |
{ return __builtin_ccoshl(__z); } |
|
|
729 |
|
|
|
730 |
template |
|
|
731 |
inline complex<_Tp> |
|
|
732 |
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); } |
|
|
733 |
#else |
|
|
734 |
template |
|
|
735 |
inline complex<_Tp> |
|
|
736 |
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); } |
|
|
737 |
#endif |
|
|
738 |
|
|
|
739 |
// 26.2.8/3 exp(__z): Returns the complex base e exponential of x |
|
|
740 |
template |
|
|
741 |
inline complex<_Tp> |
|
|
742 |
__complex_exp(const complex<_Tp>& __z) |
|
|
743 |
{ return std::polar<_Tp>(exp(__z.real()), __z.imag()); } |
|
|
744 |
|
|
|
745 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
746 |
inline __complex__ float |
|
|
747 |
__complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); } |
|
|
748 |
|
|
|
749 |
inline __complex__ double |
|
|
750 |
__complex_exp(__complex__ double __z) { return __builtin_cexp(__z); } |
|
|
751 |
|
|
|
752 |
inline __complex__ long double |
|
|
753 |
__complex_exp(const __complex__ long double& __z) |
|
|
754 |
{ return __builtin_cexpl(__z); } |
|
|
755 |
|
|
|
756 |
template |
|
|
757 |
inline complex<_Tp> |
|
|
758 |
exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); } |
|
|
759 |
#else |
|
|
760 |
template |
|
|
761 |
inline complex<_Tp> |
|
|
762 |
exp(const complex<_Tp>& __z) { return __complex_exp(__z); } |
|
|
763 |
#endif |
|
|
764 |
|
|
|
765 |
// 26.2.8/5 log(__z): Returns the natural complex logarithm of __z. |
|
|
766 |
// The branch cut is along the negative axis. |
|
|
767 |
template |
|
|
768 |
inline complex<_Tp> |
|
|
769 |
__complex_log(const complex<_Tp>& __z) |
|
|
770 |
{ return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); } |
|
|
771 |
|
|
|
772 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
773 |
inline __complex__ float |
|
|
774 |
__complex_log(__complex__ float __z) { return __builtin_clogf(__z); } |
|
|
775 |
|
|
|
776 |
inline __complex__ double |
|
|
777 |
__complex_log(__complex__ double __z) { return __builtin_clog(__z); } |
|
|
778 |
|
|
|
779 |
inline __complex__ long double |
|
|
780 |
__complex_log(const __complex__ long double& __z) |
|
|
781 |
{ return __builtin_clogl(__z); } |
|
|
782 |
|
|
|
783 |
template |
|
|
784 |
inline complex<_Tp> |
|
|
785 |
log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); } |
|
|
786 |
#else |
|
|
787 |
template |
|
|
788 |
inline complex<_Tp> |
|
|
789 |
log(const complex<_Tp>& __z) { return __complex_log(__z); } |
|
|
790 |
#endif |
|
|
791 |
|
|
|
792 |
template |
|
|
793 |
inline complex<_Tp> |
|
|
794 |
log10(const complex<_Tp>& __z) |
|
|
795 |
{ return std::log(__z) / log(_Tp(10.0)); } |
|
|
796 |
|
|
|
797 |
// 26.2.8/10 sin(__z): Returns the sine of __z. |
|
|
798 |
template |
|
|
799 |
inline complex<_Tp> |
|
|
800 |
__complex_sin(const complex<_Tp>& __z) |
|
|
801 |
{ |
|
|
802 |
const _Tp __x = __z.real(); |
|
|
803 |
const _Tp __y = __z.imag(); |
|
|
804 |
return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y)); |
|
|
805 |
} |
|
|
806 |
|
|
|
807 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
808 |
inline __complex__ float |
|
|
809 |
__complex_sin(__complex__ float __z) { return __builtin_csinf(__z); } |
|
|
810 |
|
|
|
811 |
inline __complex__ double |
|
|
812 |
__complex_sin(__complex__ double __z) { return __builtin_csin(__z); } |
|
|
813 |
|
|
|
814 |
inline __complex__ long double |
|
|
815 |
__complex_sin(const __complex__ long double& __z) |
|
|
816 |
{ return __builtin_csinl(__z); } |
|
|
817 |
|
|
|
818 |
template |
|
|
819 |
inline complex<_Tp> |
|
|
820 |
sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); } |
|
|
821 |
#else |
|
|
822 |
template |
|
|
823 |
inline complex<_Tp> |
|
|
824 |
sin(const complex<_Tp>& __z) { return __complex_sin(__z); } |
|
|
825 |
#endif |
|
|
826 |
|
|
|
827 |
// 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z. |
|
|
828 |
template |
|
|
829 |
inline complex<_Tp> |
|
|
830 |
__complex_sinh(const complex<_Tp>& __z) |
|
|
831 |
{ |
|
|
832 |
const _Tp __x = __z.real(); |
|
|
833 |
const _Tp __y = __z.imag(); |
|
|
834 |
return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y)); |
|
|
835 |
} |
|
|
836 |
|
|
|
837 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
838 |
inline __complex__ float |
|
|
839 |
__complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); } |
|
|
840 |
|
|
|
841 |
inline __complex__ double |
|
|
842 |
__complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); } |
|
|
843 |
|
|
|
844 |
inline __complex__ long double |
|
|
845 |
__complex_sinh(const __complex__ long double& __z) |
|
|
846 |
{ return __builtin_csinhl(__z); } |
|
|
847 |
|
|
|
848 |
template |
|
|
849 |
inline complex<_Tp> |
|
|
850 |
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); } |
|
|
851 |
#else |
|
|
852 |
template |
|
|
853 |
inline complex<_Tp> |
|
|
854 |
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); } |
|
|
855 |
#endif |
|
|
856 |
|
|
|
857 |
// 26.2.8/13 sqrt(__z): Returns the complex square root of __z. |
|
|
858 |
// The branch cut is on the negative axis. |
|
|
859 |
template |
|
|
860 |
complex<_Tp> |
|
|
861 |
__complex_sqrt(const complex<_Tp>& __z) |
|
|
862 |
{ |
|
|
863 |
_Tp __x = __z.real(); |
|
|
864 |
_Tp __y = __z.imag(); |
|
|
865 |
|
|
|
866 |
if (__x == _Tp()) |
|
|
867 |
{ |
|
|
868 |
_Tp __t = sqrt(abs(__y) / 2); |
|
|
869 |
return complex<_Tp>(__t, __y < _Tp() ? -__t : __t); |
|
|
870 |
} |
|
|
871 |
else |
|
|
872 |
{ |
|
|
873 |
_Tp __t = sqrt(2 * (std::abs(__z) + abs(__x))); |
|
|
874 |
_Tp __u = __t / 2; |
|
|
875 |
return __x > _Tp() |
|
|
876 |
? complex<_Tp>(__u, __y / __t) |
|
|
877 |
: complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u); |
|
|
878 |
} |
|
|
879 |
} |
|
|
880 |
|
|
|
881 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
882 |
inline __complex__ float |
|
|
883 |
__complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); } |
|
|
884 |
|
|
|
885 |
inline __complex__ double |
|
|
886 |
__complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); } |
|
|
887 |
|
|
|
888 |
inline __complex__ long double |
|
|
889 |
__complex_sqrt(const __complex__ long double& __z) |
|
|
890 |
{ return __builtin_csqrtl(__z); } |
|
|
891 |
|
|
|
892 |
template |
|
|
893 |
inline complex<_Tp> |
|
|
894 |
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); } |
|
|
895 |
#else |
|
|
896 |
template |
|
|
897 |
inline complex<_Tp> |
|
|
898 |
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); } |
|
|
899 |
#endif |
|
|
900 |
|
|
|
901 |
// 26.2.8/14 tan(__z): Return the complex tangent of __z. |
|
|
902 |
|
|
|
903 |
template |
|
|
904 |
inline complex<_Tp> |
|
|
905 |
__complex_tan(const complex<_Tp>& __z) |
|
|
906 |
{ return std::sin(__z) / std::cos(__z); } |
|
|
907 |
|
|
|
908 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
909 |
inline __complex__ float |
|
|
910 |
__complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); } |
|
|
911 |
|
|
|
912 |
inline __complex__ double |
|
|
913 |
__complex_tan(__complex__ double __z) { return __builtin_ctan(__z); } |
|
|
914 |
|
|
|
915 |
inline __complex__ long double |
|
|
916 |
__complex_tan(const __complex__ long double& __z) |
|
|
917 |
{ return __builtin_ctanl(__z); } |
|
|
918 |
|
|
|
919 |
template |
|
|
920 |
inline complex<_Tp> |
|
|
921 |
tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); } |
|
|
922 |
#else |
|
|
923 |
template |
|
|
924 |
inline complex<_Tp> |
|
|
925 |
tan(const complex<_Tp>& __z) { return __complex_tan(__z); } |
|
|
926 |
#endif |
|
|
927 |
|
|
|
928 |
|
|
|
929 |
// 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z. |
|
|
930 |
|
|
|
931 |
template |
|
|
932 |
inline complex<_Tp> |
|
|
933 |
__complex_tanh(const complex<_Tp>& __z) |
|
|
934 |
{ return std::sinh(__z) / std::cosh(__z); } |
|
|
935 |
|
|
|
936 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
937 |
inline __complex__ float |
|
|
938 |
__complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); } |
|
|
939 |
|
|
|
940 |
inline __complex__ double |
|
|
941 |
__complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); } |
|
|
942 |
|
|
|
943 |
inline __complex__ long double |
|
|
944 |
__complex_tanh(const __complex__ long double& __z) |
|
|
945 |
{ return __builtin_ctanhl(__z); } |
|
|
946 |
|
|
|
947 |
template |
|
|
948 |
inline complex<_Tp> |
|
|
949 |
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); } |
|
|
950 |
#else |
|
|
951 |
template |
|
|
952 |
inline complex<_Tp> |
|
|
953 |
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); } |
|
|
954 |
#endif |
|
|
955 |
|
|
|
956 |
|
|
|
957 |
// 26.2.8/9 pow(__x, __y): Returns the complex power base of __x |
|
|
958 |
// raised to the __y-th power. The branch |
|
|
959 |
// cut is on the negative axis. |
|
|
960 |
template |
|
|
961 |
complex<_Tp> |
|
|
962 |
__complex_pow_unsigned(complex<_Tp> __x, unsigned __n) |
|
|
963 |
{ |
|
|
964 |
complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1); |
|
|
965 |
|
|
|
966 |
while (__n >>= 1) |
|
|
967 |
{ |
|
|
968 |
__x *= __x; |
|
|
969 |
if (__n % 2) |
|
|
970 |
__y *= __x; |
|
|
971 |
} |
|
|
972 |
|
|
|
973 |
return __y; |
|
|
974 |
} |
|
|
975 |
|
|
|
976 |
// In C++11 mode we used to implement the resolution of |
|
|
977 |
// DR 844. complex pow return type is ambiguous. |
|
|
978 |
// thus the following overload was disabled in that mode. However, doing |
|
|
979 |
// that causes all sorts of issues, see, for example: |
|
|
980 |
// http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html |
|
|
981 |
// and also PR57974. |
|
|
982 |
template |
|
|
983 |
inline complex<_Tp> |
|
|
984 |
pow(const complex<_Tp>& __z, int __n) |
|
|
985 |
{ |
|
|
986 |
return __n < 0 |
|
|
987 |
? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n) |
|
|
988 |
: std::__complex_pow_unsigned(__z, __n); |
|
|
989 |
} |
|
|
990 |
|
|
|
991 |
template |
|
|
992 |
complex<_Tp> |
|
|
993 |
pow(const complex<_Tp>& __x, const _Tp& __y) |
|
|
994 |
{ |
|
|
995 |
#ifndef _GLIBCXX_USE_C99_COMPLEX |
|
|
996 |
if (__x == _Tp()) |
|
|
997 |
return _Tp(); |
|
|
998 |
#endif |
|
|
999 |
if (__x.imag() == _Tp() && __x.real() > _Tp()) |
|
|
1000 |
return pow(__x.real(), __y); |
|
|
1001 |
|
|
|
1002 |
complex<_Tp> __t = std::log(__x); |
|
|
1003 |
return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag()); |
|
|
1004 |
} |
|
|
1005 |
|
|
|
1006 |
template |
|
|
1007 |
inline complex<_Tp> |
|
|
1008 |
__complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
|
|
1009 |
{ return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); } |
|
|
1010 |
|
|
|
1011 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
1012 |
inline __complex__ float |
|
|
1013 |
__complex_pow(__complex__ float __x, __complex__ float __y) |
|
|
1014 |
{ return __builtin_cpowf(__x, __y); } |
|
|
1015 |
|
|
|
1016 |
inline __complex__ double |
|
|
1017 |
__complex_pow(__complex__ double __x, __complex__ double __y) |
|
|
1018 |
{ return __builtin_cpow(__x, __y); } |
|
|
1019 |
|
|
|
1020 |
inline __complex__ long double |
|
|
1021 |
__complex_pow(const __complex__ long double& __x, |
|
|
1022 |
const __complex__ long double& __y) |
|
|
1023 |
{ return __builtin_cpowl(__x, __y); } |
|
|
1024 |
|
|
|
1025 |
template |
|
|
1026 |
inline complex<_Tp> |
|
|
1027 |
pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
|
|
1028 |
{ return __complex_pow(__x.__rep(), __y.__rep()); } |
|
|
1029 |
#else |
|
|
1030 |
template |
|
|
1031 |
inline complex<_Tp> |
|
|
1032 |
pow(const complex<_Tp>& __x, const complex<_Tp>& __y) |
|
|
1033 |
{ return __complex_pow(__x, __y); } |
|
|
1034 |
#endif |
|
|
1035 |
|
|
|
1036 |
template |
|
|
1037 |
inline complex<_Tp> |
|
|
1038 |
pow(const _Tp& __x, const complex<_Tp>& __y) |
|
|
1039 |
{ |
|
|
1040 |
return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()), |
|
|
1041 |
__y.imag() * log(__x)) |
|
|
1042 |
: std::pow(complex<_Tp>(__x), __y); |
|
|
1043 |
} |
|
|
1044 |
|
|
|
1045 |
/// 26.2.3 complex specializations |
|
|
1046 |
/// complex specialization |
|
|
1047 |
template<> |
|
|
1048 |
struct complex |
|
|
1049 |
{ |
|
|
1050 |
typedef float value_type; |
|
|
1051 |
typedef __complex__ float _ComplexT; |
|
|
1052 |
|
|
|
1053 |
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } |
|
|
1054 |
|
|
|
1055 |
_GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f) |
|
|
1056 |
#if __cplusplus >= 201103L |
|
|
1057 |
: _M_value{ __r, __i } { } |
|
|
1058 |
#else |
|
|
1059 |
{ |
|
|
1060 |
__real__ _M_value = __r; |
|
|
1061 |
__imag__ _M_value = __i; |
|
|
1062 |
} |
|
|
1063 |
#endif |
|
|
1064 |
|
|
|
1065 |
explicit _GLIBCXX_CONSTEXPR complex(const complex&); |
|
|
1066 |
explicit _GLIBCXX_CONSTEXPR complex(const complex&); |
|
|
1067 |
|
|
|
1068 |
#if __cplusplus >= 201103L |
|
|
1069 |
// _GLIBCXX_RESOLVE_LIB_DEFECTS |
|
|
1070 |
// DR 387. std::complex over-encapsulated. |
|
|
1071 |
__attribute ((__abi_tag__ ("cxx11"))) |
|
|
1072 |
constexpr float |
|
|
1073 |
real() const { return __real__ _M_value; } |
|
|
1074 |
|
|
|
1075 |
__attribute ((__abi_tag__ ("cxx11"))) |
|
|
1076 |
constexpr float |
|
|
1077 |
imag() const { return __imag__ _M_value; } |
|
|
1078 |
#else |
|
|
1079 |
float& |
|
|
1080 |
real() { return __real__ _M_value; } |
|
|
1081 |
|
|
|
1082 |
const float& |
|
|
1083 |
real() const { return __real__ _M_value; } |
|
|
1084 |
|
|
|
1085 |
float& |
|
|
1086 |
imag() { return __imag__ _M_value; } |
|
|
1087 |
|
|
|
1088 |
const float& |
|
|
1089 |
imag() const { return __imag__ _M_value; } |
|
|
1090 |
#endif |
|
|
1091 |
|
|
|
1092 |
// _GLIBCXX_RESOLVE_LIB_DEFECTS |
|
|
1093 |
// DR 387. std::complex over-encapsulated. |
|
|
1094 |
void |
|
|
1095 |
real(float __val) { __real__ _M_value = __val; } |
|
|
1096 |
|
|
|
1097 |
void |
|
|
1098 |
imag(float __val) { __imag__ _M_value = __val; } |
|
|
1099 |
|
|
|
1100 |
complex& |
|
|
1101 |
operator=(float __f) |
|
|
1102 |
{ |
|
|
1103 |
_M_value = __f; |
|
|
1104 |
return *this; |
|
|
1105 |
} |
|
|
1106 |
|
|
|
1107 |
complex& |
|
|
1108 |
operator+=(float __f) |
|
|
1109 |
{ |
|
|
1110 |
_M_value += __f; |
|
|
1111 |
return *this; |
|
|
1112 |
} |
|
|
1113 |
|
|
|
1114 |
complex& |
|
|
1115 |
operator-=(float __f) |
|
|
1116 |
{ |
|
|
1117 |
_M_value -= __f; |
|
|
1118 |
return *this; |
|
|
1119 |
} |
|
|
1120 |
|
|
|
1121 |
complex& |
|
|
1122 |
operator*=(float __f) |
|
|
1123 |
{ |
|
|
1124 |
_M_value *= __f; |
|
|
1125 |
return *this; |
|
|
1126 |
} |
|
|
1127 |
|
|
|
1128 |
complex& |
|
|
1129 |
operator/=(float __f) |
|
|
1130 |
{ |
|
|
1131 |
_M_value /= __f; |
|
|
1132 |
return *this; |
|
|
1133 |
} |
|
|
1134 |
|
|
|
1135 |
// Let the compiler synthesize the copy and assignment |
|
|
1136 |
// operator. It always does a pretty good job. |
|
|
1137 |
// complex& operator=(const complex&); |
|
|
1138 |
|
|
|
1139 |
template |
|
|
1140 |
complex& |
|
|
1141 |
operator=(const complex<_Tp>& __z) |
|
|
1142 |
{ |
|
|
1143 |
__real__ _M_value = __z.real(); |
|
|
1144 |
__imag__ _M_value = __z.imag(); |
|
|
1145 |
return *this; |
|
|
1146 |
} |
|
|
1147 |
|
|
|
1148 |
template |
|
|
1149 |
complex& |
|
|
1150 |
operator+=(const complex<_Tp>& __z) |
|
|
1151 |
{ |
|
|
1152 |
__real__ _M_value += __z.real(); |
|
|
1153 |
__imag__ _M_value += __z.imag(); |
|
|
1154 |
return *this; |
|
|
1155 |
} |
|
|
1156 |
|
|
|
1157 |
template |
|
|
1158 |
complex& |
|
|
1159 |
operator-=(const complex<_Tp>& __z) |
|
|
1160 |
{ |
|
|
1161 |
__real__ _M_value -= __z.real(); |
|
|
1162 |
__imag__ _M_value -= __z.imag(); |
|
|
1163 |
return *this; |
|
|
1164 |
} |
|
|
1165 |
|
|
|
1166 |
template |
|
|
1167 |
complex& |
|
|
1168 |
operator*=(const complex<_Tp>& __z) |
|
|
1169 |
{ |
|
|
1170 |
_ComplexT __t; |
|
|
1171 |
__real__ __t = __z.real(); |
|
|
1172 |
__imag__ __t = __z.imag(); |
|
|
1173 |
_M_value *= __t; |
|
|
1174 |
return *this; |
|
|
1175 |
} |
|
|
1176 |
|
|
|
1177 |
template |
|
|
1178 |
complex& |
|
|
1179 |
operator/=(const complex<_Tp>& __z) |
|
|
1180 |
{ |
|
|
1181 |
_ComplexT __t; |
|
|
1182 |
__real__ __t = __z.real(); |
|
|
1183 |
__imag__ __t = __z.imag(); |
|
|
1184 |
_M_value /= __t; |
|
|
1185 |
return *this; |
|
|
1186 |
} |
|
|
1187 |
|
|
|
1188 |
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } |
|
|
1189 |
|
|
|
1190 |
private: |
|
|
1191 |
_ComplexT _M_value; |
|
|
1192 |
}; |
|
|
1193 |
|
|
|
1194 |
/// 26.2.3 complex specializations |
|
|
1195 |
/// complex specialization |
|
|
1196 |
template<> |
|
|
1197 |
struct complex |
|
|
1198 |
{ |
|
|
1199 |
typedef double value_type; |
|
|
1200 |
typedef __complex__ double _ComplexT; |
|
|
1201 |
|
|
|
1202 |
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } |
|
|
1203 |
|
|
|
1204 |
_GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0) |
|
|
1205 |
#if __cplusplus >= 201103L |
|
|
1206 |
: _M_value{ __r, __i } { } |
|
|
1207 |
#else |
|
|
1208 |
{ |
|
|
1209 |
__real__ _M_value = __r; |
|
|
1210 |
__imag__ _M_value = __i; |
|
|
1211 |
} |
|
|
1212 |
#endif |
|
|
1213 |
|
|
|
1214 |
_GLIBCXX_CONSTEXPR complex(const complex& __z) |
|
|
1215 |
: _M_value(__z.__rep()) { } |
|
|
1216 |
|
|
|
1217 |
explicit _GLIBCXX_CONSTEXPR complex(const complex&); |
|
|
1218 |
|
|
|
1219 |
#if __cplusplus >= 201103L |
|
|
1220 |
// _GLIBCXX_RESOLVE_LIB_DEFECTS |
|
|
1221 |
// DR 387. std::complex over-encapsulated. |
|
|
1222 |
__attribute ((__abi_tag__ ("cxx11"))) |
|
|
1223 |
constexpr double |
|
|
1224 |
real() const { return __real__ _M_value; } |
|
|
1225 |
|
|
|
1226 |
__attribute ((__abi_tag__ ("cxx11"))) |
|
|
1227 |
constexpr double |
|
|
1228 |
imag() const { return __imag__ _M_value; } |
|
|
1229 |
#else |
|
|
1230 |
double& |
|
|
1231 |
real() { return __real__ _M_value; } |
|
|
1232 |
|
|
|
1233 |
const double& |
|
|
1234 |
real() const { return __real__ _M_value; } |
|
|
1235 |
|
|
|
1236 |
double& |
|
|
1237 |
imag() { return __imag__ _M_value; } |
|
|
1238 |
|
|
|
1239 |
const double& |
|
|
1240 |
imag() const { return __imag__ _M_value; } |
|
|
1241 |
#endif |
|
|
1242 |
|
|
|
1243 |
// _GLIBCXX_RESOLVE_LIB_DEFECTS |
|
|
1244 |
// DR 387. std::complex over-encapsulated. |
|
|
1245 |
void |
|
|
1246 |
real(double __val) { __real__ _M_value = __val; } |
|
|
1247 |
|
|
|
1248 |
void |
|
|
1249 |
imag(double __val) { __imag__ _M_value = __val; } |
|
|
1250 |
|
|
|
1251 |
complex& |
|
|
1252 |
operator=(double __d) |
|
|
1253 |
{ |
|
|
1254 |
_M_value = __d; |
|
|
1255 |
return *this; |
|
|
1256 |
} |
|
|
1257 |
|
|
|
1258 |
complex& |
|
|
1259 |
operator+=(double __d) |
|
|
1260 |
{ |
|
|
1261 |
_M_value += __d; |
|
|
1262 |
return *this; |
|
|
1263 |
} |
|
|
1264 |
|
|
|
1265 |
complex& |
|
|
1266 |
operator-=(double __d) |
|
|
1267 |
{ |
|
|
1268 |
_M_value -= __d; |
|
|
1269 |
return *this; |
|
|
1270 |
} |
|
|
1271 |
|
|
|
1272 |
complex& |
|
|
1273 |
operator*=(double __d) |
|
|
1274 |
{ |
|
|
1275 |
_M_value *= __d; |
|
|
1276 |
return *this; |
|
|
1277 |
} |
|
|
1278 |
|
|
|
1279 |
complex& |
|
|
1280 |
operator/=(double __d) |
|
|
1281 |
{ |
|
|
1282 |
_M_value /= __d; |
|
|
1283 |
return *this; |
|
|
1284 |
} |
|
|
1285 |
|
|
|
1286 |
// The compiler will synthesize this, efficiently. |
|
|
1287 |
// complex& operator=(const complex&); |
|
|
1288 |
|
|
|
1289 |
template |
|
|
1290 |
complex& |
|
|
1291 |
operator=(const complex<_Tp>& __z) |
|
|
1292 |
{ |
|
|
1293 |
__real__ _M_value = __z.real(); |
|
|
1294 |
__imag__ _M_value = __z.imag(); |
|
|
1295 |
return *this; |
|
|
1296 |
} |
|
|
1297 |
|
|
|
1298 |
template |
|
|
1299 |
complex& |
|
|
1300 |
operator+=(const complex<_Tp>& __z) |
|
|
1301 |
{ |
|
|
1302 |
__real__ _M_value += __z.real(); |
|
|
1303 |
__imag__ _M_value += __z.imag(); |
|
|
1304 |
return *this; |
|
|
1305 |
} |
|
|
1306 |
|
|
|
1307 |
template |
|
|
1308 |
complex& |
|
|
1309 |
operator-=(const complex<_Tp>& __z) |
|
|
1310 |
{ |
|
|
1311 |
__real__ _M_value -= __z.real(); |
|
|
1312 |
__imag__ _M_value -= __z.imag(); |
|
|
1313 |
return *this; |
|
|
1314 |
} |
|
|
1315 |
|
|
|
1316 |
template |
|
|
1317 |
complex& |
|
|
1318 |
operator*=(const complex<_Tp>& __z) |
|
|
1319 |
{ |
|
|
1320 |
_ComplexT __t; |
|
|
1321 |
__real__ __t = __z.real(); |
|
|
1322 |
__imag__ __t = __z.imag(); |
|
|
1323 |
_M_value *= __t; |
|
|
1324 |
return *this; |
|
|
1325 |
} |
|
|
1326 |
|
|
|
1327 |
template |
|
|
1328 |
complex& |
|
|
1329 |
operator/=(const complex<_Tp>& __z) |
|
|
1330 |
{ |
|
|
1331 |
_ComplexT __t; |
|
|
1332 |
__real__ __t = __z.real(); |
|
|
1333 |
__imag__ __t = __z.imag(); |
|
|
1334 |
_M_value /= __t; |
|
|
1335 |
return *this; |
|
|
1336 |
} |
|
|
1337 |
|
|
|
1338 |
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } |
|
|
1339 |
|
|
|
1340 |
private: |
|
|
1341 |
_ComplexT _M_value; |
|
|
1342 |
}; |
|
|
1343 |
|
|
|
1344 |
/// 26.2.3 complex specializations |
|
|
1345 |
/// complex specialization |
|
|
1346 |
template<> |
|
|
1347 |
struct complex |
|
|
1348 |
{ |
|
|
1349 |
typedef long double value_type; |
|
|
1350 |
typedef __complex__ long double _ComplexT; |
|
|
1351 |
|
|
|
1352 |
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { } |
|
|
1353 |
|
|
|
1354 |
_GLIBCXX_CONSTEXPR complex(long double __r = 0.0L, |
|
|
1355 |
long double __i = 0.0L) |
|
|
1356 |
#if __cplusplus >= 201103L |
|
|
1357 |
: _M_value{ __r, __i } { } |
|
|
1358 |
#else |
|
|
1359 |
{ |
|
|
1360 |
__real__ _M_value = __r; |
|
|
1361 |
__imag__ _M_value = __i; |
|
|
1362 |
} |
|
|
1363 |
#endif |
|
|
1364 |
|
|
|
1365 |
_GLIBCXX_CONSTEXPR complex(const complex& __z) |
|
|
1366 |
: _M_value(__z.__rep()) { } |
|
|
1367 |
|
|
|
1368 |
_GLIBCXX_CONSTEXPR complex(const complex& __z) |
|
|
1369 |
: _M_value(__z.__rep()) { } |
|
|
1370 |
|
|
|
1371 |
#if __cplusplus >= 201103L |
|
|
1372 |
// _GLIBCXX_RESOLVE_LIB_DEFECTS |
|
|
1373 |
// DR 387. std::complex over-encapsulated. |
|
|
1374 |
__attribute ((__abi_tag__ ("cxx11"))) |
|
|
1375 |
constexpr long double |
|
|
1376 |
real() const { return __real__ _M_value; } |
|
|
1377 |
|
|
|
1378 |
__attribute ((__abi_tag__ ("cxx11"))) |
|
|
1379 |
constexpr long double |
|
|
1380 |
imag() const { return __imag__ _M_value; } |
|
|
1381 |
#else |
|
|
1382 |
long double& |
|
|
1383 |
real() { return __real__ _M_value; } |
|
|
1384 |
|
|
|
1385 |
const long double& |
|
|
1386 |
real() const { return __real__ _M_value; } |
|
|
1387 |
|
|
|
1388 |
long double& |
|
|
1389 |
imag() { return __imag__ _M_value; } |
|
|
1390 |
|
|
|
1391 |
const long double& |
|
|
1392 |
imag() const { return __imag__ _M_value; } |
|
|
1393 |
#endif |
|
|
1394 |
|
|
|
1395 |
// _GLIBCXX_RESOLVE_LIB_DEFECTS |
|
|
1396 |
// DR 387. std::complex over-encapsulated. |
|
|
1397 |
void |
|
|
1398 |
real(long double __val) { __real__ _M_value = __val; } |
|
|
1399 |
|
|
|
1400 |
void |
|
|
1401 |
imag(long double __val) { __imag__ _M_value = __val; } |
|
|
1402 |
|
|
|
1403 |
complex& |
|
|
1404 |
operator=(long double __r) |
|
|
1405 |
{ |
|
|
1406 |
_M_value = __r; |
|
|
1407 |
return *this; |
|
|
1408 |
} |
|
|
1409 |
|
|
|
1410 |
complex& |
|
|
1411 |
operator+=(long double __r) |
|
|
1412 |
{ |
|
|
1413 |
_M_value += __r; |
|
|
1414 |
return *this; |
|
|
1415 |
} |
|
|
1416 |
|
|
|
1417 |
complex& |
|
|
1418 |
operator-=(long double __r) |
|
|
1419 |
{ |
|
|
1420 |
_M_value -= __r; |
|
|
1421 |
return *this; |
|
|
1422 |
} |
|
|
1423 |
|
|
|
1424 |
complex& |
|
|
1425 |
operator*=(long double __r) |
|
|
1426 |
{ |
|
|
1427 |
_M_value *= __r; |
|
|
1428 |
return *this; |
|
|
1429 |
} |
|
|
1430 |
|
|
|
1431 |
complex& |
|
|
1432 |
operator/=(long double __r) |
|
|
1433 |
{ |
|
|
1434 |
_M_value /= __r; |
|
|
1435 |
return *this; |
|
|
1436 |
} |
|
|
1437 |
|
|
|
1438 |
// The compiler knows how to do this efficiently |
|
|
1439 |
// complex& operator=(const complex&); |
|
|
1440 |
|
|
|
1441 |
template |
|
|
1442 |
complex& |
|
|
1443 |
operator=(const complex<_Tp>& __z) |
|
|
1444 |
{ |
|
|
1445 |
__real__ _M_value = __z.real(); |
|
|
1446 |
__imag__ _M_value = __z.imag(); |
|
|
1447 |
return *this; |
|
|
1448 |
} |
|
|
1449 |
|
|
|
1450 |
template |
|
|
1451 |
complex& |
|
|
1452 |
operator+=(const complex<_Tp>& __z) |
|
|
1453 |
{ |
|
|
1454 |
__real__ _M_value += __z.real(); |
|
|
1455 |
__imag__ _M_value += __z.imag(); |
|
|
1456 |
return *this; |
|
|
1457 |
} |
|
|
1458 |
|
|
|
1459 |
template |
|
|
1460 |
complex& |
|
|
1461 |
operator-=(const complex<_Tp>& __z) |
|
|
1462 |
{ |
|
|
1463 |
__real__ _M_value -= __z.real(); |
|
|
1464 |
__imag__ _M_value -= __z.imag(); |
|
|
1465 |
return *this; |
|
|
1466 |
} |
|
|
1467 |
|
|
|
1468 |
template |
|
|
1469 |
complex& |
|
|
1470 |
operator*=(const complex<_Tp>& __z) |
|
|
1471 |
{ |
|
|
1472 |
_ComplexT __t; |
|
|
1473 |
__real__ __t = __z.real(); |
|
|
1474 |
__imag__ __t = __z.imag(); |
|
|
1475 |
_M_value *= __t; |
|
|
1476 |
return *this; |
|
|
1477 |
} |
|
|
1478 |
|
|
|
1479 |
template |
|
|
1480 |
complex& |
|
|
1481 |
operator/=(const complex<_Tp>& __z) |
|
|
1482 |
{ |
|
|
1483 |
_ComplexT __t; |
|
|
1484 |
__real__ __t = __z.real(); |
|
|
1485 |
__imag__ __t = __z.imag(); |
|
|
1486 |
_M_value /= __t; |
|
|
1487 |
return *this; |
|
|
1488 |
} |
|
|
1489 |
|
|
|
1490 |
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; } |
|
|
1491 |
|
|
|
1492 |
private: |
|
|
1493 |
_ComplexT _M_value; |
|
|
1494 |
}; |
|
|
1495 |
|
|
|
1496 |
// These bits have to be at the end of this file, so that the |
|
|
1497 |
// specializations have all been defined. |
|
|
1498 |
inline _GLIBCXX_CONSTEXPR |
|
|
1499 |
complex::complex(const complex& __z) |
|
|
1500 |
: _M_value(__z.__rep()) { } |
|
|
1501 |
|
|
|
1502 |
inline _GLIBCXX_CONSTEXPR |
|
|
1503 |
complex::complex(const complex& __z) |
|
|
1504 |
: _M_value(__z.__rep()) { } |
|
|
1505 |
|
|
|
1506 |
inline _GLIBCXX_CONSTEXPR |
|
|
1507 |
complex::complex(const complex& __z) |
|
|
1508 |
: _M_value(__z.__rep()) { } |
|
|
1509 |
|
|
|
1510 |
// Inhibit implicit instantiations for required instantiations, |
|
|
1511 |
// which are defined via explicit instantiations elsewhere. |
|
|
1512 |
// NB: This syntax is a GNU extension. |
|
|
1513 |
#if _GLIBCXX_EXTERN_TEMPLATE |
|
|
1514 |
extern template istream& operator>>(istream&, complex&); |
|
|
1515 |
extern template ostream& operator<<(ostream&, const complex&); |
|
|
1516 |
extern template istream& operator>>(istream&, complex&); |
|
|
1517 |
extern template ostream& operator<<(ostream&, const complex&); |
|
|
1518 |
extern template istream& operator>>(istream&, complex&); |
|
|
1519 |
extern template ostream& operator<<(ostream&, const complex&); |
|
|
1520 |
|
|
|
1521 |
#ifdef _GLIBCXX_USE_WCHAR_T |
|
|
1522 |
extern template wistream& operator>>(wistream&, complex&); |
|
|
1523 |
extern template wostream& operator<<(wostream&, const complex&); |
|
|
1524 |
extern template wistream& operator>>(wistream&, complex&); |
|
|
1525 |
extern template wostream& operator<<(wostream&, const complex&); |
|
|
1526 |
extern template wistream& operator>>(wistream&, complex&); |
|
|
1527 |
extern template wostream& operator<<(wostream&, const complex&); |
|
|
1528 |
#endif |
|
|
1529 |
#endif |
|
|
1530 |
|
|
|
1531 |
// @} group complex_numbers |
|
|
1532 |
|
|
|
1533 |
_GLIBCXX_END_NAMESPACE_VERSION |
|
|
1534 |
} // namespace |
|
|
1535 |
|
|
|
1536 |
namespace __gnu_cxx _GLIBCXX_VISIBILITY(default) |
|
|
1537 |
{ |
|
|
1538 |
_GLIBCXX_BEGIN_NAMESPACE_VERSION |
|
|
1539 |
|
|
|
1540 |
// See ext/type_traits.h for the primary template. |
|
|
1541 |
template |
|
|
1542 |
struct __promote_2, _Up> |
|
|
1543 |
{ |
|
|
1544 |
public: |
|
|
1545 |
typedef std::complex::__type> __type; |
|
|
1546 |
}; |
|
|
1547 |
|
|
|
1548 |
template |
|
|
1549 |
struct __promote_2<_Tp, std::complex<_Up> > |
|
|
1550 |
{ |
|
|
1551 |
public: |
|
|
1552 |
typedef std::complex::__type> __type; |
|
|
1553 |
}; |
|
|
1554 |
|
|
|
1555 |
template |
|
|
1556 |
struct __promote_2, std::complex<_Up> > |
|
|
1557 |
{ |
|
|
1558 |
public: |
|
|
1559 |
typedef std::complex::__type> __type; |
|
|
1560 |
}; |
|
|
1561 |
|
|
|
1562 |
_GLIBCXX_END_NAMESPACE_VERSION |
|
|
1563 |
} // namespace |
|
|
1564 |
|
|
|
1565 |
#if __cplusplus >= 201103L |
|
|
1566 |
|
|
|
1567 |
namespace std _GLIBCXX_VISIBILITY(default) |
|
|
1568 |
{ |
|
|
1569 |
_GLIBCXX_BEGIN_NAMESPACE_VERSION |
|
|
1570 |
|
|
|
1571 |
// Forward declarations. |
|
|
1572 |
template std::complex<_Tp> acos(const std::complex<_Tp>&); |
|
|
1573 |
template std::complex<_Tp> asin(const std::complex<_Tp>&); |
|
|
1574 |
template std::complex<_Tp> atan(const std::complex<_Tp>&); |
|
|
1575 |
|
|
|
1576 |
template std::complex<_Tp> acosh(const std::complex<_Tp>&); |
|
|
1577 |
template std::complex<_Tp> asinh(const std::complex<_Tp>&); |
|
|
1578 |
template std::complex<_Tp> atanh(const std::complex<_Tp>&); |
|
|
1579 |
// DR 595. |
|
|
1580 |
template _Tp fabs(const std::complex<_Tp>&); |
|
|
1581 |
|
|
|
1582 |
template |
|
|
1583 |
inline std::complex<_Tp> |
|
|
1584 |
__complex_acos(const std::complex<_Tp>& __z) |
|
|
1585 |
{ |
|
|
1586 |
const std::complex<_Tp> __t = std::asin(__z); |
|
|
1587 |
const _Tp __pi_2 = 1.5707963267948966192313216916397514L; |
|
|
1588 |
return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag()); |
|
|
1589 |
} |
|
|
1590 |
|
|
|
1591 |
#if _GLIBCXX_USE_C99_COMPLEX_TR1 |
|
|
1592 |
inline __complex__ float |
|
|
1593 |
__complex_acos(__complex__ float __z) |
|
|
1594 |
{ return __builtin_cacosf(__z); } |
|
|
1595 |
|
|
|
1596 |
inline __complex__ double |
|
|
1597 |
__complex_acos(__complex__ double __z) |
|
|
1598 |
{ return __builtin_cacos(__z); } |
|
|
1599 |
|
|
|
1600 |
inline __complex__ long double |
|
|
1601 |
__complex_acos(const __complex__ long double& __z) |
|
|
1602 |
{ return __builtin_cacosl(__z); } |
|
|
1603 |
|
|
|
1604 |
template |
|
|
1605 |
inline std::complex<_Tp> |
|
|
1606 |
acos(const std::complex<_Tp>& __z) |
|
|
1607 |
{ return __complex_acos(__z.__rep()); } |
|
|
1608 |
#else |
|
|
1609 |
/// acos(__z) [8.1.2]. |
|
|
1610 |
// Effects: Behaves the same as C99 function cacos, defined |
|
|
1611 |
// in subclause 7.3.5.1. |
|
|
1612 |
template |
|
|
1613 |
inline std::complex<_Tp> |
|
|
1614 |
acos(const std::complex<_Tp>& __z) |
|
|
1615 |
{ return __complex_acos(__z); } |
|
|
1616 |
#endif |
|
|
1617 |
|
|
|
1618 |
template |
|
|
1619 |
inline std::complex<_Tp> |
|
|
1620 |
__complex_asin(const std::complex<_Tp>& __z) |
|
|
1621 |
{ |
|
|
1622 |
std::complex<_Tp> __t(-__z.imag(), __z.real()); |
|
|
1623 |
__t = std::asinh(__t); |
|
|
1624 |
return std::complex<_Tp>(__t.imag(), -__t.real()); |
|
|
1625 |
} |
|
|
1626 |
|
|
|
1627 |
#if _GLIBCXX_USE_C99_COMPLEX_TR1 |
|
|
1628 |
inline __complex__ float |
|
|
1629 |
__complex_asin(__complex__ float __z) |
|
|
1630 |
{ return __builtin_casinf(__z); } |
|
|
1631 |
|
|
|
1632 |
inline __complex__ double |
|
|
1633 |
__complex_asin(__complex__ double __z) |
|
|
1634 |
{ return __builtin_casin(__z); } |
|
|
1635 |
|
|
|
1636 |
inline __complex__ long double |
|
|
1637 |
__complex_asin(const __complex__ long double& __z) |
|
|
1638 |
{ return __builtin_casinl(__z); } |
|
|
1639 |
|
|
|
1640 |
template |
|
|
1641 |
inline std::complex<_Tp> |
|
|
1642 |
asin(const std::complex<_Tp>& __z) |
|
|
1643 |
{ return __complex_asin(__z.__rep()); } |
|
|
1644 |
#else |
|
|
1645 |
/// asin(__z) [8.1.3]. |
|
|
1646 |
// Effects: Behaves the same as C99 function casin, defined |
|
|
1647 |
// in subclause 7.3.5.2. |
|
|
1648 |
template |
|
|
1649 |
inline std::complex<_Tp> |
|
|
1650 |
asin(const std::complex<_Tp>& __z) |
|
|
1651 |
{ return __complex_asin(__z); } |
|
|
1652 |
#endif |
|
|
1653 |
|
|
|
1654 |
template |
|
|
1655 |
std::complex<_Tp> |
|
|
1656 |
__complex_atan(const std::complex<_Tp>& __z) |
|
|
1657 |
{ |
|
|
1658 |
const _Tp __r2 = __z.real() * __z.real(); |
|
|
1659 |
const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag(); |
|
|
1660 |
|
|
|
1661 |
_Tp __num = __z.imag() + _Tp(1.0); |
|
|
1662 |
_Tp __den = __z.imag() - _Tp(1.0); |
|
|
1663 |
|
|
|
1664 |
__num = __r2 + __num * __num; |
|
|
1665 |
__den = __r2 + __den * __den; |
|
|
1666 |
|
|
|
1667 |
return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x), |
|
|
1668 |
_Tp(0.25) * log(__num / __den)); |
|
|
1669 |
} |
|
|
1670 |
|
|
|
1671 |
#if _GLIBCXX_USE_C99_COMPLEX_TR1 |
|
|
1672 |
inline __complex__ float |
|
|
1673 |
__complex_atan(__complex__ float __z) |
|
|
1674 |
{ return __builtin_catanf(__z); } |
|
|
1675 |
|
|
|
1676 |
inline __complex__ double |
|
|
1677 |
__complex_atan(__complex__ double __z) |
|
|
1678 |
{ return __builtin_catan(__z); } |
|
|
1679 |
|
|
|
1680 |
inline __complex__ long double |
|
|
1681 |
__complex_atan(const __complex__ long double& __z) |
|
|
1682 |
{ return __builtin_catanl(__z); } |
|
|
1683 |
|
|
|
1684 |
template |
|
|
1685 |
inline std::complex<_Tp> |
|
|
1686 |
atan(const std::complex<_Tp>& __z) |
|
|
1687 |
{ return __complex_atan(__z.__rep()); } |
|
|
1688 |
#else |
|
|
1689 |
/// atan(__z) [8.1.4]. |
|
|
1690 |
// Effects: Behaves the same as C99 function catan, defined |
|
|
1691 |
// in subclause 7.3.5.3. |
|
|
1692 |
template |
|
|
1693 |
inline std::complex<_Tp> |
|
|
1694 |
atan(const std::complex<_Tp>& __z) |
|
|
1695 |
{ return __complex_atan(__z); } |
|
|
1696 |
#endif |
|
|
1697 |
|
|
|
1698 |
template |
|
|
1699 |
std::complex<_Tp> |
|
|
1700 |
__complex_acosh(const std::complex<_Tp>& __z) |
|
|
1701 |
{ |
|
|
1702 |
// Kahan's formula. |
|
|
1703 |
return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0))) |
|
|
1704 |
+ std::sqrt(_Tp(0.5) * (__z - _Tp(1.0)))); |
|
|
1705 |
} |
|
|
1706 |
|
|
|
1707 |
#if _GLIBCXX_USE_C99_COMPLEX_TR1 |
|
|
1708 |
inline __complex__ float |
|
|
1709 |
__complex_acosh(__complex__ float __z) |
|
|
1710 |
{ return __builtin_cacoshf(__z); } |
|
|
1711 |
|
|
|
1712 |
inline __complex__ double |
|
|
1713 |
__complex_acosh(__complex__ double __z) |
|
|
1714 |
{ return __builtin_cacosh(__z); } |
|
|
1715 |
|
|
|
1716 |
inline __complex__ long double |
|
|
1717 |
__complex_acosh(const __complex__ long double& __z) |
|
|
1718 |
{ return __builtin_cacoshl(__z); } |
|
|
1719 |
|
|
|
1720 |
template |
|
|
1721 |
inline std::complex<_Tp> |
|
|
1722 |
acosh(const std::complex<_Tp>& __z) |
|
|
1723 |
{ return __complex_acosh(__z.__rep()); } |
|
|
1724 |
#else |
|
|
1725 |
/// acosh(__z) [8.1.5]. |
|
|
1726 |
// Effects: Behaves the same as C99 function cacosh, defined |
|
|
1727 |
// in subclause 7.3.6.1. |
|
|
1728 |
template |
|
|
1729 |
inline std::complex<_Tp> |
|
|
1730 |
acosh(const std::complex<_Tp>& __z) |
|
|
1731 |
{ return __complex_acosh(__z); } |
|
|
1732 |
#endif |
|
|
1733 |
|
|
|
1734 |
template |
|
|
1735 |
std::complex<_Tp> |
|
|
1736 |
__complex_asinh(const std::complex<_Tp>& __z) |
|
|
1737 |
{ |
|
|
1738 |
std::complex<_Tp> __t((__z.real() - __z.imag()) |
|
|
1739 |
* (__z.real() + __z.imag()) + _Tp(1.0), |
|
|
1740 |
_Tp(2.0) * __z.real() * __z.imag()); |
|
|
1741 |
__t = std::sqrt(__t); |
|
|
1742 |
|
|
|
1743 |
return std::log(__t + __z); |
|
|
1744 |
} |
|
|
1745 |
|
|
|
1746 |
#if _GLIBCXX_USE_C99_COMPLEX_TR1 |
|
|
1747 |
inline __complex__ float |
|
|
1748 |
__complex_asinh(__complex__ float __z) |
|
|
1749 |
{ return __builtin_casinhf(__z); } |
|
|
1750 |
|
|
|
1751 |
inline __complex__ double |
|
|
1752 |
__complex_asinh(__complex__ double __z) |
|
|
1753 |
{ return __builtin_casinh(__z); } |
|
|
1754 |
|
|
|
1755 |
inline __complex__ long double |
|
|
1756 |
__complex_asinh(const __complex__ long double& __z) |
|
|
1757 |
{ return __builtin_casinhl(__z); } |
|
|
1758 |
|
|
|
1759 |
template |
|
|
1760 |
inline std::complex<_Tp> |
|
|
1761 |
asinh(const std::complex<_Tp>& __z) |
|
|
1762 |
{ return __complex_asinh(__z.__rep()); } |
|
|
1763 |
#else |
|
|
1764 |
/// asinh(__z) [8.1.6]. |
|
|
1765 |
// Effects: Behaves the same as C99 function casin, defined |
|
|
1766 |
// in subclause 7.3.6.2. |
|
|
1767 |
template |
|
|
1768 |
inline std::complex<_Tp> |
|
|
1769 |
asinh(const std::complex<_Tp>& __z) |
|
|
1770 |
{ return __complex_asinh(__z); } |
|
|
1771 |
#endif |
|
|
1772 |
|
|
|
1773 |
template |
|
|
1774 |
std::complex<_Tp> |
|
|
1775 |
__complex_atanh(const std::complex<_Tp>& __z) |
|
|
1776 |
{ |
|
|
1777 |
const _Tp __i2 = __z.imag() * __z.imag(); |
|
|
1778 |
const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real(); |
|
|
1779 |
|
|
|
1780 |
_Tp __num = _Tp(1.0) + __z.real(); |
|
|
1781 |
_Tp __den = _Tp(1.0) - __z.real(); |
|
|
1782 |
|
|
|
1783 |
__num = __i2 + __num * __num; |
|
|
1784 |
__den = __i2 + __den * __den; |
|
|
1785 |
|
|
|
1786 |
return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)), |
|
|
1787 |
_Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x)); |
|
|
1788 |
} |
|
|
1789 |
|
|
|
1790 |
#if _GLIBCXX_USE_C99_COMPLEX_TR1 |
|
|
1791 |
inline __complex__ float |
|
|
1792 |
__complex_atanh(__complex__ float __z) |
|
|
1793 |
{ return __builtin_catanhf(__z); } |
|
|
1794 |
|
|
|
1795 |
inline __complex__ double |
|
|
1796 |
__complex_atanh(__complex__ double __z) |
|
|
1797 |
{ return __builtin_catanh(__z); } |
|
|
1798 |
|
|
|
1799 |
inline __complex__ long double |
|
|
1800 |
__complex_atanh(const __complex__ long double& __z) |
|
|
1801 |
{ return __builtin_catanhl(__z); } |
|
|
1802 |
|
|
|
1803 |
template |
|
|
1804 |
inline std::complex<_Tp> |
|
|
1805 |
atanh(const std::complex<_Tp>& __z) |
|
|
1806 |
{ return __complex_atanh(__z.__rep()); } |
|
|
1807 |
#else |
|
|
1808 |
/// atanh(__z) [8.1.7]. |
|
|
1809 |
// Effects: Behaves the same as C99 function catanh, defined |
|
|
1810 |
// in subclause 7.3.6.3. |
|
|
1811 |
template |
|
|
1812 |
inline std::complex<_Tp> |
|
|
1813 |
atanh(const std::complex<_Tp>& __z) |
|
|
1814 |
{ return __complex_atanh(__z); } |
|
|
1815 |
#endif |
|
|
1816 |
|
|
|
1817 |
template |
|
|
1818 |
inline _Tp |
|
|
1819 |
/// fabs(__z) [8.1.8]. |
|
|
1820 |
// Effects: Behaves the same as C99 function cabs, defined |
|
|
1821 |
// in subclause 7.3.8.1. |
|
|
1822 |
fabs(const std::complex<_Tp>& __z) |
|
|
1823 |
{ return std::abs(__z); } |
|
|
1824 |
|
|
|
1825 |
/// Additional overloads [8.1.9]. |
|
|
1826 |
template |
|
|
1827 |
inline typename __gnu_cxx::__promote<_Tp>::__type |
|
|
1828 |
arg(_Tp __x) |
|
|
1829 |
{ |
|
|
1830 |
typedef typename __gnu_cxx::__promote<_Tp>::__type __type; |
|
|
1831 |
#if (_GLIBCXX_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC) |
|
|
1832 |
return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L) |
|
|
1833 |
: __type(); |
|
|
1834 |
#else |
|
|
1835 |
return std::arg(std::complex<__type>(__x)); |
|
|
1836 |
#endif |
|
|
1837 |
} |
|
|
1838 |
|
|
|
1839 |
template |
|
|
1840 |
inline typename __gnu_cxx::__promote<_Tp>::__type |
|
|
1841 |
imag(_Tp) |
|
|
1842 |
{ return _Tp(); } |
|
|
1843 |
|
|
|
1844 |
template |
|
|
1845 |
inline typename __gnu_cxx::__promote<_Tp>::__type |
|
|
1846 |
norm(_Tp __x) |
|
|
1847 |
{ |
|
|
1848 |
typedef typename __gnu_cxx::__promote<_Tp>::__type __type; |
|
|
1849 |
return __type(__x) * __type(__x); |
|
|
1850 |
} |
|
|
1851 |
|
|
|
1852 |
template |
|
|
1853 |
inline typename __gnu_cxx::__promote<_Tp>::__type |
|
|
1854 |
real(_Tp __x) |
|
|
1855 |
{ return __x; } |
|
|
1856 |
|
|
|
1857 |
template |
|
|
1858 |
inline std::complex::__type> |
|
|
1859 |
pow(const std::complex<_Tp>& __x, const _Up& __y) |
|
|
1860 |
{ |
|
|
1861 |
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; |
|
|
1862 |
return std::pow(std::complex<__type>(__x), __type(__y)); |
|
|
1863 |
} |
|
|
1864 |
|
|
|
1865 |
template |
|
|
1866 |
inline std::complex::__type> |
|
|
1867 |
pow(const _Tp& __x, const std::complex<_Up>& __y) |
|
|
1868 |
{ |
|
|
1869 |
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; |
|
|
1870 |
return std::pow(__type(__x), std::complex<__type>(__y)); |
|
|
1871 |
} |
|
|
1872 |
|
|
|
1873 |
template |
|
|
1874 |
inline std::complex::__type> |
|
|
1875 |
pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y) |
|
|
1876 |
{ |
|
|
1877 |
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type; |
|
|
1878 |
return std::pow(std::complex<__type>(__x), |
|
|
1879 |
std::complex<__type>(__y)); |
|
|
1880 |
} |
|
|
1881 |
|
|
|
1882 |
// Forward declarations. |
|
|
1883 |
// DR 781. |
|
|
1884 |
template std::complex<_Tp> proj(const std::complex<_Tp>&); |
|
|
1885 |
|
|
|
1886 |
template |
|
|
1887 |
std::complex<_Tp> |
|
|
1888 |
__complex_proj(const std::complex<_Tp>& __z) |
|
|
1889 |
{ |
|
|
1890 |
const _Tp __den = (__z.real() * __z.real() |
|
|
1891 |
+ __z.imag() * __z.imag() + _Tp(1.0)); |
|
|
1892 |
|
|
|
1893 |
return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den, |
|
|
1894 |
(_Tp(2.0) * __z.imag()) / __den); |
|
|
1895 |
} |
|
|
1896 |
|
|
|
1897 |
#if _GLIBCXX_USE_C99_COMPLEX |
|
|
1898 |
inline __complex__ float |
|
|
1899 |
__complex_proj(__complex__ float __z) |
|
|
1900 |
{ return __builtin_cprojf(__z); } |
|
|
1901 |
|
|
|
1902 |
inline __complex__ double |
|
|
1903 |
__complex_proj(__complex__ double __z) |
|
|
1904 |
{ return __builtin_cproj(__z); } |
|
|
1905 |
|
|
|
1906 |
inline __complex__ long double |
|
|
1907 |
__complex_proj(const __complex__ long double& __z) |
|
|
1908 |
{ return __builtin_cprojl(__z); } |
|
|
1909 |
|
|
|
1910 |
template |
|
|
1911 |
inline std::complex<_Tp> |
|
|
1912 |
proj(const std::complex<_Tp>& __z) |
|
|
1913 |
{ return __complex_proj(__z.__rep()); } |
|
|
1914 |
#else |
|
|
1915 |
template |
|
|
1916 |
inline std::complex<_Tp> |
|
|
1917 |
proj(const std::complex<_Tp>& __z) |
|
|
1918 |
{ return __complex_proj(__z); } |
|
|
1919 |
#endif |
|
|
1920 |
|
|
|
1921 |
// DR 1137. |
|
|
1922 |
template |
|
|
1923 |
inline typename __gnu_cxx::__promote<_Tp>::__type |
|
|
1924 |
proj(_Tp __x) |
|
|
1925 |
{ return __x; } |
|
|
1926 |
|
|
|
1927 |
template |
|
|
1928 |
inline typename __gnu_cxx::__promote<_Tp>::__type |
|
|
1929 |
conj(_Tp __x) |
|
|
1930 |
{ return __x; } |
|
|
1931 |
|
|
|
1932 |
#if __cplusplus > 201103L |
|
|
1933 |
|
|
|
1934 |
inline namespace literals { |
|
|
1935 |
inline namespace complex_literals { |
|
|
1936 |
|
|
|
1937 |
#define __cpp_lib_complex_udls 201309 |
|
|
1938 |
|
|
|
1939 |
constexpr std::complex |
|
|
1940 |
operator""if(long double __num) |
|
|
1941 |
{ return std::complex{0.0F, static_cast(__num)}; } |
|
|
1942 |
|
|
|
1943 |
constexpr std::complex |
|
|
1944 |
operator""if(unsigned long long __num) |
|
|
1945 |
{ return std::complex{0.0F, static_cast(__num)}; } |
|
|
1946 |
|
|
|
1947 |
constexpr std::complex |
|
|
1948 |
operator""i(long double __num) |
|
|
1949 |
{ return std::complex{0.0, static_cast(__num)}; } |
|
|
1950 |
|
|
|
1951 |
constexpr std::complex |
|
|
1952 |
operator""i(unsigned long long __num) |
|
|
1953 |
{ return std::complex{0.0, static_cast(__num)}; } |
|
|
1954 |
|
|
|
1955 |
constexpr std::complex |
|
|
1956 |
operator""il(long double __num) |
|
|
1957 |
{ return std::complex{0.0L, __num}; } |
|
|
1958 |
|
|
|
1959 |
constexpr std::complex |
|
|
1960 |
operator""il(unsigned long long __num) |
|
|
1961 |
{ return std::complex{0.0L, static_cast(__num)}; } |
|
|
1962 |
|
|
|
1963 |
} // inline namespace complex_literals |
|
|
1964 |
} // inline namespace literals |
|
|
1965 |
|
|
|
1966 |
#endif // C++14 |
|
|
1967 |
|
|
|
1968 |
_GLIBCXX_END_NAMESPACE_VERSION |
|
|
1969 |
} // namespace |
|
|
1970 |
|
|
|
1971 |
#endif // C++11 |
|
|
1972 |
|
|
|
1973 |
#endif /* _GLIBCXX_COMPLEX */ |