complex
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// The template and inlines for the -*- C++ -*- complex number classes.
// Copyright (C) 1997-2021 Free Software Foundation, Inc.
//
// This file is part of the GNU ISO C++ Library. This library is free
// software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the
// Free Software Foundation; either version 3, or (at your option)
// any later version.
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// Under Section 7 of GPL version 3, you are granted additional
// permissions described in the GCC Runtime Library Exception, version
// 3.1, as published by the Free Software Foundation.
// You should have received a copy of the GNU General Public License and
// a copy of the GCC Runtime Library Exception along with this program;
// see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
// <http://www.gnu.org/licenses/>.
/** @file include/complex
* This is a Standard C++ Library header.
*/
//
// ISO C++ 14882: 26.2 Complex Numbers
// Note: this is not a conforming implementation.
// Initially implemented by Ulrich Drepper <drepper@cygnus.com>
// Improved by Gabriel Dos Reis <dosreis@cmla.ens-cachan.fr>
//
#ifndef _GLIBCXX_COMPLEX
#define _GLIBCXX_COMPLEX 1
#pragma GCC system_header
#include <bits/c++config.h>
#include <bits/cpp_type_traits.h>
#include <ext/type_traits.h>
#include <cmath>
#include <sstream>
// Get rid of a macro possibly defined in <complex.h>
#undef complex
#if __cplusplus > 201703L
# define __cpp_lib_constexpr_complex 201711L
#endif
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
/**
* @defgroup complex_numbers Complex Numbers
* @ingroup numerics
*
* Classes and functions for complex numbers.
* @{
*/
// Forward declarations.
template<typename _Tp> class complex;
template<> class complex<float>;
template<> class complex<double>;
template<> class complex<long double>;
/// Return magnitude of @a z.
template<typename _Tp> _Tp abs(const complex<_Tp>&);
/// Return phase angle of @a z.
template<typename _Tp> _Tp arg(const complex<_Tp>&);
/// Return @a z magnitude squared.
template<typename _Tp> _Tp _GLIBCXX20_CONSTEXPR norm(const complex<_Tp>&);
/// Return complex conjugate of @a z.
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex<_Tp> conj(const complex<_Tp>&);
/// Return complex with magnitude @a rho and angle @a theta.
template<typename _Tp> complex<_Tp> polar(const _Tp&, const _Tp& = 0);
// Transcendentals:
/// Return complex cosine of @a z.
template<typename _Tp> complex<_Tp> cos(const complex<_Tp>&);
/// Return complex hyperbolic cosine of @a z.
template<typename _Tp> complex<_Tp> cosh(const complex<_Tp>&);
/// Return complex base e exponential of @a z.
template<typename _Tp> complex<_Tp> exp(const complex<_Tp>&);
/// Return complex natural logarithm of @a z.
template<typename _Tp> complex<_Tp> log(const complex<_Tp>&);
/// Return complex base 10 logarithm of @a z.
template<typename _Tp> complex<_Tp> log10(const complex<_Tp>&);
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, const _Tp&);
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&,
const complex<_Tp>&);
/// Return @a x to the @a y'th power.
template<typename _Tp> complex<_Tp> pow(const _Tp&, const complex<_Tp>&);
/// Return complex sine of @a z.
template<typename _Tp> complex<_Tp> sin(const complex<_Tp>&);
/// Return complex hyperbolic sine of @a z.
template<typename _Tp> complex<_Tp> sinh(const complex<_Tp>&);
/// Return complex square root of @a z.
template<typename _Tp> complex<_Tp> sqrt(const complex<_Tp>&);
/// Return complex tangent of @a z.
template<typename _Tp> complex<_Tp> tan(const complex<_Tp>&);
/// Return complex hyperbolic tangent of @a z.
template<typename _Tp> complex<_Tp> tanh(const complex<_Tp>&);
// 26.2.2 Primary template class complex
/**
* Template to represent complex numbers.
*
* Specializations for float, double, and long double are part of the
* library. Results with any other type are not guaranteed.
*
* @param Tp Type of real and imaginary values.
*/
template<typename _Tp>
class complex
{
public:
/// Value typedef.
typedef _Tp value_type;
/// Default constructor. First parameter is x, second parameter is y.
/// Unspecified parameters default to 0.
_GLIBCXX_CONSTEXPR complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
: _M_real(__r), _M_imag(__i) { }
// Let the compiler synthesize the copy constructor
#if __cplusplus >= 201103L
constexpr complex(const complex&) = default;
#endif
/// Converting constructor.
template<typename _Up>
_GLIBCXX_CONSTEXPR complex(const complex<_Up>& __z)
: _M_real(__z.real()), _M_imag(__z.imag()) { }
#if __cplusplus >= 201103L
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
_GLIBCXX_ABI_TAG_CXX11
constexpr _Tp
real() const { return _M_real; }
_GLIBCXX_ABI_TAG_CXX11
constexpr _Tp
imag() const { return _M_imag; }
#else
/// Return real part of complex number.
_Tp&
real() { return _M_real; }
/// Return real part of complex number.
const _Tp&
real() const { return _M_real; }
/// Return imaginary part of complex number.
_Tp&
imag() { return _M_imag; }
/// Return imaginary part of complex number.
const _Tp&
imag() const { return _M_imag; }
#endif
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
_GLIBCXX20_CONSTEXPR void
real(_Tp __val) { _M_real = __val; }
_GLIBCXX20_CONSTEXPR void
imag(_Tp __val) { _M_imag = __val; }
/// Assign a scalar to this complex number.
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const _Tp&);
/// Add a scalar to this complex number.
// 26.2.5/1
_GLIBCXX20_CONSTEXPR complex<_Tp>&
operator+=(const _Tp& __t)
{
_M_real += __t;
return *this;
}
/// Subtract a scalar from this complex number.
// 26.2.5/3
_GLIBCXX20_CONSTEXPR complex<_Tp>&
operator-=(const _Tp& __t)
{
_M_real -= __t;
return *this;
}
/// Multiply this complex number by a scalar.
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const _Tp&);
/// Divide this complex number by a scalar.
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const _Tp&);
// Let the compiler synthesize the copy assignment operator
#if __cplusplus >= 201103L
_GLIBCXX20_CONSTEXPR complex& operator=(const complex&) = default;
#endif
/// Assign another complex number to this one.
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator=(const complex<_Up>&);
/// Add another complex number to this one.
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator+=(const complex<_Up>&);
/// Subtract another complex number from this one.
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator-=(const complex<_Up>&);
/// Multiply this complex number by another.
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator*=(const complex<_Up>&);
/// Divide this complex number by another.
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>& operator/=(const complex<_Up>&);
_GLIBCXX_CONSTEXPR complex __rep() const
{ return *this; }
private:
_Tp _M_real;
_Tp _M_imag;
};
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex<_Tp>&
complex<_Tp>::operator=(const _Tp& __t)
{
_M_real = __t;
_M_imag = _Tp();
return *this;
}
// 26.2.5/5
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex<_Tp>&
complex<_Tp>::operator*=(const _Tp& __t)
{
_M_real *= __t;
_M_imag *= __t;
return *this;
}
// 26.2.5/7
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex<_Tp>&
complex<_Tp>::operator/=(const _Tp& __t)
{
_M_real /= __t;
_M_imag /= __t;
return *this;
}
template<typename _Tp>
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>&
complex<_Tp>::operator=(const complex<_Up>& __z)
{
_M_real = __z.real();
_M_imag = __z.imag();
return *this;
}
// 26.2.5/9
template<typename _Tp>
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>&
complex<_Tp>::operator+=(const complex<_Up>& __z)
{
_M_real += __z.real();
_M_imag += __z.imag();
return *this;
}
// 26.2.5/11
template<typename _Tp>
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>&
complex<_Tp>::operator-=(const complex<_Up>& __z)
{
_M_real -= __z.real();
_M_imag -= __z.imag();
return *this;
}
// 26.2.5/13
// XXX: This is a grammar school implementation.
template<typename _Tp>
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>&
complex<_Tp>::operator*=(const complex<_Up>& __z)
{
const _Tp __r = _M_real * __z.real() - _M_imag * __z.imag();
_M_imag = _M_real * __z.imag() + _M_imag * __z.real();
_M_real = __r;
return *this;
}
// 26.2.5/15
// XXX: This is a grammar school implementation.
template<typename _Tp>
template<typename _Up>
_GLIBCXX20_CONSTEXPR complex<_Tp>&
complex<_Tp>::operator/=(const complex<_Up>& __z)
{
const _Tp __r = _M_real * __z.real() + _M_imag * __z.imag();
const _Tp __n = std::norm(__z);
_M_imag = (_M_imag * __z.real() - _M_real * __z.imag()) / __n;
_M_real = __r / __n;
return *this;
}
// Operators:
///@{
/// Return new complex value @a x plus @a y.
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r += __y;
return __r;
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator+(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r += __y;
return __r;
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator+(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __y;
__r += __x;
return __r;
}
///@}
///@{
/// Return new complex value @a x minus @a y.
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r -= __y;
return __r;
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator-(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r -= __y;
return __r;
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator-(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = -__y;
__r += __x;
return __r;
}
///@}
///@{
/// Return new complex value @a x times @a y.
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r *= __y;
return __r;
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator*(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r *= __y;
return __r;
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator*(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __y;
__r *= __x;
return __r;
}
///@}
///@{
/// Return new complex value @a x divided by @a y.
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r /= __y;
return __r;
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator/(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r /= __y;
return __r;
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator/(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r /= __y;
return __r;
}
///@}
/// Return @a x.
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator+(const complex<_Tp>& __x)
{ return __x; }
/// Return complex negation of @a x.
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
operator-(const complex<_Tp>& __x)
{ return complex<_Tp>(-__x.real(), -__x.imag()); }
///@{
/// Return true if @a x is equal to @a y.
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR bool
operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __x.real() == __y.real() && __x.imag() == __y.imag(); }
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR bool
operator==(const complex<_Tp>& __x, const _Tp& __y)
{ return __x.real() == __y && __x.imag() == _Tp(); }
#if !(__cpp_impl_three_way_comparison >= 201907L)
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR bool
operator==(const _Tp& __x, const complex<_Tp>& __y)
{ return __x == __y.real() && _Tp() == __y.imag(); }
///@}
///@{
/// Return false if @a x is equal to @a y.
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR bool
operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __x.real() != __y.real() || __x.imag() != __y.imag(); }
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR bool
operator!=(const complex<_Tp>& __x, const _Tp& __y)
{ return __x.real() != __y || __x.imag() != _Tp(); }
template<typename _Tp>
inline _GLIBCXX_CONSTEXPR bool
operator!=(const _Tp& __x, const complex<_Tp>& __y)
{ return __x != __y.real() || _Tp() != __y.imag(); }
#endif
///@}
/// Extraction operator for complex values.
template<typename _Tp, typename _CharT, class _Traits>
basic_istream<_CharT, _Traits>&
operator>>(basic_istream<_CharT, _Traits>& __is, complex<_Tp>& __x)
{
bool __fail = true;
_CharT __ch;
if (__is >> __ch)
{
if (_Traits::eq(__ch, __is.widen('(')))
{
_Tp __u;
if (__is >> __u >> __ch)
{
const _CharT __rparen = __is.widen(')');
if (_Traits::eq(__ch, __rparen))
{
__x = __u;
__fail = false;
}
else if (_Traits::eq(__ch, __is.widen(',')))
{
_Tp __v;
if (__is >> __v >> __ch)
{
if (_Traits::eq(__ch, __rparen))
{
__x = complex<_Tp>(__u, __v);
__fail = false;
}
else
__is.putback(__ch);
}
}
else
__is.putback(__ch);
}
}
else
{
__is.putback(__ch);
_Tp __u;
if (__is >> __u)
{
__x = __u;
__fail = false;
}
}
}
if (__fail)
__is.setstate(ios_base::failbit);
return __is;
}
/// Insertion operator for complex values.
template<typename _Tp, typename _CharT, class _Traits>
basic_ostream<_CharT, _Traits>&
operator<<(basic_ostream<_CharT, _Traits>& __os, const complex<_Tp>& __x)
{
basic_ostringstream<_CharT, _Traits> __s;
__s.flags(__os.flags());
__s.imbue(__os.getloc());
__s.precision(__os.precision());
__s << '(' << __x.real() << ',' << __x.imag() << ')';
return __os << __s.str();
}
// Values
#if __cplusplus >= 201103L
template<typename _Tp>
constexpr _Tp
real(const complex<_Tp>& __z)
{ return __z.real(); }
template<typename _Tp>
constexpr _Tp
imag(const complex<_Tp>& __z)
{ return __z.imag(); }
#else
template<typename _Tp>
inline _Tp&
real(complex<_Tp>& __z)
{ return __z.real(); }
template<typename _Tp>
inline const _Tp&
real(const complex<_Tp>& __z)
{ return __z.real(); }
template<typename _Tp>
inline _Tp&
imag(complex<_Tp>& __z)
{ return __z.imag(); }
template<typename _Tp>
inline const _Tp&
imag(const complex<_Tp>& __z)
{ return __z.imag(); }
#endif
// 26.2.7/3 abs(__z): Returns the magnitude of __z.
template<typename _Tp>
inline _Tp
__complex_abs(const complex<_Tp>& __z)
{
_Tp __x = __z.real();
_Tp __y = __z.imag();
const _Tp __s = std::max(abs(__x), abs(__y));
if (__s == _Tp()) // well ...
return __s;
__x /= __s;
__y /= __s;
return __s * sqrt(__x * __x + __y * __y);
}
#if _GLIBCXX_USE_C99_COMPLEX
inline float
__complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
inline double
__complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
inline long double
__complex_abs(const __complex__ long double& __z)
{ return __builtin_cabsl(__z); }
template<typename _Tp>
inline _Tp
abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
#else
template<typename _Tp>
inline _Tp
abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
#endif
// 26.2.7/4: arg(__z): Returns the phase angle of __z.
template<typename _Tp>
inline _Tp
__complex_arg(const complex<_Tp>& __z)
{ return atan2(__z.imag(), __z.real()); }
#if _GLIBCXX_USE_C99_COMPLEX
inline float
__complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
inline double
__complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
inline long double
__complex_arg(const __complex__ long double& __z)
{ return __builtin_cargl(__z); }
template<typename _Tp>
inline _Tp
arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
#else
template<typename _Tp>
inline _Tp
arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
#endif
// 26.2.7/5: norm(__z) returns the squared magnitude of __z.
// As defined, norm() is -not- a norm is the common mathematical
// sense used in numerics. The helper class _Norm_helper<> tries to
// distinguish between builtin floating point and the rest, so as
// to deliver an answer as close as possible to the real value.
template<bool>
struct _Norm_helper
{
template<typename _Tp>
static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return __x * __x + __y * __y;
}
};
template<>
struct _Norm_helper<true>
{
template<typename _Tp>
static inline _GLIBCXX20_CONSTEXPR _Tp _S_do_it(const complex<_Tp>& __z)
{
//_Tp __res = std::abs(__z);
//return __res * __res;
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return __x * __x + __y * __y;
}
};
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR _Tp
norm(const complex<_Tp>& __z)
{
return _Norm_helper<__is_floating<_Tp>::__value
&& !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
}
template<typename _Tp>
inline complex<_Tp>
polar(const _Tp& __rho, const _Tp& __theta)
{
__glibcxx_assert( __rho >= 0 );
return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR complex<_Tp>
conj(const complex<_Tp>& __z)
{ return complex<_Tp>(__z.real(), -__z.imag()); }
// Transcendentals
// 26.2.8/1 cos(__z): Returns the cosine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_cos(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
inline __complex__ double
__complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
inline __complex__ long double
__complex_cos(const __complex__ long double& __z)
{ return __builtin_ccosl(__z); }
template<typename _Tp>
inline complex<_Tp>
cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
#endif
// 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_cosh(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
inline __complex__ double
__complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
inline __complex__ long double
__complex_cosh(const __complex__ long double& __z)
{ return __builtin_ccoshl(__z); }
template<typename _Tp>
inline complex<_Tp>
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
#endif
// 26.2.8/3 exp(__z): Returns the complex base e exponential of x
template<typename _Tp>
inline complex<_Tp>
__complex_exp(const complex<_Tp>& __z)
{ return std::polar<_Tp>(exp(__z.real()), __z.imag()); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
inline __complex__ double
__complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
inline __complex__ long double
__complex_exp(const __complex__ long double& __z)
{ return __builtin_cexpl(__z); }
template<typename _Tp>
inline complex<_Tp>
exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
#endif
// 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
// The branch cut is along the negative axis.
template<typename _Tp>
inline complex<_Tp>
__complex_log(const complex<_Tp>& __z)
{ return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
inline __complex__ double
__complex_log(__complex__ double __z) { return __builtin_clog(__z); }
inline __complex__ long double
__complex_log(const __complex__ long double& __z)
{ return __builtin_clogl(__z); }
template<typename _Tp>
inline complex<_Tp>
log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
log(const complex<_Tp>& __z) { return __complex_log(__z); }
#endif
template<typename _Tp>
inline complex<_Tp>
log10(const complex<_Tp>& __z)
{ return std::log(__z) / log(_Tp(10.0)); }
// 26.2.8/10 sin(__z): Returns the sine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_sin(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
inline __complex__ double
__complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
inline __complex__ long double
__complex_sin(const __complex__ long double& __z)
{ return __builtin_csinl(__z); }
template<typename _Tp>
inline complex<_Tp>
sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
#endif
// 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_sinh(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
inline __complex__ double
__complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
inline __complex__ long double
__complex_sinh(const __complex__ long double& __z)
{ return __builtin_csinhl(__z); }
template<typename _Tp>
inline complex<_Tp>
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
#endif
// 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
// The branch cut is on the negative axis.
template<typename _Tp>
complex<_Tp>
__complex_sqrt(const complex<_Tp>& __z)
{
_Tp __x = __z.real();
_Tp __y = __z.imag();
if (__x == _Tp())
{
_Tp __t = sqrt(abs(__y) / 2);
return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
}
else
{
_Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
_Tp __u = __t / 2;
return __x > _Tp()
? complex<_Tp>(__u, __y / __t)
: complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
}
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
inline __complex__ double
__complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
inline __complex__ long double
__complex_sqrt(const __complex__ long double& __z)
{ return __builtin_csqrtl(__z); }
template<typename _Tp>
inline complex<_Tp>
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
#endif
// 26.2.8/14 tan(__z): Return the complex tangent of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_tan(const complex<_Tp>& __z)
{ return std::sin(__z) / std::cos(__z); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
inline __complex__ double
__complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
inline __complex__ long double
__complex_tan(const __complex__ long double& __z)
{ return __builtin_ctanl(__z); }
template<typename _Tp>
inline complex<_Tp>
tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
#endif
// 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_tanh(const complex<_Tp>& __z)
{ return std::sinh(__z) / std::cosh(__z); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
inline __complex__ double
__complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
inline __complex__ long double
__complex_tanh(const __complex__ long double& __z)
{ return __builtin_ctanhl(__z); }
template<typename _Tp>
inline complex<_Tp>
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
#endif
// 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
// raised to the __y-th power. The branch
// cut is on the negative axis.
template<typename _Tp>
complex<_Tp>
__complex_pow_unsigned(complex<_Tp> __x, unsigned __n)
{
complex<_Tp> __y = __n % 2 ? __x : complex<_Tp>(1);
while (__n >>= 1)
{
__x *= __x;
if (__n % 2)
__y *= __x;
}
return __y;
}
// In C++11 mode we used to implement the resolution of
// DR 844. complex pow return type is ambiguous.
// thus the following overload was disabled in that mode. However, doing
// that causes all sorts of issues, see, for example:
// http://gcc.gnu.org/ml/libstdc++/2013-01/msg00058.html
// and also PR57974.
template<typename _Tp>
inline complex<_Tp>
pow(const complex<_Tp>& __z, int __n)
{
return __n < 0
? complex<_Tp>(1) / std::__complex_pow_unsigned(__z, -(unsigned)__n)
: std::__complex_pow_unsigned(__z, __n);
}
template<typename _Tp>
complex<_Tp>
pow(const complex<_Tp>& __x, const _Tp& __y)
{
#if ! _GLIBCXX_USE_C99_COMPLEX
if (__x == _Tp())
return _Tp();
#endif
if (__x.imag() == _Tp() && __x.real() > _Tp())
return pow(__x.real(), __y);
complex<_Tp> __t = std::log(__x);
return std::polar<_Tp>(exp(__y * __t.real()), __y * __t.imag());
}
template<typename _Tp>
inline complex<_Tp>
__complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_pow(__complex__ float __x, __complex__ float __y)
{ return __builtin_cpowf(__x, __y); }
inline __complex__ double
__complex_pow(__complex__ double __x, __complex__ double __y)
{ return __builtin_cpow(__x, __y); }
inline __complex__ long double
__complex_pow(const __complex__ long double& __x,
const __complex__ long double& __y)
{ return __builtin_cpowl(__x, __y); }
template<typename _Tp>
inline complex<_Tp>
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __complex_pow(__x.__rep(), __y.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
{ return __complex_pow(__x, __y); }
#endif
template<typename _Tp>
inline complex<_Tp>
pow(const _Tp& __x, const complex<_Tp>& __y)
{
return __x > _Tp() ? std::polar<_Tp>(pow(__x, __y.real()),
__y.imag() * log(__x))
: std::pow(complex<_Tp>(__x), __y);
}
/// 26.2.3 complex specializations
/// complex<float> specialization
template<>
class complex<float>
{
public:
typedef float value_type;
typedef __complex__ float _ComplexT;
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
_GLIBCXX_CONSTEXPR complex(float __r = 0.0f, float __i = 0.0f)
#if __cplusplus >= 201103L
: _M_value{ __r, __i } { }
#else
{
__real__ _M_value = __r;
__imag__ _M_value = __i;
}
#endif
explicit _GLIBCXX_CONSTEXPR complex(const complex<double>&);
explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
#if __cplusplus >= 201103L
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
__attribute ((__abi_tag__ ("cxx11")))
constexpr float
real() const { return __real__ _M_value; }
__attribute ((__abi_tag__ ("cxx11")))
constexpr float
imag() const { return __imag__ _M_value; }
#else
float&
real() { return __real__ _M_value; }
const float&
real() const { return __real__ _M_value; }
float&
imag() { return __imag__ _M_value; }
const float&
imag() const { return __imag__ _M_value; }
#endif
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
_GLIBCXX20_CONSTEXPR void
real(float __val) { __real__ _M_value = __val; }
_GLIBCXX20_CONSTEXPR void
imag(float __val) { __imag__ _M_value = __val; }
_GLIBCXX20_CONSTEXPR complex&
operator=(float __f)
{
_M_value = __f;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator+=(float __f)
{
_M_value += __f;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator-=(float __f)
{
_M_value -= __f;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator*=(float __f)
{
_M_value *= __f;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator/=(float __f)
{
_M_value /= __f;
return *this;
}
// Let the compiler synthesize the copy and assignment
// operator. It always does a pretty good job.
#if __cplusplus >= 201103L
_GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
#endif
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator=(const complex<_Tp>& __z)
{
__real__ _M_value = __z.real();
__imag__ _M_value = __z.imag();
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator+=(const complex<_Tp>& __z)
{
_M_value += __z.__rep();
return *this;
}
template<class _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator-=(const complex<_Tp>& __z)
{
_M_value -= __z.__rep();
return *this;
}
template<class _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator*=(const complex<_Tp>& __z)
{
const _ComplexT __t = __z.__rep();
_M_value *= __t;
return *this;
}
template<class _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator/=(const complex<_Tp>& __z)
{
const _ComplexT __t = __z.__rep();
_M_value /= __t;
return *this;
}
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
private:
_ComplexT _M_value;
};
/// 26.2.3 complex specializations
/// complex<double> specialization
template<>
class complex<double>
{
public:
typedef double value_type;
typedef __complex__ double _ComplexT;
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
_GLIBCXX_CONSTEXPR complex(double __r = 0.0, double __i = 0.0)
#if __cplusplus >= 201103L
: _M_value{ __r, __i } { }
#else
{
__real__ _M_value = __r;
__imag__ _M_value = __i;
}
#endif
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
: _M_value(__z.__rep()) { }
explicit _GLIBCXX_CONSTEXPR complex(const complex<long double>&);
#if __cplusplus >= 201103L
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
__attribute ((__abi_tag__ ("cxx11")))
constexpr double
real() const { return __real__ _M_value; }
__attribute ((__abi_tag__ ("cxx11")))
constexpr double
imag() const { return __imag__ _M_value; }
#else
double&
real() { return __real__ _M_value; }
const double&
real() const { return __real__ _M_value; }
double&
imag() { return __imag__ _M_value; }
const double&
imag() const { return __imag__ _M_value; }
#endif
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
_GLIBCXX20_CONSTEXPR void
real(double __val) { __real__ _M_value = __val; }
_GLIBCXX20_CONSTEXPR void
imag(double __val) { __imag__ _M_value = __val; }
_GLIBCXX20_CONSTEXPR complex&
operator=(double __d)
{
_M_value = __d;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator+=(double __d)
{
_M_value += __d;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator-=(double __d)
{
_M_value -= __d;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator*=(double __d)
{
_M_value *= __d;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator/=(double __d)
{
_M_value /= __d;
return *this;
}
// The compiler will synthesize this, efficiently.
#if __cplusplus >= 201103L
_GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
#endif
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator=(const complex<_Tp>& __z)
{
_M_value = __z.__rep();
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator+=(const complex<_Tp>& __z)
{
_M_value += __z.__rep();
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator-=(const complex<_Tp>& __z)
{
_M_value -= __z.__rep();
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator*=(const complex<_Tp>& __z)
{
const _ComplexT __t = __z.__rep();
_M_value *= __t;
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator/=(const complex<_Tp>& __z)
{
const _ComplexT __t = __z.__rep();
_M_value /= __t;
return *this;
}
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
private:
_ComplexT _M_value;
};
/// 26.2.3 complex specializations
/// complex<long double> specialization
template<>
class complex<long double>
{
public:
typedef long double value_type;
typedef __complex__ long double _ComplexT;
_GLIBCXX_CONSTEXPR complex(_ComplexT __z) : _M_value(__z) { }
_GLIBCXX_CONSTEXPR complex(long double __r = 0.0L,
long double __i = 0.0L)
#if __cplusplus >= 201103L
: _M_value{ __r, __i } { }
#else
{
__real__ _M_value = __r;
__imag__ _M_value = __i;
}
#endif
_GLIBCXX_CONSTEXPR complex(const complex<float>& __z)
: _M_value(__z.__rep()) { }
_GLIBCXX_CONSTEXPR complex(const complex<double>& __z)
: _M_value(__z.__rep()) { }
#if __cplusplus >= 201103L
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
__attribute ((__abi_tag__ ("cxx11")))
constexpr long double
real() const { return __real__ _M_value; }
__attribute ((__abi_tag__ ("cxx11")))
constexpr long double
imag() const { return __imag__ _M_value; }
#else
long double&
real() { return __real__ _M_value; }
const long double&
real() const { return __real__ _M_value; }
long double&
imag() { return __imag__ _M_value; }
const long double&
imag() const { return __imag__ _M_value; }
#endif
// _GLIBCXX_RESOLVE_LIB_DEFECTS
// DR 387. std::complex over-encapsulated.
_GLIBCXX20_CONSTEXPR void
real(long double __val) { __real__ _M_value = __val; }
_GLIBCXX20_CONSTEXPR void
imag(long double __val) { __imag__ _M_value = __val; }
_GLIBCXX20_CONSTEXPR complex&
operator=(long double __r)
{
_M_value = __r;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator+=(long double __r)
{
_M_value += __r;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator-=(long double __r)
{
_M_value -= __r;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator*=(long double __r)
{
_M_value *= __r;
return *this;
}
_GLIBCXX20_CONSTEXPR complex&
operator/=(long double __r)
{
_M_value /= __r;
return *this;
}
// The compiler knows how to do this efficiently
#if __cplusplus >= 201103L
_GLIBCXX14_CONSTEXPR complex& operator=(const complex&) = default;
#endif
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator=(const complex<_Tp>& __z)
{
_M_value = __z.__rep();
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator+=(const complex<_Tp>& __z)
{
_M_value += __z.__rep();
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator-=(const complex<_Tp>& __z)
{
_M_value -= __z.__rep();
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator*=(const complex<_Tp>& __z)
{
const _ComplexT __t = __z.__rep();
_M_value *= __t;
return *this;
}
template<typename _Tp>
_GLIBCXX20_CONSTEXPR complex&
operator/=(const complex<_Tp>& __z)
{
const _ComplexT __t = __z.__rep();
_M_value /= __t;
return *this;
}
_GLIBCXX_CONSTEXPR _ComplexT __rep() const { return _M_value; }
private:
_ComplexT _M_value;
};
// These bits have to be at the end of this file, so that the
// specializations have all been defined.
inline _GLIBCXX_CONSTEXPR
complex<float>::complex(const complex<double>& __z)
: _M_value(__z.__rep()) { }
inline _GLIBCXX_CONSTEXPR
complex<float>::complex(const complex<long double>& __z)
: _M_value(__z.__rep()) { }
inline _GLIBCXX_CONSTEXPR
complex<double>::complex(const complex<long double>& __z)
: _M_value(__z.__rep()) { }
// Inhibit implicit instantiations for required instantiations,
// which are defined via explicit instantiations elsewhere.
// NB: This syntax is a GNU extension.
#if _GLIBCXX_EXTERN_TEMPLATE
extern template istream& operator>>(istream&, complex<float>&);
extern template ostream& operator<<(ostream&, const complex<float>&);
extern template istream& operator>>(istream&, complex<double>&);
extern template ostream& operator<<(ostream&, const complex<double>&);
extern template istream& operator>>(istream&, complex<long double>&);
extern template ostream& operator<<(ostream&, const complex<long double>&);
#ifdef _GLIBCXX_USE_WCHAR_T
extern template wistream& operator>>(wistream&, complex<float>&);
extern template wostream& operator<<(wostream&, const complex<float>&);
extern template wistream& operator>>(wistream&, complex<double>&);
extern template wostream& operator<<(wostream&, const complex<double>&);
extern template wistream& operator>>(wistream&, complex<long double>&);
extern template wostream& operator<<(wostream&, const complex<long double>&);
#endif
#endif
/// @} group complex_numbers
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace
namespace __gnu_cxx _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
// See ext/type_traits.h for the primary template.
template<typename _Tp, typename _Up>
struct __promote_2<std::complex<_Tp>, _Up>
{
public:
typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
};
template<typename _Tp, typename _Up>
struct __promote_2<_Tp, std::complex<_Up> >
{
public:
typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
};
template<typename _Tp, typename _Up>
struct __promote_2<std::complex<_Tp>, std::complex<_Up> >
{
public:
typedef std::complex<typename __promote_2<_Tp, _Up>::__type> __type;
};
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace
#if __cplusplus >= 201103L
namespace std _GLIBCXX_VISIBILITY(default)
{
_GLIBCXX_BEGIN_NAMESPACE_VERSION
// Forward declarations.
template<typename _Tp> std::complex<_Tp> acos(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> asin(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> atan(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> acosh(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> asinh(const std::complex<_Tp>&);
template<typename _Tp> std::complex<_Tp> atanh(const std::complex<_Tp>&);
// DR 595.
template<typename _Tp> _Tp fabs(const std::complex<_Tp>&);
template<typename _Tp>
inline std::complex<_Tp>
__complex_acos(const std::complex<_Tp>& __z)
{
const std::complex<_Tp> __t = std::asin(__z);
const _Tp __pi_2 = 1.5707963267948966192313216916397514L;
return std::complex<_Tp>(__pi_2 - __t.real(), -__t.imag());
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_acos(__complex__ float __z)
{ return __builtin_cacosf(__z); }
inline __complex__ double
__complex_acos(__complex__ double __z)
{ return __builtin_cacos(__z); }
inline __complex__ long double
__complex_acos(const __complex__ long double& __z)
{ return __builtin_cacosl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
acos(const std::complex<_Tp>& __z)
{ return __complex_acos(__z.__rep()); }
#else
/// acos(__z) [8.1.2].
// Effects: Behaves the same as C99 function cacos, defined
// in subclause 7.3.5.1.
template<typename _Tp>
inline std::complex<_Tp>
acos(const std::complex<_Tp>& __z)
{ return __complex_acos(__z); }
#endif
template<typename _Tp>
inline std::complex<_Tp>
__complex_asin(const std::complex<_Tp>& __z)
{
std::complex<_Tp> __t(-__z.imag(), __z.real());
__t = std::asinh(__t);
return std::complex<_Tp>(__t.imag(), -__t.real());
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_asin(__complex__ float __z)
{ return __builtin_casinf(__z); }
inline __complex__ double
__complex_asin(__complex__ double __z)
{ return __builtin_casin(__z); }
inline __complex__ long double
__complex_asin(const __complex__ long double& __z)
{ return __builtin_casinl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
asin(const std::complex<_Tp>& __z)
{ return __complex_asin(__z.__rep()); }
#else
/// asin(__z) [8.1.3].
// Effects: Behaves the same as C99 function casin, defined
// in subclause 7.3.5.2.
template<typename _Tp>
inline std::complex<_Tp>
asin(const std::complex<_Tp>& __z)
{ return __complex_asin(__z); }
#endif
template<typename _Tp>
std::complex<_Tp>
__complex_atan(const std::complex<_Tp>& __z)
{
const _Tp __r2 = __z.real() * __z.real();
const _Tp __x = _Tp(1.0) - __r2 - __z.imag() * __z.imag();
_Tp __num = __z.imag() + _Tp(1.0);
_Tp __den = __z.imag() - _Tp(1.0);
__num = __r2 + __num * __num;
__den = __r2 + __den * __den;
return std::complex<_Tp>(_Tp(0.5) * atan2(_Tp(2.0) * __z.real(), __x),
_Tp(0.25) * log(__num / __den));
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_atan(__complex__ float __z)
{ return __builtin_catanf(__z); }
inline __complex__ double
__complex_atan(__complex__ double __z)
{ return __builtin_catan(__z); }
inline __complex__ long double
__complex_atan(const __complex__ long double& __z)
{ return __builtin_catanl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
atan(const std::complex<_Tp>& __z)
{ return __complex_atan(__z.__rep()); }
#else
/// atan(__z) [8.1.4].
// Effects: Behaves the same as C99 function catan, defined
// in subclause 7.3.5.3.
template<typename _Tp>
inline std::complex<_Tp>
atan(const std::complex<_Tp>& __z)
{ return __complex_atan(__z); }
#endif
template<typename _Tp>
std::complex<_Tp>
__complex_acosh(const std::complex<_Tp>& __z)
{
// Kahan's formula.
return _Tp(2.0) * std::log(std::sqrt(_Tp(0.5) * (__z + _Tp(1.0)))
+ std::sqrt(_Tp(0.5) * (__z - _Tp(1.0))));
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_acosh(__complex__ float __z)
{ return __builtin_cacoshf(__z); }
inline __complex__ double
__complex_acosh(__complex__ double __z)
{ return __builtin_cacosh(__z); }
inline __complex__ long double
__complex_acosh(const __complex__ long double& __z)
{ return __builtin_cacoshl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
acosh(const std::complex<_Tp>& __z)
{ return __complex_acosh(__z.__rep()); }
#else
/// acosh(__z) [8.1.5].
// Effects: Behaves the same as C99 function cacosh, defined
// in subclause 7.3.6.1.
template<typename _Tp>
inline std::complex<_Tp>
acosh(const std::complex<_Tp>& __z)
{ return __complex_acosh(__z); }
#endif
template<typename _Tp>
std::complex<_Tp>
__complex_asinh(const std::complex<_Tp>& __z)
{
std::complex<_Tp> __t((__z.real() - __z.imag())
* (__z.real() + __z.imag()) + _Tp(1.0),
_Tp(2.0) * __z.real() * __z.imag());
__t = std::sqrt(__t);
return std::log(__t + __z);
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_asinh(__complex__ float __z)
{ return __builtin_casinhf(__z); }
inline __complex__ double
__complex_asinh(__complex__ double __z)
{ return __builtin_casinh(__z); }
inline __complex__ long double
__complex_asinh(const __complex__ long double& __z)
{ return __builtin_casinhl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
asinh(const std::complex<_Tp>& __z)
{ return __complex_asinh(__z.__rep()); }
#else
/// asinh(__z) [8.1.6].
// Effects: Behaves the same as C99 function casin, defined
// in subclause 7.3.6.2.
template<typename _Tp>
inline std::complex<_Tp>
asinh(const std::complex<_Tp>& __z)
{ return __complex_asinh(__z); }
#endif
template<typename _Tp>
std::complex<_Tp>
__complex_atanh(const std::complex<_Tp>& __z)
{
const _Tp __i2 = __z.imag() * __z.imag();
const _Tp __x = _Tp(1.0) - __i2 - __z.real() * __z.real();
_Tp __num = _Tp(1.0) + __z.real();
_Tp __den = _Tp(1.0) - __z.real();
__num = __i2 + __num * __num;
__den = __i2 + __den * __den;
return std::complex<_Tp>(_Tp(0.25) * (log(__num) - log(__den)),
_Tp(0.5) * atan2(_Tp(2.0) * __z.imag(), __x));
}
#if _GLIBCXX_USE_C99_COMPLEX_TR1
inline __complex__ float
__complex_atanh(__complex__ float __z)
{ return __builtin_catanhf(__z); }
inline __complex__ double
__complex_atanh(__complex__ double __z)
{ return __builtin_catanh(__z); }
inline __complex__ long double
__complex_atanh(const __complex__ long double& __z)
{ return __builtin_catanhl(__z); }
template<typename _Tp>
inline std::complex<_Tp>
atanh(const std::complex<_Tp>& __z)
{ return __complex_atanh(__z.__rep()); }
#else
/// atanh(__z) [8.1.7].
// Effects: Behaves the same as C99 function catanh, defined
// in subclause 7.3.6.3.
template<typename _Tp>
inline std::complex<_Tp>
atanh(const std::complex<_Tp>& __z)
{ return __complex_atanh(__z); }
#endif
template<typename _Tp>
inline _Tp
/// fabs(__z) [8.1.8].
// Effects: Behaves the same as C99 function cabs, defined
// in subclause 7.3.8.1.
fabs(const std::complex<_Tp>& __z)
{ return std::abs(__z); }
/// Additional overloads [8.1.9].
template<typename _Tp>
inline typename __gnu_cxx::__promote<_Tp>::__type
arg(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
#if (_GLIBCXX11_USE_C99_MATH && !_GLIBCXX_USE_C99_FP_MACROS_DYNAMIC)
return std::signbit(__x) ? __type(3.1415926535897932384626433832795029L)
: __type();
#else
return std::arg(std::complex<__type>(__x));
#endif
}
template<typename _Tp>
_GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
imag(_Tp)
{ return _Tp(); }
template<typename _Tp>
_GLIBCXX20_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
norm(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return __type(__x) * __type(__x);
}
template<typename _Tp>
_GLIBCXX_CONSTEXPR inline typename __gnu_cxx::__promote<_Tp>::__type
real(_Tp __x)
{ return __x; }
template<typename _Tp, typename _Up>
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
pow(const std::complex<_Tp>& __x, const _Up& __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return std::pow(std::complex<__type>(__x), __type(__y));
}
template<typename _Tp, typename _Up>
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
pow(const _Tp& __x, const std::complex<_Up>& __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return std::pow(__type(__x), std::complex<__type>(__y));
}
template<typename _Tp, typename _Up>
inline std::complex<typename __gnu_cxx::__promote_2<_Tp, _Up>::__type>
pow(const std::complex<_Tp>& __x, const std::complex<_Up>& __y)
{
typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
return std::pow(std::complex<__type>(__x),
std::complex<__type>(__y));
}
// Forward declarations.
// DR 781.
template<typename _Tp>
std::complex<_Tp> proj(const std::complex<_Tp>&);
// Generic implementation of std::proj, does not work for infinities.
template<typename _Tp>
inline std::complex<_Tp>
__complex_proj(const std::complex<_Tp>& __z)
{ return __z; }
#if _GLIBCXX_USE_C99_COMPLEX
inline complex<float>
__complex_proj(const complex<float>& __z)
{ return __builtin_cprojf(__z.__rep()); }
inline complex<double>
__complex_proj(const complex<double>& __z)
{ return __builtin_cproj(__z.__rep()); }
inline complex<long double>
__complex_proj(const complex<long double>& __z)
{ return __builtin_cprojl(__z.__rep()); }
#elif defined _GLIBCXX_USE_C99_MATH_TR1
inline complex<float>
__complex_proj(const complex<float>& __z)
{
if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
return complex<float>(__builtin_inff(),
__builtin_copysignf(0.0f, __z.imag()));
return __z;
}
inline complex<double>
__complex_proj(const complex<double>& __z)
{
if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
return complex<double>(__builtin_inf(),
__builtin_copysign(0.0, __z.imag()));
return __z;
}
inline complex<long double>
__complex_proj(const complex<long double>& __z)
{
if (__builtin_isinf(__z.real()) || __builtin_isinf(__z.imag()))
return complex<long double>(__builtin_infl(),
__builtin_copysignl(0.0l, __z.imag()));
return __z;
}
#endif
template<typename _Tp>
inline std::complex<_Tp>
proj(const std::complex<_Tp>& __z)
{ return __complex_proj(__z); }
// Overload for scalars
template<typename _Tp>
inline std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
proj(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return std::proj(std::complex<__type>(__x));
}
template<typename _Tp>
inline _GLIBCXX20_CONSTEXPR
std::complex<typename __gnu_cxx::__promote<_Tp>::__type>
conj(_Tp __x)
{
typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
return std::complex<__type>(__x, -__type());
}
#if __cplusplus > 201103L
inline namespace literals {
inline namespace complex_literals {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wliteral-suffix"
#define __cpp_lib_complex_udls 201309
constexpr std::complex<float>
operator""if(long double __num)
{ return std::complex<float>{0.0F, static_cast<float>(__num)}; }
constexpr std::complex<float>
operator""if(unsigned long long __num)
{ return std::complex<float>{0.0F, static_cast<float>(__num)}; }
constexpr std::complex<double>
operator""i(long double __num)
{ return std::complex<double>{0.0, static_cast<double>(__num)}; }
constexpr std::complex<double>
operator""i(unsigned long long __num)
{ return std::complex<double>{0.0, static_cast<double>(__num)}; }
constexpr std::complex<long double>
operator""il(long double __num)
{ return std::complex<long double>{0.0L, __num}; }
constexpr std::complex<long double>
operator""il(unsigned long long __num)
{ return std::complex<long double>{0.0L, static_cast<long double>(__num)}; }
#pragma GCC diagnostic pop
} // inline namespace complex_literals
} // inline namespace literals
#endif // C++14
_GLIBCXX_END_NAMESPACE_VERSION
} // namespace
#endif // C++11
#endif /* _GLIBCXX_COMPLEX */