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complex
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// The template and inlines for the -*- C++ -*- complex number classes.
// Copyright (C) 1997-2016 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
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 norm(const complex<_Tp>&);
/// Return complex conjugate of @a z.
template<typename _Tp> 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>
struct complex
{
/// 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.
void
real(_Tp __val) { _M_real = __val; }
void
imag(_Tp __val) { _M_imag = __val; }
/// Assign a scalar to this complex number.
complex<_Tp>& operator=(const _Tp&);
/// Add a scalar to this complex number.
// 26.2.5/1
complex<_Tp>&
operator+=(const _Tp& __t)
{
_M_real += __t;
return *this;
}
/// Subtract a scalar from this complex number.
// 26.2.5/3
complex<_Tp>&
operator-=(const _Tp& __t)
{
_M_real -= __t;
return *this;
}
/// Multiply this complex number by a scalar.
complex<_Tp>& operator*=(const _Tp&);
/// Divide this complex number by a scalar.
complex<_Tp>& operator/=(const _Tp&);
// Let the compiler synthesize the copy assignment operator
#if __cplusplus >= 201103L
complex& operator=(const complex&) = default;
#endif
/// Assign another complex number to this one.
template<typename _Up>
complex<_Tp>& operator=(const complex<_Up>&);
/// Add another complex number to this one.
template<typename _Up>
complex<_Tp>& operator+=(const complex<_Up>&);
/// Subtract another complex number from this one.
template<typename _Up>
complex<_Tp>& operator-=(const complex<_Up>&);
/// Multiply this complex number by another.
template<typename _Up>
complex<_Tp>& operator*=(const complex<_Up>&);
/// Divide this complex number by another.
template<typename _Up>
complex<_Tp>& operator/=(const complex<_Up>&);
_GLIBCXX_CONSTEXPR complex __rep() const
{ return *this; }
private:
_Tp _M_real;
_Tp _M_imag;
};
template<typename _Tp>
complex<_Tp>&
complex<_Tp>::operator=(const _Tp& __t)
{
_M_real = __t;
_M_imag = _Tp();
return *this;
}
// 26.2.5/5
template<typename _Tp>
complex<_Tp>&
complex<_Tp>::operator*=(const _Tp& __t)
{
_M_real *= __t;
_M_imag *= __t;
return *this;
}
// 26.2.5/7
template<typename _Tp>
complex<_Tp>&
complex<_Tp>::operator/=(const _Tp& __t)
{
_M_real /= __t;
_M_imag /= __t;
return *this;
}
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator=(const complex<_Up>& __z)
{
_M_real = __z.real();
_M_imag = __z.imag();
return *this;
}
// 26.2.5/9
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator+=(const complex<_Up>& __z)
{
_M_real += __z.real();
_M_imag += __z.imag();
return *this;
}
// 26.2.5/11
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator-=(const complex<_Up>& __z)
{
_M_real -= __z.real();
_M_imag -= __z.imag();
return *this;
}
// 26.2.5/13
// XXX: This is a grammar school implementation.
template<typename _Tp>
template<typename _Up>
complex<_Tp>&
complex<_Tp>::operator*=(const complex<_Up>& __z)
{
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>
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 complex<_Tp>
operator+(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r += __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator+(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r += __y;
return __r;
}
template<typename _Tp>
inline 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 complex<_Tp>
operator-(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r -= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator-(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r -= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator-(const _Tp& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r(__x, -__y.imag());
__r -= __y.real();
return __r;
}
//@}
//@{
/// Return new complex value @a x times @a y.
template<typename _Tp>
inline complex<_Tp>
operator*(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r *= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator*(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r *= __y;
return __r;
}
template<typename _Tp>
inline 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 complex<_Tp>
operator/(const complex<_Tp>& __x, const complex<_Tp>& __y)
{
complex<_Tp> __r = __x;
__r /= __y;
return __r;
}
template<typename _Tp>
inline complex<_Tp>
operator/(const complex<_Tp>& __x, const _Tp& __y)
{
complex<_Tp> __r = __x;
__r /= __y;
return __r;
}
template<typename _Tp>
inline 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 complex<_Tp>
operator+(const complex<_Tp>& __x)
{ return __x; }
/// Return complex negation of @a x.
template<typename _Tp>
inline 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(); }
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(); }
//@}
/// 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)
{
_Tp __re_x, __im_x;
_CharT __ch;
__is >> __ch;
if (__ch == '(')
{
__is >> __re_x >> __ch;
if (__ch == ',')
{
__is >> __im_x >> __ch;
if (__ch == ')')
__x = complex<_Tp>(__re_x, __im_x);
else
__is.setstate(ios_base::failbit);
}
else if (__ch == ')')
__x = __re_x;
else
__is.setstate(ios_base::failbit);
}
else
{
__is.putback(__ch);
__is >> __re_x;
__x = __re_x;
}
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 _Tp _S_do_it(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return __x * __x + __y * __y;
}
};
template<>
struct _Norm_helper<true>
{
template<typename _Tp>
static inline _Tp _S_do_it(const complex<_Tp>& __z)
{
_Tp __res = std::abs(__z);
return __res * __res;
}
};
template<typename _Tp>
inline _Tp
norm(const complex<_Tp>& __z)
{
return _Norm_helper<__is_floating<_Tp>::__value
&& !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
}
template<typename _Tp>
inline complex<_Tp>
polar(const _Tp& __rho, const _Tp& __theta)
{
__glibcxx_assert( __rho >= 0 );
return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta));
}
template<typename _Tp>
inline complex<_Tp>
conj(const complex<_Tp>& __z)
{ return complex<_Tp>(__z.real(), -__z.imag()); }
// Transcendentals
// 26.2.8/1 cos(__z): Returns the cosine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_cos(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
inline __complex__ double
__complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
inline __complex__ long double
__complex_cos(const __complex__ long double& __z)
{ return __builtin_ccosl(__z); }
template<typename _Tp>
inline complex<_Tp>
cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
#endif
// 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
template<typename _Tp>
inline complex<_Tp>
__complex_cosh(const complex<_Tp>& __z)
{
const _Tp __x = __z.real();
const _Tp __y = __z.imag();
return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
}
#if _GLIBCXX_USE_C99_COMPLEX
inline __complex__ float
__complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
inline __complex__ double
__complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
inline __complex__ long double
__complex_cosh(const __complex__ long double& __z)
{ return __builtin_ccoshl(__z); }
template<typename _Tp>
inline complex<_Tp>
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
#else
template<typename _Tp>
inline complex<_Tp>
cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
#endif
// 26.2.8/3 exp(__z): Returns the complex base e exponential of x
template<typename _Tp>
inline complex<_Tp>
__complex_exp(const complex<_Tp>& __z)
{ return std::polar<_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();