--- /dev/null
+// The template and inlines for the -*- C++ -*- complex number classes.
+
+// Copyright (C) 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005,
+// 2006, 2007, 2008, 2009
+// 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>
+
+_GLIBCXX_BEGIN_NAMESPACE(std)
+
+ /**
+ * @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>&);
+#ifndef __GXX_EXPERIMENTAL_CXX0X__
+ // DR 844.
+ /// Return @a x to the @a y'th power.
+ template<typename _Tp> complex<_Tp> pow(const complex<_Tp>&, int);
+#endif
+ /// 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.
+ complex(const _Tp& __r = _Tp(), const _Tp& __i = _Tp())
+ : _M_real(__r), _M_imag(__i) { }
+
+ // Lets the compiler synthesize the copy constructor
+ // complex (const complex<_Tp>&);
+ /// Copy constructor.
+ template<typename _Up>
+ complex(const complex<_Up>& __z)
+ : _M_real(__z.real()), _M_imag(__z.imag()) { }
+
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+ // _GLIBCXX_RESOLVE_LIB_DEFECTS
+ // DR 387. std::complex over-encapsulated.
+ _Tp real() const
+ { return _M_real; }
+
+ _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 this complex number to scalar @a t.
+ complex<_Tp>& operator=(const _Tp&);
+
+ /// Add @a t to this complex number.
+ // 26.2.5/1
+ complex<_Tp>&
+ operator+=(const _Tp& __t)
+ {
+ _M_real += __t;
+ return *this;
+ }
+
+ /// Subtract @a t 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 t.
+ complex<_Tp>& operator*=(const _Tp&);
+ /// Divide this complex number by @a t.
+ complex<_Tp>& operator/=(const _Tp&);
+
+ // Lets the compiler synthesize the
+ // copy and assignment operator
+ // complex<_Tp>& operator= (const complex<_Tp>&);
+ /// Assign this complex number to complex @a z.
+ template<typename _Up>
+ complex<_Tp>& operator=(const complex<_Up>&);
+ /// Add @a z to this complex number.
+ template<typename _Up>
+ complex<_Tp>& operator+=(const complex<_Up>&);
+ /// Subtract @a z from this complex number.
+ template<typename _Up>
+ complex<_Tp>& operator-=(const complex<_Up>&);
+ /// Multiply this complex number by @a z.
+ template<typename _Up>
+ complex<_Tp>& operator*=(const complex<_Up>&);
+ /// Divide this complex number by @a z.
+ template<typename _Up>
+ complex<_Tp>& operator/=(const complex<_Up>&);
+
+ const 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 bool
+ operator==(const complex<_Tp>& __x, const complex<_Tp>& __y)
+ { return __x.real() == __y.real() && __x.imag() == __y.imag(); }
+
+ template<typename _Tp>
+ inline bool
+ operator==(const complex<_Tp>& __x, const _Tp& __y)
+ { return __x.real() == __y && __x.imag() == _Tp(); }
+
+ template<typename _Tp>
+ inline 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 bool
+ operator!=(const complex<_Tp>& __x, const complex<_Tp>& __y)
+ { return __x.real() != __y.real() || __x.imag() != __y.imag(); }
+
+ template<typename _Tp>
+ inline bool
+ operator!=(const complex<_Tp>& __x, const _Tp& __y)
+ { return __x.real() != __y || __x.imag() != _Tp(); }
+
+ template<typename _Tp>
+ inline 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
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+ template<typename _Tp>
+ inline _Tp
+ real(const complex<_Tp>& __z)
+ { return __z.real(); }
+
+ template<typename _Tp>
+ inline _Tp
+ imag(const complex<_Tp>& __z)
+ { return __z.imag(); }
+#else
+ template<typename _Tp>
+ inline _Tp&
+ real(complex<_Tp>& __z)
+ { return __z.real(); }
+
+ template<typename _Tp>
+ inline const _Tp&
+ real(const complex<_Tp>& __z)
+ { return __z.real(); }
+
+ template<typename _Tp>
+ inline _Tp&
+ imag(complex<_Tp>& __z)
+ { return __z.imag(); }
+
+ template<typename _Tp>
+ inline const _Tp&
+ imag(const complex<_Tp>& __z)
+ { return __z.imag(); }
+#endif
+
+ // 26.2.7/3 abs(__z): Returns the magnitude of __z.
+ template<typename _Tp>
+ inline _Tp
+ __complex_abs(const complex<_Tp>& __z)
+ {
+ _Tp __x = __z.real();
+ _Tp __y = __z.imag();
+ const _Tp __s = std::max(abs(__x), abs(__y));
+ if (__s == _Tp()) // well ...
+ return __s;
+ __x /= __s;
+ __y /= __s;
+ return __s * sqrt(__x * __x + __y * __y);
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline float
+ __complex_abs(__complex__ float __z) { return __builtin_cabsf(__z); }
+
+ inline double
+ __complex_abs(__complex__ double __z) { return __builtin_cabs(__z); }
+
+ inline long double
+ __complex_abs(const __complex__ long double& __z)
+ { return __builtin_cabsl(__z); }
+
+ template<typename _Tp>
+ inline _Tp
+ abs(const complex<_Tp>& __z) { return __complex_abs(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline _Tp
+ abs(const complex<_Tp>& __z) { return __complex_abs(__z); }
+#endif
+
+
+ // 26.2.7/4: arg(__z): Returns the phase angle of __z.
+ template<typename _Tp>
+ inline _Tp
+ __complex_arg(const complex<_Tp>& __z)
+ { return atan2(__z.imag(), __z.real()); }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline float
+ __complex_arg(__complex__ float __z) { return __builtin_cargf(__z); }
+
+ inline double
+ __complex_arg(__complex__ double __z) { return __builtin_carg(__z); }
+
+ inline long double
+ __complex_arg(const __complex__ long double& __z)
+ { return __builtin_cargl(__z); }
+
+ template<typename _Tp>
+ inline _Tp
+ arg(const complex<_Tp>& __z) { return __complex_arg(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline _Tp
+ arg(const complex<_Tp>& __z) { return __complex_arg(__z); }
+#endif
+
+ // 26.2.7/5: norm(__z) returns the squared magnitude of __z.
+ // As defined, norm() is -not- a norm is the common mathematical
+ // sens used in numerics. The helper class _Norm_helper<> tries to
+ // distinguish between builtin floating point and the rest, so as
+ // to deliver an answer as close as possible to the real value.
+ template<bool>
+ struct _Norm_helper
+ {
+ template<typename _Tp>
+ static inline _Tp _S_do_it(const complex<_Tp>& __z)
+ {
+ const _Tp __x = __z.real();
+ const _Tp __y = __z.imag();
+ return __x * __x + __y * __y;
+ }
+ };
+
+ template<>
+ struct _Norm_helper<true>
+ {
+ template<typename _Tp>
+ static inline _Tp _S_do_it(const complex<_Tp>& __z)
+ {
+ _Tp __res = std::abs(__z);
+ return __res * __res;
+ }
+ };
+
+ template<typename _Tp>
+ inline _Tp
+ norm(const complex<_Tp>& __z)
+ {
+ return _Norm_helper<__is_floating<_Tp>::__value
+ && !_GLIBCXX_FAST_MATH>::_S_do_it(__z);
+ }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ polar(const _Tp& __rho, const _Tp& __theta)
+ { return complex<_Tp>(__rho * cos(__theta), __rho * sin(__theta)); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ conj(const complex<_Tp>& __z)
+ { return complex<_Tp>(__z.real(), -__z.imag()); }
+
+ // Transcendentals
+
+ // 26.2.8/1 cos(__z): Returns the cosine of __z.
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_cos(const complex<_Tp>& __z)
+ {
+ const _Tp __x = __z.real();
+ const _Tp __y = __z.imag();
+ return complex<_Tp>(cos(__x) * cosh(__y), -sin(__x) * sinh(__y));
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_cos(__complex__ float __z) { return __builtin_ccosf(__z); }
+
+ inline __complex__ double
+ __complex_cos(__complex__ double __z) { return __builtin_ccos(__z); }
+
+ inline __complex__ long double
+ __complex_cos(const __complex__ long double& __z)
+ { return __builtin_ccosl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ cos(const complex<_Tp>& __z) { return __complex_cos(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ cos(const complex<_Tp>& __z) { return __complex_cos(__z); }
+#endif
+
+ // 26.2.8/2 cosh(__z): Returns the hyperbolic cosine of __z.
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_cosh(const complex<_Tp>& __z)
+ {
+ const _Tp __x = __z.real();
+ const _Tp __y = __z.imag();
+ return complex<_Tp>(cosh(__x) * cos(__y), sinh(__x) * sin(__y));
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_cosh(__complex__ float __z) { return __builtin_ccoshf(__z); }
+
+ inline __complex__ double
+ __complex_cosh(__complex__ double __z) { return __builtin_ccosh(__z); }
+
+ inline __complex__ long double
+ __complex_cosh(const __complex__ long double& __z)
+ { return __builtin_ccoshl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ cosh(const complex<_Tp>& __z) { return __complex_cosh(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ cosh(const complex<_Tp>& __z) { return __complex_cosh(__z); }
+#endif
+
+ // 26.2.8/3 exp(__z): Returns the complex base e exponential of x
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_exp(const complex<_Tp>& __z)
+ { return std::polar(exp(__z.real()), __z.imag()); }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_exp(__complex__ float __z) { return __builtin_cexpf(__z); }
+
+ inline __complex__ double
+ __complex_exp(__complex__ double __z) { return __builtin_cexp(__z); }
+
+ inline __complex__ long double
+ __complex_exp(const __complex__ long double& __z)
+ { return __builtin_cexpl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ exp(const complex<_Tp>& __z) { return __complex_exp(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ exp(const complex<_Tp>& __z) { return __complex_exp(__z); }
+#endif
+
+ // 26.2.8/5 log(__z): Returns the natural complex logarithm of __z.
+ // The branch cut is along the negative axis.
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_log(const complex<_Tp>& __z)
+ { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_log(__complex__ float __z) { return __builtin_clogf(__z); }
+
+ inline __complex__ double
+ __complex_log(__complex__ double __z) { return __builtin_clog(__z); }
+
+ inline __complex__ long double
+ __complex_log(const __complex__ long double& __z)
+ { return __builtin_clogl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ log(const complex<_Tp>& __z) { return __complex_log(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ log(const complex<_Tp>& __z) { return __complex_log(__z); }
+#endif
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ log10(const complex<_Tp>& __z)
+ { return std::log(__z) / log(_Tp(10.0)); }
+
+ // 26.2.8/10 sin(__z): Returns the sine of __z.
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_sin(const complex<_Tp>& __z)
+ {
+ const _Tp __x = __z.real();
+ const _Tp __y = __z.imag();
+ return complex<_Tp>(sin(__x) * cosh(__y), cos(__x) * sinh(__y));
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_sin(__complex__ float __z) { return __builtin_csinf(__z); }
+
+ inline __complex__ double
+ __complex_sin(__complex__ double __z) { return __builtin_csin(__z); }
+
+ inline __complex__ long double
+ __complex_sin(const __complex__ long double& __z)
+ { return __builtin_csinl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ sin(const complex<_Tp>& __z) { return __complex_sin(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ sin(const complex<_Tp>& __z) { return __complex_sin(__z); }
+#endif
+
+ // 26.2.8/11 sinh(__z): Returns the hyperbolic sine of __z.
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_sinh(const complex<_Tp>& __z)
+ {
+ const _Tp __x = __z.real();
+ const _Tp __y = __z.imag();
+ return complex<_Tp>(sinh(__x) * cos(__y), cosh(__x) * sin(__y));
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_sinh(__complex__ float __z) { return __builtin_csinhf(__z); }
+
+ inline __complex__ double
+ __complex_sinh(__complex__ double __z) { return __builtin_csinh(__z); }
+
+ inline __complex__ long double
+ __complex_sinh(const __complex__ long double& __z)
+ { return __builtin_csinhl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ sinh(const complex<_Tp>& __z) { return __complex_sinh(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ sinh(const complex<_Tp>& __z) { return __complex_sinh(__z); }
+#endif
+
+ // 26.2.8/13 sqrt(__z): Returns the complex square root of __z.
+ // The branch cut is on the negative axis.
+ template<typename _Tp>
+ complex<_Tp>
+ __complex_sqrt(const complex<_Tp>& __z)
+ {
+ _Tp __x = __z.real();
+ _Tp __y = __z.imag();
+
+ if (__x == _Tp())
+ {
+ _Tp __t = sqrt(abs(__y) / 2);
+ return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
+ }
+ else
+ {
+ _Tp __t = sqrt(2 * (std::abs(__z) + abs(__x)));
+ _Tp __u = __t / 2;
+ return __x > _Tp()
+ ? complex<_Tp>(__u, __y / __t)
+ : complex<_Tp>(abs(__y) / __t, __y < _Tp() ? -__u : __u);
+ }
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_sqrt(__complex__ float __z) { return __builtin_csqrtf(__z); }
+
+ inline __complex__ double
+ __complex_sqrt(__complex__ double __z) { return __builtin_csqrt(__z); }
+
+ inline __complex__ long double
+ __complex_sqrt(const __complex__ long double& __z)
+ { return __builtin_csqrtl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ sqrt(const complex<_Tp>& __z) { return __complex_sqrt(__z); }
+#endif
+
+ // 26.2.8/14 tan(__z): Return the complex tangent of __z.
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_tan(const complex<_Tp>& __z)
+ { return std::sin(__z) / std::cos(__z); }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_tan(__complex__ float __z) { return __builtin_ctanf(__z); }
+
+ inline __complex__ double
+ __complex_tan(__complex__ double __z) { return __builtin_ctan(__z); }
+
+ inline __complex__ long double
+ __complex_tan(const __complex__ long double& __z)
+ { return __builtin_ctanl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ tan(const complex<_Tp>& __z) { return __complex_tan(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ tan(const complex<_Tp>& __z) { return __complex_tan(__z); }
+#endif
+
+
+ // 26.2.8/15 tanh(__z): Returns the hyperbolic tangent of __z.
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_tanh(const complex<_Tp>& __z)
+ { return std::sinh(__z) / std::cosh(__z); }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_tanh(__complex__ float __z) { return __builtin_ctanhf(__z); }
+
+ inline __complex__ double
+ __complex_tanh(__complex__ double __z) { return __builtin_ctanh(__z); }
+
+ inline __complex__ long double
+ __complex_tanh(const __complex__ long double& __z)
+ { return __builtin_ctanhl(__z); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ tanh(const complex<_Tp>& __z) { return __complex_tanh(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ tanh(const complex<_Tp>& __z) { return __complex_tanh(__z); }
+#endif
+
+
+ // 26.2.8/9 pow(__x, __y): Returns the complex power base of __x
+ // raised to the __y-th power. The branch
+ // cut is on the negative axis.
+#ifndef __GXX_EXPERIMENTAL_CXX0X__
+ // _GLIBCXX_RESOLVE_LIB_DEFECTS
+ // DR 844. complex pow return type is ambiguous.
+ template<typename _Tp>
+ inline complex<_Tp>
+ pow(const complex<_Tp>& __z, int __n)
+ { return std::__pow_helper(__z, __n); }
+#endif
+
+ template<typename _Tp>
+ complex<_Tp>
+ pow(const complex<_Tp>& __x, const _Tp& __y)
+ {
+#ifndef _GLIBCXX_USE_C99_COMPLEX
+ if (__x == _Tp())
+ return _Tp();
+#endif
+ if (__x.imag() == _Tp() && __x.real() > _Tp())
+ return pow(__x.real(), __y);
+
+ complex<_Tp> __t = std::log(__x);
+ return std::polar(exp(__y * __t.real()), __y * __t.imag());
+ }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ __complex_pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
+ { return __x == _Tp() ? _Tp() : std::exp(__y * std::log(__x)); }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_pow(__complex__ float __x, __complex__ float __y)
+ { return __builtin_cpowf(__x, __y); }
+
+ inline __complex__ double
+ __complex_pow(__complex__ double __x, __complex__ double __y)
+ { return __builtin_cpow(__x, __y); }
+
+ inline __complex__ long double
+ __complex_pow(const __complex__ long double& __x,
+ const __complex__ long double& __y)
+ { return __builtin_cpowl(__x, __y); }
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
+ { return __complex_pow(__x.__rep(), __y.__rep()); }
+#else
+ template<typename _Tp>
+ inline complex<_Tp>
+ pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
+ { return __complex_pow(__x, __y); }
+#endif
+
+ template<typename _Tp>
+ inline complex<_Tp>
+ pow(const _Tp& __x, const complex<_Tp>& __y)
+ {
+ return __x > _Tp() ? std::polar(pow(__x, __y.real()),
+ __y.imag() * log(__x))
+ : std::pow(complex<_Tp>(__x), __y);
+ }
+
+ // 26.2.3 complex specializations
+ // complex<float> specialization
+ template<>
+ struct complex<float>
+ {
+ typedef float value_type;
+ typedef __complex__ float _ComplexT;
+
+ complex(_ComplexT __z) : _M_value(__z) { }
+
+ complex(float __r = 0.0f, float __i = 0.0f)
+ {
+ __real__ _M_value = __r;
+ __imag__ _M_value = __i;
+ }
+
+ explicit complex(const complex<double>&);
+ explicit complex(const complex<long double>&);
+
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+ // _GLIBCXX_RESOLVE_LIB_DEFECTS
+ // DR 387. std::complex over-encapsulated.
+ float real() const
+ { return __real__ _M_value; }
+
+ 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.
+ void real(float __val)
+ { __real__ _M_value = __val; }
+
+ void imag(float __val)
+ { __imag__ _M_value = __val; }
+
+ complex<float>&
+ operator=(float __f)
+ {
+ __real__ _M_value = __f;
+ __imag__ _M_value = 0.0f;
+ return *this;
+ }
+
+ complex<float>&
+ operator+=(float __f)
+ {
+ __real__ _M_value += __f;
+ return *this;
+ }
+
+ complex<float>&
+ operator-=(float __f)
+ {
+ __real__ _M_value -= __f;
+ return *this;
+ }
+
+ complex<float>&
+ operator*=(float __f)
+ {
+ _M_value *= __f;
+ return *this;
+ }
+
+ complex<float>&
+ operator/=(float __f)
+ {
+ _M_value /= __f;
+ return *this;
+ }
+
+ // Let the compiler synthesize the copy and assignment
+ // operator. It always does a pretty good job.
+ // complex& operator=(const complex&);
+
+ template<typename _Tp>
+ complex<float>&
+ operator=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value = __z.real();
+ __imag__ _M_value = __z.imag();
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<float>&
+ operator+=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value += __z.real();
+ __imag__ _M_value += __z.imag();
+ return *this;
+ }
+
+ template<class _Tp>
+ complex<float>&
+ operator-=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value -= __z.real();
+ __imag__ _M_value -= __z.imag();
+ return *this;
+ }
+
+ template<class _Tp>
+ complex<float>&
+ operator*=(const complex<_Tp>& __z)
+ {
+ _ComplexT __t;
+ __real__ __t = __z.real();
+ __imag__ __t = __z.imag();
+ _M_value *= __t;
+ return *this;
+ }
+
+ template<class _Tp>
+ complex<float>&
+ operator/=(const complex<_Tp>& __z)
+ {
+ _ComplexT __t;
+ __real__ __t = __z.real();
+ __imag__ __t = __z.imag();
+ _M_value /= __t;
+ return *this;
+ }
+
+ const _ComplexT& __rep() const { return _M_value; }
+
+ private:
+ _ComplexT _M_value;
+ };
+
+ // 26.2.3 complex specializations
+ // complex<double> specialization
+ template<>
+ struct complex<double>
+ {
+ typedef double value_type;
+ typedef __complex__ double _ComplexT;
+
+ complex(_ComplexT __z) : _M_value(__z) { }
+
+ complex(double __r = 0.0, double __i = 0.0)
+ {
+ __real__ _M_value = __r;
+ __imag__ _M_value = __i;
+ }
+
+ complex(const complex<float>& __z)
+ : _M_value(__z.__rep()) { }
+
+ explicit complex(const complex<long double>&);
+
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+ // _GLIBCXX_RESOLVE_LIB_DEFECTS
+ // DR 387. std::complex over-encapsulated.
+ double real() const
+ { return __real__ _M_value; }
+
+ 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.
+ void real(double __val)
+ { __real__ _M_value = __val; }
+
+ void imag(double __val)
+ { __imag__ _M_value = __val; }
+
+ complex<double>&
+ operator=(double __d)
+ {
+ __real__ _M_value = __d;
+ __imag__ _M_value = 0.0;
+ return *this;
+ }
+
+ complex<double>&
+ operator+=(double __d)
+ {
+ __real__ _M_value += __d;
+ return *this;
+ }
+
+ complex<double>&
+ operator-=(double __d)
+ {
+ __real__ _M_value -= __d;
+ return *this;
+ }
+
+ complex<double>&
+ operator*=(double __d)
+ {
+ _M_value *= __d;
+ return *this;
+ }
+
+ complex<double>&
+ operator/=(double __d)
+ {
+ _M_value /= __d;
+ return *this;
+ }
+
+ // The compiler will synthesize this, efficiently.
+ // complex& operator=(const complex&);
+
+ template<typename _Tp>
+ complex<double>&
+ operator=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value = __z.real();
+ __imag__ _M_value = __z.imag();
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<double>&
+ operator+=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value += __z.real();
+ __imag__ _M_value += __z.imag();
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<double>&
+ operator-=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value -= __z.real();
+ __imag__ _M_value -= __z.imag();
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<double>&
+ operator*=(const complex<_Tp>& __z)
+ {
+ _ComplexT __t;
+ __real__ __t = __z.real();
+ __imag__ __t = __z.imag();
+ _M_value *= __t;
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<double>&
+ operator/=(const complex<_Tp>& __z)
+ {
+ _ComplexT __t;
+ __real__ __t = __z.real();
+ __imag__ __t = __z.imag();
+ _M_value /= __t;
+ return *this;
+ }
+
+ const _ComplexT& __rep() const { return _M_value; }
+
+ private:
+ _ComplexT _M_value;
+ };
+
+ // 26.2.3 complex specializations
+ // complex<long double> specialization
+ template<>
+ struct complex<long double>
+ {
+ typedef long double value_type;
+ typedef __complex__ long double _ComplexT;
+
+ complex(_ComplexT __z) : _M_value(__z) { }
+
+ complex(long double __r = 0.0L, long double __i = 0.0L)
+ {
+ __real__ _M_value = __r;
+ __imag__ _M_value = __i;
+ }
+
+ complex(const complex<float>& __z)
+ : _M_value(__z.__rep()) { }
+
+ complex(const complex<double>& __z)
+ : _M_value(__z.__rep()) { }
+
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+ // _GLIBCXX_RESOLVE_LIB_DEFECTS
+ // DR 387. std::complex over-encapsulated.
+ long double real() const
+ { return __real__ _M_value; }
+
+ 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.
+ void real(long double __val)
+ { __real__ _M_value = __val; }
+
+ void imag(long double __val)
+ { __imag__ _M_value = __val; }
+
+ complex<long double>&
+ operator=(long double __r)
+ {
+ __real__ _M_value = __r;
+ __imag__ _M_value = 0.0L;
+ return *this;
+ }
+
+ complex<long double>&
+ operator+=(long double __r)
+ {
+ __real__ _M_value += __r;
+ return *this;
+ }
+
+ complex<long double>&
+ operator-=(long double __r)
+ {
+ __real__ _M_value -= __r;
+ return *this;
+ }
+
+ complex<long double>&
+ operator*=(long double __r)
+ {
+ _M_value *= __r;
+ return *this;
+ }
+
+ complex<long double>&
+ operator/=(long double __r)
+ {
+ _M_value /= __r;
+ return *this;
+ }
+
+ // The compiler knows how to do this efficiently
+ // complex& operator=(const complex&);
+
+ template<typename _Tp>
+ complex<long double>&
+ operator=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value = __z.real();
+ __imag__ _M_value = __z.imag();
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<long double>&
+ operator+=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value += __z.real();
+ __imag__ _M_value += __z.imag();
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<long double>&
+ operator-=(const complex<_Tp>& __z)
+ {
+ __real__ _M_value -= __z.real();
+ __imag__ _M_value -= __z.imag();
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<long double>&
+ operator*=(const complex<_Tp>& __z)
+ {
+ _ComplexT __t;
+ __real__ __t = __z.real();
+ __imag__ __t = __z.imag();
+ _M_value *= __t;
+ return *this;
+ }
+
+ template<typename _Tp>
+ complex<long double>&
+ operator/=(const complex<_Tp>& __z)
+ {
+ _ComplexT __t;
+ __real__ __t = __z.real();
+ __imag__ __t = __z.imag();
+ _M_value /= __t;
+ return *this;
+ }
+
+ const _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
+ complex<float>::complex(const complex<double>& __z)
+ : _M_value(__z.__rep()) { }
+
+ inline
+ complex<float>::complex(const complex<long double>& __z)
+ : _M_value(__z.__rep()) { }
+
+ inline
+ 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
+
+_GLIBCXX_BEGIN_NAMESPACE(__gnu_cxx)
+
+ // 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
+
+#ifdef __GXX_EXPERIMENTAL_CXX0X__
+# if defined(_GLIBCXX_INCLUDE_AS_TR1)
+# error C++0x header cannot be included from TR1 header
+# endif
+# if defined(_GLIBCXX_INCLUDE_AS_CXX0X)
+# include <tr1_impl/complex>
+# else
+# define _GLIBCXX_INCLUDE_AS_CXX0X
+# define _GLIBCXX_BEGIN_NAMESPACE_TR1
+# define _GLIBCXX_END_NAMESPACE_TR1
+# define _GLIBCXX_TR1
+# include <tr1_impl/complex>
+# undef _GLIBCXX_TR1
+# undef _GLIBCXX_END_NAMESPACE_TR1
+# undef _GLIBCXX_BEGIN_NAMESPACE_TR1
+# undef _GLIBCXX_INCLUDE_AS_CXX0X
+# endif
+
+_GLIBCXX_BEGIN_NAMESPACE(std)
+
+ // Forward declarations.
+ // DR 781.
+ template<typename _Tp> std::complex<_Tp> proj(const std::complex<_Tp>&);
+
+ template<typename _Tp>
+ std::complex<_Tp>
+ __complex_proj(const std::complex<_Tp>& __z)
+ {
+ const _Tp __den = (__z.real() * __z.real()
+ + __z.imag() * __z.imag() + _Tp(1.0));
+
+ return std::complex<_Tp>((_Tp(2.0) * __z.real()) / __den,
+ (_Tp(2.0) * __z.imag()) / __den);
+ }
+
+#if _GLIBCXX_USE_C99_COMPLEX
+ inline __complex__ float
+ __complex_proj(__complex__ float __z)
+ { return __builtin_cprojf(__z); }
+
+ inline __complex__ double
+ __complex_proj(__complex__ double __z)
+ { return __builtin_cproj(__z); }
+
+ inline __complex__ long double
+ __complex_proj(const __complex__ long double& __z)
+ { return __builtin_cprojl(__z); }
+
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ proj(const std::complex<_Tp>& __z)
+ { return __complex_proj(__z.__rep()); }
+#else
+ template<typename _Tp>
+ inline std::complex<_Tp>
+ proj(const std::complex<_Tp>& __z)
+ { return __complex_proj(__z); }
+#endif
+
+ 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));
+ }
+
+_GLIBCXX_END_NAMESPACE
+
+#endif
+
+#endif /* _GLIBCXX_COMPLEX */
projects / msp430-gcc.git / blobdiff