Initial checkin of GCC 4.9.0 from trunk (r208799).

Change-Id: I48a3c08bb98542aa215912a75f03c0890e497dba

1 files changed, 1966 insertions, 0 deletions

diff --git a/gcc-4.9/libstdc++-v3/include/std/complex b/gcc-4.9/libstdc++-v3/include/std/complex
new file mode 100644
index 000000000..34fa1ddbc
--- /dev/null
+++ b/gcc-4.9/libstdc++-v3/include/std/complex
@@ -0,0 +1,1966 @@
+// The template and inlines for the -*- C++ -*- complex number classes.
+
+// Copyright (C) 1997-2014 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) { }
+
+      // Lets the compiler synthesize the copy constructor   
+      // complex (const complex<_Tp>&);
+      ///  Copy 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() { return _M_real; }
+
+      _GLIBCXX_ABI_TAG_CXX11
+      constexpr _Tp 
+      imag() { 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>&);
+
+      _GLIBCXX_USE_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
+  //     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.
+  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)
+    {
+#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;
+
+      _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.
+      void 
+      real(float __val) { __real__ _M_value = __val; }
+
+      void 
+      imag(float __val) { __imag__ _M_value = __val; }
+
+      complex&
+      operator=(float __f)
+      {
+	_M_value = __f;
+	return *this;
+      }
+
+      complex&
+      operator+=(float __f)
+      {
+	_M_value += __f;
+	return *this;
+      }
+
+      complex&
+      operator-=(float __f)
+      {
+	_M_value -= __f;
+	return *this;
+      }
+
+      complex&
+      operator*=(float __f)
+      {
+	_M_value *= __f;
+	return *this;
+      }
+
+      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.
+      // complex& operator=(const complex&);
+
+      template<typename _Tp>
+        complex&
+        operator=(const complex<_Tp>&  __z)
+	{
+	  __real__ _M_value = __z.real();
+	  __imag__ _M_value = __z.imag();
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+        operator+=(const complex<_Tp>& __z)
+	{
+	  __real__ _M_value += __z.real();
+	  __imag__ _M_value += __z.imag();
+	  return *this;
+	}
+
+      template<class _Tp>
+        complex&
+        operator-=(const complex<_Tp>& __z)
+	{
+	  __real__ _M_value -= __z.real();
+	  __imag__ _M_value -= __z.imag();
+	  return *this;
+	}
+
+      template<class _Tp>
+        complex&
+        operator*=(const complex<_Tp>& __z)
+	{
+	  _ComplexT __t;
+	  __real__ __t = __z.real();
+	  __imag__ __t = __z.imag();
+	  _M_value *= __t;
+	  return *this;
+	}
+
+      template<class _Tp>
+        complex&
+        operator/=(const complex<_Tp>& __z)
+	{
+	  _ComplexT __t;
+	  __real__ __t = __z.real();
+	  __imag__ __t = __z.imag();
+	  _M_value /= __t;
+	  return *this;
+	}
+
+      _GLIBCXX_USE_CONSTEXPR _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;
+
+      _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.
+      void 
+      real(double __val) { __real__ _M_value = __val; }
+
+      void 
+      imag(double __val) { __imag__ _M_value = __val; }
+
+      complex&
+      operator=(double __d)
+      {
+	_M_value = __d;
+	return *this;
+      }
+
+      complex&
+      operator+=(double __d)
+      {
+	_M_value += __d;
+	return *this;
+      }
+	
+      complex&
+      operator-=(double __d)
+      {
+	_M_value -= __d;
+	return *this;
+      }
+
+      complex&
+      operator*=(double __d)
+      {
+	_M_value *= __d;
+	return *this;
+      }
+
+      complex&
+      operator/=(double __d)
+      {
+	_M_value /= __d;
+	return *this;
+      }
+
+      // The compiler will synthesize this, efficiently.
+      // complex& operator=(const complex&);
+
+      template<typename _Tp>
+        complex&
+        operator=(const complex<_Tp>& __z)
+	{
+	  __real__ _M_value = __z.real();
+	  __imag__ _M_value = __z.imag();
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+        operator+=(const complex<_Tp>& __z)
+	{
+	  __real__ _M_value += __z.real();
+	  __imag__ _M_value += __z.imag();
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+        operator-=(const complex<_Tp>& __z)
+	{
+	  __real__ _M_value -= __z.real();
+	  __imag__ _M_value -= __z.imag();
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+        operator*=(const complex<_Tp>& __z)
+	{
+	  _ComplexT __t;
+	  __real__ __t = __z.real();
+	  __imag__ __t = __z.imag();
+	  _M_value *= __t;
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+        operator/=(const complex<_Tp>& __z)
+	{
+	  _ComplexT __t;
+	  __real__ __t = __z.real();
+	  __imag__ __t = __z.imag();
+	  _M_value /= __t;
+	  return *this;
+	}
+
+      _GLIBCXX_USE_CONSTEXPR _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;
+
+      _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.
+      void 
+      real(long double __val) { __real__ _M_value = __val; }
+
+      void 
+      imag(long double __val) { __imag__ _M_value = __val; }
+
+      complex&
+      operator=(long double __r)
+      {
+	_M_value = __r;
+	return *this;
+      }
+
+      complex&
+      operator+=(long double __r)
+      {
+	_M_value += __r;
+	return *this;
+      }
+
+      complex&
+      operator-=(long double __r)
+      {
+	_M_value -= __r;
+	return *this;
+      }
+
+      complex&
+      operator*=(long double __r)
+      {
+	_M_value *= __r;
+	return *this;
+      }
+
+      complex&
+      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&
+        operator=(const complex<_Tp>& __z)
+	{
+	  __real__ _M_value = __z.real();
+	  __imag__ _M_value = __z.imag();
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+	operator+=(const complex<_Tp>& __z)
+	{
+	  __real__ _M_value += __z.real();
+	  __imag__ _M_value += __z.imag();
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+	operator-=(const complex<_Tp>& __z)
+	{
+	  __real__ _M_value -= __z.real();
+	  __imag__ _M_value -= __z.imag();
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+	operator*=(const complex<_Tp>& __z)
+	{
+	  _ComplexT __t;
+	  __real__ __t = __z.real();
+	  __imag__ __t = __z.imag();
+	  _M_value *= __t;
+	  return *this;
+	}
+
+      template<typename _Tp>
+        complex&
+	operator/=(const complex<_Tp>& __z)
+	{
+	  _ComplexT __t;
+	  __real__ __t = __z.real();
+	  __imag__ __t = __z.imag();
+	  _M_value /= __t;
+	  return *this;
+	}
+
+      _GLIBCXX_USE_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 (_GLIBCXX_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>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    imag(_Tp)
+    { return _Tp(); }
+
+  template<typename _Tp>
+    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>
+    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>&);
+
+  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
+
+  // DR 1137.
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    proj(_Tp __x)
+    { return __x; }
+
+  template<typename _Tp>
+    inline typename __gnu_cxx::__promote<_Tp>::__type
+    conj(_Tp __x)
+    { return __x; }
+
+#if __cplusplus > 201103L
+
+inline namespace literals {
+inline namespace complex_literals {
+
+  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)}; }
+
+} // inline namespace complex_literals
+} // inline namespace literals
+
+#endif // C++14
+
+_GLIBCXX_END_NAMESPACE_VERSION
+} // namespace
+
+#endif  // C++11
+
+#endif  /* _GLIBCXX_COMPLEX */