std_complex.h

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	      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
  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(); }

  // 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 magintude 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): Reurns the natural complex logaritm 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>
    inline complex<_Tp>
    pow(const complex<_Tp>& __z, int __n)
    { return std::__pow_helper(__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()),