std_complex.h

gcc-you can use this code to learn something about gcc, and inquire further into linux,

          return complex<_Tp>(__t, __y < _Tp() ? -__t : __t);
        }
      else
        {
          _Tp __t = sqrt(2 * (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);
        }
    }

  template<typename _Tp>
    inline complex<_Tp>
    tan(const complex<_Tp>& __z)
    {
      return sin(__z) / cos(__z);
    }

  template<typename _Tp>
    inline complex<_Tp>
    tanh(const complex<_Tp>& __z)
    {
      return sinh(__z) / cosh(__z);
    }

  template<typename _Tp>
    inline complex<_Tp>
    pow(const complex<_Tp>& __z, int __n)
    {
      return __pow_helper(__z, __n);
    }

  template<typename _Tp>
    complex<_Tp>
    pow(const complex<_Tp>& __x, const _Tp& __y)
    {
      if (__x.imag() == _Tp())
        return pow(__x.real(), __y);

      complex<_Tp> __t = log(__x);
      return polar(exp(__y * __t.real()), __y * __t.imag());
    }

  template<typename _Tp>
    inline complex<_Tp>
    pow(const complex<_Tp>& __x, const complex<_Tp>& __y)
    {
      return __x == _Tp() ? _Tp() : exp(__y * log(__x));
    }

  template<typename _Tp>
    inline complex<_Tp>
    pow(const _Tp& __x, const complex<_Tp>& __y)
    {
      return __x == _Tp()
        ? _Tp()
        : polar(pow(__x, __y.real()), __y.imag() * log(__x));
    }

  // 26.2.3  complex specializations
  // complex<float> specialization
  template<> class complex<float>
  {
  public:
    typedef float value_type;
    
    complex(float = 0.0f, float = 0.0f);
#ifdef _GLIBCPP_BUGGY_COMPLEX
    complex(const complex& __z) : _M_value(__z._M_value) { }
#endif
    explicit complex(const complex<double>&);
    explicit complex(const complex<long double>&);

    float real() const;
    float imag() const;

    complex<float>& operator=(float);
    complex<float>& operator+=(float);
    complex<float>& operator-=(float);
    complex<float>& operator*=(float);
    complex<float>& operator/=(float);
        
    // Let's the compiler synthetize 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>&);
    template<typename _Tp>
      complex<float>& operator+=(const complex<_Tp>&);
    template<class _Tp>
      complex<float>& operator-=(const complex<_Tp>&);
    template<class _Tp>
      complex<float>& operator*=(const complex<_Tp>&);
    template<class _Tp>
      complex<float>&operator/=(const complex<_Tp>&);

  private:
    typedef __complex__ float _ComplexT;
    _ComplexT _M_value;

    complex(_ComplexT __z) : _M_value(__z) { }
        
    friend class complex<double>;
    friend class complex<long double>;
  };

  inline float
  complex<float>::real() const
  { return __real__ _M_value; }

  inline float
  complex<float>::imag() const
  { return __imag__ _M_value; }

  inline
  complex<float>::complex(float r, float i)
  {
    __real__ _M_value = r;
    __imag__ _M_value = i;
  }

  inline complex<float>&
  complex<float>::operator=(float __f)
  {
    __real__ _M_value = __f;
    __imag__ _M_value = 0.0f;
    return *this;
  }

  inline complex<float>&
  complex<float>::operator+=(float __f)
  {
    __real__ _M_value += __f;
    return *this;
  }

  inline complex<float>&
  complex<float>::operator-=(float __f)
  {
    __real__ _M_value -= __f;
    return *this;
  }

  inline complex<float>&
  complex<float>::operator*=(float __f)
  {
    _M_value *= __f;
    return *this;
  }

  inline complex<float>&
  complex<float>::operator/=(float __f)
  {
    _M_value /= __f;
    return *this;
  }

  template<typename _Tp>
  inline complex<float>&
  complex<float>::operator=(const complex<_Tp>& __z)
  {
    __real__ _M_value = __z.real();
    __imag__ _M_value = __z.imag();
    return *this;
  }

  template<typename _Tp>
  inline complex<float>&
  complex<float>::operator+=(const complex<_Tp>& __z)
  {
    __real__ _M_value += __z.real();
    __imag__ _M_value += __z.imag();
    return *this;
  }
    
  template<typename _Tp>
    inline complex<float>&
    complex<float>::operator-=(const complex<_Tp>& __z)
    {
     __real__ _M_value -= __z.real();
     __imag__ _M_value -= __z.imag();
     return *this;
    } 

  template<typename _Tp>
    inline complex<float>&
    complex<float>::operator*=(const complex<_Tp>& __z)
    {
      _ComplexT __t;
      __real__ __t = __z.real();
      __imag__ __t = __z.imag();
      _M_value *= __t;
      return *this;
    }

  template<typename _Tp>
    inline complex<float>&
    complex<float>::operator/=(const complex<_Tp>& __z)
    {
      _ComplexT __t;
      __real__ __t = __z.real();
      __imag__ __t = __z.imag();
      _M_value /= __t;
      return *this;
    }

  // 26.2.3  complex specializations
  // complex<double> specialization
  template<> class complex<double>
  {
  public:
    typedef double value_type;

    complex(double  =0.0, double =0.0);
#ifdef _GLIBCPP_BUGGY_COMPLEX
    complex(const complex& __z) : _M_value(__z._M_value) { }
#endif
    complex(const complex<float>&);
    explicit complex(const complex<long double>&);
        
    double real() const;
    double imag() const;
        
    complex<double>& operator=(double);
    complex<double>& operator+=(double);
    complex<double>& operator-=(double);
    complex<double>& operator*=(double);
    complex<double>& operator/=(double);

    // The compiler will synthetize this, efficiently.
    // complex& operator= (const complex&);
    template<typename _Tp>
      complex<double>& operator=(const complex<_Tp>&);
    template<typename _Tp>
      complex<double>& operator+=(const complex<_Tp>&);
    template<typename _Tp>
      complex<double>& operator-=(const complex<_Tp>&);
    template<typename _Tp>
      complex<double>& operator*=(const complex<_Tp>&);
    template<typename _Tp>
      complex<double>& operator/=(const complex<_Tp>&);

  private:
    typedef __complex__ double _ComplexT;
    _ComplexT _M_value;

    complex(_ComplexT __z) : _M_value(__z) { }
        
    friend class complex<float>;
    friend class complex<long double>;
  };

  inline double
  complex<double>::real() const
  { return __real__ _M_value; }

  inline double
  complex<double>::imag() const
  { return __imag__ _M_value; }

  inline
  complex<double>::complex(double __r, double __i)
  {
    __real__ _M_value = __r;
    __imag__ _M_value = __i;
  }

  inline complex<double>&
  complex<double>::operator=(double __d)
  {
    __real__ _M_value = __d;
    __imag__ _M_value = 0.0;
    return *this;
  }

  inline complex<double>&
  complex<double>::operator+=(double __d)
  {
    __real__ _M_value += __d;
    return *this;
  }

  inline complex<double>&
  complex<double>::operator-=(double __d)
  {
    __real__ _M_value -= __d;
    return *this;
  }

  inline complex<double>&
  complex<double>::operator*=(double __d)
  {
    _M_value *= __d;
    return *this;
  }

  inline complex<double>&
  complex<double>::operator/=(double __d)
  {
    _M_value /= __d;
    return *this;
  }

  template<typename _Tp>
    inline complex<double>&
    complex<double>::operator=(const complex<_Tp>& __z)
    {
      __real__ _M_value = __z.real();
      __imag__ _M_value = __z.imag();
      return *this;
    }
    
  template<typename _Tp>
    inline complex<double>&
    complex<double>::operator+=(const complex<_Tp>& __z)
    {
      __real__ _M_value += __z.real();
      __imag__ _M_value += __z.imag();
      return *this;
    }

  template<typename _Tp>
    inline complex<double>&
    complex<double>::operator-=(const complex<_Tp>& __z)
    {
      __real__ _M_value -= __z.real();
      __imag__ _M_value -= __z.imag();
      return *this;
    }

  template<typename _Tp>
    inline complex<double>&
    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>
    inline complex<double>&
    complex<double>::operator/=(const complex<_Tp>& __z)
    {
      _ComplexT __t;
      __real__ __t = __z.real();
      __imag__ __t = __z.imag();
      _M_value /= __t;
      return *this;
    }

  // 26.2.3  complex specializations
  // complex<long double> specialization
  template<> class complex<long double>
  {
  public:
    typedef long double value_type;

    complex(long double = 0.0L, long double = 0.0L);
#ifdef _GLIBCPP_BUGGY_COMPLEX
    complex(const complex& __z) : _M_value(__z._M_value) { }
#endif
    complex(const complex<float>&);
    complex(const complex<double>&);

    long double real() const;
    long double imag() const;

    complex<long double>& operator= (long double);
    complex<long double>& operator+= (long double);
    complex<long double>& operator-= (long double);
    complex<long double>& operator*= (long double);
    complex<long double>& operator/= (long double);

    // The compiler knows how to do this efficiently
    // complex& operator= (const complex&);
    template<typename _Tp>
      complex<long double>& operator=(const complex<_Tp>&);
    template<typename _Tp>
      complex<long double>& operator+=(const complex<_Tp>&);
    template<typename _Tp>
      complex<long double>& operator-=(const complex<_Tp>&);
    template<typename _Tp>
      complex<long double>& operator*=(const complex<_Tp>&);
    template<typename _Tp>
      complex<long double>& operator/=(const complex<_Tp>&);

  private:
    typedef __complex__ long double _ComplexT;
    _ComplexT _M_value;

    complex(_ComplexT __z) : _M_value(__z) { }

    friend class complex<float>;
    friend class complex<double>;
  };

  inline
  complex<long double>::complex(long double __r, long double __i)
  {
    __real__ _M_value = __r;
    __imag__ _M_value = __i;
  }

  inline long double
  complex<long double>::real() const
  { return __real__ _M_value; }

  inline long double
  complex<long double>::imag() const
  { return __imag__ _M_value; }

  inline complex<long double>&   
  complex<long double>::operator=(long double __r)
  {
    __real__ _M_value = __r;
    __imag__ _M_value = 0.0L;
    return *this;
  }

  inline complex<long double>&
  complex<long double>::operator+=(long double __r)
  {
    __real__ _M_value += __r;
    return *this;
  }

  inline complex<long double>&
  complex<long double>::operator-=(long double __r)
  {
    __real__ _M_value -= __r;
    return *this;
  }

  inline complex<long double>&
  complex<long double>::operator*=(long double __r)
  {
    _M_value *= __r;
    return *this;
  }

  inline complex<long double>&
  complex<long double>::operator/=(long double __r)
  {
    _M_value /= __r;
    return *this;
  }

  template<typename _Tp>
    inline complex<long double>&
    complex<long double>::operator=(const complex<_Tp>& __z)
    {
      __real__ _M_value = __z.real();
      __imag__ _M_value = __z.imag();
      return *this;
    }

  template<typename _Tp>
    inline complex<long double>&
    complex<long double>::operator+=(const complex<_Tp>& __z)
    {
      __real__ _M_value += __z.real();
      __imag__ _M_value += __z.imag();
      return *this;
    }

  template<typename _Tp>
    inline complex<long double>&
    complex<long double>::operator-=(const complex<_Tp>& __z)
    {
      __real__ _M_value -= __z.real();
      __imag__ _M_value -= __z.imag();
      return *this;
    }
    
  template<typename _Tp>
    inline complex<long double>&
    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>
    inline complex<long double>&
    complex<long double>::operator/=(const complex<_Tp>& __z)
    {
      _ComplexT __t;
      __real__ __t = __z.real();
      __imag__ __t = __z.imag();
      _M_value /= __t;
      return *this;
    }

  // These bits have to be at the end of this file, so that the
  // specializations have all been defined.
  // ??? No, they have to be there because of compiler limitation at
  // inlining.  It suffices that class specializations be defined.
  inline
  complex<float>::complex(const complex<double>& __z)
  : _M_value(_ComplexT(__z._M_value)) { }

  inline
  complex<float>::complex(const complex<long double>& __z)
  : _M_value(_ComplexT(__z._M_value)) { }

  inline
  complex<double>::complex(const complex<float>& __z) 
  : _M_value(_ComplexT(__z._M_value)) { }

  inline
  complex<double>::complex(const complex<long double>& __z)
  {
    __real__ _M_value = __z.real();
    __imag__ _M_value = __z.imag();
  }

  inline
  complex<long double>::complex(const complex<float>& __z)
  : _M_value(_ComplexT(__z._M_value)) { }

  inline
  complex<long double>::complex(const complex<double>& __z)
  : _M_value(_ComplexT(__z._M_value)) { }
} // namespace std

#endif	/* _CPP_COMPLEX */