complex

mingw32.rar

    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
  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(); }

  template<typename _Tp>
    inline _Tp
    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);
    }

  template<typename _Tp>
    inline _Tp
    arg(const complex<_Tp>& __z)
    { return atan2(__z.imag(), __z.real()); }

  // 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>::_M_type && !_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
  template<typename _Tp>
    inline complex<_Tp>
    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));
    }

  template<typename _Tp>
    inline complex<_Tp>
    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));
    }

  template<typename _Tp>
    inline complex<_Tp>
    exp(const complex<_Tp>& __z)
    { return std::polar(exp(__z.real()), __z.imag()); }

  template<typename _Tp>
    inline complex<_Tp>
    log(const complex<_Tp>& __z)
    { return complex<_Tp>(log(std::abs(__z)), std::arg(__z)); }

  template<typename _Tp>
    inline complex<_Tp>
    log10(const complex<_Tp>& __z)
    { return std::log(__z) / log(_Tp(10.0)); }

  template<typename _Tp>
    inline complex<_Tp>
    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)); 
    }

  template<typename _Tp>
    inline complex<_Tp>
    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));
    }

  template<typename _Tp>
    complex<_Tp>
    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);
        }
    }

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

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

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

  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, _Tp()), __y);
    }

  // 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 _GLIBCXX_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& real() const;
    float& imag();
    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()
  { return __real__ _M_value; }

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

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

  inline const 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;