class Point {
private: 
  mutable bool is_polar_cached;
  mutable double r, a;          // Cached polar representation of point.

  double x, y;
  void do_polar_caching() const;

public:
  Point(double, double);
  Point();
  double getx () const;
  double gety () const;
  double getr () const;
  double geta () const;
  void move(double, double);
  double distance_to(Point) const;
};

std::ostream& operator<<(std::ostream&, const Point&);