Rapid and precise interpolation of curves has been a key issue in development of computer numerical control(CNC) systems. With the development of firmware, it is a new attempt to perform the interpolation by means of firmware. This paper presents a method to develop a rapid and precise interpolator that can produce a smooth interpolating curve. An algorithm is first shown to construct a smooth interpolating curve and a way is put forward to calculate the constructed curve with firmware; then details are introduced to design and implement the firmware units that perform rapid and precise calculations. Factors related with the computational process control and precision control are also investigated and made clear in the paper.