An optimized Mitchell-based logarithmic conversion circuit

Abstract

The logarithmic conversion method is a heated topic in computer arithmetic. Among the three mainstream conversion method categories for digital integrated circuits, the polynomial approximation method was proposed by Mitchell in 1962. Further, The Range Mapping method based on Mitchell's method compresses the approximation range for a smaller gradient variation. Hence, this method achieves an outstanding accuracy performance, while its circuit architecture complexity needs to be optimized. In this work, an optimized method of Range Mapping by eliminating the mapping stage, called ReMap, is proposed, implemented and evaluated in STM90nm CMOS process. First, two experimental routes are developed to verify the basic design ideas of directly remapping and maximum fitting respectively. From their simulation and synthesis results, an advanced version is then developed. As a result, the final ReMap comes with a comparable maximum error with Range Mapping, while its overall accuracy and error distribution are improved. For the synthesized circuit, delay and power dissipation are reduced by 8.4% and 13.1% respectively. This dissertation reviews the logarithmic conversion methods for integrated circuits, describes the proposed new methods, presents and evaluates the performances.