High-speed reciprocal approximations

Abstract

This paper presents a high-speed algorithm for computing reciprocal approximations. This algorithm uses two parallel table lookups and an addition to obtain an initial approximation to the reciprocal. This is followed by a modified Newton-Raphson iteration, consisting of one multiply-complement and one multiply-add operation to obtain a more accurate reciprocal approximation. The initial approximation and Newton-Raphson iteration use specialized hardware to reduce the area requirements. Application of this algorithm is illustrated through the design of a reciprocal approximation unit that has a latency of three cycles and a peak throughput of one result per cycle for operands in the IEEE single precision format.