The application of redundant encoding in iterative implementation of division and square root

The purpose of this paper is to discuss the speed improvement in division and square root computation with small area penalty. The digit recurrence SRT algorithm and functional iteration Newton-Raphson algorithm are generally used in modern processor design. To reduce the latency of each iteration, the redundant number is introduced to present an intermediate value in iterative computation. The carry save number is applied in the SRT algorithm and Newton-Raphson algorithm to avoid the long carry propagation delay in iteration addition. Borrow save numbers are applied in the initial approximation lookup table for the same purpose. Redundant binary Booth recoding is introduced to facilitate the conversion of the intermediate redundant number in Booth multipliers. The techniques presented facilitate improved division and square root calculation, which is significant for overall system performance.