Adaptive Booth Algorithm for Three-Integers Multiplication for Reconfigurable Mesh

Abstract

This paper presents a three-integers multiplication algorithm R = A * X * Y for Reconfigurable Mesh (RM). It is based on a three-integer multiplication algorithm for faster FPGA implementations. We show that multiplying three integers of n bits can be performed on a 3D RM of size (3n+log n + 1)×(2√n+1+3) × √n+1 using 44+18.log log MNO steps, where MNO is a bound which is related to the number of sequences of '1's in the multiplied numbers. The value of MNO is bounded by n but experimentally we show that on the average it is sqrt n. Two algorithms for solving multiplication on a RM exists and their techniques are asymptotically better time wise, O(1) and O(log*n), but they suffer from large hidden constants and slow data insertion time O(√n) respectively. The proposed algorithm is relatively simple and faster on the average (via sampling input values) then the previous two algorithms thus contributes in making the RM a practical and feasible model. Our experiments show a significant improvement in the expected number of elementary operations for the proposed algorithm.