Adaptive Booth Algorithm for Three-integers Multiplication for Reconfigurable Mesh

Yosi Ben Asher, Esti Stein

Research output: Contribution to journalArticlepeer-review

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 + logn + 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 √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.

Original languageEnglish
Article number1550009
JournalJournal of Interconnection Networks
Volume16
Issue number1
DOIs
StatePublished - 1 Mar 2016

Bibliographical note

Publisher Copyright:
© 2016 World Scientific Publishing Company.

Keywords

  • Reconfigurable mesh
  • booth multiplication
  • cartesian addition
  • extended summing

ASJC Scopus subject areas

  • Computer Networks and Communications

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