Adaptive booth algorithm for three-integers multiplication for reconfigurable mesh

Esti Stein, Yosi Ben Asher

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-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+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.

Original languageAmerican English
Title of host publicationProceedings - IEEE 28th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2014
PublisherIEEE Computer Society
Pages211-219
Number of pages9
ISBN (Electronic)9780769552088
DOIs
StatePublished - 27 Nov 2014
Externally publishedYes
Event28th IEEE International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2014 - Phoenix, United States
Duration: 19 May 201423 May 2014

Publication series

NameProceedings - IEEE 28th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2014

Conference

Conference28th IEEE International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2014
Country/TerritoryUnited States
CityPhoenix
Period19/05/1423/05/14

Keywords

  • Booth multiplication
  • Cartesian addition
  • Extended summing
  • Reconfigurable mesh

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Hardware and Architecture
  • Software

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