## 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 language | English |
---|---|

Title of host publication | Proceedings - IEEE 28th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2014 |

Publisher | IEEE Computer Society |

Pages | 211-219 |

Number of pages | 9 |

ISBN (Electronic) | 9780769552088 |

DOIs | |

State | Published - 27 Nov 2014 |

Externally published | Yes |

Event | 28th IEEE International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2014 - Phoenix, United States Duration: 19 May 2014 → 23 May 2014 |

### Publication series

Name | Proceedings - IEEE 28th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2014 |
---|

### Conference

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

Country/Territory | United States |

City | Phoenix |

Period | 19/05/14 → 23/05/14 |

### Bibliographical note

Publisher Copyright:© 2014 IEEE.

## Keywords

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

## ASJC Scopus subject areas

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