An Optimal and Practical Approach to Single Constant Multiplication

Author

Thong, Jason ; Nicolici, Nicola

Author_Institution

Dept. of Electr. & Comput. Eng., McMaster Univ., Hamilton, ON, Canada

Volume

30

Issue

9

fYear

2011

Firstpage

1373

Lastpage

1386

Abstract

We propose an exact solution to the single constant multiplication (SCM) problem. Existing optimal algorithms are limited to constants of up to 19 bits. Our algorithm requires less than 10 s on average to find a solution for a 32 bit constant. Optimality is guaranteed via an exhaustive search. We analyze two common SCM frameworks and the corresponding search strategies that each framework facilitates. Combining the strengths of both frameworks, we obtain highly aggressive pruning. The various strategies used in our algorithm and their underlying intuition are discussed extensively in this paper.

Keywords

digital filters; digital signal processing chips; multiplying circuits; query formulation; SCM framework; aggressive pruning; optimal algorithm; search strategy; single constant multiplication; Adders; Algorithm design and analysis; Digital signal processing; Hardware; Heuristic algorithms; Redundancy; Search problems; Common subexpression elimination; directed acyclic graphs; optimal algorithm; single constant multiplication;

fLanguage

English

Journal_Title

Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0278-0070

Type

jour

DOI

10.1109/TCAD.2011.2153853

Filename

5989990