Combined optimal and heuristic approaches for multiple constant multiplication

Abstract

We propose new optimal and heuristic approaches for solving the multiple constant multiplication (MCM) problem. Bounded depth first search (BDFS), our proposed optimal algorithm, is benchmarked on problem sizes that are impractical for the existing optimal method. We focus on MCM problems with few constants but on large bit widths. In this scenario, we outperform the existing heuristics in minimizing the number of adders. In addition, subject to a given quality of solution, our run time is faster. We reuse our heuristics for pruning within BDFS.