Multiplierless multiple constant multiplication

Abstract

A variable can be multiplied by a given set of fixed-point constants using a multiplier block that consists exclusively of additions, subtractions, and shifts. The generation of a multiplier block from the set of constants is known as the multiple constant multiplication (MCM) problem. Finding the optimal solution, namely, the one with the fewest number of additions and subtractions, is known to be NP-complete. We propose a new algorithm for the MCM problem, which produces solutions that require up to 20% less additions and subtractions than the best previously known algorithm. At the same time our algorithm, in contrast to the closest competing algorithm, is not limited by the constant bitwidths. We present our algorithm using a unifying formal framework for the best, graph-based MCM algorithms and provide a detailed runtime analysis and experimental evaluation. We show that our algorithm can handle problem sizes as large as 100 32-bit constants in a time acceptable for most applications. The implementation of the new algorithm is available at www.spiral.net.