This article presents a joint framework for quantization and Multiple Constant Multiplication (MCM) optimization, which yields a computationally efficient implementation of multiplierless multiplication in hardware and software. Frameworks of this nature have been developed in the context of Finite Impulse Response (FIR) filters, where frequency response specifications are used to drive the design. In this work, we look at a general case, considering as given a vector of ideal, real constants, which may come from any application and do not necessarily represent FIR filter coefficients. We first formulate a joint optimization problem for finding a fixed-point vector and a shift-add network that are optimal in terms of quantization error and MCM complexity. We then describe ways to finitize and prune the search space, leading to an efficient algorithm called JOINT SOLVE that solves the problem. Finally, via extensive randomized experiments, we show that our joint framework is notably more computationally efficient than a disjointed one, reducing the MCM cost by 15%-60% on moderate size problems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.