Abstract
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.
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