Algebraic techniques to enhance common sub-expression elimination for polynomial system synthesis

Common sub-expression elimination (CSE) serves as a useful optimization technique in the synthesis of arithmetic datapaths described at RTL. However, CSE has a limited potential for optimization when many common sub-expressions are not exposed. Given a suitable transformation of the polynomial system representation, which exposes many common sub-expressions, subsequent CSE can offer a higher degree of optimization. The objective of this paper is to develop algebraic techniques that perform such a transformation, and present a methodology to integrate it with CSE to further enhance the potential for optimization. In our experiments, we show that this integrated approach outperforms conventional methods in deriving area-efficient hardware implementations of polynomial systems.