Lazy Demand-driven Partial Redundancy Elimination

Abstract

Partial redundancy elimination (PRE) is a code optimization algorithm that simultaneously performs common sub-expression elimination and loop-invariant code motion. Traditional PREs analyze the entire program and eliminate redundancies. By contrast, demand-driven PRE (DDPRRE) is proposed as an algorithm to analyze only a part of the program to determine whether each expression is redundant by query propagation. The previous DDPRE reduces the analysis time because it limits the analysis range; however, it is known that redundancy may not be eliminated when the nodes in the loop are revisited. We propose a novel DDPRE, named lazy demand-driven PRE (LDPRE), which eliminates redundancy by delaying the decision of whether the analyzing expression is redundant or not when a node in a loop is revisited and redundancy cannot be analyzed. LDPRE uses a semi-lattice as the answer space during the query propagation. The semi-lattice includes not only true/false implying that the queried expression is redundant or not, but also ⊤ for undecidability. While maintaining the analytical efficiency characteristic of demand-driven analysis, our algorithm eliminates redundancy that previous DDPRE could not eliminate by determining the answer using semi-lattice.