C-SSAPRE: Eliminating redundancy over copies

Partial Redundancy Elimination (PRE) is an optimization that prevents, where possible, the re-computation of an expression along some paths in a program. PRE is general enough to automatically implement loop-invariant code hoisting and global common sub-expression elimination. PRE appears to be especially beneficial for functional programs, where the class of expressions that may be moved is much richer: in addition to arithmetic and memory loads, we may also move and coalesce projections from tuples, calls to total functions, and even allocations of persistent values. The SSAPRE [5, 7] algorithm implements Partial Redundancy Elimination for programs in a static single assignment (SSA) intermediate representation (IR). However, the algorithms makes several assumptions about the intermediate representation that do not hold in all cases. In particular, they do not hold for the SSA IR of MLton [2], a high performance whole-program compiler for Standard ML [8]. We introduce a new PRE algorithm, CSSAPRE, which finds PRE optimization across copies, detecting redundencies not possible with the original SSAPRE algorithm. Our algorithm can be applied directly to MLton’s IR, which lacks explicit copies. We begin by describing the MLton SSA IR and its differences from what we will call “standard” SSA, as given by Cytron et al. [6]. This provides a concrete framework for our discussion of our generalization of the SSAPRE algorithm. We then provide detailed pseudocode for the pre-pass that we use before invoking a modified version of SSAPRE. Finally, we discuss our conclusions, important open questions, and potential ideas for future work. An appendix gives an improved pre-pass algorithm.