Detection of redundant expressions: A complete and polynomial-time algorithm in SSA

Abstract

Detection of redundant expressions in a program based on values is a well researched problem done with a view to eliminate the redundancies so as to improve the run-time efficiency of the program. The problem entails the detection of equivalent expressions in a program. Here we present an iterative data-flow analysis algorithm to detect equivalent expressions in SSA for the purpose of detection of redundancies. The central challenge in this static analysis is to define a “join” operation to detect all equivalences at a join point such that any later occurrences of redundant expressions are detected in polynomial time. We achieve this by introducing the notion of value φ-function. We claim the algorithm is complete and takes only polynomial time. We implemented the algorithm in LLVM and demonstrated its performance.