Global Value Numbering: A Precise and Efficient Algorithm

Global Value Numbering (GVN) is an important static analysis to detect equivalent expressions in a program. We present an iterative data-flow analysis GVN algorithm in SSA for the purpose of detecting total redundancies. The central challenge is defining a join operation to detect equivalences at a join point in polynomial time such that later occurrences of redundant expressions could be detected. For this purpose, we introduce the novel concept of value $\phi$-function. We claim the algorithm is precise and takes only polynomial time.