Global Value Numbering: A Precise and Efficient Algorithm

TL;DR

This paper introduces a precise and efficient global value numbering algorithm in SSA form that detects all redundant expressions using a novel value φ-function, ensuring polynomial-time analysis.

Contribution

It presents a new iterative data-flow analysis algorithm with a novel join operation and value φ-function for detecting redundancies in SSA form.

Findings

Algorithm is both precise and polynomial-time.

Introduces the concept of value φ-function for equivalence detection.

Effectively detects total redundancies in static analysis.

Abstract

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.