An efficient SSA-based algorithm for complete global value numbering

Abstract

Global value numbering (GVN) is an important static analysis technique both for optimizing compilers and program verification tools. Existing complete GVN algorithms discovering all Herbrand equivalences are all inefficient. One reason of this is the intrinsic exponential complexity of the problem, but in practice, since the exponential case is quite rare, the more important reason is the huge data structures annotated to every program point and slow abstract evaluations on them site by site. In this paper, we present an SSA-based algorithm for complete GVN, which uses just one global graph to represent all equivalences at different program points and performs fast abstract evaluations on it. This can be achieved because in SSA form, interferences among equivalence relations at different program points can be entirely resolved with dominance information. We implement the new algorithm in GCC. The average proportion of execution time of the new algorithm in the total compilation time is only 0.36%. To the best of our knowledge, this is the first practical complete GVN algorithm. © Springer-Verlag Berlin Heidelberg 2007.