Incremental computation of static single assignment form

Abstract

Static single assignment (SSA) form is an intermediate representation that is well suited for solving many data flow optimization problems. However, since the standard algorithm for building SSA form is exhaustive, maintaining correct SSA form throughout a multi-pass compilation process can be expensive. In this paper, we present incremental algorithms for restoring correct SSA form after program transformations. First, we specify incremental SSA algorithms for insertion and deletion of a use/definition of a variable, and for a large class of updates on intervals. We characterize several cases for which the cost of these algorithms will be proportional to the size of the transformed region and hence potentially much smaller than the cost of the exhaustive algorithm. Secondly, we specify customized SSA-update algorithms for a set of common loop transformations. These algorithms are highly efficient: the cost depends at worst on the size of the transformed code, and in many cases the cost is independent of the loop body size and depends only on the number of loops.