Precise dependence test for scalars within nested loops

Exact direction and distance vectors are essential for detecting hierarchical parallelism and examining legality of loop transformation for a multiple level loop nest. Much of this work has been concentrated on array references. Little has been done to address the problems of finding precise dependences between scalar references, except to use extended SSA form with factored use-def links. In this paper, we present a technique for calculating precise direction and distance vectors for scalar references within nested loops without using any forms of SSA. To do this, we use conventional use-def links in combination with joint dominator and joint postdominator relationships, which are extended from dominator and postdominator respectively in standard data flow analysis. The precision of dependence information gathered by our algorithm can not be achieved by traditional analysis of dominator or reaching definitions.