Static Single Assignment Form for Explicitly Parallel Programs: Theory and Practice

To sensibly reason about parallel programs, a coherent intermediate form needs to be developed. We describe and prove correctness and safety of algorithms to convert programs that use the Parallel Computing Forum Parallel Sections construct into a parallel Static Single Assignment (SSA) form. We deene what the concept of dominator and dominance frontier mean in parallel programs. How to extend the SSA form to handle parallel updates and still preserve the SSA properties is described by introducing a new parallel merge operator, the-function. The minimal placement points for-functions are identiied and proved correct by introducing the meet of two nodes in a Parallel Precedence Graph (PPG), which is the dual concept of join in a sequential control ow graph (CFG). The resulting intermediate form allows compilers to apply classical scalar optimization algorithms to explicitly parallel programs. We also discuss issues encountered while implementing these constructs in Nascent, our restructuring research compiler.