Symbolic Array Dataflow Analysis for Array Privatization and Program Parallelization

Array dataflow information plays an important role for successful automatic parallelization of Fortran programs. This paper proposes a powerful symbolic array dataflow analysis to support array privatization and loop parallelization for programs with arbitrary control flow graphs and acyclic call graphs. Our scheme summarizes array access information using guarded array regions and propagates such regions over a Hierarchical Supergraph (HSG). The use of guards allows us to use the information in IF conditions to sharpen the array dataflow analysis and thereby to handle difficult cases which elude other existing techniques. The guarded array regions retain the simplicity of set operations for regular array regions in common cases, and they enhance regular array regions in complicated cases by using guards to handle complex symbolic expressions and array shapes. Scalar values that appear in array subscripts and loop limits are substituted on the fly during the array information propagation, which disambiguates the symbolic values precisely for set operations. We present efficient algorithms that implement our scheme. Initial experiments of applying our analysis to Perfect Benchmarks show promising results of improved array privatization.