The mathematical model for the parallelization, or ``space-time mapping'', of loop nests is the polyhedron model. The presence of while loops in the nest complicates matters because the parallelized loop nest does not correspond to a polyhedron but instead to a subset that resembles a (multi-dimensional) comb. This comb can take on shapes that make the precise enumeration of its points by any parallel target loop nest impossible. We describe how to augment the target loop code to scan a finite superset of the comb and restrict execution of the loop body to the points of the comb.
Ulrike Peiker, Martin Griebl