A simple algorithm for the generation of efficient loop structures

Generating code to enumerate the integer points of a polyhedron is a key problem of the parallelizing compiler technology. For efficiency reasons we plant to obtain loop bounds of the generated code that are as simple as possible and we would like to avoid executing iterations of outer loops for which no iterations of inner loops are executed. This paper describes a simple algorithm to build an adequate representation of the domain to enumerate, the Hierarchical Domain Descriptor (HDD). Starting from the HDD, generating such efficient loop structures is straightforward. In some particular but frequently occurring cases the HDD may also be used to count in a symbolic way the number of integer points contained in the domain.