Published in : in Special Issue of {em Parallel Processing Letters} on "parallelization Techniques for Uniform Algorithms", Transformation of Nested Loops with modulo Indexing to Aane Recurrences

For multi-dimensional (M-D) signal and data processing systems , transformation of algorithmic speciications is a major instrument both in code optimization and code generation for parallelizing compilers and in control ow optimization as a pre-processor for architecture synthesis. State-of-the-art transformation techniques are limited to aane index expressions. This is however not suucient for many important applications in image , speech and numerical processing. In this paper, a novel transformation method is introduced, oriented to the subclass of algorithm speciications that contains modulo expressions of aane functions to index M-D signals. The method employs extensively the concept of Hermite normal form. The transformation method can be carried out in polynomial time, applying only integer arithmetic.