For multi-dimensional (M-D) signal and data processing systems, transformation of algorithmic specifications is a major instrument both in code optimization and code generation for parallelizing compilers and in control flow optimization as a preprocessor for architecture synthesis. State-of-the-art transformation techniques are limited to affine index expressions. This is however not sufficient 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 specifications that contains modulo expressions of affine 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.
Combining Retiming and Scheduling Techniques for Loop Parallelization and Loop Tiling