Loop parallelization: revisiting framework of unimodular transformations

The paper extends the framework of linear loop transformations adding a new nonlinear step at the transformation process. The current framework of linear loop transformation cannot identify a significant fraction of parallelism. For this reason, we present a method to complement it with some basic transformations in order to extract the maximum loop parallelism in perfect nested loops with tight recurrences in the dependence graph. The parallelizing algorithm solves the important problem of deciding the set of transformations to apply in order to maximize the degree of parallelism, the number of parallel loops within a loop nest, and presents a way of generating efficient transformed code that exploits coarse grain parallelism on a MIMD system.