Eigenvectors-based parallelisation of nested loops with affine dependences

Abstract This paper presents a method for parallelising nested loops with affine dependences. The data dependences of a program are represented exactly using a dependence matrix rather than an imprecise dependence abstraction. By a careful analysis of the eigenvectors and eigenvalues of the dependence matrix, we detect the parallelism inherent in the program, partition the iteration space of the program into sequential and parallel regions and generate parallel code to execute these regions. For a class of programs considered in the paper, the proposed method can expose more coarse-grain and fine-grain parallelism than a hyperplane-based loop transformation.