Parallel Tiled Code for Computing General Linear Recurrence Equations

In this article, we present a technique that allows us to generate parallel tiled code to calculate general linear recursion equations (GLRE). That code deals with multidimensional data and it is computing-intensive. We demonstrate that data dependencies available in an original code computing GLREs do not allow us to generate any parallel code because there is only one solution to the time partition constraints built for that program. We show how to transform the original code to another one that exposes dependencies such that there are two linear distinct solutions to the time partition restrictions derived from these dependencies. This allows us to generate parallel 2D tiled code computing GLREs. The wavefront technique is used to achieve parallelism, and the generated code conforms to the OpenMP C/C++ standard. The experiments that we conducted with the resulting parallel 2D tiled code show that this code is much more efficient than the original serial code computing GLREs. Code performance improvement is achieved by allowing parallelism and better locality of the target code.