Theory of linear and integer programming
Theory of linear and integer programming
Improving locality and parallelism in nested loops
Improving locality and parallelism in nested loops
Some efficient solutions to the affine scheduling problem: I. One-dimensional time
International Journal of Parallel Programming
Automating non-unimodular loop transformations for massive parallelism
Parallel Computing
Beyond unimodular transformations
The Journal of Supercomputing
The Banerjee-Wolfe and GCD tests on exact data dependence information
Journal of Parallel and Distributed Computing
Minimizing communication while preserving parallelism
ICS '96 Proceedings of the 10th international conference on Supercomputing
Static and Dynamic Evaluation of Data Dependence Analysis Techniques
IEEE Transactions on Parallel and Distributed Systems
Unimodular transformations of non-perfectly nested loops
Parallel Computing
Maximizing parallelism and minimizing synchronization with affine partitions
Parallel Computing - Special issues on languages and compilers for parallel computers
Loop Parallelization
Loop Transformations for Restructuring Compilers: The Foundations
Loop Transformations for Restructuring Compilers: The Foundations
The range test: a dependence test for symbolic, non-linear expressions
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
On Uniformization of Affine Dependence Algorithms
IEEE Transactions on Computers
A Loop Transformation Theory and an Algorithm to Maximize Parallelism
IEEE Transactions on Parallel and Distributed Systems
Partitioning and Labeling of Loops by Unimodular Transformations
IEEE Transactions on Parallel and Distributed Systems
The Fortran parallel transformer and its programming environment
Information Sciences: an International Journal
Removing false code dependencies to speedup software build processes
CASCON '03 Proceedings of the 2003 conference of the Centre for Advanced Studies on Collaborative research
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A new technique to parallelize loops with variable distance vectors is presented. The method extends previous methods in two ways. First, the present method makes it possible for array subscripts to be any linear combination of all loop indices. The solutions to the linear dependence equations established from such array subscripts are characterized by a pseudo distance matrix (PDM). Second, it allows us to exploit loop parallelism from the PDM by applying uni-modular and partitioning transformations that preserve the lexicographical order of the dependent iterations. The algorithms to derive the PDM, to find a suitable loop transformation and to generate parallel code are described, showing that it is possible to parallelize a wider range of loops automatically.