Scanning polyhedra with DO loops
PPOPP '91 Proceedings of the third ACM SIGPLAN symposium on Principles and practice of parallel programming
Some efficient solutions to the affine scheduling problem: I. One-dimensional time
International Journal of Parallel Programming
Compiler transformations for high-performance computing
ACM Computing Surveys (CSUR)
The Omega Library interface guide
The Omega Library interface guide
Maximizing parallelism and minimizing synchronization with affine transforms
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Affine scheduling on bounded convex polyhedric domains is asymptotically optimal
Theoretical Computer Science - Special issue on parallel computing
Optimal fine and medium grain parallelism detection in polyhedral reduced dependence graphs
International Journal of Parallel Programming
An affine partitioning algorithm to maximize parallelism and minimize communication
ICS '99 Proceedings of the 13th international conference on Supercomputing
Generation of Efficient Nested Loops from Polyhedra
International Journal of Parallel Programming - Special issue on instruction-level parallelism and parallelizing compilation, part 2
International Journal of Parallel Programming - Special issue on parallel architectures and compilation techniques
Scheduling and Automatic Parallelization
Scheduling and Automatic Parallelization
Constructive Methods for Scheduling Uniform Loop Nests
IEEE Transactions on Parallel and Distributed Systems
An Exact Method for Analysis of Value-based Array Data Dependences
Proceedings of the 6th International Workshop on Languages and Compilers for Parallel Computing
On the Optimality of Feautrier's Scheduling Algorithm
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
Code Generation in the Polyhedral Model Is Easier Than You Think
Proceedings of the 13th International Conference on Parallel Architectures and Compilation Techniques
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An approach, permitting us to build free schedules for affine loops with affine dependences represented with a single dependence relation, is described. The iterations of each time under the free schedule can be executed as soon as their operands are available. This allows us to extract maximal fine-grained loop parallelism. The approach requires an exact dependence analysis. To describe the approach and carry out experiments, the dependence analysis by Pugh and Wonnacott has been chosen where dependences are represented in the form of tuple relations. The approach can be applied to both non-parameterized and parameterized loops. Problems to be resolved in the future to utilize the entire power of the presented technique are discussed.