Theory of linear and integer programming
Theory of linear and integer programming
POPL '88 Proceedings of the 15th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the 1989 ACM/IEEE conference on Supercomputing
A data locality optimizing algorithm
PLDI '91 Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementation
Integration, the VLSI Journal
Optimal tile size adjustment in compiling general DOACROSS loop nests
ICS '95 Proceedings of the 9th international conference on Supercomputing
Communication-minimal tiling of uniform dependence loops
Journal of Parallel and Distributed Computing
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
A Loop Transformation Theory and an Algorithm to Maximize Parallelism
IEEE Transactions on Parallel and Distributed Systems
Minimal Data Dependence Abstractions for Loop Transformations
LCPC '94 Proceedings of the 7th International Workshop on Languages and Compilers for Parallel Computing
Optimal Fine and Medium Grain Parallelism Detection in Polyhedral Reduced Dependence Graphs
PACT '96 Proceedings of the 1996 Conference on Parallel Architectures and Compilation Techniques
On the Parallel Execution Time of Tiled Loops
IEEE Transactions on Parallel and Distributed Systems
Efficient and Accurate Analytical Modeling of Whole-Program Data Cache Behavior
IEEE Transactions on Computers
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This paper applies unimodular transformations and tiling to improve data locality of a loop nest. Due to data dependences and reuse information, not all dimensions of the iteration space will and can be tiled. By using cones to represent data dependences and vector spaces to quantify data reuse in the program, a reuse-driven transformational approach is presented, which aims at maximizing the amount of data reuse carried in the tiled dimensions of the iteration space while keeping the number of tiled dimensions to a minimum (to reduce loop control overhead). In the special case of one single fully permutable loop nest, an algorithm is presented that tiles the program optimally so that all data reuse is carried in the tiled dimensions. In the general case of multiple fully permutable loop nests, data dependences can prevent all data reuse to be carried in the tiled dimensions. An algorithm is presented that aims at localizing data reuse in the tiled dimensions so that the reuse space localized has the largest dimensionality possible.