A hyperplane based approach for optimizing spatial locality in loop nests
ICS '98 Proceedings of the 12th international conference on Supercomputing
Computer architecture (2nd ed.): a quantitative approach
Computer architecture (2nd ed.): a quantitative approach
Maximizing parallelism and minimizing synchronization with affine partitions
Parallel Computing - Special issues on languages and compilers for parallel computers
A Linear Algebra Framework for Automatic Determination of Optimal Data Layouts
IEEE Transactions on Parallel and Distributed Systems
An affine partitioning algorithm to maximize parallelism and minimize communication
ICS '99 Proceedings of the 13th international conference on Supercomputing
Statement-Level Communication-Free Partitioning Techniques for Parallelizing Compilers
The Journal of Supercomputing
High Performance Compilers for Parallel Computing
High Performance Compilers for Parallel Computing
Solving Alignment Using Elementary Linear Algebra
LCPC '94 Proceedings of the 7th International Workshop on Languages and Compilers for Parallel Computing
Alignment and Distribution is NOT (Always) NP-Hard
ICPADS '98 Proceedings of the 1998 International Conference on Parallel and Distributed Systems
IEEE Transactions on Parallel and Distributed Systems
APPT'05 Proceedings of the 6th international conference on Advanced Parallel Processing Technologies
ISPA'05 Proceedings of the Third international conference on Parallel and Distributed Processing and Applications
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Bau et al. proposed an efficient and precise data alignment method to ascertain whether there is communication-free alignment of array reference function with linear subscripts in one loop index variable. Chu et al. presented an efficient and precise data alignment method to determine whether there is communication-free alignment of array reference function with linear subscripts in two loop index variables or quadratic subscripts (ai^2+bi+d). However, for array reference function with linear subscripts in three loop index variables or quadratic subscripts (ai^2+bi+cj+d), their methods cannot be applied. In this paper, we propose two new alignment functions for loop iteration space and array elements. The new alignment functions can be applied towards checking whether there is communication-free alignment of array reference function with linear subscripts in three loop index variables or quadratic subscripts. Experiments with benchmarks taken from Parallel loop and Vector loop showed that among the 7 nested loops tested, three of them had their data alignment improved by the method proposed.