Solving Alignment Using Elementary Linear Algebra
Data and computation alignment is an important part of compiling sequential programs to architectures with non-uniform memory access times. In this paper, we show that elementary matrix methods can be used to determine communication-free alignment of code and data. We also solve the problem of replicating data to eliminate communication. Our matrix-based approach leads to algorithms which work well for a variety of applications, and which are simpler and faster than other matrix-based algorithms in the literature.
KeywordsExtra Dimension Null Space Loop Nest Alignment System Block Column
Unable to display preview. Download preview PDF.
- 1.Jennifer M. Anderson and Monica S. Lam. Global optimizations for parallelism and locality on scalable parallel machines. ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI), pages 112–125, June 1993.Google Scholar
- 2.Siddartha Chatterjee, John Gilbert, and Robert Schreiber. The alignment-distribution graph. In U. Banerjee, D. Gelernter, A. Nicolau, and D. Padua, editors, Languages and Compilers for Parallel Computing. Sixth International Workshop., number 768 in LNCS. Springer-Verlag, 1993.Google Scholar
- 3.Siddartha Chatterjee, John Gilbert, Robert Schreiber, and Shang-Hua Teng. Optimal evaluation of array expressions on massively parallel machines. Technical Report CSL-92-11, XEROX PARC, December 1992.Google Scholar
- 4.Henri Cohen. A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics. Springer-Verlag, 1995.Google Scholar
- 5.Paul Feautrier. Toward automatic distribution. Technical Report 92.95, IBP/MASI, December 1992.Google Scholar
- 6.C.-H. Huang and P. Sadayappan. Communication-free hyperplane partitioning of nested loops. In U. Banerjee, D. Gelernter, A. Nicolau, and D. Padua, editors, Languages and Compilers for Parallel Computing. Fourth International Workshop. Santa Clara, CA., number 589 in LNCS, pages 186–200. Springer-Verlag, August 1991.Google Scholar
- 7.Kathleen Knobe, Joan D. Lucas, and William J. Dally. Dynamic alignment on distributed memory systems. In Proceedings of the Third Workshop on Compilers for Parallel Computers, July 1992.Google Scholar
- 8.Kathleen Knobe and Venkataraman Natarajan. Data optimization: minimizing residual interprocessor motion on SIMD machines. In Proceedings of the 3rd Symposium on the Frontiers of Massively Parallel Computation-Frontiers’ 90, pages 416–423, October 1990.Google Scholar
- 9.Vipin Kumar, Ananth Grama, Anshul Gupta, and George Karypis. Introduction to Parallel Computing. Design and Analysis of Algorithms. The Benjamin/ Cummings Publishing Company, 1994.Google Scholar
- 10.Jingke Li and Marina Chen. Index domain alignment: minimizing cost of cross-referencing between distributed arrays. Technical Report YALEU/DCS/TR-725, Department of Computer Science, Yale University, September 1989.Google Scholar