Abstract
Parallel loops account for the greatest percentage of program parallelism. The degree to which parallelism can be exploited and the amount of overhead involved during parallel execution of a nested loop directly depend on partitioning, i.e., the way the different iterations of a parallel loop are distributed across different processors. Thus, partitioning of parallel loops is of key importance for high performance and efficient use of multiprocessor systems. Although a significant amount of work has been done in partitioning and scheduling of rectangular iteration spaces, the problem of partitioning of non-rectangular iteration spaces – e.g. triangular, trapezoidal iteration spaces – has not been given enough attention so far. In this paper, we present a geometric approach for partitioning N-dimensional non-rectangular iteration spaces for optimizing performance on parallel processor systems. Speedup measurements for kernels (loop nests) of linear algebra packages are presented.
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References
Padua, D.A.: Multiprocessors: Discussion of theoritical and practical problems. Technical Report 79-990, Dept. of Computer Science, University of Illinois at Urbana-Champaign (November 1979)
Cytron, R.: Doacross: Beyond vectorization for multiprocessors. In: Proceedings of the 1986 International Conference on Parallel Processing, St. Charles, IL (August 1986)
Davies, J.: Parallel loop constructs for multiprocessors. Technical Report 81-1070, Dept. of Computer Science, University of Illinois at Urbana-Champaign (May 1981)
Polychronopoulos, C., Kuck, D.J., Padua, D.A.: Execution of parallel loops on parallel processor systems. In: Proceedings of the 1986 International Conference on Parallel Processing, August 1986, pp. 519–527 (1986)
D’Hollander, E.H.: Partitioning and labeling of loops by unimodular transformations. IEEE Trans. Parallel Distrib. Syst. 3(4), 465–476 (1992)
Mohammad, R.: Haghighat and Constantine D. Polychronopoulos. Symbolic analysis for parallelizing compilers. ACM Transactions on Programming Languages and Systems 18(4), 477–518 (1996)
Sakellariou, R.: On the Quest for Perfect Load Balance in Loop-Based Parallel Computations. PhD thesis, Department of Computer Science, University of Manchester (October 1996)
Banerjee, U.: Data dependence in ordinary programs. Master’s thesis, Dept. of Computer Science, University of Illinois at Urbana-Champaign (November 1976); Report No. 76-837
Burke, M., Cytron, R.: Interprocedural dependence analysis and parallelization. In: Proceedings of the SIGPLAN 1986 Symposium on Compiler Construction, Palo Alto, CA (June 1986)
Iyengar, M.K., Jain, S.R.K., Jain, R.K.: Numerical Methods for Scientific and Engineering Computation. John Wiley and Sons, Chichester (1985)
O’Boyle, M., Hedayat, G.A.: Load balancing of parallel affine loops by unimodular transformations. Technical Report UMCS-92-1-1, Department of Computer Science, University of Manchester (January 1992)
Banerjee, U.: Loop Transformation for Restructuring Compilers. Kluwer Academic Publishers, Boston (1993)
Pugh, W.: The Omega test: A fast and practical integer programming algorithm for dependence analysis. In: Proceedings of Supercomputing 1991, Albuquerque, NM (November 1991)
Clauss, P., Loechner, V.: Parametric analysis of polyhedral iteration spaces. In: IEEE (ed.) Int. Conf. on Application Specific Array Processors, Chicago, Illinois (August 1996)
Polychronopoulos, C.: Loop coalescing: A compiler transformation for parallel machines. In: Sahni, S. (ed.) Proceedings of the 1987 International Conference on Parallel Processing, August 1987. Pennsylvania State University Press (1987)
Carr, S.: Memory-Hierarchy Management. PhD thesis, Dept. of Computer Science, Rice University (September 1992)
Banerjee, U.: Loop Parallelization. Kluwer Academic Publishers, Boston (1994)
Lundstrom, S., Barnes, G.: A controllable MIMD architectures. In: Proceedings of the 1980 International Conference on Parallel Processing, St. Charles, IL (August 1980)
Kuck, D., et al.: The effects of program restructuring, algorithm change and architecture choice on program performance. In: Proceedings of the 1984 International Conference on Parallel Processing (August 1984)
Wolfe, M.J.: Optimizing Supercompilers for Supercomputers. The MIT Press, Cambridge (1989)
Anik, S., Hwu, W.W.: Executing nested parallel loops on shared-memory multiprocessors. In: Proceedings of the 1992 International Conference on Parallel Processing, Boca Raton, Florida, August 1992, ppIII. 241–244 (1992)
Wolfe, M.J.: High Performance Compilers for Parallel Computing. Addison-Wesley, Redwood City (1996)
Padua, D.A., Wolfe, M.J.: Advanced compiler optimizations for supercomputers. Communications of the ACM 29(12), 1184–1201 (1986)
Irigoin, F., Triolet, R.: Supernode partitioning. In: Proceedings of the Fifteenth Annual ACM Symposium on the Principles of Programming Languages, San Diego, CA (January 1988)
Kruskal, C.P., Weiss, A.: Allocating independent subtasks on parallel processors. IEEE Transactions on Software Engineering 11(10), 1001–1016 (1985)
Haghighat, M., Polychronopoulos, C.: Symbolic program analysis and optimization for parallelizing compilers. In: Proceedings of the Fifth Workshop on Languages and Compilers for Parallel Computing, New Haven, CT (August 1992)
Koziris, N., Papakonstantinou, G., Tsanakas, P.: Mapping nested loops onto distributed memory multiprocessors. In: International Conference on Parallel and Distributed Systems, December 1997, pp. 35–43 (1997)
Dion, M., Robert, Y.: Mapping affine loop nests: new results. In: HPCN Europe 1995, pp. 184–189 (1995)
Dion, M., Robert, Y.: Mapping affine loop nests. Parallel Computing 22(10), 1373–1397 (1996)
Matlab, http://www.mathworks.com
Weisstein, E.W.: Abel’s Impossibility Theorem. From MathWorld–A Wolfram Web Resource, http://mathworld.wolfram.com/AbelsImpossibilityTheorem.html
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Kejariwal, A., D’Alberto, P., Nicolau, A., Polychronopoulos, C.D. (2005). A Geometric Approach for Partitioning N-Dimensional Non-rectangular Iteration Spaces. In: Eigenmann, R., Li, Z., Midkiff, S.P. (eds) Languages and Compilers for High Performance Computing. LCPC 2004. Lecture Notes in Computer Science, vol 3602. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11532378_9
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DOI: https://doi.org/10.1007/11532378_9
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