Abstract
The mathematical model for the parallelization, or “spacetime mapping”, of loop nests is the polyhedron model. The presence of while loops in the nest complicates matters because the parallelized loop nest does not correspond to a polyhedron but instead to a subset that resembles a (multi-dimensional) comb. This comb can take on shapes that make the precise enumeration of its points by any parallel target loop nest impossible. We describe how to augment the target loop code to scan a finite superset of the comb and restrict execution of the loop body to the points of the comb.
Preview
Unable to display preview. Download preview PDF.
References
M. Barnett and C. Lengauer. Unimodularity and the parallelization of loops. Parallel Processing Letters, 2(2–3):273–281, 1992.
J.-F. Collard. Code generation in automatic parallelizers. In C. Girault, editor, Proc. Int. Conf. on Applications in Parallel and Distributed Computing, IFIP W.G. 10.3, pages 185–194. North-Holland, April 1994.
J.-F. Collard. Space-time transformation of while-loops using speculative execution. In Proc. 1994 Scalable High Performance Computing Conf. IEEE Computer Society Press, May 1994.
E. W. Dijkstra and C. S. Scholten. Predicate Calculus and Program Semantics. Texts and Monographs in Computer Science. Springer-Verlag, 1990.
M. Griebl and C. Lengauer. A communication scheme for the distributed execution of while loops. Technical Report MIP-9406, Fakultät für Mathematik und Informatik, Universität Passau, May 1994.
M. Griebl and C. Lengauer. On the space-time mapping of WHILE-loops. Parallel Processing Letters, 1994. To appear. Also: Technical Report MIP-9304, Fakultät für Mathematik und Informatik, Universität Passau, July 1993.
R. M. Karp, R. E. Miller, and S. Winograd. The organization of computations for uniform recurrence equations. J. ACM, 14(3):563–590, July 1967.
C. Lengauer. Loop parallelization in the polytope model. In E. Best, editor, CONCUR'93, Lecture Notes in Computer Science 715, pages 398–416. Springer-Verlag, 1993.
P. Quinton. The systematic design of systolic arrays. In F. F. Soulié, Y. Robert, and M. Tchuente, editors, Automata Networks in Computer Science, chapter 9, pages 229–260. Manchester University Press, 1987. Also: Technical Reports 193 and 216, IRISA (INRIA-Rennes), 1983.
S. K. Rao and T. Kailath. Regular iterative algorithms and their implementations on processor arrays. Proc. IEEE, 76(3):259–282, March 1988.
P. P. Tirumalai, M. Lee, and M. S. Schlansker. Parallelization of while loops on pipelined architectures. J. of Supercomputing, 5:119–136, 1991.
Y. Wu and T. G. Lewis. Parallelizing while loops. In H. D. Schwetman, editor, Int. Conf. on Parallel Processing, volume II, pages 1–8. CRC Press, 1990.
J. Xue. Automating non-unimodular transformations of loop nests. Parallel Computing, 20(5):711–728, May 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Griebl, M., Lengauer, C. (1994). On scanning space-time mapped while loops. In: Buchberger, B., Volkert, J. (eds) Parallel Processing: CONPAR 94 — VAPP VI. VAPP CONPAR 1994 1994. Lecture Notes in Computer Science, vol 854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58430-7_59
Download citation
DOI: https://doi.org/10.1007/3-540-58430-7_59
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58430-8
Online ISBN: 978-3-540-48789-0
eBook Packages: Springer Book Archive