Abstract
In data-parallel languages such as High Performance Fortran and Fortran D, arrays are mapped to processors through a two step process involving alignment followed by distribution. A compiler that generates code for each processor has to compute the sequence of local memory addresses accessed by each processor and the sequence of sends and receives for a given processor to access non-local data. In this paper, we present a novel approach based on integer lattices. The set of elements referenced can be generated by integer linear combinations of basis vectors. Our linear algorithm determines the basis vectors as a function of the mapping. Using the basis vectors, we derive a loop nest that enumerates the addresses, which are points in the lattice generated by the basis vectors. Experimental results show that our approach is better than that of a recent linear time solution to this problem.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. Ancourt, F. Coelho, F. Irigoin and R. Keryell. A linear algebra framework for static HPF code distribution. In Proc. of the 4th Workshop on Compilers for Parallel Computers, Delft, The Netherlands, December 1993.
B. Chapman, P. Mehrotra, and H. Zima. Programming in Vienna Fortran. Scientific Programming, 1(1):31–50, Fall 1992.
S. Chatterjee, J. R. Gilbert, F. J. E. Long, R. Schreiber, and S.-H. Teng. Generating local addresses and communication sets for data parallel programs. In Proc. of ACM Symposium on Principles and Practices of Parallel Programming, pages 149–158, May 1993.
G. Fox, S. Hiranandani, K. Kennedy, C. Koelbel, U. Kremer, C. Tseng, and M. Wu. Fortran D Language Specification. Technical Report CRPC-TR90079, Rice University, Dec. 1990.
P. M. Gruber and C. G. Lekkerkerker. Geometry of numbers. North-Holland Mathematical Library Volume 37, North-Holland, Amsterdam, 1987 (Second Edition).
S. K. S. Gupta, S. D. Kaushik, C.-H. Huang, and P. Sadayappan. On compiling array expressions for efficient execution on distributed-memory machines. Technical Report OSU-CISRC-94-TR19, The Ohio State University, April 1994.
High Performance Fortran Forum. High Performance Fortran language specification. Scientific Programming, 2(1–2):1–170, 1993.
S. Hiranandani, K. Kennedy, J. Mellor-Crummey, and A. Sethi. Compilation techniques for block-cyclic distributions. In Proc. ACM Intl. Conf. Supercomputing, July 1994.
K. Kennedy, N. Nedeljkovic, and A. Sethi. A linear-time algorithm for computing the memory access sequence in data-parallel programs. In Proc. of Fifth ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, Santa Barbara, CA, July 1995.
C. Koelbel. Compile-time generation of communication for scientific programs. In Supercomputing '91, pages 101–110, Nov. 1991.
C. Koelbel, D. Loveman, R. Schreiber, G. Steele, and M. Zosel. High Performance Fortran Handbook. The MIT Press, 1994.
J. Ramanujam. Non-unimodular transformations of nested loops. In Proc. Supercomputing 92, pages 214–223, Nov. 1992.
J. M. Stichnoth. Efficient compilation of array statements for private memory multicomputers. Technical Report CMU-CS-93-109, Carnegie-Mellon University, Feb. 1993.
A. Thirumalai and J. Ramanujam. Code generation and optimization for array statements in HPF. Technical Report ECE-TR-94-11-02, Louisiana State University, Nov. 1994.
A. Thirumalai and J. Ramanujam. Address sequence generation for data-parallel programs using integer lattices. Technical Report ECE-TR-95-04-03, Louisiana State University, Apr. 1995.
A. Thirumalai and J. Ramanujam. An efficient compile-time approach to compute address sequences in data parallel programs. In Proc. 5th International Workshop on Compilers for Parallel Computers, Malaga, Spain, pp. 581–605, June 1995.
Michael Wolfe. High performance compilers for parallel computing. Addison-Wesley Publishing Co., 1996.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thirumalai, A., Ramanujam, J. (1996). Fast address sequence generation for data-parallel programs using integer lattices. In: Huang, CH., Sadayappan, P., Banerjee, U., Gelernter, D., Nicolau, A., Padua, D. (eds) Languages and Compilers for Parallel Computing. LCPC 1995. Lecture Notes in Computer Science, vol 1033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014200
Download citation
DOI: https://doi.org/10.1007/BFb0014200
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60765-6
Online ISBN: 978-3-540-49446-1
eBook Packages: Springer Book Archive