Abstract
Most work on the problem of scheduling computations onto a systolic array is restricted to systems of uniform recurrence equations. In this paper, this restriction is relaxed to include systems of affine recurrence equations. In this broader class, a sufficient condition is given for the system to be computable. Necessary and sufficient conditions are given for the existence of an affine schedule, along with a procedure that constructs the schedule vector, when one exists.
Similar content being viewed by others
References
Richard M. Karp, Richard E. Miller, and Shmuel Winograd. The organization of computations for uniform recurrence equations.J. ACM, 14:563–590, 1967.
Richard M. Karp, Richard E. Miller, and Shmuel Winograd. Properties of a model for parallel computations: determinacy, termination, queueing.SIAM J. Appl. Math, 14:1390–1411, 1966.
Peter R. Cappello.VLSI Architectures for Digital Signal Processing. PhD thesis, Princeton University, Princeton, NJ, Oct. 1982.
Peter R. Cappello and Kenneth Steiglitz. Unifying VLSI array design with linear transformations of space-time. In F.P. Preparata, editor,Advances in Computing Research, pages 23–65, JAI Press, Inc., 1984.
Jean-Marc Delosme and Ilse C.F. Ipsen. An illustration of a methodology for the construction of efficient systolic architectures in VLSI.Proc. 2nd Int. Symp. on VLSI Technology, Systems and Applications, pages 268–273, Taipei, 1985.
José A.B. Fortes and Dan I. Moldovan. Parallelism detection and algorithm transformation techniques useful for VLSI architecture design.J. Parallel Distrib. Comput, 2:277–301, Aug. 1985.
Sun Yuan Kung.VLSI Array Processors. Prentice-Hall, Englewood Cliffs, NJ, 1988.
Willard L. Miranker and Andrew Winkler. Spactime representations of computational structures.Computing, 32:93–114, 1984.
Dan I. Moldovan. On the analysis of VLSI algorithms.IEEE Trans. Computers., C-31:1121–1126, Nov. 1982.
Dan I. Moldovan. On the design of algorithms for VLSI systolic arrays.Proc. IEEE, 71(1):113–120, Jan. 1983.
Dan I. Moldovan and José A.B. Fortes. Partitioning and mapping algorithms into fixed systolic arrays.IEEE Trans. Computers, C-35(1):1–12, Jan. 1986.
Patrice Quinton. Automatic synthesis of systolic arrays from uniform recurrent equations.Proc. 11th Ann. Symp. on Computer Architecture, pages 208–214, 1984.
I.V. Ramakrishnan, D.S. Fussell, and A. Silberschatz. Mapping homogeneous graphs on linear arrays.IEEE Trans. Computers, C-35(3):189–209, March 1986.
Sailash K. Rao.Regular Iterative Algorithms and Their Implementation on Processor Arrays. PhD thesis, Stanford University, Oct. 1985.
José A.B. Fortes and E Parisi-Presicce. Optimal linear schedules for the parallel execution of algorithms.Int. Conf. on Parallel Processing, pages 322–328, Aug. 1984.
Jean-Marc Delosme and Ilse C.F. Ipsen.Systolic Array Synthesis: Computability and Time Cones. Technical Report Yale/DCS/RR-474, Yale, May 1986.
Mathew T. O’Keefe and José A.B. Fortes. A comparative study of two systematic design methodologies for systolic arrays.Proc. Int. Conf. Parallel Processing, 672–675, Aug. 1986.
Weija Shang and and José A.B. Fortes. Time optimal linear schedules for algorithms with uniform dependencies.Int. Conf. on Systolic Arrays, pages 393–402, San Diego, May 1988.
Charles E. Leiserson, Flavio M. Rose, and James B. Saxe. Optimizing synchronous circuitry by retiming.Proc. Third Caltech Conf. on VLSI, Computer Science Press, Rockville, MD, 1983.
Charles E. Leiserson and James B. Saxe. Optimizing synchronous systems.Proc. IEEE 22nd Annual Symp. Foundations of Computer Science, Oct. 1981.
Yiwan Wong and Jean-Marc Delosme. Broadcast removal in systolic algorithms.Int. Conf on Systolic Arrays, pages 403–412, San Diego, May 1988.
Yoav Yaacoby and Peter R. Cappello.Converting Affine Recurrence Equations to Quasi-Uniform Recurrence Equations. Technical Report 18, Dept. Computer Science, UCSB, Santa Barbara, CA 93106, Feb. 1988.
Yoav Yaacoby and Peter R. Cappello.Decoupling the Dimensions of a System of Affine Recurrence Equations. Technical Report 12, Dept. Computer Science, UCSB, Santa Barbara, CA 93106, April 1988.
Gene H. Golub and Charles F. Van Loan.Matrix Computations. The Johns Hopkins University Press, 1983.
Christos H. Papadimitriou and Kenneth Steiglitz.Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1982.
Author information
Authors and Affiliations
Additional information
This material is based upon work supported by the Office of Naval Research under contract nos. N00014-84-K-0664 and N00014-85-K-0553.
Rights and permissions
About this article
Cite this article
Yaacoby, Y., Cappello, P.R. Scheduling a system of nonsingular affine recurrence equations onto a processor array. J VLSI Sign Process Syst Sign Image Video Technol 1, 115–125 (1989). https://doi.org/10.1007/BF02477177
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02477177