Constructive Methods for Scheduling Uniform Loop Nests

This paper surveys scheduling techniques for loop nests with uniform dependences. First, we introduce the hyperplane method and related variants. Then we extend it by using a different affine scheduling for each statement within the nest. In both cases, we present a new, constructive, and efficient method to determine optimal solutions, i.e., schedules whose total execution time is minimum. >

[1]  Patrice Quinton,et al.  Scheduling affine parameterized recurrences by means of variable dependent timing functions , 1990 .

[2]  Thomas Kailath,et al.  Regular iterative algorithms and their implementation on processor arrays , 1988, Proc. IEEE.

[3]  Sanjay V. Rajopadhye,et al.  Synthesizing systolic arrays from recurrence equations , 1990, Parallel Comput..

[4]  Weijia Shang,et al.  Time Optimal Linear Schedules for Algorithms with Uniform Dependencies , 1991, IEEE Trans. Computers.

[5]  Patrice Quinton,et al.  Scheduling affine parameterized recurrences by means of , 1990, [1990] Proceedings of the International Conference on Application Specific Array Processors.

[6]  Jang-Ping Sheu,et al.  On the Parallelism of Nested For-Loops Using Index Shift Method , 1990, ICPP.

[7]  Constantine D. Polychronopoulos Compiler Optimizations for Enhancing Parallelism and Their Impact on Architecture Design , 1988, IEEE Trans. Computers.

[8]  Charles E. Leiserson,et al.  Optimizing synchronous systems , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[9]  Jih-Kwon Peir,et al.  Minimum Distance: A Method for Partitioning Recurrences for Multiprocessors , 1989, IEEE Trans. Computers.

[10]  Yves Robert,et al.  Revisiting cycle shrinking , 1992, Parallel Comput..

[11]  Sailesh K. Rao,et al.  Regular interactive algorithms and their implementations on processor arrays , 1986 .

[12]  Ken Kennedy,et al.  Compiling Fortran D for MIMD distributed-memory machines , 1992, CACM.

[13]  Ken Kennedy,et al.  Compiler optimizations for Fortran D on MIMD distributed-memory machines , 1991, Proceedings of the 1991 ACM/IEEE Conference on Supercomputing (Supercomputing '91).

[14]  Patrice Quinton,et al.  The systematic design of systolic arrays , 1987 .

[15]  Leslie Lamport,et al.  The parallel execution of DO loops , 1974, CACM.

[16]  Michael L. Dowling Optimal code parallelization using unimodular transformations , 1990, Parallel Comput..