Automatic benchmark generation for cache optimization of matrix operations

ABSTRACT

Computationally intensive algorithms must usually be restructured to make the best use of cache memory in current high-performance, hierarchical memory computers. Unfortunately, cache conscious algorithms are sensitive to object sizes and addresses as well as the details of the cache and translation lookaside buffer geometries, and this sensitivity makes both automatic restructuring and hand-turning difficult tasks. An optimization approach is presented in this paper that automatically generates and executes a benchmark program from a concise specification of the algorithm's structure. This technique provides the performance data needed for verification of code generation heuristics or search among the various restructuring options. Matrix transpose and matrix multiplication are examined using this approach for several workstations with restructuring options of loop order, tiling (blocking), and unrolling.

REFERENCES

• 1: D. H. Bailey, RISC microprocessors and scientific computing, Proceedings of the 1993 ACM/IEEE conference on Supercomputing, p.645-654, December 1993, Portland, Oregon, United States [doi>10.1145/169627.169813]
• 2: R. Bell, IBM RISC System/6000 Performance Tuning for Numerically Intensive Fortran and C Programs, IBM ITSC Technical Bulletin GG24-3611, October 1990.
• 3: Mark Bromley , Steven Heller , Tim McNerney , Guy L. Steele, Jr., Fortran at ten gigaflops: the connection machine convolution compiler, Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementation, p.145-156, June 24-28, 1991, Toronto, Ontario, Canada
• 4: Monica D. Lam , Edward E. Rothberg , Michael E. Wolf, The cache performance and optimizations of blocked algorithms, Proceedings of the fourth international conference on Architectural support for programming languages and operating systems, p.63-74, April 08-11, 1991, Santa Clara, California, United States
• 5: O. Temam , E. D. Granston , W. Jalby, To copy or not to copy: a compile-time technique for assessing when data copying should be used to eliminate cache conflicts, Proceedings of the 1993 ACM/IEEE conference on Supercomputing, p.410-419, December 1993, Portland, Oregon, United States [doi>10.1145/169627.169762]
• 6: Michael E. Wolf , Monica S. Lam, A data locality optimizing algorithm, Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementation, p.30-44, June 24-28, 1991, Toronto, Ontario, Canada