Auto-Blocking Matrix-Multiplication or Tracking BLAS3 Performance from Source Code

SIGPLAN Notices (ACM Special Interest Group on Programming Languages)

Volumn 32, Issue 7, 1997, Pages 206-216

  Frens, Jeremy D ^a   Wise, David S ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347771690     PISSN: 03621340     EISSN: None     Source Type: Journal    
DOI: 10.1145/263767.263789     Document Type: Article

References (25)

1. J. M. Anderson, S. P. Amarainghe, & M. S. Lam. Data and computation transformations for multiprocessors. Proc. 5th ACM SIGPLAN Symp. on Principles and Practice of Parallel Programming, SIGPLAN Notices 30, 8 (August 1995), 166-178.
2. R. Bordawekar, A. Choudhary, K. Kennedy, C. Koelbel, & M. Paleczny. A model and compilation strategy for out-of-core data parallel programs. Proc. 5th ACM SIGPLAN Symp. on Principles and Practice of Parallel Programming, SIGPLAN Notices 30, 8 (August 1995), 1-17.
3. F. W. Burton & J. G. Kollias. Comment on 'The explicit quad tree as a structure for computer graphics.' Comput. J. 26, 2 (May 1983), 188.
4. D. Cann. Retire FORTRAN? : a debate rekindled. Comm. ACM 35, 8 (August 1992), 81-89.
5. S. Carr & R. B. Lehoucq. Compiler Blockability of dense matrix factorizations. ACM Trans. Math.Software (to appear).
6. M. Cierniak & W. Li. Unifying data and control transformations for distributed shared-memory machines. Proc. ACM SIGPLAN '95 Conf. on Programming Lang. Design and Implementation, SIGPLAN Notices 30, 6 (June 1995), 205-217.
7. J. Cohen & M. Roth. On the implementation of Strassen's fast multiplication algorithm. Acta Informat. 6, 4 (August 1976), 341-355.
8. D. Culler, R. Karp, D. Patterson, A. Sahay, K. E. Schauser, E. Santos, R. Subramonian, & T. von Eicken. LogP: a practical model of parallel computation. Comm. ACM 39, 11 (November 1996), 78-85.
9. J. W. Demmel & N. J. Higham. Stability of block algorithms with fast Level 3 BLAS. ACM Trans. Math. Software 18, 3 (September 1992), 274-291.
10. J. Dongarra, J. DuCroz, S. Hammarling, & R. Hanson. An extended set of FORTRAN basic linear algebra subprograms. ACM Trans. Math. Softw. 14(1988), 1-17.
11. R. J. Fateman. Symbolic mathematics system evaluators (extended abstract). In Y. N. Lakshman (ed.), Proc 1996 Intl. Symp. on Symbolic and Algebraic Computation, New York, ACM Press, 86-94.
12. P. C. Fischer & R. L. Probert. Storage reorganization techniques for matrix computation in a paging environment. Comm. ACM 22, 7 (July 1979), 405-415.
13. J. Frens & D. S. Wise. Matrix inversion using quadtrees implemented in GOFER. Technical Report 433, Computer Science Dept., Indiana University (May 1995).
14. K. A. Gallivan, R. J. Plemmons, & A. H. Sameh. Parallel Algorithms for dense linear algebra. SIAM Review 32, 1 (March 1990), 54-135. Reprinted in Gallivan et al. Parallel Algorithms for Matrix Computation, Philadelphia, SIAM (1990), 1-82.
15. K. A. Gallivan, R. J. Plemmons, & A. H. Sameh. Parallel Algorithms for dense linear algebra. SIAM Review 32, 1 (March 1990), 54-135. Reprinted in Gallivan et al. Parallel Algorithms for Matrix Computation, Philadelphia, SIAM (1990), 1-82.
16. G. H. Golub & C. F. Van Loan. Matrix Computations 2nd edition. The Johns Hopkins University Press, Baltimore (1989).
17. J. Fasel, P. Hudak, S. Peyton Jones, & P. Wadler (eds.) HASKELL special issue. ACM SIGPLAN Notices 27, 5 (May 1992).
18. N. J. Higham. Exploiting fast matrix multiplication within the Level 3 BLAS. ACM Trans. Math. Software 16, 4 (December 1990), 352-368.
19. D. E. Knuth. The Art of Computer Programming I, Fundamental Algorithms (2nd ed.), Reading, MA, Addison-Wesley, (1973).
20. A. C. McKellar & E. G. Coffman, Jr. Organizing matrices and matrix operations for paged-memory systems Comm. ACM 12, 3 (March 1969), 153-165.
21. J. Spiess. Untersuchungen des Zeitgewinns durch neue Algorithmen zur Matrix-Multiplikation. Computing 17, 1 (1976), 23-36.
22. V. Strassen. Gaussian elimination is not optimal. Numer. Math. 13 (1969), 354-356.
23. G. L. Steele, Jr. Debunking the "expensive procedure call" myth, or Procedure call implementations considered harmful, or LAMBDA: the ultimate GOTO. ACM77: Proc. 1977 Annual Conf., New York, ACM (1977), 153-162.
24. D. S. Wise. Representing matrices as quadtrees for parallel processors (extended abstract). ACM SIGSAM Bulletin 18, 3 (August 1984), 24-25.
25. D. S. Wise. Undulant block elimination and integerpreserving matrix inversion. Sci. Comput. Programming (to appear). Technical Report 418, Computer Science Department, Indiana University (revised, August 1995).