Algorithm 663: Translation of Algorithm 539: basic linear algebra subprograms for FORTRAN usage in FORTRAN 200 for the Cyber 205

ABSTRACT

This paper describes the vectorization of the BLAS, a set of basic linear algebra subprograms for FORTRAN usage. The efficiency of the BLAS, as standard available on the CDC Cyber 205, has been examined, and suggestions for improvements were given. This examination has led to the vectorized BLAS as presented here. Moreover, this version admits negative increment values; that is, vectors can also be treated in reverse order. The number of data movements has been kept to a minimum. This BLAS version has been written in CDC FORTRAN 200. It has been optimized for a 1-pipe Cyber 205, but is also appropriate for the 2- and 4-pipe versions.

REFERENCES

• 1: AMERICAN NATIONAL STANDARDS INSTITUTE. American National Standard Programming Language FORTRAN, ANSI X3.g-1978. ANSI, New York, 1978.
• 2: CDC. Cyber 200 ASSEMBLER reference manual. Ver. 2. Publ. 60485010, CDC, Sunnyvale, Calif., 1981.
• 3: CDC. Cyber 200 FORTRAN reference manual. Ver. 1. Publ. 60480200B, CDC, Sunnyvale, Calif., 1983.
• 4: CENTER FOR MATHEMATICS AND COMPUTER SCIENCE. A Library of NUMerical Software for VECtor and Parallel Computers in FORTRAN. Center for Mathematics and Computer Science, Amsterdam, 1985.
• 5: DONGARRA, J. J., BUNCH, J. R., MOLER, C. B., AND STEWART, G.W. Linpack User's Guide. SIAM, Philadelphia, Pa., 1979.
• 6: DONGARRA, J. J., Du CROZ, J., HAMMERLING, S., AND HANSON, R.J. An extended set of Fortran basic linear algebra subprograms. Tech. Memo. 41 (rev. 3), Argonne National Laboratory, Argonne, Ill., Nov. 1986.
• 7: C. L. Lawson , R. J. Hanson , F. T. Krogh , D. R. Kincaid, Algorithm 539: Basic Linear Algebra Subprograms for Fortran Usage [F1], ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.324-325, Sept. 1979 [doi>10.1145/355841.355848]
• 8: C. L. Lawson , R. J. Hanson , D. R. Kincaid , F. T. Krogh, Basic Linear Algebra Subprograms for Fortran Usage, ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.308-323, Sept. 1979 [doi>10.1145/355841.355847]
• 9: LOUTER-NOOL, M. Basic linear algebra subprograms (BLAS) on the CDC CYBER 205. Parallel Comput. 4 (1987), 143-165.
• 10: SCHLICHTING, J. Double precision BLAS; Implementation design for double precision basic linear algebra subprograms on the Control Data Cyber 205. In Applications on Vector and Parallel Computers, H. J. J. te Riele, Th.J. Dekker, and H. A. van der Vorst, Eds., North-Holland, Amsterdam, 1987.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: FORTRAN

  G. Mathematics of Computing
  G.4 MATHEMATICAL SOFTWARE
      Subjects: Efficiency

General Terms:
Algorithms, Measurement, Performance