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Expression optimization using high-level knowledge

  • Applications And Systems
  • Conference paper
  • First Online:
Eurocal '87 (EUROCAL 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 378))

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Abstract

Combining symbolic algebra with numerical computation has become an effective way of solving many scientific and engineering problems. One of the difficulties in practice is producing concise, efficient, stable code from the large expressions generated in symbolic algebra. Most of the existing optimization techniques are applied after an operation or algorithm has been performed. We introduce techniques using high-level knowledge which are to be applied while the output expressions are generated.

This work was supported by grants A5471 and A5471 of the Natural Sciences and Engineering Research Council of Canada. Second author's present address: Department of Computer Science, University of Tennessee, Knoxville Tennessee U.S.A. 37996-1301.

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References

  1. Melvin A. Breuer. Generation of Optimal Code for Expressions via Factorization. Communications of the ACM, 12(6):333–340, June 1969.

    Article  Google Scholar 

  2. Richard L. Brenner. Simplifying Large Algebraic Expressions by Computer. In V. Ellen Golden, editor, Proceedings of the 1984 Macsyma User's Conference, pages 50–109. General Electric, Schenectady, New York, July 1984.

    Google Scholar 

  3. B. W. Char, K. O. Geddes, G. H. Gonnet, and S. M. Watt. Maple User's Guide. WATCOM Publications Ltd., Waterloo, Ontario, Canada, 4 edition, 1985.

    Google Scholar 

  4. Cook Jr., G. O. Development of a Magnetohydrodynamic Code for Axisymmetric, High-Beta Plasmas with Complex Magnetic Fields. PhD thesis, Lawrence Livermore National Laboratory, University of California, Livermore, 1982. Also available as report from Lawrence Livermore National Laboratory, Livermore.

    Google Scholar 

  5. Kevin Cahill and Randolph Reeder. Using MACSYMA to Write Long FORTRAN Codes for Simplicial-Interpolative Lattice Gauge Theory. Research Report DOE-UNM-85/3, Department of Physics and Astronomy, University of New Mexico, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, July 1985.

    Google Scholar 

  6. Richard J. Fateman. Optimal Code for Serial and Parallel Computation. Communications of the ACM, 12(12):694–695, December 1969.

    Article  Google Scholar 

  7. Andreas Griewank. Book review of Numerical Derivatives and Nonlinear Analysis. SIAM Review, 30(2):327–329, June 1988.

    Article  Google Scholar 

  8. Leo P. Harten. Using Macsyma to Generate (Somewhat) Optimized FORTRAN Code. In V. Ellen Golden, editor, Proceedings of the 1984 Macsyma User's Conference, pages 524–544. General Electric, Schenectady, New York, July 1984.

    Google Scholar 

  9. Anthony C. Hearn. Structure: The Key to Improved Algebraic Computation. In The Second Symposium on Symbolic and Algebraic Computation by Computers, RIKEN, Japan, 21–22 August 1984, pages 18-1–18-16. RSYMSAC, 1984.

    Google Scholar 

  10. B. J. A. Hulshof and J. A. van Hulzen. An Expression Compression Package for REDUCE based on Factorization and Controlled Expansion. Twente University of Technology, Department of Computer Science, Enschede, the Netherlands, 1985.

    Google Scholar 

  11. Masao Iri. Simultaneous computation of functions, partial derivatives and estimates of rounding errors — complexity and practicality —. Japan Journal of Applied Mathematics, 1:223–252, 1984.

    Google Scholar 

  12. G. Kedem. Automatic Differentiation of Computer Programs. ACM Transactions on Mathematical Software, 6(2):150–165, June 1980.

    Article  Google Scholar 

  13. Harriet Kagiwada, Robert Kalaba, Nima Rosakhoo, and Karl Spingarn. Numerical Derivatives and Nonlinear Analysis, volume 31 of Mathematical Concepts and Methods in Science and Engineering. Plenum Press, Inc., 1986.

    Google Scholar 

  14. D. E. Knuth. The Art of Computer Programming, volume 2. Addison-Wesley Publishing Company, Reading, Massachusetts, 2nd edition, 1981. Seminumerical Algorithms.

    Google Scholar 

  15. C. Mesztenyi and C. Witzgall. Stable Evaluation of Polynomials. Journal of Research of the National Bureau of Standards — B. Mathematics and Mathematical Physics, 71B(1):11–17, January–March 1967.

    Google Scholar 

  16. E. Ng and B. W. Char. Gradient and Jacobian Computation for Numerical Applications. In V. Ellen Golden, editor, Proceedings of the 1979 Macsyma User's Conference, pages 604–621. NASA, Washington, D.C., June 1979.

    Google Scholar 

  17. Louis B. Rall. Automatic Differentiation: Techniques and Applications. Lecture Notes in Computer Science 120. Spring-Verlag, Berlin, Germany, 1981.

    Google Scholar 

  18. John R. Rice. Numerical Methods, Software, and Analysis, chapter 3, pages 33–58. McGraw-Hill, Inc., New York, IMSL Reference edition, 1983.

    Google Scholar 

  19. R. H. Risch. The Problem of Integration in Finite Terms. Transactions of the American Mathematical Society, 139:167–189, May 1969.

    Google Scholar 

  20. Bert Speelpenning. Compiling Fast Partial Derivatives of Functions Given by Algorithms. PhD thesis, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, January 1980.

    Google Scholar 

  21. Stanly Steinberg and Patrick Roache. Using Vaxima to Write Fortran Code. In V. Ellen Golden, editor, Proceedings of the 1984 Macsyma User's Conference, pages 1–22. General Electric, Schenectady, New York, July 1984.

    Google Scholar 

  22. J. A. van Hulzen. Breuer's grow factor algorithm in computer algebra. In Proceedings of the 1981 ACM Symposium on Symbolic and Algebraic Computation, pages 100–104, 1981.

    Google Scholar 

  23. J. A. van Hulzen. Code Optimization of Multivariate Polynomial Schemes: A Pragmatic Approach. In J. A. van Hulzen, editor, Computer Algebra, Eurocal 83 (European Computer Algebra Conference, London, England, March 1983, pages 286–300, Berlin, 1983. Springer-Verlag.

    Google Scholar 

  24. J. A. van Hulzen and B. J. A. Hulshof. An Expression Analysis Package for REDUCE. SIGSAM Bulletin, 16(4):32–44, 1982.

    Google Scholar 

  25. Paul S. Wang. FINGER: A Symbolic System for Automatic Generation of Numerical Programs in Finite Element Analysis. Journal of Symbolic Computation, 2(3):305–316, September 1986.

    Google Scholar 

  26. Michael C. Wirth. On the Automation of Computational Physics. PhD thesis, University of California, Davis, October 1980. Also available as Lawrence Livermore National Laboratory, Livermore, Report UCRL-52996 (October 1980).

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Mark P. W. Mutrie, Bruce W. Char & Richard H. Bartels

Authors
  1. Mark P. W. Mutrie
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  2. Bruce W. Char
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  3. Richard H. Bartels
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James H. Davenport

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© 1989 Springer-Verlag Berlin Heidelberg

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Mutrie, M.P.W., Char, B.W., Bartels, R.H. (1989). Expression optimization using high-level knowledge. In: Davenport, J.H. (eds) Eurocal '87. EUROCAL 1987. Lecture Notes in Computer Science, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51517-8_90

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  • DOI: https://doi.org/10.1007/3-540-51517-8_90

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51517-3

  • Online ISBN: 978-3-540-48207-9

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