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Precision control, exception handling and a choice of numerical algorithms

Part of the Lecture Notes in Mathematics book series (LNM,volume 912)

Abstract

We require more appropriate programming language facilities if we are to implement the numerical processes we would like to have. The needs for precision control and exception handling are particularly urgent, and some specific proposals for meeting these needs are outlined. A number of examples are then used to illustrate the effectiveness of these new facilities, and in particular, to show what a wide choice of possible numerical processes is made available to the user with the help of these facilities. Finally, brief mention is made of the use of preprocessors, of the design of a new language for numerical computation, and of an arithmetic unit that is now under construction. Experience with these systems helps support the claim that the proposed facilities can be provided both economically and efficiently.

Keywords

  • Double Precision
  • Interval Arithmetic
  • Numerical Process
  • Decimal Digit
  • Exception Handling

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. M. Cohen, V.C. Hamacher and T.E. Hull. CADAC: An Arithmetic Unit for Clean Decimal Arithmetic and Controlled Precision, Proceedings 5th Symposium on Computer Arithmetic, IEEE Computer Society, Ann Arbor, Michigan, 1981, pp. 106–112.

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  2. Austin Curley. PNCL: A Prototype Numerical Computation Language, M.Sc. thesis, Department of Computer Science, University of Toronto, in preparation.

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  4. T.E. Hull. Semantics of Floating Point Arithmetic and Elementary Functions, Portability of Numerical Software, edited by Wayne Cowell, Springer-Verlag, 1977, pp. 37–48.

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  5. T.E. Hull. Desirable Floating-Point and Elementary Functions for Numerical Computation, Proceedings Conference on the Programming Environment for Development of Numerical Software, SIGNUM Newsletter 14, 96–99, 1979, and a similar paper in Proceedings 4th Symposium on Computer Arithmetic, IEEE Computer Society, Santa Monica, California, 1978, pp.63–69.

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  6. T.E. Hull and J.J. Hofbauer. Language Facilities for Multiple Precision Floating Point Computation, with Examples, and the Description of a Preprocessor, Technical Report 63, Department of Computer Science, University of Toronto, 1974.

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  7. T.E. Hull and J.J. Hofbauer. Language Facilities for Numerical Computation, Proceedings ACM-SIAM Conference on Mathematical Software II, Purdue University, 1974, pp. 1–18.

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© 1982 Springer-Verlag

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Hull, T.E. (1982). Precision control, exception handling and a choice of numerical algorithms. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093156

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  • DOI: https://doi.org/10.1007/BFb0093156

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11199-3

  • Online ISBN: 978-3-540-39009-1

  • eBook Packages: Springer Book Archive