Advertisement

Mathematical Functions and Array Processing

  • John B. Gosling

Abstract

The earlier chapters of this book have described the design criteria for performing the basic arithmetic operations, together with some extensions needed for most machines. This chapter will discuss some additional functions that the unit could perform. Most of these are only useful for machines intended primarily for mathematical applications, though some, such as vector operations, have been shown to have applications in data processing as well. Some of the procedures to be described have been applied; others are possible contenders for the future, when the cost of the hardware has been further reduced.

Keywords

Digital Computer Array Processor Array Processing Polynomial Evaluation Arithmetic Unit 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baker, P. W., ‘More Efficient Radix 2 Algorithms for Some Elementary Functions’, I.E.E.E. Trans. Comput., 24 (1975) 1049–54.CrossRefzbMATHGoogle Scholar
  2. Baskett, F., and Keller, T. W., ‘An Evaluation of the Cray-1 Computer’, in High Speed Computer and Algorithm Organization, ed. David J. Kuck et al. (Academic Press, New York, 1977) pp. 71–84.Google Scholar
  3. Chen, T. C, ‘Automatic Computation of Exponentials, Logarithms, Ratios and Square Roots’, IBM Jl Res. Dev., 16 (1972) 380–8.CrossRefzbMATHGoogle Scholar
  4. de Lugish, B. G., ‘A Class of Algorithms for Automatic Evaluation of Certain Elementary Functions in a Binary Computer’, University of Illinois Report 399 (1970).Google Scholar
  5. Ercegovac, M. D., ‘Radix 16 Evaluation of Certain Elementary Functions’, I.E.E.E. Trans. Comput., 22 (1973) 561–6.CrossRefzbMATHGoogle Scholar
  6. Flanders, P. M., Hunt, D. J., Reddaway, S. F., and Parkinson, D., ‘Efficient High. Speed Computing with the Distributed Array Processor’, in High Speed Computer and Algorithm Organization, ed. David J. Kuck et al. (Academic Press, New York, 1977) pp. 71–84.Google Scholar
  7. Hart, J. F., Computer Approximations (Wiley, Chichester, 1968). Contains lists of constants for polynomials and their derivations.Google Scholar
  8. Meggitt, J. E., ‘Pseudo Division and Pseudo Multiplication Processes’, IBM Jl Res. Dev., 6 (1962) 210–26. Does, in fact, refer to function evaluation.CrossRefzbMATHGoogle Scholar
  9. Rodrigues, M. R. D., ‘Algorithms for the Fast Hardware Evaluation of Mathematical Functions’, M.Sc. Thesis (University of Manchester, 1978).Google Scholar
  10. Schmidt, H., Decimal Computation (Wiley, Chichester, 1974). Despite the title, the algorithms can be used in binary as well as decimal. A useful book.Google Scholar
  11. Voider, J. E., ‘The CORDIC Trigonometric Computing Technique’, LE.E.E. Trans. electronic Comput., 8 (1959) 330–4.Google Scholar
  12. Walther, T. S., ‘A Unified Algorithm for Elementary Functions’, AFIPS SJCC, 38 (1971) 379–85.Google Scholar

Copyright information

© John B. Gosling 1980

Authors and Affiliations

  • John B. Gosling
    • 1
  1. 1.Department of Computer ScienceUniversity of ManchesterUK

Personalised recommendations