Computing

, Volume 53, Issue 3–4, pp 219–232 | Cite as

The computation of elementary functions in radix 2p

  • X. Merrheim
Article
  • 41 Downloads

Abstract

Many hardware-oriented algorithms computing the usual elementary functions (sine, cosine, exponential, logarithm, ...) only use shifts and additions. In this paper, we present new algorithms using shifts, adds and “small multiplications” (i. e. multiplications by few-digit-numbers). These CORDIC-like algorithms compute the elementary functions in radix 2p (instead of the standard radix 2) and use table look-ups. The number of the required steps to compute functions with a given accuracy is reduced and since we use a quick “small multiplier”, the computation time is reduced.

Key words

Computer arithmetic elementary functions high radices CORDIC-like algorithms discrete bases 

Berechnung elementarer Funktionen in der Basis 2p

Zusammenfassung

Viele hardware-orientierte Algorithmen zur Berechnung der üblichen Elementarfunktionen (Sinus, Cosinus, Exponentialfunktion, Logarithmus, ...) benützen nur Shifts und Additionen. In dieser Arbeit stellen wir neue Algorithmen vor, die zusätzlich noch “kleine Multiplikationen” (mit Zahlen von wenigen Stellen) benützen. Diese CORDIC-artigen Algorithmen berechnen die Elementarfunktionen in der Basis 2p (statt der standardbasis 2) und benützen Wertetabellen. Da-durch wird die Anzahl der für eine bestimmte Genauigkeit notwendigen Schritte reduziert und bei der Verwendung einer schnellen “kleinen Multiplikation” auch die Rechenzeit.

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References

  1. [1]
    Volder, J. A.: The cordic trigonometric computing technique. IRE Trans. Electron. Comput.8, 330–334 (1959).Google Scholar
  2. [2]
    Mazenc, C., Merrheim, X., Muller, J.-M.: Computing functions arccos and arcsin using cordic. Trans. Comput.42, 118–122 (1993).Google Scholar
  3. [3]
    Walther, J. S.: A unify algorithm for elementary functions. Proceedings of the Spring Joint Computer Conference, pp. 379–385, 1971.Google Scholar
  4. [4]
    Bajard, J.-C., Kla, S., Muller, J.-M.: Bkm: A new harware algorithm for complex elementary functions. Proceedings of the 11th symposium on computer arithmetic, 1993.Google Scholar
  5. [5]
    Schmid, H., Bogacki, A.: Use decimal cordic for generation of many transcendental functions. EDN, pp. 64–73, Feb. 1973.Google Scholar
  6. [6]
    Kropa, J. C.: Calculator algorithms. Math. Mag.51, 106–109 (1978).MATHGoogle Scholar
  7. [7]
    Muller, J.-M.: Discrete basis and computation of elementary functions. IEEE Trans. Comput.34, 857–862 (1985).MathSciNetGoogle Scholar
  8. [8]
    Ercegovac, M. D.: Radix-16 evaluation of certain elementary functions. IEEE Trans. Comput.22, 561–566 (1973).MATHGoogle Scholar
  9. [9]
    Wallace: A suggestion for parallel multipliers. IEEE Trans. Electron. Comput.,13, 14–17 (1964).MATHGoogle Scholar
  10. [10]
    Briggs, W. S., Matula, D. W.: A 17×69 bit multiply and add unit with redundant binary feedback and single cycle latency. Proceedings of the 11th Symposium on Computer Arithmetic, 1993.Google Scholar
  11. [11]
    Parikh, S. N., Matula, D. W.: A redundant binary euclidean gcd algorithm. Proceedings of the 10th Symposium on Computer Arithmetic, 1991.Google Scholar
  12. [12]
    Merrheim, X.: Calcul des fonctions elementaires par material et bases discretes (in French). Ecole Normal Superieure de Lyon, 1994.Google Scholar
  13. [13]
    Ferguson, W. E., Brightman, T.: Accurate and monotone approximations of some transcendental functions. Proceedings of the 10th Symposium on Computer Arithmetic, 1992.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • X. Merrheim
    • 1
  1. 1.Laboratory LIPEcole Normale Supérieure de LyonLyon Cédex 07France

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