Skip to main content
SpringerLink
Log in

Software for high radix on-line arithmetic

Программное обеспечение для компьютерной арифметики оперативного доступа с больщим основанием системы счисления

  • Published:
Reliable Computing

Abstract

High radix on-line arithmetic provides an efficient method for performing variable-precision arithmetic. It can be implemented on conventional microprocessors using sequences of three operand instructions. This paper presents software support for high radix on-line arithmetic. This software includes emulation modules for high radix operations, and a precision analysis program for setting the input and intermediate variable tolerances necessary for guaranteed result accuracy over a specified domain.

Abstract

Компьютерная арифметика оперативного доступа с большим основанием системы счисления предоставляет эффективный метод для вычислений с переменной разрядностью. Ее можно реализовать на обычных микропроцессорах с помощью последовательностей инструкций с тремя операндами. В работе представлена программная поддержка для компьютерной арифметики оперативного доступа с большим основанием системы счисления. Программное обеспечение включает в себя модули эмуляции для операций с большим основанием системы счисления, а также программу анализа разрядности, служащую для задания лопусков на исходные и промежуточные переменные, обеспечивающих гарантированную точность результата на заданной области.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alefeld, G. and Herzberger, J.Introduction to interval computations. Academic Press, 1983.

  2. Avizienis, A.Signed-digit number representations for fast parallel arithmetic. IRE Transactions on Electronic Computers10 (1961), pp. 389–400.

    Article  MathSciNet  Google Scholar 

  3. Bajard, J. C., Guyot, A., Muller, J.-M., and Skaf, A.Design of a VLSI circuit for on-line evaluation of several elementary functions using their Taylor expansions. In: “Proceedings of the 1993 International Conference on Application Specific Array Processors”, 1993, pp. 526–535.

  4. Benouamer, M. O., Jailon, P., Michelucci, D., and Moreau, J.-M.A lazy exact arithmetic. In: “Proceedings of the 11th Symposium on Computer Arithmetic”, IEEE Computer Society Press, 1993, pp. 242–249.

  5. Ercegovac, M. D. and Lang, T.Fast multiplication without carry-propagate addition. IEEE Transactions on ComputersC-39 (1990), pp. 1385–1390.

    Article  Google Scholar 

  6. Ercegovac, M. D. and Lang, T.On-line arithmetic: a design methodology and applications to digital signal processing. IEEE Press, 1988, pp. 252–263.

  7. Herzberger, J.Basic definitions and properties of interval arithmetic. In: Herzberger, J. (ed.) “Topics in Validated Computations. Proceedings of IMACS-GAMM International Workshop on Validated Numerics”, North Holland, 1994, pp. 1–6.

  8. Knüppel, O.PROFIL/BIAS—a fast interval library. Computing53 (1994), pp. 277–288.

    Article  MATH  MathSciNet  Google Scholar 

  9. Lynch, T. and Schulte, M. J.A high radix on-line arithmetic for credible and accurate computing. Journal of Universal Computer Science1 (7) (1995), pp. 435–449.

    MathSciNet  Google Scholar 

  10. Moore, R. E.Interval analysis. Prentice Hall, 1966.

  11. Phatak, D. S. and Koren, I.Hybrid signed-digit number systems: a unified framework for redundant number representations with bounded carry propagation chains. IEEE Transactions on ComputersC-43 (8) (1994), pp. 880–891.

    Article  Google Scholar 

  12. Trivedi, K. S. and Ercegovac, M. D.On-line algorithms for division and multiplication. IEEE Transactions on ComputersC-26 (7) (1977), pp. 681–687.

    MathSciNet  Google Scholar 

  13. Watanuki, O. and Ercegovac, M. D.Error analysis of certain floating-point on-line algorithms. IEEE Transactions on ComputersC-32 (4) (1983), pp. 352–358.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Advanced Architecture Development, Advanced Micro Devices, MS 615, 5204 East Ben White Blvd, 78741, Austin, TX, USA

    Thomas Lynch

  2. Department of Electrical and Computer Engineering, University of Texas at Austin, 78712, Austin, TX, USA

    Michael J. Schulte

Authors
  1. Thomas Lynch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael J. Schulte
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

© Th. Lynch, M. J. Schulte, 1996

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lynch, T., Schulte, M.J. Software for high radix on-line arithmetic. Reliable Comput 2, 133–138 (1996). https://doi.org/10.1007/BF02425915

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02425915

Keywords

Search

Navigation