Error-coded algorithms for on-line arithmetic

  • George Sinaki
Submitted Contributions Error Correcting Codes: Theory And Applications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 508)


A method is presented for detection and correction of errors in multi-module networks for high-speed numerical computations. The modules execute on-line arithmetic operations in which the results are generated during the digit-serial input of the operands, beginning always with the most significant digit. The error detection/correction method effectively uses low-cost arithmetic codes since the interconnections between on-line modules are of minimum bandwidth. By detecting errors in on-line manner, i.e., as they occur, an effective gracefully degradable organization could be achieved. An uncorrected error at the j-th step leads to restriction of precision in the remaining steps but not to a catastrophic termination of the computation. The code-preserving algorithms are developed and their performance and effectiveness evaluated. Two particular schemes based on residue and AN encoding are discussed.


Arithmetic Unit Uncorrected Error Arithmetic Algorithm Quotient Digit High Radix 
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6 References

  1. 1).
    Ercegovac, M.D., “A General Method for Evaluation of Functions and Computations in a Digital Computer”, Ph.D. Thesis, Report No. 750, Department of Computer Science, University of Illinois, Urbana, August 1975.Google Scholar
  2. 2).
    Trivedi, K.S. and Ercegovac, M.D., “On-Line Algorithms for Division and Multiplication” IEEE Trans. on Comput., Vol. C-26, No.7, July 1977.Google Scholar
  3. 3).
    Irwin, M.J., “An Arithmetic Unit for On-Line Computation”, Ph.D. dissertation, University of Illinois at Urbana-Champaign, report No. UIUCDCS-R-77-873.Google Scholar
  4. 4).
    Ercegovac, M.D. and Grnarov, A.L., “On The Performance of On-Line Arithmetic”, Proc. 1980 International Conference on Parallel Processing, Michigan, 1980.Google Scholar
  5. 5).
    Avizienis, A. “Signed Digit Number Representation for Fast Parallel Arithmetic”, IRE Trans. Electron. Comput., Vol. EC-10, pp. 389–400, 1961.Google Scholar
  6. 6).
    Ercegovac, M.D., “An On-Line Square Rooting Algorithm”, Proc. 4th IEEE Symp. Comput. Arithmetic, pp. 183–189, October 1978.Google Scholar
  7. 7).
    Oklobdzija, V.G., “An On-Line Higher Radix Square Rooting Algorithm”, M.S. Thesis, Computer Science Department, University of California, Los Angeles, June 1978.Google Scholar
  8. 8).
    Grnarov, A.L. and Ercegovac, M.D., “An Algorithm for On-Line Normalization,” UCLA Computer Science Department Quarterly, Vol.7, No.3, pp. 81–94, July 1979.Google Scholar
  9. 9).
    Sinaki, G., “Error-Coded Algorithms for On-Line Arithmetic”, Technical Report UCLA-ENG-8197, Computer Science Department, University of California, Los Angeles, February 1981.Google Scholar
  10. 10).
    Trivedi, K.S. and Rusnak, J.G., “Higher Radix On-Line Division”, Proc. 4th IEEE Symp. Comput. Arithmetic, pp. 164–174, October 1978.Google Scholar
  11. 11).
    Grnarov, A.L. and Ercegovac, M.D., “VLSI-Oriented Iterative Networks for Array Computations”, Proc. of International Conference on Circuits and Computers, 1980.Google Scholar
  12. 12).
    Atkins, D.E., “Higher Radix Division Using Estimates of the Divisor and Partial Remainders”, IEEE Trans. on Computers, Vol.C-17, No. 10, pp. 925–931, October 1968.Google Scholar
  13. 13).
    Avizienis, A., “Arithmetic Error Codes: Cost and Effectiveness Studies for Application in Digital System Design”, IEEE Trans. on Comput., Vol. C-20, No. 11, Nov. 1971, pp. 1322–1331.Google Scholar
  14. 14).
    Sinaki, G. and Ercegovac, M.D., “Design of a Digit-Slice On-Line Arithmetic Unit”, in Proceedings of the Fifth Symposium on Computer Arithmetic, Ann Arbor, Michigan, May 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • George Sinaki
    • 1
  1. 1.Delco Systems OperationsGoletaUSA

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