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A pipelined processing unit for on-line division

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Mary Jane IrwinAuthors Info & Claims

ISCA '78: Proceedings of the 5th annual symposium on Computer architecture

Pages 24 - 30

https://doi.org/10.1145/800094.803023

Published: 03 April 1978 Publication History

Abstract

A division algorithm suitable for pipelining is presented. The algorithm possesses the on-line property: that is, to generate the j^th digit of a result (where a digit consists of n bits for base 2ⁿ), it is necessary and sufficient to have the operands available only up to the j^th digit plus a predetermined number of extra digits which correspond to an “on-line delay”. This delay is shown to be a small, positive, radix dependent constant. The implementation of this algorithm and the implications on cost and speed are then presented. Finally, alterations in the design making the algorithm suitable for pipelining and its benefits are discussed.

References

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Anderson, S. F., et. al., "The System/360 Model 91 Floating Point Execution Unit," IBM System Journal 11, Vol. 34, 1967.

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Atkins, D. E., "Higher Radix Division Using Estimates of the Divisor and Partial Remainders," IEEE Transactions on Computers, Vol. C-17, No. 10, pp. 925-934, October 1968.

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Atkins, D. E., "A Study of Methods for Selection of Quotient Digits During Digital Division," Ph.D. Thesis, Report 397, Department of Computer Science, University of Illinois, Urbana, June 1970.

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Atkins, D. E., "Introduction to the Role of Redundancy in Computer Arithmetic," Computer, Vol. 8, No. 6, pp. 74-76, June 1975.

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Chen, T. C., "Overlap and Pipeline Processing," Introduction to Computer Architecture, H. S. Stone, (Ed.), SRA, Chicago, IL, 1975.

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DeLugish, B. G., "A Class of Algorithms for Automatic Evaluation of Certain Elementary Functions in a Binary Computer," Ph.D. Thesis, Report 399, Department of Computer Science, University of Illinois, Urbana, June 1970.

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Hallin, T. and M. Flynn, "Pipelining of Arithmetic Functions," IEEE Transactions on Computers, Vol. C-21, pp. 880-886, August 1972.

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Irwin, M. J., "An Arithmetic Unit for On-line Computation," Report No. UIUCDCS-R-77-873, Department of Computer Science, University of Illinois, Urbana, May 1977.

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Ramamoorthy, C. V. and H. F. Li, "Pipeline Architecture," Computing Surveys, Vol. 9, No. 1, pp. 61-102, March 1977.

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Trivedi, K. S. and M. D. Ercegovac, "On-line Algorithms for Division and Multiplication," Proceedings of Third IEEE Symposium on Computer Arithmetic, Dallas, Texas, November 1975.

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Trivedi, K. and M. D. Ercegovac, "On-line Algorithms for Division and Multiplication," IEEE Transaction on Computers, Vol. C-26, No. 7, pp. 681-687, July 1977.

Cited By

Lin HSips H(1990)On-Line CORDIC AlgorithmsIEEE Transactions on Computers10.1109/12.5704339:8(1038-1052)Online publication date: 1-Aug-1990
https://dl.acm.org/doi/10.1109/12.57043
Duprat JHerreros YMuller J(1989)Some results about on-line computation of functionsProceedings of 9th Symposium on Computer Arithmetic10.1109/ARITH.1989.72816(112-118)Online publication date: 1989
https://doi.org/10.1109/ARITH.1989.72816
Guyot AHerreros YMuller J(1989)JANUS, an on-line multiplier/divider for manipulating large numbersProceedings of 9th Symposium on Computer Arithmetic10.1109/ARITH.1989.72815(106-111)Online publication date: 1989
https://doi.org/10.1109/ARITH.1989.72815
Show More Cited By

Index Terms

A pipelined processing unit for on-line division
1. Computer systems organization
  1. Architectures
    1. Serial architectures
      1. Pipeline computing

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cover image ACM Conferences

ISCA '78: Proceedings of the 5th annual symposium on Computer architecture

April 1978

256 pages

ISBN:9781450374002

DOI:10.1145/800094

Copyright © 1978 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 03 April 1978

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Cited By

Lin HSips H(1990)On-Line CORDIC AlgorithmsIEEE Transactions on Computers10.1109/12.5704339:8(1038-1052)Online publication date: 1-Aug-1990
https://dl.acm.org/doi/10.1109/12.57043
Duprat JHerreros YMuller J(1989)Some results about on-line computation of functionsProceedings of 9th Symposium on Computer Arithmetic10.1109/ARITH.1989.72816(112-118)Online publication date: 1989
https://doi.org/10.1109/ARITH.1989.72816
Guyot AHerreros YMuller J(1989)JANUS, an on-line multiplier/divider for manipulating large numbersProceedings of 9th Symposium on Computer Arithmetic10.1109/ARITH.1989.72815(106-111)Online publication date: 1989
https://doi.org/10.1109/ARITH.1989.72815
Lin HSips H(1989)On-line CORDIC algorithmsProceedings of 9th Symposium on Computer Arithmetic10.1109/ARITH.1989.72806(26-33)Online publication date: 1989
https://doi.org/10.1109/ARITH.1989.72806
Owens R(1983)Techniques to Reduce the Inherent Limitations of Fully Digit On-Line ArithmeticIEEE Transactions on Computers10.1109/TC.1983.167624432:4(406-411)Online publication date: 1-Apr-1983
https://dl.acm.org/doi/10.1109/TC.1983.1676244
Irwin MOwens R(1983)Fully Digit On-Line NetworksIEEE Transactions on Computers10.1109/TC.1983.167624332:4(402-406)Online publication date: 1-Apr-1983
https://dl.acm.org/doi/10.1109/TC.1983.1676243
Hwang KSu SNi L(1981)Vector Computer Architecture and Processing TechniquesAdvances in Computers Volume 2010.1016/S0065-2458(08)60497-0(115-197)Online publication date: 1981
https://doi.org/10.1016/S0065-2458(08)60497-0
Irwin MHeller DLenfant JBorgerson BAtkins DIrani KKinniment DAiso H(1980)Online pipeline systems for recursive numeric computationsProceedings of the 7th annual symposium on Computer Architecture10.1145/800053.801937(292-299)Online publication date: 6-May-1980
https://dl.acm.org/doi/10.1145/800053.801937
Irwin MAusting RConti DEngel G(1978)Reconfigurable Pipeline SystemsProceedings of the 1978 annual conference10.1145/800127.804073(86-92)Online publication date: 4-Dec-1978
https://dl.acm.org/doi/10.1145/800127.804073

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