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Performance optimization of single-phase level-sensitive circuits using time borrowing and non-zero clock skew

Published: 02 December 2002 Publication History
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  • Abstract

    This paper describes a linear programming (LP) formulation for performance optimization of large-scale, synchronous circuits with level-sensitive latches. The proposed formulation permits circuits to operate at a higher clock frequency---that is, with a lower clock period---by the application of both non-zero clock skew scheduling [7] and time borrowing [9]. This LP formulation is computationally efficient and demonstrates significant circuit performance improvement. Unlike the approach documented in [2], the LP model of the clock period minimization problem presented here is stand-alone and independent of the specific LP solver (solution algorithm) used. The modified big M (MBM) method is introduced and applied to the linearization of the non-linear timing constraints of level-sensitive circuits into a solvable set of fully linear constraints. Clock period improvements as large as 63% are demonstrated over conventional flip-flop based circuits with zero clock skew. These improvements are shown on the ISCAS'89 benchmark circuits by using the industrial linear solver CPLEX [1].

    References

    [1]
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    [2]
    M. R. Dagenais and N. C. Rumin. On the calculation of optimal clocking parameters in synchronous circuits with level-sensitive latches. IEEE Transactions on Computer-Aided Design, CAD-8(3):268--278, March 1989.
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    J. P. Fishburn. Clock skew optimization. IEEE Transactions on Computers, C--39(7):945--951, July 1990.
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    E. G. Friedman. Clock Distribution Networks in VLSI Circuits and Systems. IEEE Press, 1995.
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    I. S. Kourtev and E. G. Friedman. A quadratic programming approach to clock skew scheduling for reduced sensitivity to process parameter variations. In Proceedings of the 1999 IEEE ASIC/SOC Conference, 1999.
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    I. S. Kourtev and E. G. Friedman. Timing Optimization Through Clock Skew Scheduling. Kluwer Academic Publishers, 2000.
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    J. Lee, D. T. Tang, and C. K. Wong. A timing analysis algorithm for circuits with level-sensitive latches. IEEE Transactions on Computer-Aided Design, CAD-15(5):535--543, May 1996.
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    I. Lin, J. A. Ludwig, and K. Eng. Analyzing cycle stealing on synchronous circuits with level-sensitive latches. Proceedings of the 29th ACM/IEEE Design Automation Conference, pages 393--398, June 1992.
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    K. A. Sakallah, T. N. Mudge, and O. A. Olukotun. checkTc and minTc: Timing verification and optimal clocking of synchronous digital circuits. Proceedings of the IEEE/ACM International Conference on Computer--Aided Design, pages 552--555, November 1990.
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    K. A. Sakallah, T. N. Mudge, and O. A. Olukotun. Analysis and design of latch-controlled synchronous digital circuits. IEEE Transactions on Computer-Aided Design, CAD-11(3):322--333, March 1992.
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    N. Shenoy, R. K. Brayton, and A. L. Sangiovanni-Vincentelli. Graph algorithms for clock schedule optimization. Proceedings of the IEEE/ACM International Conference on Computer--Aided Design, pages 132--136, November 1992.
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    T. G. Syzmanski and N. Shenoy. Verifying clock schedules. Proceedings of the IEEE/ACM International Conference on Computer--Aided Design, pages 124--131, November 1992.
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    T. G. Szymanski. Computing optimal clock schedules. Proceedings of the 29th ACM/IEEE Design Automation Conference, pages 399--404, June 1992.
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    W. L. Winston. Operations Research Application and Algorithms. PWS-Kent Publishing Company, second edition, 1991.

    Cited By

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    • (2013)Algebraic approach to time borrowingIET Computers & Digital Techniques10.1049/iet-cdt.2012.01037:1(1-10)Online publication date: Jan-2013
    • (2006)Delay insertion method in clock skew schedulingIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2006.87007225:4(651-663)Online publication date: 1-Nov-2006
    • (2005)Delay insertion method in clock skew schedulingProceedings of the 2005 international symposium on Physical design10.1145/1055137.1055149(47-54)Online publication date: 3-Apr-2005
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    cover image ACM Conferences
    TAU '02: Proceedings of the 8th ACM/IEEE international workshop on Timing issues in the specification and synthesis of digital systems
    December 2002
    156 pages
    ISBN:1581135262
    DOI:10.1145/589411
    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: 02 December 2002

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    Author Tags

    1. clock skew
    2. cycle stealing
    3. linear programming
    4. optimization

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    TAU '02 Paper Acceptance Rate 19 of 42 submissions, 45%;
    Overall Acceptance Rate 19 of 42 submissions, 45%

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    Cited By

    View all
    • (2013)Algebraic approach to time borrowingIET Computers & Digital Techniques10.1049/iet-cdt.2012.01037:1(1-10)Online publication date: Jan-2013
    • (2006)Delay insertion method in clock skew schedulingIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2006.87007225:4(651-663)Online publication date: 1-Nov-2006
    • (2005)Delay insertion method in clock skew schedulingProceedings of the 2005 international symposium on Physical design10.1145/1055137.1055149(47-54)Online publication date: 3-Apr-2005
    • (2004)Statistical timing analysis in sequential circuit for on-chip global interconnect pipeliningProceedings of the 41st annual Design Automation Conference10.1145/996566.996806(904-907)Online publication date: 7-Jun-2004
    • (2004)Advanced timing of level-sensitive sequential circuitsProceedings of the 2004 11th IEEE International Conference on Electronics, Circuits and Systems, 2004. ICECS 2004.10.1109/ICECS.2004.1399753(603-606)Online publication date: 2004

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