Interval Valued Analysis for Efficient Variational/Range Modeling of Circuits and Systems

Group members: Claire F. Fang, James D. Ma, , Amith Singhee

Collaborators: Duane Boning, MIT; Tsuhan Chen, CMU; Markus Pueschel, CMU

Recent advances in the handling of correlated interval representations of range uncertainty can be used to predict the impact of statistical manufacturing variations on nanoscale circuits and interconnect structures, and to predict how many bits are sufficient — or insufficient — in DSP algorithms that use custom hardware to process unknown streams of input data. We represent correlated statistical variations (in circuit/interconnect parameters, or in DSP input data) as sets of correlated intervals, and show how several important classical algorithms can be re-targeted to compute interval-valued, rather than scalar-valued outputs. By applying a statistical interpretation and sampling to the resulting compact interval-valued outputs of these algorithms, we can efficiently estimate the impact of statistical/range variations on the original circuit/system. We have successfully implemented a range of classical model order reduction methods (AWE, PRIMA), technology CAD algorithms (chemical mechanical polishing, CMP), and very efficiently analyzed the impacts of DSP fixed-point precision effects.


Key Papers/Talks

  • Claire F. Fang, Tsuhan, Rob A. Rutenbar, “Floating-point error analysis based on affine arithmetic,” Proc. IEEE International Conference onAcoustics, Speech, and Signal Processing, 2003. (ICASSP ’03), Volume 2, April 2003. pdf links to rutenbar-icassp03.pdf)
  • Claire F. Fang, Rob A. Rutenbar, Markus Pueschel, Tsuhan Chen, “Toward efficient static analysis of finite-precision effects in DSP applications via affine arithmetic modeling,” Proc, ACM/IEEE Design Automation Conference, Jun 2003. (Best Paper Nominee.) pdf
  • Claire F. Fang, Rob A. Rutenbar, Tsuhan Chen, “Fast, accurate static analysis for fixed-point finite-precision effects in DSP designs,” Proc. ACM/IEEE International Conf. on Computer Aided Design, Nov. 2003. pdf
  • J.D. Ma, R.A. Rutenbar, “Interval-valued reduced order statistical interconnect modeling,” Proc. ACM/IEEE International Conference on CAD, Nov. 2004. pdf
  • J.D. Ma, R.A. Rutenbar, “Fast interval-valued statistical interconnect modeling and reduction,” Proc. ACM International Symposium on Physical Design (ISPD05), APril 2005. pdf
  • J.D. Ma, R.A. Rutenbar, “Fast interval-valued statistical modeling of interconnect and effective capacitance,” IEEE Trans. CAD, Volume 25, Issue 4, April 2006. pdf
  • A. Singhee, C. Fang, J.D. ma, R.A. Rutenbar, “Probabilistic interval-valued computation: toward a practical surrogate for statistics inside CAD tools,” Proc. ACM/IEEE 43rd Design Automation Conference, July 2006. pdf
  • J.D. Ma, C.F. Fang, R.A. Rutenbar, X. Xie, D.S. Boning, “Interval-valued statistical modeling of oxide chemical-mechanical polishing,” Proc. IEEE/ACM International Conference on CAD, Nov. 2006. pdf
  • J.D. Ma, R.A. Rutenbar, “Interval-Valued Reduced-Order Statistical Interconnect Modeling, IEEE Trans. CAD, Volume 26, Issue 9, Sept. 2007. pdf

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