Skip to main content

Process Variation Aware Performance Analysis of Asynchronous Circuits Considering Spatial Correlation

  • Conference paper
Integrated Circuit and System Design. Power and Timing Modeling, Optimization and Simulation (PATMOS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5953))

Abstract

Current technology trends have led to the growing impact of process variations on performance of asynchronous circuits. As it is imperative to model process parameter variations for sub-100nm technologies to produce a more real performance metric, it is equally important to consider the correlation of these variations to increase the accuracy of the performance computation. In this paper, we present an efficient method for performance evaluation of asynchronous circuits considering inter and intra-die process variation. The proposed method includes both statistical static timing analysis (SSTA) and statistical Timed Petri-Net based simulation. Template-based asynchronous circuit has been modeled using Variant-Timed Petri-Net. Based on this model, the proposed SSTA calculates the probability density function of the delay of global critical cycle. The efficiency for the proposed SSTA is obtained from a technique that is derived from the principal component analysis (PCA) method. This technique simplifies the computation of mean, variance and covariance values of a set of correlated random variables. In order to consider spatial correlation in the Petri-Net based simulation, we also include a correlation coefficient to the proposed Variant-Timed Petri-Net which is obtained from partitioning the circuit. We also present a simulation tool of Variant-Timed Petri-Net and the results of the experiments are compared with Monte-Carlo simulation-based method.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tang, Lin, C.Y., Lu, Y.C.: An Asynchronous Circuit Design with Fast Forwarding Technique at Advanced Technology Node. In: Proceedings of ISQED 2008. IEEE Computer Society, Los Alamitos (2008)

    Google Scholar 

  2. Beerel, P.A.: Asynchronous Circuits: An Increasingly Practical Design Solution. In: Proceedings of ISQED 2002. IEEE Computer Society, Los Alamitos (2002)

    Google Scholar 

  3. Martin, A.J., et al.: The Lutonium: A Sub-Nanojoule Asynchronous 8051 Microcontroller. In: ASYNC 2003 (2003)

    Google Scholar 

  4. Yun, K.Y., Beerel, P.A., Vakilotojar, V., Dooply, A.E., Arceo, J.: A low-control-overhead asynchronous differential equation solver. In: Proceedings of ASYNC (1997)

    Google Scholar 

  5. Garnica, O., Lanchares, J., Hermida, R.: Fine-grain asynchronous circuits for low-power high performance DSP implementations. In: SiPS 2000 (2000)

    Google Scholar 

  6. McGee, P.B., Nowick, S.M., Coffman Jr., E.G.: Efficient performance analysis of asynchronous systems based on periodicity. In: Proceedings of the 3rd IEEE/ACM/IFIP international conference on Hardware/software codesign and system synthesis (2005)

    Google Scholar 

  7. Visweswariah, C., et al.: First-order incremental block-based statistical timing analysis. In: Proc. of DAC (2004)

    Google Scholar 

  8. Wang, W.-S., Kreinovich, V., Orshansky, M.: Statistical timing based on incomplete probabilistic descriptions of parameter uncertainty. In: Proc. of DAC (2006)

    Google Scholar 

  9. Pang, P.B., Greenstreet, M.: Self-timed meshesare faster than synchronous

    Google Scholar 

  10. Xie, A., Kim, S., Beerel, P.A.: Bounding average time separationsof events in stochastictimed petrinets with choice. In: Proceedings of ASYNC (1999)

    Google Scholar 

  11. Pang, P.B., Greenstreet, M.: Self-timed meshesare faster than synchronous. In: Proceedings of ASYNC (1997)

    Google Scholar 

  12. Yahya, E., Renaudin, M.: Performance Modeling and Analysis of Asynchronous Linear-Pipeline with Time Variable Delays. In: ICECS 2007 (2007)

    Google Scholar 

  13. Commoner, F., Holt, A., Even, S., Pnueli, A.: Marked directed graphs. Journal of Computer and System Sciences 5, 511–523 (1971)

    MATH  MathSciNet  Google Scholar 

  14. Wong, C.G., Martin, A.J.: High-Level Synthesis of Asynchronous Systems by Data Driven Decomposition. In: Proc. of 40th DAC, Anneheim, CA, USA (June 2003)

    Google Scholar 

  15. Dinh Duc, A.V., Rigaud, J.B., Rezzag, A., Sirianni, A., Fragoso, J., Fesquet, L., Renaudin, M.: TASTCAD Tools: Tutorial. In: Proc. of Advanced Research in Asynchronous Circuits and Systems, ASYNC 2002 (2002)

    Google Scholar 

  16. Ghavami, B., Pedram, H.: Design of Dual Threshold Voltages Asynchronous Circuits. In: ISLPED 2008, pp. 185–188 (2008)

    Google Scholar 

  17. Prakash, P., Martin, A.J.: Slack Matching Quasi Delay-Insensitive Circuits. In: ASYNC 2006, pp. 195–204 (2006)

    Google Scholar 

  18. Xie, A., Kim, S., Beerel, P.A.: Bounding average time separations of events in stochastic timed Petri nets with choice. In: ASYNC, pp. 94–107 (1999)

    Google Scholar 

  19. Burns, S.M., Martin, A.J.: Performance Analysis and Optimization of Asynchronous circuits. In: Advanced Research in VLSI conference, Santa Cruz, CA (March 1991)

    Google Scholar 

  20. Kim, S.: Pipeline Optimization for Asynchronous circuits. PHD Thesis, University of Southern California (August 2003)

    Google Scholar 

  21. Orshansky, M., Nassif, S.R., Boning, D.: Design for Manufacturability and Statistical Design, A Constructive Approach, pp. 11–15. Springer, Heidelberg (2008)

    Google Scholar 

  22. Lines, A.M.: Pipelined asynchronous circuits. Master’s thesis, California Institute of Technology, Computer Science Department, 1995 CS-TR-95-21 (1995)

    Google Scholar 

  23. Beerel, P.A., Kim, N.-H., Lines, A., Davies, M.: Slack Matching Asynchronous Designs. In: Proceedings of the 12th IEEE International Symposium on Asynchronous Circuits and Systems, Washington, DC, USA (2006)

    Google Scholar 

  24. Karp, R.M.: A characterization of the minimum cycle mean in a diagraph. Discrete Mathematics  23, 309–311 (1978)

    MATH  MathSciNet  Google Scholar 

  25. Dasdan, A., Gupta, R.K.: Faster maximum and minimum mean cycle algorithms for system performance analysis. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems 17(10), 889–899 (1998)

    Article  Google Scholar 

  26. Liu, H., Wang, J.: A new way to enumerate cycles in graph. In: Proceedings of the Advanced International Conference on Telecommunications and International Conference on Internet and Web Applications and Services, AICT/ICIW (2006)

    Google Scholar 

  27. Clark, C.E.: The Greatest of a Finite Set of Random Variable. Operations Research 9, 85–91 (1961)

    Google Scholar 

  28. Lane, B.: SystemC Language Reference Manual. Copyright © 2003 Open SystemC Initiative,San Jose, CA

    Google Scholar 

  29. PTM: http://www.eas.asu.edu/~ptm

  30. Raji, M., Ghavami, B., Pedram, H.: Statistical Static Performance Analysis of Asynchronous Circuits Considering Process Variation. In: Proceedings of ISQED 2009. IEEE Computer Society, Los Alamitos (2009)

    Google Scholar 

  31. Agarwal, A., Blaauw, D., Zolotov, V.: Statistical timing analysis forintra - die process variations with spatial correlations. In: IEEE International Conference on Computer Aided Design, pp. 900–907 (2003)

    Google Scholar 

  32. Seber, G.: MultivariateObservations. Wiley Series (1984)

    Google Scholar 

  33. Li, X., Le, J., Pileggi, L.T.: Statistical Performance Modeling and Optimization. Foundation and Trends in Electronic Design Automation 1(4) (2003)

    Google Scholar 

  34. Nassif, S.R.: Modeling and Analysis of Manufacturing Variations. In: IEEE 2001 Custom Integrated Circuits Conference, pp. 223–228 (2001)

    Google Scholar 

  35. Chang, H., Sapatnekar, S.: Statistical timing analysis under spatial correlations. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems 24(9), 1467–1482 (2005)

    Article  Google Scholar 

  36. Persia: A QDI Asynchronous Synthesis Tool. In: ASYNC 2008 (2008)

    Google Scholar 

  37. Morrison, D.F.: Multivariate Statistical Methods. McGraw-Hill, New York (1976)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Raji, M., Ghavami, B., Zarandi, H.R., Pedram, H. (2010). Process Variation Aware Performance Analysis of Asynchronous Circuits Considering Spatial Correlation. In: Monteiro, J., van Leuken, R. (eds) Integrated Circuit and System Design. Power and Timing Modeling, Optimization and Simulation. PATMOS 2009. Lecture Notes in Computer Science, vol 5953. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11802-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11802-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11801-2

  • Online ISBN: 978-3-642-11802-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics