Skip to main content

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

Abstract

This paper investigates the residue arithmetic as a solution for the design of variation-tolerant circuits. Motivated by the modular organization of residue processors, we comparatively study the sensitivity of residue arithmetic-based and binary processors to delay variations, and in particular the impact of delay variations onto the maximum critical path. Experiments are performed on two multiply-add (MAC) circuits based on residue and binary arithmetic. Results reveal that residue arithmetic-based circuits are up to 94% less sensitive to delay variation than binary circuits, thus leading to increased timing yield.

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. Michael, O., Sani, N., Boning, D.: Design for Manufacturability and Statistical Design: A Constructive Approach. Springer-Verlag New York, Inc., Secaucus (2006)

    Google Scholar 

  2. Srivastava, A., Sylvester, D., Blaauw, D.: Statistical Analysis and Optimization for VLSI: Timing and Power. Kluwer Academic Publishers, Dordrecht (2005)

    Google Scholar 

  3. Sapatnekar, S.: Timing. Kluwer Academic Publishers, Dordrecht (2004)

    MATH  Google Scholar 

  4. Najm, F.N.: On the need for statistical timing analysis. In: DAC 2005: Proceedings of the 42nd annual conference on Design automation, pp. 764–765. ACM, New York (2005)

    Chapter  Google Scholar 

  5. Rubanov, N.: An information theoretic framework to compute the MAX/MIN operations in parameterized statistical timing analysis. In: International Symposium on Quality Electronic Design, pp. 728–733 (2009)

    Google Scholar 

  6. Viswanath, P., Murthy, P., Das, D., Venkatraman, R., Mandal, A., Veeravalli, A.: Optimization strategies to improve statistical timing. In: International Symposium on Quality Electronic Design, pp. 476–481 (2009)

    Google Scholar 

  7. Singhee, A., Singhal, S., Rutenbar, R.A.: Practical, fast monte carlo statistical static timing analysis: Why and how. In: International Conference on Computer-Aided Design, pp. 190–195 (2008)

    Google Scholar 

  8. Jaffari, J., Anis, M.: On efficient monte carlo-based statistical static timing analysis of digital circuits. In: International Conference on Computer-Aided Design, pp. 196–203 (2008)

    Google Scholar 

  9. Liu, J.H., Zeng, J.K., Hong, A.S., Chen, L., Chen, C.C.P.: Process-variation statistical modeling for VLSI timing analysis. In: International Symposium on Quality Electronic Design, pp. 730–733 (2008)

    Google Scholar 

  10. Mutlu, A., Le, K.J., Celik, M., sun Tsien, D., Shyu, G., Yeh, L.C.: An exploratory study on statistical timing analysis and parametric yield optimization. In: International Symposium on Quality Electronic Design, pp. 677–684 (2007)

    Google Scholar 

  11. Mangassarian, H., Anis, M.: On statistical timing analysis with inter- and intra-die variations. In: Design, Automation and Test in Europe Conference and Exhibition, pp. 132–137 (2005)

    Google Scholar 

  12. Najm, F.N., Menezes, N.: Statistical timing analysis based on a timing yield model. In: Design Automation Conference, pp. 460–465 (2004)

    Google Scholar 

  13. Liou, J.J., Cheng, K.T., Mukherjee, D.A.: Path selection for delay testing of deep sub-micron devices using statistical performance sensitivity analysis. In: VLSI Test Symposium, p. 97. IEEE, Los Alamitos (2000)

    Google Scholar 

  14. Huang, J.F., Chang, V.C., Liu, S., Doong, K.Y., Chang, K.J.: Modeling sub-90nm on-chip variation using monte carlo method for DFM. In: Asia and South Pacific Design Automation Conference, pp. 221–225 (2007)

    Google Scholar 

  15. Efstathiou, C., Vergos, H.T., Nikolos, D.: Modulo 2n±1 adder design using select-prefix blocks. IEEE Transactions on Computers 52(11) (November 2003)

    Google Scholar 

  16. Hiasat, A.A.: High-speed and reduced area modular adder structures for RNS. IEEE Transactions on Computers 51(1), 84–89 (2002)

    Article  MathSciNet  Google Scholar 

  17. Wang, Z., Jullien, G.A., Miller, W.C.: An algorithm for multiplication modulo (2n + 1). In: Proceedings of 29th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, pp. 956–960 (1996)

    Google Scholar 

  18. Bernocchi, G.L., Cardarilli, G.C., Re, A.D., Nannarelli, A., Re, M.: Low-power adaptive filter based on rns components. In: ISCAS, pp. 3211–3214 (2007)

    Google Scholar 

  19. Nannarelli, A., Re, M., Cardarilli, G.C.: Tradeoffs Between Residue Number System and Traditional FIR Filters. In: Proceedings of the 2001 IEEE International Symposium on Circuits and Systems (ISCAS), vol. II, pp. 305–308 (2001)

    Google Scholar 

  20. Soderstrand, M.A., Jenkins, W.K., Jullien, G.A., Taylor, F.J.: Residue Number System Arithmetic: Modern Applications in Digital Signal Processing. IEEE Press, Los Alamitos (1986)

    MATH  Google Scholar 

  21. Kouretas, I., Paliouras, V.: Mixed radix-2 and high-radix RNS bases for low-power multiplication. In: Svensson, L., Monteiro, J. (eds.) PATMOS 2008. LNCS, vol. 5349, pp. 93–102. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  22. Bowman, K., Duvall, S., Meindl, J.: Impact of die-to-die and within-die parameter fluctuations on the maximum clock frequency distribution for gigascale integration. IEEE Journal of Solid-State Circuits 37(2), 183–190 (2002)

    Article  Google Scholar 

  23. Zimmermann, R.: Efficient VLSI implementation of modulo (2n ±1) addition and multiplication. In: ARITH 1999: Proceedings of the 14th IEEE Symposium on Computer Arithmetic, p. 158 (1999)

    Google Scholar 

  24. Efstathiou, C., Vergos, H.T., Dimitrakopoulos, G., Nikolos, D.: Efficient diminished-1 modulo 2n + 1 multipliers. IEEE Transactions on Computers 54(4), 491–496 (2005)

    Article  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

Kouretas, I., Paliouras, V. (2010). Residue Arithmetic for Variation-Tolerant Design of Multiply-Add Units. 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_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-11802-9_7

  • 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