Nothing Special   »   [go: up one dir, main page]

Skip to main content

An Automated Logic-Level Framework for Approximate Modular Arithmetic Circuits

  • Chapter
  • First Online:
Approximate Computing

Abstract

The manual design techniques for approximate arithmetic circuits are very time-demanding as they require optimal trade-offs among the hardware savings and the approximation error. Therefore, there is a need to automate this design process so that multiple approximate design points can be generated from the original circuit. In this chapter, we present an automated framework called approximate solution finder (ASF) that exploits logic-level approximations under a given error constraint to design approximate arithmetic circuits. Our proposed methodology improves on existing state-of-the-art manual design techniques and is evaluated by using them in error-tolerant case studies such as image sharpening and canny edge detection.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover 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

Similar content being viewed by others

References

  1. Huang P, Wang C, Liu W, Qiao F, Lombardi F. A hardware/software co-design methodology for adaptive approximate computing in clustering and ANN learning. IEEE Open J Comput Soc. 2021;2:38–52

    Article  Google Scholar 

  2. Biasielli M, Bolchini C, Cassano L, Mazzeo A, Miele A. Approximation-based fault tolerance in image processing applications. IEEE Trans Emerg Top Comput. 2021. https://doi.ieeecomputersociety.org/10.1109/TETC.2021.3100623

  3. Liu W, Lombardi F, Schulte M. A retrospective and prospective view of approximate computing. Proc IEEE (PIEEE). 2020;108(3):394–9

    Article  Google Scholar 

  4. Xu Q, Mytkowicz T, Kim NS. Approximate computing: a survey. IEEE Des Test 2016;33(1):8–22

    Article  Google Scholar 

  5. Yuan T, Liu W, Han J, Lombardi F. High performance CNN accelerators based on hardware and algorithm co-optimization. IEEE Trans Circ Syst I: Regul Pap. 2021;68(1):250–263

    MathSciNet  Google Scholar 

  6. Venkataramani S, Chakradhar ST, Roy K, Raghunathan A. Approximate computing and the quest for computing efficiency. In: Proceedings of the 52nd annual design automation conference (DAC);2015. pp 1–6

    Google Scholar 

  7. Vahdat S, Kamal M, Afzali-Kusha A, Pedram M. TOSAM: an energy-efficient truncation- and rounding-based scalable approximate multiplier. IEEE Trans Very Large Scale Integr (VLSI) Syst. 2019;27(5):1161–73

    Article  Google Scholar 

  8. Jiang H, Liu C, Lombardi F, Han J. Low-power approximate unsigned multipliers with configurable error recovery. IEEE Trans Circ Syst I: Regul Pap. 2019;66(1):189–202

    Google Scholar 

  9. Yin P, Wang C, Liu W, Waris H, Han Y, Lombardi F. Design and analysis of dynamic range approximate logarithmic multipliers (DR-ALMs) for machine learning applications. IEEE Trans Sustain Comput. 2020. https://doi.org/10.1109/TSUSC.2020.3004980

  10. Leon V, Asimakopoulos K, Xydis S, Soudris D, Pekmestzi K. Cooperative arithmetic-aware approximation techniques for energy-efficient multipliers. In: Proceedings of the 56th ACM/IEEE design automation conference (DAC);2019. pp 1–6

    Google Scholar 

  11. Liu W, Qian L, Wang C, Jiang H, Han J, Lombardi F. Design of approximate radix-4 Booth multipliers for error-tolerant computing. IEEE Trans Comput. 2017;66(8):1435–1441

    Article  MathSciNet  Google Scholar 

  12. Ullah S, Schmidl H, Sahoo SS, Rehman S, Kumar A. Area-optimized accurate and approximate softcore signed multiplier architectures. IEEE Trans Comput. 2021;70(3):384–392

    Article  MathSciNet  Google Scholar 

  13. Shin D, Gupta SK. Approximate logic synthesis for error tolerant applications. In: Proceedings of the design, automation and test in Europe (DATE);2010. pp 957–960

    Google Scholar 

  14. Venkataramani S, Sabne A, Kozhikkottu V, Roy K, Raghunathan A. SALSA: systematic logic synthesis of approximate circuits. In: Proceedings of the 49th design automation conference (DAC);2012. pp 796–801

    Google Scholar 

  15. Lingamneni A, Enz C, Palem, Piguet C. Synthesizing parsimonious inexact circuits through probabilistic design techniques. ACM Trans Embedd Comput Syst (TECS) 2013;12(2):1–26

    Google Scholar 

  16. Samadi M, Lee J, Jamshidi DA, Hormati A, Mahlke S. SAGE: self-tuning approximation for graphics engines. In: Proceedings of the 46th IEEE/ACM International Symposium on Microarchitecture (MICRO);2013. pp 13–24

    Google Scholar 

  17. Miao J, Gerstlauer A, Orshansky M. Approximate logic synthesis under general error magnitude and frequency constraints. In: Proceedings of the international conference on computer-aided design (ICCAD);2013. pp 779–786

    Google Scholar 

  18. Ranjan A, Raha A, Venkataramani S, Roy K, Raghunathan A. ASLAN: synthesis of approximate sequential circuits. In: Proceedings of the design, automation and test in Europe (DATE);2014. p 364

    Google Scholar 

  19. Nepal K, Li Y, Bahar RI, Reda S. ABACUS: a technique for automated behavioral synthesis of approximate computing circuits. In: Proceedings of the design, automation and test in Europe (DATE);2014. pp 1–6

    Google Scholar 

  20. Nepal K, Hashemi S, Tann H, Bahar RI, Reda S. Automated high-level generation of low-power approximate computing circuits. IEEE Trans Emerg Top Comput 2019;7(1):18–30

    Article  Google Scholar 

  21. Hashemi S, Reda S. Generalized matrix factorization techniques for approximate logic synthesis. In: Proceedings of the design, automation & test in Europe conference & exhibition (DATE);2019. pp 1289–92

    Google Scholar 

  22. Bernasconi A, Ciriani V, Villa T. Approximate logic synthesis by symmetrization. In: Proceedings of the design, automation & test in Europe conference & exhibition (DATE);2019. pp 1655–60

    Google Scholar 

  23. Venkataramani S, Kozhikkottu VJ, Sabne A, Roy K, Raghunathan A. Logic synthesis of approximate circuits. IEEE Trans Comput-Aid Des Integr Circ Syst. 2020;39(10):2503–15

    Article  Google Scholar 

  24. Wu Y, Qian W. ALFANS: multilevel approximate logic synthesis framework by approximate node simplification. IEEE Trans Comput-Aid Des Integr Circ Syst. 2020;39(7):1470–83

    Article  Google Scholar 

  25. Su S, Zou C, Kong W, Han J, Qian W. A novel heuristic search method for two-level approximate logic synthesis. IEEE Trans Comput-Aid Des Integr Circ Syst. 2020;39(3):654–69

    Article  Google Scholar 

  26. Rabaey JM, Chandrakasan AP, Nikolic B. Digital integrated circuits, vol 2. Englewood Cliffs: Prentice Hall; 2002

    Google Scholar 

  27. Meng C, Qian W, Mishchenko A. ALSRAC: approximate logic synthesis by resubstitution with approximate care set. In: Proceedings of the 57th ACM/IEEE design automation conference (DAC); 2020. pp 1–6

    Google Scholar 

  28. Debnath D, Sasao T. A heuristic algorithm to design AND-OR-EXOR three-level networks. In: Proceedings of the Asia and South Pacific design automation conference (ASP-DAC);1998. pp 69–74

    Google Scholar 

  29. Brayton RK, Logic minimization algorithms for VLSI synthesis. Berlin/Heidelberg: Springer Science & Business Media; 1984

    Google Scholar 

  30. Kulkarni P, Gupta P, Ercegovac M. Trading accuracy for power with an underdesigned multiplier architecture. In: Proceedings of the international conference on VLSI design (VLSID);2011. pp 346–51

    Google Scholar 

  31. Lin C, Lin I, High accuracy approximate multiplier with error correction. In: Proceedings of the international conference on computer design (ICCD); 2013. pp 33–8

    Google Scholar 

  32. Ansari MS, Jiang H, Cockburn BF, Han J. Low-power approximate multipliers using encoded partial products and approximate compressors. IEEE J Emerg Select Top Circ Syst. 2018;8(3):404–416

    Article  Google Scholar 

  33. Guo Y, Sun H, Kimura S, Design of power and area efficient lower-part-or approximate multiplier. In: Proceedings of the IEEE region 10 conference (TENCON); 2018. pp 2110–5

    Google Scholar 

  34. Strollo AGM, Napoli E, De Caro D, Petra N, Meo GD. Comparison and extension of approximate 4-2 compressors for low-power approximate multipliers. IEEE Trans Circ Syst I: Regul Pap. 2020;67(9):3021–34

    MathSciNet  MATH  Google Scholar 

  35. Sabetzadeh F, Moaiyeri MH, Ahmadinejad M. A majority-based imprecise multiplier for ultra-efficient approximate image multiplication. IEEE Trans Circ Syst I: Regul Pap. 2019;66(11):4200–8

    Google Scholar 

  36. Mrazek V, Hrbacek R, Vasicek Z, Sekanina L. EvoApprox8b: library of approximate adders and multipliers for circuit design and benchmarking of approximation methods. In: Proceedings of design, automation & test in Europe conference & exhibition (DATE); 2017. pp 258–261

    Google Scholar 

  37. Waris H, Wang C, Liu W, Han J, Lombardi F. Hybrid partial product-based high-performance approximate recursive multipliers. IEEE Trans Emerg Top Comput. 2020. https://doi.org/10.1109/TETC.2020.3013977

  38. Waris H, Wang C, Liu W, Lombardi F. AxBMs: high performance approximate radix-8 Booth multipliers for FPGA-based accelerators. IEEE Trans Circ Syst II: Brief Expr. 2021;68(5), 1566–1570

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Haroon Waris .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Waris, H., Wang, C., Liu, W. (2022). An Automated Logic-Level Framework for Approximate Modular Arithmetic Circuits. In: Liu, W., Lombardi, F. (eds) Approximate Computing. Springer, Cham. https://doi.org/10.1007/978-3-030-98347-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-98347-5_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-98346-8

  • Online ISBN: 978-3-030-98347-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics