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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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
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
Liu W, Lombardi F, Schulte M. A retrospective and prospective view of approximate computing. Proc IEEE (PIEEE). 2020;108(3):394–9
Xu Q, Mytkowicz T, Kim NS. Approximate computing: a survey. IEEE Des Test 2016;33(1):8–22
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Rabaey JM, Chandrakasan AP, Nikolic B. Digital integrated circuits, vol 2. Englewood Cliffs: Prentice Hall; 2002
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
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
Brayton RK, Logic minimization algorithms for VLSI synthesis. Berlin/Heidelberg: Springer Science & Business Media; 1984
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
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
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
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
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
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
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
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
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
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
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)