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2019 | OriginalPaper | Chapter

3. Heterogeneous Approximate Multipliers: Architectures and Design Methodologies

Authors : Semeen Rehman, Bharath Srinivas Prabakaran, Walaa El-Harouni, Muhammad Shafique, Jörg Henkel

Published in: Approximate Circuits

Publisher: Springer International Publishing

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Abstract

Multipliers are an integral block of a wide range of error-resilient applications like audio, image, and video processing, and machine learning. However, these multiplier architectures are computationally complex, and hence consume more power and occupy more area with long carry-adder trees when implementing multipliers with high bit-width. Approximate computing is an emerging design paradigm and is currently exploited to alleviate such area and power overheads, with slight/affordable degradation in the output quality of error-resilient application. An approximate multiplier architecture could either be approximated at the partial-product generation, accumulation, or summation stages. In this chapter, we focus on the different design aspects of energy-efficient approximate multipliers for both ASICs- and FPGAs-based systems.

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Footnotes
1
The Neural Network which won the ImageNet Large-Scale Visual Recognition Competition (ILSVRC) in the year 2015 to surpass human accuracy in classifying images of the image-net dataset [30].
 
Literature
1.
go back to reference Ataei S, Stine JE (2018) A 64 kb approximate SRAM architecture for low-power video applications. Embed Syst Lett 10:10–13CrossRef Ataei S, Stine JE (2018) A 64 kb approximate SRAM architecture for low-power video applications. Embed Syst Lett 10:10–13CrossRef
2.
go back to reference Bhardwaj K, Mane PS, Henkel J (2014) Power-and area-efficient approximate Wallace tree multiplier for error-resilient systems. In: 15th international symposium on quality electronic design (ISQED). IEEE, New York Bhardwaj K, Mane PS, Henkel J (2014) Power-and area-efficient approximate Wallace tree multiplier for error-resilient systems. In: 15th international symposium on quality electronic design (ISQED). IEEE, New York
3.
go back to reference Boroumand S, Parandeh-Afshar H, Brisk P, Mohammadi S (2018) Exploration of approximate multipliers design space using carry propagation free compressors. In: 23rd Asia and South Pacific design automation conference, ASP-DAC 2018, Jeju, January 22–25, 2018 Boroumand S, Parandeh-Afshar H, Brisk P, Mohammadi S (2018) Exploration of approximate multipliers design space using carry propagation free compressors. In: 23rd Asia and South Pacific design automation conference, ASP-DAC 2018, Jeju, January 22–25, 2018
4.
go back to reference Chen L, Han J, Liu W, Lombardi F (2015) Design of approximate unsigned integer non-restoring divider for inexact computing. In: Proceedings of the 25th edition on Great Lakes symposium on VLSI. ACM, New York Chen L, Han J, Liu W, Lombardi F (2015) Design of approximate unsigned integer non-restoring divider for inexact computing. In: Proceedings of the 25th edition on Great Lakes symposium on VLSI. ACM, New York
5.
go back to reference Dadda L (1965) Some schemes for parallel multipliers. Alta frequenza 34:349–356 Dadda L (1965) Some schemes for parallel multipliers. Alta frequenza 34:349–356
6.
go back to reference Gupta V, Mohapatra D, Raghunathan A, Roy K (2013) Low-power digital signal processing using approximate adders. In: IEEE transactions on computer-aided design of integrated circuits and systems (TCAD) Gupta V, Mohapatra D, Raghunathan A, Roy K (2013) Low-power digital signal processing using approximate adders. In: IEEE transactions on computer-aided design of integrated circuits and systems (TCAD)
7.
go back to reference Ha M, Lee S (2018) Multipliers with approximate 4–2 compressors and error recovery modules. Embed Syst Lett 10:6–9CrossRef Ha M, Lee S (2018) Multipliers with approximate 4–2 compressors and error recovery modules. Embed Syst Lett 10:6–9CrossRef
8.
go back to reference Hashemi S, Bahar R, Reda S (2015) Drum: a dynamic range unbiased multiplier for approximate applications. In: Proceedings of the IEEE/ACM international conference on computer-aided design. IEEE, New York Hashemi S, Bahar R, Reda S (2015) Drum: a dynamic range unbiased multiplier for approximate applications. In: Proceedings of the IEEE/ACM international conference on computer-aided design. IEEE, New York
9.
go back to reference Hashemi S, Bahar R, Reda S (2016) A low-power dynamic divider for approximate applications. In: Proceedings of the 53rd annual design automation conference. ACM, New York Hashemi S, Bahar R, Reda S (2016) A low-power dynamic divider for approximate applications. In: Proceedings of the 53rd annual design automation conference. ACM, New York
10.
go back to reference Hellebrand S, Henkel J, Raghunathan A, Wunderlich H (2018) Guest editors’ introduction to special issue on approximate computing. Embed Syst Lett 10:1CrossRef Hellebrand S, Henkel J, Raghunathan A, Wunderlich H (2018) Guest editors’ introduction to special issue on approximate computing. Embed Syst Lett 10:1CrossRef
11.
go back to reference Imani M, Peroni D, Rosing T (2018) Nvalt: nonvolatile approximate lookup table for GPU acceleration. Embed Syst Lett 10:14–17CrossRef Imani M, Peroni D, Rosing T (2018) Nvalt: nonvolatile approximate lookup table for GPU acceleration. Embed Syst Lett 10:14–17CrossRef
12.
go back to reference Isenberg T, Jakobs M-C, Pauck F, Wehrheim H (2018) Validity of software verification results on approximate hardware. Embed Syst Lett 10:22–25CrossRef Isenberg T, Jakobs M-C, Pauck F, Wehrheim H (2018) Validity of software verification results on approximate hardware. Embed Syst Lett 10:22–25CrossRef
13.
go back to reference Kahng AB, Kang S (2012) Accuracy-configurable adder for approximate arithmetic designs. In 49th ACM/EDAC/IEEE design automation conference (DAC). IEEE, New York Kahng AB, Kang S (2012) Accuracy-configurable adder for approximate arithmetic designs. In 49th ACM/EDAC/IEEE design automation conference (DAC). IEEE, New York
14.
go back to reference Kulkarni P, Gupta P, Ercegovac M (2011) Trading accuracy for power with an underdesigned multiplier architecture. In 24th international conference on VLSI Design (VLSI Design). IEEE, New York Kulkarni P, Gupta P, Ercegovac M (2011) Trading accuracy for power with an underdesigned multiplier architecture. In 24th international conference on VLSI Design (VLSI Design). IEEE, New York
15.
go back to reference Kyaw KY, Goh WL, Yeo KS (2010) Low-power high-speed multiplier for error-tolerant application. In IEEE international conference of electron devices and solid-state circuits (EDSSC). IEEE, New York Kyaw KY, Goh WL, Yeo KS (2010) Low-power high-speed multiplier for error-tolerant application. In IEEE international conference of electron devices and solid-state circuits (EDSSC). IEEE, New York
16.
go back to reference Lee S, Gerstlauer A (2018) Data-dependent loop approximations for performance-quality driven high-level synthesis. Embed Syst Lett 10:18–21CrossRef Lee S, Gerstlauer A (2018) Data-dependent loop approximations for performance-quality driven high-level synthesis. Embed Syst Lett 10:18–21CrossRef
17.
go back to reference Lin C-H, Lin C (2013) High accuracy approximate multiplier with error correction. In IEEE 31st international conference on computer design (ICCD). IEEE, New York Lin C-H, Lin C (2013) High accuracy approximate multiplier with error correction. In IEEE 31st international conference on computer design (ICCD). IEEE, New York
19.
go back to reference Liu C, Han J, Lombardi F (2014) A low-power, high-performance approximate multiplier with configurable partial error recovery. In Design, automation and test in Europe conference and exhibition (DATE). IEEE, New York Liu C, Han J, Lombardi F (2014) A low-power, high-performance approximate multiplier with configurable partial error recovery. In Design, automation and test in Europe conference and exhibition (DATE). IEEE, New York
20.
go back to reference Ma J, Man KL, Zhang N, Guan S-U, Jeong TT (2013) High-speed area-efficient and power-aware multiplier design using approximate compressors along with bottom-up tree topology. In Fifth international conference on machine vision (ICMV): algorithms, pattern recognition, and basic technologies. International Society for Optics and Photonics Ma J, Man KL, Zhang N, Guan S-U, Jeong TT (2013) High-speed area-efficient and power-aware multiplier design using approximate compressors along with bottom-up tree topology. In Fifth international conference on machine vision (ICMV): algorithms, pattern recognition, and basic technologies. International Society for Optics and Photonics
21.
go back to reference Mahdiani HR, Ahmadi A, Fakhraie SM, Lucas C (2010) Bio-inspired imprecise computational blocks for efficient VLSI implementation of soft-computing applications. IEEE Trans Circuits Syst Regul Pap 57:850–862MathSciNetCrossRef Mahdiani HR, Ahmadi A, Fakhraie SM, Lucas C (2010) Bio-inspired imprecise computational blocks for efficient VLSI implementation of soft-computing applications. IEEE Trans Circuits Syst Regul Pap 57:850–862MathSciNetCrossRef
22.
go back to reference Mazahir S, Hasan O, Hafiz R, Shafique M, Henkel J (2016) An area-efficient consolidated configurable error correction for approximate hardware accelerators. In Proceedings of the 53rd annual design automation conference. ACM, New York Mazahir S, Hasan O, Hafiz R, Shafique M, Henkel J (2016) An area-efficient consolidated configurable error correction for approximate hardware accelerators. In Proceedings of the 53rd annual design automation conference. ACM, New York
23.
go back to reference Momeni A, Han J, Montuschi P, Lombardi F (2015) Design and analysis of approximate compressors for multiplication. IEEE Trans Comput 64:984–994MathSciNetCrossRef Momeni A, Han J, Montuschi P, Lombardi F (2015) Design and analysis of approximate compressors for multiplication. IEEE Trans Comput 64:984–994MathSciNetCrossRef
24.
go back to reference Moreau T, San Miguel J, Wyse M, Bornholt J, Alaghi A, Ceze L, Jerger NDE, Sampson A (2018) A taxonomy of general purpose approximate computing techniques. Embed Syst Lett 10:2–5CrossRef Moreau T, San Miguel J, Wyse M, Bornholt J, Alaghi A, Ceze L, Jerger NDE, Sampson A (2018) A taxonomy of general purpose approximate computing techniques. Embed Syst Lett 10:2–5CrossRef
25.
go back to reference Polian I (2018) Test and reliability challenges for approximate circuitry. Embed Syst Lett 10:26–29CrossRef Polian I (2018) Test and reliability challenges for approximate circuitry. Embed Syst Lett 10:26–29CrossRef
26.
go back to reference Rehman S, El-Harouni W, Shafique M, Kumar A, Henkel J (2016) Architectural-space exploration of approximate multipliers. In 2016 IEEE/ACM international conference on computer-aided design (ICCAD) Rehman S, El-Harouni W, Shafique M, Kumar A, Henkel J (2016) Architectural-space exploration of approximate multipliers. In 2016 IEEE/ACM international conference on computer-aided design (ICCAD)
27.
go back to reference Shafique M, Ahmad W, Hafiz R, Henkel J (2015) A low latency generic accuracy configurable adder. In 52nd ACM/EDAC/IEEE design automation conference (DAC). IEEE, New York Shafique M, Ahmad W, Hafiz R, Henkel J (2015) A low latency generic accuracy configurable adder. In 52nd ACM/EDAC/IEEE design automation conference (DAC). IEEE, New York
28.
go back to reference Shin D, Gupta SK (2010) Approximate logic synthesis for error tolerant applications. In Proceedings of the conference on design, automation and test in Europe Shin D, Gupta SK (2010) Approximate logic synthesis for error tolerant applications. In Proceedings of the conference on design, automation and test in Europe
29.
go back to reference Snigdha FS, Sengupta D, Hu J, Sapatnekar SS (2016) Optimal design of jpeg hardware under the approximate computing paradigm. In Proceedings of the 53rd annual design automation conference. ACM, New York Snigdha FS, Sengupta D, Hu J, Sapatnekar SS (2016) Optimal design of jpeg hardware under the approximate computing paradigm. In Proceedings of the 53rd annual design automation conference. ACM, New York
30.
go back to reference Sze V, Chen Y-H, Yang T-J, Emer JS (2017) Efficient processing of deep neural networks: a tutorial and survey. CoRR. abs/1703.09039 Sze V, Chen Y-H, Yang T-J, Emer JS (2017) Efficient processing of deep neural networks: a tutorial and survey. CoRR. abs/1703.09039
31.
go back to reference Wallace CS (1964) A suggestion for a fast multiplier. IEEE Trans Electron Comput EC-13:14–17CrossRef Wallace CS (1964) A suggestion for a fast multiplier. IEEE Trans Electron Comput EC-13:14–17CrossRef
32.
go back to reference Zendegani R, Kamal M, Fayyazi A, Afzali-Kusha A, Safari S, Pedram M (2016) SEERAD: a high speed yet energy-efficient rounding-based approximate divider. In Design, automation & test in Europe conference & exhibition (DATE). IEEE, New York Zendegani R, Kamal M, Fayyazi A, Afzali-Kusha A, Safari S, Pedram M (2016) SEERAD: a high speed yet energy-efficient rounding-based approximate divider. In Design, automation & test in Europe conference & exhibition (DATE). IEEE, New York
33.
go back to reference Zhu N, Goh WL, Zhang W, Yeo KS, Kong ZH (2010) Design of low-power high-speed truncation-error-tolerant adder and its application in digital signal processing. IEEE transactions on very large scale integration (VLSI) systems Zhu N, Goh WL, Zhang W, Yeo KS, Kong ZH (2010) Design of low-power high-speed truncation-error-tolerant adder and its application in digital signal processing. IEEE transactions on very large scale integration (VLSI) systems
Metadata
Title
Heterogeneous Approximate Multipliers: Architectures and Design Methodologies
Authors
Semeen Rehman
Bharath Srinivas Prabakaran
Walaa El-Harouni
Muhammad Shafique
Jörg Henkel
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-99322-5_3