Approximate Computing

607 Pages·2022·20.524 MB·English

by  Weiqiang Liu (editor), Fabrizio Lombardi (editor)

Weiqiang Liu
Fabrizio Lombardi   Editors
Approximate
Computing
Approximate Computing
Weiqiang Liu • Fabrizio Lombardi
Editors
Approximate Computing
Editors
WeiqiangLiu FabrizioLombardi
NanjingUniversityofAeronauticsand NortheasternUniversity
Astronautics Boston,MA,USA
Nanjing,China
ISBN978-3-030-98346-8 ISBN978-3-030-98347-5 (eBook)
https://doi.org/10.1007/978-3-030-98347-5
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Preface
Computingsystemsatallscales(frommobilehandhelddevicestosupercomputers,
servers, and large cloud-based data centers) have seen significant performance
gains,mostlythroughthecontinuousshrinkingofthecomplementarymetal-oxide
semiconductor (CMOS)featuresizethathasdoubled thenumber oftransistorson
a chip with every technology generation. However, power dissipation has become
the fundamental barrier to scale computing performance across all platforms. As
the classical Dennard scaling is coming to an end, reduction in on-chip power
consumption as well as a throughput increase (as per Moore’s Law) have become
serious challenges. Computation at the nanoscales necessitates fundamentally
differentapproaches.Theseapproachesrelyondifferentcomputationalparadigms
that exploit features in the targeted set of applications as well as exploiting
uniqueinteractionsbetweenhardware,software,andtheprocessingalgorithmsofa
computingsystem.
Approximate computing has been proposed as a novel paradigm for efficient
and low-power design at nanoscales [1]. Efficiency is related to the computation
of approximate results with at least comparable performance and lower power
consumption compared to the fully accurate counterpart. Therefore, approximate
computinggeneratesresultsthataregoodenoughratherthanalwaysfullyaccurate.
Althoughcomputationalerrorsgenerallyarenotdesirable,applicationssuchasmul-
timedia,signalprocessing,machinelearning,patternrecognition,anddatamining
are tolerant to the occurrence of some errors; this application-driven microcosm
is shown in Fig. 1. Therefore, approximate computing is mostly applicable to
computingsystemsthatarerelatedtohumanperception/cognitionandhaveinherent
errorresilience.Manyoftheseapplicationsarebasedonstatisticalorprobabilistic
computation,wheredifferentapproximationscanbemadetobettersuitthedesired
objectives. Therefore, it is possible to achieve not only energy efficiency but also
a simpler design and lower latency, while relaxing the accuracy requirement for
theseapplications.Thebasicprinciplesofapproximatecomputingarefoundacross
theentiretechnologydesignstack:devicesexhibitapproximatebehavioratreduced
dimensions,circuitscanberedesignedtobetterfitspecificoperationalfeatures,and
v
vi Preface
Fig.1 Error-tolerantapplicationsamenabletoapproximatecomputing
Fig.2 Thethree-dimensionaldesignspaceofapproximatecomputing
modulesandsystemscanbeoperatedataleveltoguaranteeanacceptableaccuracy
(Fig.2).
Approximatetechniqueshavebeenstudiedatseverallevelsincludingnanoscale
hardware (devices, circuits, and architectures), software/algorithms, programming
languages, logic synthesis, and automated design processes. Various computing
and memory architectures have been proposed for several applications. At hard-
ware level, the design of approximate arithmetic units has received significant
research interest. Design metrics and analytical approaches have been proposed
for the evaluation of approximate circuits such as adders and multipliers [2, 3].
Approximate algorithms and systems have been studied for emerging computing
applications,suchasdeepneuralnetworks[4].Designautomation,test,andsecurity
Preface vii
issues of approximate computing systems have also been investigated [5–7]. It
is generally accepted that the full potential of approximate computing cannot be
fully exploited without considering the interactions between these different levels
under often conflicting constraints, such as error analysis/control. Approximate
computingaccomplishesareductioninpowerconsumptionandhigherperformance
by carefully controlling the introduced errors based on an error analysis to ensure
that the measurable quality features of an error-tolerant application are still fully
met. Generally, such error analysis involves the least significant parts of the
computational media, either hardware and/or software; then, errors are selectively
introducedinthedesignattheappropriatelevel(s)toachievethedesiredbenefitsand
meetthetrade-offsbetweenfiguresofmeritssuchaspower,accuracy,anddelay.
Approximate computing has received significant attention from both research
andindustrialcommunitiesinthepastfewyearsduetothechallengeofdesigning
power-efficient systems for emerging applications. The research community from
electronicengineering,computerscienceandcomputerengineering,andmanyother
related areas has widely expanded on a worldwide basis to study approximate
techniquesatdifferentlevels.
It should also be noted that leading companies (such as IBM, Google, and
Samsung) are involved in experimental research and implementing commercial
products and services based on approximate computing. For example, Google’s
TensorProcessingUnits(TPUs)useapproximatecomputingtoreducetheirpower
consumption[8].IBMhasfabricatedanAIacceleratorchiptoachievemulti-TOPs
performance by applying multiple approximate techniques (including hardware,
architecture, algorithms, and programs) [9]. Samsung has adopted approximate
multipliersintheDSPblockofahigh-speedtransceiver[10].Anincreasednumber
offundingagencies(suchasNSF,DARPA,NSFC,andtheEUFrameworkHorizon
2020)aresponsoringresearchinthisfield.
Although approximate computing has gained significant attention from both
academicandindustrialcommunitiesinthepastdecade,itstillrequiressignificant
effortsforimplementationasmainstreamcomputingparadigmforenergy-efficient
and high-performance systems This book focuses initially on approximate arith-
metic and then on new applications of approximate computing such as machine
learning,security,andcommunication.Thisbookextendsthecoverageofexisting
books and articles found in the technical literature such as the special issue
published by Proceedings of the IEEE and other leading journals. Therefore, this
book explores the technological contributions and developments at various levels
of this new emerging paradigm. With this book, it is expected to collect state-
of-the-art progress in this area. This has been achieved by chapters covering the
entirespectrumofresearchactivitiesinapproximatecomputing,sobridgingdevice,
circuit,architecture,andsystemlevels.
The chapters in this book are organized into five parts. The first part presents
approximate arithmetic circuits that are the fundamental components for approx-
imate computing systems, and approximate arithmetic circuits based on both
conventional and emerging devices are included. The second part introduces the
designautomationandtestingtechniquestofacilitateapproximatedesign.Thenext
three parts cover a wide range of applications that utilize approximate computing,
viii Preface
includingsecurity,neuralnetworks,machinelearning,digitalsignalprocessing,and
communication.Thesecurityandtestingissuesofapproximatecomputingitselfare
alsostudiedinPartIIandPartIII.
Although approximate computing is not yet at a fully mature stage, it is very
promising for future highly energy-efficient and high-performance error-tolerant
applications;currentapproximatecomputingtechniqueshavebeenusedinanumber
of AI-based applications and services by leading companies. There is also an
increasing trend in EDA and the software engineering community to support
approximatecomputingdesigns.
In the coming decade, it is anticipated that approximate computing techniques
willlikelybeemployedinenergy-efficientsystemsforapplicationssuchasAIand
signal processing [8–10]. Furthermore, new approximate computing applications
will be exploited; for instance, approximate computing can also provide new
approaches for hardware security and post-quantum cryptography based on lattice
[7]. It is believed more applications will utilize approximate computing due to
power limitations. Therefore, it is likely that there will be a growing demand
for approximate computing with diverse contributions, hardware designer, system
developer, test engineer, and research and teaching community to enable such
computingasamainstreamparadigm.Bibliography
References
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Acknowledgment
This book is dedicated to our families whose supports have made it possible. The
researchofWeiqiangLiuissupportedbyNSFC(62022041and61871216),while
the research of Fabrizio Lombardi is supported by NSF under CCF-1953961 and
1812467grants.
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Contents
PartI Introduction:ApproximateArithmeticCircuits
WeiqiangLiuandFabrizioLombardi
1 Introduction:ApproximateArithmeticCircuits........................ 3
KeChen,WeiqiangLiu,andFabrizioLombardi
2 AnAutomatedLogic-LevelFrameworkforApproximate
ModularArithmeticCircuits.............................................. 23
HaroonWaris,ChenghuaWang,andWeiqiangLiu
3 ApproximateMultiplierDesignforEnergyEfficiency:From
CircuittoAlgorithm........................................................ 51
Ying Wu, Chuangtao Chen, Chenyi Wen, Weikang Qian,
XunzhaoYin,andChengZhuo
4 Low-Precision Floating-Point Formats: From
General-PurposetoApplication-Specific ................................ 77
Amir Sabbagh Molahosseini, Leonel Sousa,
AzadehAlsadatEmraniZarandi,andHansVandierendonck
5 SpintronicSolutionsforApproximateComputing ..................... 99
YouWang,HaoCai,KailiZhang,BoWu,BoLiu,DemingZhang,
andWeishengZhao
6 Majority Logic-Based Approximate Multipliers for
Error-TolerantApplications............................................... 119
TingtingZhang,HonglanJiang,WeiqiangLiu,FabrizioLombardi,
LeiboLiu,Seok-BumKo,andJieHan
xi