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BOOLEAN CIRCUIT
REWIRING
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BOOLEAN CIRCUIT
REWIRING:
BRIDGING LOGICAL AND PHYSICAL
DESIGNS
Tak-KeiLam
TheChineseUniversityofHongKong,HongKong,P.R.China
Wai-ChungTang
QueenMaryUniversityofLondon,UK
XingWei
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Easy-LogicTechnologyLtd.HongKong,HongKong,P.R.China
YiDiao
Easy-LogicTechnologyLtd.HongKong,HongKong,P.R.China
David Yu-LiangWu
Easy-LogicTechnologyLtd.HongKong,HongKong,P.R.China
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Thiseditionfirstpublished2016
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1 2016
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Contents
ListofFigures ix
ListofTables xiii
Preface xv
Introduction xvii
1 Preliminaries 1
1.1 BooleanCircuits 1
(cid:2) 1.2 RedundancyandStuck-atFaults 4 (cid:2)
1.3 AutomaticTestPatternGeneration(ATPG) 6
1.4 Dominators 6
1.5 MandatoryAssignmentsandRecursiveLearning 7
1.6 GraphTheoryandBooleanCircuits 8
References 10
2 ConceptofLogicRewiring 11
2.1 WhatisRewiring? 11
2.2 ATPG-basedRewiringTechniques 12
2.2.1 Add-First 12
2.2.2 Delete-First 18
2.3 Non-ATPG-basedRewiringTechniques 24
2.3.1 Graph-basedAlternateWiring(GBAW) 24
2.3.2 SPFD 25
2.4 WhyareRewiringTechniquesImportant? 31
References 33
3 Add-FirstandNon-ATPG-BasedRewiringTechniques 37
3.1 RedundancyAdditionandRemoval(RAR) 37
3.1.1 RAMBO 37
3.1.2 REWIRE 38
3.1.3 RAMFIRE 41
3.1.4 ComparisonBetweenRAR-BasedRewiringTechniques 43
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vi Contents
3.2 Node-BasedNetworkAdditionandRemoval(NAR) 43
3.2.1 NodeMerging 43
3.2.2 NodeAdditionandRemoval 48
3.3 OtherRewiringTechniques 51
3.3.1 SPFD-BasedRewiring 51
References 65
4 Delete-FirstRewiringTechniques 67
4.1 IRRA 69
4.1.1 DestinationofAlternativeWires 71
4.1.2 SourceofAlternativeWires 72
4.2 ECR 76
4.2.1 DestinationofAlternativeWires 80
4.2.2 SourceofAlternativeWires 85
4.2.3 OverviewoftheApproachofError-Cancellation-BasedRewiring 86
4.2.4 ComplexityAnalysisofECR 87
4.2.5 ComparisonBetweenECRandOtherResynthesisTechniques 90
4.2.6 ExperimentalResult 92
4.3 FECR 96
4.3.1 ErrorFlowGraphConstruction 97
4.3.2 DestinationNodeIdentification 98
4.3.3 SourceNodeIdentification 102
4.3.4 ECRisaSpecialCaseofFECR 104
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4.3.5 ComplexityAnalysisofFECR 105
4.3.6 ExperimentalResult 105
4.4 Cut-BasedErrorCancellationRewiring 107
4.4.1 Preliminaries 107
4.4.2 ErrorFrontier 109
4.4.3 Cut-BasedErrorCancellationRewiring 117
4.4.4 VerificationofAlternativeWires 121
4.4.5 ComplexityAnalysisofCECR 122
4.4.6 RelationshipBetweenECR,FECR,andCECR 122
4.4.7 ExtendingCECRforn-to-mRewiring 123
4.4.8 SpeedupforCECR 124
4.4.9 ExperimentalResults 125
References 129
5 Applications 133
5.1 AreaReduction 133
5.1.1 Preliminaries 134
5.1.2 OurMethodology(“Longtail”vs“Bumptail”Curves) 135
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Contents vii
5.1.3 DetailsofourApproach 140
5.1.4 ExperimentalResults 143
5.2 PostplacementOptimization 145
5.2.1 Wire-Length-DrivenRewiring-BasedPostplacementOptimization 145
5.2.2 Timing-DrivenRewiring-BasedPostplacementOptimization 151
5.3 ECOTimingOptimization 158
5.3.1 Preliminaries 160
5.3.2 Nego-RoutOperation 161
5.3.3 Path-RestructuringOperation 164
5.3.4 ExperimentalResults 166
5.4 AreaReductioninFPGATechnologyMapping 167
5.4.1 IncrementalLogicResynthesis(ILR):Depth-OrientedMode 170
5.4.2 IncrementalLogicResynthesis(ILR):Area-OrientedMode 171
5.4.3 ExperimentalResults 173
5.4.4 Conclusion 183
5.5 FPGAPostlayoutRoutingOptimization 184
5.5.1 OptimizationbyAlternativeFunctions 185
5.5.2 OptimizationwithMapping-to-RoutingLogicRewirings 187
5.5.3 OptimizationbySPFD-BasedRewiring 198
5.6 LogicSynthesisforLowPowerUsingClockGatingandRewiring 199
5.6.1 MechanismofClockGating 199
5.6.2 Rewiring-BasedOptimization 203
References 207
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6 Summary 211
Index 213
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