Online Aging Monitoring and Resilience Hao-Chun Chang, Li-An Huang, - - PowerPoint PPT Presentation

Selective Sensor Placement for Cost-Effective Online Aging Monitoring and Resilience

Hao-Chun Chang, Li-An Huang, Kai-Chang Wu

Department of Computer Science, National Chiao Tung University

Yu-Guang Chen

Department of Electrical Engineering, National Central University

Outline

Introduction

• Background
• Motivation
• Contribution

Preliminaries Proposed Framework Experimental Results Conclusion

⚫ Aging effect is the major challenge of reliability-aware IC/SOC

design techniques

⚫ The effects of device aging

⚫ Performance degradation ⚫ Potential failure

Background

⚫ Traditional design method adopts guard-band by adding extra timing

margin

⚫ Razor flip-flop is a well-known technique of timing speculation

⚫

May need to be deployed widely throughout a circuit

⚫ The sensitization rate of critical paths is negligibly small ⚫ Many critical paths have common sub-paths in the forward section

Motivation

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

The Deployment

RFF3 RFF2 RFF1 P2 P1 P3

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

The Deployment

RFF3 RFF2 RFF1 P2 P1 P3 TDG3

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

The Deployment

RFF3 RFF2 RFF1 P2 P1 P3 TDG2

⚫ Reduction in hardware cost with insignificant performance loss ⚫ Tradeoff between extra hardware cost and performance by adjusting

the weights of cost function

Contribution

Outline

Introduction Preliminaries

• Razor Flip-Flop
• Transition Detector

Proposed Framework Experimental Results Conclusion

⚫ Consist of a regular main flip-flop, an additional shadow latch and

some control logic

Razor Flip-Flop (RFF)

⚫ Detect whether the signal transition has happened lately ⚫ Forecast the excessive aging from forwarding gates ⚫ Send a warning signal to stall for one clock cycle

Transition Detector (TD)

D D Q Q

Detection window The monitored signal (D) Warning signal CLK The monitored signal (D) Warning signal Detection window T1 T2

⚫ Detect whether the signal transition has happened lately ⚫ Reserve the execution time with worst-case aging for the remaining

sub-paths

⚫

,∀p monitored by TDg

TD: Detection Window

⚫TDg: Transition detector at gate g ⚫DWg: Detection window on TDg ⚫Tc: Clock period ⚫t: Current clock cycle beginning time ⚫𝜀w: (Worst-case) 10-years aging of the long path ⚫RDp: The remaining delay of vulnerable path p

) (

,g p w g

RD Max Tc t DW  − + = 

Outline

Introduction Preliminaries Proposed Framework

• Problem Formulation
• Exact Set Cover
• Maximum Satisfiability

Experimental Results Conclusion

⚫ TD deployment to monitor vulnerable paths ⚫ A TD monitors those vulnerable paths, passing through it ⚫ It’s a covering problem!

Problem Formulation

P2 P1 P3 G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

⚫ The universal set U: {1, 2, 3, 4} ⚫ Given a collection C of subsets of U

⚫ C: {{1, 3}, {2, 3}, {2, 4},{1, 2}}

⚫ An exact cover is a sub-collection C* of C

⚫ Each element in U is covered by exactly one subset in C* ⚫ C*: {{1, 3}, {2, 4}}

Exact Set Cover (ESC)

U

1 2 4 3

⚫ Each vulnerable path represents a variable of the universal set

⚫ U: {P1, P2, P3}

ESC: The Universal Set U

P2 P1 P3 G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

⚫ Each gate that including FF and PI on vulnerable paths defines a set

Sg and Sg is a subset of the universal set

⚫ C: {SPI, SG1, SG2, …, SG8, SFF1, …, SFF3} ⚫ SG2: {P1, P2, P3} ⚫ SG3: {P1, P2} ⚫ SFF3: {P3}

P2 P1 P3

ESC: A Collection C of Subsets of U

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

⚫ Each element in U is covered by exactly one subset in C*

⚫ C*: {SG1} = {{P1, P2, P3}} ⚫ C*: {SG3, SG6} = {{P1, P2}, {P3}} ⚫ C*: {SFF1, SFF2, SFF3} = {{P1}, {P2}, {P3}}

ESC: A Sub-collection C* of C

P2 P1 P3 G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

⚫ Maximum number of clauses can be made true by an assignment ⚫ Weighted MAX-SAT solver

⚫ The minimum sum of costs of unsatisfied clauses

⚫ CNF: Conjunctive Normal Form

⚫ For each candidate g introduce a new variable Vg ⚫ Hard clauses I &II

⚫ Boolean constraint

⚫ Soft clause

⚫ Cost function

Maximum Satisfiability

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

⚫ If two subsets Sg and Sh intersect, produce a hard clause ⚫

, ∀g, h; g ≠ h and Sg ∩ Sh ≠ ∅

⚫

MAX-SAT: Hard Clause I

T ∨ F

h g

V V

• 
• P2

P1 P3 TDG2

{P1, P2, P3} {P1, P2}

G3 G2

V V

• 

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

⚫ For each vulnerable path p, produce a hard clause ⚫

⚫

MAX-SAT: Hard Clause II

FF2 G5 G3 G2 G1 PI

V V V V V V     

F F F F ∨ ∨ ∨ ∨ T

RFF2 P2 P1 P3

∨ F

g p S

V

g 





⚫ For each candidate g with COST(g), produce a soft clause

⚫

⚫ The minimum sum of costs of unsatisfied clauses

⚫ The minimum sum of costs of C*

MAX-SAT: Soft Clause

g

V

• ( )

g COST

⚫ Cost function

⚫

⚫ Ag: Area cost

⚫ TD: 1.5 ⚫ RFF: 1

Definition: Cost

( )

g A S p M

A W p g M W g COST

g

 +  =



 

) , (

⚫ WM: The weight of misprediction rate ⚫ M(g, p): Misprediction rate at gate g on the vulnerable path p ⚫ WA: The weight of area cost ⚫ Ag: Area cost for deployment

⚫ Probability that consecutive side-inputs from starting point are non-

controlling value

0.4 0.3 0.6 0.7 0.1 G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

Cost: Sensitization Rate

⚫Sensitization rate ⚫Probability of side inputs being 1 ⚫SR(g, p): Sensitization rate at gate g on path p

SR(G3,P1) = SR(G3,P2 ) SR(G2, P1) = SR(G2,P2) = SR(G2,P3)

0.5*(1-0.7) 0.15*(1-0.6)

⚫ Probability that the sensitization from the starting point but not

propagate to the endpoint

⚫

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

Cost: Misprediction Rate

⚫Sensitization rate ⚫SR(g, p): Sensitization rate at gate g on path p ⚫M(g, p): Misprediction rate at gate g on the vulnerable path p

SR(G2, (∀p ϵ SG2)) SR(FF1, P1) SR(FF2, P2) SR(FF3, P3)

( )

) , ( / ) , ( 1 ) , ( ) , ( p g SR p FF SR p g SR p g M −  =

M(G2, P1): 0.09 M(G2, P2): 0.144 M(G2, P3): 0.108

∑∀pϵSG2 M(G2, p): 0.342 0.15 0.06 0.042 0.006

⚫ Finally, Combine three kinds of clauses

⚫

⚫ The deployment by the output of MAX-SAT solver

⚫ Expected: an acceptable solution exists

⚫ Or no more improvement

⚫ Unexpected: WM and WA adjustment

The Input & Output of MAX-SAT

SC HC HC   2 1

⚫ WM:WA = 1:10

⚫ More consideration on hardware cost ⚫ Total cost: 15.342

Weight Adjustment: Case 1

15.342 TDG2 G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

⚫ WM:WA = 5:1

⚫ More consideration on performance ⚫ Total cost: 1.77+1

Weight Adjustment: Case 2

1 1 1 RFF3 TDG3

G1 G3 G5 FF1 G4 G7 G6 G8 G2 FF2 FF3 PI

⚫ WM:WA = 10:1

⚫ More consideration on performance ⚫ Total cost: 1+1+1

Weight Adjustment: Case 3

1 1 1 RFF3 RFF2 RFF1

Outline

Introduction Preliminaries Proposed Framework Experimental Results Conclusion

Setting

⚫ The benchmark are chosen from the IWLS’05 and ISCAS’89 ⚫ The technology used is TSMC 65nm GP standard cell series ⚫ Timing reports are provided by ITRI ⚫ Workstation:

⚫ Linux ⚫ C++ ⚫ MAXHS 2.9

Outline

Introduction Preliminaries Proposed Framework Experimental Results Conclusion

⚫ Cost-effective TD deployment for aging resilience with

insignificant performance loss

⚫ Tradeoff between extra hardware cost and performance

Conclusion

Thanks for listening!

The End