Address comments to lhe@ee.ucla.eduAddress comments to lhe@ee.ucla.edu

Robust FPGA Resynthesis Based on Fault-Tolerant Boolean Matching

Yu Hu1, Zhe Feng1, Lei He1 and Rupak Majumdar2 1Electrical Engineering Dept., UCLA

2Computer Science Dept., UCLAPresented by Yu HuPresented by Yu Hu

Outline Background and Motivation Preliminaries Robust Resynthesis Algorithms Experimental Results Conclusion and Future Work

Background Late CMOS scaling reduces device reliability

Single event upset (SEU) due to cosmic rays

Affects configuration SRAM cells in FPGAs Permanent soft error rate (SER) Need rewriting SRAM for recovery

Affects combinational circuits and FFs Transient SER Can be recovered in multiple clock cycles

Fault Tolerance Techniques for FPGAs

Metrics TMR Manufacturer Masking

Chipwise Multi-Config “Ideal”

Defect Coverage

High Low/Medium High Medium High

Area Overhead

High Low None Medium Low

Delay Overhead

High Medium Low Low Low

Testing Cost

Low Medium High Medium Low

Synthesis Cost

Low Medium High Low Low

Fault Tolerance Techniques for FPGAs

TMR Manufacturer Masking

Chipwise Multi-Config Stochastic-Synthesis

Defect Coverage

High Low/Medium High Medium Medium

Area Overhead

High Low None Medium None/Low

Delay Overhead

High Medium Low Low Low

Testing Cost

Low Medium High Medium Low

Synthesis Cost

Low Low High Low Low

Our workLow-cost, complementary

approach to existing techniques!

[A. Djupdal and P. Haddow, Yield Enhancing Defect Tolerance Techniques for FPGAs, MAPLD 2006]

Stochastic Synthesis and Logic Masking

Stochastic synthesis assumes probabilistic logic values to model effect of random defects Break the conventional Boolean view which assumes

deterministic Boolean ‘0’ and ‘1’ values

Key to stochastic synthesis: Logic Masking

a

c

bg

Circuit (b)

Masked faults

0

1

Stochastic Synthesis and Logic Masking (cont.)

Stochastic Synthesis intelligently places logic masking.

Logic Masking reduces the probability of the propagation of random faults Maximizes the stochastic yield

However, logic synthesis to maximize yield rate w/o explicit redundancy and testing has not been studied for fault tolerance!

Key questions How much does logic masking affect robustness? How and where to place logic masking?

How much Logic Masking Affect Robustness?

18 synthesis solutions obtained by Berkeley ABC (for MCNC i10, LUT bit fault rate = 0.1%)

Different synthesis leads to different logic masking.

Stochastic synthesis maximizes logic

masking!

How and Where to Place Logic Masking?— Our Major Contributions

Propose a Robust FPGA resynthesis (ROSE) Maximize the stochastic yield rate for FPGAs No need to locate faults Use the same synthesis for different chips of one

FPGA application Proposed a new PLB template for robustness ROSE + Robust Template reduces fault rate by 25%

with 1% fewer LUTs, and increases MTBF by 31% while preserving the logic depth compared to Berkeley ABC

Outline Background Preliminaries Robust Resynthesis Experimental Results Conclusion and Future Work

FPGA Synthesis Flow

Attempt to re-map a logic block by Boolean matching Boolean matching can be used to handle both homogenous

and heterogeneous PLBs

RTL Synthesis

LogicSynthesis

Technology Mapping Resynthesis Packing P&R

FPGA Synthesis Flow (cont.)

Multi-iterations of Boolean Matching-based Resynthesis

(Source: Andrew Ling, University of Toronto, DAC'05)

RTL Synthesis

LogicSynthesis

Technology Mapping Resynthesis Packing P&R

Boolean Matching for Resynthesis

2-LUT

2-LUT

2-LUT

2-LUT

2-LUT

ff gg??

Formulate the sub-problem of resynthesis to Boolean matching (BM) BM: Can function f be implemented in circuit g ? Resynthesis: Is there a configuration to g so that for all

inputs to g, f is equivalent to g? Existing algorithms: area/delay-optimal

(Source: Andrew Ling, University of Toronto, DAC'05)

Outline Background Preliminaries Robust Resynthesis

Problem Formulation FTBM Algorithm Robust PLB Template

Experimental Results Conclusion and Future Work

Modeling of Faults

LB1LB2

Intermediate logics

Fault rateof LB1

Input faults of LB2

CIs

Faults in config-bits

X

Faults in config-bits

X

Model both faults in LUT configurations and the faults in intermediate wires as random variables, whose probabilities are given as inputs of our problem.

Resynthesis(Boolean matching)

ROSE: Robust Resynthesis w/ FTBM

Boolean Matching Inputs

PLB H and Boolean function F Fault rates for the inputs and the SRAM bits of the PLB

Outputs Either that F cannot be implemented by PLB H Or the configuration of H which minimizes the probability that

the faults are observable in the output of the PLB under all input vectors.

FTBM tasks breakdown: Step 1: Find a Boolean matching solution Step 2: Evaluation the stochastic fault rate of a solution

RTL Synthesis

LogicSynthesis

Technology Mapping

ROSE(FTBM)

Packing P&R

Fault-Tolerant Boolean Matching

FTBM Step1: SAT Encoding for FTBM

LUT1

c0, SRAM

c1, SRAM

c15, SRAM

x'1 x'2 x'3 x'4

LUT2

c16, SRAM

c17, SRAM

c31, SRAM

x'5 x'6 x'7z1

G

x1 x2 x3 x4 x5 x6 x7 F0 0 0 0 0 0 0 F0

1 0 0 0 0 0 0 F1

0 1 0 0 0 0 0

1 1 1 1 1 1 1 F127

F2

PLB

tem

plat

eB

oole

an fu

nctio

n

If implementable, multiple configurations might exist The one with minimal fault rate is needed!

Conjunctive Normal Form (CNF)

Deterministic SAT vs. SSAT

FTBM Step2: Fault Rate Calculation Based on SSAT

Deterministic SAT Stochastic SAT

Simulation-based fault rate calculation Not scalable for multiple defects

SAT-based fault rate calculation Intelligently modeling random defects

SSAT Encoding for Fault Rate Calculation

Faults in intermediate wiresFaults in LUT configurations

Binary search is performed to find

the maximal β

Example: SAT-Based FTBM

abc g

000 1

001 1

010 1

011 0

100 1

101 1

110 0

111 0

g= !x1!x3+ !x2

2-LUT

2-LUT

2-LUT

x1

x2

x3

fz1

z2

Boolean function

PLB Template

Boolean matching

Example: SAT-Based FTBMStep1: CNFs for the PLB template

2-LUT

2-LUT

2-LUT

x1

x2

x3

fz1

z2

G LUT = ( x1 + x2+ ¬L0 + z) ( x1 + x2+ L0 + ¬ z)

( x1 + ¬ x2+ ¬L1 + z) ( x1 + ¬ x2+ L1 + ¬ z)

(¬ x1 + x2+ ¬L2 + z) (¬ x1 + x2+ L2 + ¬ z)

(¬ x1 + ¬ x2+ ¬L3 + z) (¬ x1 + ¬ x2+ L3 + ¬ z)

L0

L3

L1 4-1 MUX

x1

z

LUT-2

00

11

01

L2 10

x2

PLB Characteristic Function: G = G LUT1 · G LUT2 · G LUT3

Example: SAT-Based FTBMStep2: Replication based on Truth Table

abc g

000 1

001 1

010 1

011 0

100 1

101 1

110 0

111 0

SAT Instance:G expand = G[X/000, f/1, z/z0] · G[X/001, f/1, z/z1]

G[X/010, f/1, z/z2] · G[X/011, f/0, z/z3]

G[X/100, f/1, z/z4] · G[X/101, f/1, z/z5]

G[X/110, f/0, z/z6] · G[X/111, f/0, z/z7]

G = G LUT1 · G LUT2 · G LUT3

Replication

Example: SAT-Based FTBMStep3: SAT Solving and Mapping

SAT Instance:G expand = G[X/000, f/1, z/z0] · G[X/001, f/1, z/z1]

G[X/010, f/1, z/z2] · G[X/011, f/0, z/z3]

G[X/100, f/1, z/z4] · G[X/101, f/1, z/z5]

G[X/110, f/0, z/z6] · G[X/111, f/0, z/z7]

SAT!

x1

fx2

x3

2-LUT

2-LUT

2-LUT

x1

x2

x3

fz1

z2

Returned SAT assignments: L1(00) = 0, L1(01)=0, L1(10)=0, L1(11)=1, …

Example: SAT-Based FTBMStep4: Exploring More SAT Solutions

Augmented SAT Instance:G expand = G[X/000, f/1, z/z0] · G[X/001, f/1, z/z1]

G[X/010, f/1, z/z2] · G[X/011, f/0, z/z3]

G[X/100, f/1, z/z4] · G[X/101, f/1, z/z5]

G[X/110, f/0, z/z6] · G[X/111, f/0, z/z7]

¬ (L1(00) = 0, L1(01)=0, L1(10)=0, L1(11)=1, …)/* Complement of previous SAT assignments */

2-LUT

2-LUT

2-LUT

x1

x2

x3

fz1

z2

x1

fx2

x3

New Configuration

x1

fx2

x3

Previous Configuration

Fault rate = 0.2Fault rate = 0.3

PLB Templates for SAT-based Resynthesis

4LUT

4LUT

4LUT

X1

X2

X3

X4

X5

X6

X7X8X9

X10G

4LUT

4LUT

X1

X2

X3

X4

X5

X6

X7

G

F

F1

F2

4LUT

4LUT

4LUT

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10 G

F1

F2

Area efficient templates [A. Ling, DAC’05]

Proposed robust template w/ path-reconvergence Can be configured by existing FPGAs

4-LUT

4-LUT

4-LUT4-LUT

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10

X11

X12

z1

z3

z2

G

F1

F2

Templates for SAT-based Resynthesis (cont.)

LUT4

LUT4

LUT4 LUT4

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10

X11

X12

z1

z3

z2

G

F1

F2

Robust PLB template introduces more potential of don’t-cares

ROSE maximizes don’t-cares iteratively at each template output

LUT2

LUT2

00 101 110 x11 1

z1

z3

z2

X1

X2

X3

X4

LUT2

00 x01 x10 x11 x

LUT2z1

z3

z2

X1

X2

1

1

G

(a) (b)

Satisfiability don’t-

care

Observability don’t-

care

Outline Background Preliminaries Robust Resynthesis Experimental Results Conclusion and Future Work

Experimental Settings

Implementation in OAGear SAT-BM uses miniSAT2.0

QUIP benchmarks are tested Are first mapped with 4-LUTs by Berkeley ABC

Resynthesis settings One traversal is performed Blocks with up to 10 inputs are considered

The fault rate of the chip is calculated by Monte Carlo simulation with 20K random vectors assuming the single fault

Results are verified by ABC equivalency checkers

Full-chip Fault Rate by Monte Carlo Simulation

0.00%0.50%1.00%1.50%2.00%2.50%3.00%3.50%

Full-chip fault rate

QUIP benchmarks

ABC ROSE/A ROSE/R

>30% fault rate reduction!

Fault rate is the percentage of input vectors that cause observable output errors assuming the single fault.

4LUT

4LUT

4LUT

X1

X2

X3

X4

X5

X6

X7X8X9

X10G

F1

F2

4LUT

4LUT

4LUT

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10 G

F1

F2

A-PLB1A-PLB2

LUT4

LUT4

LUT4 LUT4

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10

X11

X12

z1

z3

z2

G

F1

F2

R-PLB

Area (LUT#)

0500

100015002000250030003500

LUT#

QUIP benchmarks

ABC ROSE/A ROSE/R

ABC vs. ROSE/A vs. ROSE/R:1: 0.9 : 0.99

4LUT

4LUT

4LUT

X1

X2

X3

X4

X5

X6

X7X8X9

X10G

F1

F2

4LUT

4LUT

4LUT

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10 G

F1

F2

A-PLB1A-PLB2

LUT4

LUT4

LUT4 LUT4

X1

X2

X3

X4

X5

X6

X7

X8

X9

X10

X11

X12

z1

z3

z2

G

F1

F2

R-PLB

Estimation of Mean Time Between Failure

SER modeling: [Mukherjee, HPCA, 2005] Assume max-size FPGA: 330,000 LUTs

20.6627.15

0 5 10 15 20 25 30

MTB

F (y

ear)

ABC ROSE/R 31% MTBF increase!

Outline Background Preliminaries Robust Resynthesis Experimental Results Conclusion and Future Work

Conclusions and Future Work

Developed ROSE and a robust template. ROSE is an orthogonal approach compared to existing

fault-tolerant technique. Virtually no overhead on power, delay and area

In the future, we will consider Multiple correlated faults, Alternative algorithms, Extension to standard cell-based circuits, Impacts on testability.

Robust FPGA Resynthesis Based on Fault-Tolerant Boolean Matching

Yu Hu, Zhe Feng, Rupak Majumdar and Lei HeUniversity of California, Los Angeles