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Cross-layer Optimized Placement and Routing for FPGA Soft Error Mitigation Keheng Huang 1,2, Yu Hu...
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Cross-layer Optimized Placement and Routing for FPGA Soft Error Mitigation
Keheng Huang1,2, Yu Hu1, and Xiaowei Li1
1Key Laboratory of Computer System and Architecture
Institute of Computing Technology
Chinese Academy of Sciences
2Graduate University of Chinese Academy of Sciences
2
Outline• Background
• Motivation
• Cross-layer optimized placement and routing
• Experimental results
• Conclusions
3
Background• Architecture of SRAM-based FPGAs
4
Background• Architecture of SRAM-based FPGAs
Segments
(a) An overview of FPGA structure
5
Background• Architecture of SRAM-based FPGAs
Segments
(a) An overview of FPGA structure
W1
Wi
E1
Ei
S1 Sj
N1 Nj
(b) Switching block
.
.
.
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
.
.
.
CB
CB
. . .
. . .
S
S Switching block
6
Background• Architecture of SRAM-based FPGAs
• Configuration bits (>98% of all SRAM bits)–Routing resources (80% of configuration bits)
• User bits (<2% of all SRAM bits)
CLB CLB
CLB CLB
(a) An overview of FPGA structure
W1
Wi
E1
Ei
S1 Sj
N1 Nj
(b) Switching block
.
.
.
MUXsANDFFs Output
(c) Configurable logic block
.
.
.
CB
CB
CB
CB
CB
CB
CB
CB
CB
CB
.
.
.
CB
CB
. . .
. . .
LUTentry0: CBentry1: CB
entry14: CBentry15: CB
S
S Switching block
CLB Configurable logic blockThe reliability of routing resources needs to be seriously considered during placement and routing
Segments
7
Reliability Oriented EDA Flow
Synthesis and mapping
Design specification
Gate-level netlist
Bit Stream
Placement and routing
Application design level
Physical design level
• RoRA [TC’06]
TMR designs only
• SEU-Aware P & R[ISQED’07]
Dimensions of bounding box
• Reliability-aware P & R[ITC’10] Dimensions of bounding box
• SEU-Aware Router [DAC’07] Number of configuration bits
8
Soft Error Rate (SER)
Input Output
CBCBCBCB
CB
OutputInput
Propagation probability
Occurrence probability
SER evaluation criterion
Application level factor(EPP)
Physical level factor(Node error rate)
+
9
Key Observation
Application level factor(EPP)
Physical level factor(Node error rate)
Prior P & R guidance criterion
All EPPs are equal?
Physical level factor(Bounding boxes,
Configuration bits)
Estimated SER+
SER evaluation criterion
10
Key Observation• Application level factor (EPPs) varies significantly
Gini coefficient Inequality degree<0.2 Absolutely equal0.2-0.3 Relatively equal0.3-0.4 Moderately unequal0.4-0.5 The gap is relatively large>0.6 Quite unequal
0.0
0.2
0.4
0.6
0.8
1.0
avera
getse
ngseq
s385
84.1
s384
17frisc
ellipt
icdif
feqdes
dsip
clma
bigke
yap
ex2
ex5p
ex10
10spla
s298pd
c
misex3
apex
4
Gin
i coe
ffic
ient
of
EP
Ps Gini coefficient of EPPs
alu4
avg.=0.646
Circuit name
11
Key Observation• Application level factor (EPPs) varies significantly
Gini coefficient Inequality degree<0.2 Absolutely equal0.2-0.3 Relatively equal0.3-0.4 Moderately unequal0.4-0.5 The gap is relatively large>0.6 Quite unequal
0.0
0.2
0.4
0.6
0.8
1.0
avera
getse
ngseq
s385
84.1
s384
17frisc
ellipt
icdif
feqdes
dsip
clma
bigke
yap
ex2
ex5p
ex10
10spla
s298pd
c
misex3
apex
4
Gin
i coe
ffic
ient
of
EP
Ps Gini coefficient of EPPs
alu4
avg.=0.646
Circuit name
12
Cross-layer Optimized Placement and Routing
• Overview
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Physical level
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis Application level
Cross-layer optimization
Physicallevel factor
SER
High Low
SER
13
Cross-layer Optimized Placement and Routing
• Overview
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Physical level
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis Application level
Cross-layer optimization
Physicallevel factor
SER
High Low
SER
14
Cross-layer Optimized Placement and Routing
• Overview
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Physical level
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis Application level
Cross-layer optimization
Physicallevel factor
SER
High Low
SER
15
Cross-layer Optimized Placement and Routing
• Overview
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Physical level
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis Application level
Cross-layer optimization
Physicallevel factor
SER
High Low
SER
16
Cross-layer Optimized Placement and Routing
• Overview
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Physical level
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis Application level
Cross-layer optimization
Physicallevel factor
SER
High Low
SER
17
Cross-layer Optimized Placement and Routing
• Overview
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Physical level
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis Application level
Cross-layer optimization
Physicallevel factor
SER
High Low
SER
18
Cube-based EPP Analysis• Error propagation probability (EPP)
• Monte Carlo simulation–Test vectors (high accuracy)–Traverse the design N times (high complexity)
• Static analysis–Signal probability and error propagation rules (lower accuracy)–Traverse the design twice per fault (lower complexity)
19
Cube-based EPP Analysis• Error propagation probability (EPP)
• Monte Carlo simulation–Test vectors (high accuracy)–Traverse the design N times (high complexity)
• Static analysis–Signal probability and error propagation rules (lower accuracy)–Traverse the design twice per fault (lower complexity)
A method with high accuracy and low complexity?
20
Cube-based EPP Analysis• Besides 0 and 1, “X” bit is introduced
• Introduce the cube and cover in logic synthesis
• Covers adjoin V:(set union: )∪ • Covers interface I:(set intersection: ∩)
0XX = {000,001,010,011}
cover ={0XX, 1XX}
cube
adjoin :{00X} V {01X} = {0XX}
interface: {00X} I {001} = {001}
21
Cube-based EPP Analysis• Forward traverse: compute the vectors that set
the logic of the wire as 0 and 1 respectively
0
0
0
1
Input0
Input1
control-cover 0 {X0}control-cover 1 {X1}
control-cover 0 {0X}control-cover 1 {1X} Output
LUTi
control-cover 0 {0X,10}control-cover 1 {11}
22
Cube-based EPP Analysis• Forward traverse: compute the vectors that set
the logic of the wire as 0 and 1 respectively
0
0
0
1
Input0
Input1
control-cover 0 {X0}control-cover 1 {X1}
control-cover 0 {0X}control-cover 1 {1X} Output
LUTi
control-cover 0 {0X,10}control-cover 1 {11}
23
Cube-based EPP Analysis• Forward traverse: compute the vectors that set
the logic of the wire as 0 and 1 respectively
• Backward traverse: compute the vectors that can propagate the fault to outputs
Output
LUTi
care-cover 0 {01,10}care-cover 1 {11}
care-cover 0 {0X}care-cover 1 {11}
0
0
0
1care-cover 0 {0X,10}care-cover 1 {11}
Fanout0
Fanout1
0
0
0
1
Input0
Input1
control-cover 0 {X0}control-cover 1 {X1}
control-cover 0 {0X}control-cover 1 {1X} Output
LUTi
control-cover 0 {0X,10}control-cover 1 {11}
24
Cube-based EPP Analysis• Forward traverse: compute the vectors that set
the logic of the wire as 0 and 1 respectively
• Backward traverse: compute the vectors that can propagate the fault to outputs
Output
LUTi
care-cover 0 {01,10}care-cover 1 {11}
care-cover 0 {0X}care-cover 1 {11}
0
0
0
1care-cover 0 {0X,10}care-cover 1 {11}
Fanout0
Fanout1
0
0
0
1
Input0
Input1
control-cover 0 {X0}control-cover 1 {X1}
control-cover 0 {0X}control-cover 1 {1X} Output
LUTi
control-cover 0 {0X,10}control-cover 1 {11}
25
Application level factor• Error propagation probability (EPP)
• Compare with traditional Monte Carlo simulation• For each fault, traverse the design N times
care-cover
inputs
NEPP
N
0
0
0
1Logic 0:
0
0
0
1
1
0
1
1
Input vectors
V0V1V2V3
Logic 1: 00
01
10
11
LUTi
11
00 01 10
Ncare-cover: number of vectors stored in care-cover
Ninputs: total number of input vectors
26
Application level factor• Comparison of computational complexity
• N: number of input vectors• V: number of LUTs• E: number of interconnecting wires• g: number of configuration bits per LUT or wire• Cavg: average compression ratio of all covers
Algorithm Computational complexity
Monte Carlo Simulation O(N*V*g*(V+E))
Static Analysis O(V2*(V +E))
Cube-based EPP Analysis O((N/Cavg)2*(V+E))
27
Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost
SER cost= Phy cost * App cost
placer
bby
bbx
SER costCube-based
EPP AnalysisEPPi
NETi
bbx+bby
cbby
cbbx
cbbx+cbby
Cross-layer optimizationEPPi+EPPj
NETj
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
28
Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost
SER cost= Phy cost * App cost
placer
bby
bbx
SER costCube-based
EPP AnalysisEPPi
NETi
bbx+bby
cbby
cbbx
cbbx+cbby
Cross-layer optimizationEPPi+EPPj
NETj
open0
[ ( ) ( )]*netsi N
x y ii
SER cost bb i bb i EPP
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
29
Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost
SER cost= Phy cost * App cost
bby
placerbbx
SER costCube-based
EPP AnalysisEPPi
NETi
bbx+bby
cbby
cbbx
cbbx+cbby
Cross-layer optimizationEPPi+EPPj
NETj
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
open0
[ ( ( ]) *)netsi N
ii
x ybb i bbSER cost Pi E P
30
Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost
SER cost= Phy cost * App cost
bby
placerbbx
SER costCube-based
EPP AnalysisEPPi
NETi
bbx+bby
cbby
cbbx
cbbx+cbby
Cross-layer optimizationEPPi+EPPj
NETj
open0
[ ( ( ]) *)netsi
x y i
N
i
bb i bbSER cost i EPP
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
31
Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost
SER cost= Phy cost * App cost
placer
bby
bbx
SER costCube-based
EPP AnalysisEPPi
NETi
bbx+bby
cbby
cbbx
cbbx+cbby
Cross-layer optimizationEPPi+EPPj
NETj
open0
[ ( ) ( )]*netsi N
x y ii
SER cost bb i bb i EPP
short0 0,
{[ ( ) ( )]*( )}nets netsi N j N
x y i ji j j i
SER cost cbb i cbb i EPP EPP
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
32
Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost
SER cost= Phy cost * App cost
cbby
placer
bby
bbx
SER costCube-based
EPP AnalysisEPPi
NETi
bbx+bby
cbbx
cbbx+cbby
Cross-layer optimizationEPPi+EPPj
NETj
open0
[ ( ) ( )]*netsi N
x y ii
SER cost bb i bb i EPP
short0 0,
( {[ ]*() )}( )nets netsi N j N
i ji j
x yj i
cbb i cbSER cost EPP EPi Pb
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
33
Cross-layer Optimized Placement Total cost=a*timing cost + b*congestion cost + c*SER cost
SER cost= Phy cost * App cost
cbby
placer
bby
bbx
SER costCube-based
EPP AnalysisEPPi
NETi
bbx+bby
cbbx
cbbx+cbby
Cross-layer optimizationEPPi+EPPj
NETj
open0
[ ( ) ( )]*netsi N
x y ii
SER cost bb i bb i EPP
short0 0,
( {[ ]*() )}( )nets netsi N j N
ix y i
j j ijcbb i cbSER cost b i EPP EPP
Cross-layer optimized placement
Placer
Physicallevel factor
Cross-layer optimized routing
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
34
Cross-layer Optimized Routing• Finer granularity estimate of SER
router
SER costCube-based
EPP Analysis
NCBk
EPPi+EPPk_net Cross-layer optimizationEPPi
CB
CBCB
CB
CLB
CLB
CLB
CLB
CLB
CLB
Bridgek
SEGjNETi
NETk_net
open0 0
( * )segsnets
j Ni N
j ji j
SER cost NCB EPP
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
35
Cross-layer Optimized Routing• Finer granularity estimate of SER
router
SER costCube-based
EPP Analysis
NCBk
EPPi+EPPk_net Cross-layer optimizationEPPi
CB
CBCB
CB
CLB
CLB
CLB
CLB
CLB
CLB
Bridgek
SEGjNETi
NETk_net
open0 0
( * )segsnets
ji
ij
NN
jj
SER cost NCB EPP
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
36
Cross-layer Optimized Routing• Finer granularity estimate of SER
router
SER costCube-based
EPP Analysis
NCBk
EPPi+EPPk_net Cross-layer optimizationEPPi
CB
CBCB
CB
CLB
CLB
CLB
CLB
CLB
CLB
Bridgek
SEGjNETi
NETk_net
open0 0
( * )segsnets
ji
ij j
NN
j
SER cost NCB EPP
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
37
Cross-layer Optimized Routing• Finer granularity estimate of SER
router
SER costCube-based
EPP Analysis
NCBk
EPPi+EPPk_net Cross-layer optimizationEPPi
CB
CBCB
CB
CLB
CLB
CLB
CLB
CLB
CLB
Bridgek
SEGjNETi
NETk_net
open0 0
( * )segsnets
j Ni N
j ji j
SER cost NCB EPP
short _0 0 0
[ *( )]segs bridgenets
j N k Ni N
k i k neti j k
SER cost NCB EPP EPP
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
38
Cross-layer Optimized Routing• Finer granularity estimate of SER
router
SER costCube-based
EPP Analysis
NCBk
EPPi+EPPk_net Cross-layer optimizationEPPi
CB
CBCB
CB
CLB
CLB
CLB
CLB
CLB
CLB
Bridgek
SEGjNETi
NETk_net
open0 0
( * )segsnets
j Ni N
j ji j
SER cost NCB EPP
short _0 0 0
[ *( )]segs bridgenets
j N k Ni N
i k neti
kj k
SER cost EP EN B P PPC
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
39
Cross-layer Optimized Routing• Finer granularity estimate of SER
router
SER costCube-based
EPP Analysis
NCBk
EPPi+EPPk_net Cross-layer optimizationEPPi
CB
CBCB
CB
CLB
CLB
CLB
CLB
CLB
CLB
Bridgek
SEGjNETi
NETk_net
open0 0
( * )segsnets
j Ni N
j ji j
SER cost NCB EPP
short0 0 0
_ [ *( )]segs bridgenets
j N k Ni N
i j kk i k netSER co NCB EP Est P PP
Cross-layer optimized routingCross-layer optimized placement
Placer
Physicallevel factor
Router
Cube-basedEPP analysis
SER
Application level factor
Applicationlevel factor
Logic synthesis
Physicallevel factor
SER
SER
40
Experimental Setup
MCNC benchmark set
Berkeley ABC mapper
Gate-level netlist
Bit Stream
VPR: Academic FPGA placement and routing tool
Logic resources: 4 6-input LUTs per CLBRouting channel width: 30% increase
41
Experimental results• Comparison of EPP accuracy and run time
• Monte Carlo simulation• DCOW: partial Monte Carlo simulation• Cube-based EPP analysis
• Comparison of SER mitigation• Original VPR• Guided by physical level factor only (PPL)• Cross-layer optimized placement and routing
algorithm (COPAR)
42
Comparison of EPP Accuracy and Run Time
• Monte Carlo simulation (golden model)
• DCOW: partial Monte Carlo simulation (DAC’10)
• Cube-based analysis (our method)
faultscube sim
0 inputs
( )N
i
N NGap
N
Ncube: number of test vectors computed by cube-based analysis
Nsim: number of test vectors computed by Monte Carlo simulation
Ninputs: total number of input vectors
43
CircuitMonte Carlo simulation Cube-based analysis Gap(10-4)†
Nsim(105) Time(s) Ncube(105) Time(s) Gcube GDCOW
alu4 20.46 3314 20.45 186 0.212 0apex2 122.85 N/A 122.69 42/itr 0.257 1052apex4 2.89 461 2.89 54 0 0clma 126.79 N/A 126.89 35/itr 0.0529 1336
misex3 31.27 98528 31.23 78 0.604 0pdc 533.11 647142 533.27 4230 0.195 0s298 36.70 1055 36.70 1 0 0
s38417 2724.22 N/A 2725.37 395/itr 0.533 344s38584.1 2385.31 N/A 2385.50 252/itr 0.095 122
seq 689.72 N/A 689.41 13/itr 0.236 516spla 698.48 569302 698.48 1440 0.00013 0
bigkey 876.46 N/A 876.46 14/itr 0 14des 868.03 N/A 868.03 12/itr 0 0
diffeq 432.85 N/A 432.85 9/itr 0 379dsip 1158.63 N/A 1158.63 24/itr 0 0
elliptic 240.35 N/A 240.35 3/itr 0 192ex1010 2.50 109325 2.50 69 0 0
ex5p 0.47 305 0.47 16 0.024 0frisc 1706.43 N/A 1706.44 107/itr 0.00585 472
tseng 1436.15 N/A 1436.24 13/itr 0.0786 247
Geomean 704.68 178679 704.74 759 0.115 234
Comparison of EPP Accuracy and Run Time
44
CircuitMonte Carlo simulation Cube-based analysis Gap(10-4)†
Nsim(105) Time(s) Ncube(105) Time(s) Gcube GDCOW
alu4 20.46 3314 20.45 186 0.212 0apex2 122.85 N/A 122.69 42/itr 0.257 1052apex4 2.89 461 2.89 54 0 0clma 126.79 N/A 126.89 35/itr 0.0529 1336
misex3 31.27 98528 31.23 78 0.604 0pdc 533.11 647142 533.27 4230 0.195 0s298 36.70 1055 36.70 1 0 0
s38417 2724.22 N/A 2725.37 395/itr 0.533 344s38584.1 2385.31 N/A 2385.50 252/itr 0.095 122
seq 689.72 N/A 689.41 13/itr 0.236 516spla 698.48 569302 698.48 1440 0.00013 0
bigkey 876.46 N/A 876.46 14/itr 0 14des 868.03 N/A 868.03 12/itr 0 0
diffeq 432.85 N/A 432.85 9/itr 0 379dsip 1158.63 N/A 1158.63 24/itr 0 0
elliptic 240.35 N/A 240.35 3/itr 0 192ex1010 2.50 109325 2.50 69 0 0
ex5p 0.47 305 0.47 16 0.024 0frisc 1706.43 N/A 1706.44 107/itr 0.00585 472
tseng 1436.15 N/A 1436.24 13/itr 0.0786 247
Geomean 704.68 178679 704.74 759 0.115 234
Comparison of EPP Accuracy and Run Time
45
CircuitMonte Carlo simulation Cube-based analysis Gap(10-4)†
Nsim(105) Time(s) Ncube(105) Time(s) Gcube GDCOW
alu4 20.46 3314 20.45 186 0.212 0apex2 122.85 N/A 122.69 42/itr 0.257 1052apex4 2.89 461 2.89 54 0 0clma 126.79 N/A 126.89 35/itr 0.0529 1336
misex3 31.27 98528 31.23 78 0.604 0pdc 533.11 647142 533.27 4230 0.195 0s298 36.70 1055 36.70 1 0 0
s38417 2724.22 N/A 2725.37 395/itr 0.533 344s38584.1 2385.31 N/A 2385.50 252/itr 0.095 122
seq 689.72 N/A 689.41 13/itr 0.236 516spla 698.48 569302 698.48 1440 0.00013 0
bigkey 876.46 N/A 876.46 14/itr 0 14des 868.03 N/A 868.03 12/itr 0 0
diffeq 432.85 N/A 432.85 9/itr 0 379dsip 1158.63 N/A 1158.63 24/itr 0 0
elliptic 240.35 N/A 240.35 3/itr 0 192ex1010 2.50 109325 2.50 69 0 0
ex5p 0.47 305 0.47 16 0.024 0frisc 1706.43 N/A 1706.44 107/itr 0.00585 472
tseng 1436.15 N/A 1436.24 13/itr 0.0786 247
Geomean 704.68 178679 704.74 759 0.115 234
Comparison of EPP Accuracy and Run Time
46
Comparison of SER Mitigation Circuit
VPR(baseline) PPL COPAR
SER(FIT†) SER(FIT) Ratio SER(FIT) Ratio
alu4 17.05 17.08 100.17% 14.25 83.58%
apex2 18.40 18.07 98.21% 14.04 76.30%
apex4 118.40 105.98 89.52% 98.08 82.84%
clma 23.31 20.12 86.33% 19.78 84.85%
misex3 24.76 30.05 121.33% 21.56 87.05%
pdc 175.04 212.12 121.18% 141.09 80.60%
s298 2.68 1.92 71.52% 1.69 63.11%
s38417 547.02 503.30 92.01% 524.95 95.96%
s38584.1 620.70 586.47 94.49% 567.22 91.38%
seq 49.23 46.07 93.56% 38.64 78.48%
spla 269.48 247.18 91.72% 200.03 74.23%
bigkey 159.87 151.56 94.80% 130.09 81.38%
des 130.70 118.60 90.75% 123.79 94.72%
diffeq 91.08 82.81 90.92% 81.81 89.83%
dsip 208.98 168.53 80.65% 207.93 99.50%
elliptic 42.66 39.51 92.63% 39.90 93.55%
ex1010 122.41 117.97 96.37% 96.01 78.44%
ex5p 32.02 29.23 91.29% 28.76 89.84%
frisc 488.89 431.86 88.33% 455.16 93.10%
tseng 125.74 106.53 84.72% 117.58 93.51%
Geomean 163.42 151.75 93.53% 146.12 85.61%
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Comparison of SER Mitigation
0%
20%
40%
60%
80%
100%
120%
140% VPR (baseline)PPLCOPAR
100% 93.53% 85.61%
48
Conclusions• Observe the gap between the SER evaluation
criterion and guidance criterion for soft error mitigation (gini coefficient=0.646)
• Introduce cube-based EPP analysis to compute the application level factor (gap<1%)
• Propose a cross-layer optimized placement and routing algorithm (SER mitigation>14%)
49
• Thank You for Your Attention
• Question?