University of Colorado at Boulder Core Research Lab ZDDs for Dynamic Trace Analysis Graham Price...
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University of Colorado at Boulde Core Research Lab ZDDs for Dynamic Trace Analysis Graham Price Manish Vachharajani John Giacomoni John Michalakes Sreyasi Vinjamuri
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Transcript of University of Colorado at Boulder Core Research Lab ZDDs for Dynamic Trace Analysis Graham Price...
University of Colorado at Boulder
Core Research Lab
ZDDs for Dynamic Trace Analysis
Graham Price Manish VachharajaniJohn GiacomoniJohn MichalakesSreyasi Vinjamuri
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
Motivation
• Chip Multiprocessor (CMP) solutions are becoming more prevalent
• Dynamic program analysis can aid location of parallelism in sequential programs
• BDDs are useful
But they take days to create!
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
DIN vs. Ready Time
li r1, &fibarr
mov r2, 8
mov r4, 1
mov r3, 1
add r5,r3,r4
st 0(r1),r5
mov r3,r4
mov r4,r5
addi r2,r2,-1
addi r1,r1,4
bnz r2, loop
add r5,r3,r4
st 0(r1),r5
mov r3,r4
…
0xbee0
0xbee4
Instruction Mem Addr
1
2
3
4
5
6
7
8
9
10
11
12
13
14
DIN
1
2
3
4
5
6
7
8
9
10
11
12
13
14
DIN Ready Time
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1
2
3
4
13
5
7
9
10
6
8
11
14
12
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
Video
Details: Price, Giacomoni, and Vachharajani PACT 2008
http://www.youtube.com/watch?v=KdeRtDrPEY4
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
The BDD Data StructureFalse ArcInvertingFalse ArcTrue Arc
F(X,Y,Z) = x’y + xy’ + z
1
X
Y
Z
Y
ZZ Z
1 10 01 11
X
Y
Z
Y
1
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
Trace BDD Construction
It = (X’ * Y’ * Z’ * W’)
1
X
Y
W
Z
It = (X * Y * Z * W)
= +
1
X
Y
W
Z
1
X
Y
W
Z
Y
W
Itrace = (X * Y * Z * W) + (X’ * Y’ * Z’ * W’)
0
Itrace = 0
0
1
X
Y
W
Z
Itrace = (X * Y * Z * W)
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
Trace BDD Construction
It = (X’ * Y’ * Z’ * W’)
1
X
Y
W
Z
It = (X * Y * Z * W)
= +
1
X
Y
W
Z
1
X
Y
W
Z
Y
W
Itrace = (X * Y * Z * W) + (X’ * Y’ * Z’ * W’)
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
Trace BDD Construction Cont..• Garbage Problem
1
X
Y
W
Z
1
X
Y
W
Z
Y
W
1
X
Y
W
Z
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
ZDDsBDDs
1. Remove isomorpic graphs2. Skip and remove nodes whose pointers
point to the same child
ZDDs1. Remove isomorpic graphs2. Remove “1” nodes whose pointers
point to “0”
64641100 ... yxyxyx
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
ZDD vs. BDD SizeIt = (X’ * Y’ * Z’ * W’) It = (X * Y * Z * W) + (X’ * Y * Z * W)
~ 20% Reduction
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
DD Creation Time
DIN x RDY Tuples
Over 9 times faster!
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
ZDD Construction
It = (X’ * Y’ * Z’ * W’)
1
X
Y
W
Z
It = (X * Y * Z * W)
= +
1
Itrace = (X * Y * Z * W) + (X’ * Y’ * Z’ * W’)
0
Itrace = 0
0
1
X
Y
W
Z
Itrace = (X * Y * Z * W)
1
Z
X
Y
W
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
Where BDDs Compress
1
X
Y
W
Z
1
X
Y
W
Z
Y
W
1
X
Y
W
Z
No Compression No CompressionCompression
= +
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
Where ZDDs Compress
1
X
Y
W
Z
Compression CompressionLittle/No Compression
= +
1
Z
X
Y
W
1
Details: Price and Vachharajani, to appear CGO 2010
University of Colorado at Boulder
Core Research LabUniversity of Colorado at Boulder
Core Research Lab
Questions?
