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 Vachharajani


Core Research LabUniversity of Colorado at Boulder

Core Research Lab

Motivation

• Tools can be useful

Representation take days to create!

• ParaMeter

Fabrel Studio

• Are they useable?



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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

0

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DIN

0

1

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DIN Ready Time

0 1 2 3 4 5 6 7 8 9 10 11 12 13

0

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11



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Video

Details: Price, Giacomoni, and Vachharajani PACT 2008



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Trace BDD Construction

fd0 = (0,0)

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DIN Ready Time

0 1 2 3 4 5 6 7 8 9 10 11 12 13

fd1 = (0,1)

fd2 = (0,2)



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(X’ * Y’ * Z’ * W)

(X’ * Y’ * Z’ * W’)

ftrace = (X’ * Y’ * Z’ * W’) + (X’ * Y’ * Z’ * W) + (X’ * Y’ * Z * W’)

(0,0) (00,00)

(0,1) (00,01)

(X’ * Y’ * Z * W’)(0,2) (00,10)

Data Tuple Binary Tuple Boolean Function

{{X’ * Y’ * Z’ * W’}, {X’ * Y’ * Z’ * W}, {X’ * Y’ * Z’ * W}}



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The BDD Data StructureFalse ArcInvertingFalse ArcTrue Arc

F(X,Y,Z,W) = X*Y*Z*W

0

Y

W

Z

W

ZZ Z

0 00 00 00 0

Y

W

Z

W

ZZ Z

0 0 00 100

X

0



Core Research Lab



Y

W

Z

W

ZZ Z

Y

W

Z

W

ZZ Z

1

X

Z

0



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Y

WW

Y

WW

Z

1

X

Z

0

W



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Y Y

W

Z

1

X

Z

0

W

0



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Y

W

Z

1

X

0 1

X

Y

W

Z



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fd1 = (X’ * Y’ * Z’ * W)fd0 = (X’ * Y’ * Z’ * W’)

= +

ftrace = (X * Y * Z * W) + (X’ * Y’ * Z’ * W’)

1

X

Y

Z

1

X

Y

W

Z

1

X

Y

W

Z



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Trace BDD Construction Cont..

Unique Table

fd1 = (X’ * Y’ * Z’ * W)

1

X

Y

W

Z

fd0 = (X’ * Y’ * Z’ * W’)

= +

ftrace = (X’ * Y’ * Z’ * W’) + (X’ * Y’ * Z’ * W)

1

X

Y

W

Z

ftrace = (X’ * Y’ * Z’ * W’)

11

Itrace = 0

1

X

Y

W

Z

1

X

Y

Z

Compute Cache

Dead Nodes



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Trace BDD Construction Cont..

1

X

Y

W

Z= +

ftrace

1

X

Y

Z

1

X

Y

W

Z

fd3 = (X’ * Y’ * Z * W’)

Unique Table

Compute Cache

Dead Nodes



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BDD Garbage Collection Time



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ZDDsBDDs

1. Remove isomorpic graphs2. Skip and remove nodes whose pointers

point to the same child

ZDDs1. Remove isomorpic graphs2. Remove nodes whose “then” arc

points to the constant 0

64641100 ... yxyxyx



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Trace ZDD Construction

fd1 = (X’ * Y’ * Z’ * W)fd0 = (X’ * Y’ * Z’ * W’)

=+

ftrace = (X’ * Y’ * Z’ * W’) + (X’ * Y’ * Z’ * W)

1 0 1

W

01

W

0

Compute Cache

Dead Nodes

Unique Table



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fd3 = (X’ * Y’ * Z * W’)

=+

ftrace

1

Z

01

W

0

ftrace (new)

1

W

0

Z

Unique Table

Compute Cache

Dead Nodes



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Trace ZDD Gains

~ 20% Reduction



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Trace ZDD Losses

3x Slower!



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fd3 = (X’ * Y’ * Z * W’)

=+

ftrace

1

Z

01

W

0

ftrace (new)

1

W

0

Z

Unique Table

Compute Cache

Death Row



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DIN x RDY Tuples

Over 9 times faster!



Core Research Lab

Questions?

University of Colorado at Boulder Core Research Lab ZDDs for Dynamic Trace Analysis Graham Price...

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