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Precise Dynamic Slicing Precise Dynamic Slicing AlgorithmsAlgorithms

Xiangyu Zhang, Rajiv Gupta and Xiangyu Zhang, Rajiv Gupta and Youtao ZhangYoutao Zhang

Presented By: Krishna BalasubramanianPresented By: Krishna Balasubramanian

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SlicingSlicing TechniquesTechniques??

Dynamic SlicingDynamic Slicing Isolates unique statements computing variable

for given inputs Criteria: <i, v, n>Criteria: <i, v, n>

Static Slicing Static Slicing Isolates all possible statements computing a

particular variable Criteria: <v, n>

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Example – Data dependencesExample – Data dependences

Static Slice <10, z> = {1, 2, 3, 4, 7, 8, 9, 10}Static Slice <10, z> = {1, 2, 3, 4, 7, 8, 9, 10} Dynamic Slice <input, variable, execution point>Dynamic Slice <input, variable, execution point>

<N=1, z, 10<N=1, z, 1011> = {3, 4, 9, 10}> = {3, 4, 9, 10}

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Slice Sizes: Static vs DynamicSlice Sizes: Static vs Dynamic

ProgramProgram StatementStatementss

StaticStatic DynamicDynamic Static/Static/DynamicDynamic

126.gcc126.gcc 585,491585,491 51,098 51,098 6,6146,614

7.727.72

099.go099.go 95,45995,459 16,941 16,941 5,3825,382

3.143.14

134.perl134.perl 116,182116,182 5,242 5,242 765765

6.856.85

130.li130.li 31,82931,829 2,450 2,450 206206

11.8911.89

008.express008.expressoo

74,03974,039 2,353 2,353 350350

6.726.72 Static slicing gives huge slicesStatic slicing gives huge slices On an average, static slices much largerOn an average, static slices much larger

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Precise Dynamic SlicingPrecise Dynamic Slicing

Data dependences exercised during program Data dependences exercised during program execution captured precisely and savedexecution captured precisely and saved

Only dependences occurring in a Only dependences occurring in a specific specific execution of program are consideredexecution of program are considered

Dynamic slices constructed upon users requests Dynamic slices constructed upon users requests by traversing captured dynamic dependence by traversing captured dynamic dependence informationinformation

Limitation : Costly to computeLimitation : Costly to compute

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Imprecise Dynamic SlicingImprecise Dynamic Slicing

Reduces cost of slicing Reduces cost of slicing

Found to greatly increase slice sizesFound to greatly increase slice sizes

Reduces effectivenessReduces effectiveness

Worthwhile to use precise algorithmsWorthwhile to use precise algorithms

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Precise vs Imprecise: Slice SizePrecise vs Imprecise: Slice Size

Implemented two imprecise algorithms: Algorithm Implemented two imprecise algorithms: Algorithm I and Algorithm III and Algorithm II

Imprecise increases the Slice SizeImprecise increases the Slice Size Algorithm II better than Algorithm IAlgorithm II better than Algorithm I

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Precise Dynamic Slicing - Precise Dynamic Slicing - ApproachApproach

Program executedProgram executed

Execution trace collectedExecution trace collected

PDS involves:PDS involves: Preprocessing:Preprocessing:

Builds dependence graph by recovering dynamic Builds dependence graph by recovering dynamic dependences from program’s execution tracedependences from program’s execution trace

SlicingSlicing Computes slices for given slicing requests by Computes slices for given slicing requests by

traversing dynamic dependence graphtraversing dynamic dependence graph

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3 Algorithms Proposed3 Algorithms Proposed

Full preprocessing (FP) – Builds entire Full preprocessing (FP) – Builds entire dependence graph before slicingdependence graph before slicing

No preprocessing (NP)No preprocessing (NP) No preprocessing performedNo preprocessing performed Does demand driven analysis during slicing Does demand driven analysis during slicing Caches the recovered dependenciesCaches the recovered dependencies

Limited preprocessing (LP)Limited preprocessing (LP) Adds summary info to execution traceAdds summary info to execution trace Uses demand driven analysis to recover dynamic Uses demand driven analysis to recover dynamic

dependences from compacted execution tracedependences from compacted execution trace

What do you think is better and What do you think is better and why?why?

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ComparisonComparison

FP algorithm impractical for real programsFP algorithm impractical for real programs Runs out of memory during preprocessing Runs out of memory during preprocessing

phasephase Dynamic dependence graphs extremely largeDynamic dependence graphs extremely large

NP algorithm does not run out of memory NP algorithm does not run out of memory but is slowbut is slow

LP algorithm is practicalLP algorithm is practical Never runs out of memoryNever runs out of memory FastFast

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1)1) Full PreprocessingFull Preprocessing

Edges corresponding to data dependences Edges corresponding to data dependences extracted from execution trace extracted from execution trace

Added to statement level control flow graphAdded to statement level control flow graph

Execution instances labeled on graphExecution instances labeled on graph

Uses instance labels during slicingUses instance labels during slicing

Only relevant edges traversedOnly relevant edges traversed

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FP - ExampleFP - Example Load to store edge on left Load to store edge on left

labeled (1,1)labeled (1,1)

Load to store edge on right Load to store edge on right labeled (2,1)labeled (2,1)

11stst/2/2ndnd instance of load’s instance of load’s execution gets value from 1execution gets value from 1stst instance of execution of store instance of execution of store on the left/righton the left/right

When load included in When load included in dynamic slice, not necessary dynamic slice, not necessary to include both stores in to include both stores in dynamic slice.dynamic slice.

Instance LabelsInstance Labels

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FP - Example

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FP - ExampleFP - Example Dynamic data dependence edges shownDynamic data dependence edges shown

Edges labeled with execution instances of statements Edges labeled with execution instances of statements involved in data dependencesinvolved in data dependences

Data dependence edges traversed during slice computation Data dependence edges traversed during slice computation of Z used in the only execution of statement 16 is:of Z used in the only execution of statement 16 is:

(16(1611, 14, 1433), (14), (1433, 13, 1322), (13), (1322, 12, 1222), (13), (1322, 15, 1533),),

(15(1533, 3, 311), (15), (1533, 15, 1522), (15), (1522, 3, 311), (15), (1522, 15, 1511),),

(15(1511, 3, 311), (15), (1511, 4, 411) )

Precise dynamic slice computed is:Precise dynamic slice computed is:

DS<x=6, z, 16DS<x=6, z, 1611> = {16,14,13,12,4,15,3}> = {16,14,13,12,4,15,3}

Compute the slice corresponding to the value of x used Compute the slice corresponding to the value of x used during the first execution of statement 15 ?? during the first execution of statement 15 ??

DS <x=6, x, 15DS <x=6, x, 1511> = Slice {4,15}> = Slice {4,15}

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2) No Preprocessing2) No Preprocessing

Demand driven analysis to recover dynamic Demand driven analysis to recover dynamic dependencesdependences

Requires less storage compared to FPRequires less storage compared to FP

Takes more timeTakes more time

Caching used to avoid repetitive computationsCaching used to avoid repetitive computations

Cost of maintaining cache vs repeated Cost of maintaining cache vs repeated recovery of same dependences from tracerecovery of same dependences from trace

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NP ExampleNP Example

No dynamic data dependence No dynamic data dependence edges present initiallyedges present initially

To compute slice for z at only To compute slice for z at only execution of st 16:execution of st 16: single backward traversal of trace single backward traversal of trace

(16(1611, 14, 1433), (14), (1433, 13, 1322), (13), (1322, 12, 1222), (13), (1322, 15, 1533),),

(15(1533, 3, 311), (15), (1533, 15, 1522), (15), (1522, 3, 311), (15), (1522, 15, 1511),),

(15(1511, 3, 311), (15), (1511, 4, 411) extracted) extracted

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NP with CacheNP with Cache

Data dependence edges added to program Data dependence edges added to program flow graphflow graph

Compute slice for use of x in 3rd instance Compute slice for use of x in 3rd instance of st 14of st 14 All dependences required already present in graph All dependences required already present in graph Trace not reexaminedTrace not reexamined

Compute slice for use of x by 2nd instance Compute slice for use of x by 2nd instance of st 10of st 10 Trace traversed againTrace traversed again Additional dynamic data dependences extractedAdditional dynamic data dependences extracted

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3) Limited Preprocessing3) Limited Preprocessing

LP strikes a balance b/w preprocessing & LP strikes a balance b/w preprocessing & slicing costsslicing costs Limited preprocessing of traceLimited preprocessing of trace Augments trace with summary informationAugments trace with summary information Faster traversal of augmented traceFaster traversal of augmented trace Demand driven analysis to compute slice using Demand driven analysis to compute slice using

augmented traceaugmented trace

Addresses Addresses Space problems of FPSpace problems of FP Time problems of NPTime problems of NP

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LP – ApproachLP – Approach Trace divided into trace blocksTrace divided into trace blocks

Each trace block of fixed Each trace block of fixed sizesize

Store summary of all downward exposed Store summary of all downward exposed definitions of variable names & memory definitions of variable names & memory addresses addresses

Look for variable definition in summary of Look for variable definition in summary of downward exposed definitionsdownward exposed definitions

If definition found, traverse trace block to locate If definition found, traverse trace block to locate itit

Else, use Else, use sizesize information to skip to start of trace information to skip to start of trace blockblock

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EvaluationEvaluation

Execution traces on 3 different input sets for Execution traces on 3 different input sets for each benchmark computedeach benchmark computed

Computed 25 different slices for each Computed 25 different slices for each execution traceexecution trace

Slices computed wrt end of program’s Slices computed wrt end of program’s execution (@ End)execution (@ End)

Computed 25 slices at an additional point in Computed 25 slices at an additional point in program’s execution (@ midpoint) for 1program’s execution (@ midpoint) for 1stst input input

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Results – Slice sizesResults – Slice sizes

PDS Sizes for additional InputPDS Sizes for additional Input

PDS sizes for 2PDS sizes for 2ndnd & 3 & 3rdrd program inputs for @ End are shown program inputs for @ End are shown

No. of statements in dynamic slice is small fraction of statements No. of statements in dynamic slice is small fraction of statements executedexecuted

Different inputs give similar observationsDifferent inputs give similar observations

Thus, Dynamic slicing is effective across different inputsThus, Dynamic slicing is effective across different inputs

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Evaluation - Slice computation timesEvaluation - Slice computation times

Compared FP, NPwoC, NPwC, and LP Compared FP, NPwoC, NPwC, and LP

Cumulative execution time in seconds as slices Cumulative execution time in seconds as slices are computed one by one is shownare computed one by one is shown

Graphs include both preprocessing times & Graphs include both preprocessing times & slice computation timesslice computation times

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Execution TimesExecution Times

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ObservationsObservations FP rarely runs to completionFP rarely runs to completion

Mostly runs out of memoryMostly runs out of memory

NPwoC, NPwC and LP successfulNPwoC, NPwC and LP successful

Makes computation of PDS feasibleMakes computation of PDS feasible

NPwoC shows linear increase in cumulative NPwoC shows linear increase in cumulative exec time with no. of slicesexec time with no. of slices

LP cumulative exec time rises much more LP cumulative exec time rises much more slowly than NPwoC and NPwCslowly than NPwoC and NPwC

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ObservationsObservations

Exec times of LP are Exec times of LP are 1.13 to 3.43 times < 1.13 to 3.43 times < than NPthan NP

Due to % of trace Due to % of trace blocks skipped by LPblocks skipped by LP

Shows that limited Shows that limited preprocessing does preprocessing does pay offpay off

Cumulative times: NP vs Cumulative times: NP vs LPLP

Trace Blocks skipped by Trace Blocks skipped by LPLP

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LP (Precise) vs Algorithm II LP (Precise) vs Algorithm II (Imprecise)(Imprecise)

Slice Sizes:Slice Sizes: Slices computed by LP 1.2 to 17.33 times Slices computed by LP 1.2 to 17.33 times

smaller than imprecise data slices of smaller than imprecise data slices of Algorithm IIAlgorithm II

Relative performance was similarRelative performance was similar

Execution Times:Execution Times: @ End, total time taken by LP 0.55 to 2.02 @ End, total time taken by LP 0.55 to 2.02

times Algorithm IItimes Algorithm II @ Midpoint, total time taken by LP is 0.51 to @ Midpoint, total time taken by LP is 0.51 to

1.86 times Algorithm II1.86 times Algorithm II

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ResultsResults

Both have no memory problemsBoth have no memory problems

Smaller slice sizes for LPSmaller slice sizes for LP

For large slices, execution time greater than For large slices, execution time greater than impreciseimprecise

For small slices, execution time less than For small slices, execution time less than impreciseimprecise

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SummarySummary

Precise LP algorithm performs the bestPrecise LP algorithm performs the best

Imprecise dynamic slicing algorithms are too Imprecise dynamic slicing algorithms are too imprecise, hence not an attractive optionimprecise, hence not an attractive option

LP algorithm is practicalLP algorithm is practical

Provides Precise Dynamic Slices at reasonable Provides Precise Dynamic Slices at reasonable space and time costsspace and time costs

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Thank you!Thank you!