Dataflow Analysis Introduction

School of EECS, Peking University

“Advanced Compiler Techniques” (Fall 2011)

Dataflow Dataflow Analysis Analysis

IntroductionIntroductionGuo, YaoGuo, Yao

Part of the slides are adapted from MIT 6.035 “Computer Language Engineering”

2Fall 2011“Advanced Compiler

Techniques”

Dataflow AnalysisDataflow Analysis Last lecture: Last lecture:

How to analyze and transform within a How to analyze and transform within a basic blockbasic block

This lecture: This lecture: How to do it for the entire procedureHow to do it for the entire procedure


Techniques”

OutlineOutline Reaching DefinitionsReaching Definitions Available ExpressionsAvailable Expressions Live VariablesLive Variables


Techniques”

Reaching DefinitionsReaching Definitions Concept of definition and useConcept of definition and use

a = x+ya = x+y

is a is a definitiondefinition of a of a

is a is a useuse of x and y of x and y A definition reaches a use if A definition reaches a use if

value written by definitionvalue written by definition

may be read by usemay be read by use


Techniques”

Reaching DefinitionsReaching Definitions s = 0; a = 4; i = 0;

k == 0

b = 1; b = 2;

i < n

s = s + a*b;i = i + 1; return s


Techniques”

Reaching Definitions and Reaching Definitions and Constant PropagationConstant Propagation

Is a use of a variable a constant?Is a use of a variable a constant? Check all reaching definitionsCheck all reaching definitions If all assign variable to same constantIf all assign variable to same constant Then use is in fact a constantThen use is in fact a constant

Can replace variable with constantCan replace variable with constant


Techniques”

Is Is aa Constant in Constant in s = s = s+a*bs+a*b??

s = 0; a = 4; i = 0;

k == 0

b = 1; b = 2;

i < n


Yes!On all reaching

definitionsa = 4


Techniques”

Constant Propagation Constant Propagation TransformTransform

s = 0; a = 4; i = 0;

k == 0

b = 1; b = 2;

i < n

s = s + 4*b;i = i + 1; return s

Yes!On all reaching

definitionsa = 4


Techniques”

Is Is bb Constant in Constant in s = s = s+a*bs+a*b??

s = 0; a = 4; i = 0;

k == 0

b = 1; b = 2;

i < n


No!One reaching definition with

b = 1 One reaching definition with

b = 2


Techniques”

SplittingSplittingPreserves Information Lost Preserves Information Lost

At MergesAt Merges

s = 0; a = 4; i = 0;

k == 0

b = 1; b = 2;

i < n


s = 0; a = 4; i = 0;

k == 0

b = 1; b = 2;

i < n


i < n



Techniques”

SplittingSplittingPreserves Information Lost Preserves Information Lost

At MergesAt Merges

s = 0; a = 4; i = 0;

k == 0

b = 1; b = 2;

i < n


s = 0; a = 4; i = 0;

k == 0

b = 1; b = 2;

i < n

s = s + a*1;i = i + 1;

return s

i < n

s = s + a*2;i = i + 1;

return s


Techniques”

Computing Reaching Computing Reaching DefinitionsDefinitions

Compute with sets of definitionsCompute with sets of definitions represent sets using bit vectorsrepresent sets using bit vectors each definition has a position in bit vectoreach definition has a position in bit vector

At each basic block, computeAt each basic block, compute definitions that reach start of blockdefinitions that reach start of block definitions that reach end of blockdefinitions that reach end of block

Do computation by simulating Do computation by simulating execution of program until reach fixed execution of program until reach fixed pointpoint


Techniques”

1: s = 0; 2: a = 4; 3: i = 0;k == 0

4: b = 1; 5: b = 2;

0000000

11100001110000

1111100

1111100 1111100

1111111

1111111 1111111

1 2 3 4 5 6 7

1 2 3 4 5 6 7 1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1 2 3 4 5 6 7

1110000

1111000 1110100

1111100

01011111111100

1111111i < n

1111111return s6: s = s + a*b;

7: i = i + 1;


Techniques”

Data-Flow Analysis Data-Flow Analysis SchemaSchema

Data-flow value: at every program point

Domain: The set of possible data-flow values for this application

IN[S] and OUT[S]: the data-flow values before and after each statement s

Data-flow problem: find a solution to a set of constraints on the IN [s] ‘s and OUT[s] ‘s, for all statements s. based on the semantics of the

statements ("transfer functions" ) based on the flow of control.


Techniques”

ConstraintsConstraints Transfer function: relationship

between the data-flow values before and after a statement. Forward: OUT[s] = fs(IN[s])

Backward: IN[s] = fs(OUT[s])

Within a basic block (sWithin a basic block (s11,s,s22,…,s,…,snn)) IN[si+1 ] = OUT[si], for all i = 1, 2, ..., n-

1


Techniques”

Data-Flow Schemas on Data-Flow Schemas on Basic BlocksBasic Blocks

Each basic block B (sEach basic block B (s11,s,s22,…,s,…,snn) has) has IN IN –– data-flow values immediately before a data-flow values immediately before a

blockblock OUT OUT –– data-flow values immediately after a data-flow values immediately after a

blockblock

IN[B] = IN[S1]

OUT[B] = OUT[Sn]

OUT[B] = fB (IN[B] ) Where fB = fsn ◦ ••• ◦ fs2 ◦ fs1


Techniques”

Between BlocksBetween Blocks Forward analysisForward analysis

(eg: Reaching definitions)(eg: Reaching definitions) IN[B] = UP a predecessor of B OUT[P]

Backward analysisBackward analysis (eg: live variables) IN[B] = fB (OUT[B])

OUT[B] = US a successor of B IN[S].


Techniques”

Formalizing Reaching Formalizing Reaching DefinitionsDefinitions

Each basic block hasEach basic block has IN - set of definitions that reach beginning of IN - set of definitions that reach beginning of

blockblock OUT - set of definitions that reach end of blockOUT - set of definitions that reach end of block GEN - set of definitions generated in blockGEN - set of definitions generated in block KILL - set of definitions killed in blockKILL - set of definitions killed in block

GEN[s = s + a*b; i = i + 1;] = 0000011GEN[s = s + a*b; i = i + 1;] = 0000011 KILL[s = s + a*b; i = i + 1;] = 1010000KILL[s = s + a*b; i = i + 1;] = 1010000 Compiler scans each basic block to derive Compiler scans each basic block to derive

GEN and KILL setsGEN and KILL sets


Techniques”

ExampleExample


Techniques”

Dataflow EquationsDataflow Equations IN[b] = OUT[b1] U ... U OUT[bn]IN[b] = OUT[b1] U ... U OUT[bn]

where b1, ..., bn are predecessors of b in CFGwhere b1, ..., bn are predecessors of b in CFG OUT[b] = (IN[b] - KILL[b]) U GEN[b]OUT[b] = (IN[b] - KILL[b]) U GEN[b] IN[entry] = 0000000IN[entry] = 0000000 Result: system of equationsResult: system of equations


Techniques”

Solving EquationsSolving Equations Use fixed point algorithmUse fixed point algorithm Initialize with solution of OUT[b] = 0000000Initialize with solution of OUT[b] = 0000000 Repeatedly apply equationsRepeatedly apply equations

IN[b] = OUT[b1] U ... U OUT[bn]IN[b] = OUT[b1] U ... U OUT[bn] OUT[b] = (IN[b] - KILL[b]) U GEN[b]OUT[b] = (IN[b] - KILL[b]) U GEN[b]

Until reach fixed point Until reach fixed point Until equation application has no further Until equation application has no further

effecteffect Use a worklist to track which equation Use a worklist to track which equation

applications may have a further effectapplications may have a further effect


Techniques”

Reaching Definitions Reaching Definitions AlgorithmAlgorithm

for all nodes n in N for all nodes n in N OUT[n] = emptyset; OUT[n] = emptyset; // OUT[n] = GEN[n];// OUT[n] = GEN[n];

IN[Entry] = emptyset; IN[Entry] = emptyset; OUT[Entry] = GEN[Entry]; OUT[Entry] = GEN[Entry]; Changed = N - { Entry }; Changed = N - { Entry }; // N = all nodes in graph// N = all nodes in graph

while (Changed != emptyset)while (Changed != emptyset) choose a node n in Changed;choose a node n in Changed; Changed = Changed - { n };Changed = Changed - { n };

IN[n] = emptyset;IN[n] = emptyset; for all nodes p in predecessors(n) for all nodes p in predecessors(n)

IN[n] = IN[n] U OUT[p];IN[n] = IN[n] U OUT[p];

OUT[n] = GEN[n] U (IN[n] - KILL[n]);OUT[n] = GEN[n] U (IN[n] - KILL[n]);

if (OUT[n] changed)if (OUT[n] changed) for all nodes s in successors(n) for all nodes s in successors(n)

Changed = Changed U { s };Changed = Changed U { s };


Techniques”

QuestionsQuestions Does the algorithm halt?Does the algorithm halt?

yes, because transfer function is monotonicyes, because transfer function is monotonic if increase IN, increase OUTif increase IN, increase OUT in limit, all bits are 1in limit, all bits are 1

If bit is 0, does the corresponding If bit is 0, does the corresponding definition ever reach basic block?definition ever reach basic block?

If bit is 1, does the corresponding If bit is 1, does the corresponding definition always reach the basic block?definition always reach the basic block?


Techniques”



Techniques”

Available ExpressionsAvailable Expressions An expression x+y is available at a point p An expression x+y is available at a point p

if if every path from the initial node to p must every path from the initial node to p must

evaluate x+y before reaching p, evaluate x+y before reaching p, and there are no assignments to x or y after and there are no assignments to x or y after

the evaluation but before p.the evaluation but before p. Available Expression information can be Available Expression information can be

used to do global (across basic blocks) CSEused to do global (across basic blocks) CSE If expression is available at use, no need If expression is available at use, no need

to reevaluate itto reevaluate it


Techniques”

Example: Available Example: Available ExpressionExpression

a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f


Techniques”

Is the Expression Is the Expression Available?Available?

a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f

YES!


Techniques”


a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f

YES!


Techniques”


a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f

NO!


Techniques”


a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f

NO!


Techniques”


a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f

NO!


Techniques”


a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f

YES!


Techniques”


a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f

YES!


Techniques”

Use of Available Use of Available ExpressionsExpressions

a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f


Techniques”


a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f


Techniques”


a = b + cd = e + ff = a + c

g = a + c

j = a + b + c + d

b = a + dh = c + f


Techniques”


a = b + cd = e + ff = a + c

g = f

j = a + b + c + d

b = a + dh = c + f


Techniques”


a = b + cd = e + ff = a + c

g = f

j = a + b + c + d

b = a + dh = c + f


Techniques”


a = b + cd = e + ff = a + c

g = f

j = a + c + b + d

b = a + dh = c + f


Techniques”


a = b + cd = e + ff = a + c

g = f

j = f + b + d

b = a + dh = c + f


Techniques”


a = b + cd = e + ff = a + c

g = f

j = f + b + d

b = a + dh = c + f


Techniques”

Computing Available Computing Available ExpressionsExpressions

Represent sets of expressions using bit Represent sets of expressions using bit vectorsvectors

Each expression corresponds to a bitEach expression corresponds to a bit Run dataflow algorithm similar to reaching Run dataflow algorithm similar to reaching

definitionsdefinitions Big differenceBig difference

definition reaches a basic block if it comes definition reaches a basic block if it comes from ANY predecessor in CFGfrom ANY predecessor in CFG

expression is available at a basic block only if it expression is available at a basic block only if it is available from ALL predecessors in CFG is available from ALL predecessors in CFG


Techniques”

a = x+y;x == 0

x = z;b = x+y;

i < n

c = x+y;i = i+c;

d = x+y

i = x+y;

Expressions1: x+y2: i<n3: i+c4: x==0

0000

1001

1000

1000

1100 1100


Techniques”

a = x+y;t = a

x == 0

x = z;b = x+y;

t = b

i < n

c = x+y;i = i+c;

d = x+y

i = x+y;


0000

1001

1000

1000

1100 1100

Global CSE Transform

must use same tempfor CSE in all blocks


Techniques”

a = x+y;t = a

x == 0

x = z;b = x+y;

t = b

i < n

c = t;i = i+c;

d = t

i = t;


0000

1001

1000

1000

1100 1100

Global CSE Transform

must use same tempfor CSE in all blocks


Techniques”

Formalizing AnalysisFormalizing Analysis Each basic block hasEach basic block has

IN - set of expressions available at start of blockIN - set of expressions available at start of block OUT - set of expressions available at end of OUT - set of expressions available at end of

blockblock GEN - set of expressions computed in block (and GEN - set of expressions computed in block (and

not killed later)not killed later) KILL - set of expressions killed in in block (and KILL - set of expressions killed in in block (and

not re-computed later)not re-computed later) GEN[x = z; b = x+y] = 1000GEN[x = z; b = x+y] = 1000 KILL[x = z; b = x+y] = 0001KILL[x = z; b = x+y] = 0001 Compiler scans each basic block to derive Compiler scans each basic block to derive

GEN and KILL setsGEN and KILL sets


Techniques”

Dataflow EquationsDataflow Equations

IN[b] = OUT[b1] IN[b] = OUT[b1] ... ... OUT[bn] OUT[bn] where b1, ..., bn are predecessors of b in CFGwhere b1, ..., bn are predecessors of b in CFG

OUT[b] = (IN[b] - KILL[b]) U GEN[b]OUT[b] = (IN[b] - KILL[b]) U GEN[b] IN[entry] = 0000IN[entry] = 0000 Result: system of equationsResult: system of equations


Techniques”

Solving EquationsSolving Equations Use fixed point algorithmUse fixed point algorithm IN[entry] = 0000IN[entry] = 0000 Initialize OUT[b] = 1111Initialize OUT[b] = 1111 Repeatedly apply equationsRepeatedly apply equations

IN[b] = OUT[b1] IN[b] = OUT[b1] ... ... OUT[bn] OUT[bn] OUT[b] = (IN[b] - KILL[b]) U GEN[b]OUT[b] = (IN[b] - KILL[b]) U GEN[b]

Use a worklist algorithm to reach fixed Use a worklist algorithm to reach fixed pointpoint


Techniques”

Available Expressions Available Expressions AlgorithmAlgorithm

for all nodes n in Nfor all nodes n in NOUT[n] = E; OUT[n] = E;

IN[Entry] = emptyset; IN[Entry] = emptyset; OUT[Entry] = GEN[Entry]; OUT[Entry] = GEN[Entry]; Changed = N - { Entry }; Changed = N - { Entry }; // N = all nodes in graph// N = all nodes in graph


IN[n] = E; IN[n] = E; // E is set of all expressions// E is set of all expressions for all nodes p in predecessors(n) for all nodes p in predecessors(n)

IN[n] = IN[n] IN[n] = IN[n] OUT[p]; OUT[p];

OUT[n] = GEN[n] U (IN[n] - KILL[n]);OUT[n] = GEN[n] U (IN[n] - KILL[n]);

if (OUT[n] changed)if (OUT[n] changed) for all nodes s in successors(n) for all nodes s in successors(n)

Changed = Changed U { s };Changed = Changed U { s };


Techniques”

QuestionsQuestions Does algorithm always halt?Does algorithm always halt?

If expression is available in some If expression is available in some execution, is it always marked as available execution, is it always marked as available in analysis?in analysis?

If expression is not available in some If expression is not available in some execution, can it be marked as available in execution, can it be marked as available in analysis?analysis?


Techniques”

Duality In Two Duality In Two AlgorithmsAlgorithms

Reaching definitionsReaching definitions Confluence operation is Confluence operation is set unionset union OUT[b] initialized to empty setOUT[b] initialized to empty set

Available expressionsAvailable expressions Confluence operation is Confluence operation is set intersectionset intersection OUT[b] initialized to set of available expressionsOUT[b] initialized to set of available expressions

General framework for dataflow algorithms.General framework for dataflow algorithms. Build parameterized dataflow analyzer Build parameterized dataflow analyzer

once, use for all dataflow problemsonce, use for all dataflow problems


Techniques”



Techniques”

Live Variable AnalysisLive Variable Analysis A variable v is live at point p if A variable v is live at point p if

v is used along some path starting at p, and v is used along some path starting at p, and no definition of v along the path before the no definition of v along the path before the

use.use.

When is a variable v dead at point p?When is a variable v dead at point p? No use of v on any path from p to exit node, orNo use of v on any path from p to exit node, or If all paths from p redefine v before using v.If all paths from p redefine v before using v.


Techniques”

What Use is Liveness What Use is Liveness Information?Information?

Register allocation.Register allocation. If a variable is dead, can reassign its registerIf a variable is dead, can reassign its register

Dead code elimination.Dead code elimination. Eliminate assignments to variables not read Eliminate assignments to variables not read

later.later. But must not eliminate last assignment to But must not eliminate last assignment to

variable (such as instance variable) visible variable (such as instance variable) visible outside CFG.outside CFG.

Can eliminate other dead assignments.Can eliminate other dead assignments. Handle by making all externally visible variables Handle by making all externally visible variables

live on exit from CFGlive on exit from CFG


Techniques”

Conceptual Idea of Conceptual Idea of AnalysisAnalysis

Simulate executionSimulate execution But start from exit and go backwards in But start from exit and go backwards in

CFGCFG Compute liveness information from end to Compute liveness information from end to

beginning of basic blocksbeginning of basic blocks


Techniques”

Liveness ExampleLiveness Example a = x+y;

t = a;c = a+x;x == 0

b = t+z;

c = y+1;

1100100

1110000

Assume a,b,c Assume a,b,c visible outside visible outside methodmethod

So are live on exitSo are live on exit Assume x,y,z,t not Assume x,y,z,t not

visiblevisible Represent Liveness Represent Liveness

Using Bit VectorUsing Bit Vector order is abcxyztorder is abcxyzt

1100111

1000111

1100100

0101110

a b c x y z t

a b c x y z t

a b c x y z t


Techniques”

Dead Code EliminationDead Code Elimination a = x+y;

t = a;c = a+x;x == 0

b = t+z;

c = y+1;

1100100

1110000

Assume a,b,c Assume a,b,c visible outside visible outside methodmethod

So are live on exitSo are live on exit Assume x,y,z,t not Assume x,y,z,t not

visiblevisible Represent Liveness Represent Liveness

Using Bit VectorUsing Bit Vector order is abcxyztorder is abcxyzt

1100111

1000111

1100100

0101110

a b c x y z t

a b c x y z t

a b c x y z t


Techniques”

Formalizing AnalysisFormalizing Analysis Each basic block hasEach basic block has

IN - set of variables live at start of blockIN - set of variables live at start of block OUT - set of variables live at end of blockOUT - set of variables live at end of block USE - set of variables with upwards exposed USE - set of variables with upwards exposed

uses in block (use prior to definition)uses in block (use prior to definition) DEF - set of variables defined in block prior to DEF - set of variables defined in block prior to

useuse USE[x = z; x = x+1;] = { z } USE[x = z; x = x+1;] = { z } (x not in USE)(x not in USE) DEF[x = z; x = x+1; y = 1;] = {x, y}DEF[x = z; x = x+1; y = 1;] = {x, y} Compiler scans each basic block to derive Compiler scans each basic block to derive

USE and DEF setsUSE and DEF sets


Techniques”

AlgorithmAlgorithmfor all nodes n in N - { Exit } for all nodes n in N - { Exit }

IN[n] = emptyset;IN[n] = emptyset;OUT[Exit] = emptyset; OUT[Exit] = emptyset; IN[Exit] = use[Exit];IN[Exit] = use[Exit];Changed = N - { Exit };Changed = N - { Exit };


OUT[n] = emptyset;OUT[n] = emptyset; for all nodes s in successors(n) for all nodes s in successors(n)

OUT[n] = OUT[n] U IN[p];OUT[n] = OUT[n] U IN[p];

IN[n] = use[n] U (out[n] - def[n]);IN[n] = use[n] U (out[n] - def[n]);

if (IN[n] changed)if (IN[n] changed) for all nodes p in predecessors(n)for all nodes p in predecessors(n) Changed = Changed U { p };Changed = Changed U { p };


Techniques”

Similar to Other Similar to Other Dataflow AlgorithmsDataflow Algorithms

Backward analysis, not forwardBackward analysis, not forward Still have transfer functionsStill have transfer functions Still have confluence operatorsStill have confluence operators Can generalize framework to work Can generalize framework to work

for both forwards and backwards for both forwards and backwards analysesanalyses


Techniques”

ComparisonComparison


Techniques”

ComparisonComparisonAvailable Available

ExpressionsExpressions

for all nodes n in Nfor all nodes n in N

OUT[n] = E; OUT[n] = E;

IN[Entry] = emptyset; IN[Entry] = emptyset;

OUT[Entry] = GEN[Entry]; OUT[Entry] = GEN[Entry];

Changed = N - { Entry }; Changed = N - { Entry };

while (Changed != emptyset)while (Changed != emptyset)

choose a node n in Changed;choose a node n in Changed;

Changed = Changed - { n };Changed = Changed - { n };

IN[n] = E; IN[n] = E;

for all nodes p in predecessors(n) for all nodes p in predecessors(n)

IN[n] = IN[n] IN[n] = IN[n] OUT[p];OUT[p];

OUT[n] = GEN[n] U (IN[n] - OUT[n] = GEN[n] U (IN[n] - KILL[n]);KILL[n]);

if (OUT[n] changed)if (OUT[n] changed)

for all nodes s in for all nodes s in successors(n) successors(n)

Changed = Changed U { s Changed = Changed U { s };};

Reaching Reaching DefinitionsDefinitions

for all nodes n in N for all nodes n in N

OUT[n] = emptyset; OUT[n] = emptyset;







IN[n] = emptyset;IN[n] = emptyset;






Changed = Changed U Changed = Changed U { s };{ s };

Live VariablesLive Variables

for all nodes n in N - { Exit } for all nodes n in N - { Exit }


OUT[Exit] = emptyset; OUT[Exit] = emptyset;

IN[Exit] = use[Exit];IN[Exit] = use[Exit];

Changed = N - { Exit };Changed = N - { Exit };




OUT[n] = emptyset;OUT[n] = emptyset;

for all nodes s in successors(n) for all nodes s in successors(n)



if (IN[n] changed)if (IN[n] changed)

for all nodes p in for all nodes p in predecessors(n)predecessors(n)

Changed = Changed U Changed = Changed U { p };{ p };


Techniques”

ComparisonComparisonAvailable Available

ExpressionsExpressions


OUT[n] = E; OUT[n] = E;







IN[n] = E; IN[n] = E;


IN[n] = IN[n] IN[n] = IN[n] OUT[p];OUT[p];




Changed = Changed U { s Changed = Changed U { s };};

Reaching Reaching DefinitionsDefinitions

















Techniques”

ComparisonComparisonReaching Reaching

DefinitionsDefinitions
















Live VariableLive Variable



OUT[Exit] = emptyset; OUT[Exit] = emptyset;

IN[Exit] = use[Exit];IN[Exit] = use[Exit];

Changed = N - { Exit };Changed = N - { Exit };




OUT[n] = emptyset;OUT[n] = emptyset;

for all nodes s in successors(n) for all nodes s in successors(n)



if (IN[n] changed)if (IN[n] changed)

for all nodes p in for all nodes p in predecessors(n)predecessors(n)

Changed = Changed U Changed = Changed U { p };{ p };


Techniques”

Pessimistic vs. Optimistic Pessimistic vs. Optimistic AnalysesAnalyses

Available expressions is optimistic Available expressions is optimistic (for common sub-expression (for common sub-expression elimination)elimination) Assume expressions are available at start of Assume expressions are available at start of

analysisanalysis Analysis eliminates all that are not availableAnalysis eliminates all that are not available Cannot stop analysis early and use current resultCannot stop analysis early and use current result

Live variables is pessimistic (for dead code Live variables is pessimistic (for dead code elimination)elimination) Assume all variables are live at start of analysisAssume all variables are live at start of analysis Analysis finds variables that are deadAnalysis finds variables that are dead Can stop analysis early and use current resultCan stop analysis early and use current result

Dataflow setup same for both analysesDataflow setup same for both analyses Optimism/pessimism depends on intended useOptimism/pessimism depends on intended use


Techniques”

SummarySummary Dataflow AnalysisDataflow Analysis

Control flow graphControl flow graph IN[b], OUT[b], transfer functions, join pointsIN[b], OUT[b], transfer functions, join points

Paired analyses and transformationsPaired analyses and transformations Reaching definitions/constant propagationReaching definitions/constant propagation Available expressions/common sub-expression Available expressions/common sub-expression

eliminationelimination Live-variable analysis/Dead code eliminationLive-variable analysis/Dead code elimination

Stacked analysis and transformations work Stacked analysis and transformations work togethertogether


Techniques”

Next TimeNext Time Data Flow Analysis: FoundationData Flow Analysis: Foundation

DragonBook: §9.3DragonBook: §9.3

Documents

Dataflow Analysis Introduction