Lecture Compilers SS 2009 Dr.-Ing. Ina Schaefer · Lecture Compilers SS 2009 Dr.-Ing. Ina Schaefer ... 2.3 Context-Dependent Syntax Analysis 3. Translation to Target Language 3.1

Selected Aspects of CompilersLecture Compilers SS 2009

Dr.-Ing. Ina Schaefer

Software Technology GroupTU Kaiserslautern

Ina Schaefer Selected Aspects of Compilers 1

Content of Lecture

1. Introduction: Overview and Motivation2. Syntax- and Type Analysis

2.1 Lexical Analysis2.2 Context-Free Syntax Analysis2.3 Context-Dependent Syntax Analysis

3. Translation to Target Language3.1 Translation of Imperative Language Constructs3.2 Translation of Object-Oriented Language Constructs

4. Selected Aspects of Compilers4.1 Intermediate Languages4.2 Optimization4.3 Data Flow Analysis4.4 Register Allocation4.5 Code Generation

5. Garbage Collection6. XML Processing (DOM, SAX, XSLT)


Outline1. Intermediate Languages

3-Address CodeFurther Intermediate Languages

2. OptimizationOptimization TechniquesOptimization Potential

3. Data Flow AnalysisLiveness AnalysisData Flow EquationsNon-Local Program Analysis

4. Register AllocationEvaluation Ordering with Minimal RegistersRegister Allocation by Graph ColoringFurther Aspects of Register Allocation

5. Code GenerationIna Schaefer Selected Aspects of Compilers 3

Selected Aspects of Compilers

Focus:• Techniques that go beyond the direct translation of source

languages to target languges• Concentrate on concepts instead of language-dependent details• We use program representations tailored for the considered tasks

(instead of source language syntax)! simplifies representation! but makes practical integration more difficult


Selected Aspects of Compilers (2)

Educational Objectives:• Intermediate languages for translation and optimization of

imperative languages• Different optimization techniques• Different static analysis techniques for (intermediate) programs• Register allocation• Some aspects of code generation


Intermediate Languages


• Intermediate languages are used as! appropriate program representation for certain language

implementation tasks! common representation of programs of different source languages

Source Language 1

Source Language 2

Source Language n

Intermediate Language

Target Language 1

Target Language 2

Target Language m

...

...



Intermediate Languages (2)

• Intermediate languages for translation are comparable to datastructures in algorithm design, i.e., for each task, an intermediatelanguage is more or less suitable.

• Intermediate languages can conceptually be seen as abstractmachines.


Intermediate Languages 3-Address Code

3-Address Code

3-Address Code (3AC) is a common intermediate language with manyvariants.

Properties:

• only elementary data types (but often arrays)• no nested expressions• sequential execution, jumps and procedure calls as statements• named variables as in a high level language• unbounded number of temporary variables



3-Address Code (2)

A program in 3AC consists of• a list of global variables• a list of procedures with parameters and local variables• a main procedure• each procedure has a sequence of 3AC commands as body



3AC commands

Syntax Explanation

x := y bop zx : = uop zx:= y

x: variable (global, local, parameter, temporary)y,z: variable or constantbop: binary operatoruop: unary operator

goto Lif x cop y goto L

jump or conditional jump to label Lcop: comparison operatoronly procedure-local jumps

x:= a[i]a[i]:= y a one-dimensional arrayx : = & ax:= *y*x := y

a global, local variable or parameter& a address of a* dereferencing operator



3AC commands (2)

Syntax Explanation

param xcall preturn y

call p(x1, ..., xn) is encoded as:(block is considered as one command)param x1

...

param xn

call p

return y causes jump to return addresswith (optional) result y

We assume that 3AC only contains labelsfor which jumps are used in the program.



Basic Blocks

A sequence of 3AC commands can be uniquely partitioned into basicblocks.

A basic block B is a maximal sequence of commands such that• only one jump, procedure call and return command occurs at the

end of B• labels only occur at the first command of a basic block



Basic Blocks (2)

Remarks:• The commands of a basic block are always executed sequentially,

there are no jumps to the inside• Often, a designated exit-block for a procedure containing the

return jump at its end is required. This is handled by additionaltransformations.

• The transitions between basic blocks are often denoted by flowcharts.



Example: 3 AC and Basic Blocks

Consider the following C program:Beispiel: (3AC und Basisblöcke)

Wir betrachten den 3AC für ein C-Programm:

int a[2];

int b[7];

int skprod(int i1, int i2, int lng) {... }

int main( ) {

a[0] = 1; a[1] = 2;

b[0] = 4; b[1] = 5; b[2] = 6;

skprod(0 1 2);skprod(0,1,2);

return 0;

}

3AC mit Basisblockzerlegung für die Prozedur main:

main:

a[0] := 1a[0] := 1

a[1] := 2

b[0] := 4

b[1] := 5

b[2] := 6

param 0

param 1

param 2

call skprod

28.06.2007 296© A. Poetzsch-Heffter, TU Kaiserslautern

return 0



Example: 3 AC and Basic Blocks (2)

3AC with basic block partitioning for main procedure

Beispiel: (3AC und Basisblöcke)

Wir betrachten den 3AC für ein C-Programm:

int a[2];

int b[7];

int skprod(int i1, int i2, int lng) {... }

int main( ) {

a[0] = 1; a[1] = 2;

b[0] = 4; b[1] = 5; b[2] = 6;

skprod(0 1 2);skprod(0,1,2);

return 0;

}

3AC mit Basisblockzerlegung für die Prozedur main:

main:

a[0] := 1a[0] := 1

a[1] := 2

b[0] := 4

b[1] := 5

b[2] := 6

param 0

param 1

param 2

call skprod


return 0




Procedure skprod:Prozedur skprod mit 3AC und Basisblockzerlegung:

int skprod(int i1, int i2, int lng) {

int ix, res = 0;

for( ix=0; ix <= lng-1; ix++ ){

res += a[i1+ix] * b[i2+ix];

}

skprod:

}

return res;

}

res:= 0

ix := 0

t0 := lng-1

if ix<=t0

true false

t1 := i1+ix

t2 := a[t1]

t1 := i2+ix

t3 := b[t1]

t1 := t2*t3

return res

t1 := t2*t3

res:= es+t1

ix := ix+1





Procedure skprod as 3AC with basic blocks

Prozedur skprod mit 3AC und Basisblockzerlegung:

int skprod(int i1, int i2, int lng) {

int ix, res = 0;

for( ix=0; ix <= lng-1; ix++ ){

res += a[i1+ix] * b[i2+ix];

}

skprod:

}

return res;

}

res:= 0

ix := 0

t0 := lng-1

if ix<=t0

true false

t1 := i1+ix

t2 := a[t1]

t1 := i2+ix

t3 := b[t1]

t1 := t2*t3

return res

t1 := t2*t3

res:= es+t1

ix := ix+1




Intermediate Language Variations3 AC after elimination of array operations (at above example)

Variation im Rahmen einer Zwischensprache:

3-Adress-Code nach Elimination von Feldoperationen

anhand des obigen Beispiels:

skprod:p

res:= 0

ix := 0

t0 := lng-1

if ix<=t0

t1 := i1+ix

tx := t1*4

ta := a+tx

true false

return res

t2 := *ta

t1 := i2+ix

tx := t1*4

tb := b+tx

t3 *tbt3 := *tb

t1 := t2*t3

res:= res+t1

ix := ix+1




Characteristics of 3-Address Code

• Control flow is explicit.• Only elementary operations• Rearrangement and exchange of commands can be handled

relatively easily.


Intermediate Languages Further Intermediate Languages

Further Intermediate Languages

We consider• 3AC in Static Single Assignment (SSA) representation• Stack Machine Code



Static Single Assignment Form

If a variable a is read at a program position, this is an application of a.

If a variable a is written at a program position, this is a definition of a.

For optimizations, the relationship between application and definition ofvariables is important.

In SSA representation, each variable has exactly one definition. Thus,relationship between application and definition in the intermediatelanguage is explicit.



Static Single Assignment Form (2)

SSA is essentially a refinement of 3AC.

The different definitions of one variable are represented by indexingthe variable.

For sequential command lists, this means• At each definition position, the variable gets a different index.• At the application position, the variable has the the index of its last

definition.



Example: SSA

In SSA-Repräsentation besitzt jede Variable genau

eine Definition. Dadurch wird der Zusammenhang

ischen An end ng nd Definition in derzwischen Anwendung und Definition in der

Zwischensprache explizit, d.h. eine zusätzliche

def-use-Verkettung oder use-def-Verkettung wird

unnötig.

SSA ist im Wesentlichen eine Verfeinerung von 3AC.

Die Unterscheidung zwischen den Definitionsstellen

wird häufig durch Indizierung der Variablen dargestelltwird häufig durch Indizierung der Variablen dargestellt.

Für sequentielle Befehlsfolgen bedeutet das:

• An jeder Definitionsstelle bekommt die Variable

einen anderen Indexeinen anderen Index.

• An der Anwendungsstelle wird die Variable mit

dem Index der letzten Definitionsstelle notiert.

a := x + y

Beispiel:

a := x + y 1 0 0

b := a – 1

a := y + b

b := x * 4

a := a + b

b := a - 1

a := y + b

b := x * 4

a := a + b

1 1

2

2

0

0 1


a := a + b a := a + b 3 2 2



SSA - Join Points of Control Flow

At join points of control flow, an additional mechanism is required:

An Stellen, an denen der Kontrollfluß zusammen-

führt bedarf es eines zusätzlichen Mechanismus:führt, bedarf es eines zusätzlichen Mechanismus:

3 2 2a := x + y a := a – b1 0 0

?b := a3

...

Einführung der fiktiven Orakelfunktion“ ! dieEinführung der fiktiven „Orakelfunktion !, die

quasi den Wert der Variable im zutreffenden Zweig

auswählt:

3 2 2a := x + y a := a – b1 0 0

a := !(a ,a )b := a

43

1 34


...



SSA - Join Points of Control Flow (2)Introduce an "oracle" ! that selects the value of the variable of theapplicable branch:

An Stellen, an denen der Kontrollfluß zusammen-

führt bedarf es eines zusätzlichen Mechanismus:führt, bedarf es eines zusätzlichen Mechanismus:

3 2 2a := x + y a := a – b1 0 0

?b := a3

...

Einführung der fiktiven Orakelfunktion“ ! dieEinführung der fiktiven „Orakelfunktion !, die

quasi den Wert der Variable im zutreffenden Zweig

auswählt:

3 2 2a := x + y a := a – b1 0 0

a := !(a ,a )b := a

43

1 34


...



SSA - Remarks

• The construction of an SSA representation with a minimal numberof applications of the ! oracle is a non-trivial task.(cf. Appel, Sect. 19.1. and 19.2)

• The term Static Single Assignment form reflects that for eachvariable in the program text, there is only one assignment.Dynamically, a variable in SSA representation can be assignedarbitrarily often (e.g., in loops).



Further Intermediate Languages

While 3AC and SSA representation are mostly used as intermediatelanguages in compilers, intermediate languages and abstractmachines are more and more often used as connections betweencompilers and runtime environments.

Java Byte Code and CIL (Common Intermediate Language, cf. .NET)are examples for stack machine code, i.e., intermediate results arestored on a runtime stack.

Further intermediate languages are, for instance, used foroptimizations.



Stack Machine Code as Intermediate Language

Homogeneous Scenario for Java:Sprachlich homogenes Szenario bei Java:

C1.java

C2.javajikes

C1.class

C2 class

Java ByteCode

C2.java

C3.java javac2

C2.class

C3.class

JVM

Sprachlich ggf. inhomogenes Szenario bei .NET:

ProgrammeIntermediate

C# -

C il

prog1.cs prog1.il

verschiedener

Hochsprachen

Intermediate

Language

Compilerprog2.cs prog2.il

prog3.il

CLR

Haskell -

Compilerprog3.hs

Java-ByteCode und die MS-Intermediate Language

sind Beispiele für Kellermaschinencode, d.h.

Z i h b i d f i L f itk ll


Zwischenergebnisse werden auf einem Laufzeitkeller

verwaltet.



Stack Machine Code as Intermediate Language (2)

Inhomogeneous Scenario for .NET:

Sprachlich homogenes Szenario bei Java:

C1.java

C2.javajikes

C1.class

C2 class

Java ByteCode

C2.java

C3.java javac2

C2.class

C3.class

JVM

Sprachlich ggf. inhomogenes Szenario bei .NET:

ProgrammeIntermediate

C# -

C il

prog1.cs prog1.il

verschiedener

Hochsprachen

Intermediate

Language

Compilerprog2.cs prog2.il

prog3.il

CLR

Haskell -

Compilerprog3.hs

Java-ByteCode und die MS-Intermediate Language

sind Beispiele für Kellermaschinencode, d.h.

Z i h b i d f i L f itk ll


Zwischenergebnisse werden auf einem Laufzeitkeller

verwaltet.



Example: Stack Machine Code

Beispiel: (Kellermaschinencode)

package beisp;

class Weltklasse extends Superklasse

implements BesteBohnen {

Qualifikation studieren ( Arbeit schweiss){

return new Qualifikation();

}}

}

Compiled from Weltklasse.java

class beisp Weltklasse extends beisp Superklasseclass beisp.Weltklasse extends beisp.Superklasse

implements beisp.BesteBohnen{

beisp.Weltklasse();

beisp.Qualifikation studieren( beisp.Arbeit);

}

Method beisp.Weltklasse()

0 aload_0

1 invokespecial #6 <Method beisp.Superklasse()>

4 return

Method beisp.Qualifikation studieren( beisp.Arbeit )

0 new #2 <Class beisp.Qualifikation>

3 dup

4 invokespecial #5 <Method beisp.Qualifikation()>

7 areturn7 areturn

Bemerkung:

Weitere Zwischensprachen werden insbesondere auch



im Zusammenhang mit Optimierungen eingesetzt.



Example: Stack Machine Code (2)

Beispiel: (Kellermaschinencode)

package beisp;

class Weltklasse extends Superklasse

implements BesteBohnen {

Qualifikation studieren ( Arbeit schweiss){

return new Qualifikation();

}}

}

Compiled from Weltklasse.java

class beisp Weltklasse extends beisp Superklasseclass beisp.Weltklasse extends beisp.Superklasse

implements beisp.BesteBohnen{

beisp.Weltklasse();

beisp.Qualifikation studieren( beisp.Arbeit);

}

Method beisp.Weltklasse()

0 aload_0

1 invokespecial #6 <Method beisp.Superklasse()>

4 return

Method beisp.Qualifikation studieren( beisp.Arbeit )

0 new #2 <Class beisp.Qualifikation>

3 dup

4 invokespecial #5 <Method beisp.Qualifikation()>

7 areturn7 areturn

Bemerkung:




im Zusammenhang mit Optimierungen eingesetzt.



Example: Stack Machine Code - CIL!"#$%#"&'"#(")'"#(*+,-"('."/0"(1'23('4($5)065#3("(''

7"8"9"('$"#'"#("'60)1"'$5+5#$,-"':"5-3;"'<"$5:"5-3;='

'

!"#$%&'()*)%&'+,%-'./()0/)1,-'2%3)'*4'%3)'#5'66'*78"9/3)(':'' %3)'&;'%3)'-;'%3)'/;'66'$,&*$('' &'<'*'='#;'' -'<'>?;'' /'<'&'='-;'@''

'

>#"$"$'.5?,6'@3,-$%)+,-"'A#);'23B'CDEC3B%#&")'#('C4FEC3;"'?9")$"515='

'

A9/)1,-'!"#$%&'1%-/#B(%8'()*)%&'+,%-''./()0/)1,-2%3)CD'*4%3)CD'#5'&%$'9*3*8/-':'''66'E,-/'(%F/'''''''>D'2?G&5'''A9*G()*&H''D'''A$,&*$('%3%)'2I?J'%3)CD'&4''''''''''''I>J'%3)CD'-4''''''''''''IDJ'%3)CD'/5'''KLM????N''$-*78A?'''KLM???>N''$-*78A>'''KLM???DN''*--'''KLM???CN''()$,&A?'''KLM???ON''$-&A%OA('''>?'''KLM???PN''()$,&A>'''KLM???QN''$-$,&A?'''KLM???RN''$-$,&A>'''KLM???SN''*--'''KLM???*N''()$,&AD'''KLM???#N''7/)'@'66'/3-',T'9/)1,-'E$*((>NN./()0/)1,-''

'

!"#$%'!"#' ' $,*-'*78"9/3)'3,A'!"#',3),')1/'()*&H'&'!'&(')#!*+''

'

!"!,-'$!%&' ' $,*-'$,&*$'+*7%*#$/'3,A'%3-G',3),')1/'()*&H'&'!'&(')#!*+''

'

!"-'!"#' ' $,*-'3"9/7%&'&,3()*3)'&'!'&('.*/''

'



Example: Stack Machine Code - CIL (2)

!"#$%#"&'"#(")'"#(*+,-"('."/0"(1'23('4($5)065#3("(''

7"8"9"('$"#'"#("'60)1"'$5+5#$,-"':"5-3;"'<"$5:"5-3;='

'

!"#$%&'()*)%&'+,%-'./()0/)1,-'2%3)'*4'%3)'#5'66'*78"9/3)(':'' %3)'&;'%3)'-;'%3)'/;'66'$,&*$('' &'<'*'='#;'' -'<'>?;'' /'<'&'='-;'@''

'

>#"$"$'.5?,6'@3,-$%)+,-"'A#);'23B'CDEC3B%#&")'#('C4FEC3;"'?9")$"515='

'

A9/)1,-'!"#$%&'1%-/#B(%8'()*)%&'+,%-''./()0/)1,-2%3)CD'*4%3)CD'#5'&%$'9*3*8/-':'''66'E,-/'(%F/'''''''>D'2?G&5'''A9*G()*&H''D'''A$,&*$('%3%)'2I?J'%3)CD'&4''''''''''''I>J'%3)CD'-4''''''''''''IDJ'%3)CD'/5'''KLM????N''$-*78A?'''KLM???>N''$-*78A>'''KLM???DN''*--'''KLM???CN''()$,&A?'''KLM???ON''$-&A%OA('''>?'''KLM???PN''()$,&A>'''KLM???QN''$-$,&A?'''KLM???RN''$-$,&A>'''KLM???SN''*--'''KLM???*N''()$,&AD'''KLM???#N''7/)'@'66'/3-',T'9/)1,-'E$*((>NN./()0/)1,-''

'

!"#$%'!"#' ' $,*-'*78"9/3)'3,A'!"#',3),')1/'()*&H'&'!'&(')#!*+''

'

!"!,-'$!%&' ' $,*-'$,&*$'+*7%*#$/'3,A'%3-G',3),')1/'()*&H'&'!'&(')#!*+''

'

!"-'!"#' ' $,*-'3"9/7%&'&,3()*3)'&'!'&('.*/''

'


Optimization

Optimization

Optimization refers to improving the code with the following goals:• Runtime behavior• Memory consumption• Size of code• Energy consumption


Optimization

Optimization (2)

We distinguish the following kinds of optimizations:• machine-independent optimizations• machine-dependent optimizations (exploit properties of a

particular real machine)and

• local optimizations• intra-procedural optimizations• inter-procedural/global optimizations


Optimization

Remark on Optimization

Appel (Chap. 17, p 350):

"In fact, there can never be a complete list [of optimizations]. "

"Computability theory shows that it will always be possible to inventnew optimizing transformations."


Optimization Optimization Techniques

Constant Propagation

If the value of a variable is constant, the variable can be replaced withthe constant.



Constant FoldingEvaluate all expressions with constants as operands at compile time.

Iteration of Constant Folding and Propagation:



Non-local Constant Optimization

For each program position, the possible values for each variable arerequired. If the set of possible values is infinite, it has to be abstractedappropriately.



Copy Propagation

Eliminate all copies of variables, i.e., if there exist several variablesx,y,z at a program position, that are known to have the same value, allapplications of y and z are replaced by x.



Copy Propagation (2)

This can also be done at join points of control flow or for loops:

For each program point, the information which variables have the samevalue is required.



Common Subexpression Elimination

If an expression or a statement contains the same partial expressionseveral times, the goal is to evaluate this subexpression only once.



Common Subexpression Elimination (2)

Optimization of a basic block is done after transformation to SSA andconstruction of a DAG:



Common Subexpression Elimination (3)

Remarks:• The elimination of repeated computations is often done before

transformation to 3AC, but can also be reasonable following othertransformations.

• The DAG representation of expressions is also used asintermediate language by some authors.



Algebraic Optimizations

Algebraic laws can be applied in order to be able to use otheroptimizations. For example, use associativity and commutativity ofaddition:

Caution: For finite data type, common algebraic laws are not valid ingeneral.



Strength Reduction

Replace expensive operations by more efficient operations (partiallymachine-dependent).

For example: y: = 2* x can be replaced by

y : = x + x

or by

y: = x « 1



Inline Expansion of Procedure Calls

Replace call to non-recursive procedure by its body with appropriatesubstitution of parameters.

Note: This reduces execution time, but increases code size.



Inline Expansion of Procedure Calls (2)

Remarks:• Expansion is in general more than text replacement:



Inline Expansion of Procedure Calls (3)

• In OO programs with relatively short methods, expansion is animportant optimization technique. But, precise information aboutthe target object is required.

• A refinement of inline expansion is the specialization ofprocedures/functions if some of the current parameters areknown. This technique can also be applied to recursiveprocedures/functions.



Dead Code Elimination

Remove code that is not reached during execution or that has noinfluence on execution.

In one of the above examples, constant folding and propagationproduced the following code:

Provided, t3 and t4 are no longer used after the basic block (not live).



Dead Code Elimination (2)

A typical example for non-reachable and thus, dead code that can beeliminated:



Dead Code Elimination (3)

Remarks:

• Dead code is often caused by optimizations.• Another source of dead code are program modifications.• In the first case, liveness information is the prerequiste for dead

code elimination.



Code Motion

Move commands between branches such that commands get are inbasic blocks that are less often executed.

We consider two cases:

• Move commands in succeeding or preceeding branches• Move code out of loops

Optimization of loops is very profitable, because code inside loops isexecuted more often than code not contained in a loop.



Move Code between Execution Branches

If a sequential computation branches, the branches are less oftenexecuted than the sequence.



Move Code between Execution Branches (2)

Prerequisite for this optimization is that a defined variable is only usedin one branch.

Moving the command to a preceeding branch is reasonable, if thecommand can be removed from one branch.



Partial Redundancy Elimination

Definition (Partial Redundancy)An assignment is redundant at a program position s, if it has alreadybeen executed on all paths to s.

An expression e is redundant at s, if the value of e has already beencalculated on all paths to s.

An assignment/expression is partially redundant at s, if it is redundantwith respect to some execution paths leading to s.



Partial Redundancy Elimination (2)

Example:




Elimination of partial redundancy:




Remarks:

• PRE can be seen as a combination and extension of commonsubexpression elimination and code motion.

• Extension: Elimination of partial redundancy according toestimated probability for execution of specific paths.



Code Motion from Loops

Idea: Computations in loops whose operations are not changed insidethe loop should be done outside the loop.

Provided, t1 is not live at the end of the top-most block on the left side.



Optimization of Loop Variables

Variables and expressions that are not changed during the executionof a loop are called loop invariants.

Loops often have variables that are increased/decreasedsystematically in each loop execution, e.g., for-loops.

Often, a loop variable depends on another loop variable,e.g., a relative address depends on the loop counter variable.



Optimization of Loop Variables (2)

Definition (Loop Variables)A variable i is called explicit loop variable of a loop S, if there is exactlyone definition of i in S of the form i := i + c where c is a loop invariant.

A variable k is called derived loop variable of a loop S, if there isexactly one definition of k in S of the form k := j * c or k := j + dwhere j is a loop variable and c and d are loop invariants



Induction Variable AnalysisCompute derived loop variables inductively, i.e., instead of computingthem from the value of the loop variable, compute them from thevalued of the previous loop execution.

Note: For optimization of derived loop variables, dependenciesbetween variable definitions have to be considered precisely.



Loop Unrolling

If the number of loop executions is known statically or properties about thenumber of loop executions (e.g., always an even number) can be inferred, theloop body can be copied several times to save comparisons and jumps.

Provided, ix is dead at the end of the fragment. Note ,the static computationof ix in the unrolled loop.



Loop Unrolling (2)

Remarks:

• Partial loop unrolling aims at obtaining larger basic blocks in loopsto have more optimization options.

• Loop unrolling is in particular important for parallel processorarchitectures and pipelined processing (machine-dependent).



Optimization for Other Language Classes

The discussed optimizations aim at imperative languages. Foroptimizing programs of other language classes, special techniqueshave been developed.

For example:

• Object-oriented languages: Optimization of dynamic binding(type analysis)

• Non-strict functional languages: Optimization of lazy function calls(strictness analysis)

• Logic programming languages: Optimization of unification


Optimization Optimization Potential

Optimization Potential - ExampleConsider procedure skprod for the evaluation of the optimization techniques:

Evaluation: Number of steps (lng): 2 + 2 + 13* lng +1 = 13 lng + 5Ina Schaefer Selected Aspects of Compilers 67


Optimization Potential - Example (2)Move computation of loop invariant out of loop:

Evaluation: 3+1+12*lng+1 = 12 *lng + 5Ina Schaefer Selected Aspects of Compilers 68


Optimization Potential - Example (3)Optimization of loop variables: There are no derived loop variables, becauset1 and tx have several definitions; Transformation to SSA for t1 and tx yieldsthat t11, tx1, ta, t12, tb become derived loop variables.



Optimization Potential - Example (4)Optimization of loop variables(2): Inductive definition of loop variables



Optimization Potential - Example (5)Dead Code Elimination: t11, tx1, t12, tx2 do not influence the result.

Evaluation: 9 + 1 + 8 * lng +1 = 8 * lng +11Ina Schaefer Selected Aspects of Compilers 71


Optimization Potential - Example (6)

Algebraic Optimizations: Use invariants ta = 4 ! (i1" 1 + ix) + a for thecomparison ta # 4 ! (i1" 1 + t0) + a



Optimization Potential - Example (7)Dead Code Elimination: Assignment to ix is dead code and can be eliminated.

Evaluation: 11 + 1 + 7 * Ing +1 = 7 * lng + 13Ina Schaefer Selected Aspects of Compilers 73


Optimization Potential - Example (8)

Remarks:

• Reduction of execution steps by almost half, where the mostsignificant reductions are achieved by loop optimization.

• Combination of optimization techniques is important. Determiningthe ordering of optimizations is in general difficult.

• We have only considered optimizations at examples. The difficultyis to find algorithms and heuristics for detecting optimizationpotential automatically and for executing the optimizingtransformations.


Data Flow Analysis

Data Flow Analysis

For optimizations, data flow information is required that can beobtained by data flow analysis.

Goal: Explanation of basic concepts of data flow analysis at examples

Outline:• Liveness analysis (Typical example of data flow analysis)• Data flow equations• Important Analyses Classes

Each analysis has an exact specification which information it provides.


Data Flow Analysis Liveness Analysis

Liveness Analysis

Definition (Liveness Analysis)Let P be a program. A variable v is live at a program position S, if thereis an execution path from S on which an application of v preceds adefinition of v.

The liveness analysis determines for al positions S in P whichvariables are live at S.



Liveness Analysis (2)

Remarks:• The definition of liveness of variables is static/syntactic. We have

defined dead code dynamically/semantically.• The result of the liveness analysis for a programm P can be

represented as a function live mapping positions in P to bitvectors, where a bit vector contains an entry for each variable in P.Let i be the index of a variable in P, then it holds that:

live(s)[i] = 1 iff v is live at position s




Idea:

• For a procedure-local analysis, at the end of the procedure theglobal variables are live.

• If the live variables out(b) at the end of a basic block B are known,the live variables in(B) at the beginning of B are computed by:

in(B) = gen(B) $ (out(B) \ kill(B))

where! gen(B) is the set of variables v such that v is applied in B without a

prior definition of v! kill(B) is the set of variables that are defined in B




As the set in(B) is computed from out(B), we have a backward analysis.

out(B) is obtained by

out(B) =!

in(Bi) for all successors Bi of B

For a program without loops, in and out for all basic blocks are defined.Otherwise, we obtain a recursive system of equations.



Liveness Analysis - Example

Question: How do we compute out(B2)?Ina Schaefer Selected Aspects of Compilers 80

Data Flow Analysis Data Flow Equations

Data Flow Equations

Theory:

• There is always a solution for the equations of the consideredform.

• There is always a smallest solution that is obtained by an iterationstarting from empty in and out sets.

Note: The solution is not necessarily unique.



Ambiguity of Solutions - Example

Thus, out(B0) = in(B0) and in(B0) = {a} $ in(B0).

Possible Solutions: in(B0) = {a} or in(B0) = {a, b}



Computation of Smallest Fixpoint

1. Compute gen(B), kill(B) for all B.

2. Set out(B) = % for all B except for the exit block. For the exit block,out(B) comes from the program context.

3. While out(B) or in(B) changes for any B:

Compute in(B) from current out(B) for all B.

Compute out(B) from in(B) of its successors.



Further Analyses Classes

Many data flow analyses can be described as bit vector problems:• Reaching definitions: Which definitions reach a position S?• Available expressions for elimination of repeated computations• Very busy expressions: Which expression is needed for the

subsequent computations?

The according analyses can be treated analogue to liveness analysis,but differ in

• the definition of the data flow information• the definition of gen and kill• the direction of the analysis and the equations



Further Analyses Classes (2)

For backward analyses, the data flow information at the entry of abasic block B is obtained from the information at the exit of B:

in(B) = gen(B) $ (out(B) \ kill(B))

Analyses can be distinguished if they consider the conjunction or theintersection of the successor information:

out(B) =!

Bi!succ(B)

in(Bi)

or

out(B) ="

Bi!succ(B)

in(Bi)




For forward analyses, the dependency is the other way round:

out(B) = gen(B) $ (in(B) \ kill(B))

with

in(B) =!

Bi!pred(B)

out(Bi)

or

in(B) ="

Bi!pred(B)

out(Bi)




Overview of Analysis Classes:

conjunction intersectionforward reachable definitions available expressions

backward live variables busy expressions




For bit vector problems, data flow information consists of subsets offinite sets.

For other analyses, the collected information is more complex, e.g., forconstant propagation, we consider mappings from variables to values.

For interprocedural analyses, complexity increases because the flowgraph is not static.

Formal basis for the development and correctness of optimizations isprovided by the theory of abstract interpretation.


Data Flow Analysis Non-Local Program Analysis

Non-Local Program Analysis

At the example of a points-to analysis, we consider• interprocedural aspects: The analysis crosses the borders of

single procedures.• constraints: Program analysis very often involves solving or

refining constraints.• complex analysis results: The analysis result cannot be

represented locally for a statement.• analysis as abstraction: The result of the analysis is an

abstraction of all possible program executions.



Points-to Analysis

Analysis for programs with pointers and for object-oriented programs

Goal: Compute which references to which records/objects a variablecan hold.

Applications of Analysis Results:

Basis for optimizations• Alias information (e.g., important for code motion)

! Can p.f = x cause changes to an object referenced by q?! Can z = p.f read information that is written by p.f = x?

• Call graph construction• Resolution of virtual method calls• Escape analysis



Alias InformationBeispiele: (Verwendung von Points-to-

Analyseinformation)Analyseinformation)

(1) p.f = x;

(2) f

A. Nutzen von Alias-Information:

(2) y = q.f;

(3) q.f = z;

p == q: (1)

(2) y = x;(2) y x;

(3) q.f = z;

p != q: Erste Anweisung lässt sich mit den

anderen beiden vertauschenanderen beiden vertauschen.

B. Elimination dynamischer Bindung:

class A {class A {

void m( ... ) { ... }

}

class B extends A {

void m( ) { }void m( ... ) { ... }

}

...

A p;


p = new B();

p.m(...) // Aufruf von B::m

First two statements can

be switched.



Elimination of Dynamic Binding

Beispiele: (Verwendung von Points-to-

Analyseinformation)Analyseinformation)

(1) p.f = x;

(2) f

A. Nutzen von Alias-Information:

(2) y = q.f;

(3) q.f = z;

p == q: (1)

(2) y = x;(2) y x;

(3) q.f = z;

p != q: Erste Anweisung lässt sich mit den

anderen beiden vertauschenanderen beiden vertauschen.

B. Elimination dynamischer Bindung:

class A {class A {

void m( ... ) { ... }

}

class B extends A {

void m( ) { }void m( ... ) { ... }

}

...

A p;

© A. Poetzsch-Heffter, TU Kaiserslautern

p = new B();

p.m(...) // Aufruf von B::mCall of B::m



Escape Analysis

C. Escape-Analyse:

R m( A p ) {( p ) {

B q;

q = new B(); // Kellerverwaltung möglich

q.f = p;

q.g = p.n(); q g p ();

return q.g;

}

Eine Points-to-Analyse für Java:

Vereinfachungen:

• Gesamte Programm ist bekannt.

• Nur Zuweisungen und Methodenaufrufe der

folgenden Form:

Di kt Z i- Direkte Zuweisung: l = r

- Schreiben auf Instanzvariablen: l.f = r

- Lesen von Instanzvariablen: l = r.f

Objekterzeugung: l C()- Objekterzeugung: l = new C()

- Einfacher Methodenaufruf: l = r0.m(r1,..)

• Ausdrücke ohne Seiteneffekte

• Zusammengesetzte Anweisungen

© A. Poetzsch-Heffter, TU Kaiserslautern

• Zusammengesetzte Anweisungen

Can be stored on stack



A Points-to Analysis for Java

Simplifications• Complete program is known.• Only assignments and method calls of the following form are

used:! Direct assignment: l = r! Write to instance variables: l.f = r! Read of instance variables: l = r.f! Object creation: l = new C()! Simple method call: l = r0.m(r1, ...)

• Expressions without side effects• Nested Expressions



A Points-to Analysis for Java (2)

Analysis Type• Flow-insensitive: The control flow of the program has no

influence on the analysis result. The states of the variables atdifferent program points are combined.

• Context-insensitive: Method calls at different program points arenot distinguished.



A Points-to Analysis for Java (3)

Points-to Graph as Abstraction

Result of the analysis is a points-to graph with• abstract variables and abstract objects as nodes• edges represent that an abstract variable may have a reference to

an abstract object

Abstract variables V represent sets of concrete variables at runtime.

Abstract objects O represent sets of concrete objects at runtime.

An edge between V and O means, that in a certain program state, aconcrete variable in V may reference an object in O.



Points-to Graph - ExampleBeispiel: (Points-to-Graph)

class Y { ... }

class X {

Y f;

void set( Y r ) { this.f = r; }

static void main() {

X p = new X(); // s1 „erzeugt“ o1

Y q = new Y(); // s2 „erzeugt“ o2q (); // „ g

p.set(q);

}

}

p

o1

this

o1

f

q

r

o2


r



Points-to Graph - Example (2)



Definition of the Points-to Graph

For all method implementations,• create node o for each object creation• create nodes for

! each local variable v! each formal parameter p of any method

(incl. this and results (ret))! each static variable s

(Instance variables are modeled by labeled edges.)



Definition of the Points-to Graph (2)Edges: Smallest Fixpoint of f : PtGraph & Stmt ' PtGraph with

• f (G, l = new C()) = G $ {(l , oi)}• f (G, l = r) = G $ {(l , oi) |oi ( Pt(G, r)}• f (G, l .f = r) = G $ {(< oi , f >, oj) |oi ( Pt(G, l), oj ( Pt(G, r)}• f (G, l = r .f ) = G $ {(l , oi) | )oj ( Pt(G, r).oi ( Pt(G, < oj , f >)}• f (G, l = r0.m(r1, . . . , rn)) =

G $#

oi!Pt(G,r0)solve(G, m, oi , r1, . . . , rn, l)

where Pt(G, x) is the points-to set of x in G,

solve(G, m, oi , r1, . . . , rn, l) =let mj(p0, p1, . . . , pn, retj) = dispatch(oi , m) in{(p0, oi)} $ f (G, p1 = r1) $ . . . $ f (G, l = retj) end

and dispatch(oi , m) returns the actual implementation of m for oi with formalparameters p1, . . . , pn, result variable retj , p0 refers to this.



Definition of the Points-to Graph (3)

Remark:

The main problem for practical use of the analysis is the efficientimplementation of the computation of the points-to graph.

Literature:

A. Rountev, A. Milanova, B. Ryder: Points-to Analysis for Java UsingAnnotated Constraints. OOPSLA 2001.


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Lecture Compilers SS 2009 Dr.-Ing. Ina Schaefer · Lecture Compilers SS 2009 Dr.-Ing. Ina Schaefer ... 2.3 Context-Dependent Syntax Analysis 3. Translation to Target Language 3.1