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CSE341: Programming Languages

Lecture 1 Course Mechanics

ML Variable Bindings

Dan Grossman Fall 2011





CSEP590–ProgrammingSystemsUniversityofWashington

Lecture2:OverviewPartII–BackEnd

MichaelRingenburgSpring2017









CourseNews•  SubmitpresentaPontopicproposalsbyApril14

–  Ifyouwouldliketoworkwithapartner,bothofyouwillhavetopresent,andIwillexpectamoreindepth/longerpresentaPon

–  We’reupto19students–trickytofit>18intofinal3weeks.Letmeknowifyou’dbewillingtopresentMay9.

•  Otherwisemayhavetocomeearlyorstaylateoneclass(we’llvote)•  Todayandnextweek:

–  Finishcompileroverview–  Cover1or2advancedtopicsincompilers:

•  RegisterallocaPonviagraphcoloring•  PossiblySSAform

•  A]erthat,broadenourhorizonsabitandlookatothertypesofprogrammingsystems

Spring2017 UWCSEP590(PMPProgrammingSystems):Ringenburg 1

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Reminder:CompilerStructure

Source Target

Scanner

Parser

OpPmizer

CodeGen

characters

tokens

IR

IR (often different)

Machine code

SemanPcAnalysis

IR (may be different)

“FrontEnd”

“BackEnd”


IntermediateRepresenta.ons


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IntermediateRepresentaPons

•  TheparserbuildsanintermediaterepresentaPonoftheprogram– TypicallyanAST

•  RestofthecompilerchecksandtransformstheIRtoimprove(“opPmize”)it,andeventuallytranslatesittofinalcode– TypicallywilltransforminiPalIRtooneormorelowerlevelIRsalongtheway










IRDesignTaxonomy

•  Structure– Graphical(trees,graphs,etc.)– Linear(codeforsomeabstractmachine)– Hybridsarecommon(e.g.,control-flowgraphswithlinearcodeinbasicblocks)

•  AbstracPonLevel– High-level,neartosourcelanguage– Low-level,closertomachine


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Example:ArrayReference

Source:A[i,j]AST:

High-levellinear:t1 ← A[i,j]

Low-levellinear(3address):loadI 1 => r1sub rj,r1 => r2loadI 10 => r3mult r2,r3 => r4sub ri,r1 => r5add r4,r5 => r6loadI @A => r7add r7,r6 => r8load r8 => r9

subscript

A i j










GraphicalIRs

•  IRsrepresentedasagraph(ortree)•  Nodesandedgestypicallyreflectsomestructureoftheprogram–  E.g.,source,controlflow,datadependence

•  Maybelarge(especiallysyntaxtrees)•  High-levelexamples:

–  Syntaxtrees–  Controlflowgraphs– Datadependencegraphs– O]enusedinopPmizaPonandcodegeneraPon


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GraphicalIR:ConcreteSyntaxTrees

•  Thefullgrammarisneededtoguidetheparser,butcontainsmanyextraneousdetails–  E.g.,syntacPctokens,rulesthatcontrolprecedence

•  Typicallythefullsyntaxtreedoesnotneedtobeusedexplicitly

E

T

T * F

F Id(y)

Id(x)

Subscript

A [ i ]










GraphicalIR:AbstractSyntaxTrees

•  WantonlyessenPalstructuralinformaPon•  Canberepresentedexplicitlyasatreeorinalinearform,e.g.,

intheorderofadepth-firsttraversal.Fora[i+j],thismightbe:Subscript Id(A) Plus Id(i) Id(j)

•  Commonoutputfromparser;usedforstaPcsemanPcs(typechecking,etc.)andsomePmeshigh-levelopPmizaPons

Mult

Id(x) Id(y)

Subscript

A Plus


Id(i) Id(j)

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ControlFlowGraph(CFG)•  NodesareBasicBlocks

–  Codethatalwaysexecutestogether(i.e.,nobranchesintooroutofthemiddleoftheblock).

–  I.e.,“straightlinecode”•  Edgesrepresentpathsthatcontrolflowcouldtake.–  I.e.,possibleexecuPonorderings.–  EdgefromBasicBlockAtoBasicBlockBmeansBlockBcouldexecuteimmediatelya]erBlockAcompletes.

•  RequiredformuchoftheanalysisdoneintheopPmizer.










CFGExampleprint(“hello”);a = 7;if (x == y) { print(“equal”); b = 9;} else { b = 10;}while (a < b) { a++; print(“increase”);}print(“done”);Spring2017 UWCSEP590(PMPProgrammingSystems):

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CFGExampleprint(“hello”);a = 7;if (x == y)

print(“hello”);a = 7;if (x == y) { print(“equal”); b = 9;} else { b = 10;}while (a < b) { a++; print(“increase”);}print(“done”);Spring2017 UWCSEP590(PMPProgrammingSystems):

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CFGExampleprint(“hello”);a = 7;if (x == y)

print(“equal”);b = 9;

print(“hello”);a = 7;if (x == y) { print(“equal”); b = 9;} else { b = 10;}while (a < b) { a++; print(“increase”);}print(“done”);Spring2017 UWCSEP590(PMPProgrammingSystems):

Ringenburg 13

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CFGExampleprint(“hello”);a = 7;if (x == y) { print(“equal”); b = 9;} else { b = 10;}while (a < b) { a++; print(“increase”);}print(“done”);

print(“hello”);a = 7;if (x == y)

b = 10;print(“equal”);b = 9;













while (a < b)


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while (a < b)

a++;print(“increase”);













while (a < b)

a++;print(“increase”);

print(“done”);Spring2017 UWCSEP590(PMPProgrammingSystems):

Ringenburg 17

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(Program/Data)DependenceGraph

•  O]enusedinconjuncPonwithanotherIR.•  Inadatadependencegraph,edgesbetweennodesrepresent“dependencies”betweenthecoderepresentedbythosenodes.–  IfAandBaccessthesamedata,andAmustoccurbeforeBtoachievecorrectbehavior,thenthereisadependenceedgefromAtoB.

–  AàBmeanscompilercan’tmoveBbeforeA.–  Granularityofnodesvaries.DependsonabstracPonlevelofrestofIR.E.g.,nodescouldbeloads/stores,orwholestatements.

–  E.g.,a=2;b=2;c=a+7;• Where’sthedependence?










Typesofdependencies•  Read-a]er-write(RAW)/“flowdependence”

–  E.g.,a=7;b=a+1;–  Thereadof‘a’mustfollowthewriteto‘a’,otherwiseitwon’tseethecorrectvalue.

•  Write-a]er-read(WAR)/“anPdependence”–  E.g.,b=a*2;a=5;–  Thewriteto‘a’mustfollowthereadof‘a’,otherwisethereadwon’tseethecorrectvalue.

•  Write-a]er-write(WAW)/“outputdependence”–  E.g.,a=1;…a=2;…–  Thewritesto‘a’musthappeninthecorrectorder,otherwise‘a’willhavethewrongfinalvalue.

•  WhataboutRAR/”inputdependence”??


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Loop-CarriedDependence

•  Loopcarrieddependence:AdependenceacrossiteraPonsofaloop

for(i=0;i<size;i++) x=foo(x);

•  RAWloopcarrieddependence:thereadof‘x’dependsonthewriteof‘x’inthepreviousiteraPon

•  IdenPfyingandunderstandingtheseiscriPcalforloopparallelizaPon/vectorizaPon–  Ifthecompiler“understands”thenatureofthedependence,itcansomePmesberemovedordealtwith

–  O]enusesophisPcatedarraysubscriptanalysisforthis










DependenceGraphExample

a = 7;print(“hello”);while (a < b) { print(“increase”); a++;}print(“done”);


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LCD

LCD:Loop-CarriedDependence


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LCD

LCD

LCD:Loop-CarriedDependence










LinearIRs

•  Pseudo-codeforsomeabstractmachine•  LevelofabstracPonvaries•  Simple,compactdatastructures

– Commonlyused:arrays,linkedstructures

•  Examples:3-addresscode,stackmachinecode T1ß2

T2ßbT3ßT1*T2T4ßaT5ßT4–T3

push2pushbmulPplypushasubtract


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WhatIRtoUse?

•  Commonchoice:all(!)–  ASTorotherstructuralrepresentaPonbuiltbyparserandusedinearlystagesofthecompiler

•  Closertosourcecode•  GoodforsemanPcanalysis•  Facilitatessomehigher-levelopPmizaPons

–  Lowertolow-levellinearIRforlaterstagesofcompiler•  Closertomachinecode•  Exposesmachine-relatedopPmizaPons•  GoodforresourceallocaPonandscheduling


Seman.cAnalysis


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Whatdoweneedtochecktocompilethis?

classC{inta;C(intiniPal){ a=iniPal;}voidsetA(intval){ a=val;}

}

classMain{publicstaPcvoid

main(String[]args){ Cc=newC(17); c.setA(42);

}}










BeyondSyntax

•  Thereisalevelofcorrectnessthatisnotcapturedbyacontext-freegrammar–  Hasavariablebeendeclared?–  Aretypesconsistentinanexpression?–  Intheassignmentx=y,isyassignabletox?–  Doesamethodcallhavetherightnumberandtypesofparameters?

–  Inaselectorp.q,isqamethodorfieldofclassinstancep?–  IsvariablexguaranteedtobeiniPalizedbeforeitisused?–  Inp.q,couldpbenull?–  Etc.


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CheckedProperPes

•  SomeenforcedatcompilePme,othersatrunPme(typicallydependsonlanguagespec).

•  Differentlanguageshavedifferentrequirements–  E.g.,Cvs.Javatypingrules,iniPalizaPonrequirements–  SomeoftheseproperPesareo]endesirableinprograms,evenifthelanguagedoesn’trequirethem.

–  Compilersshouldn’tenforceapropertythatisnotrequiredbythelanguage(butcanwarn).

– However,therearestaPccheckersforsomeoftheseproperPesthatusecompiler-stylealgorithms.










Whatelsedoweneedtoknowtogeneratecode?

•  Wherearefieldsallocatedinanobject?•  Howbigareobjects?(i.e.,howmuchstorageneedstobeallocated)

•  Wherearelocalvariablesstoredwhenamethodiscalled?–  Stack?Whatoffset?Orexclusivelyinregister?Whichregister?

•  Whichmethodsareassociatedwithanobject/class?–  InparPcular,howdowefigureoutwhichmethodtocallbasedontherun-Pmetypeofanobject?


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SemanPcAnalysis•  Maintasks:

–  ExtracttypesandotherinformaPonfromtheprogram–  Checklanguagerulesthatgobeyondthecontext-freegrammar–  Resolvenames

•  RelatedeclaraPonsandusesofeachvariable–  “Understand”theprogramwellenoughforsynthesis

•  E.g.,sizes,layoutsofclasses/structs•  Keydatastructure:Symboltables

–  MapeachidenPfierintheprogramtoinformaPonaboutit(kind,type,etc.)

•  Thisistypicallyconsideredthefinalpartofthe“frontend”ofthecompiler(oncecomplete,knowwhetherornotprogramislegal).










SomeKindsofSemanPcInformaPon

Information Generated From Used to process

Symbol names (variables, methods)

Declarations Expressions, statements

Type information Declarations, expressions

Operations

Memory layout information

Assigned by compiler Target code generation

Values Constants Expressions (constant folding)


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ASamplingofSemanPcChecksandComputaPons

•  Appearanceofanameinanexpression:id– Check:Symbolhasbeendeclaredandisinscope– Compute:Inferredtypeisthedeclaredtypeofsymbol

•  Constant:v– Compute:Inferredtypeandvalueareexplicit– Example:42.0hastypedoubleandvalue42.0










ASamplingofSemanPcChecksandComputaPons

•  Binaryoperator:exp1opexp2– Check:exp1andexp2havecompaPbletypes

•  EitheridenPcal,orwell-definedconversiontoappropriatetypes

•  TypesarecompaPblewithop•  Example:42 + truefails,20 + 21.9999passes

– Compute:InferredtypeofexpressionisafuncPonoftheoperatorandoperandtypes

•  Example:20 + 21.999hastypedouble,42 + “, the answer”hastypeString(inJava).


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AyributeGrammars

•  AsystemaPcwaytothinkaboutsemanPcanalysis

•  FormalizeproperPeschecked/computedduringsemanPcanalysisandrelatethemtogrammarproducPonsintheCFG.

•  SomePmesuseddirectly,butevenwhennot,AGsareausefulwaytoorganizetheanalysisandthinkaboutit










AyributeGrammars

•  Idea:associateayributeswitheachnodeinthesyntaxtree

•  Examplesofayributes–  TypeinformaPon–  StorageinformaPon– Assignable(e.g.,expressionvsvariable–lvaluevsrvalueforC/C++programmers)

–  Value(forconstantexpressions)–  etc.…

•  NotaPon:X.aifaisanayributeofnodeXSpring2017 UWCSEP590(PMPProgrammingSystems):

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InheritedandSynthesizedAyributes

•  GivenaproducPonX::=Y1Y2…Yn•  AsynthesizedayributeX.aisafuncPonofsomecombinaPonofayributesofYi’s(boyomup)–  E.g.,avalueayribute

•  AninheritedayributeYi.bisafuncPonofsomecombinaPonofayributesX.aandotherYj.c(topdown)– O]enrestrictedabit:onlyY’stothele]canbeused.–  E.g.,a“typeenvironment”ora“valueenvironment”–mappingsofsymbolstotypesorvalues(iftheyareknownconstants).










AyributeEquaPons

•  ForeachkindofnodewegiveasetofequaPonsrelaPngayributevaluesofthenodeanditschildren–  Example:

plus.val=exp1.val+exp2.val

•  AyribuPon(aka,evaluaPon)meansimplicitlyfindingasoluPonthatsaPsfiesalloftheequaPonsinthetree

Plus

exp1 exp2


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InformalExampleofAyributeRules

•  Supposewehavethefollowinggrammarforatriviallanguageprogram::=declListstmtdeclList::=declListdecl|decltwostmts::=stmtstmtdecl::=intid;stmt::=exp=exp;exp::=id|exp+exp|INTEGER_LITERAL

•  Wewanttogivesuitableayributesforbasictypeandlvalue/rvaluechecking,andconstantfolding










InformalExampleofAyributeRules

•  Ayributesofnodes–  env(typeenvironment)storesthetypesofalldeclaredvariables;synthesizedbydeclaraPons,inheritedbythestatement

•  Eachentrymapsanametoitstype–  envPre(fordeclaraPons)–Usedtobuilduptheenvironment

•  RepresentstheenvironmentpriortothedeclaraPon.•  E.g.,“intx;inty;”.TheenvPreof“inty”willmapxtoanint.Theenvof“inty”willmapxtointandytoint.

–  type(forexpressions);synthesizedfromchildren(andpossibleenvlookup)

–  kind:var(assignable)orval(notassignable);synthesized–  value(forexpressions):UNK(unknown)oranInteger,representscomputedconstantvalue;synthesized


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AyributesforDeclaraPons

•  decl::=intid;–  decl.env=decl.preEnvU{(id,int)}–  IntuiPon:add(id,int)mappingtoanenvironmentcontainingmappingsforpreviousdeclaraPons

•  Example:AyribuPonforint y,giventhatwepreviouslysawint x–  Sawint xearlier,soassumedecl.preEnv={(x,int)}–  decl::=int y;–  decl.env=decl.preEnvU{(y,int)}=

{(x,int)}U{(y,int)}= {(x,int),(y,int)}











•  declList1::=declList2decl– decl.preEnv=declList2.env– declList1.env=decl.env–  IntuiPon:declList2.envcontainsallofthepreviouslyseenmappings,souseitasthepre-environmentforournewdeclaraPon.Theenvironmentforthecombinedlist(list1)willbetheresultofaddingthemappingfordecltothemappingsofthesublist(list2).


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•  declList::=decl– decl.preEnv={}– declList.env=decl.env–  IntuiPon:ForthefirstelementinourdeclaraPonlist,wecanstartwithanemptyenvironment,becausewewon’thaveseenanydeclaraPonsyet.(Truehere,butprobablynotinareallanguage.)










ExampleDeclaraPonList

int a; int b; int c;

•  declList::=decl•  decl.preEnv={}•  declList.env=decl.env

•  declList1::=declList2decl•  decl.preEnv=declList2.env•  declList1.env=decl.env

•  decl::=intid;•  decl.env=decl.preEnvU{(id,int)}Spring2017

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•  decl::=intid;•  decl.env=decl.preEnvU{(id,int)}


declList

declList

declList

decl

decl

decl

inta

intb

intc

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declList

declList

declList

decl

decl

decl

inta

intb

intc

pre:{}

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declList

declList

declList

decl

decl

decl

inta

intb

intc

pre:{},env:{a,int}

env:{a,int}

Spring2017














declList

declList

declList

decl

decl

decl

inta

intb

intc

pre:{},env:{a,int}

env:{a,int} pre:{a,int}

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declList

declList

declList

decl

decl

decl

inta

intb

intc

pre:{},env:{a,int}

env:{a,int} pre:{a,int},env:{(a,int)(b,int)}

Spring2017














declList

declList

declList

decl

decl

decl

inta

intb

intc

pre:{},env:{a,int}

env:{a,int} pre:{a,int},env:{(a,int)(b,int)}

env:{(a,int)(b,int)} pre:{(a,int)(b,int)},env:{(a,int)(b,int)(c,int)}

env:{(a,int)(b,int)(c,int)}

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AyributesforProgram

•  program::=declListstmt–  stmt.env=declList.env–  IntuiPon:WewanttotypecheckourstatementgiventhetypeenvironmentsynthesizedbyourdeclaraPonlist.

•  Example:Ifprogramwas

int a; int b; b = a + 1;

Wewouldtypechecktheassignmentstatementwiththeenvironment{(a,int),(b,int)}










AyributesforConstants

•  exp::=INTEGER_LITERAL– exp.kind=val– exp.type=int– exp.value=INTEGER_LITERAL–  IntuiPon:Anintegerconstant(literal)clearlyhastypeint,andexplicitvalue.Youcan’tassigntoit(5=xisnotlegal),soitisavalue(val)notavariable(var).


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AyributesforIdenPfierExpressions

•  exp::=id–  id.type=exp.env.lookup(id)

•  Ifthislookupfails,issueanundeclaredvariableerror.–  exp.type=id.type–  exp.kind=var–  exp.value=UNK–  IntuiPon:WelookuptheidenPfier’stypeintheenvironment,andusethatastheexpression’stype.Ifitdoesn’texistintheenvironment,itmustnothavebeendeclared,soit’sanerror.Sinceitisavariable,itisassignableandhasunknownvalue.

–  Example:Typecheckingawithenvironment{(a,int)}givestypeint.Typecheckingbwiththesameenvironmentgivesanerror.










AyributesforAddiPon

•  exp::=exp1+exp2–  exp1.env=exp2.env=exp.env–  errorifexp1.type!=exp2.type(orifnotcompaPbleifusingmore

complexrules)

–  exp.type=exp1.type(orconvertedtypeifmorecomplexrules)

–  exp.kind=val–  exp.value=(exp1.value==UNK||exp2.value==UNK)?

UNK:exp1.value+exp2.value–  IntuiPon:TypecheckoperandswithsameenvironmentasoperaPon.VerifythattypesarecompaPble,andsetresulttypeappropriately.Notassignable,sosetkindtoval.Computevalueifbothoperandshaveconstantvalue.

Spring2017 UWCSEP590(PMPProgrammingSystems):

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AyributeRulesforAssignment

•  stmt::=exp1=exp2;– exp1.env=stmt.env– exp2.env=stmt.env– Errorifexp2.typeisnotassignmentcompaPblewithexp1.type

– Errorifexp1.kindisnotvar(can’tbeval)–  IntuiPon:Verifythatle]handsideisassignable,andthattypesofle]andrighthandsidesarecompaPble.










Exampleintx;inty;intz;x=y+(1+2);

program

declList stmt(=)

exp

id(x)

exp

+

exp exp

id(y)+

…

INT(1) INT(2)

•  program::=declListstmt•  stmt.env=declList.env

•  exp::=INTEGER_LITERAL•  exp.kind=val•  exp.type=int•  exp.value=INTEGER_LITERAL

•  exp::=id•  type=exp.env.lookup(id)

•  (erroriffails)•  exp.type=id.type•  exp.kind=var•  exp.value=UNKSpring2017

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program

declList stmt(=)

exp

id(x)

exp

+

exp exp

id(y)+

…

INT(1) INT(2)




•  (erroriffails)•  exp.type=id.type•  exp.kind=var•  exp.value=UNK

TypecheckywithdeclListenvKind:var,Value:UNK

Spring2017










program

declList stmt(=)

exp

id(x)

exp

+

exp exp

id(y)+

…

INT(1) INT(2)




•  (erroriffails)•  exp.type=id.type•  exp.kind=var•  exp.value=UNK

Type:int,Value:1,Kind:val


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program

declList stmt(=)

exp

id(x)

exp

+

exp exp

id(y)+

…

INT(1) INT(2)

•  exp::=exp1+exp2•  exp1.env=exp2.env=exp.env

•  errorifexp1.type!=exp2.type(orifnotcompaPble)

•  exp.type=exp1.type(orconvertedtype)

•  exp.kind=val•  exp.value=(exp1.value==

UNK||exp2.value==UNK)?UNK:exp1.value+exp2.value


Spring2017










program

declList stmt(=)

exp

id(x)

exp

+

exp exp

id(y)+

…

INT(1) INT(2)

•  exp::=exp1+exp2•  exp1.env=exp2.env=exp.env

•  errorifexp1.type!=exp2.type(orifnotcompaPble)

•  exp.type=exp1.type(orconvertedtype)

•  exp.kind=val•  exp.value=(exp1.value==

UNK||exp2.value==UNK)?UNK:exp1.value+exp2.value

Type:int,Value:UNK,Kind:val

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program

declList stmt(=)

exp

id(x)

exp

+

exp exp

id(y)+

…

INT(1) INT(2)

•  stmt::=exp1=exp2;•  exp1.env=stmt.env•  exp2.env=stmt.env•  Errorifexp2.typeisnot

assignmentcompaPblewithexp1.type

•  Errorifexp1.kindisnotvar(can’tbeval)


TypecheckxwithdeclListenvType:int,Kind:var

Spring2017










program

declList stmt(=)

exp

id(x)

exp

+

exp exp

id(y)+

…

INT(1) INT(2)

•  stmt::=exp1=exp2;•  exp1.env=stmt.env•  exp2.env=stmt.env•  Errorifexp2.typeisnot

assignmentcompaPblewithexp1.type

•  Errorifexp1.kindisnotvar(can’tbeval)


TypecheckxwithdeclListenvType:int,Kind:var

Passesbothchecks!

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ObservaPons•  TheseareequaPonal(funcPonal)computaPons•  Thiscanbeautomated(ifequaPonsarenon-circular)•  ButimplementaPonproblems

–  Non-localcomputaPon:AyributeequaPonscanonlyrefertovaluesassociatedwithsymbolsthatappearinasingleproducPonrule.

•  Ifyouneednon-localvalues,youneedtoaddspecialrulestothegrammartocopythemaround.Canmakegrammarverylarge.

–  Can’taffordtoliterallypassaroundcopiesoflarge,aggregatestructureslikeenvironments.

–  UseofproducPonrulesbindsayributestotheparsetreeratherthanthe(typicallysmaller,andmoreuseful)AST.Canworkaroundthis(use“ASTgrammar”),butresultsinmorecomplexayributerules.










InPracPce

•  AyributegrammarsgiveusagoodwayofthinkingabouthowtostructuresemanPcchecks

•  SymboltableswillholdenvironmentinformaPon•  AddfieldstoASTnodestorefertoappropriateayributes(symboltableentriesforidenPfiers,typesforexpressions,etc.)–  PutinappropriateplacesinASTclassinheritancetree–moststatementsdon’tneedtypes,forexample


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SymbolTables•  MapidenPfiersto<type,kind,locaPon,otherproperPes>

•  OperaPons–  Lookup(id)=>informaPon–  Enter(id,informaPon)– Open/closescopes

•  Build&useduringsemanPcspass–  BuildfirstfromdeclaraPons–  ThenusetochecksemanPcrules

•  Use(andaddto)duringlaterphasesaswell


CodeGenera.on


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BasicCodeGeneraPonStrategy

•  WalktheASTorotherIR,outpu�ngcodeforeachconstructencountered

•  Handlingofnode’schildrenisdependentontypeofnode–  E.g.,forbinaryoperaPonlike+:

•  Generatecodetocomputeoperand1(andstoreresult)•  Generatecodetocomputeoperand2(andstoreresult)•  Generatecodetoloadoperandresultsandaddthemtogether

•  Todayisjustasamplingofbasicconstructs,togivebasicidea










ConvenPonsforExamples

•  Thefollowingslideswillwalkthroughhowthisisdoneformanycommonlanguageconstructs

•  ExamplesshowcodesnippetsinisolaPon•  Registereaxusedbelowasagenericexample

–  RenameasneededformorecomplexcodeusingmulPpleregisters

•  Afewpeepholeop7miza7onsincludedbelowforaflavorofwhat’spossible–  LocalizedopPmizaPonsperformedonsmallASMinstrucPonsequences.


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Variables

•  Forourpurposes,assumealldatawillbeineither:– Astackframe(methodlocalvariables)– Anobject(instancevariables)

•  Localvariablesaccessedviaebp(stackbasepointer) moveax,[ebp-12]

•  Objectinstancevariablesaccessedviaanobjectaddressinaregister










CodeGeneraPonforConstants

•  Source17

•  x86moveax,17

–  Idea:realizeconstantvalueinaregister

•  OpPmizaPon:ifconstantis0 xoreax,eax

– Maybesmallerandfaster


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AssignmentStatement

•  Sourcevar=exp;

•  x86<codetoevaluateexpinto,say,eax>mov[ebp+offsetvar],eax










UnaryMinus

•  Source-exp

•  x86<codeevaluaPngexpintoeax>negeax

•  OpPmizaPon– Collapse-(-exp)toexp

•  Unaryplusisano-op


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Binary+

•  Sourceexp1+exp2

•  x86<codeevaluaPngexp1intoeax><codeevaluaPngexp2intoedx>addeax,edx










Binary+

•  OpPmizaPons–  Ifexp2isasimplevariableorconstant,don’tneedtoloaditintoanotherregisterfirst.Instead:

addeax,immConst;immisconstantaddeax,[ebp+offsetvar];offsetisvariable’sstackoffset

–  Changeexp1+(-exp2)intoexp1-exp2–  Ifexp2is1

inceax•  Somewhatsurprising:whetherthisisbeyerthanaddeax,1dependsonprocessorimplementaPonandhaschangedoverPme

Spring2017 UWCSEP590(PMPProgrammingSystems):

Ringenburg 77

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ControlFlow

•  Basicidea:decomposehigherleveloperaPonintocondiPonalanduncondiPonalgotos

•  Inthefollowing,jfalseisusedtomeanjumpwhenacondiPonisfalse–  NosuchinstrucPononx86–  CanrealizewithappropriatesequenceofinstrucPonstosetcondiPoncodesfollowedbycondiPonaljumps

–  Normallydon’tactuallygeneratethevalue“true”or“false”inaregister










While

•  Sourcewhile(cond)stmt

•  X86test: <codeevaluaPngcond> jfalsedone <codeforstmt> jmptest

done:

– Note:Ingeneratedasmcodewe’llneedtogenerateuniquelabelsforeachloop


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If

•  Sourceif(cond)stmt

•  x86 <codeevaluaPngcond> jfalseskip <codeforstmt>

skip:










BooleanExpressions

•  Whatdowedowiththis?x>y

•  Itisanexpressionthatevaluatestotrueorfalse– Couldgeneratethevalue(0/1orwhateverthelocalconvenPonis)

– Butnormallywedon’twant/needthevalue;we’reonlytryingtodecidewhethertojump

•  OneexcepPon:assignmentexpressions,e.g.,while(my_bool=(x<y)){…}


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Codeforexp1>exp2

•  Generatedcodedependsoncontext– Whatisthejumptarget?–  JumpifthecondiPonistrueoriffalse?

•  Example:evaluateexp1>exp2,jumponfalse,targetifjumptakenisL123

<evaluateexp1toeax><evaluateexp2toedx>cmpeax,edxjngL123 ;greater-thantest,jumponfalse,sojng ;(jumpnotgreater)


Op.miza.onOverview


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OpPmizaPons•  UseaddedpassestoidenPfyinefficienciesinintermediate

ortargetcode•  Replacewithequivalent(“hasthesameexternallyvisible

behavior”)butbeyersequences–  Beyercanmeanmanythings:faster,smaller,lessmemory,moreenergy-efficient,etc.

•  Target-independentopPmizaPonsbestdoneonIRcode–  RemovingredundantcomputaPons,deadcode,etc.

•  Target-dependentopPmizaPonsbestdoneontargetcode–  GeneraPngsequencethataremoreefficientonaparPcularmachine

•  “OpPmize”overlyopPmisPc:“usuallyimprove”isgenerallymoreaccurate–  And“clever”programmerscanoutwityou!










Anexamplex = a[i] + b[2]; c[i] = x - 5;

t1 = *(fp + ioffset); // i t2 = t1 * 4; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t5 = 2; t6 = t5 * 4; t7 = fp + t6; t8 = *(t7 + boffset); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t11 = 5; t12 = t10 - t11; t13 = *(fp + ioffset); // i t14 = t13 * 4; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t5 = 2; t6 = t5 << 2; t7 = fp + t6; t8 = *(t7 + boffset); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t11 = 5; t12 = t10 - t11; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

StrengthReducPon:shi]o]encheaperthanmulPply

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t5 = 2; t6 = 2 << 2; // was t5 << 2 t7 = fp + t6; t8 = *(t7 + boffset); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t11 = 5; t12 = t10 – 5; // was t10 – t11 t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

ConstantpropagaPon:Replacevariableswithknownconstantvalue.

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t5 = 2; t6 = 2 << 2; t7 = fp + t6; t8 = *(t7 + boffset); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t11 = 5; t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

DeadStore(orDeadAssignment)EliminaPon:Removeassignementstoprovablyunusedvariables.

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t6 = 2 << 2; t7 = fp + t6; t8 = *(t7 + boffset); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

DeadStore(orDeadAssignment)EliminaPon:Removestorestoprovablyunusedvariables.

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t6 = 8; // was 2 << 2 t7 = fp + t6; t8 = *(t7 + boffset); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

ConstantFolding:StaPcallycomputeoperaPonswithonlyconstantoperands.

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t6 = 8; t7 = fp + 8; // was fp + t6 t8 = *(t7 + boffset); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

ConstantPropagaPon,thenDeadStoreEliminaPon

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t7 = fp + 8; t8 = *(t7 + boffset); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

ConstantPropagaPon,thenDeadStoreEliminaPon

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t7 = boffset + 8; t8 = *(t7 + fp); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

ApplyingarithmePcidenPPes:Weknow+iscommutaPve&associaPve.boffsetistypicallyaknowncompile-Pmeconstant(say,-30),sothisenables…

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t7 = -22; // was boffset(-30) + 8 t8 = *(t7 + fp); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

…moreconstantfolding.Whichinturnenables…

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t7 = -22; t8 = *(fp - 22); // b[2] (was t7+fp) t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

MoreconstantpropagaPonanddeadstoreeliminaPon.

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = *(fp + ioffset); // i t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

MoreconstantpropagaPonanddeadstoreeliminaPon.

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = *(fp + xoffset); // x t12 = t10 – 5; t13 = t1; // i (was *(fp+ioffset)) t14 = t13 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

CommonsubexpressioneliminaPon:Noneedtocompute*(fp+ioffset)twiceifweknowitwon’tchange.

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = t9; // x (was *(fp+xoffset)) t12 = t10 – 5; t13 = t1; // i t14 = t1 << 2; // was t13 << 2 t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

CopypropagaPon:Replaceassignmenttargetswiththeirvalues.E.g.,replacet13witht1.

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = t9; // x t12 = t9 – 5; // Was t10 - 5 t13 = t1; // i t14 = t1 << 2; t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

MorecopypropagaPon

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = t9; // x t12 = t9 – 5; t13 = t1; // i t14 = t2; // was t1 << 2 t15 = fp + t14; *(t15 + coffset) = t12; // c[i] := …

CommonsubexpressioneliminaPon.

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = t9; // x t12 = t9 – 5; t13 = t1; // i t14 = t2; t15 = fp + t2; // was fp + t14 *(t15 + coffset) = t12; // c[i] := …

CopyPropagaPon

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t10 = t9; // x t12 = t9 – 5; t13 = t1; // i t14 = t2; t15 = fp + t2; *(t15 + coffset) = t12; // c[i] := …

DeadAssignmentEliminaPon

x = a[i] + b[2]; c[i] = x - 5;










Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t12 = t9 – 5; t15 = fp + t2; *(t15 + coffset) = t12; // c[i] := …

DeadAssignmentEliminaPon

x = a[i] + b[2]; c[i] = x - 5;


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Anexamplet1 = *(fp + ioffset); // i t2 = t1 << 2; t3 = fp + t2; t4 = *(t3 + aoffset); // a[i] t8 = *(fp - 22); // b[2] t9 = t4 + t8; *(fp + xoffset) = t9; // x = … t12 = t9 – 5; t15 = fp + t2; *(t15 + coffset) = t12; // c[i] := …

•  Final:3loads(i,a[i],b[2]),2stores(x,c[i]),5register-onlymoves,9+/-,1shi]•  Original:5loads,2stores,10register-onlymoves,12+/-,3*

•  (OpPmizertypicallydealsin“pseudo-registers”–canhaveasmanyasyouwant–andletsregisterallocatorfigureoutopPmalassignmentsofpseudo-registerstorealregisters.)

x = a[i] + b[2]; c[i] = x - 5;










KindsofOpPmizaPons•  peephole:lookatadjacentinstrucPons•  local:lookatindividualbasicblocks

–  Straight-linesequenceofstatements•  intraprocedural:lookatwholeprocedure

–  Commonlycalled“global”•  interprocedural:lookacrossprocedures

–  “wholeprogram”analysis–  gcc’s“linkPmeopPmizaPon”isaversionofthis

•  Largerscope=>usuallybeyeropPmizaPonbutmorecostandcomplexity–  Analysisiso]enlessprecisebecauseofmorepossibiliPes


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PeepholeOpPmizaPon

•  A]ertargetcodegeneraPon,lookatadjacentinstrucPons(a“peephole”onthecodestream)–  trytoreplaceadjacentinstrucPonswithsomethingfaster,e.g.,storeandloadwithstoreandregistermove:

–  JumpchainingcanalsobeconsideredaformofpeepholeopPmizaPon(removingjump-to-jump)

movq %r9,12(%rsp) movq 12(%rsp),%r12

movq %r9,12(%rsp) movq %r9,%r12










AlgebraicSimplificaPon•  “constantfolding”:pre-calculateoperaPononconstant•  “strengthreducPon”:replaceoperaPonwithacheaperoperaPon•  “simplificaPon”:applyingalgebraicidenPPes

–  z = 3 + 4; à z = 7; –  z = x + 0; à z = x; –  z = x * 1; à z = x; –  z = x * 2; à z = x << 1; or z = x + x; –  z = x * 8; à z = x << 3; –  z = x / 8; à z = x >> 3; –  z = (x + y) - y; à z = x;

•  Canbedoneatmanylevels,frompeepholeonup.•  Whydotheseexampleshappen?

–  O]encreated:Conversiontolower-levelIR,OtheropPmizaPons,CodegeneraPon


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Higher-levelExample:Loop-basedStrengthReducPon

•  SomePmesmulPplicaPonbytheloopvariableinaloopcanbereplacedbyaddiPonsintoatemporaryaccumulator

•  Similarly,exponenPaPoncanbereplacedbymulPplicaPon.

for(inti=0;i<size;i++){foo[i]=i;}

for(inti=0;i<size;i++){*(foo+i*elementSize)=i;}

t1=0;for(inti=0;i<size;i++){*(foo+t1)=i;t1=t1+8;}










LocalOpPmizaPons

•  AnalysisandopPmizaPonswithinabasicblock•  Basicblock:straight-linesequenceofstatements– nocontrolflowintooroutofmiddleofsequence

•  NottoohardtoimplementwithareasonableIR


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LocalConstantPropagaPon

•  Ifvariableassignedaconstant,replacedownstreamusesofthevariablewithconstant(unPlvariableisnextassigned)

•  Canenablemoreconstantfolding–  Code;unopPmizedintermediatecode:

count = 10; ... // No count assigns x = count * 5; y = x ^ 3;

count = 10 t1 = count; t2 = 5; t3 = t1 * t2; x = t3; t4 = x; t5 = 3; t6 = exp(t4, t5); y = t6;












count = 10 t1 = 10; // CP count t2 = 5; t3 = 10 * 5; // CP t1 x = t3; t4 = x; t5 = 3; t6 = exp(t4, 3); // CP t5 y = t6;


•  Canenablemoreconstantfolding–  Code;propagatedintermediatecode:


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count = 10 t1 = 10; t2 = 5; t3 = 50; // CF 5 * 10 x = t3; t4 = x; t5 = 3; t6 = exp(t4, 3); y = t6;


•  Canenablemoreconstantfolding–  Code;foldedintermediatecode:












count = 10 t1 = 10; t2 = 5; t3 = 50; x = 50; // CP t3 t4 = 50; // CP x t5 = 3; t6 = exp(50, 3); // CP t4 y = t6;


•  Canenablemoreconstantfolding–  Code;repropagatedintermediatecode:


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count = 10 t1 = 10; t2 = 5; t3 = 50; x = 50; t4 = 50; t5 = 3; t6 = 125000; // CF 50^3 y = t6;


•  Canenablemoreconstantfolding–  Code;refoldedintermediatecode:












count = 10 t1 = 10; t2 = 5; t3 = 50; x = 50; t4 = 50; t5 = 3; t6 = 125000; y = 125000; // CP t6


•  Canenablemoreconstantfolding–  Code;repropagatedintermediatecode:


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LocalDeadAssignmentEliminaPon



•  Ifle]sideofassignmentneverreferencedagainbeforebeingoverwriyen,thencandeleteassignment–  Whywouldthishappen?–  Clean-upa]erpreviousopPmizaPons,o]en

•  Intermediatecodea]erconstantpropagaPon:










LocalDeadAssignmentEliminaPon



•  Ifle]sideofassignmentneverreferencedagainbeforebeingoverwriyen,thencandeleteassignment–  Whywouldthishappen?–  Clean-upa]erpreviousopPmizaPons,o]en

•  Intermediatecodea]erconstantpropagaPon:


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LocalCommonSubexpressionEliminaPon

•  LooksforrepePPonsofthesamecomputaPon,andeliminatethemiftheresultwon’thavechanged(andnosideeffects)–  AvoidsrepeaPngthesamecalculaPon–  Eliminatesredundantloads

•  Idea:walkbasicblock,keepingtrackofavailableexpressions ... a[i] + b[i] ...

t1 = *(fp + ioffset); t2 = t1 * 4; t3 = fp + t2; t4 = *(t3 + aoffset); t5 = *(fp + ioffset); t6 = t5 * 4; t7 = fp + t6; t8 = *(t7 + boffset); t9 = t4 + t8;











... a[i] + b[i] ...

t1 = *(fp + ioffset); t2 = t1 * 4; t3 = fp + t2; t4 = *(t3 + aoffset); t5 = t1; // CSE t6 = t5 * 4; t7 = fp + t6; t8 = *(t7 + boffset); t9 = t4 + t8;

•  LooksforrepiPPonsofthesamecomputaPon,andeliminatethemiftheresultwon’thavechanged(andnosideeffects)–  AvoidsrepeaPngthesamecalculaPon–  Eliminatesredundantloads

•  Idea:walkbasicblock,keepingtrackofavailableexpressions


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... a[i] + b[i] ...

t1 = *(fp + ioffset); t2 = t1 * 4; t3 = fp + t2; t4 = *(t3 + aoffset); t5 = t1; t6 = t1 * 4; // CP t7 = fp + t6; t8 = *(t7 + boffset); t9 = t4 + t8;













... a[i] + b[i] ...

t1 = *(fp + ioffset); t2 = t1 * 4; t3 = fp + t2; t4 = *(t3 + aoffset); t5 = t1; t6 = t2; // CSE t7 = fp + t2; // CP t8 = *(t7 + boffset); t9 = t4 + t8;




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... a[i] + b[i] ...

t1 = *(fp + ioffset); t2 = t1 * 4; t3 = fp + t2; t4 = *(t3 + aoffset); t5 = t1; t6 = t2; t7 = t3; // CSE t8 = *(t3 + boffset);//CP t9 = t4 + t8;













... a[i] + b[i] ...

t1 = *(fp + ioffset); t2 = t1 * 4; t3 = fp + t2; t4 = *(t3 + aoffset); t5 = t1; // DAE t6 = t2; // DAE t7 = t3; // DAE t8 = *(t3 + boffset); t9 = t4 + t8;




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IntraproceduralopPmizaPons

•  Enlargescopeofanalysistowholeprocedure– moreopportuniPesforopPmizaPon– havetodealwithbranches,merges,andloops

•  CandoconstantpropagaPon,commonsubexpressioneliminaPon,etc.atfuncPon-widelevel

•  Candonewthings,e.g.loopopPmizaPons•  OpPmizingcompilersusuallyworkatthislevel(-O2)










CodeMoPon•  Goal:moveloop-invariantcalculaPonsoutofloops•  Candoatsourceleveloratintermediatecodelevel

for (i = 0; i < 10; i = i+1) { a[i] = a[i] + b[j]; z = z + (foo*bar)^2; }

t1 = b[j]; t2 = (foo*bar)^2; for (i = 0; i < 10; i = i+1) { a[i] = a[i] + t1; z = z + t2; }


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InterproceduralOpPmizaPon

•  Expandscopeofanalysistoprocedurescallingeachother

•  Candolocal&intraproceduralopPmizaPonsatlargerscope

•  CandonewopPmizaPons,e.g.inlining










Inlining:replacecallwithbody

•  Replaceprocedurecallwithbodyofcalledprocedure,andsubsPtuPngactualargumentsforformalparameters

•  Source:final double pi = 3.1415927; double circle_area(double radius) { return pi * (radius * radius); } ... double r = 5.0; ... double a = circle_area(r);

•  A]erinlining: double r = 5.0; ... double a = pi * r * r;

•  (Thenwhat?ConstantpropagaPon/folding.)


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DataStructuresforOpPmizaPons

•  Needtorepresentcontrolanddataflow•  Controlflowgraph(CFG)capturesflowofcontrol

–  nodesarebasicblocks–  edgesrepresent(allpossible)controlflow–  nodewithmulPplesuccessors=branch/switch–  nodewithmulPplepredecessors=mergeorjoinpoint–  loopingraph=loop

•  Dataflowgraph(DFG)captureflowofdata,e.g.def/usechains:–  nodesaredef(iniPon)sandusesofdata/variables–  edgesfromdefstousesof(potenPally)thesamedata–  adefcanreachmulPpleuses–  ausecanhavemulPplereachingdefs(differentcontrolflow,possiblealiasing,etc.)










AnalysisandTransformaPon

•  EachopPmizaPonismadeupof–  somenumberofanalyses–  followedbyatransformaPon

•  AnalyzeCFGand/orDFGbypropagaPnginfoforwardorbackwardalongCFGand/orDFGedges–  mergesingraphrequirecombininginfo–  loopsingraphrequire(conservaPve)itera7veapproxima7on

•  Perform(improving)transformaPonsbasedoninfocomputed•  AnalysismustbeconservaPve/safe/soundsothat

transformaPonspreserveprogrambehavior


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Example:ConstantPropagaPon,Folding

•  CanuseeithertheCFGortheDFG•  CFGanalysisinfo:tablemappingeachvariableinscopetooneof:

–  aparPcularconstant–  NonConstant–  Undefined

•  TransformaPonateachinstrucPon:–  Ifencounteranassignmentofaconstanttoavariable,setvariableas

constant–  ifreferenceavariablethatthetablemapstoaconstant,thenreplace

withthatconstant(constantpropagaPon)–  ifr.h.s.expressioninvolvesonlyconstants,andhasnoside-effects,then

performoperaPonatcompile-Pmeandreplacer.h.s.withconstantresult(constantfolding)

•  Forbestanalysis,doconstantfoldingaspartofanalysis,tolearnallconstantsinonepass










Mergingdataflowanalysisinfo

•  Constraint:mergeresultsmustbesound–  ifsomethingisbelievedtruea]erthemerge,thenitmustbetruenomayerwhichpathwetookintothemerge

–  onlythingstruealongallpredecessorsaretruea]erthemerge

•  TomergetwomapsofconstantinformaPon,buildmapbymergingcorrespondingvariableinformaPon

•  TomergeinformaPonabouttwovariable–  ifoneisUndefined,keeptheother(uniniPalizedvariablesinmanylanguagesallowedtohaveanyvalue)

–  ifbotharethesameconstant,keepthatconstant–  otherwise,degeneratetoNonConstant


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ExampleMerges

A {x:5}

D {x:6}

// Block Aint x;x = 5;if (foo) { // Block B x++;} else { // Block C x=6;}// Block D…

C {x:6} B {x:6}










ExampleMerges

A {x:Undefined}

D {x:5}

// Block Aint x;if (foo) { // Block B z++; x = 5;} else { // Block C z--; x = 5;}// Block D…

C {x:5} B {x:5}


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ExampleMerges

A {x:Undefined}

D {x:NonConstant}

// Block Aint x;if (foo) { // Block B z++; x = 5;} else { // Block C z--; x = 4;}// Block D…

C {x:4} B {x:5}










ExampleMerges

A {x:Undefined}

D {x:4}

// Block Aint x;if (foo) { // Block B z++;} else { // Block C z--; x = 4;}// Block D…

C {x:4} B {x:Undefined}


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Howtoanalyzeloopsi = 0; x = 10; y = 20; while (...) { // what’s true here? ... i = i + 1; y = 30; } // what’s true here? ... x ... i ... y ...

•  Safebutimprecise:forgeteverythingwhenweenterorexitaloop

•  Precisebutunsafe:keepeverythingwhenweenterorexitaloop

•  Canwedobeyer?










LoopTerminology

preheader

entry edge

head

back edge

tail

loop

exit edge


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OpPmisPcIteraPveAnalysis

•  AssuminginformaPonatloopheadissameasinformaPonatloopentry

•  Thenanalyzeloopbody,compuPnginformaPonatbackedge

•  MergeinformaPonatloopbackedgeandloopentry•  TestifmergedinformaPonissameasoriginalassumpPon–  Ifso,thenwe’redone–  Ifnot,thenreplacepreviousassumpPonwithmergedinformaPon,

–  andgobacktoanalysisofloopbody










Examplei = 0; x = 10; y = 20; while (...) { // what’s true here? ... i = i + 1; y = 30; } // what’s true here? ... x ... i ... y ...


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i=0,x=10,y=20











i=0,x=10,y=20

i=1,x=10,y=30


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i=NC,x=10,y=NC











i=NC,x=10,y=NC

i=NC,x=10,y=NC


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i=NC,x=10,y=NC

i=NC,x=10,y=NC










Whydoesthiswork?

•  WhyaretheresultsalwaysconservaPve?•  Becauseifthealgorithmstops,then

–  theloopheadinfoisatleastasconservaPveasboththeloopentryinfoandtheloopbackedgeinfo

–  theanalysiswithintheloopbodyisconservaPve,giventheassumpPonthattheloopheadinfoisconservaPve


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OpPmizaPonSummary

•  OpPmizaPonsorganizedascollecPonsofpasses,eachrewriPngILinplaceinto(hopefully)beyerversion

•  Eachpassdoesanalysistodeterminewhatispossible,followedby(orconcurrentwith)transformaPonsthat(hopefully)improvetheprogram– SomePmeshave“analysis-only”passes–produceinfousedbylaterpasses


DataflowAnalysis(ifwehaveextra.meandenergy!)


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Nexttopic:DataflowAnalysis

•  Aframeworkandalgorithmformanycommoncompileranalyses

•  IniPalexample:dataflowanalysisforcommonsubexpressioneliminaPon

•  Otheranalysisproblemsthatworkinthesameframework

•  We’llbediscussingsomeofthesameopPmizaPonswesawintheopPmizaPonoverview,butwithmoreformalismanddetails.










MoPvaPngExample:CommonSubexpressionEliminaPon(CSE)

m = a + b n = a + b

A

p = c + d r = c + d

B q = a + b r = c + d

C

e = b + 18 s = a + b u = e + f

D e = a + 17 t = c + d u = e + f

E

v = a + b w = c + d x = e + f

F

y = a + b z = c + d

G

•  Goal:Findcommonsubexpressions,replacewithtemporaries

•  Idea:calculateavailableexpressionsatbeginningofeachbasicblock

•  Avoidre-evaluaPonofanavailableexpression–copyatempinstead–  Simpleinsideasingleblock;

morecomplexdataflowanalysisusedacrossbocks


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“Available”andOtherTerms

•  AnexpressioneisdefinedatpointpintheCFG(controlflowgraph)ifitsvalueiscomputedatp–  SomePmescalleddefini7onsite

•  Anexpressioneiskilledatpointpifoneofitsoperands(components)isredefinedatp–  SomePmescalledkillsite

•  AnexpressioneisavailableatpointpifeverypathleadingtopcontainsapriordefiniPonofeandeisnotkilledbetweenthatdefiniPonandp

t1=a+b…

t10=a+b…

b=7…

a+bdefined

a+bavailable

a+bkilled










AvailableExpressionSets

•  Tocomputeavailableexpressions,foreachblockb,define– AVAIL(b)–thesetofexpressionsavailableonentrytob

– NKILL(b)–thesetofexpressionsnotkilledinb– DEF(b)–thesetofexpressionsdefinedinbandnotsubsequentlykilledinb


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CompuPngAvailableExpressions

•  AVAIL(b)(expressionsavailableonentrytob)istheset

AVAIL(b)=∩x∈preds(b)(DEF(x)∪(AVAIL(x)∩NKILL(x)))

–  preds(b)isthesetofb’sdirectpredecessorsintheCFG–  In“english”,theexpressionsavailableonentrytobaretheexpressionsthatwereavailableattheendofeverydirectlyprecedingbasicblockx.(Thisisthe∩x∈preds(b))

–  Theexpressionsavailableattheendofblockxareexactlythosethatweredefinedinx(andnotkilled),andthosethatwereavailableatthebeginningofxandnotkilledinx.

•  ApplyingtoeveryblockgivesasystemofsimultaneousequaPons–adataflowproblem











•  BigPicture– Buildcontrol-flowgraph– CalculateiniPallocaldata–DEF(b)andNKILL(b)foreveryblockb

•  Thisonlyneedstobedoneonce–  IteraPvelycalculateAVAIL(b)byrepeatedlyevaluaPngequaPonsunPlnothingchanges

•  Afixed-pointalgorithm


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CompuPngDEFandNKILL(1)

•  ForeachblockbwithoperaPonso1,o2,…,ok

KILLED=∅//Killedvariables(notexpressions)DEF(b)=∅fori=kto1//Noteweareworkingbackwards-importantassumeoiis“x=y+z” if(y∉KILLEDandz∉KILLED) //ExpressioninDEFonlyif add“y+z”toDEF(b) //theyaren’tlaterkilledaddxtoKILLED

…










Example:CompuPngDEFandKILL

x=a+b;b=c+d;m=5*n;

DEF={}KILL={}


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x=a+b;b=c+d;m=5*n;

DEF={5*n}KILL={m}











x=a+b;b=c+d;m=5*n;

DEF={5*n,c+d}KILL={m,b}


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x=a+b;b=c+d;m=5*n;

DEF={5*n,c+d}KILL={m,b,x}(biskilled,sodon’tadda+btoDEF)










CompuPngDEFandNKILL(2)

•  A]ercompuPngDEFandKILLforablockb,conceptuallywedothefollowing:

//NKILLisexpressionsnotkilled.NKILL(b)={allexpressionsinprogram}foreachexpressione//Removeanykilledforeachvariablev∈eifv∈KILLthen NKILL(b)=NKILL(b)-e


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Example:CompuPngDEFandNKILL

x=a+b;b=c+d;m=5*n;

DEF={5*n,c+d}KILL={m,b,x}NKILL=allexpressionsthatdon’tusem,b,orx











•  OnceDEF(b)andNKILL(b)arecomputedforallblocksb,computeAVAILforallblocksbyrepeatedlyapplyingthepreviousformulainafixed-pointalgorithm:

Worklist={allblocksbi}while(Worklist≠∅)removeablockbfromWorklist//IfbinWorklist,atleast1predecessorchangedletAVAIL(b)=∩x∈preds(b)(DEF(x)∪(AVAIL(x)∩NKILL(x)))ifAVAIL(b)changedWorklist=Worklist∪successors(b)


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x=a+b;b=c+d;m=5*n;

DEF={5*n,c+d}NKILL=exprsw/om,b,orx

c=5*n DEF={5*n}NKILL=exprsw/oc

j=2*ak=2*b

DEF={2*a,2*b}NKILL=exprsw/ojork

h=2*a DEF={2*a}NKILL=exprsw/oh=inWorklist

=Processing












x=a+b;b=c+d;m=5*n;



j=2*ak=2*b

AVAIL={}DEF={2*a,2*b}NKILL=exprsw/ojork

h=2*a DEF={2*a}NKILL=exprsw/oh=inWorklist

=Processing



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x=a+b;b=c+d;m=5*n;



j=2*ak=2*b


h=2*a AVAIL={5*n}DEF={2*a}NKILL=exprsw/oh

=inWorklist

=Processing












x=a+b;b=c+d;m=5*n;

AVAIL={2*a,2*b}DEF={5*n,c+d}NKILL=exprsw/om,b,orx


j=2*ak=2*b



=inWorklist

=Processing



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x=a+b;b=c+d;m=5*n;


c=5*n AVAIL={2*a,2*b}DEF={5*n}NKILL=exprsw/oc

j=2*ak=2*b



=inWorklist

=Processing












x=a+b;b=c+d;m=5*n;



j=2*ak=2*b


h=2*a AVAIL={5*n,2*a}DEF={2*a}NKILL=exprsw/oh

=inWorklist

=Processing



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x=a+b;b=c+d;m=5*n;



j=2*ak=2*b


h=2*a AVAIL={5*n,2*a}DEF={2*a}NKILL=exprsw/oh

=inWorklist

=Processing











Dataflowanalysis

•  Availableexpressionsareanexampleofadataflowanalysisproblem

•  Manyothercompileranalysescanbeexpressedinasimilarframework

•  Onlythefirstpartofthestory–oncewe’vediscoveredfacts,wethenneedtousethemtoimprovecode


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CharacterizingDataflowAnalysis

•  Allofthesealgorithmsinvolvesetsoffactsabouteachbasicblockb–  IN(b)–factstrueonentrytob–  OUT(b)–factstrueonexitfromb–  GEN(b)–factscreatedandnotkilledinb–  KILL(b)–factskilledinb

•  ThesearerelatedbytheequaPon OUT(b)=GEN(b)∪(IN(b)–KILL(b))

–  (SubtracPngKILL(b)isequivalenttointersecPngNKILL(b))–  SolvethisiteraPvelyforallblocks–  SomePmesinformaPonpropagatesforward;somePmesbackward(reverseinandout)










Example:LiveVariableAnalysis

•  Avariablevisliveatpointpifandonlyifthereisanypathfromptoauseofvalongwhichvisnotredefined(i.e.,vmightbeusedbeforeitisredefined)

•  Someuses:–  RegisterallocaPon–registersallocatedtoliveranges–  EliminaPnguselessstores–ifvariableisnotliveatstore,thestoredvaluewillneverbeused

–  DetecPngusesofuniniPalizedvariables–ifliveatdeclaraPon(beforeiniPalizaPon),maybeuseduniniPalized.

–  ImproveSSAconstrucPon–onlycreatephifuncPons(variablemerges)forlivevariables-cominglater…


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LivenessAnalysisSets

•  Foreachblockb,define– use[b]=variableusedinbbeforeanydef– def[b]=variabledefinedinbbeforeanyuse–  in[b]=variablesliveonentrytob– out[b]=variablesliveonexitfromb










EquaPonsforLiveVariables

•  GiventheprecedingdefiniPons,wehavein[b]=use[b]∪(out[b]–def[b])out[b]=∪s∈succ[b]in[s]

•  I.e.,liveatentryiffthisblocksgeneratesliveness(use[b])oritwasliveattheexitandthisblockdoesnotkillliveness(out[b]–def[b]).

•  Andliveatexitiffliveatentrytoanysuccessor.•  Algorithm

–  Setin[b]=out[b]=∅–  Computeuse[b]anddef[b]foreveryblock(onePme)–  Updatein,outunPlnochange


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