252-210: compiler design - eth zürich · pdf file252-210: compiler design 9.6 available...

252-210:CompilerDesign9.6Availableexpressions9.7Busyexpressions

ThomasR.GrossComputerScienceDepartmentETHZurich,Switzerland

Availableexpressions

§  Anexpressiona+bisavailableatapointPifa+bisevaluatedoneverypathfromENTRYtoPandthereisnodefiniNonofaorbonthispathaOera+bwasevaluated§  InterestedinsetofexpressionsavailableatthestartofabasicblockB§  SetdependsonpathsthatleadtoPbefore_B

§  Assumethata+bhasnosideeffects§  ReadingamemorylocaConmayhavesideeffectstoo!§  NotaproblemforJavaLiorJava

2

3

e1: x = a + b if (Tcond)

e2: y = a + b

??

P


§  Isa+bcomputedine1availablefore2?§  AvailableatP

§  DependsonB2

B1

B2

B3

4


e2: y = a + b

a = …

P


§  Isa+bcomputedine1availablefore2?

§  No–amayhaveatPavaluethatdiffersfromthevalueate1.

B1

B2

B3

5


e2: y = a + b

a = … e3: z = a + b

P


§  Isa+bavailablefore2?§  Yes–eithercomputed

bye1orbye3

B1

B2

B3

TransferfuncNon

§  a+bisavailableattheendofbasicblockBifthereisnostmtinBthatfollowseandthatdefinesaorb§  MustbeconservaCve§  Ifastatementintheshadedregionmaymodifya(orb)thena+bisnot

availableattheendofB

6

… e: … = a + b …

B

TransferfuncNon

§  (Maybe)a+bisavailableatPbefore_B.

§  a+bisnotavailableatPaOer_B§  UnlessthereisastatementinBthatfollowsdandre-computesa+b,

seelastslide

§  DefiniNondhas“killed”theexpressiona+b

7

… d: a = … …

B

Pbefore_B

PaOer_B

TransferfuncNon

§  DefineforbasicblockB§  genB={expr|expra+bisevaluatedinB,neitheranorb

subsequentlydefinedinB}§  killB={expr|aorbofexpra+bdefinedinBanda+bisnot

subsequentlyevaluatedinB}

§  MustbeconservaNve§  Ingenonlyifwearesuretheexpressionisevaluated§  Inkillifthereisachancethatoneoftheoperandsofa+bisdefined

8

… d: x = … e: = a + b

TransferfuncNon

§  Wanttofindsets§  IN(B):setofexpressionsavailableatstartofB§  OUT(B):setofexpressionsavailableatendofB

§  TransferfuncNoncaptureshowstatementsinBdetermineOUT(B)

9

… d: x = … e: = a + b

IN(B)

OUT(B)

B

TransferfuncNon

§  GivenOUT(B1).§  WhatshouldbeIN(B2)andIN(B3)?

§  IN(B2)=OUT(B1),IN(B3)=OUT(B1)§  Anexpressionthatisavailablea_erB1isavailableatthestartofB2

andthestartofB310

...

… …

B1

B2 B3

TransferfuncNon

§  GivenOUT(B2)andOUT(B3)§  WhatshouldbeIN(B1)?

§  ExpressionEisavailableatPifEiscomputedoneverypathfromENTRYtoP(andnoneoftheoperandsofEiskilledsubsequently)

§  MustconsiderallpathsleadingtoP§  Emustbeavailableonallpaths 11

...

… …

B1

B2 B3

P

TransferfuncNon

§  GivenOUT(Bi)

§  IN(B)=∩Bi,BiispredecessorofBinCFGOUT(Bi)

12

...

… …

B1

B2 B3

FindingIN(B)andOUT(B)

§  genandkillcapturewhathappensinsideabasicblock§  Sometextsusee_genande_killtodisCnguishbetweensetsneeded

forreachingdefiniCons§  Thesesetsaredifferent!

§  WeneedINandOUTforeachbasicblock


§  OUT(B)=genB∪(IN(B)–killB)

§  Nbasicblocks,2×NsetsIN/OUT

13


§  Nbasicblocks,2×NsetsIN/OUT§  Systemwith2×Nunknowns

§  SolvebyiteraCngunClafixedpointisfound

§  HowtostartiteraNon?SafeassumpConOUT[ENTRY]=∅

14


§  SafeassumpNonOUT[ENTRY]=∅§  WhataboutOUT[Bi]forBi≠ENTRY?

§  ForreachingdefiniCons,wewantedsmallestsetofdefiniConsthat“reach”§  OKifwesaydreachesbutitdoesnot

§  Foravailableexpressions,wewantlargestsetofexpressionsthat“reach”§  OKifexprisavailablebutnotincludedinset

§  SostartwithalargeapproximaNonandremoveexpressionsthatareclearlynotavailable§  OUT[Bi]= U!§  U isthesetofallexpressionsthatappearintheprogram!

15

Findingavailableexpressions

OUT[ENTRY]=∅IniCalizeOUT[B]=U for∀B≠ENTRY

while(changestoanyOUT(B)){for(eachbasicblockB≠ENTRY){

IN(B)=∩Bi,BiispredecessorofBinCFGOUT(Bi) OUT(B)=genB∪(IN(B)–killB)}}

16

Comments

§  Thealgorithm(previousslide)idenNfiesanexpressionexpras“available”onlyifexpristrulyavailable.§  InducCononlengthofpath§  Ifexprisnotavailable(alongsomepath)thenexprisnotinOUT(B)for

ablockB§  exprisnotavailableforsomepredecessorB’ofBasweuse∩toformIN[B]

§  Again,theorderofvisiNngnodesmakers§  Forspeedofconvergence,notcorrectness

17


§  Isthisaforwardorabackwardproblem?

18


§  Isthisaforwardorabackwardproblem?§  Forward

§  Howsimilarisitto“reachingdefiniNons”?

§  ReachingdefiniCons:IN(B)=∪Bi,BiispredecessorofBinCFGOUT(Bi)

§  Availableexpressions:IN(B)=∩Bi,BiispredecessorofBinCFGOUT(Bi)

19

§  Summaryfordataflowproblems§  ComputetwosetsforeachbasicblockB

§  SoluCon=OUT(B)/IN(B)§  Context=IN(B)/OUT(B)

§  Twosetstocapturelocaleffects§  DefineadirecCon

§  ReachingdefiniCons,availableexpressions:Forward§  Ancestor:predecessor

§  Livevariables:Backward§  Ancestor:successor

§  InitSoluCon(ENTRY)/SoluCon(EXIT)§  InitremainingSoluConsets§  Definea“meetoperator”⟗

§  ReachingdefiniCons,livevariables:∪

§  Availableexpressions:∩

§  IterateoverbasicblocksBContext(B)=⟗Bi,BiisancestorofBinCFGSoluCon(Bi) SoluCon(B)=local_newB∪(Context(B)–local_cutB) 20

Dataflowproblems

21

Forward Backward

∪

∩

Dataflowproblems

22

Forward Backward

∪

∩

ReachingdefiniCons


Livevariables

9.7Busyexpressions

…

if (…) {

A[j] = 0;

} else {

A[j] = 1;

}

23

IRview

…

if (…) {

tmp1 = j * 4

tmp2 = &A + tmp1

*tmp2 = 0

} else {

tmp3 = j * 4

tmp4 = &A + tmp3

*tmp4 = 1

} 24

§  Expression j*4 isevaluatedinbothbranchesoftheif-stmt

§  HoisNng j*4 toblockabovetheif-stmtreducesthesizeoftheobjectcode§  No(immediate)speedbenefit

§  Expressionj*4isa“(very)busyexpression”.§  Anexpressiona+bisverybusyatapointPifa+bis

evaluatedonallpathsfromPtoEXITandthereisnodefiniNonofaorbonapathbetweenPandanevaluaNonofa+b §  InterestedinsetofexpressionsavailableatthestartofabasicblockB§  SetdependsonpathsthatstartatPbefore_B 26

TransferfuncNon

§  a+bisverybusyatthestartofbasicblockBifthereisnostmtinBpriortoSthatdefinesaorb.

27

… S: … = a ⊕ b …

B

TransferfuncNon

§  a+bisnot(very)busyatthestartofbasicblockBasthereisastmtinBpriortoSthatdefinesa(stmtS’)

28

S’: a = S: … = a ⊕ b …

TransferfuncNon

§  DefineforbasicblockB§  killB={expr|anoperandofexprisdefinedinBbystmtSandexpris

notevaluatedbeforeS}§  genB={expr|exprisevaluatedinBpriortoadefiniConofanyofits

operands}

§  Setskillandgen:mustbeconservaNve§  Ingenonlyifwearesuretheexpressionisevaluated§  Inkillifthereisachancethattheexpressioniskilled

29

… S: … = a ⊕ b …

TransferfuncNon

§  NoNcethatwemaybeinterestedinthesetofbusyexpressionsatthestartofabasicblock§  Determinedbystatementsinbasicblockandstatementsin

subsequentbasicblocks

§  Setofbusyexpressionsattheendofabasicblock§  Determinedbystatementsinsubsequentbasicblocks§  Anotherterm:expressionisdownwardexposed

30

TransferfuncNon

31

§  ForabasicblockBwedefine§  IN(B)={expr|exprverybusyatPbefore_B}§  OUT(B)={expr|exprverybusyatPa_er_B}

§  Expressionb∈IN(B)§  bisevaluatedinBpriortodefiniConofanoperand,i.e.b∈genB§  b∈OUT(B)andoperandsofbnotdefinedinB,i.e.b∉killB

§  IN(B)=genB∪(OUT(B)–killB)

… S: … = a ⊕ b …

IN(B)={b1,b2,…,bn}

OUT(B)={b’1,b’2,…,v’m}

TransferfuncNon

§  GivenIN(B1)§  WhatshouldbeOUT(B2)andOUT(B3)?

§  OUT(B2)=IN(B1),OUT(B3)=IN(B1)

32

...

… …

B1

B2 B3

TransferfuncNon

§  GivenIN(B2)andIN(B3)§  WhatshouldbeOUT(B1)?

§  AnexpressionEis“verybusy”atapointPifEisevaluatedonallpathsfromPtoEXIT(andthereisnodefiniConofanoperandofEbetweenPandsuchanevaluaCon)

§  MustconsiderallpathsstarCngatP 33

...

… …

B1

B2 B3

TransferfuncNon

34

...

… …

B1

B2 B3

§  GivenIN(Bi)§  OUT(B)=∩Bi,BiissuccessorofBinCFGIN(Bi)


§  Nbasicblocks,2×NsetsIN/OUT§  Systemwith2×Nunknowns

§  SolvebyiteraCngunClafixedpointisfound

§  HowtostartiteraNon?SafeassumpConIN[EXIT]=∅Nothingisverybusyattheend

§  IN(B)=U§  U setofallexpressionsinprogram§  ForallB≠EXIT

35

CompuNngverybusyexpressions

IN[EXIT]=∅IniCalizeIN[B]=Ufor∀B≠EXITwhile(changestoanyIN(B)){for(eachbasicblockB≠EXIT){ OUT(B)=∩Bi,BiissuccessorofBinCFGIN(Bi)

IN(B)=genB∪(OUT(B)–killB)}}

36

Comments

§  CompilermustmovecodetobenefitfromverybusyexpressioninformaNon:codehoisNng

38

tmp5 = j * 4

tmp6 = &A + tmp5

if (…) {

*tmp6 = 0

} else {

*tmp6 = 1

}

…

if (…) {

tmp1 = j * 4

tmp2 = &A + tmp1

*tmp2 = 0

} else {

tmp3 = j * 4

tmp4 = &A + tmp3

*tmp4 = 1

}

Comments

§  ThereexistsanapproachtocodemoNonthatdealswithallkindsofcodemoNon§  Loopinvariantremoval§  Commonsub-expressioneliminaCon§  VerybusyexpressionhoisCng§  …

together(andalsodealswithotheropNmizaNons)andthereforecodehoisNng(ofbusyexpressionsinisolaNon)isnotemployedinmoderncompilers.

39

9.8Dataflowproblems

40

Forward Backward

∪

∩

ReachingdefiniCons


Livevariables

Verybusyexpressions

§  Summaryfordataflowproblems§  ComputetwosetsforeachbasicblockB

§  SoluCon=OUT(B)/IN(B)§  Context=IN(B)/OUT(B)

§  Twosetstocapturelocaleffects(local_new,local_cut)§  DefineadirecCon

§  ReachingdefiniCons,availableexpressions:Forward§  Ancestor:predecessor

§  Livevariables,verybusyexpressions:Backward§  Ancestor:successor

§  InitSoluCon(ENTRY)/SoluCon(EXIT)§  InitremainingSoluConsets§  Definea“meetoperator”⟗

§  ReachingdefiniCons,livevariables:∪

§  Availableexpressions,verybusyexpressions:∩

§  IterateoverbasicblocksBContext(B)=⟗Bi,BiisancestorofBinCFGSoluCon(Bi) SoluCon(B)=local_newB∪(Context(B)–local_cutB) 41

CompilerimplementaNon

§  FrameworkwithabstractfuncNonstoallowspecificaNonof§  IniCalizaConoflocal_new,local_cut§  DirecCon§  Meet(confluence)operator§  IniCalINandOUTsets§  TransferfuncCon(dependsondirecCon)

§  OUT=(IN–local_cut)∪local_gen§  IN=(OUT–local_cut)∪local_gen

§  UsetheframeworktoinstanNatespecificdataflowanalyses

42

43

Classhierarchy

9.9CodetransformaNons

§  CompilerusesglobaldataflowinformaNontoimplementcodetransformaNons

§  Coveredonlybrieflyinthisclass

44

9.9.1Constantfolding

§  Need:constantpropagaNoninformaNonasdiscussedin9.1§  OrreachingdefiniConsasdiscussedin9.2

§  TransformaNon:ifbothoperandsareconstant,computevalueincompiler§  AwenCon:carefulifthecompilerdoesnotrunontargetsystem

(“cross-compiler”)§  Mustmakesurecompilerproducesresultthatwouldhavebeen

obtainedatrunCme

§  TransformaNonmaycreatenewopportuniNes

45

9.9.2DeadassignmenteliminaNon

§  Need:livevariableanalysis§  Deadassignment:targetofstoreisnotlive

§  TransformaNon:removeuselessassignmentstatement§  AssumpCon:ReuseofavailableexpressionsCedto(designated

temporary)variables

§  TransformaNonmayrenderotherstatementsdead

46

9.9.3DeadcodeeliminaNon

§  Need:constantpropagaNoninformaNon,reachingdefiniNons

§  Deadcode:unreachablecode§  Forwell-structuredprograms:if-thenorif-then-elsestatementswith

condiConexpressionsthatcanbeevaluatedatcompileCme

§  TransformaNon:removeunreachablecode§  Mayrendervariablesdead

47

9.9.4CopypropagaNon

§  VarioustransformaNonsintroducecopies

x = a + b

if (..) {

z = a + b

}

y = a + b

48

x = a + b

t = x

if (..) {

z = t

}

y = t

CopypropagaNon

§  Maywanttoeliminatethecopies§  Replacetbyx

x = a + b

if (..) {

z = a + b

}

y = a + b

§  DeadassignmenteliminaNontakescareoft=x

49

x = a + b

t = x

if (..) {

z = x

}

y = x

CopypropagaNon

§  Mayalsohavebeneficialeffectsonregisterallocator

§  GivencopystmtS: t = x

§  CompilercansubsNtutexfortatpointPif1.  DefiniConSistheonlydefiniConoftthatreachesP2.  OneverypathfromStoPtherearenoassignmentstox

§  ApathmaygothroughPmulCpleCmesbutnotgothroughSasecondCmeandsCllmustsaCsfythiscondiCon

§  CondiNon(1)iseasilycheckedgivenreachingdefiniNons

50

Newdataflowproblem:“reachingcopystatements”§  ForeachbasicblockB

§  genB={copy-stmt|copy-stmta=bappearsinBandthereisnosubsequentdefiniConofbinB}

§  killB={copy-stmt|forthecopy-stmta=bthereisadefiniConofaorbinB(andcopy-stmtdoesnotappeara_erthesedefiniConsinB)}

§  Notethatdifferentassignments(copystatements)a=bkilleachother

§  TransferfuncNon§  IN(B):SetofcopiesS:a=bsuchthateverypathtoPbefore_BcontainsS

andthereisnodefiniConofbsubsequenttothelastoccurrenceofS§  OUT(B):…toPa_er_B…

51

TransferfuncNon

§  OUT(ENTRY)=∅§  OUT(B)=U

§  U setofallcopystatementsinprogram§  ForallB≠ENTRY


§  OUT(B)=genB∪(IN(B)–killB)

52

Findingreachingcopystatements

OUT[ENTRY]=∅IniCalizeOUT[B]=U for∀B≠ENTRY

while(changestoanyOUT(B)){for(eachbasicblockB≠ENTRY){

IN(B)=∩Bi,BiispredecessorofBinCFGOUT(Bi) OUT(B)=genB∪(IN(B)–killB)}}

53

54

S1: x = y

S2: y =

ExampleB1

B2S3: x = z B3

S4: … = x B4

S4: … = x B5

55

S1: x = y

S2: y =

ExampleB1

B2S3: x = z B3

S4: … = x B4

S4: … = x B5

gen={S1:x=y}kill={S3:x=z}

gen={S3:x=z}kill={S1:x=y}

gen={}kill={S1:x=y}

Example

§  IN(B2)=IN(B3)=OUT(B1)={S1:x=y}§  OUT(B2)=∅§  OUT(B3)=IN(B4)=OUT(B4)={S3:x=z}

§  IN(B5)=OUT(B2)∩OUT(B4)=∅

Pleasenotethatfor“reachingdefiniNons”,thedefiniNonofxinS1“reaches”B5(viaB2)

56

9.10“…mustbeconservaNve”

§  PointersnotanissueforJavaLi–mustbecarefuliflanguageallowsaddressestobetaken§  Riskofaliases

§  Arrays–don’tincludethemindataflowcomputaNon§  NoefforttounderstandmodificaConofindividualarrayelements

57

MethodinvocaNon

§  Java(andJavaLi)allowonlyvalueparameters*and*thereisnotwaytogetareferencetoalocalvariable§  Treatactualparameteras“uses”ofavariableresp.evaluaConofan

expression

§  Otherlanguagessupportpointers(andmayhaveglobalvariables)ret = foo (p1, p2, …, pn)

§  Variableretisdefined,p1,p2,…,pnareused§  Whatismodifiedbyfoo?

§  Anyparameterpi?§  LocaConsreachableviapi?§  Globals?

§  Mustmakeworst-caseassumpConintheabsenceofbewerinformaCon 58

ConservaNsm

int a, *b;

d1: a = 3;

d2: *b = ….

P:….

§  ForreachingdefiniNons,d1reachesP§  Can’tbesurethat*bwritesa

§  ForconstantpropagaNon,(a=3)isfalseatP§  *bmightdestroyvalueofa

59

252-210: compiler design - eth zürich · pdf file252-210: compiler design 9.6 available...

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