CompilerDesignSpring2017

8.5Reachingdefinitions

Dr.Zoltán Majó

CompilerGroup– JavaHotSpot VirtualMachineOracleCorporation

Adminissues

§ Briefreminder:Codereviewtakesplacetoday§ @15:15§ You’vereceivedroominformationbyemail

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Lastlecture:Definition(ofreachingdefinitions)

§ Adefinitiondreaches apointPifthereisapathfromdtoPsuchthatdisnotkilledalongthatpath.

§ Remember:Therearearbitrarilymanypaths§ Notfeasibletoreason/processallofthem

§ Reasonaboutclaims atprogrampointsinstead§ Exampleclaim:D=={d1,d2,d5}@Pbefore_S

§ DisthesetofdefinitionsthatreachesPbefore_S

§ Howdowedefineaappropriatetransferfunction?

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Transferfunction

§ d1 reachestheendofthebasicblockifthereisnostatementfollowingd1 thatmightkilld1

§ DefineforbasicblockB§ killB = {d|diskilledinB}§ genB ={d|dappearsinBandnosubsequentstatementinBkillsd}

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…d1: var =…

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d1: a = b + 1d2: a = …

if (Tcond)

d5: a = …d6: c = …

d3: a = … d4: b = …

P

gen={d2}kill={d1,d2,d3,d5}

gen={d3}kill={d1,d2,d5}

gen={d5,d6}kill={d1,d2,d3}

gen={d4}kill=∅

a:{d1,d2,d3,d5}b:{d4}c:{d6}

Runningexample

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d1: i = m – 1d2: j = n d3: a = …

d7: i = …

d4: i = i + 1d5: j = j - 1

d6: a = …

ENTRY

EXIT

gen={d1,d2,d3}kill={d4,d5,d6,d7}

FromAho etal“Compilers”,p 604

gen={d4,d5}kill={d1,d2,d7}

gen={d6}kill={d3}

gen={d7}kill={d1,d4}

i:{d1,d4,d7}j:{d2,d5}a:{d3,d6}

Transferfunction

§ Sofar:Effectofabasicblockinisolation§ killB = {d|diskilledinB}§ genB ={d|dappearsinBandnosubsequentstatementinBkillsd}

§ (Localanalysis)

§ HowdoweextendtransferfunctionstodefinitionsthatreachPbefore_B andPafter_B

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…d1: var =…

Transferfunction

§ ForabasicblockBwedefine§ IN(B) ={d|dreachesPbefore_B }§ OUT(B) ={d|dreachesPafter_B }

§ d∈OUT(B)§ disinBandreachestheendofB,i.e.d∈ genB§ d∈ IN(B)anddnotkilledbystatementsinB,i.e.d∉ killB

§ OUT(B)=genB∪ (IN(B)– killB)

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…d”: var =…

IN(B)={d1,d2,…,dn}

OUT(B)={d’1,d’2,…,d’m}

Transferfunction

§ GivenOUT(B1).

§ WhatshouldbeIN(B2)andIN(B3)?

§ IN(B2)=OUT(B1),IN(B3)=OUT(B1)

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...

… …

B1

B2 B3

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Transferfunction

§ GivenOUT(B2) andOUT(B3)

§ WhatshouldbeIN(B1)?§ Adefinitiondreaches apointPifthereisapathfromdtoPsuchthat

disnotkilledalongthatpath.§ Mustconsiderall pathsleadingtoP

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...

… …

B1

B2 B3

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Transferfunction

§ GivenOUT(Bi)

§ IN(B)=∪ Bi,Bi ispredecessorofBinCFG OUT(Bi)

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...

… …

B1

B2 B3

Wehavetheingredients(again)

§ Controlflow(basicblocks,CGF),points,paths§ Sameasforconstantpropagationinpreviouslecture

§ Transferfunction§ Specificforreachingdefinitions

§ Howdoestheanalysiswork?

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Simplificationsinexamples

§ Donotshowpointsbefore/afterbasicblock

§ Omitconditionaltest§ Evaluationofcondition§ Ifstatement

§ Capturecontroltransfersthroughedges§ Noexplicit“jump”or“branch”statements

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d1: i = m – 1d2: j = n d3: a = …

d7: i = …

d4: i = i + 1d5: j = j - 1

d6: a = …

ENTRY

EXIT

gen={d1,d2,d3}kill={d4,d5,d6,d7}

FromAho etal“Compilers”,p 604

gen={d4,d5}kill={d1,d2,d7}

gen={d6}kill={d3}

gen={d7}kill={d1,d4}

i:{d1,d4,d7}j:{d2,d5}a:{d3,d6}

IN(B1)=?

OUT(B1)=?

IN(B2)=?

IN(B3)=?

IN(B4)=?

OUT(B2)=?

OUT(B3)=?

OUT(B4)=?

FindingIN(B)andOUT(B)

§ genandkillcapturewhathappensinsideabasicblock§ Or…theeffectofeachstatement

§ WeneedINandOUTforeachbasicblock§ IN(B)=∪ Bi,BiispredecessorofBinCFG OUT(Bi)§ OUT(B)=genB∪ (IN(B)– killB)

§ Nbasicblocks,2×NsetsIN/OUT

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FindingIN(B)andOUT(B)(cont’d)

§ Systemwith2×Nunknowns§ Solvebyiteratinguntilafixedpointisfound

§ Howtostartiteration?§ SafeassumptionOUT[ENTRY]=∅

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Findingreachingdefinitions

OUT[ENTRY]=∅

InitializeOUT[B]=∅ for∀ B≠ENTRY

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

IN(B)=∪ Bi,Bi ispredecessorofBinCFG OUT(Bi)OUT(B)=genB∪ (IN(B)– killB)

}}

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Findingreachingdefinitions

OUT[ENTRY]=∅

InitializeOUT[B]=∅ for∀ B≠ENTRY

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

IN(B)=∪ Bi,Bi ispredecessorofBinCFG OUT(Bi)OUT(B)=genB∪ (IN(B)– killB)

}}

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d1: i = m – 1d2: j = n d3: a = …

d7: i = …

d4: i = i + 1d5: j = j - 1

d6: a = …

ENTRY

EXIT

IN(B1)

OUT(B1)

IN(B2)

IN(B4)

OUT(B2)

OUT(B4)

∅

{d1,d2,d3}

{d1,d2,d3,d5,d6,d7}

{d3,d4,d5,d6}

{d3,d4,d5,d6}

{d3,d5,d6,d7}

IN(B3)

OUT(B3)

{d3,d4,d5,d6}

{d4,d5,d6}

gen={d6}kill={d3}

gen={d1,d2,d3}kill={d4,d5,d6,d7}

gen={d4,d5}kill={d1,d2,d7}

gen={d7}kill={d1,d4}

InitializeOUT[B]=∅while(changestoanyOUT(B)){

for(eachbasicblockB≠ENTRY){IN(B)=∪ Bi,Bi ispredecessorofBinCFG OUT(Bi)OUT(B)=genB∪ (IN(B)– killB)

}

Comments

§ Solutionnotunique§ CouldalwaysuseOUT(B)=alldefinitions§ Notreallyuseful§ Iterativealgorithmfindsleastfixedpoint

§ Orderofvisitingbasicblocksmatters§ Forspeedofiteration,notfortheresult

§ Iterationterminates§ Finitenumberofbasicblocks,finitenumberofdefinitions§ INandOUTcanonlygrow

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Why?

void foo(int x) {

int a, b, c;

a = x + 1;

b = a;

if (…) { … }

else { … }

c = b + 1;

return c;

}

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d1: a = x + 1d2: b = a

if (Tcond)

d3: c = b + 1return c

… //noa,b … //noa,b

IN={d1,d2}

Why?

void foo(int x) {

int a, b, c;

a = x + 1;

b = a;

if (…) { … }

else { … }

c = b + 1;

return c;

}

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d1: a = x + 1d2: b = a

if (Tcond)

d3: c = a + 1return c

… //noa,b … //noa,b

IN={d1,d2}

Comments

§ Changeappearstobeminor– butitisnot§ d2 canberemoved(ifthereisnootheruseofb – seenexttopic)§ Valueofvariableacanbepickedupfromregister

§ Thereareotherreasonsforthecompilertocomputereachingdefinitions

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Foodforthought

void foo(int x) {

int a, b, c;

a = x + 1;

if (…) {

b = x;

} else { … }

c = b + 1;

return c;

}

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d1: a = x + 1if (Tcond)

d3: c = b + 1return c

… //noa,b d2: b = x

IN={d1,d2}

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Foodforthought

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d1: a = x + 1if (Tcond1)

d5: c = a + 1return c

… //noa,b d2: b = x

IN={d3,d2}

d3: a = y + 1if (Tcond2)

… //noa,b d4: c = b + 1

Programisbroken

§ Asfaraswecantell,d4 mayreadanundefinedvalueofb§ Maybenot– cannotdecideingeneral

§ Couldweuse“reachingdefinitions”toidentifysuchtroublespots§ Backtotheuseofflowanalysisforprogramchecking

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Uninitializedvariables

§ Reachingdefinitions:setofdefinitionsthatreachstartofabasicblock

§ Idea:insert“fake”definitionsintotheENTRYnode§ Oneforeachvariable§ “fake”meansthereisnocorrespondenceinthesourceprogram§ Identifybytag,number,… (herenumber>100)§ StartiterationwithOUT(ENTRY)=setoffakedefinitions

§ Ifafakedefinitiondthatsetsdestinationdest reachesablockB,andthereisauseofdest inBpriortoanydefinitionofdest inB,thendest ispotentiallyuninitialized§ Compilercan(ingeneral)onlyissuewarning,cannotbesurevariable

isuninitialized

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Uninitializedvariables

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d1: a = x + 1if (Tcond1)

d5: c = a + 1return c

… //noa,b d2: b = x

d3: a = y + 1if (Tcond2)

… //noa,b d4: c = b + 1

d100: a = …d101: b = …d102: c = …

ENTRY

IN:{d100,d101,d102}

IN:{d1,d101,d102}

IN:{d1,d2,d101,d102}

IN:{d3,d2,d101,d102}

IN:{d3,d2,d4,d101,d102}

IN:{d3,d2,d101,d102}

IN:{d1,d101,d102}

EXIT

xoryareglobalorparameterssowedonotneeda“fake”definition

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Uninitializedvariables

…// no a or bif (Tcond1)

d1: a = x + 1 d2: b = x + 2

d3: x = a + 1d4: b = y + 1d5: y = b + 1

d100: a = …d101: b = …

ENTRY

IN:{d1,d2,d101,d100}

xoryareglobalorparameterssowedonotneeda“fake”definition

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Uninitializedvariables

…// no a or bif (Tcond1)

d1: a = x + 1 d2: a = x + 2

d3: a = a + 1return a

d100: a = …

ENTRY

IN:{d1,d2}

xisaglobalorparametersowedonotneeda“fake”definition

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Programanalysis

§ Compilerneedsinformation§ Specificproblem

§ Deviseflowanalysistocomputeinformation

§ Letcompileruseinformationtodealwithspecificproblem

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