Compiler Design Spring 2017 8.5 Reaching definitions Dr. Zoltán Majó Compiler Group – Java HotSpot Virtual Machine Oracle Corporation
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;
}
6363
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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