Compiler Design - ETH Zpeople.inf.ethz.ch/zmajo/teaching/cd_ss17/slides/w11-02-constant... ·...
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Compiler Design Spring 2017 8.4 Transfer functions; constant propagation Dr. Zoltán Majó Compiler Group – Java HotSpot Virtual Machine Oracle Corporation
Transcript of Compiler Design - ETH Zpeople.inf.ethz.ch/zmajo/teaching/cd_ss17/slides/w11-02-constant... ·...
CompilerDesignSpring2017
8.4Transferfunctions;constantpropagation
Dr.Zoltán Majó
CompilerGroup– JavaHotSpot VirtualMachineOracleCorporation
Constantpropagation
§ Weareinterestedinknowingthatavariablehasaconstantvalueatagivenpointintheprogram.
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a = 4;
if (…) {
c = 7;}
else {
b = d + 2;}
// S:
d = a * 2;
…3
Constantpropagation
§ Weareinterestedinknowingthatavariablehasaconstantvalueatagivenpointintheprogram.
§ Canweestablishthat“a==4”beforestatementSisexecuted?
§ NeedtoconsiderallpathsthatleadtopointPbefore_S
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a = 4;
if (…) {
c = 7;}
else {
b = d + 2;}
// S:
d = a * 2;
…5
Pbefore
a = 4Tcond =if (Tcond)
b = d + 2 c = 7
d = a * 2
a = 4;
if (…) {
c = 7;}
else {
b = d + 2;}
// S:
d = a * 2;
…6
a = 4Tcond =if (Tcond)
b = d + 2 c = 7
d = a * 2
Pbefore
a = 4;
if (…) {
c = 7;}
else {
b = d + 2;}
// S:
d = a * 2;
…7
a = 4Tcond =if (Tcond)
b = d + 2 c = 7
d = a * 2
Pbefore
Constantpropagation
§ Weareinterestedinknowingthatavariablehasaconstantvalueatagivenpointintheprogram.
§ Canweestablishthat“a==4”beforestatementSisexecuted?
§ NeedtoconsiderallpathsthatleadtopointPbefore_S§ Whatistheeffectofstatementsalongthesepaths?
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Path(basicblocks)
§ Apathisasequenceofpoints(x0,x1,x2,…,xn)suchthatforanypair(xj,xj+1)with0≤j<noneoftheseconditionsholds1. xj isthepointbeforebasicblockBandxj+1 isthepoint
afterbasicblockB2. xj isthepointafterbasicblockBk andxj+1 isthepoint
beforebasicblockBm andthereisanedgefromBk toBmintheCFG
§ Definitioncanbeextendedtodealwithpointsbefore/afterstatements.
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Path(forstatements)
§ GivenaCFG,foreachnodeB(i.e.,basicblock)thereexistsan(ordered)sequenceofstatementsSB,0,SB,1,…SB,m.§ Emptybasicblock?-- Allow“noopstatement”§ SB,0:firststatement,SB,m: laststatement§ Order:programorder
§ Apathisasequenceofpoints(x0,x1,x2,…,xn)suchthatforanypair(xj,xj+1)with0≤j<noneoftheseconditionsholds1. xj isthepointbeforestatementSandxj+1 isthepoint
afterstatementS2. xj isthepointafterthelaststatementS’ofbasicblockBk
andxj+1 isthepointbeforethefirststatementS”ofbasicblockBm andthereisanedgefromBk toBm intheCFG
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Claim:a==4@S
§ WhatistheeffectofstatementsalongthepathsthatendatPbefore_S?
§ Considereachstatementonapath§ Ifthelastassignmenttovariablea supportstheclaim,thentheclaim
isvalid§ Iftheclaimisvalidalongallpathsthenit’svalidatPbefore_S
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Transferfunction
§ ThetransferfunctioncapturestheeffectofastatementSonourclaim§ ClaimIn(atPbefore_S)➞ ClaimOut(atPafter_S)
§ (Alternatively)Thetransferfunctioncapturestheeffectofthestatementsinabasicblockonourclaim.
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Claim(forxandv)atPbefore_S
Claim(forxandv)atPafter_S
T:Transferfunction
Transferfunction(cont’d)
§ Transferfunctionforeachclaim(analysis)§ Here:wanttoseeifvariablexhasavaluev,withvaconstant
§ Transferfunction(forS)mapsinputclaimtooutputclaim
§ Here,thetransferfunctionallowsthreedifferentinputoroutputvaluesforourclaim:§ ⟙:(forTop)variablexisnotaconstant§ value:xhasthe(constant)valuevalue
§ Differentvariablesimplydifferentclaims
§ ⊥:(forBottom)wedon’tknow;statementisasfarasweknownotexecuted
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Transferfunction(cont’d)
§ Transferfunctionmustbeconservative.§ Donotmisleadthecompiler
§ Variablexhasconstantvaluevbuttransferfunctionreturns⟙.§ Acceptable
§ Variablexhasconstantvaluevandtransferfunctionreturnsv.§ Great
§ Variablexhasconstantvaluevbuttransferfunctionreturnskwithk≠v.§ NotOK
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notaccurateandnotsafe
