Domain: Software and its engineering
Sentence 1: ThisscenarioisdepictedinFigure1foranexampleappli­cation.Figure1(a)showsbreakdownoftheexecutionpro­fleoftheoriginal(unoptimized)codeintotwosegments: CPUandof-chipmemory.Aftertheoptimizations,theof­chipmemorypartis,hopefully,reducedsignifcantly.De­pendingonthetypesandoverheadofthecompileropti­mizationsused,theCPUportioncanincrease,decrease,or staythesame.Theexecutionprofleaftertheoptimization isillustratedinFigure1(b).Now,whenweapplysupply voltagescalingtotheCPUpart,weobtaintheproflein Figure1(c).Thesupplyvoltageisselectedsuchthatthe lengthoftheprofleinFigure1(c)isequaltothatofthe originalprofleinFigure1(a).Inmathematicalterms,let Xo=LoTobetheoriginalexecutiontime(intermsofcy­cles).Here,LoandToaretheoriginalnumberofexecution cyclesandclockcycletime,respectively.Assumefurther thatXi=LiToistheexecutiontimeafterthecompiler optimizations.Wecandecomposethisoptimizedtimeinto twoportionsXi=LicpuTo+Xm,whereLicpuisthenum­berofcyclesspentinCPUandandXmisthetimespentin of-chipmemoryaccesses.Obviously,iftheoptimizationis successful,wehaveLi<Lo.Wenowapplyvoltagescaling andobtainanewclockcycletime,Tr,fortheCPUsuchthat theexecutiontime,Xn=LicpuTr+Xm,becomesequalto Xo.
Sentence 2: thereareacoupleofissuesthatneedtobeclarifedbefore continuing.First,inorderforthisvoltagescalingstrategyto besuccessful,theenergyconsumptionoftheoptimizedcode withvoltagescalingshouldbelessthanitsenergyconsump­tionwithoutvoltagescaling.Otherwise,thereisnopointin usingthevoltagescaledversionasthecodebeforevoltage scalinghastypicallymuchbetterexecutiontime.Second,it isalsointerestingtostudytheimpactofthisenergyopti­mizationonenergy-delayproduct.LetXobeoriginalexecu­tiontimeoftheoriginalcodeandletXibetheoptimizedex­ecutiontimeifwedonotuseanyvoltagescaling.Theenergy consumptionoftheoriginalcodeEoisrelatedtothenewen­ergyconsumptionafteroptimizingthecodeandscalingthe supplyvoltage,En,byEn=EoVr 2VVo 2 .Now,byapplying dynamicvoltagescalingtotheoptimizedcode,wechange itsenergy-delayproductfromXiEitoXoEoVr 2VVo 2 ,where Eiistheenergyconsumptionoftheoptimizedcodebefore voltagereduction.WecantypicallyexpectthatEi<Eo(as thesecompileroptimizationsdecreasetheenergyconsumed inthememorysystemsignifcantly[26])andXi<Xowhich meansthatXiEi<XoEo.Consequently,inordertoget anenergy-delayimprovementusingourstaticvoltagescal­ingapproach,themagnitudeoftheratioVr 2VVo 2should besmallenoughtomakeadiference.whilethe analysisintheprevioussectionreducesdynamicenergycon­sumptionwithoutnegativelyimpactingexecutiontime,it doesnotguaranteethattheresultingcodehasanaccept­ableenergy-delayproduct.Thisisbecauseitispossible thatXiEi<XoEoVr 2VVo 2 maybetrueevenaftervoltage scaling;thatis,theenergy-delayproductoftheoptimized codebeforevoltagescalingmightbelowerthanthatafter voltagescaling.Analternativeobjectivethenistominimize theenergy-delayproduct,whichcanbedoneasfollows.Let theenergy-delayproductofagivencodebeproportionalto KCVo 2VoV(Vo;Vt)2 ,whereKCVo 2istheenergyconsump-tionandVoV(Vo;Vt)2istheclockcycletime.Tominimize thisvalue,wecantakethederivativeofthisexpressionwith respecttoVoandmakeitequalto0.Itcanbeshownthat thisgivesusaVovalueof3Vt.Whilethiscodemaynothave agoodperformanceasitisnotoptimized,wecanapplythe sameideatotheloop-transformed(optimized)codeaswell.
Relationship: reasoning