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29-Slave Memories and Dynamic Storage Allocation.pdf

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29-Slave Memories and Dynamic Storage Allocation.pdf

IEEETRANSACTIONSONELECTRONICCOMPUTERSTherangeof,isfrom0to27r.Therootsofsareconfinedby4R0SqLI4L2Thesqsareusedtocalculatetheresiduesforthefinalsolution.Theuseofthedifferenceequationsapproachreducesthedifficultpartoftheproblemtosolving28insteadofaninvolvedprocedureofdiagonalizinganmbymmatrix.Thusthecomputertimebecomesextremelyshortandinexpensiveformofathousandorgreater,andcalculationratherthenmeasurementbecomesmuchmorepractical.SlaveMemoriesandDynamicStorageAllocationM.V.WILKESSUMMARYTheuseisdiscussedofafastcorememoryof,say,32000wordsasaslavetoaslowercorememoryof,say,onemillionwordsinsuchawaythatinpracticalcasestheeffectiveaccesstimeisnearerthatofthefastmemorythanthatoftheslowmemory.INTRODUCTIONInthehierarchicstoragesystemsusedatpresent,corememoriesarebackedupbymagneticdrumsordiskswhichare,intheirturn,backedupbymagnetictape.Inthesesystemsitisnaturalandefficientforinformationtobemovedinandoutofthecorememoryinblocks.Thesituationisverydifferent,however,whenafastcorememoryisbackedupbyalargeslowcorememory,sincebothmemoriesaretrulyrandomaccessandthereisnolatencytimeproblem.Thetimespentintransferringtothefastmemorywordsofaprogramwhicharenotusedinasubsequentrunningissimplywasted.Iwishinthisnotetodrawattentiontotheuseofafastmemoryasaslavememory.ByaslavememoryImeanonewhichautomaticallyaccumulatestoitselfwordsthatcomefromaslowermainmemory,andkeepsthemavailableforsubsequentusewithoutitbeingnecessaryforthepenaltyofmainmemoryaccesstobeincurredagain.Sincetheslavememorycanonlybeafractionofthesizeofthemainmemory,wordscannotbepreservedinitindefinitely,andtheremustbewiredintothesystemanalgorithmbywhichtheyareprogressivelyoverwritten.Infavorablecircumstances,however,agoodproportionofthewordswillsurvivelongenoughtobeusedonsubsequentoccasionsandadistinctgainofspeedresults.Theactualgaindependsonthestatisticsoftheparticularsituation.Slavememorieshaverecentlycomeintoprominenceasawayofreducinginstructionaccesstimeinanotherwiseconventionalcomputer.2Asmall,veryhighspeedmemoryof,say,32words,accumulatesinstructionsastheyaretakenoutofthemainmemory.Sinceinstructionsoftenoccurinsmallloopsaquiteappreciablespeedingupcanbeobtained.Onemethodofdesigningaslavememoryforinstructionsisasfollows.Supposethatthemainmemoryhas64KwordswhereK1024and,therefore,16addressbits,andthattheslavememoryhas32wordsand,therefore,5addressbits.Theslavememoryisconstructedwithawordlengthequaltothatofthemainmemoryplus11extrabits,whichwillbereferredtoastagbits.Aninstructionextractedfromregisterrofthemainmemoryiscopiedintoregisterrmod32oftheslavememoryand,atthesametime,the11mostManuscriptreceivedNovember30,1964.TheworkreportedinthisnotewassupportedinpartbyProjectMAC,aMassachusettsInstituteofTechnology,Cambridge,researchprogram,sponsoredbytheAdvancedResearchProjectsAgency,Dept.ofDefense,underOfficeofNavalResearchContractNo.Nonr410201.TheauthoriswiththeUniversityMathematicalLab.,Cambridge,England.1Takahashi,S.,H.Nishino,K.Yoshihiro,andK.Fuchi,SystemdesignoftheETLMk6computers.InformationProcessing1962Proc.IFIPCongress62,Amsterdam,TheNetherlandsNorthHollandPublishingCo.,1963,p690.2FerrantiComputingSystemsAtlas2,LondonFerrantiLtd.,1963.significantbitsofrarecopiedintothe11tagbits.Forexample,supposer10259,thatis,320.2519.Theinstructionfromthisregisteriscopiedintoregister19oftheslaveandthenumber320iscopiedintothetagbitsofthatregister.Wheneveraninstructionisrequired,theslaveisfirstexaminedtoseewhetheritalreadycontainsthatinstruction.Thisisdonebyaccessingtheregisterthatmightcontaintheinstructionnamely,registerrmod32,andexaminingthetagbitstoseewhethertheyareequaltothe11mostsignificantdigitsofr.Iftheyare,theinstructionistakenfromtheslaveotherwise,itisobtainedfromthemainmemoryandacopyleftintheslave.Ifthesystemistopreservefullfreedomfortheprogrammertomodifyinstructionsintheaccumulator,itisnecessarythateverytimeawritingoperationistotakeplace,theslaveshallbeexaminedtoseewhetheritcontainsthewordabouttobeupdated.Ifitdoes,thenthewordmustbeupdatedintheslaveaswellasinthemainmemory.LARGESLAVEMEMORYSofartheslaveprinciplehasbeenappliedtoverysmallsuperspeedmemoriesassociatedwiththecontrolofacomputer.Therewould,however,appeartobepossibilitiesintheuseofanormalsizedcorememoryasaslavetoalargecorememory,andIwillnowdiscussvariouswaysinwhichthismightbedone.Ishallbeconcernedprimarilywithacomputersystemdesignedforonlinetimesharinginwhichalargenumberofuserprogramsareheldinauxiliarystorageandactivated,inturn,accordingtoasequencedeterminedbyaschedtulingalgorithm.Whenactivated,eachprogramrunsuntilitiseithercompletedorheldupbyaninput/outputwait,oruntiltheperiodoftimeallocatedtoitbytheschedulingalgorithmisexhausted.Anotherprogramisthenactivated.SeeCorbat6.3Consideracomputerinwhichaworkingmemoryof,say,32Kand1,usaccesstimeisbackedupbyalargecorememoryof,say,onemillionwordsand8,usaccesstime.Inthesimplestschemetobedescribed,programsaresplitinto32Kwordblocks,eachusermakinguseofoneormoreblocksforhisprogram.Thelargecorememoryisprovidedwithabaseregister,whichcontainsthestartingaddressofthe32Kblockcurrentlyactive.Whatwewishtoavoidistransferringthewholeblocktothefastcorememoryeverytimeitbecomesactivethiswouldbewastefulsincechancesareonlyasmallfractionofthe32Kwordswillactuallybeaccessedbeforetheblockceasestobeactive.Ifthefastcorememoryisoperatedontheslaveprinciple,nowordiscopiedintoituntilthatwordhasactuallybeencalledforbytheprogram.Whenthishappens,thewordisautomaticallycopiedbythehardwareintothefastmemory,andthefactthatcopyinghastakenplaceisindicatedbythefirstoftwotagbitsbeingchangedfroma0toa1.Whenanyreferencetostoragetakesplacethefastmemoryisaccessedfirst,4and,ifthefirsttagbitisa1,noreferenceismadetothelargememorythisistruewhetherreadingorwritingiscalledfor.Ifawordinthefastmemoryischanged,asecondtagbitischangedfrom0to1.Twotagbitsareallthatarerequiredinthissystem.Astimegoeson,thefastmemorywillaccumulateallthewordsoftheprograminactiveuse.Whenthenumberinthebaseregisterischangedsothatanewprogrambecomesactiveintheplaceoftheonecurrentlyactiveachangethatisbroughtaboutbythesupervisor,ascanofthefastmemoryisinitiated.Eachregisterisexaminedinturnand,ifthefirsttagbitisa0,noactionistakenforthatregister.Noactionissimilarlytakenifthefirsttagbitisa1andthesecondtagbitisa0.If,however,bothtagbitsareIs,thewordintheregisterunderexaminationiscopiedintoitsappropriateplaceinthelargememory.Manyvariantsofthesimpleschemearepossible.Thetagbitsmay,forexample,bestoredinaseparatesuperspeedmemory.A3Corbat6,F.J.Proc.1962InternatlFederationofInformationProcessingCongress,Amsterdam,TheNetherlandsNorthHollandPublishingCo.,1963,p711.4Ifthedesignofthelargecorememorypermits,accesstoitcanbeinitiatedsimultaneouslywithaccesstothefastmemory,andcancelledifitturnsoutnottoberequired.270AprilShortNotes1024wordmemory,eachhaving64bits,wouldbesuitablesuchamemorycouldbemadewithanaccesstimeofabout100ns,andwouldenablethescanningprocesstobecompletedmorerapidly.Similarly,anumberofbaseregisterscouldbeprovidedandthefastcorememorydividedintosections,eachservingasaslavetoaseparateprogramblockinthemainmemory.Suchaprovisionwould,inprinciple,enableshortprogramsbelongingtoanumberofuserstoremaininthefastmemorywhilesomeotheruserwasactive,beingdisplacedonlywhenthespacetheyoccupiedwasrequiredforsomeotherpurpose.ThiswouldpresentthedesignerofthesupervisorwithproblemssimilartothosepresentedbyanAtlastypesystemofdynamicstorageallocation.5Analternative,andperhapsmoreattractive,schemewouldbetoretain32Korwhateverthesizeofthefastmemorymaybeastheblocklength,buttoarrangethatthefastmemoryactsasaslavetomorethanoneblockinthemainmemory,itbeingrecognizedthatthiswillleadtosomeoverwritingofinformationintheslave,butwill,nevertheless,ontheaverage,beadvantageous.Suppose,forexample,thattherearesevenbaseregisters,eachcontaininganaddressofaregisterinthemainmemoryatwhichaprogramblockstarts.Fourtagbitsarenecessary,thefirstthreecontainingeitherzerosorthenumberofoneofthebaseregisters.Thefourthtagbitindicateswhetherawordhasbeenalteredwhileintheslave.Atanygiventime,oneofthesevenprogramblocksisactive.Wheneveraccessisrequiredtoawordinthememory,thehardwarelookstoseewhetherthatwordistobefoundintheslave.Thisisdonebyreadingthewordintheappropriateplaceintheslaveandcomparingthefirst3tagbitswiththenumberofthebaseregistercorrespondingtotheprogramblockthenactive.Ifthereisagreement,andifareadingoperationistobeperformed,thewordfromsKilburn,T.,D.B.G.Edwards,M.J.Lanigan,andF.H.Sumner,Onelevelstoragesystem,IRETrans.onElectronicComputers,vol11,Apr1962,pp223235.theslaveisusedandoperationproceeds.Ifthethreetagbitsareallzero,thewordisobtainedfromthemainmemoryandacopyputintotheslavememoryforfutureuse.Ifthethreetagbitsarenotzerobutcorrespondtoanotherbaseregister,thefourthdigitisexamined.Ifthisisazero,actionproceedsasbefore,thewordintheslavebeingoverwrittenbythewordfromthenewprogramblock.If,however,thefourthbitisa1,indicatingthatthewordhasbeenalteredwhileintheslave,thatwordiscopiedbackintoitsproperplaceinthemainmemorybeforebeingoverwrittenbythewordfromthenewprogramblock.Inthecaseofawritingoperationthesequenceofeventsissimilar,exceptthatthefourthtagbitismadeintoa1whenawordintheslaveismodified.Thus,ifthesevenprogramsbecomeactiveinturn,theymaybesaidtosharetheslavebetweenthemand,ifeachrunsinshortbursts,thereisafairchancethatonlyafewwordsbelongingtoaparticularprogramblockgetoverwrittenintheslavebeforethatprogramblockisactivatedagain.Therewill,normally,bemorethansevenprogramblocksreadytotaketheirturnforrunningandthesupervisorwill,fromtimetotime,changetheaddressinoneofthebaseregisters.Whenthishappens,ascanoftheslaveisinitiated,andallwordswhichbelongtotheprogramblockbeingdisplacedandwhichhavea1inthefourthbitofthetag,arecopiedintothemainmemory.Onthefaceofit,theschemejustoutlinedappearstoofferthebasisforasatisfactorytwolevelcorestoragesystemwithoutinvolvingtoohighadegreeofcomplexityinthehardware.ACKNOWLEDGMENTTheauthorwishestoexpresshisgratitudetoProf.R.M.Fano,DirectorofProjectMAC,forinvitinghimtoparticipateintheproject.HeisalsogratefultohiscolleaguesinCambridge,England,fordiscussions,particularlytoDr.D.J.WheelerandN.E.Wiseman,whodesignedtheslavememoryofAtlas2.G.Scarrotfirstsuggestedtheideaofaslavememorytothem.1965271

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