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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,ISFROM0TO27RTHEROOTSOFSARECONFINEDBY4R0SQLI4L2THESQSAREUSEDTOCALCULATETHERESIDUESFORTHEFINALSOLUTIONTHEUSEOFTHEDIFFERENCEEQUATIONSAPPROACHREDUCESTHEDIFFICULTPARTOFTHEPROBLEMTOSOLVING28INSTEADOFANINVOLVEDPROCEDUREOFDIAGONALIZINGANMBYMMATRIXTHUSTHECOMPUTERTIMEBECOMESEXTREMELYSHORTANDINEXPENSIVEFORMOFATHOUSANDORGREATER,ANDCALCULATIONRATHERTHENMEASUREMENTBECOMESMUCHMOREPRACTICALSLAVEMEMORIESANDDYNAMICSTORAGEALLOCATIONMVWILKESSUMMARYTHEUSEISDISCUSSEDOFAFASTCOREMEMORYOF,SAY,32000WORDSASASLAVETOASLOWERCOREMEMORYOF,SAY,ONEMILLIONWORDSINSUCHAWAYTHATINPRACTICALCASESTHEEFFECTIVEACCESSTIMEISNEARERTHATOFTHEFASTMEMORYTHANTHATOFTHESLOWMEMORYINTRODUCTIONINTHEHIERARCHICSTORAGESYSTEMSUSEDATPRESENT,COREMEMORIESAREBACKEDUPBYMAGNETICDRUMSORDISKSWHICHARE,INTHEIRTURN,BACKEDUPBYMAGNETICTAPEINTHESESYSTEMSITISNATURALANDEFFICIENTFORINFORMATIONTOBEMOVEDINANDOUTOFTHECOREMEMORYINBLOCKSTHESITUATIONISVERYDIFFERENT,HOWEVER,WHENAFASTCOREMEMORYISBACKEDUPBYALARGESLOWCOREMEMORY,SINCEBOTHMEMORIESARETRULYRANDOMACCESSANDTHEREISNOLATENCYTIMEPROBLEMTHETIMESPENTINTRANSFERRINGTOTHEFASTMEMORYWORDSOFAPROGRAMWHICHARENOTUSEDINASUBSEQUENTRUNNINGISSIMPLYWASTEDIWISHINTHISNOTETODRAWATTENTIONTOTHEUSEOFAFASTMEMORYASASLAVEMEMORYBYASLAVEMEMORYIMEANONEWHICHAUTOMATICALLYACCUMULATESTOITSELFWORDSTHATCOMEFROMASLOWERMAINMEMORY,ANDKEEPSTHEMAVAILABLEFORSUBSEQUENTUSEWITHOUTITBEINGNECESSARYFORTHEPENALTYOFMAINMEMORYACCESSTOBEINCURREDAGAINSINCETHESLAVEMEMORYCANONLYBEAFRACTIONOFTHESIZEOFTHEMAINMEMORY,WORDSCANNOTBEPRESERVEDINITINDEFINITELY,ANDTHEREMUSTBEWIREDINTOTHESYSTEMANALGORITHMBYWHICHTHEYAREPROGRESSIVELYOVERWRITTENINFAVORABLECIRCUMSTANCES,HOWEVER,AGOODPROPORTIONOFTHEWORDSWILLSURVIVELONGENOUGHTOBEUSEDONSUBSEQUENTOCCASIONSANDADISTINCTGAINOFSPEEDRESULTSTHEACTUALGAINDEPENDSONTHESTATISTICSOFTHEPARTICULARSITUATIONSLAVEMEMORIESHAVERECENTLYCOMEINTOPROMINENCEASAWAYOFREDUCINGINSTRUCTIONACCESSTIMEINANOTHERWISECONVENTIONALCOMPUTER2ASMALL,VERYHIGHSPEEDMEMORYOF,SAY,32WORDS,ACCUMULATESINSTRUCTIONSASTHEYARETAKENOUTOFTHEMAINMEMORYSINCEINSTRUCTIONSOFTENOCCURINSMALLLOOPSAQUITEAPPRECIABLESPEEDINGUPCANBEOBTAINEDONEMETHODOFDESIGNINGASLAVEMEMORYFORINSTRUCTIONSISASFOLLOWSSUPPOSETHATTHEMAINMEMORYHAS64KWORDSWHEREK1024AND,THEREFORE,16ADDRESSBITS,ANDTHATTHESLAVEMEMORYHAS32WORDSAND,THEREFORE,5ADDRESSBITSTHESLAVEMEMORYISCONSTRUCTEDWITHAWORDLENGTHEQUALTOTHATOFTHEMAINMEMORYPLUS11EXTRABITS,WHICHWILLBEREFERREDTOASTAGBITSANINSTRUCTIONEXTRACTEDFROMREGISTERROFTHEMAINMEMORYISCOPIEDINTOREGISTERRMOD32OFTHESLAVEMEMORYAND,ATTHESAMETIME,THE11MOSTMANUSCRIPTRECEIVEDNOVEMBER30,1964THEWORKREPORTEDINTHISNOTEWASSUPPORTEDINPARTBYPROJECTMAC,AMASSACHUSETTSINSTITUTEOFTECHNOLOGY,CAMBRIDGE,RESEARCHPROGRAM,SPONSOREDBYTHEADVANCEDRESEARCHPROJECTSAGENCY,DEPTOFDEFENSE,UNDEROFFICEOFNAVALRESEARCHCONTRACTNONONR410201THEAUTHORISWITHTHEUNIVERSITYMATHEMATICALLAB,CAMBRIDGE,ENGLAND1TAKAHASHI,S,HNISHINO,KYOSHIHIRO,ANDKFUCHI,SYSTEMDESIGNOFTHEETLMK6COMPUTERSINFORMATIONPROCESSING1962PROCIFIPCONGRESS62,AMSTERDAM,THENETHERLANDSNORTHHOLLANDPUBLISHINGCO,1963,P6902FERRANTICOMPUTINGSYSTEMS;ATLAS2,LONDONFERRANTILTD,1963SIGNIFICANTBITSOFRARECOPIEDINTOTHE11TAGBITSFOREXAMPLE,SUPPOSER10259,THATIS,3202519THEINSTRUCTIONFROMTHISREGISTERISCOPIEDINTOREGISTER19OFTHESLAVEANDTHENUMBER320ISCOPIEDINTOTHETAGBITSOFTHATREGISTERWHENEVERANINSTRUCTIONISREQUIRED,THESLAVEISFIRSTEXAMINEDTOSEEWHETHERITALREADYCONTAINSTHATINSTRUCTIONTHISISDONEBYACCESSINGTHEREGISTERTHATMIGHTCONTAINTHEINSTRUCTIONNAMELY,REGISTERRMOD32,ANDEXAMININGTHETAGBITSTOSEEWHETHERTHEYAREEQUALTOTHE11MOSTSIGNIFICANTDIGITSOFRIFTHEYARE,THEINSTRUCTIONISTAKENFROMTHESLAVE;OTHERWISE,ITISOBTAINEDFROMTHEMAINMEMORYANDACOPYLEFTINTHESLAVEIFTHESYSTEMISTOPRESERVEFULLFREEDOMFORTHEPROGRAMMERTOMODIFYINSTRUCTIONSINTHEACCUMULATOR,ITISNECESSARYTHATEVERYTIMEAWRITINGOPERATIONISTOTAKEPLACE,THESLAVESHALLBEEXAMINEDTOSEEWHETHERITCONTAINSTHEWORDABOUTTOBEUPDATEDIFITDOES,THENTHEWORDMUSTBEUPDATEDINTHESLAVEASWELLASINTHEMAINMEMORYLARGESLAVEMEMORYSOFARTHESLAVEPRINCIPLEHASBEENAPPLIEDTOVERYSMALLSUPERSPEEDMEMORIESASSOCIATEDWITHTHECONTROLOFACOMPUTERTHEREWOULD,HOWEVER,APPEARTOBEPOSSIBILITIESINTHEUSEOFANORMALSIZEDCOREMEMORYASASLAVETOALARGECOREMEMORY,ANDIWILLNOWDISCUSSVARIOUSWAYSINWHICHTHISMIGHTBEDONEISHALLBECONCERNEDPRIMARILYWITHACOMPUTERSYSTEMDESIGNEDFORONLINETIMESHARINGINWHICHALARGENUMBEROFUSERPROGRAMSAREHELDINAUXILIARYSTORAGEANDACTIVATED,INTURN,ACCORDINGTOASEQUENCEDETERMINEDBYASCHEDTULINGALGORITHMWHENACTIVATED,EACHPROGRAMRUNSUNTILITISEITHERCOMPLETEDORHELDUPBYANINPUT/OUTPUTWAIT,ORUNTILTHEPERIODOFTIMEALLOCATEDTOITBYTHESCHEDULINGALGORITHMISEXHAUSTEDANOTHERPROGRAMISTHENACTIVATEDSEECORBAT63CONSIDERACOMPUTERINWHICHAWORKINGMEMORYOF,SAY,32KAND1,USACCESSTIMEISBACKEDUPBYALARGECOREMEMORYOF,SAY,ONEMILLIONWORDSAND8,USACCESSTIMEINTHESIMPLESTSCHEMETOBEDESCRIBED,PROGRAMSARESPLITINTO32KWORDBLOCKS,EACHUSERMAKINGUSEOFONEORMOREBLOCKSFORHISPROGRAMTHELARGECOREMEMORYISPROVIDEDWITHABASEREGISTER,WHICHCONTAINSTHESTARTINGADDRESSOFTHE32KBLOCKCURRENTLYACTIVEWHATWEWISHTOAVOIDISTRANSFERRINGTHEWHOLEBLOCKTOTHEFASTCOREMEMORYEVERYTIMEITBECOMESACTIVE;THISWOULDBEWASTEFULSINCECHANCESAREONLYASMALLFRACTIONOFTHE32KWORDSWILLACTUALLYBEACCESSEDBEFORETHEBLOCKCEASESTOBEACTIVEIFTHEFASTCOREMEMORYISOPERATEDONTHESLAVEPRINCIPLE,NOWORDISCOPIEDINTOITUNTILTHATWORDHASACTUALLYBEENCALLEDFORBYTHEPROGRAMWHENTHISHAPPENS,THEWORDISAUTOMATICALLYCOPIEDBYTHEHARDWAREINTOTHEFASTMEMORY,ANDTHEFACTTHATCOPYINGHASTAKENPLACEISINDICATEDBYTHEFIRSTOFTWOTAGBITSBEINGCHANGEDFROMA0TOA1WHENANYREFERENCETOSTORAGETAKESPLACETHEFASTMEMORYISACCESSEDFIRST,4AND,IFTHEFIRSTTAGBITISA1,NOREFERENCEISMADETOTHELARGEMEMORY;THISISTRUEWHETHERREADINGORWRITINGISCALLEDFORIFAWORDINTHEFASTMEMORYISCHANGED,ASECONDTAGBITISCHANGEDFROM0TO1TWOTAGBITSAREALLTHATAREREQUIREDINTHISSYSTEMASTIMEGOESON,THEFASTMEMORYWILLACCUMULATEALLTHEWORDSOFTHEPROGRAMINACTIVEUSEWHENTHENUMBERINTHEBASEREGISTERISCHANGEDSOTHATANEWPROGRAMBECOMESACTIVEINTHEPLACEOFTHEONECURRENTLYACTIVEACHANGETHATISBROUGHTABOUTBYTHESUPERVISOR,ASCANOFTHEFASTMEMORYISINITIATEDEACHREGISTERISEXAMINEDINTURNAND,IFTHEFIRSTTAGBITISA0,NOACTIONISTAKENFORTHATREGISTERNOACTIONISSIMILARLYTAKENIFTHEFIRSTTAGBITISA1ANDTHESECONDTAGBITISA0IF,HOWEVER,BOTHTAGBITSAREIS,THEWORDINTHEREGISTERUNDEREXAMINATIONISCOPIEDINTOITSAPPROPRIATEPLACEINTHELARGEMEMORYMANYVARIANTSOFTHESIMPLESCHEMEAREPOSSIBLETHETAGBITSMAY,FOREXAMPLE,BESTOREDINASEPARATESUPERSPEEDMEMORYA3CORBAT6,FJPROC1962INTERNATLFEDERATIONOFINFORMATIONPROCESSINGCONGRESS,AMSTERDAM,THENETHERLANDSNORTHHOLLANDPUBLISHINGCO,1963,P7114IFTHEDESIGNOFTHELARGECOREMEMORYPERMITS,ACCESSTOITCANBEINITIATEDSIMULTANEOUSLYWITHACCESSTOTHEFASTMEMORY,ANDCANCELLEDIFITTURNSOUTNOTTOBEREQUIRED270APRILSHORTNOTES1024WORDMEMORY,EACHHAVING64BITS,WOULDBESUITABLE;SUCHAMEMORYCOULDBEMADEWITHANACCESSTIMEOFABOUT100NS,ANDWOULDENABLETHESCANNINGPROCESSTOBECOMPLETEDMORERAPIDLYSIMILARLY,ANUMBEROFBASEREGISTERSCOULDBEPROVIDEDANDTHEFASTCOREMEMORYDIVIDEDINTOSECTIONS,EACHSERVINGASASLAVETOASEPARATEPROGRAMBLOCKINTHEMAINMEMORYSUCHAPROVISIONWOULD,INPRINCIPLE,ENABLESHORTPROGRAMSBELONGINGTOANUMBEROFUSERSTOREMAININTHEFASTMEMORYWHILESOMEOTHERUSERWASACTIVE,BEINGDISPLACEDONLYWHENTHESPACETHEYOCCUPIEDWASREQUIREDFORSOMEOTHERPURPOSETHISWOULDPRESENTTHEDESIGNEROFTHESUPERVISORWITHPROBLEMSSIMILARTOTHOSEPRESENTEDBYANATLASTYPESYSTEMOFDYNAMICSTORAGEALLOCATION5ANALTERNATIVE,ANDPERHAPSMOREATTRACTIVE,SCHEMEWOULDBETORETAIN32KORWHATEVERTHESIZEOFTHEFASTMEMORYMAYBEASTHEBLOCKLENGTH,BUTTOARRANGETHATTHEFASTMEMORYACTSASASLAVETOMORETHANONEBLOCKINTHEMAINMEMORY,ITBEINGRECOGNIZEDTHATTHISWILLLEADTOSOMEOVERWRITINGOFINFORMATIONINTHESLAVE,BUTWILL,NEVERTHELESS,ONTHEAVERAGE,BEADVANTAGEOUSSUPPOSE,FOREXAMPLE,THATTHEREARESEVENBASEREGISTERS,EACHCONTAININGANADDRESSOFAREGISTERINTHEMAINMEMORYATWHICHAPROGRAMBLOCKSTARTSFOURTAGBITSARENECESSARY,THEFIRSTTHREECONTAININGEITHERZEROSORTHENUMBEROFONEOFTHEBASEREGISTERSTHEFOURTHTAGBITINDICATESWHETHERAWORDHASBEENALTEREDWHILEINTHESLAVEATANYGIVENTIME,ONEOFTHESEVENPROGRAMBLOCKSISACTIVEWHENEVERACCESSISREQUIREDTOAWORDINTHEMEMORY,THEHARDWARELOOKSTOSEEWHETHERTHATWORDISTOBEFOUNDINTHESLAVETHISISDONEBYREADINGTHEWORDINTHEAPPROPRIATEPLACEINTHESLAVEANDCOMPARINGTHEFIRST3TAGBITSWITHTHENUMBEROFTHEBASEREGISTERCORRESPONDINGTOTHEPROGRAMBLOCKTHENACTIVEIFTHEREISAGREEMENT,ANDIFAREADINGOPERATIONISTOBEPERFORMED,THEWORDFROMSKILBURN,T,DBGEDWARDS,MJLANIGAN,ANDFHSUMNER,ONELEVELSTORAGESYSTEM,IRETRANSONELECTRONICCOMPUTERS,VOL11,APR1962,PP223235THESLAVEISUSEDANDOPERATIONPROCEEDSIFTHETHREETAGBITSAREALLZERO,THEWORDISOBTAINEDFROMTHEMAINMEMORYANDACOPYPUTINTOTHESLAVEMEMORYFORFUTUREUSEIFTHETHREETAGBITSARENOTZEROBUTCORRESPONDTOANOTHERBASEREGISTER,THEFOURTHDIGITISEXAMINEDIFTHISISAZERO,ACTIONPROCEEDSASBEFORE,THEWORDINTHESLAVEBEINGOVERWRITTENBYTHEWORDFROMTHENEWPROGRAMBLOCKIF,HOWEVER,THEFOURTHBITISA1,INDICATINGTHATTHEWORDHASBEENALTEREDWHILEINTHESLAVE,THATWORDISCOPIEDBACKINTOITSPROPERPLACEINTHEMAINMEMORYBEFOREBEINGOVERWRITTENBYTHEWORDFROMTHENEWPROGRAMBLOCKINTHECASEOFAWRITINGOPERATIONTHESEQUENCEOFEVENTSISSIMILAR,EXCEPTTHATTHEFOURTHTAGBITISMADEINTOA1WHENAWORDINTHESLAVEISMODIFIEDTHUS,IFTHESEVENPROGRAMSBECOMEACTIVEINTURN,THEYMAYBESAIDTOSHARETHESLAVEBETWEENTHEMAND,IFEACHRUNSINSHORTBURSTS,THEREISAFAIRCHANCETHATONLYAFEWWORDSBELONGINGTOAPARTICULARPROGRAMBLOCKGETOVERWRITTENINTHESLAVEBEFORETHATPROGRAMBLOCKISACTIVATEDAGAINTHEREWILL,NORMALLY,BEMORETHANSEVENPROGRAMBLOCKSREADYTOTAKETHEIRTURNFORRUNNINGANDTHESUPERVISORWILL,FROMTIMETOTIME,CHANGETHEADDRESSINONEOFTHEBASEREGISTERSWHENTHISHAPPENS,ASCANOFTHESLAVEISINITIATED,ANDALLWORDSWHICHBELONGTOTHEPROGRAMBLOCKBEINGDISPLACEDANDWHICHHAVEA1INTHEFOURTHBITOFTHETAG,ARECOPIEDINTOTHEMAINMEMORYONTHEFACEOFIT,THESCHEMEJUSTOUTLINEDAPPEARSTOOFFERTHEBASISFORASATISFACTORYTWOLEVELCORESTORAGESYSTEMWITHOUTINVOLVINGTOOHIGHADEGREEOFCOMPLEXITYINTHEHARDWAREACKNOWLEDGMENTTHEAUTHORWISHESTOEXPRESSHISGRATITUDETOPROFRMFANO,DIRECTOROFPROJECTMAC,FORINVITINGHIMTOPARTICIPATEINTHEPROJECTHEISALSOGRATEFULTOHISCOLLEAGUESINCAMBRIDGE,ENGLAND,FORDISCUSSIONS,PARTICULARLYTODRDJWHEELERANDNEWISEMAN,WHODESIGNEDTHESLAVEMEMORYOFATLAS2GSCARROTFIRSTSUGGESTEDTHEIDEAOFASLAVEMEMORYTOTHEM1965271

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