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47-How to Make a Multiprocessor Computer That Correctly Executes Multiprocess Programs.pdf

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47-How to Make a Multiprocessor Computer That Correctly Executes Multiprocess Programs.pdf

IEEETRANSACTIONSONCOMPUTERS,VOLC28,NO9,SEPTEMBER1979REFERENCES1CBLACK,CESUNDBERG,ANDWKSWALKER,DEVELOPMENTOFASPACEBORNEMEMORYWITHASINGLEERRORANDERASURECORRECTIONSCHEME,INCONFREC,1977FAULTTOLERANTCOMPUTINGSYMP,FTCS7,JUNE1977,PP50552CBLACKETAL,HIGHLYRELIABLESEMICONDUCTORMEMORYFORTHEONBOARDCOMPUTER,FINALREPESTECCONTR2528/75/HP,BRITISHAIRCRAFTCORP,BRISTOL,ENGLAND3RWLUCKY,JSALZ,ANDEJWELDON,JR,PRINCIPLESOFDATACOMMUNICATIONNEWYORKMCGRAWHILL,19684WWPETERSONANDEJWELDON,JR,ERRORCORRECTINGCODES,2NDEDCAMBRIDGE,MAMITPRESS,19725MYHSIAO,ACLASSOFOPTIMALMINIMUMODDWEIGHTCOLUMNSEC/DEDCODES,IBMJRESDEVELOP,PP395401,JULY19706GLONGO,ALGEBRAICCODINGANDCOMBINATORICSATUTORIALSURVEY,NATOADVANCEDSTUDYINSTITUTE,DARLINGTON,ENGLAND,AUG820,1977,CONFREC,SIJTHOFFNOORDHOFF,1978,SERIESE,NO25,PP1511697ERBERLEKAMP,ALGEBRAICCODINGTHEORYNEWYORKMCGRAWHILL,19688RPCAPECE,MEMORYRICHMINISGETAGGRESSIVE,ELECTRONICS,PP6970,AUG18,19779HJHELGERTANDRDSTINAFF,MINIMUMDISTANCEBOUNDSFORBINARYLINEARCODES,IEEETRANSINFORMATIONTHEORY,VOLIT19,PP344356,MAY197310CESUNDBERG,SOMETRANSPARENTSHORTENEDCODESFORSEMICONDUCTORMEMORIES,TELECOMMUNICATIONTHEORY,UNIVOFLUND,LUND,SWEDEN,TECHREPTR91,SEPT197711ERASURESANDERRORSDECODINGFORSEMICONDUCTORMEMORIES,IEEETRANSCOMPUT,VOLC27,PP696705,AUG197812WCCARTERANDCEMCCARTHY,IMPLEMENTATIONOFANEXPERIMENTALFAULTTOLERANTMEMORYSYSTEM,IEEETRANSCOMPUT,VOLC25,PP557568,JUNE1976OFEACHINDIVIDUALPROCESSORDOESNOTGUARANTEETHATTHEMULTIPROCESSORCOMPUTERISSEQUENTIALLYCONSISTENTINTHISBRIEFNOTE,WEDESCRIBEAMETHODOFINTERCONNECTINGSEQUENTIALPROCESSORSWITHMEMORYMODULESTHATINSURESTHESEQUENTIALCONSISTENCYOFTHERESULTINGMULTIPROCESSORWEASSUMETHATTHECOMPUTERCONSISTSOFACOLLECTIONOFPROCESSORSANDMEMORYMODULES,ANDTHATTHEPROCESSORSCOMMUNICATEWITHONEANOTHERONLYTHROUGHTHEMEMORYMODULESANYSPECIALCOMMUNICATIONREGISTERSMAYBEREGARDEDASSEPARATEMEMORYMODULESTHEONLYPROCESSOROPERATIONSTHATCONCERNUSARETHEOPERATIONSOFSENDINGFETCHANDSTOREREQUESTSTOMEMORYMODULESWEASSUMETHATEACHPROCESSORISSUESASEQUENCEOFSUCHREQUESTSITMUSTSOMETIMESWAITFORREQUESTSTOBEEXECUTED,BUTTHATDOESNOTCONCERNUSWEILLUSTRATETHEPROBLEMBYCONSIDERINGASIMPLETWOPROCESSMUTUALEXCLUSIONPROTOCOLEACHPROCESSCONTAINSACRITICALSECTION,ANDTHEPURPOSEOFTHEPROTOCOLISTOINSURETHATONLYONEPROCESSMAYBEEXECUTINGITSCRITICALSECTIONATANYTIMETHEPROTOCOLISASFOLLOWSPROCESS1IFB0THENCRITICALSECTION;ELSEFIHOWTOMAKEAMULTIPROCESSORCOMPUTERTHATCORRECTLYEXECUTESMULTIPROCESSPROGRANMLESLIELAMPORTABSTRACTMANYLARGESEQUENTIALCOMPUTERSEXECUTEOPERATIONSINADIFFERENTORDERTHANISSPECIFIEDBYTHEPROGRAMACORRECTEXECUTIONISACHIEVEDIFTHERESULTSPRODUCEDARETHESAMEASWOULDBEPRODUCEDBYEXECUTINGTHEPROGRAMSTEPSINORDERFORAMULTIPROCESSORCOMPUTER,SUCHACORRECTEXECUTIONBYEACHPROCESSORDOESNOTGUARANTEETHECORRECTEXECUTIONOFTHEENTIREPROGRAMADDITIONALCONDITIONSAREGIVENWHICHDOGUARANTEETHATACOMPUTERCORRECTLYEXECUTESMULTIPROCESSPROGRAMSINDEXTERMSCOMPUTERDESIGN,CONCURRENTCOMPUTING,HARDWARECORRECTNESS,MULTIPROCESSING,PARALLELPROCESSINGAHIGHSPEEDPROCESSORMAYEXECUTEOPERATIONSINADIFFERENTORDERTHANISSPECIFIEDBYTHEPROGRAMTHECORRECTNESSOFTHEEXECUTIONISGUARANTEEDIFTHEPROCESSORSATISFIESTHEFOLLOWINGCONDITIONTHERESULTOFANEXECUTIONISTHESAMEASIFTHEOPERATIONSHADBEENEXECUTEDINTHEORDERSPECIFIEDBYTHEPROGRAMAPROCESSORSATISFYINGTHISCONDITIONWILLBECALLEDSEQUENTIALCONSIDERACOMPUTERCOMPOSEDOFSEVERALSUCHPROCESSORSACCESSINGACOMMONMEMORYTHECUSTOMARYAPPROACHTODESIGNINGANDPROVINGTHECORRECTNESSOFMULTIPROCESSALGORITHMS13FORSUCHACOMPUTERASSUMESTHATTHEFOLLOWINGCONDITIONISSATISFIEDTHERESULTOFANYEXECUTIONISTHESAMEASIFTHEOPERATIONSOFALLTHEPROCESSORSWEREEXECUTEDINSOMESEQUENTIALORDER,ANDTHEOPERATIONSOFEACHINDIVIDUALPROCESSORAPPEARINTHISSEQUENCEINTHEORDERSPECIFIEDBYITSPROGRAMAMULTIPROCESSORSATISFYINGTHISCONDITIONWILLBECALLEDSEQUENTIALLYCONSISTENTTHESEQUENTIALITYMANUSCRIPTRECEIVEDSEPTEMBER28,1977;REVISEDMAY8,1979THEAUTHORISWITHTHECOMPUTERSCIENCELABORATORY,SRIINTERNATIONAL,MERLSPARK,CA94025PROCESS2B1;IFA0THENCRITICALSECTION;B0ELSEFITHEELSECLAUSESCONTAINSOMEMECHANISMFORGUARANTEEINGEVENTUALACCESSTOTHECRITICALSECTION,BUTTHATISIRRELEVANTTOTHEDISCUSSIONITISEASYTOPROVETHATTHISPROTOCOLGUARANTEESMUTUALLYEXCLUSIVEACCESSTOTHECRITICALSECTIONSDEVISINGAPROOFPROVIDESANICEEXERCISEINUSINGTHEASSERTIONALTECHNIQUESOF2AND3,ANDISLEFTTOTHEREADERHENCE,WHENTHISTWOPROCESSPROGRAMISEXECUTEDBYASEQUENTIALLYCONSISTENTMULTIPROCESSORCOMPUTER,THETWOPROCESSORSCANNOTBOTHBEEXECUTINGTHEIRCRITICALSECTIONSATTHESAMETIMEWEFIRSTOBSERVETHATASEQUENTIALPROCESSORCOULDEXECUTETHEB1ANDFETCHBOPERATIONSOFPROCESS1INEITHERORDERWHENPROCESSLSPROGRAMISCONSIDEREDBYITSELF,ITDOESNOTMATTERINWHICHORDERTHESETWOOPERATIONSAREPERFORMEDHOWEVER,ITISEASYTOSEETHATEXECUTINGTHEFETCHBOPERATIONFIRSTCANLEADTOANERRORBOTHPROCESSESCOULDTHENEXECUTETHEIRCRITICALSECTIONSATTHESAMETIMETHISIMMEDIATELYSUGGESTSOURFIRSTREQUIREMENTFORAMULTIPROCESSORCOMPUTERREQUIREMENTRLEACHPROCESSORISSUESMEMORYREQUESTSINTHEORDERSPECIFIEDBYITSPROGRAMSATISFYINGREQUIREMENTRIISCOMPLICATEDBYTHEFACTTHATSTORINGAVALUEISPOSSIBLEONLYAFTERTHEVALUEHASBEENCOMPUTEDAPROCESSORWILLOFTENBEREADYTOISSUEAMEMORYFETCHREQUESTBEFOREITKNOWSTHEVALUETOBESTOREDBYAPRECEDINGSTOREREQUESTTOMINIMIZEWAITING,THEPROCESSORCANISSUETHESTOREREQUESTTOTHEMEMORYMODULEWITHOUTSPECIFYINGTHEVALUETOBESTOREDOFCOURSE,THESTOREREQUESTCANNOTACTUALLYBEEXECUTEDBYTHEMEMORYMODULE,UNTILITRECEIVESTHEVALUETOBESTORED00189340/79/090006900075C1979IEEE690IEEETRANSACTIONSONCOMPUTERS,VOLC28,NO9,SEPTEMBER1979REQUIREMENTRIISNOTSUFFICIENTTOGUARANTEECORRECTEXECUTIONTOSEETHIS,SUPPOSETHATEACHMEMORYMODULEHASSEVERALPORTS,ANDEACHPORTSERVICESONEPROCESSORORI/OCHANNELLETTHEVALUESOFAANDBBESTOREDINSEPARATEMEMORYMODULES,ANDCONSIDERTHEFOLLOWINGSEQUENCEOFEVENTS1PROCESSOR1SENDSTHEA1REQUESTTOITSPORTINMEMORYMODULE1THEMODULEISCURRENTLYBUSYEXECUTINGANOPERATIONFORSOMEOTHERPROCESSORORI/OCHANNEL2PROCESSOR1SENDSTHEFETCHBREQUESTTOITSPORTINMEMORYMODULE2THEMODULEISFREE,ANDEXECUTIONISBEGUN3PROCESSOR2SENDSITSB1REQUESTTOMEMORYMODULE2THISREQUESTWILLBEEXECUTEDAFTERPROCESSORLSFETCHBREQUESTISCOMPLETED4PROCESSOR2SENDSITSFETCHAREQUESTTOITSPORTINMEMORYMODULE1THEMODULEISSTILLBUSYTHEREARENOWTWOOPERATIONSWAITINGTOBEPERFORMEDBYMEMORYMODULE1IFPROCESSOR2SFETCHAOPERATIONISPERFORMEDFIRST,THENBOTHPROCESSESCANENTERTHEIRCRITICALSECTIONSATTHESAMETIME,ANDTHEPROTOCOLFAILSTHISCOULDHAPPENIFTHEMEMORYMODULEUSESAROUNDROBINSCHEDULINGDISCIPLINEINSERVICINGITSPORTSINTHISSITUATION,ANERROROCCURSONLYIFTHETWOREQUESTSTOMEMORYMODULE1ARENOTEXECUTEDINTHESAMEORDERINWHICHTHEYWERERECEIVEDTHISSUGGESTSTHEFOLLOWINGREQUIREMENTREQUIREMENTR2MEMORYREQUESTSFROMALLPROCESSORSISSUEDTOANINDIVIDUALMEMORYMODULEARESERVICEDFROMASINGLEFIFOQUEUEISSUINGAMEMORYREQUESTCONSISTSOFENTERINGTHEREQUESTONTHISQUEUECONDITIONRIIMPLIESTHATAPROCESSORMAYNOTISSUEANYFURTHERMEMORYREQUESTSUNTILAFTERITSCURRENTREQUESTHASBEENENTEREDONTHEQUEUEHENCE,ITMUSTWAITIFTHEQUEUEISFULLIFTWOORMOREPROCESSORSARETRYINGTOENTERREQUESTSINTHEQUEUEATTHESAMETIME,THENITDOESNOTMATTERINWHICHORDERTHEYARESERVICEDNOTEIFAFETCHREQUESTSTHECONTENTSOFAMEMORYLOCATIONFORWHICHTHEREISALREADYAWRITEREQUESTONTHEQUEUE,THENTHEFETCHNEEDNOTBEENTEREDONTHEQUEUEITMAYSIMPLYRETURNTHEVALUEFROMTHELASTSUCHWRITEREQUESTONTHEQUEUEOREQUIREMENTSRIANDR2INSURETHATIFTHEINDIVIDUALPROCESSORSARESEQUENTIAL,THENTHEENTIREMULTIPROCESSORCOMPUTERISSEQUENTIALLYCONSISTENTTODEMONSTRATETHIS,ONEFIRSTINTRODUCESARELATIONONMEMORYREQUESTSASFOLLOWSDEFINEABIFANDONLYIF1AANDBAREISSUEDBYTHESAMEPROCESSORANDAISISSUEDBEFOREB,OR2AANDBAREISSUEDTOTHESAMEMEMORYMODULE,ANDAISENTEREDINTHEQUEUEBEFOREBANDISTHUSEXECUTEDBEFOREBITISEASYTOSEETHATRIANDR2IMPLYTHATISAPARTIALORDERINGONTHESETOFMEMORYREQUESTSUSINGTHESEQUENTIALITYOFEACHPROCESSOR,ONECANTHENPROVETHEFOLLOWINGRESULTEACHFETCHANDSTOREOPERATIONFETCHESORSTORESTHESAMEVALUEASIFALLTHEOPERATIONSWEREEXECUTEDSEQUENTIALLYINANYORDERSUCHTHATABIMPLIESTHATAISEXECUTEDBEFOREBTHISINTURNPROVESTHESEQUENTIALCONSISTENCYOFTHEMULTIPROCESSORCOMPUTERREQUIREMENTR2STATESTHATAMEMORYMODULESREQUESTQUEUEMUSTBESERVICEDINAFIFOORDERTHISIMPLIESTHATTHEMEMORYMODULEMUSTREMAINIDLEIFTHEREQUESTATTHEHEADOFITSQUEUEISASTOREREQUESTFORWHICHTHEVALUETOBESTOREDHASNOTYETBEENRECEIVEDCONDITIONR2CANBEWEAKENEDTOALLOWTHEMEMORYMODULETOSERVICEOTHERREQUESTSINTHISSITUATIONWENEEDONLYREQUIRETHATALLREQUESTSTOTHESAMEMEMORYCELLBESERVICEDINTHEORDERTHATTHEYAPPEARINTHEQUEUEREQUESTSTODIFFERENTMEMORYCELLSMAYBESERVICEDOUTOFORDERSEQUENTIALCONSISTENCYISPRESERVEDBECAUSESUCHASERVICEPOLICYISLOGICALLYEQUIVALENTTOCONSIDERINGEACHMEMORYCELLTOBEASEPARATEMEMORYMODULEWITHITSOWNREQUESTQUEUETHEFACTTHATTHESEMODULESMAYSHARESOMEHARDWAREAFFECTSTHERATEATWHICHTHEYSERVICEREQUESTSANDTHECAPACITYOFTHEIRQUEUES,BUTITDOESNOTAFFECTTHELOGICALPROPERTYOFSEQUENTIALCONSISTENCYTHEREQUIREMENTSNEEDEDTOGUARANTEESEQUENTIALCONSISTENCYRULEOUTSOMETECHNIQUESWHICHCANBEUSEDTOSPEEDUPINDIVIDUALSEQUENTIALPROCESSORSFORSOMEAPPLICATIONS,ACHIEVINGSEQUENTIALCONSISTENCYMAYNOTBEWORTHTHEPRICEOFSLOWINGDOWNTHEPROCESSORSINTHISCASE,ONEMUSTBEAWARETHATCONVENTIONALMETHODSFORDESIGNINGMULTIPROCESSALGORITHMSCANNOTBERELIEDUPONTOPRODUCECORRECTLYEXECUTINGPROGRAMSPROTOCOLSFORSYNCHRONIZINGTHEPROCESSORSMUSTBEDESIGNEDATTHELOWESTLEVELOFTHEMACHINEINSTRUCTIONCODE,ANDVERIFYINGTHEIRCORRECTNESSBECOMESAMONUMENTALTASKREFERENCES1EWDIJKSTRA,HIERARCHICALORDERINGOFSEQUENTIALPROCESSES,ACTAINFORMATICA,VOL1,PP115138,19712LLAMPORT,PROVINGTHECORRECTNESSOFMULTIPROCESSPROGRAMS,IEEETRANSSOFTWAREENG,VOLSE3,PP125143,MAR19773SOWICKIANDDGRIES,VERIFYINGPROPERTIESOFPARALLELPROGRAMSANAXIOMATICAPPROACH,COMMUNASSOCCOMPUTMACH,VOL19,PP279285,MAY1976COMMENTSONANAPPROACHTOHIGHLYINTEGRATEDCOMPUTERMAINTAINEDCELLULARARRAYSVISHWANIDAGRAWALABSTRACTTHEABOVEPAPERDESCRIBESMACHINESCONSTRUCTEDONFAULTYLOGICARRAYSTHESEMACHINESUSESOMEORALLOFTHEGOODCELLSTHATFORMACONNECTIVECLUSTERITISPOINTEDOUTHERETHATWHENTHEFAULTYCELLSARERANDOMLYDISTRIBUTEDOVERTHEARRAY,THEPROPAGATIONOFAFREELYEXPANDINGSIGNAL,WHICHMUSTAVOIDTHEFAULTYCELLS,ISAPERCOLATIONPROCESSTHEPERCOLATIONPROCESSDETERMINESTHELIMITTOTHESIZEOFAMACHINEEMBEDDEDINAFAULTYARRAYSOMEUSEFULCHARACTERISTICSOFTHISPROCESSAREDISCUSSEDINDEXTERMSCELLULARARRAYS,FAULTSINLOGICARRAYS,PERCOLATIONPROCESS,PROGRAMMABLELOGIC,RANDOMPROCESSESMANNING,INARECENTPAPER,HASDESCRIBEDTHEEMBEDDEDMACHINESWHICHARECONFIGUREDINALOG

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