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PrinciplesofSoftwareConstruction: Objects,Design,andConcurrencyPart3:ConcurrencyIntroductiontoconcurrency,part4InthetrenchesofparallelismJoshBloch CharlieGarrod

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Administrivia

•  Homework5BestFrameworksavailabletoday•  Homework5cdueTuesday,11:59p.m.

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KeyconceptsfromTuesday

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Policiesforthreadsafety

1.   Thread-confinedstate–mutatebutdon’tshare2.   Sharedread-onlystate–sharebutdon’tmutate3.   Sharedthread-safe–objectsynchronizesitselfinternally4.   Sharedguarded–clientsynchronizesobject(s)externally

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3.Sharedthread-safestate

•  Thread-safeobjectsthatperforminternalsynchronization•  Youcanbuildyourown,butnotforthefaintofheart•  You’rebetteroffusingonesfromjava.util.concurrent•  j.u.calsoprovidesskeletalimplementations

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Adviceforbuildingthread-safeobjects

•  Doaslittleaspossibleinsynchronizedregion:getin,getout–  Obtainlock–  Examineshareddata–  Transformasnecessary–  Dropthelock

•  Ifyoumustdosomethingslow,moveitoutsidethesynchronizedregion

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Thefork-joinpattern

if(myportionoftheworkissmall)dotheworkdirectlyelsesplitmyworkintopiecesrecursivelyprocessthepieces

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Today

•  Concurrencyinpractice:Inthetrenchesofparallelism

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Concurrencyatthelanguagelevel

•  Consider:Collection<Integer>collection=…;intsum=0;for(inti:collection){sum+=i;}

•  Inpython:collection=…sum=0foritemincollection:sum+=item

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ParallelquicksortinNesl

functionquicksort(a)=if(#a<2)thenaelseletpivot=a[#a/2];lesser={eina|e<pivot}; equal={eina|e==pivot};greater={eina|e>pivot};result={quicksort(v):vin[lesser,greater]};inresult[0]++equal++result[1];•  Operationsin{}occurinparallel•  210-esquequestions:Whatistotalwork?Whatisspan?

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Prefixsums(a.k.a.inclusivescan,a.k.a.scan)

•  Goal:givenarrayx[0…n-1],computearrayofthesumofeachprefixofx[sum(x[0…0]),sum(x[0…1]),sum(x[0…2]),…sum(x[0…n-1])]

•  e.g.,x = [13, 9, -4, 19, -6, 2, 6, 3]prefixsums:[13, 22, 18, 37, 31, 33, 39, 42]

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Parallelprefixsums

•  Intuition:Partialsumscanbeefficientlycombinedtoformmuchlargerpartialsums.E.g.,ifweknowsum(x[0…3])andsum(x[4…7]),thenwecaneasilycomputesum(x[0…7])

•  e.g.,x = [13, 9, -4, 19, -6, 2, 6, 3]

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Parallelprefixsumsalgorithm,upsweep

Computethepartialsumsinamoreusefulmanner

[13, 9, -4, 19, -6, 2, 6, 3]

[13, 22, -4, 15, -6, -4, 6, 9]

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Parallelprefixsumsalgorithm,upsweep

Computethepartialsumsinamoreusefulmanner

[13, 9, -4, 19, -6, 2, 6, 3]

[13, 22, -4, 15, -6, -4, 6, 9]

[13, 22, -4, 37, -6, -4, 6, 5]

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Parallelprefixsumsalgorithm,upsweep

Computethepartialsumsinamoreusefulmanner

[13, 9, -4, 19, -6, 2, 6, 3]

[13, 22, -4, 15, -6, -4, 6, 9]

[13, 22, -4, 37, -6, -4, 6, 5]

[13, 22, -4, 37, -6, -4, 6, 42]

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Parallelprefixsumsalgorithm,downsweep

Nowunwindtocalculatetheothersums

[13, 22, -4, 37, -6, -4, 6, 42]

[13, 22, -4, 37, -6, 33, 6, 42]

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Parallelprefixsumsalgorithm,downsweep

Nowunwindtocalculatetheothersums

[13, 22, -4, 37, -6, -4, 6, 42]

[13, 22, -4, 37, -6, 33, 6, 42]

[13, 22, 18, 37, 31, 33, 39, 42]

•  Recall,westartedwith:[13, 9, -4, 19, -6, 2, 6, 3]

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Doublingarraysizeaddstwomorelevels

Upsweep

Downsweep

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Parallelprefixsums

pseudocode//Upsweepprefix_sums(x):fordin0to(lgn)-1://disdepthparallelforiin2d-1ton-1,by2d+1:x[i+2d]=x[i]+x[i+2d]//Downsweepfordin(lgn)-1to0:parallelforiin2d-1ton-1-2d,by2d+1:if(i-2d>=0):x[i]=x[i]+x[i-2d]

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Parallelprefixsumsalgorithm,incode

•  AniterativeJava-esqueimplementation:voiditerativePrefixSums(long[]a){intgap=1;for(;gap<a.length;gap*=2){parfor(inti=gap-1;i+gap<a.length;i+=2*gap){a[i+gap]=a[i]+a[i+gap];}}for(;gap>0;gap/=2){parfor(inti=gap-1;i<a.length;i+=2*gap){a[i]=a[i]+((i-gap>=0)?a[i-gap]:0);}}

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Parallelprefixsumsalgorithm,incode•  ArecursiveJava-esqueimplementation:

voidrecursivePrefixSums(long[]a,intgap){if(2*gap–1>=a.length){return;}parfor(inti=gap-1;i+gap<a.length;i+=2*gap){a[i+gap]=a[i]+a[i+gap];}recursivePrefixSums(a,gap*2);parfor(inti=gap-1;i<a.length;i+=2*gap){a[i]=a[i]+((i-gap>=0)?a[i-gap]:0);}}

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Parallelprefixsumsalgorithm

•  Howgoodisthis?

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Parallelprefixsumsalgorithm

•  Howgoodisthis?–  Work:O(n)–  Span:O(lgn)

•  SeePrefixSums.java,PrefixSumsSequentialWithParallelWork.java

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Goal:parallelizethePrefixSumsimplementation

•  Specifically,parallelizetheparallelizableloopsparfor(inti=gap-1;i+gap<a.length;i+=2*gap){a[i+gap]=a[i]+a[i+gap];}

•  Partitionintomultiplesegments,runindifferentthreadsfor(inti=left+gap-1;i+gap<right;i+=2*gap){a[i+gap]=a[i]+a[i+gap];}

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Recallfromthepreviouslecture:Fork/joininJava

•  Thejava.util.concurrent.ForkJoinPoolclass–  ImplementsExecutorService–  Executes java.util.concurrent.ForkJoinTask<V>or

java.util.concurrent.RecursiveTask<V>or java.util.concurrent.RecursiveAction

•  Inalongcomputation:–  Forkathread(ormore)todosomework–  Jointhethread(s)toobtaintheresultofthework

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TheRecursiveAction abstractclasspublicclassMyActionFooextendsRecursiveAction{publicMyActionFoo(…){storethedatafieldsweneed}@Overridepublicvoidcompute(){if(thetaskissmall){dotheworkhere;return;}invokeAll(newMyActionFoo(…),//smallernewMyActionFoo(…),//subtasks…);//…}}

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AForkJoinexample

•  SeePrefixSumsParallelForkJoin.java•  Seetheprocessorgo,gogo!

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Parallelprefixsumsalgorithm

•  Howgoodisthis?–  Work:O(n)–  Span:O(lgn)

•  SeePrefixSumsParallelArrays.java

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Parallelprefixsumsalgorithm

•  Howgoodisthis?–  Work:O(n)–  Span:O(lgn)

•  SeePrefixSumsParallelArrays.java•  SeePrefixSumsSequential.java

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Parallelprefixsumsalgorithm

•  Howgoodisthis?–  Work:O(n)–  Span:O(lgn)

•  SeePrefixSumsParallelArrays.java•  SeePrefixSumsSequential.java

–  n-1additions–  Memoryaccessissequential

•  ForPrefixSumsSequentialWithParallelWork.java–  About2nusefuladditions,plusextraadditionsfortheloopindexes–  Memoryaccessisnon-sequential

•  Thepunchline:–  Don'trollyourown.Knowthelibraries–  Cacheandconstantsmatter