Power and Energy Normalized Speedup Models for ...async.org.uk/presentations/ACSD_34.pdf · Gustafson’s Law • Workload scales with compuHng faciliHes – (50% parallelizable P=0.5)

Power and Energy Normalized Speedup Models for Heterogeneous Many Core Computing

MohammedA.N.Al-hayanni1,AshurRafiev2,RishadShafik1,FeiXia1

SchoolofEEE1andCS2,NewcastleUniversityNewcastleUponTyne,NE17RU,UK

ACSD 2016

Outline •  ExisHngspeedupmodels•  MoHvaHon•  Extendedheterogeneousspeedupmodels•  PowerconsumpHonmodels•  Powerandenergynormalizedspeedup•  ExperimentalresultsandcrossvalidaHon•  Conclusions

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Amdahl’s Law •  Fixedworkload

–  (50%parallelizableP=0.5)–  OnasequenHalprocessor(singlecore)takes1unitofHmetocomplete

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Amdahl’s Law •  Withtwocores…

–  Parallelizablepartisdistributedbetweenthetwocores–  TotalHme0.75–  Speedup=1/0.75=1.333

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Amdahl’s Law •  Withthreecores…

–  Speedup=1/0.667=1.5

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Amdahl’s Law •  Withtencores…

–  Speedup=1.82!" ! = !(1)!(!) =

11− ! + !!

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Amdahl’s Law •  With∞cores…

–  Speedup=2!" ! = !(1)!(!) =

11− ! + !!

!" ∞ = 11− !

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Amdahl’s Law

!" ! = !(1)!(!) =1

1− ! + !!

!" ∞ = 11− ! 8

Gustafson’s Law •  WorkloadscaleswithcompuHngfaciliHes

–  (50%parallelizableP=0.5)–  OnasequenHalprocessor(singlecore)takes1unitofHmetocompleteworkloadW(1)designedwithasinglecoreinmind

OpenCLhostoperaHon OCLKernelsfor480x270pixels

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Gustafson’s Law •  Withfourcores…

–  Complete960x540imageinthesameHme–  0.5x5=2.5Hmestheworkload(speedup=2.5)


OCLKernelsfor480x270pixels



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OCLKernelsfor480x270pixels Gustafson’s Law •  With16cores…

–  CompleteFHDimageinthesameHme–  Speedup=0.5x17=8.5







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Gustafson’s Law •  SpeedupistheraHobetweentheimprovedworkloadand

theworkloadbeforeimprovement

–  CalculatedatfixedHme!(1) = 1− ! ! + !!!(!) = 1− ! ! + !!!!" ! =!(!)!(1) = 1− ! + !"

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Gustafson’s Law

!(1) = 1− ! ! + !!!(!) = 1− ! ! + !!!!" ! =!(!)!(1) = 1− ! + !"

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Sun-Ni Law •  Memory-boundspeedupmodel

–  Parallelworkloadpercorerestrictedbymemorystructure(mulH-levelcaches,sharedmemory/interfaces,etc.)

–  Onecore’sworkloadcapabilityrestrictedbyM–thememoryofonecore,Ncores’workloadcapabilityrestrictedbyNxM

–  ForthePpart: !(1) = !(!)! ! = ! !×! = !(!×!!! ! 1 )

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Sun-Ni Law •  MulH-corespeedupisderivedthusly:

! ! = 1− ! ! 1 + !×!(!×!!! ! 1 )! 1 = 1− ! ! 1 + !×!(!)! 1 = 1− ! ! 1 + !×!(!×!

!! ! 1 )!

!" ! =!(!)!(1) =

1− ! !(1)+ !×!(!×!!! ! 1 )

1− ! !(1)+ !×!(!×!!! ! 1 )!

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Sun-Ni Law •  TryingtoremoveW(1):

!" ! ! = !!! !"#ℎ !"#$%&"' ! !"# !

! !×! = !!×!"! = !!×! ! , !ℎ!"! !×!!! ! 1 = !!×!(!!! ! 1 = !!×!(1)!" ! = 1− ! + !×!(!)

1− ! + !×!(!)!,!"#ℎ ! ! = !!

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!" ! =!(!)!(1) =1− ! !(1)+ !×!(!×!!! ! 1 )

1− ! !(1)+ !×!(!×!!! ! 1 )!

Sun-Ni Law •  Dependingong(N)

–  Sub-linearscaling(Amdahl’sifg(N)=1)–  Linearscaling(Gustafson’sifg(N)=N)–  Super-linearscaling(ifg(N)>N)

•  Ifyouhadmorememorythancores,andtheproblemismemory-bound,youcanscaletohigherspeedupthanwhatyourcoresallowforcompute-boundproblems

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Comparing the three models

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0

S(k)

k

Speed-up, k/ 1

5 10 15

1

5

10

15

20

20

1

p = 1

p = 0

p = 0.95

p = 0.9

p = 0.85p = 0.8

...

Amdahl's Law

1

S(k) = 1(1 – p) + pk

2S(k) = (1 – p) + pk

3S(k) =

(1 – p) + pg(k)(1 – p) + pg(k)k

Gustafson's Model Sun and Ni's Model0 k5 10 151

5

10

15

20

20

1

p = 1

p = 0

p = 0.95p = 0.9p = 0.85

p = 0.5

...

p = 0.15p = 0.1p = 0.05

...

S(k)Speed-up, k/ 1

0 k5 10 151

5

10

15

20

20

1

p = 1

p = 0

p = 0.15

p = 0.1

p = 0.05

p = 0.2

...

g(k) = k3/2

p = 0.25

S(k)Speed-up, k/ 1


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Motivation •  Extendtoahigherdegreeofcoreheterogeneity•  Extendtopower/energy/efficiencyandcovermodeslike

dynamicvoltageandfrequencyscaling(DVFS)

•  PotenHalapplicaHonsinrun-Hmemanagementsystemsofparallelsystems

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Existing Speedup Models and the Extended Model

Homogeneity Heterogeneity Power Amdahl Gustafson SunandNiAmdahl Yes No No Yes No No

Gustafson Yes No No Yes Yes No

SunandNi Yes No No Yes Yes Yes

Hill-Marty Yes Simple No Yes No No

HaoandXie Yes Simple No Yes Yes Yes

WooandLee Yes Simple Yes Yes No No

SunandChen Yes No No Yes Yes Yes

ExtendedModel

Yes Normal Yes Yes Yes Yes

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Heterogeneity •  ExisHngheterogeneity

include‘asymmetric’and‘dynamic’structures(b)L

•  WeextendtocoverthenormalformofcoreheterogeneityJ

•  SHlliso-ISAandnotfullygeneralL

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Heterogeneity •  ParallelcomputaHonmaynotallfinishtogether(Amdahl’s)

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!! = min! ∙ !!!

!!!

! = !! ,!! ,… ,!!

BCE performance equivalence •  CalculaHngtheperformanceequivalentnumberofBCEs

–  Basedontheslowest(lasttofinish)core

max!,avr!,opt! alsopossible

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Speedup extension Amdahl’s •  CalculaHngtheperformanceequivalentnumberofBCEs


!! = min! ∙ !!!

!!!

!" ! = 11− !

!! +!!!

, (!"#$ℎ!!!)

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SequenHalonfastestcore,ifαXisfastest

Speedup extension Amdahl’s •  CalculaHngtheperformanceequivalentnumberofBCEs


!! = min! ∙ !!!

!!!

!" ! = 11− !

!! +!!!

, (!"#$ℎ!!!)

Parallelsyncedtotheslowest,incaseofminα !" ! = !(1)!(!) =

11− ! + !!

Nowinvectorspace

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Speedup extension Gustafson’s •  Gustafson’sspeedupmodelextension

–  AgainassumingsequenHalonatypeXcoreandparallelonNα

!" ! = 1− ! + !"


Parallelsyncedtotheslowest,incaseofminα

!" ! = 1− ! !! + !!!

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Speedup extension Sun-Ni’s •  ExtendingSun-Ni’smodel

–  AgainassumingsequenHalonatypeXcoreandparallelonNα


Parallelsyncedtotheslowest,incaseofminα !" ! = 1− ! + !!(!)

1− ! + !!(!)!

MemoryboundfuncHonforallcores

!" ! = 1− ! + !"(!)1− ! !! + !"(!)!!

29 ReducestoextendedAmdahl’sandGustafson’sasexpected


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Power •  DividepowerintoeffecHveandidle

!!"!#$ =!(!)+!!"#$

EffecHvepower:powerusedbyworkload

IdlepowerincludesbothstaHcpowerandacHvepowerthat’snotusedby

workload

whenNiBCEsareidle31

!(!) =!!!! ! +!!!!(!)!! ! + !!(!)

!! = !!!! ,!! is the power of one !"#

!! =!! !!!!!

!!!= !!!!

!!"#$ = !! ∙!!

Effective power

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•  Theβsaresimilartotheαs,butpertaintopower–  Anith-typecoreconsumesβiW1powerandhasαispeed(speedofone

coreis1–forthroughput,wedealwithspeedup,forpower,wedealwithwaqageandnotraHos)

–  Nβisthepower-equivalentnumberofBCEs–  Forsynchronizingontheslowestcore:

!! = min! ∙!!!!!!

!

!!!

Effective power

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•  EffecHvepowerformulashavebeenderivedforallthreetypesofmodels/laws

–  Canbeviewedasresultsof‘powerscaling’withPSfuncHons:

!(!) = !" ! ∙ !"(!) ∙!!

With!! = !! = 1,∀!,and! = !allmodelstransformtohomogeneousforms

Efficiency

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•  Power-normalizedperformance–  IPS/Waq

•  EnergyperinstrucHon–  Joules/InstrucHon

•  Energy-normalizedperformance–  IPS/Joule

•  Allmodelsinthepaper


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Experimental platform

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System characterization

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•  BuildparametersthroughexperimentaHon–  WA7,WA15,Widle(forthe‘whole’–didnottrydifferenHaHngdifferent

Wi–coresnotturnedoffeveninNA7=0andNA15=0cases)–  αA7,αA15,βA7,βA15–  Maybedifferentfordifferentapps/computaHons–  CPU-heavytasksmainlyexperimentedinthisiniHalstudy,minα

scheduling

–  log,sqrt,andintegerarithmeHctested

Exploration with models

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•  RunmodelswithvariousexecuHonscenariostoinvesHgatetheeffectsofP,DVFS,corescaling,etc.(largedatabaseavailablefromtechnicalreport,someexampledatainthepaper)

hqp://async.org.uk/tech-reports/NCL-EEE-MICRO-TR-2016-198.pdf

Exploration with models

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•  RunmodelswithvariousexecuHonscenariostoinvesHgatetheeffectsofP,DVFS,corescaling,etc.(largedatabaseavailablefromtechnicalreport,someexampledatainthepaper)

hqp://async.org.uk/tech-reports/NCL-EEE-MICRO-TR-2016-198.pdf

P=0.9 P=0.1

Cross-validation

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•  Amdahl’swithprogrammer-controlledPvalues

Max0.24%

Max2.17%


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Conclusions

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•  ExtendedpopularparallelizaHonspeedupmodelstocoverawiderrangeofiso-ISA(orcoefficient-equivalentISA)heterogeneity

•  Extendedpowermodelsandefficiencymodels•  Firstcross-validaHonstudysuccessful•  NeedtoinvesHgateevenwiderscopesofheterogeneity•  Needtostudyotherspeedupmodels(e.g.Downey’s)•  NeedtoinvesHgaterealisHcmemorysubsystems(cachemisses)•  Needtoexploreusingthesemodelsforrun-Hmemanagement

Documents

Power and Energy Normalized Speedup Models for ...async.org.uk/presentations/ACSD_34.pdf · Gustafson’s Law • Workload scales with compuHng faciliHes – (50% parallelizable P=0.5)