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FFTC FastestFourierTransformontheIBMCellBroadbandEngine DavidA Bader ViratAgarwal 太原房产网 ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 2 CellSystemFeatures Heterogeneousmulti coresystemarchitecturePowerProcessorElementforcontroltasksSynergisticProcessorElementsfordata intensiveprocessing SynergisticProcessorElement SPE consistsofSynergisticProcessorUnit SPU SynergisticMemoryFlowControl MFC Datamovement synchronizationInterfacetohigh performanceElementInterconnectBus ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 3 FastFourierTransform FFTsareusedin DataCompression SeismicImaging FluidDynamics ImageProcessing etc MediumSizeFFTsComplexsingle precision1DFFT Inputsamplesandoutputresultsresideinmainmemory Radix2 3and5 Optimizedfor1K 16Kpoints ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 4 ExistingFFTResearchonCell B E Williamsetal 2006 analyzedpeakperformance Cico CooperandGreene 2006 estimated22 1GFlops sforan8Kcomplex1DFFTthatresidesintheLocalStoreofoneSPE 8independentFFTsinlocalstoreof8SPEsgives176 8GFlops s Chow FossumandBrokenshire 2005 achieved46 8GFlops sfor16McomplexFFT Highlyspecializedforthisparticularinputsize FFTWisahighlyportableFFTlibraryofvarioustypes precisionandinputsize ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 5 OurFFTCisbasedonCooleyTukey OutofPlace1DFFTrequirestwoarraysA Bforcomputationateachstage ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 6 ButterfliesoftheorderedDIF DiscreteinFrequency FFTAlgorithm Doesnotrequirebitreveralattheendofallstages IllustrationoftheAlgorithm ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 7 FFTCdesignonCell B E SynchronizestepaftereverystageleadstosignificantoverheadLoadbalancingtoachievebetterSPUutilizationVectorizationdifficultforeverystageLimitedlocalstorerequirespacefortwiddlefactorsandinputdata loopunrollingandduplicationincreasessizeofthecode Algorithmisbranchy DoublynestedforloopwithintheouterwhileloopLackofbranchpredictorcompromisesperformance ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 8 ParallelingFFTC Numberofchunks 2 pp NumberofSPEsChunkiandi pareallocatedtoSPEi EachchunkisfetchedusingDMAgetwithmultibuffering Achievesloadbalancing ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 9 TreeSynchronization Eachsynchronizationstagetakes1microsecIncomparisontoPPUcoordinatedsync thattakes20microsec Minimizessync overhead SynchronizationaftereverystageusingInter SPEDMAcommunication Achievedin 2 logn stages ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 10 OptimizationforSPE LoopduplicationforStages1 2Forvectorizationofthesestagesweneedtousespu shuffleonoutputvector LoopduplicationforNP buffersizeandotherwise NeedtostallforDMAgetatdifferentplaceswithintheloop CodesizeincreaseswhichlimitsthesizeofFFTthatcanbecomputed ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 11 PseudoCodefortheAlgorithmonCell ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 12 ExperimentalSetup ManualLoopunrolling multi buffering interSPEcommunication odd evenpipelining vectorization InstructionlevelprofilingandperformanceanalysisusingCellSDK2 1FLOPanalysisOperationCount 5 NlogN floatingpointoperationsFor2complexvaluecomputationswerequire Onecomplexsubtraction 2FLOP Onecomplexaddition 2FLOP andonecomplexmultiplication 6FLOP ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 13 Performanceanalysis ScalingacrossSPEs ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 14 PerformanceComparisonofFFTs PerformancenumbersfromBenchFFT ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 15 FFTCisourhighperformancedesignofanFFTforasingle1 DimensionalDIFFFT UsevariousoptimizationtechniquessuchasManualLoopunrolling multi buffering interSPEcommunication odd evenpipelining vectorization Demonstratesuperiorperformanceof18 6GigaFlop sforanFFTofsize8k 16K Codeavailableat Conclusions ViratAgarwal FFTC FastestFourierTransformontheIBMCellBroadbandEngine 16 AcknowledgmentofSupport NationalScienceFoundationCSR AFrameworkforOptimizingScientificApplications 06 14915 CAREER High PerformanceAlgorithmsforScientificApplications 06 11589 00 93039 ITR BuildingtheTreeofLife ANationalResourceforPhyloinformaticsandComputationalPhylogenetics EF BIO03 31654 DBI AcquisitionofaHighPerformanceShared MemoryComputerforC