CUDA

CUFFT Library

PG-05327-032_V01
August, 2010
CUFFT Library PG-05327-032_V01

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 Table of Contents

CUFFT Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
CUFFT Types and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Type cufftHandle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Type cufftResult . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Type cufftReal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Type cufftDoubleReal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Type cufftComplex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Type cufftDoubleComplex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Type cufftCompatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
CUFFT Transform Types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
CUFFT Transform Directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Streamed CUFFT Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
FFTW Compatibility Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
CUFFT API Functions . . . . . . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 11
Function cufftPlan1d(). . . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 12
Function cufftPlan2d(). . . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 12
Function cufftPlan3d(). . . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 13
Function cufftPlanMany(). . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 14
Function cufftDestroy() . . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 15
Function cufftExecC2C() . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 15
Function cufftExecR2C() . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 16
Function cufftExecC2R() . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 17
Function cufftExecZ2Z() . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 18
Function cufftExecD2Z() . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 19
Function cufftExecZ2D() . . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 19
Function cufftSetStream() . . . . . . . . . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 20
Function cufftSetCompatibilityMode() . . . . .... .... ... . . . . . . . . . . . . . . . . . . .... 21
Accuracy and Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
CUFFT Code Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .... .... ... .... 23
1D Complex-to-Complex Transforms . . . . . . . . . . . . . . . . . . .. . . . .... .... ... .... 24
1D Real-to-Complex Transforms . . . . . . . . . . . . . . . . . . . . . .. . . . .... .... ... .... 25
2D Complex-to-Complex Transforms . . . . . . . . . . . . . . . . . . .. . . . .... .... ... .... 26
Batched 2D Complex-to-Complex Transforms. . . . . . . . . . . . .. . . . .... .... ... .... 27
2D Complex-to-Real Transforms . . . . . . . . . . . . . . . . . . . . . .. . . . .... .... ... .... 28
3D Complex-to-Complex Transforms . . . . . . . . . . . . . . . . . . .. . . . .... .... ... .... 29

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 CUFFT Library

ThisȱdocumentȱdescribesȱCUFFT,ȱtheȱNVIDIA®ȱCUDA™™ȱFastȱFourierȱ
Transformȱ(FFT)ȱlibrary.ȱTheȱFFTȱisȱaȱdivideȬandȬconquerȱalgorithmȱ
forȱefficientlyȱcomputingȱdiscreteȱFourierȱtransformsȱofȱcomplexȱorȱ
realȬvaluedȱdataȱsets,ȱandȱitȱisȱoneȱofȱtheȱmostȱimportantȱandȱwidelyȱ
usedȱnumericalȱalgorithms,ȱwithȱapplicationsȱthatȱincludeȱ
computationalȱphysicsȱandȱgeneralȱsignalȱprocessing.ȱTheȱCUFFTȱ
libraryȱprovidesȱaȱsimpleȱinterfaceȱforȱcomputingȱparallelȱFFTsȱonȱanȱ
NVIDIAȱGPU,ȱwhichȱallowsȱusersȱtoȱleverageȱtheȱfloatingȬpointȱpowerȱ
andȱparallelismȱofȱtheȱGPUȱwithoutȱhavingȱtoȱdevelopȱaȱcustom,ȱGPUȬ
basedȱFFTȱimplementation.
FFTȱlibrariesȱtypicallyȱvaryȱinȱtermsȱofȱsupportedȱtransformȱsizesȱandȱ
dataȱtypes.ȱForȱexample,ȱsomeȱlibrariesȱonlyȱimplementȱRadixȬ2ȱFFTs,ȱ
restrictingȱtheȱtransformȱsizeȱtoȱaȱpowerȱofȱtwo,ȱwhileȱotherȱ
implementationsȱsupportȱarbitraryȱtransformȱsizes.ȱThisȱversionȱofȱtheȱ
CUFFTȱlibraryȱsupportsȱtheȱfollowingȱfeatures:
‰ 1D,ȱ2D,ȱandȱ3DȱtransformsȱofȱcomplexȱandȱrealȬvaluedȱdata
‰ Batchȱexecutionȱforȱdoingȱmultipleȱtransformsȱofȱanyȱdimensionȱinȱ
parallel
‰ 2Dȱandȱ3Dȱtransformȱsizesȱinȱtheȱrangeȱ[2,ȱ16384]ȱinȱanyȱ
dimension
‰ 1Dȱtransformȱsizesȱupȱtoȱ8ȱmillionȱelements
‰ InȬplaceȱandȱoutȬofȬplaceȱtransformsȱforȱrealȱandȱcomplexȱdata
‰ DoubleȬprecisionȱtransformsȱonȱcompatibleȱhardwareȱ(GT200ȱandȱ
laterȱGPUs)ȱ
‰ Supportȱforȱstreamedȱexecution,ȱenablingȱsimultaneousȱ
computationȱtogetherȱwithȱdataȱmovement

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CUDA CUFFT Library

CUFFT Types and Definitions

TheȱnextȱsectionsȱdescribeȱtheȱCUFFTȱtypesȱandȱtransformȱdirections:
‰ ““TypeȱcufftHandle””ȱonȱpage 5
‰ ““TypeȱcufftResult””ȱonȱpage 6
‰ ““TypeȱcufftReal””ȱonȱpage 6
‰ ““TypeȱcufftDoubleReal””ȱonȱpage 6
‰ ““TypeȱcufftComplex””ȱonȱpage 6
‰ ““TypeȱcufftDoubleComplex””ȱonȱpage 7
‰ ““TypeȱcufftCompatibility””ȱonȱpage 7
‰ ““CUFFTȱTransformȱTypes””ȱonȱpage 7
‰ ““CUFFTȱTransformȱDirections””ȱonȱpage 8

Type cufftHandle
typedefunsignedintcufftHandle;
AȱhandleȱtypeȱusedȱtoȱstoreȱandȱaccessȱCUFFTȱplansȱ(seeȱ““CUFFTȱAPIȱ
Functions””ȱonȱpage 11ȱforȱmoreȱinformationȱaboutȱplans).ȱForȱ
example,ȱtheȱuserȱreceivesȱaȱhandleȱafterȱcreatingȱaȱCUFFTȱplanȱandȱ
usesȱthisȱhandleȱtoȱexecuteȱtheȱplan.

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Type cufftResult
typedefenumcufftResult_tcufftResult;
AnȱenumerationȱofȱvaluesȱusedȱexclusivelyȱasȱAPIȱfunctionȱreturnȱ
values.ȱTheȱpossibleȱreturnȱvaluesȱareȱdefinedȱasȱfollows:
Return Values
CUFFT_SUCCESS AnyȱCUFFTȱoperationȱisȱsuccessful.
CUFFT_INVALID_PLAN CUFFTȱisȱpassedȱanȱinvalidȱplanȱhandle.
CUFFT_ALLOC_FAILED CUFFTȱfailedȱtoȱallocateȱGPUȱmemory.
CUFFT_INVALID_TYPE Theȱuserȱrequestsȱanȱunsupportedȱtype.
CUFFT_INVALID_VALUE Theȱuserȱspecifiesȱaȱbadȱmemoryȱpointer.
CUFFT_INTERNAL_ERROR Usedȱforȱallȱinternalȱdriverȱerrors.
CUFFT_EXEC_FAILED CUFFTȱfailedȱtoȱexecuteȱanȱFFTȱonȱtheȱGPU.
CUFFT_SETUP_FAILED TheȱCUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_INVALID_SIZE TheȱuserȱspecifiesȱanȱunsupportedȱFFTȱsize.
CUFFT_UNALIGNED_DATA Inputȱorȱoutputȱdoesȱnotȱsatisfyȱtextureȱ
alignmentȱrequirements.

Type cufftReal
typedeffloatcufftReal;
AȱsingleȬprecision,ȱfloatingȬpointȱrealȱdataȱtype.

Type cufftDoubleReal
typedefdoublecufftDoubleReal;
AȱdoubleȬprecision,ȱfloatingȬpointȱrealȱdataȱtype.

Type cufftComplex
typedefcuComplexcufftComplex;
AȱsingleȬprecision,ȱfloatingȬpointȱcomplexȱdataȱtypeȱthatȱconsistsȱofȱ
interleavedȱrealȱandȱimaginaryȱcomponents.

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Type cufftDoubleComplex
typedefcuDoubleComplexcufftDoubleComplex;
AȱdoubleȬprecision,ȱfloatingȬpointȱcomplexȱdataȱtypeȱthatȱconsistsȱofȱ
interleavedȱrealȱandȱimaginaryȱcomponents.

Type cufftCompatibility
typedefenumcufftCompatibility_tcufftCompatibility;
AnȱenumerationȱofȱvaluesȱusedȱtoȱcontrolȱFFTWȱdataȱcompatibility.ȱ
Seeȱ““FFTWȱCompatibilityȱMode””ȱonȱpage 9ȱforȱdetails.

CUFFT Transform Types

TheȱCUFFTȱlibraryȱsupportsȱcomplexȬȱandȱrealȬdataȱtransforms.ȱTheȱ
cufftTypeȱdataȱtypeȱisȱanȱenumerationȱofȱtheȱtypesȱofȱtransformȱdataȱ
supportedȱbyȱCUFFT:ȱ
typedefenumcufftType_t{
CUFFT_R2C=0x2a,//Realtocomplex(interleaved)
CUFFT_C2R=0x2c,//Complex(interleaved)toreal
CUFFT_C2C=0x29,//Complextocomplex,interleaved
CUFFT_D2Z=0x6a,//DoubletodoubleŞcomplex
CUFFT_Z2D=0x6c,//DoubleŞcomplextodouble
CUFFT_Z2Z=0x69//DoubleŞcomplextodoubleŞcomplex
}cufftType;
ForȱcomplexȱFFTs,ȱtheȱinputȱandȱoutputȱarraysȱmustȱinterleaveȱtheȱrealȱ
andȱimaginaryȱpartsȱ(theȱcufftComplexȱtype).ȱTheȱtransformȱsizeȱinȱ
eachȱdimensionȱisȱtheȱnumberȱofȱcufftComplexȱelements.ȱTheȱ
CUFFT_C2Cȱconstantȱcanȱbeȱpassedȱtoȱanyȱplanȱcreationȱfunctionȱtoȱ
configureȱaȱsingleȬprecisionȱcomplexȬtoȬcomplexȱFFT.ȱPassȱtheȱ
CUFFT_Z2ZȱconstantȱtoȱconfigureȱaȱdoubleȬprecisionȱcomplexȬtoȬ
complexȱFFT.ȱ
ForȱrealȬtoȬcomplexȱFFTs,ȱtheȱoutputȱarrayȱholdsȱonlyȱtheȱnonȬ
redundantȱcomplexȱcoefficients.ȱSoȱforȱanȱNȬelementȱtransform,ȱtheȱ
outputȱarrayȱholdsȱ N e 2 + 1 ȱcufftComplexȱterms.ȱForȱhigherȬ
dimensionalȱrealȱtransformsȱofȱtheȱformȱ N0 u N1 u } u Nn ,ȱtheȱlastȱ
dimensionȱisȱcutȱinȱhalfȱsuchȱthatȱtheȱoutputȱdataȱisȱ

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N0 u N1 u } u  Nn e 2 + 1  ȱcomplexȱelements.ȱTherefore,ȱinȱorderȱtoȱ
performȱanȱinȬplaceȱFFT,ȱtheȱuserȱhasȱtoȱpadȱtheȱinputȱarrayȱinȱtheȱlastȱ
dimensionȱtoȱ Nn e 2 + 1 ȱcomplexȱelementsȱorȱ 2 *  N e 2 + 1  ȱrealȱ
elements.ȱNoteȱthatȱtheȱrealȬtoȬcomplexȱtransformȱisȱimplicitlyȱ
forward.ȱPassingȱtheȱCUFFT_R2Cȱconstantȱtoȱanyȱplanȱcreationȱfunctionȱ
configuresȱaȱsingleȬprecisionȱrealȬtoȬcomplexȱFFT.ȱPassingȱtheȱ
CUFFT_D2ZȱconstantȱconfiguresȱaȱdoubleȬprecisionȱrealȬtoȬcomplexȱFFT.ȱ
TheȱrequirementsȱforȱcomplexȬtoȬrealȱFFTsȱareȱsimilarȱtoȱthoseȱforȱrealȬ
toȬcomplex.ȱInȱthisȱcase,ȱtheȱinputȱarrayȱholdsȱonlyȱtheȱnonȬredundant,ȱ
N e 2 + 1 complexȱcoefficientsȱfromȱaȱrealȬtoȬcomplexȱtransform.ȱTheȱ
outputȱisȱsimplyȱNȱelementsȱofȱtypeȱcufftReal.ȱHowever,ȱforȱanȱinȬ
placeȱtransform,ȱtheȱinputȱsizeȱmustȱbeȱpaddedȱtoȱ 2 *  N e 2 + 1  ȱrealȱ
elements.ȱTheȱcomplexȬtoȬrealȱtransformȱisȱimplicitlyȱinverse.ȱPassingȱ
theȱCUFFT_C2Rȱconstantȱtoȱanyȱplanȱcreationȱfunctionȱconfiguresȱaȱ
singleȬprecisionȱcomplexȬtoȬrealȱFFT.ȱPassingȱCUFFT_Z2Dȱconstantȱ
configuresȱaȱdoubleȬprecisionȱcomplexȬtoȬrealȱFFT.ȱ
Forȱ1DȱcomplexȬtoȬcomplexȱtransforms,ȱtheȱstrideȱbetweenȱsignalsȱinȱaȱ
batchȱisȱassumedȱtoȱbeȱtheȱnumberȱofȱcufftComplexȱelementsȱinȱtheȱ
logicalȱtransformȱsize.ȱHowever,ȱforȱrealȬdataȱFFTs,ȱtheȱdistanceȱ
betweenȱsignalsȱinȱaȱbatchȱdependsȱonȱwhetherȱtheȱtransformȱisȱinȬ
placeȱorȱoutȬofȬplace.ȱForȱinȬplaceȱFFTs,ȱtheȱinputȱstrideȱisȱassumedȱtoȱ
beȱ 2 *  N e 2 + 1  ȱcufftRealȱelementsȱorȱ N e 2 + 1 ȱcufftComplexȱelements.ȱ
ForȱoutȬofȬplaceȱtransforms,ȱinputȱandȱoutputȱstridesȱmatchȱtheȱlogicalȱ
transformȱsizeȱNȱandȱtheȱnonȬredundantȱsizeȱ N e 2 + 1 ,ȱrespectively.
StartingȱwithȱCUFFTȱversionȱ3.0,ȱbatchedȱtransformsȱareȱsupportedȱ
throughȱtheȱcufftPlanMany()ȱfunction.ȱAlthoughȱthisȱfunctionȱtakesȱ
inputȱparametersȱthatȱspecifyȱinputȬȱandȱoutputȬdataȱstrides,ȱasȱofȱ
versionȱ3.0ȱitȱisȱassumedȱtheȱdataȱforȱeachȱsignalȱwithinȱtheȱbatchȱ
immediatelyȱfollowȱtheȱdataȱofȱtheȱpreviousȱoneȱ(aȱstrideȱofȱ1).

CUFFT Transform Directions

TheȱCUFFTȱlibraryȱdefinesȱforwardȱandȱinverseȱFastȱFourierȱ
Transformsȱaccordingȱtoȱtheȱsignȱofȱtheȱcomplexȱexponentialȱterm:
#defineCUFFT_FORWARDŞ1
#defineCUFFT_INVERSE1

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ForȱhigherȬdimensionalȱtransformsȱ(2Dȱandȱ3D),ȱCUFFTȱperformsȱ
FFTsȱinȱrowȬmajorȱorȱCȱorder.ȱForȱexample,ȱifȱtheȱuserȱrequestsȱaȱ3Dȱ
transformȱplanȱforȱsizesȱX,ȱY,ȱandȱZ,ȱCUFFTȱtransformsȱalongȱZ,ȱY,ȱandȱ
thenȱX.ȱTheȱuserȱcanȱconfigureȱcolumnȬmajorȱFFTsȱbyȱsimplyȱchangingȱ
theȱorderȱofȱtheȱsizeȱparametersȱtoȱtheȱplanȱcreationȱAPIȱfunctions.
CUFFTȱperformsȱunȬnormalizedȱFFTs;ȱthatȱis,ȱperformingȱaȱforwardȱ
FFTȱonȱanȱinputȱdataȱsetȱfollowedȱbyȱanȱinverseȱFFTȱonȱtheȱresultingȱ
setȱyieldsȱdataȱthatȱisȱequalȱtoȱtheȱinputȱscaledȱbyȱtheȱnumberȱofȱ
elements.ȱScalingȱeitherȱtransformȱbyȱtheȱreciprocalȱofȱtheȱsizeȱofȱtheȱ
dataȱsetȱisȱleftȱforȱtheȱuserȱtoȱperformȱasȱseenȱfit.

Streamed CUFFT Transforms

Executionȱofȱaȱtransformȱofȱaȱparticularȱsizeȱandȱtypeȱmayȱtakeȱseveralȱ
stagesȱofȱprocessing.ȱAȱplanȱforȱtheȱtransformȱisȱgenerated,ȱinȱwhichȱ
CUFFTȱspecifiesȱtheȱinternalȱstepsȱthatȱneedȱtoȱbeȱtaken.ȱTheseȱstepsȱ
mayȱincludeȱmultipleȱkernelȱlaunches,ȱmemoryȱcopies,ȱandȱsoȱon.
EveryȱCUFFTȱplanȱmayȱbeȱassociatedȱwithȱaȱCUDAȱstream.ȱOnceȱsoȱ
associated,ȱallȱlaunchesȱofȱtheȱinternalȱstagesȱofȱthatȱplanȱtakeȱplaceȱ
throughȱtheȱspecifiedȱstream.ȱStreamingȱofȱlaunchesȱallowsȱforȱ
potentialȱoverlapȱbetweenȱtransformsȱandȱmemoryȱcopies——seeȱtheȱ
NVIDIAȱCUDAȱProgrammingȱGuideȱforȱmoreȱinformationȱonȱstreams.ȱIfȱ
noȱstreamȱisȱassociatedȱwithȱaȱplan,ȱlaunchesȱtakeȱplaceȱinȱstreamȱ0ȱ
(theȱdefaultȱCUDAȱstream).

FFTW Compatibility Mode

Forȱsomeȱtransformȱsizes,ȱFFTWȱrequiresȱadditionalȱpaddingȱbytesȱ
betweenȱrowsȱandȱplanesȱofȱReal2Complexȱ(R2C)ȱandȱComplex2Realȱ
(C2R)ȱtransformsȱofȱrankȱgreaterȱthanȱ1.ȱ(Forȱdetails,ȱpleaseȱreferȱtoȱtheȱ
FFTWȱonlineȱdocumentationȱatȱhttp://www.fftw.org.)
ToȱspeedȱupȱR2CȱandȱC2RȱtransformsȱforȱpowerȬofȬ2ȱsizesȱsimilarȱtoȱ
theirȱComplex2Complexȱ(C2C)ȱequivalent,ȱoneȱcanȱdisableȱFFTWȬ
compatibleȱlayoutȱusingȱcufftSetCompatibilityMode(),ȱintroducedȱinȱ
releaseȱ3.1ȱandȱdescribedȱonȱpageȱ21.ȱWhenȱnativeȱmodeȱisȱselectedȱforȱ
thisȱfunction,ȱpowerȬofȬ2ȱtransformȱsizesȱwillȱbeȱcompactȱandȱCUFFTȱ
willȱnotȱuseȱpadding.ȱNonȬpowerȬofȬ2ȱsizesȱwillȱcontinueȱtoȱuseȱtheȱ
sameȱpaddingȱlayoutȱasȱFFTW.ȱ

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CUDA CUFFT Library

TheȱFFTWȱcompatibilityȱmodesȱareȱasȱfollows:
CUFFT_COMPATIBILITY_NATIVEȱ
CUFFT_COMPATIBILITY_FFTW_PADDINGȱ
CUFFT_COMPATIBILITY_FFTW_ASYMMETRICȱ
CUFFT_COMPATIBILITY_FFTW_ALLȱ
CUFFT_COMPATIBILITY_NATIVEȱmodeȱdisablesȱFFTWȱcompatibility,ȱbutȱ
achievesȱtheȱhighestȱperformance.ȱ
CUFFT_COMPATIBILITY_FFTW_PADDINGȱsupportsȱFFTWȱdataȱpaddingȱbyȱ
insertingȱextraȱpaddingȱbetweenȱpackedȱinȬplaceȱtransformsȱforȱ
batchedȱtransformsȱwithȱpowerȬofȬ2ȱsize.ȱ
CUFFT_COMPATIBILITY_FFTW_ASYMMETRICȱwaivesȱtheȱC2Rȱsymmetryȱ
requirement.ȱOnceȱset,ȱitȱguaranteesȱFFTWȬcompatibleȱoutputȱforȱnonȬ
symmetricȱcomplexȱinputsȱforȱtransformsȱwithȱpowerȬofȬ2ȱsize.ȱThisȱisȱ
onlyȱusefulȱforȱartificialȱ(thatȱis,ȱrandom)ȱdataȱsetsȱasȱactualȱdataȱwillȱ
alwaysȱbeȱsymmetricȱifȱitȱhasȱcomeȱfromȱtheȱrealȱplane.ȱEnablingȱthisȱ
modeȱcanȱsignificantlyȱimpactȱperformance.ȱ
CUFFT_COMPATIBILITY_FFTW_ALLȱenablesȱfullȱFFTWȱcompatibility.ȱReferȱ
toȱtheȱFFTWȱdocumentationȱ(http://www.fftw.org)ȱforȱFFTWȱdataȱ
layoutȱspecifications.ȱ

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CUDA CUFFT Library

CUFFT API Functions

TheȱCUFFTȱAPIȱisȱmodeledȱafterȱFFTW,ȱwhichȱisȱoneȱofȱtheȱmostȱ
popularȱandȱefficientȱCPUȬbasedȱFFTȱlibraries.ȱFFTWȱprovidesȱaȱ
simpleȱconfigurationȱmechanismȱcalledȱaȱplanȱthatȱcompletelyȱspecifiesȱ
theȱoptimal——thatȱis,ȱtheȱminimumȱfloatingȬpointȱoperationȱ(flop)——
planȱofȱexecutionȱforȱaȱparticularȱFFTȱsizeȱandȱdataȱtype.ȱTheȱ
advantageȱofȱthisȱapproachȱisȱthatȱonceȱtheȱuserȱcreatesȱaȱplan,ȱtheȱ
libraryȱstoresȱwhateverȱstateȱisȱneededȱtoȱexecuteȱtheȱplanȱmultipleȱ
timesȱwithoutȱrecalculationȱofȱtheȱconfiguration.ȱTheȱFFTWȱmodelȱ
worksȱwellȱforȱCUFFTȱbecauseȱdifferentȱkindsȱofȱFFTsȱrequireȱdifferentȱ
threadȱconfigurationsȱandȱGPUȱresources,ȱandȱplansȱareȱaȱsimpleȱwayȱ
toȱstoreȱandȱreuseȱconfigurations.ȱ
TheȱCUFFTȱlibraryȱinitializesȱinternalȱdataȱuponȱtheȱfirstȱinvocationȱofȱ
anȱAPIȱfunction.ȱTherefore,ȱallȱAPIȱfunctionsȱcouldȱreturnȱtheȱ
CUFFT_SETUP_FAILEDȱerrorȱcodeȱifȱtheȱlibraryȱfailsȱtoȱinitialize.ȱCUFFTȱ
shutsȱdownȱautomaticallyȱwhenȱallȱuserȬcreatedȱFFTȱplansȱareȱ
destroyed.ȱ
TheȱCUFFTȱfunctionsȱareȱasȱfollows:
‰ ““FunctionȱcufftPlan1d()””ȱonȱpage 12
‰ ““FunctionȱcufftPlan2d()””ȱonȱpage 12
‰ ““FunctionȱcufftPlan3d()””ȱonȱpage 13
‰ ““FunctionȱcufftPlanMany()””ȱonȱpage 14
‰ ““FunctionȱcufftDestroy()””ȱonȱpage 15
‰ ““FunctionȱcufftExecC2C()””ȱonȱpage 15ȱ
‰ ““FunctionȱcufftExecR2C()””ȱonȱpage 16
‰ ““FunctionȱcufftExecC2R()””ȱonȱpage 17
‰ ““FunctionȱcufftExecZ2Z()””ȱonȱpage 18ȱ
‰ ““FunctionȱcufftExecD2Z()””ȱonȱpage 19
‰ ““FunctionȱcufftExecZ2D()””ȱonȱpage 19
‰ ““FunctionȱcufftSetStream()””ȱonȱpage 20
‰ ““FunctionȱcufftSetCompatibilityMode()””ȱonȱpage 21

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CUDA CUFFT Library

Function cufftPlan1d()
cufftResult
cufftPlan1d(
cufftHandle*plan,intnx,cufftTypetype,intbatch);
Createsȱaȱ1DȱFFTȱplanȱconfigurationȱforȱaȱspecifiedȱsignalȱsizeȱandȱ
dataȱtype.ȱTheȱbatchȱinputȱparameterȱtellsȱCUFFTȱhowȱmanyȱ1Dȱ
transformsȱtoȱconfigure.ȱȱȱ
Input
plan PointerȱtoȱaȱcufftHandleȱobject
nx Theȱtransformȱsizeȱ(e.g.,ȱ256ȱforȱaȱ256ȬpointȱFFT)
type Theȱtransformȱdataȱtypeȱ(e.g.,ȱCUFFT_C2Cȱforȱcomplexȱtoȱcomplex)ȱ
batch Numberȱofȱtransformsȱofȱsizeȱnxȱ

Output
plan ContainsȱaȱCUFFTȱ1Dȱplanȱhandleȱvalue

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_ALLOC_FAILED AllocationȱofȱGPUȱresourcesȱforȱtheȱplanȱfailed.
CUFFT_INVALID_TYPE Theȱtypeȱparameterȱisȱnotȱsupported.
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_INVALID_SIZE Theȱnxȱparameterȱisȱnotȱaȱsupportedȱsize.

Function cufftPlan2d()
cufftResult
cufftPlan2d(
cufftHandle*plan,intnx,intny,cufftTypetype);
Createsȱaȱ2DȱFFTȱplanȱconfigurationȱaccordingȱtoȱspecifiedȱsignalȱsizesȱ
andȱdataȱtype.ȱThisȱfunctionȱisȱtheȱsameȱasȱcufftPlan1d()ȱexceptȱthatȱ
itȱtakesȱaȱsecondȱsizeȱparameter,ȱny,ȱandȱdoesȱnotȱsupportȱbatching.ȱȱȱ
Input
plan PointerȱtoȱaȱcufftHandleȱobject
nx TheȱtransformȱsizeȱinȱtheȱXȬdimensionȱ(numberȱofȱrows)
ny TheȱtransformȱsizeȱinȱtheȱYȬdimensionȱ(numberȱofȱcolumns)
type Theȱtransformȱdataȱtypeȱ(e.g.,ȱCUFFT_C2Rȱforȱcomplexȱtoȱreal)

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CUDA CUFFT Library

Output
plan ContainsȱaȱCUFFTȱ2Dȱplanȱhandleȱvalue

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_ALLOC_FAILED AllocationȱofȱGPUȱresourcesȱforȱtheȱplanȱfailed.
CUFFT_INVALID_TYPE Theȱtypeȱparameterȱisȱnotȱsupported.
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_INVALID_SIZE Theȱnxȱparameterȱisȱnotȱaȱsupportedȱsize.

Function cufftPlan3d()
cufftResult
cufftPlan3d(
cufftHandle*plan,intnx,intny,intnz,
cufftTypetype);
Createsȱaȱ3DȱFFTȱplanȱconfigurationȱaccordingȱtoȱspecifiedȱsignalȱsizesȱ
andȱdataȱtype.ȱThisȱfunctionȱisȱtheȱsameȱasȱcufftPlan2d()ȱexceptȱthatȱ
itȱtakesȱaȱthirdȱsizeȱparameterȱnz.ȱȱȱ
Input
plan PointerȱtoȱaȱcufftHandleȱobject
nx TheȱtransformȱsizeȱinȱtheȱXȬdimension
ny TheȱtransformȱsizeȱinȱtheȱYȬdimension
nz TheȱtransformȱsizeȱinȱtheȱZȬdimension
type Theȱtransformȱdataȱtypeȱ(e.g.,ȱCUFFT_R2Cȱforȱrealȱtoȱcomplex)

Output
plan ContainsȱaȱCUFFTȱ3Dȱplanȱhandleȱvalue

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_ALLOC_FAILED AllocationȱofȱGPUȱresourcesȱforȱtheȱplanȱfailed.
CUFFT_INVALID_TYPE Theȱtypeȱparameterȱisȱnotȱsupported.
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_INVALID_SIZE Theȱnxȱparameterȱisȱnotȱaȱsupportedȱsize.

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CUDA CUFFT Library

Function cufftPlanMany()
cufftResult
cufftPlanMany(
cufftHandle*plan,intrank,int*n,int*inembed,
intistride,intidist,int*onembed,intostride,
intodist,cufftTypetype,intbatch);
CreatesȱaȱFFTȱplanȱconfigurationȱofȱdimensionȱrank,ȱwithȱsizesȱ
specifiedȱinȱtheȱarrayȱn.ȱTheȱbatchȱinputȱparameterȱtellsȱCUFFTȱhowȱ
manyȱtransformsȱtoȱconfigureȱinȱparallel.ȱWithȱthisȱfunction,ȱbatchedȱ
plansȱofȱanyȱdimensionȱmayȱbeȱcreated.
Inputȱparametersȱinembed,ȱistride,ȱandȱidistȱandȱoutputȱparametersȱ
onembed,ȱostride,ȱandȱodistȱwillȱallowȱsetupȱofȱnonȬcontiguousȱinputȱ
dataȱinȱaȱfutureȱversion.ȱNoteȱthatȱforȱtheȱcurrentȱversionȱofȱCUFFT,ȱ
theseȱparametersȱareȱignoredȱandȱtheȱlayoutȱofȱbatchedȱdataȱmustȱbeȱ
sideȬbyȬsideȱandȱnotȱinterleaved.ȱȱȱ
Input
plan PointerȱtoȱaȱcufftHandleȱobject
rank Dimensionalityȱofȱtheȱtransformȱ(1,ȱ2,ȱorȱ3)
n Anȱarrayȱofȱsizeȱrank,ȱdescribingȱtheȱsizeȱofȱeachȱdimension
inembed Unused:ȱpassȱNULL
istride Unused:ȱpassȱ1
idist Unused:ȱpassȱ0
onembed Unused:ȱpassȱNULL
ostride Unused:ȱpassȱ1
odist Unused:ȱpassȱ0
type Transformȱdataȱtypeȱ(e.g.,ȱCUFFT_C2C,ȱasȱperȱotherȱCUFFTȱcalls)
batch Batchȱsizeȱforȱthisȱtransform

Output
plan ContainsȱaȱCUFFTȱplanȱhandleȱ

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_ALLOC_FAILED AllocationȱofȱGPUȱresourcesȱforȱtheȱplanȱfailed.
CUFFT_INVALID_TYPE Theȱtypeȱparameterȱisȱnotȱsupported.
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.

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CUDA CUFFT Library

Return Values (continued)

CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_INVALID_SIZE Theȱnxȱparameterȱisȱnotȱaȱsupportedȱsize.

Function cufftDestroy()
cufftResult
cufftDestroy(cufftHandleplan);
FreesȱallȱGPUȱresourcesȱassociatedȱwithȱaȱCUFFTȱplanȱandȱdestroysȱ
theȱinternalȱplanȱdataȱstructure.ȱThisȱfunctionȱshouldȱbeȱcalledȱonceȱaȱ
planȱisȱnoȱlongerȱneededȱtoȱavoidȱwastingȱGPUȱmemory.ȱȱ
Input
plan TheȱcufftHandleȱobjectȱofȱtheȱplanȱtoȱbeȱdestroyed.ȱ

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.

Function cufftExecC2C()
cufftResult
cufftExecC2C(
cufftHandleplan,cufftComplex*idata,
cufftComplex*odata,intdirection);
ExecutesȱaȱCUFFTȱsingleȬprecisionȱcomplexȬtoȬcomplexȱtransformȱ
planȱasȱspecifiedȱbyȱdirection.ȱCUFFTȱusesȱasȱinputȱdataȱtheȱGPUȱ
memoryȱpointedȱtoȱbyȱtheȱidataȱparameter.ȱThisȱfunctionȱstoresȱtheȱ
Fourierȱcoefficientsȱinȱtheȱodataȱarray.ȱIfȱidataȱandȱodataȱareȱtheȱsame,ȱ
thisȱmethodȱdoesȱanȱinȬplaceȱtransform.ȱȱȱ
Input
plan TheȱcufftHandleȱobjectȱforȱtheȱplanȱtoȱupdate
idata PointerȱtoȱtheȱsingleȬprecisionȱcomplexȱinputȱdataȱ(inȱGPUȱ
memory)ȱtoȱtransformȱ
odata PointerȱtoȱtheȱsingleȬprecisionȱcomplexȱoutputȱdataȱ(inȱGPUȱ
memory)
direction Theȱtransformȱdirection:ȱCUFFT_FORWARDȱorȱCUFFT_INVERSEȱ

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CUDA CUFFT Library

Output
odata ContainsȱtheȱcomplexȱFourierȱcoefficients

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ
CUFFT_INVALID_VALUE Theȱidata,ȱodata,ȱand/orȱdirectionȱparameterȱ
isȱnotȱvalid.ȱ
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_EXEC_FAILED CUFFTȱfailedȱtoȱexecuteȱtheȱtransformȱonȱGPU.ȱ
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_UNALIGNED_DATA Inputȱorȱoutputȱdoesȱnotȱsatisfyȱtextureȱ
alignmentȱrequirements.

Function cufftExecR2C()
cufftResult
cufftExecR2C(
cufftHandleplan,cufftReal*idata,cufftComplex*odata);
ExecutesȱaȱCUFFTȱsingleȬprecisionȱrealȬtoȬcomplexȱ(implicitlyȱ
forward)ȱtransformȱplan.ȱCUFFTȱusesȱasȱinputȱdataȱtheȱGPUȱmemoryȱ
pointedȱtoȱbyȱtheȱidataȱparameter.ȱThisȱfunctionȱstoresȱtheȱnonȬ
redundantȱFourierȱcoefficientsȱinȱtheȱodataȱarray.ȱIfȱidataȱandȱodataȱ
areȱtheȱsame,ȱthisȱmethodȱdoesȱanȱinȬplaceȱtransformȱ(Seeȱ““CUFFTȱ
TransformȱTypes””ȱonȱpage 7ȱforȱdetailsȱonȱrealȱdataȱFFTs.)ȱȱ
Input
plan TheȱcufftHandleȱobjectȱforȱtheȱplanȱtoȱupdate
idata PointerȱtoȱtheȱsingleȬprecisionȱrealȱinputȱdataȱ(inȱGPUȱmemory)ȱ
toȱtransformȱ
odata PointerȱtoȱtheȱsingleȬprecisionȱcomplexȱoutputȱdataȱ(inȱGPUȱ
memory)

Output
odata ContainsȱtheȱcomplexȱFourierȱcoefficients

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ

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CUDA CUFFT Library

Return Values (continued)

CUFFT_INVALID_VALUE Theȱidata,ȱodata,ȱand/orȱdirectionȱparameterȱ
isȱnotȱvalid.ȱ
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_EXEC_FAILED CUFFTȱfailedȱtoȱexecuteȱtheȱtransformȱonȱGPU.ȱ
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_UNALIGNED_DATA Inputȱorȱoutputȱdoesȱnotȱsatisfyȱtextureȱ
alignmentȱrequirements.

Function cufftExecC2R()
cufftResult
cufftExecC2R(
cufftHandleplan,cufftComplex*idata,cufftReal*odata);
ExecutesȱaȱCUFFTȱsingleȬprecisionȱcomplexȬtoȬrealȱ(implicitlyȱinverse)ȱ
transformȱplan.ȱCUFFTȱusesȱasȱinputȱdataȱtheȱGPUȱmemoryȱpointedȱtoȱ
byȱtheȱidataȱparameter.ȱTheȱinputȱarrayȱholdsȱonlyȱtheȱnonȬredundantȱ
complexȱFourierȱcoefficients.ȱThisȱfunctionȱstoresȱtheȱrealȱoutputȱ
valuesȱinȱtheȱodataȱarray.ȱIfȱidataȱandȱodataȱareȱtheȱsame,ȱthisȱmethodȱ
doesȱanȱinȬplaceȱtransform.ȱ(Seeȱ““CUFFTȱTransformȱTypes””ȱonȱpage 7ȱ
forȱdetailsȱonȱrealȱdataȱFFTs.)ȱȱȱ
Input
plan TheȱcufftHandleȱobjectȱforȱtheȱplanȱtoȱupdate
idata PointerȱtoȱtheȱsingleȬprecisionȱcomplexȱinputȱdataȱ(inȱGPUȱ
memory)ȱtoȱtransformȱ
odata PointerȱtoȱtheȱsingleȬprecisionȱrealȱoutputȱdataȱ(inȱGPUȱ
memory)

Output
odata ContainsȱtheȱrealȬvaluedȱoutputȱdata

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ
CUFFT_INVALID_VALUE Theȱidata,ȱodata,ȱand/orȱdirectionȱparameterȱ
isȱnotȱvalid.ȱ
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_EXEC_FAILED CUFFTȱfailedȱtoȱexecuteȱtheȱtransformȱonȱGPU.ȱ

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CUDA CUFFT Library

Return Values (continued)

CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_UNALIGNED_DATA Inputȱorȱoutputȱdoesȱnotȱsatisfyȱtextureȱ
alignmentȱrequirements.

Function cufftExecZ2Z()
cufftResult
cufftExecZ2Z(
cufftHandleplan,cufftDoubleComplex*idata,
cufftDoubleComplex*odata,intdirection);
ExecutesȱaȱCUFFTȱdoubleȬprecisionȱcomplexȬtoȬcomplexȱtransformȱ
planȱasȱspecifiedȱbyȱdirection.ȱCUFFTȱusesȱasȱinputȱdataȱtheȱGPUȱ
memoryȱpointedȱtoȱbyȱtheȱidataȱparameter.ȱThisȱfunctionȱstoresȱtheȱ
Fourierȱcoefficientsȱinȱtheȱodataȱarray.ȱIfȱidataȱandȱodataȱareȱtheȱsame,ȱ
thisȱmethodȱdoesȱanȱinȬplaceȱtransform.ȱȱȱ
Input
plan TheȱcufftHandleȱobjectȱforȱtheȱplanȱtoȱupdate
idata PointerȱtoȱtheȱdoubleȬprecisionȱcomplexȱinputȱdataȱ(inȱGPUȱ
memory)ȱtoȱtransformȱ
odata PointerȱtoȱtheȱdoubleȬprecisionȱcomplexȱoutputȱdataȱ(inȱGPUȱ
memory)
direction Theȱtransformȱdirection:ȱCUFFT_FORWARDȱorȱCUFFT_INVERSEȱ

Output
odata ContainsȱtheȱcomplexȱFourierȱcoefficients

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ
CUFFT_INVALID_VALUE Theȱidata,ȱodata,ȱand/orȱdirectionȱparameterȱ
isȱnotȱvalid.ȱ
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_EXEC_FAILED CUFFTȱfailedȱtoȱexecuteȱtheȱtransformȱonȱGPU.ȱ
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_UNALIGNED_DATA Inputȱorȱoutputȱdoesȱnotȱsatisfyȱtextureȱ
alignmentȱrequirements.

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CUDA CUFFT Library

Function cufftExecD2Z()
cufftResult
cufftExecD2Z(
cufftHandleplan,cufftDoubleReal*idata,
cufftDoubleComplex*odata);
ExecutesȱaȱCUFFTȱdoubleȬprecisionȱrealȬtoȬcomplexȱ(implicitlyȱ
forward)ȱtransformȱplan.ȱCUFFTȱusesȱasȱinputȱdataȱtheȱGPUȱmemoryȱ
pointedȱtoȱbyȱtheȱidataȱparameter.ȱThisȱfunctionȱstoresȱtheȱnonȬ
redundantȱFourierȱcoefficientsȱinȱtheȱodataȱarray.ȱIfȱidataȱandȱodataȱ
areȱtheȱsame,ȱthisȱmethodȱdoesȱanȱinȬplaceȱtransformȱ(Seeȱ““CUFFTȱ
TransformȱTypes””ȱonȱpage 7ȱforȱdetailsȱonȱrealȱdataȱFFTs.)ȱȱȱ
Input
plan TheȱcufftHandleȱobjectȱforȱtheȱplanȱtoȱupdate
idata PointerȱtoȱtheȱdoubleȬprecisionȱrealȱinputȱdataȱ(inȱGPUȱ
memory)ȱtoȱtransformȱ
odata PointerȱtoȱtheȱdoubleȬprecisionȱcomplexȱoutputȱdataȱ(inȱGPUȱ
memory)

Output
odata ContainsȱtheȱcomplexȱFourierȱcoefficients

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ
CUFFT_INVALID_VALUE Theȱidata,ȱodata,ȱand/orȱdirectionȱparameterȱ
isȱnotȱvalid.ȱ
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_EXEC_FAILED CUFFTȱfailedȱtoȱexecuteȱtheȱtransformȱonȱGPU.ȱ
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_UNALIGNED_DATA Inputȱorȱoutputȱdoesȱnotȱsatisfyȱtextureȱ
alignmentȱrequirements.

Function cufftExecZ2D()
cufftResult
cufftExecZ2D(
cufftHandleplan,cufftDoubleComplex*idata,
cufftDoubleReal*odata);

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CUDA CUFFT Library

ExecutesȱaȱCUFFTȱdoubleȬprecisionȱcomplexȬtoȬrealȱ(implicitlyȱ
inverse)ȱtransformȱplan.ȱCUFFTȱusesȱasȱinputȱdataȱtheȱGPUȱmemoryȱ
pointedȱtoȱbyȱtheȱidataȱparameter.ȱTheȱinputȱarrayȱholdsȱonlyȱtheȱnonȬ
redundantȱcomplexȱFourierȱcoefficients.ȱThisȱfunctionȱstoresȱtheȱrealȱ
outputȱvaluesȱinȱtheȱodataȱarray.ȱIfȱidataȱandȱodataȱareȱtheȱsame,ȱthisȱ
methodȱdoesȱanȱinȬplaceȱtransform.ȱ(Seeȱ““CUFFTȱTransformȱTypes””ȱ
onȱpage 7ȱforȱdetailsȱonȱrealȱdataȱFFTs.)ȱȱȱ
Input
plan TheȱcufftHandleȱobjectȱforȱtheȱplanȱtoȱupdate
idata PointerȱtoȱtheȱdoubleȬprecisionȱcomplexȱinputȱdataȱ(inȱGPUȱ
memory)ȱtoȱtransformȱ
odata PointerȱtoȱtheȱdoubleȬprecisionȱrealȱoutputȱdataȱ(inȱGPUȱ
memory)

Output
odata ContainsȱtheȱrealȬvaluedȱoutputȱdata

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱcreatedȱtheȱFFTȱplan.ȱ
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ
CUFFT_INVALID_VALUE Theȱidata,ȱodata,ȱand/orȱdirectionȱparameterȱ
isȱnotȱvalid.ȱ
CUFFT_INTERNAL_ERROR Internalȱdriverȱerrorȱisȱdetected.
CUFFT_EXEC_FAILED CUFFTȱfailedȱtoȱexecuteȱtheȱtransformȱonȱGPU.ȱ
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.
CUFFT_UNALIGNED_DATA Inputȱorȱoutputȱdoesȱnotȱsatisfyȱtextureȱ
alignmentȱrequirements.

Function cufftSetStream()
cufftResult
cufftSetStream(cufftHandleplan,cudaStream_tstream);
AssociatesȱaȱCUDAȱstreamȱwithȱaȱCUFFTȱplan.ȱAllȱkernelȱlaunchesȱ
madeȱduringȱplanȱexecutionȱareȱnowȱdoneȱthroughȱtheȱassociatedȱ
stream,ȱenablingȱoverlapȱwithȱactivityȱinȱotherȱstreamsȱ(forȱexample,ȱ

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dataȱcopying).ȱTheȱassociationȱremainsȱuntilȱtheȱplanȱisȱdestroyedȱorȱ
theȱstreamȱisȱchangedȱwithȱanotherȱcallȱtoȱcufftSetStream().ȱȱȱ
Input
plan TheȱcufftHandleȱobjectȱtoȱassociateȱwithȱtheȱstream
stream AȱvalidȱCUDAȱstreamȱcreatedȱwithȱcudaStreamCreate()ȱ(orȱ0ȱ
forȱtheȱdefaultȱstream)

Output
odata ContainsȱtheȱrealȬvaluedȱoutputȱdata

Return Values
CUFFT_SUCCESS Theȱstreamȱwasȱassociatedȱwithȱtheȱplan.
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ

Function cufftSetCompatibilityMode()
cufftResult
cufftSetCompatibilityMode(
cufftHandleplan,cufftCompatibilitymode);
ConfiguresȱtheȱlayoutȱofȱCUFFTȱoutputȱinȱFFTWȬcompatibleȱmodes.ȱ
WhenȱFFTWȱcompatibilityȱisȱdesired,ȱitȱcanȱbeȱconfiguredȱforȱpaddingȱ
only,ȱforȱasymmetricȱcomplexȱinputsȱonly,ȱorȱtoȱbeȱfullyȱcompatible.ȱȱ
Input
plan TheȱcufftHandleȱobjectȱtoȱassociateȱwithȱtheȱstream
mode TheȱcufftCompatibilityȱoptionȱtoȱbeȱusedȱ(seeȱ““Typeȱ
cufftCompatibility””ȱonȱpage 7):ȱ
CUFFT_COMPATIBILITY_NATIVE
CUFFT_COMPATIBILITY_FFTW_PADDINGȱ(Default)ȱ
CUFFT_COMPATIBILITY_FFTW_ASYMMETRIC
CUFFT_COMPATIBILITY_FFTW_ALL

Return Values
CUFFT_SUCCESS CUFFTȱsuccessfullyȱexecutedȱtheȱFFTȱplan.
CUFFT_INVALID_PLAN Theȱplanȱparameterȱisȱnotȱaȱvalidȱhandle.ȱ
CUFFT_SETUP_FAILED CUFFTȱlibraryȱfailedȱtoȱinitialize.

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Accuracy and Performance

AȱgeneralȱDFTȱcanȱbeȱimplementedȱasȱaȱmatrixȱvectorȱmultiplicationȱ
thatȱrequiresȱO(N2)ȱoperations.ȱHowever,ȱtheȱCUFFTȱLibraryȱemploysȱ
theȱCooleyȬTukeyȱalgorithmȱtoȱreduceȱtheȱnumberȱofȱrequiredȱ
operationsȱand,ȱthereby,ȱtoȱoptimizeȱtheȱperformanceȱofȱparticularȱ
transformȱsizes.ȱThisȱalgorithmȱexpressesȱaȱDFTȱrecursivelyȱinȱtermsȱofȱ
smallerȱDFTȱbuildingȱblocks.ȱTheȱCUFFTȱLibraryȱimplementsȱtheȱ
followingȱDFTȱbuildingȱblocks:ȱradixȬ2,ȱradixȬ3,ȱradixȬ5,ȱandȱradixȬ7.ȱ
Henceȱtheȱperformanceȱofȱanyȱtransformȱsizeȱthatȱcanȱbeȱfactoredȱasȱ
a b c d
2 * 3 * 5 * 7 ȱ(whereȱa,ȱb,ȱc,ȱandȱdȱareȱnonȬnegativeȱintegers)ȱisȱ
optimizedȱinȱtheȱCUFFTȱlibrary.ȱForȱotherȱsizes,ȱsingleȱdimensionalȱ
transformsȱareȱhandledȱbyȱtheȱBluesteinȱalgorithm,ȱwhichȱisȱbuiltȱonȱ
topȱofȱtheȱCooleyȬTukeyȱalgorithm.ȱTheȱaccuracyȱofȱtheȱBluesteinȱ
implementationȱdegradesȱwithȱlargerȱsizesȱcomparedȱtoȱtheȱpureȱ
CooleyȬTukeyȱcodeȱpath,ȱspecificallyȱinȱsingleȬprecisionȱmode,ȱdueȱtoȱ
theȱaccumulationȱofȱfloatingȬpointȱoperationȱinaccuracies.ȱOnȱtheȱ
otherȱhand,ȱtheȱpureȱCooleyȬTukeyȱimplementationȱhasȱexcellentȱ
accuracy,ȱwithȱtheȱrelativeȱerrorȱgrowingȱproportionallyȱtoȱlog2(N),ȱ
whereȱNȱisȱtheȱtransformȱsizeȱinȱpoints.
ForȱsizesȱhandledȱbyȱtheȱCooleyȬTukeyȱcodeȱpathȱ(thatȱis,ȱstrictlyȱ
multiplesȱofȱ2,ȱ3,ȱ5,ȱandȱ7),ȱtheȱmostȱefficientȱimplementationȱisȱ
obtainedȱbyȱapplyingȱtheȱfollowingȱconstraintsȱ(listedȱinȱorderȱofȱtheȱ
mostȱgenericȱtoȱtheȱmostȱspecializedȱconstraint,ȱwithȱeachȱsubsequentȱ
constraintȱprovidingȱtheȱpotentialȱofȱanȱadditionalȱperformanceȱ
improvement).
‰ Restrictȱtheȱsizeȱalongȱanyȱdimensionȱtoȱbeȱaȱmultipleȱofȱ2,ȱ3,ȱ5,ȱorȱ7ȱonly.ȱ
Forȱexample,ȱaȱtransformȱofȱsizeȱ3nȱwillȱlikelyȱbeȱfasterȱthanȱoneȱofȱ
i j
sizeȱ 2 * 3 ,ȱevenȱifȱtheȱlatterȱisȱslightlyȱsmaller.
‰ RestrictȱtheȱpowerȬofȬtwoȱfactorizationȱtermȱofȱtheȱXȬdimensionȱtoȱbeȱatȱ
leastȱaȱmultipleȱofȱeitherȱ16ȱforȱsingleȬprecisionȱtransformsȱorȱ8ȱforȱ
doubleȬprecisionȱtransforms.ȱThisȱaidsȱwithȱmemoryȱcoalescingȱonȱ
TeslaȬclassȱandȱFermiȬclassȱGPUs.
‰ RestrictȱtheȱpowerȬofȬtwoȱfactorizationȱtermȱofȱtheȱXȬdimensionȱtoȱbeȱaȱ
multipleȱofȱeitherȱ256ȱforȱsingleȬprecisionȱtransformsȱorȱ64ȱforȱdoubleȬ

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precisionȱtransforms.ȱThisȱfurtherȱaidsȱwithȱmemoryȱcoalescingȱonȱ
TeslaȬclassȱandȱFermiȬclassȱGPUs.
‰ RestrictȱtheȱXȬdimensionȱofȱsingleȬprecisionȱtransformsȱtoȱbeȱstrictlyȱaȱ
powerȱofȱtwoȱbetweenȱeitherȱ2ȱandȱ2048ȱforȱTeslaȬclassȱGPUsȱorȱ2ȱandȱ
8192ȱforȱFermiȬclassȱGPUs.ȱTheseȱtransformsȱareȱimplementedȱasȱ
specializedȱhandȬcodedȱkernelsȱthatȱkeepȱallȱintermediateȱresultsȱ
inȱsharedȱmemory.
Startingȱwithȱversionȱ3.1ȱofȱtheȱCUFFTȱLibrary,ȱtheȱconjugateȱ
symmetryȱpropertyȱofȱrealȬtoȬcomplexȱoutputȱdataȱarraysȱandȱ
complexȬtoȬrealȱinputȱdataȱarraysȱisȱexploited;ȱspecifically,ȱwhenȱtheȱ
powerȬofȬtwoȱfactorizationȱtermȱofȱtheȱXȬdimensionȱisȱatȱleastȱaȱ
multipleȱofȱ4.ȱLargeȱ1Dȱsizesȱ(powersȬofȬtwoȱlargerȱthanȱ65,536)ȱandȱ
2Dȱandȱ3Dȱtransformsȱbenefitȱtheȱmostȱfromȱtheȱperformanceȱ
optimizationsȱinȱtheȱimplementationȱofȱrealȬtoȬcomplexȱorȱcomplexȬtoȬ
realȱtransforms.

CUFFT Code Examples

Thisȱsectionȱprovidesȱsixȱsimpleȱexamplesȱofȱ1D,ȱ2D,ȱandȱ3Dȱcomplexȱ
andȱrealȱdataȱtransformsȱthatȱuseȱtheȱCUFFTȱtoȱperformȱforwardȱandȱ
inverseȱFFTs.ȱTheȱexamplesȱareȱasȱfollows:
‰ ““1DȱComplexȬtoȬComplexȱTransforms””ȱonȱpage 24
‰ ““1DȱRealȬtoȬComplexȱTransforms””ȱonȱpage 25
‰ ““2DȱComplexȬtoȬComplexȱTransforms””ȱonȱpage 26
‰ ““Batchedȱ2DȱComplexȬtoȬComplexȱTransforms””ȱonȱpage 27
‰ ““2DȱComplexȬtoȬRealȱTransforms””ȱonȱpage 28
‰ ““3DȱComplexȬtoȬComplexȱTransforms””ȱonȱpage 29

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1D Complex-to-Complex Transforms
#defineNX256
#defineBATCH10

cufftHandleplan;
cufftComplex*data;
cudaMalloc((void**)&data,sizeof(cufftComplex)*NX*BATCH);

/*Createa1DFFTplan.*/
cufftPlan1d(&plan,NX,CUFFT_C2C,BATCH);

/*UsetheCUFFTplantotransformthesignalinplace.*/
cufftExecC2C(plan,data,data,CUFFT_FORWARD);

/*Inversetransformthesignalinplace.*/
cufftExecC2C(plan,data,data,CUFFT_INVERSE);

/*Note:
(1)Dividebynumberofelementsindatasettogetbackoriginaldata
(2)IdenticalpointerstoinputandoutputarraysimpliesinŞplace
transformation
*/

/*DestroytheCUFFTplan.*/
cufftDestroy(plan);
cudaFree(data);

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1D Real-to-Complex Transforms
#defineNX256
#defineBATCH10

cufftHandleplan;
cufftComplex*data;
cudaMalloc((void**)&data,sizeof(cufftComplex)*(NX/2+1)*BATCH);

/*Createa1DFFTplan.*/
cufftPlan1d(&plan,NX,CUFFT_R2C,BATCH);

/*UsetheCUFFTplantotransformthesignalinplace.*/
cufftExecR2C(plan,(cufftReal*)data,data);

/*DestroytheCUFFTplan.*/
cufftDestroy(plan);
cudaFree(data);

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2D Complex-to-Complex Transforms
#defineNX256
#defineNY128

cufftHandleplan;
cufftComplex*idata,*odata;
cudaMalloc((void**)&idata,sizeof(cufftComplex)*NX*NY);
cudaMalloc((void**)&odata,sizeof(cufftComplex)*NX*NY);

/*Createa2DFFTplan.*/
cufftPlan2d(&plan,NX,NY,CUFFT_C2C);

/*UsetheCUFFTplantotransformthesignaloutofplace.*/
cufftExecC2C(plan,idata,odata,CUFFT_FORWARD);

/*Note:idata!=odataindicatesanoutŞofŞplacetransformation
toCUFFTatexecutiontime.*/
/*Inversetransformthesignalinplace*/
cufftExecC2C(plan,odata,odata,CUFFT_INVERSE);

/*DestroytheCUFFTplan.*/
cufftDestroy(plan);
cudaFree(idata);cudaFree(odata);

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Batched 2D Complex-to-Complex Transforms

#defineNX128
#defineNY256
#defineBATCHSIZE1000

intdatalen;
cufftHandleplan;
cufftComplex*indata,*outdata;

datalen=NX*NY*BATCHSIZE;
cudaMalloc((void**)&indata,sizeof(cufftComplex)*datalen);
cudaMalloc((void**)&outdata,sizeof(cufftComplex)*datalen);

/*Createabatched2Dplan*/
cufftPlanMany(&plan,2,{NX,NY},NULL,1,0,NULL,1,0,CUFFT_C2C,BATCHSIZE);

/*ExecutethetransformoutŞofŞplace*/
cufftExecC2C(plan,indata,outdata,CUFFT_FORWARD);

/*DestroytheCUFFTplan*/
cufftDestroy(plan);
cudaFree(indata);
cudaFree(outdata);

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2D Complex-to-Real Transforms
#defineNX256
#defineNY128

cufftHandleplan;
cufftComplex*idata;
cufftReal*odata;
cudaMalloc((void**)&idata,sizeof(cufftComplex)*NX*NY);
cudaMalloc((void**)&odata,sizeof(cufftReal)*NX*NY);

/*Createa2DFFTplan.*/
cufftPlan2d(&plan,NX,NY,CUFFT_C2R);

/*UsetheCUFFTplantotransformthesignaloutofplace.*/
cufftExecC2R(plan,idata,odata);

/*DestroytheCUFFTplan.*/
cufftDestroy(plan);
cudaFree(idata);cudaFree(odata);

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3D Complex-to-Complex Transforms
#defineNX64
#defineNY64
#defineNZ128

cufftHandleplan;
cufftComplex*data1,*data2;
cudaMalloc((void**)&data1,sizeof(cufftComplex)*NX*NY*NZ);
cudaMalloc((void**)&data2,sizeof(cufftComplex)*NX*NY*NZ);

/*Createa3DFFTplan.*/
cufftPlan3d(&plan,NX,NY,NZ,CUFFT_C2C);

/*Transformthefirstsignalinplace.*/
cufftExecC2C(plan,data1,data1,CUFFT_FORWARD);

/*Transformthesecondsignalusingthesameplan.*/
cufftExecC2C(plan,data2,data2,CUFFT_FORWARD);

/*DestroytheCUFFTplan.*/
cufftDestroy(plan);
cudaFree(data1);cudaFree(data2);

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