!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Frees memory allocated by  fftw_malloc#. Currently, we only need this to  free the wisdom string. Simple plan execution 8Plan a real to real transform using the guru interface. ;Plan a complex to real transform using the guru interface. ;Plan a real to complex transform using the guru interface. >Plan a complex to complex transform using the guru interface. &Types of transforms. Used to control . ITuple of transform dimensions and non-transform dimensions of the array. Logical size of dimension &Stride along dimension in input array 'Stride along dimension in output array Real to Real transform kinds.  !"#$%&'-Determine which direction of DFT to execute. ()*+The ,+@ type is used to influence the kind of plans which are created. * To specify multiple flags, use a bitwise . ,-./$A plan is an opaque foreign object. 0COur API is polymorphic over the real data type. FFTW, at least in & principle, supports single precision , double precision  and  long double CLDouble (presumable?). 12345This lock must be taken during planning of any transform. The FFTW L library is not thread-safe in the planning phase. Thankfully, the lock is & not needed during the execute phase. 6789:;<=BDefault flag. For most transforms, this is equivalent to setting E  and A:. The exceptions are complex to real and half-complex to  real transforms. >?@GAllows FFTW to overwrite the input array with arbitrary data; this can ; sometimes allow more efficient algorithms to be employed. LSetting this flag implies that two memory allocations will be done, one for + work space, and one for the result. When D is not set, we will be L doing two memory allocations anyway, so we set this flag as well (since we  don'!t retain the work array anyway). AA: specifies that an out-of-place transform must not change M its input array. This is ordinarily the default, except for complex to real  transforms for which @& is the default. In the latter cases,  passing A4 will attempt to use algorithms that do not destroy O the input, at the expense of worse performance; for multi-dimensional complex M to real transforms, however, no input-preserving algorithms are implemented " so the Haskell bindings will set @ and do a transform with two  memory allocations. BKInstruct FFTW not to generate a plan which uses SIMD instructions, even if M the memory you are planning with is aligned. This should only be needed if L you are using the guru interface and want to reuse a plan with memory that , may be unaligned (i.e. you constructed the  with  ). CKThe header claims that this flag is documented, but in reality, it is not.  I don':t know what it does and it is here only for completeness. DD= specifies that, instead of actual measurements of different N algorithms, a simple heuristic is used to pick a (probably sub-optimal) plan # quickly. With this flag, the input/)output arrays are not overwritten during  planning. PThis is the only planner flag for which a single memory allocation is possible. EE< tells FFTW to find an optimized plan by actually computing M several FFTs and measuring their execution time. Depending on your machine, 0 this can take some time (often a few seconds). E is the default  planning option. FF is like E0, but considers a wider range of algorithms and  often produces a  more optimal- plan (especially for large transforms), but L at the expense of several times longer planning time (especially for large  transforms). GG is like F& but considers an even wider range of F algorithms, including many that we think are unlikely to be fast, to K produce the most optimal plan but with a substantially increased planning  time. HIJKLMNOPQRSCorresponds to the  fftw_iodim) structure. It completely describes the ; layout of each dimension, before and after the transform. TUVW9Verify that a plan is valid. Thows an exception if not. X<Confirm that the plan is valid, then execute the transform. YIIn-place normalization outside of IO. You must be able to prove that no , reference to the original can be retained. ZNormalized general complex DFT [LNormalized general complex to real DFT where the last transformed dimension  is logically even. \LNormalized general complex to real DFT where the last transformed dimension  is logicall odd. ]Multi-dimensional forward DFT. ^Multi-dimensional inverse DFT. _,Multi-dimensional forward DFT of real data. `JMulti-dimensional inverse DFT of Hermitian-symmetric data (where only the & non-negative frequencies are given). aJMulti-dimensional inverse DFT of Hermitian-symmetric data (where only the K non-negative frequencies are given) and the last transformed dimension is  logically odd. bcdIMulti-dimensional real to real transform. The result is not normalized. eQMulti-dimensional real to half-complex transform. The result is not normalized. fQMulti-dimensional half-complex to real transform. The result is not normalized. gMMulti-dimensional Discrete Hartley Transform. The result is not normalized. h4Multi-dimensional Type 1 discrete cosine transform. iLMulti-dimensional Type 2 discrete cosine transform. This is commonly known  as the DCT. jLMulti-dimensional Type 3 discrete cosine transform. This is commonly known  as the- inverse DCT. The result is not normalized. k4Multi-dimensional Type 4 discrete cosine transform. l2Multi-dimensional Type 1 discrete sine transform. m2Multi-dimensional Type 2 discrete sine transform. n2Multi-dimensional Type 3 discrete sine transform. o2Multi-dimensional Type 4 discrete sine transform. p1-dimensional complex DFT. q/1-dimensional complex inverse DFT. Inverse of p. r#1-dimensional real to complex DFT. sM1-dimensional complex to real DFT with logically even dimension. Inverse of r. tL1-dimensional complex to real DFT with logically odd dimension. Inverse of r. u(1-dimensional real to half-complex DFT. v41-dimensional half-complex to real DFT. Inverse of u after normalization. wM1-dimensional Discrete Hartley Transform. Self-inverse after normalization. x01-dimensional Type 1 discrete cosine transform. yK1-dimensional Type 2 discrete cosine transform. This is commonly known as the DCT. zK1-dimensional Type 3 discrete cosine transform. This is commonly known as the inverse DCT. {01-dimensional Type 4 discrete cosine transform. |.1-dimensional Type 1 discrete sine transform. }.1-dimensional Type 2 discrete sine transform. ~.1-dimensional Type 3 discrete sine transform. .1-dimensional Type 4 discrete sine transform. LTry to transform a CArray with only one memory allocation (for the result). N If we can find a way to prove that FFTW already has a sufficiently good plan N for this transform size and the input will not be overwritten, then we could 3 call have a version of this that does not require D. Since this is $ not currently the case, we require D! to be set. Note that we do not  check for the A/ flag here. This is because the default is to L preserve input for all but the C->R and HC->R transforms. Therefore, this : function must not be called for those transforms, unless A is  set. LTransform a CArray with two memory allocations. This is entirely safe with O all transforms, but it must allocate a temporary array to do the planning in. UAll the logic for determining shape of resulting array, and how to do the transform. A simple helper.  A generally useful list utility 'Complex to Complex DFT, un-normalized. Real to Complex DFT. EComplex to Real DFT. The first argument determines whether the last 2 transformed dimension is logically odd or even.  implies the dimension  is odd. HComplex to Real DFT where last transformed dimension is logically even. GComplex to Real DFT where last transformed dimension is logically odd. Real to Real transforms. Queries the FFTW cache. The ! can be written to a file so the + wisdom can be reused on a subsequent run. 'Add wisdom to the FFTW cache. Returns  if it is successful. 7Tries to import wisdom from a global source, typically etcfftw/wisdom.  Returns  if it was successful. *Using this instance requires linking with -lfftw3.   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~0123456/.+,-*789:;<=?>@ABCDEFG')(&HIJ%$#"! KLMNOPQRSTUV WXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~   %$#"!  !"#$%&')(()*+,-,-./01234123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ non-portable experimental jed@59A2.orgA !"#$%'()@ADEFGZ[\]^_`adefghijklmnopqrstuvwxyz{|}~A')(%$#"! @ADEFGpq]^Zrst_`a[\uvwxyz{|}~efghijklmnod      !"#$%&'()*+,--./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ fft-0.1.6 Math.FFT.BaseMath.FFTc_freec_import_wisdom_systemc_import_wisdom_stringc_export_wisdom_string c_execute_r2rc_execute_dft_c2rc_execute_dft_r2c c_execute_dft c_executec_plan_guru_r2rc_plan_guru_dft_c2rc_plan_guru_dft_r2cc_plan_guru_dftDFTRRCROCRRCCCTSpecIODimnIODimisIODimosIODimFFTWKindKindRODFT11RODFT10RODFT01RODFT00REDFT11REDFT01REDFT10REDFT00DHTHC2RR2HCFFTWSignSign DFTBackward DFTForwardFFTWFlagFlagunFlagFFTWPlanPlanFFTWReal plan_guru_dftplan_guru_dft_r2cplan_guru_dft_c2r plan_guru_r2rlockwithLock c_measurec_destroy_input c_unalignedc_conserve_memory c_exhaustivec_preserve_input c_patient c_estimatenullFlag destroyInput preserveInput unalignedconserveMemoryestimatemeasurepatient exhaustive c_forward c_backwardunSignunKindc_r2hcc_hc2rc_dht c_redft00 c_redft10 c_redft01 c_redft11 c_rodft00 c_rodft10 c_rodft01 c_rodft11checkexecuteunsafeNormalizedftGdftCRGdftCROGdftNidftNdftRCNdftCRNdftCRONfzrdrrdftRRNdftRHNdftHRNdhtNdct1Ndct2Ndct3Ndct4Ndst1Ndst2Ndst3Ndst4NdftidftdftRCdftCRdftCROdftRHdftHRdhtdct1dct2dct3dct4dst1dst2dst3dst4hastransformCArraytransformCArray'dftShape withTSpecadjustdftGUdftRCGdftCRG_dftCRGUdftCROGUdftRRGexportWisdomStringimportWisdomStringimportWisdomSystembase Data.Bits.|.ghc-prim GHC.TypesFloatDouble carray-0.1.5Data.Array.CArray.BaseCArrayunsafeForeignPtrToCArrayGHC.BoolTrueGHC.BaseString$fFFTWRealDouble