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`The following are a number of ideas for future work that we have`

`thought of, or which have been suggested to us. Let us know`

`(fftw@theory.lcs.mit.edu) if you have other proposals, or if there is`

`something that you want to work on.`

`* Implement some sort of Prime Factor algorithm (Temperton's?) (PFA is`

`now used in the codelets.)`

`* Try the Winograd blocks for the base cases. (We now use Rader's`

`algorithm for prime size codelets.)`

`* Try on-the-fly generation of twiddle factors, to save space and`

`cache. (Done. However, not yet enabled in the standard distribution.`

`The codelet generator is capable of generating code that either loads`

`or computes the twiddle factors, and the FFTW C code supports both`

`ways. We do not have enough experimental numbers to determine which`

`way is faster, however)`

`* Since we now have "strided wisdom," it would be nice to keep the`

`stride into account when planning 1D transform recursively. We should`

`eliminate the planner table altogether, and just use the wisdom table`

`for planning.`

`* Implement fast DCT and DST codes (cosine and sine transforms);`

`equivalently, implement fast algorithms for transforms of real/even`

`and real/odd data. There are two parts to this: (i) modify the`

`codelet generator to output hard-coded transforms of small sizes [this`

`is done], and (ii) figure out & implement a recursive framework for`

`combining these codelets to achieve transforms of general lengths.`

`(Once this is done, implement multi-dimensional transforms, etcetera.)`

`* Implement a library of convolution routines, windowing, filters,`

`etcetera based on FFTW. As DSP isn't our field (we are interested in`

`FFTs for other reasons), this sort of thing is probably best left to`

`others. Let us know if you're interested in writing such a thing,`

`though, and we'll be happy to link to your site and give you feedback.`

`* Generate multi-dimensional codelets for use in two/three-dimensional`

`transforms. (i.e. implement what is sometimes called a "vector-radix"`

`algorithm.) There are potential cache benefits to this.`

`* Take advantage of the vector instructions on the Pentium-III and`

`forthcoming PowerPC architectures. (Coming from the old Cray vector`

`supercomputers and the horrible coding they encouraged, this seems`

`suspiciously like a giant step backwards in computer architectures...)`

`We'd like to see better gcc support before we do anything along these`

`lines, though.`

`* In rfftw, implement a fast O(n lg n) algorithm for prime sizes and`

`large prime factors (currently, only the complex FFTW has fast`

`algorithms for prime sizes). The basic problem is that we don't know`

`of any such algorithm specialized for real data; suggestions and/or`

`references are welcome.`

`* In the MPI transforms, implement a parallel 1D transform for real`

`data (i.e. rfftw_mpi). (Currently, there are only parallel 1D`

`transforms for complex data in the MPI code.)`

`* In the MPI transforms, implement more sophisticated (i.e. faster)`

`in-place and out-of-place transpose routines for the in-process`

`transposes (used as subroutines by the distributed transpose). The`

`current routines are quite simplistic, although it is not clear how`

`much they hurt performance.`