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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.