This is a collection of old FFT routines, and a few newer
ones based upon Haar transforms.  I have used the routine
harm.f for many years, and it works well.  I have also checked
out the routines fft.f and c2fft.f and both appear to be good.
I would be interested in speed comparisons and other information 
about their performance.  On an HP 715/75 with full optimization
for 256x256 complex arrays in Fortran, the times I obtain are:

	harm.f	0.25 seconds per FFT
	fft.f	0.4  seconds per FFT
	c2fft.f	0.4  seconds per FFT (from mfft)
	
Both fft.f and c2fft.f are sensitive (on HP) to when normalizations
are done, presumably because the computer does not like large numbers!

For cases where the sizes are not a factor of 2, fft.f and c2fft
work better, e.g. around 0.35 seconds for 243x243 or 250x250.

Caveats:
	1) Be aware that not all of these routines normalize
	the transform.
	2) I have not personaly tested them all.
	3) With larger sized arrays memory access dominates the
	speed.
	4) Not all routines will have the same origins
	5) Speed can be VERY computer and optimization dependent.  For
	instance, some optimizations of harm.f on our HP make it SLOWER.
	
L. D. Marks ldm@apollo.numis.nwu.edu
July 1995