Comments about FFT



On Sat, Aug 22, 2009 at 6:36 PM, ?iga Lenar?i?<ziga.lenarcic at gmail.com> wrote:
> ...Code like
>
> (dotimes (i ($length a1))
> ? ? ? ? ? (setf (nth (1+ i) a1) (m+ (nth (1+ i) a1) (m* '$%i (nth (1
> + i) a2)))))
>
> can't be efficient on lists of length perhaps 1024*8. Surely the list
> should be traversed in some other way....

Indeed!  This changes FFT from O(n log n) to O(n^2) -- though with a
smaller constant.

As for the m+ etc., I suppose this is to allow the use of bfloats as
well as machine numbers, and in the future perhaps to other numeric
types (intervals?).

            -s