This has the following effect on the time to compute 10,000 forward and 10,000 backward complex FFTs of 1,024 elements.

With -fno-strict-aliasing (used now by Gambit for reasons I'll explain below):

(time (do ((i 0 (fx+ i 1))) ((fx= i 10000)) (direct-fft-recursive-4 a table) (inverse-fft-recursive-4 a table) (do ((i 0 (fx+ i 1))) ((fx= i (fx* two^n 2))) (f64vector-set! a i (fl/ (f64vector-ref a i) inexact-two^n)))))
    705 ms real time
    704 ms cpu time (704 user, 0 system)
    6 collections accounting for 2 ms real time (0 user, 0 system)
    1600000 bytes allocated
    22 minor faults
    no major faults

With -fstrict-aliasing:

(time (do ((i 0 (fx+ i 1))) ((fx= i 10000)) (direct-fft-recursive-4 a table) (inverse-fft-recursive-4 a table) (do ((i 0 (fx+ i 1))) ((fx= i (fx* two^n 2))) (f64vector-set! a i (fl/ (f64vector-ref a i) inexact-two^n)))))
    590 ms real time
    592 ms cpu time (588 user, 4 system)
    6 collections accounting for 2 ms real time (4 user, 0 system)
    1600000 bytes allocated
    22 minor faults
    no major faults

That's a 19% performance improvement.  (And the performance isn't bad, 1.74 GFLOPS on my 2.33GHz Core 2 quad 6600.  Later I'll try to get gcc to vectorize the main loop.)