There's also the recursive division algorithm due
to Burnikel and Ziegler;  this might be worth a look.
I think it's the same asymptotic complexity (constant
times karatsuba multiplication complexity), but may
turn out to be faster for one reason or another.

I had a Python implementation of this somewhere;
I'll see if I can dig it out.

Assigning this to me so that it doesn't get lost or
forgotten;  but note that I don't intend to do
anything about it before 2.6/3.0 final.  If anyone else
wants to take it off my hands before then, feel free.