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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.