Mark Dickinson <[EMAIL PROTECTED]> added the comment:

Here's a pure Python implementation of the Burnikel and Ziegler recursive 
division algorithm.  I've no idea whether it's faster or slower than 
Newton, but it might be worth a look.  It depends heavily on bit 
operations, which ought to be much faster when coded in C.  (Some of the 
shifts would be completely unnecessary---replaced by changes in indexing 
instead.)

The original paper describing the algorithm is available here:

http://cr.yp.to/bib/1998/burnikel.ps

Added file: http://bugs.python.org/file11059/fast_str.py

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