On Wednesday 08 April 2009 06:08:50 am Joel B. Mohler wrote:
> > * n.exact_log can be done faster for small bases by making careful use
> > of the identity log_m(n) = log_2(n)/log_2(m) (I wrote a crappy broken
> > python implementation and timed this - I don't know how to write it
> > properly as I don't know enough about Sage yet)
>
> I have a patch that's taken a long time for me to be happy with (but I
> think I just about am now), which overhauls exact_log.  It results in 50x
> speedups for small input and selected large input.

This promised patch is now
http://trac.sagemath.org/sage_trac/ticket/5732

The one thing I'm not entirely happy with is n.exact_log(m) where n is so 
large that the *log* takes more than real interval field precision (53 bits).  
This case is kind of difficult to test because it requires numbers which 
takes lots of ram and/or patience.

--
Joel

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