On Wed, Dec 14, 2011 at 3:39 PM, Harald Schilly
<harald.schi...@gmail.com> wrote:
> On Wed, Dec 14, 2011 at 23:50, Harald Schilly <harald.schi...@gmail.com> 
> wrote:
>> I hacked something together that plots a histogram...
>
> I made a second version, that uses the timeit command directly and
> scales the x-axis manually (i.e. including the 0)
>
> It just times the factor function, but feel free to edit the .sage file!

One heads up here -- many factoring algorithms are nondeterministic.
They proceed by trying, via some heuristic, one of a million different
options, and many of those involve doing something random and hoping
to somehow find a factor.

If you do "factor(2**111-1, verbose=4)" or "factor(2**111-1,
verbose=8)" you'll see that randomized algorithms such as Pollard rho
[1] are used for factoring that number.

[1] http://en.wikipedia.org/wiki/Pollard's_rho_algorithm

I remember back in 1996 or so when I was comparing the speed of
various computers I would always try to factor some large integer in
PARI on each machine.  At some point I realized this was not the best
way to benchmark something.

Sometimes these days I'll compute factorial(10^7), say, which tests
something about MPIR at least.

William



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-- 
William Stein
Professor of Mathematics
University of Washington
http://wstein.org

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