On Wed, Feb 12, 2014 at 12:12 PM, Jori Mantysalo <jori.mantys...@uta.fi> wrote:
> On Wed, 12 Feb 2014, William Stein wrote:
>
>> 1. It is *NOT* true.    Sage just directly calls the PARI C library,
>> which is always loaded on startup of Sage.
>
>
> OK, good (or bad, which way one wants it to be...).
>
>
>> It's pretty likely that when the line of code in question was written
>> (prob in 2005 or 2006) this speed difference wasn't the case.
>
>
> Maybe somebody has just tested this once for given precision? This used
> about 1,5 seconds CPU time every time:
>
> gamma(RealField(prec=10000)(3.14159))
>
> And this one only about 0,1 seconds, except that for first time it took 10,7
> seconds:
>
> gamma(ComplexField(prec=10000)(3.14159))
>
> And reason is of course clear, as Fredrik Johansson wrote "If you cache
> Bernoulli numbers, - -".

You have just made a very, very good point.

 -- William

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

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