Re: bug in pari-gp precision?

[Walter Neumann <neumann@cpw.math.columbia.edu>]

I just came across another (the same?) problem (current CVS):

? 2.0^100 - 10^-29 - 2.0^100
%1 = 32.0000000

Admittedly, this is a big improvement over the 2.1.4 release:

(12:15) gp > 2.0^100-10^-29+2.0^100
%1 = 2.535301200456458802993406410 E30

But in both cases 0. or less would be nicer!

--walter neumann

On Fri, 4 Oct 2002, Karim BELABAS wrote:

> Dear Walter,
>
> On Fri, 4 Oct 2002, Walter Neumann wrote:
> > The numerical value of the parameter is computed as a root of an integer
> > polynomial and we write:
> >  'we quote from the manual for the pari libraries: ``The algorithm used is
> >   a modification of A. Sch\"onhage's remarkable root-finding algorithm,
> >   due to and implemented by X. Gourdon. Barring bugs, it is guaranteed to
> >   converge and to give the roots to the desired accuracy.''
> >
> > This guarantee seems to me suspect?
>
> No, this one at least is correct. The root finding algorithm uses exact
> computations, and checks (still exactly) the accuracy of the computed roots a
> posteriori [ meaning there exists a root r close to the computed one r'
> (within requested relative accuracy), _not_ that P(r') is small ].
>
> In short, no floating point numbers are involved here.
>
> > p.s. I havn't posted to pari-dev, since I am not sure how appropriate this
> > is for that list, but I'd have no objection to copying to there.
>
> This is 100% appropriate. I'm posting it to the list.
>
> Thanks!
>
>     Karim.
>