Re: precision and contfrac()

[Karim BELABAS <Karim.Belabas@math.u-psud.fr>]

On Tue, 8 Oct 2002, Bill Allombert wrote:

> On Tue, Oct 08, 2002 at 02:43:50PM +0200, Thomas Baruchel wrote:
> > Brest, le mardi 8 octobre
> >
> > Hi, I wonder how I should set the precision \p in order to
> > have n exact terms in the continued fraction expansion of
> > sqrt(x) (x being exact).
>
> It is a difficult question. The precision exhausted depend on the size of the
> partial quotients, which are very hard to control.
>
> >
> > For instance, what precision is needed in order to be sure that I
> > have 500 exact terms ? 2,000 ? 10,000 ?

Just to clarify a point: all terms given are exact. If you do not get
enough terms, restart the computation with higher precision [ it is easy to
automate this: double precision until you're happy. It is tough to guestimate
the required precision for general numbers. ]

Also keep in mind the continued fraction is normalized so that the last
partial quotient is never 1. So if the continued fraction you would obtain is
[..., n, 1], it is given as [..., n+1].

Cheers,

    Karim.
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