Re: [boost] Re: Comments on Special functions, Quaternions, Octonions

From: boost (boost_at_[hidden])
Date: 2001-05-29 08:58:15

Salut,

On Tuesday 29 May 2001 12:24, you wrote:
> Somewhere in the E.U., le 29/05/2001

Aha. Delocalized ?

[...]
>                The terminology may not be the correct one, but what I meant
> was the following:
>
>                If I create a piecewise approximation to a function, say with
> one definition on [0;1] and another on ]1;2], then there is a risk of
> discontinuity at 1, and that's bad if what I intended to model was in
> fact continuous. So instead I find one approwimation on [0;3/2],
> another on [1/2;2], and interpolate between the two approximations on
> [1/2;3/2] (which I called the "continuity" or "matching" zone). This
> generalises readilly.
>
>                We get better (order-0) behaviour, at the cost of more
> computation (especially in the matching zone).
>

Hmm, I thought that you won't have problems with of this kind sinc(x) ,
--- this functions is just too friendly ---,  setting the first interval to
|x| < pow( epsilon, 0.25 ) you still have a higher order correction below 
epsilon.  But I just realized that for long double on my g++ 2.95.3 sin()
seems to be unreliable in the last few bits and could cause some trouble.
 
Concerning atan(), you can get in big trouble :(
 
Amicalement
Peter Schmitteckert