Re: Portable syntax of interval literals
On 2013-09-29 17:13:10 -0400, Michel Hack wrote:
> Dima, replying to me:
> > > it is not much more trouble to compute an enclosure with an
> > > error bound of somewhere between half an ulp and one ulp
> >
> > This is true for rounding to nearest. For directed rounding it is easy
> > to compute enclosure with an error bound say 1.001*ulp as 754-2008 does.
>
> Dima is right. Anything other than "tightest" will require tolerating
> an error strictly larger than 1 ulp for directed rounding. So perhaps
> we should require "faithful" rounding, which allows directed rounding
> to return one of two nearest representable values on the correct side
> of the true result.
For inf-sup interval types, there's already the notion of
accuracy mode, which could be applied with some modifications
to textToInterval. In particular the "accurate" mode. Isn't
that sufficient?
I'd say nextOut(hull_T(x)) for "accurate"; "tightest" and "valid"
would keep their usual definitions.
One advantage is that this can be applied to all inf-sup types,
even when the ulp is not defined.
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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