Re: How do I bisect unbounded intervals?
On 2012-01-16 22:25:49 +0000, John Pryce wrote:
> Dan, Vincent, Nate etc.
>
> This discussion reminds me of a Level 2 issue that must be resolved.
> When discussing finite precision it's clear you've all been assuming
> an inf-sup representation. How do midpoint and the other numeric
> functions of intervals work for an _implicit_ type?
Even for inf-sup, I now think that this is not clear: is the format
of the result necessarily the same as the number format associated
with the interval type?
> I've basically defined an interval type T as a set of mathematical
> intervals plus a specified T-hull operation. No number-format is
> mentioned. But Level 2 midpoint, etc., must return a datum of some
> number format. Hence I see nothing for it but to make the revised
> definition:
>
> An interval type T is a set of mathematical intervals,
> plus a specified T-hull operation, plus a specified
> number format, let's call it the T-format.
>
> For each implemented T, each numeric operation on intervals shall
> have a T-version that returns a result of this T-format. (One might
> allow different operations to return results of different formats,
> but to me that seems way too complicated.)
I would not associate a T-format with the interval type T.
For instance, for a binary64-based inf-sup interval type T, one may
want the midpoint in binary64, but also in binary128, as allowed by
IEEE 754 (§5.4.1).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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