Re: Motion P1788/M0032.01:MidpointMeaning -- discussion period begins
On 2012-03-20 07:53:53 -0700, Dmitry Nadezhin wrote:
> > AFAIK, "based on a some floating-point system F" has not been defined
> > for implicit interval types (see the discussion about associated /
> > compatible number formats). IMHO, we could just require that each
> > non-empty interval of T must contain an element of F.
> >
> > > mid_F(X) = if ((inf(X) == -inf) && (sup(X) == +inf)) then 0
> > > else if (round2Nearest_F(mid(X)) == +inf)
> > > then nextDown_F(+inf)
> > > else if (round2Nearest_F(mid(X)) == -inf)
> > > then nextUp_F(-inf)
> > > else round2Nearest_F(mid(X))
> >
> > So, as a consequence, inf_F(X) <= mid_F(X) <= sup_F(X). This is
> > important, because this will be assumed below.
>
> Requirement "each non-empty interval of T must contain an element of F" is not necessary.
> The failure of then cna invalidate property inf(X) <= mid_F(X) <= sup(X).
> Nevertheless, property inf_F(X) <= mid_F(X) <= sup_F(X) is valid independently of the requirement.
So, there shouldn't be any specific constraint on F (e.g., in case
of IEEE 754, it could be any supported format).
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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