Re: How do I bisect unbounded intervals?
> Date: Tue, 17 Jan 2012 07:15:07 -0600
> From: Ralph Baker Kearfott <rbk@xxxxxxxxxxxxx>
> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Re: How do I bisect unbounded intervals?
>
> Vincent et al,
>
> On 01/17/2012 06:43 AM, Vincent Lefevre wrote:
> > 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?
> >
>
> It will be if we make it so. An advantage of that would be
> clarity and simplicity. Also, since "mid" is a floating point
> value, other standards could handle conversion of the target
> type of the "mid." (just my own opinion)
>
> >> . . .
>
I agree with Baker here.
After all, we cannot assume that any given implementation
will support 1788 in more than one floating-point type.
So we certainly cannot assume that support functions return
their results in some format with a greater range or
percision than that used for the interval type.
Our safest assumption is that mid(interval) returns the
same type as is used in the interval. And it will almost
certainly be the most common case WHATEVER one chooses to
support.
Dan