Re: midpoint
On 8 Mar 2012 at 11:31, Vincent Lefevre wrote:
Date sent: Thu, 8 Mar 2012 11:31:12 +0100
From: Vincent Lefevre <vincent@xxxxxxxxxx>
To: stds-1788@xxxxxxxxxxxxxxxxx
Subject: Re: midpoint
> On 2012-03-07 08:27:34 -0800, Dan Zuras Intervals wrote:
> > Thus, although things like midpoint may be easily
> > well defined among the Reals, we have to ask
>
> Among the reals, the midpoint of an unbounded interval or Empty
> is not well defined.
>
> > ourselves: What is the best representation of
> > these results within our finite floating-point
> > systems & the intervals we construct out of them?
> >
> > And, in this context, the word "best" should not
> > be interpreted as "closest" but as "most useful".
> > So: What is the most useful answer?
> >
> > In general, this will be a matter of some opinion
> > & debate (obvious from the length of this discussion
> > already). But I think your principle of avoiding
> > NaNs & infinities in so far as is possible is a good
> > place to start.
> >
> > I believe that infinities can largely be avoided &
> > that NaNs can be avoided altogether. But I must
> > admit I am not quite sure about the NaNs.
>
> But what if the most useful answer is to warn the user that he did
> something wrong? And what is the most useful way to do that?
>
very good question!
I just want to add that during a computation once
it happens that rad >= 1/2 mid then clearly the user
has done something wrong (and any further result is useless).
Instead of 1/2 any other convenient fp constant between, say,
1/10 and 1/2 can be used.
One should not forget that mid-rad numbers model approximate
numbers.
S Markov