Re: Comparisons and decorations, part 2
> Subject: Re: Comparisons and decorations, part 2
> From: John Pryce <j.d.pryce@xxxxxxxxxxxx>
> Date: Tue, 28 Sep 2010 09:13:00 +0100
> To: stds-1788 <stds-1788@xxxxxxxxxxxxxxxxx>
>
> Dan, Arnold, Nate, P1788
>
> On 26 Sep 2010, at 13:54, Dan Zuras Intervals wrote:
> >> . . .
>
> What I get from this thread is that
>
> - We have had at least four valid formulas presented
> for the topological "A interiorTo B" when A and B are
> nonempty, all of which, in principle, seem to allay
> Nate's worst fears of performance hit. My nextDown/nextUp
> method is clearly bad if these are done in software,
> but they are such trivial operations given the 754
> number encoding, and so useful, that I would hope
> a bit of chip area would be devoted to hard-wiring
> them in the near future.
>
> - I am very sceptical that anyone could predict which
> of the 4 will work best on a given commonly used
> architecture, and that probably depends strongly
> on how vectorised the code is.
>
> - An "overall best way" to represent Empty in an
> inf-sup interval type depends on many things and
> I am equally sceptical that we can predict it.
> So, reluctantly, I believe P1788 should NOT
> standardise a representation of Empty this time
> around. It can do so at the next revision of 1788,
> if existing implementations show a "best way" has
> emerged.
>
> John
A reasonable approach.
Then let me suggest that there exist a
decoration for empty.
Or, at least, some combination of the
existing decorations that implies empty.
That way we do not NEED a representation
for empty within the interval part of a
1788 interval.
And we will have anything + empty = empty
fall out to be both fast & easy no matter
what we use for empty so long as the
decoration makes it so.
Dan