Re: Explicit vs Implicit bounds on range and precision
On 14 Jul 2010 at 23:04, Michel Hack wrote:
Date sent: Wed, 14 Jul 2010 23:04:00 -2000
To: stds-1788 <stds-
1788@xxxxxxxxxxxxxxxxx>
From: Michel Hack
<hack@xxxxxxxxxxxxxx>
Subject: Re: Explicit vs Implicit bounds on range and precision
> I agree with everything Dan Zuras wrote in his reply,
> BUT I'm afraid he missed my point COMPLETELY:
>
>
.......
......
>
> In other words, what Dan ASSUMES to be there (an explicitly specified
> bound on precision and/or range) must be REQUIRED to be there for the
> definition of "tightest" to make sense. Running out of resources does
> not count because, as Vincent pointed out, that leads to non-predictable
> behaviour.
>
> Michel.
>
> P.S. There is another booboo in Dan's examples: mid-rad representations
> where the radius has a smaller exponent range than the midpoint.
> Unless the radius is RELATIVE this won't work very well, as the
> only valid enclosure for large midpoints would be Entire. Trouble
> is, relative radii have trouble with zero-centered intervals...
>
> I think Arnold's triplex formats can deal with this.
>
> That's a completely different topic however.
> ---Sent: 2010-07-15 03:31:59 UTC
I have two remarks to this last P.S.
1. the mid-rad presentation of intervals has been sufficiently
studied so that all basic interval arithmetic formulae are available.
To my knowledge this is not the case with the other two above
mentioned presentations: relative radius and triplex format. If I am not
right please those who know these forms supply references. If I am right
then I do not see why these forms should be mentioned at all.
2. mid-rad presentation in theory (level 1) works for intervals
containing zero, but in practice I cannot think of somebody
writing an intelligent numerical algorithm in mid-rad: i) using
zero-containing intervals as input data; ii) without providing
special check for zero-containing interval results during
computation. Same with infinite intervals, entire etc. I cannot
see why one should stress on these exceptional cases that
have no practical significance. In so far I understand these
details now fall into level 3 where the implementors have
the freedom to decide.
Svetoslav