Re: mid-rad, inf-sup, a caution...
On 11 May 2010 at 8:42, Michel Hack wrote:
Date sent: Tue, 11 May 2010 08:42:05 -0400
To: stds-1788 <stds-
1788@xxxxxxxxxxxxxxxxx>
From: Michel Hack
<hack@xxxxxxxxxxxxxx>
Subject: Re: mid-rad, inf-sup, a caution...
> Svetoslav's defense of mid-rad is written entirely from the
> point of view of "imprecise numbers", and not the more general
> one of intervals (which, as I keep saying, have TWO DIFFERENT
> mental models behind them). Indeed, he says so explicitly:
>
> > - the FP standard for midpoint is available, it only needs
> > to be extended and completed so that the concept of an
> > FP-number is extended to the concept approximate number
> > (which is actually an interval).
>
> This affects the types of operation to be supported, and their
> precise definition, as Arnold has pointed out already.
>
> The really nasty part here is that there is no obvious cutoff
> between narrow intervals (which might represent imprecise numbers)
> and wide intervals (which frequently represent subdomains).
Dear Michel,
what you say is correct and also amusing.
Imagine that things are reversed, the mid-rad format
has been deloped at the stage now inf-sup has reached
and someone is trying to defend the inf-sup format.
Certainly he will write entirely from the point of view of
"wide intervals" (representing subdomains).
>
> In the case of infsup, all operations, including reverse and set
> types, and be defined precisely and uniquely. Some may only be
> appropriate for one or the other of the two mental images I've
> been talking about, but that does not affect their definition.
Same is true for mid-rad at mathematical level.
Here I would also speculate that as far
as real interval arithmetic is concerned the
publications/studies relative mid-rad are most
probably of the same order as these on inf-sup.
But of course in the field SW implementations
mid-rad is far behind. Which is a pity, IMO.
Svetoslav
>
> If midrad were a primary interval type of the same nature as BFP
> vs DFP in 754, nearly *every* operation would have to be defined
> for both in a logically-uniform manner. There is an escape, in
> that 754-2008 does define certain operations explicitly for DFP
> only, and that DFP brings one additional concept to the table
> that is not applicable to BFP, namely "preferred quantum" or
> "preferred exponent" (and the notion of "cohort"). I'm not
> sure however that this approach would work for midrad vs infsup.
>
> The issue of midrad interchange formats is separate from that of
> first-class support, and can be decided independently either way.
> The basis for this decision would be usefulness and agreement on
> a well-defined set of representations, perhaps tied to the format
> used to represent the midpoint.
>
> One word of caution with respect to using a lower-precision format
> for the radius: lower precision usually brings with it a smaller
> exponent range -- and that can be a problem, because it would
> effectively limit the exponent range of the midpoint too. The
> triplex format avoids this by effectively specifying a third and
> effectively unrestricted exponent.
>
> Michel.
> ---Sent: 2010-05-11 13:41:45 UTC