Re: Discussion period started Re: Proposal of Motion 6, version 3
On 2009-07-29 10:00:45 +0200, Arnold Neumaier wrote:
> Jürgen Wolff v Gudenberg schrieb:
> > I think motion 6 will give a solid foundation of the standard
>
> I agree that Motion 6 converged to something convincing.
> (The criticism by Dominique Lohez that ± infinity are handled
> as numbers seems to me unfounded; they occur only as bounds,
> not as elements of intervals.)
>
> Therefore, I recommend voting with yes.
I completely agree. But here are a few comments:
Page 3: "3.3.14. *interval function*, *interval mapping*. A function
from intervals to intervals is called an *interval function* if it is
an interval extension of a point function, and an *interval mapping*
otherwise."
As it is said, it seems that a function from intervals to intervals
is either an interval function or an interval mapping, while interval
mappings should include interval functions. I would replace this
definition by:
3.3.14. *interval function*, *interval mapping*. A function from
intervals to intervals is called an *interval mapping*. If it is
an interval extension of a point function, it is also called an
*interval function*.
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Page 3, 3.3.17: "Mixed-format does not mean that the lower and upper
bounds of an individual interval can have different floating point
formats. The theory, as phrased here, precludes this."
But what about midrad? Having the midpoint and the radius in different
formats can be useful in multiple precision, for efficiency reasons.
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Page 4: "Mixed-radix is less easy, as there is no one best way to do
the needed radix conversions. In my view it should not be considered."
Mixed-radix can still be implemented in "valid" accuracy mode, thanks
to implicit conversions.
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Page 6, 3.5.5: "An interval mapping is called an *interval function*
if it is an interval version of some point function, as defined next."
However the definition of interval function is self-referenced.
But I think this is because the wording is incorrect. It is said:
an *interval extension* of f, also called an *interval version*
of f, is any interval function *f* such that
^^^^^^^^^^^^^^^^^
It should be "[...] is any interval mapping *f* such that".
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Page 6, 3.5.5: "Examples of interval mappings that are not interval
functions are the hull and intersection operations."
Why not the hull operation? Isn't it the sharp interval extension
of the identity function?
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Page 6, 3.6.1: "An *abstract floating point format* (*af-format*) F
is a finite subset of R* containing −∞ and +∞."
I would have called it an "abstract discrete format". In particular,
it can correspond to a fixed-point format.
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Page 7: "My view of the purpose of NaI is that it is like NaN in
floating point computation: if any operand to an operation is NaI,
the result is NaI."
In fact, it is like sNaN, but *not* like qNaN. For instance,
hypot(±∞, qNaN) is +∞.
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.org/>
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Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)