Re: Basenote drift to the value of mid-rad forms...
Dan Zuras Intervals wrote:
Date: Mon, 13 Sep 2010 09:43:17 +0200
From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
CC: stds-1788@xxxxxxxxxxxxxxxxx
Subject: Re: YES on Motion P1788/0019.01
Dan Zuras Intervals wrote:
. . .
I am moved by some papers on the subject to consider
that we must find a way to make mid-rads both efficient
& well characterized.
But this is a research project for the future, not a matter for
today's standards committee!
Let those who have the expertise and interest to do so work on
the research project and show that it can succeed.
Let us consider how to standardize their achievements when such a
project has born fruit.
Arnold, we both know you are in a better position to
judge these things than I am. So if your considered
& experienced judgement is that we should waste no
further time trying to save the mid-rad forms, then
save us now with a motion to eliminate them. I will
second it.
Motion 16 is enough.
Motion 19 would undo the effect of Motion 16.
No. My position is that the standard should follow Motion 16, which
has a _required_ infsup format, and additional formats (one of which
may be midrad) with a specified conversion behavior.
Oh, Arnold, you WROTE the Vienna document. And you
& I both wrote motion 16. I think it is a bit late
to claim to be an uninvolved scientific advisor.
I advise and am involved by contributing to the discussion
and I wrote the Vienna Proposal as a position paper to show
how a good standard could look like.
I was never involved (and will not be) in proposing or voting
on motions.
Very well, in the spirit of motion 16, if you would
like to eliminate mid-rads & don't feel you have the
right to make any further motions, state your motion
in writing & *I* will propose it.
Motion 16 is alright and contains all that needs to be said.
This middle course you are taking is the worst of
both worlds. If what you say is correct then we
are wasting our time trying to do something that
can never be done.
Save us from that & take a clear position.
The Vienna Proposal is very clear, down to every relevant detail.
We spent a lot of work creating it, and I am not prepared to repeat
this.
It still stands as the position of our group, apart from two points
that only evolved later:
(i) Decorations should replace exceptions.
(ii) I now promote a smaller set of comparison operators,
whereas the Vienna Proposal opted for a comprehensive scheme
(which, however, resulted in many combinations of questionable
usefulness).
If you feel the need for a motion to decide the issues about not infsup
matters beyond what is in Motion 16, you can copy part of the Vienna
proposal, make it fit the structure delineated by the motions already
passed, discuss the result with me if you like, and then turn it into
a motion.
The relevant passages are the following:
[From 1.1, with an improvement of the grammar:]
In this proposal, care has been taken to obtain a satisfactory balance
between the need to limit the implementation work and leave implementors
the freedom to add useful features of their own choice, and things
that need to be standardized because of one of
- frequent usage,
- necessity in an important application,
- ambiguities that require standardization,
- options that guarantee compatibility of useful extensions,
and marginally used constructs that can be left to the programmer
since they can be fabricated easily from what is provided if these
constructs are needed.
[From 1.2:]
Textbook intervals are closed and connected sets of real
numbers, the closed intervals familiar from mathematical textbooks.
Nonempty textbook intervals are represented by two bounds, their
infimum and their supremum. (See also Section 1.6.)
Standard intervals denote textbook intervals whose infimum
and supremum are representable by two B-numerals.
Nonstandard intervals do not denote textbook intervals.
Except in Part 1 and Part 2, where nonstandard intervals
are discussed, the unqualified word 'interval' always refers to
standard intervals with the above textbook interpretation.
This excludes infinite numbers as element of an interval,
which would give unduly pessimistic results in cases such as division
by an interval with a zero endpoint; e.g., it gives
[1,2]/[0,1] = Entire in place of [1,Inf] in optimal forward arithmetic.
It also excludes the consideration of arithmetic based on a
midpoint-radius representation, which is considered only in conversion
between text and interval.
This exclusion is motivated by the fact that in a midpoint-radius
representation, it is impossible to represent known uncertainty in the
form of inequalities such as x>=1000. Also, optimal rounded interval
arithmetic based on the midpoint-radius representation of intervals
with real bounds appears to cost twice the amount of work of that
needed in the standard representation. The cheaper centered
multiplication has the drawback of up to 50% of overestimation of the
width.
It also excludes the consideration of arithmetic based on
nonstandard intervals (Kahan arithmetic, Kaucher arithmetic,
modal arithmetic).
However, certain applications merit providing compatibility of the
proposed standard with these not mutually compatible nonstandard
variants of interval arithmetic.
The availability of nonstandard intervals allows (but does not force)
implementors to extend the functionality of interval arithmetic to
handle either Kahan arithmetic, or Kaucher arithmetic, or modal
arithmetic consistent with their traditional interpretation.
Arnold Neumaier