Re: Proposal for interval standardization, Version 2.0
I have noted some typos, but also some more important comments
on the proposal (sections 1.3 and 1.5) which are of interest
not only to the editor, and might arise discussion.
Section 1.2, Third paragraph, first line
"woth" should be "with"
Section 1.3 In IEEE 754 NaN:s are not unique, and from
P 754 Section 5.11, line 6: Every NaN shall compare unordered with
everything, including itself.
I therefore recommend the following rewrite of (iv)
(iv) l = NaN and u = NaN (empty interval Empty).
Section 1.5 Logical functions are discussed here, and seem to be
in the C style with values 0 and 1 instead of Fortran or Algol
TRUE and FALSE.
Item 7. In my opinion areEqual(xx,yy) should return TRUE
if xx and yy are the same set, and areDistinct(xx,yy) should return
FALSE in that case. I do not like the the word "under the same
cirumstances", it is better in a standard to repeat exactly what
is valid.
Section 2.0, line 5
"secition" should be "section"
Section 2.3
The last line should have a plus + instead of a minus -
in the second case (upper limit)
Section 2.5, line 4
"preced" should be "preceded"
Section 2.6, second paragraph, first line
"facilitate" should be "facilitates"
Section 3.0, line 3
"standard-cornforming" should be "standard-conforming"
Section 3.12, last line
"implemnting" should be "implementing"
Section 6.5, line 2
"pu (down)" should be "up (down)"
Best regards,
Bo
On Tue, November 4, 2008 10:49 am, Arnold Neumaier wrote:
>
>
> Attached is Version 2.0 of my proposal for interval standardization.
>
> I took into account all contributions to the discussion on the
> mailing list that I received before 4.11.2008, 10:00 local time.
>
> I believe that, apart from the issues about treating infinity,
> where this proposal takes the stand of
> - having +-infinity not as member of any interval, and
> - to convert a floating-point +-infinity to the empty interval,
> there are no serious obstacles to an ultimate agreement on a more
> polished, corrected, and upgraded version of this proposal.
>
> Care has been taken to make the bulk of the proposed standard
> independent of the arithmetical properties of floating-point numbers.
>
>
> Of course, all points are open to discussion and alteration.
> Some of the items proposed here (e.g., the tightest enclosure of the
> inner product of two vectors of floats) have not yet been
> discussed on the list.
>
> I'd appreciate comments regarding substance, small or large
> improvements, wishes for inclusion into the proposal,
> better formulations, pitfalls still to be considered, etc..
>
> I'd like to ask those who prefer alternatives to certain items of
> this proposal to formulate their preferences (again) clearly,
> with cogent reasons why they think their view is superior to that
> presented here.
>
> In particular, I invite
> - John Pryce, the main proponent of the infinity-as-number
> (cset interval) alternative,
> - Siegfried Rump, the main proponent of the proposal to convert
> the floating-point infinity to [maxreal, inf],
> to provide a specific version of their alternative vision,
> in order that everyone can judge the comparative merits.
>
>
> Arnold Neumaier
>
>
>
>
--
Bo Einarsson
Mathematics Department
LINKÖPING UNIVERSITY
SE-581 83 LINKÖPING
SWEDEN
Tel. +46 13 151896