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(originally from Van Snyder [Fwd: [Fwd: Rejected posting to STDS-1788@xxxxxxxxxxxxxxxxx]]

Hopefully this one doesn't bounce.  Please see Van's intended
comments.

Baker
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R. Baker Kearfott,    rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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-------- Forwarded Message --------
From: IEEE LISTSERV Server (15.5) <LISTSERV@xxxxxxxx>
To: Snyder, W Van (3284) <w.van.snyder@xxxxxxxxxxxx>
Subject: Rejected posting to STDS-1788@xxxxxxxxxxxxxxxxx
Date: Tue, 8 Sep 2009 12:05:15 -0700

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-------- Forwarded Message --------
From: Van Snyder <Van.Snyder@xxxxxxxxxxxx>
Reply-To: Snyder, W Van (3284) <w.van.snyder@xxxxxxxxxxxx>
To: stds-1788@xxxxxxxxxxxxxxxxx <stds-1788@xxxxxxxxxxxxxxxxx>
Subject: Motion 7 NO
Date: Tue, 8 Sep 2009 12:05:04 -0700

NO on Motion 7

I do not object in principle to the inclusion of NaI in the system.

My objections to Motion 7 are
  o the requirement that interval(a,b) with a>b produces NaI, and
  o the requirement that the empty interval be represented by
    interval(sNaN,sNaN).

As described by Kulisch in the rationale for Motion 3, division by an
interval containing zero produces an exterior interval.  So as not to
require two explicit intervals for its representation, a natural
representation for this result is interval(a,b) with a>b, denoting
(-oo,b] U [a,+oo).

NaI should arise only from an attempt to construct an interval from
floating-point operands, at least one of which is NaN.  The caveat about
extended interval arithmetic and extended intervals introduces a
contradiction.  Either interval(a,b) with a>b produces NaI, or it does
not.  It should not at this stage be ambiguous.

Since -oo and +oo are never within an interval, a natural representation
for the empty set is the exterior interval (+oo,-oo), i.e. {x|x>+oo} U
{x|x<-oo}.  Whether the agreed representation for the empty set is
interval(+oo,-oo) or interval(qNaN,qNaN) should be decided separately
from Motion 7.

If the requirement that interval(a,b) with a>b produces NaI, and the
specification of the representation of the empty set, were both to be
removed, I would vote YES on the motion.

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