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Re: signed zeros

Arnold et al,

Arnold Neumaier wrote:
R. Baker Kearfott schrieb:
Arnold et al,

Arnold Neumaier wrote:
Baker Kearfott schrieb:
Arnold Neumaier wrote:
R. Baker Kearfott schrieb:
Sure. 754 defines the semantics of floating-point numbers as
being based upon the extended reals.
We may define the semantics of intervals as being based on
sets of reals, or as being based on sets of extended reals.

The only point where the two semantics interact is in the
conversion of floating-point numbers to intervals.

This is why there is a problem with the conversion of inf.
But this is not worse than the conversion problem from
decimals to 754 floats, where there is also no full
compatibility, resulting in different rounding options.

There is no other consistency problem.

The fact that intervals are represented by two floats has
nothing to do with semantical issues.

Thus I think there is no contradiction at all, not even a soft

Mathematically (on level 1), there is no contradiction, if we
consider the two data types to be separate.  I was  wondering about
efficiency issues, and, in particular, if we could use
the hardware IEEE infinity arithmetic to better advantage
with one mathematical modal than with the other.  However,
these issues are certainly related to many contributions
to this discussion list.  (We've been discussing implementation
using floating point.)

Best regards,


P.S. I'm pleased that we are in the process of clarifying
     what happens with unbounded intervals.  This issue
     (lack of clarity and consensus) was a major factor
     in an intrinsic interval data type not being adopted
     in Fortran 2003.


R. Baker Kearfott,    rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
(337) 482-5270 (work)                     (337) 993-1827 (home)
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