Re: How to merge required operations under a common name
Ulrich et al,
On 01/27/2016 03:42 AM, Ulrich Kulisch wrote:
Dear colleagues,
just before the discussion period for IEEE 1788 closes let me make a
final remark.
/Interval arithmetic defined over the real and floating-point numbers
leads to an exception-free calculus./
In IEEE 754 -oo and +oo are numbers. In interval arithmetic -oo and +oo
are just used to describe unbounded sets of real numbers. But they are
themselves not elements of these intervals. This is a subtle difference!
Interval arithmetic is an arithmetic for connected sets of *real numbers*!
Indeed! This is explicitly written into IEEE 1788-2015, and the
operations are defined with this in mind. 1788-conforming
implementations can use the 754 data formats for -\infty and +\infty,
but does not use NaN.
If you take -oo and +oo as numbers, you have to study and provide
operations like oo - oo, 0 times oo, oo/oo which in IEEE 754 are set to
NaN.
Yes. We resolved this with broad consensus several years ago, and
1788 incorporates your point of view. Use of the 754 data format
and 754 directed rounding does not mean all aspects of 754 must
be adopted in an interval arithmetic standard, and indeed they are not.
It seems we are in violent agreement.
Baker
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Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
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URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
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