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Re: Edge case conversions, exceptions to IEEE FPA



Paul,

Yes.  I agree with your philosophy, and I also accept your
correction.  I was thinking of converting '0.1' to a binary
format.  Of course, if we convert '0.1' to a decimal
format, my view would be that it should be a singleton
interval, consistent with the rounding modes specified
in 754-2008.

I'm not sure we want mixed intervals.

Best regards,

Baker

P.S. Although the following comment might be slightly out-of-order, bringing up decimal
     arithmetic, on second thought, is intriguing.  Since there are two
     factors (2 and 5) in the base, a larger range of numbers can be
     represented exactly.  Because of that, there might be less build-up of
     overestimation in some instances when decimal interval arithmetic
     is used.

Paul Zimmermann wrote:
       Dear Baker,

Of course, the matter is different for external character strings.
When we convert '0.1' to interval, we know it is inexact, so we
would probably want an interval whose lower bound and upper bound enclose
the exact number '0.1'.  The lower bound and upper bound can be
specified according to the round-down and round-up rules specified
in 754-2008 for converting such character strings to the floating
point format.

I disagree. In the 754-2008 decimal64 format 0.1 is exact. I'm sure you want
to also consider intervals based on decimal numbers. We might even have mixed
intervals, e.g. the left bound represented by binary64, and the right bound by
decimal64.

Paul Zimmermann (new to the list)




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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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