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Re: Alternate floating-point results under directed rounding

Arnold et al,

I'm getting a little confused here about the line between
syntax and semantics.  Yes, say, if we want to use some kind
of epsilon inflation, we will start with a floating point
variable that is the result of a long computation (such as
a that done in an approximate solver for a system of
linear or nonlinear equations).  However, isn't that
normally a single number in the constructor.  Ultimately,
the actual constructor acts upon a single entity to
produce an interval, doesn't it?  Furthermore, aren't we
looking at standardizing these underlying operations, as
opposed to the syntactic environment in which they occur?
If the argument to the operation is the result of a long
computation, that argument (in Siegfried's case maxreal+maxreal)
could in principle be maxreal, inf, NaN, or anything else,
and I question whether it is practical or even possible
in general to figure out from the computation or the
syntax of the program what was originally intended.

However, at the risk of seeming somewhat biased, it does not
make sense to me to convert any finite number, even maxreal,
into the empty set.


Arnold Neumaier wrote:
Siegfried M. Rump schrieb:

Although examples like
are a little constructed; usually we would assume the argument of
a constructor to be a constant.

No. Frequently one needs an enclosure of a function value at a point. Then the argument of a constructor will be a float variable, computed in an arbitrary way.

In any case, definitions in the standard must work for all allowed uses.

Arnold Neumaier


R. Baker Kearfott,    rbk@xxxxxxxxxxxxx   (337) 482-5346 (fax)
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