Re: Request for motion [Fwd: Input from IFIP WG 2.5 to IEEE Interval Standards Working Group]
Dan Zuras Intervals wrote:
Date: Thu, 10 Sep 2009 13:25:08 +0200
Dan Zuras Intervals wrote:
Finally, let me caution you that how these things behave on
empty & NaI elements may turn out to be important to this
group.
I think only interval-valued results for noninterval inputs should be
provided by the standard. Then there are no problems.
Well, I am concerned about the elements chosen from empty
or NaI intervals that end up being elements of the vectors
in one of these operations.
It is impossible to choose an element from an empty set, and
it is meaningless to choose one from NaI since this has not
a set-theoretic interpretation.
Independent of that, the accurate sums etc are mappings from finite
sequences of float data to intervals, and hence whatever choices there
have been made, they are made already outside these functions. Thus the
latter's definition is independent of them.
If some element is NaN or two terms in the sum are +inf and -inf,
the result should be the empty set; otherwise the tightest enclosing
interval of the exact result should be returned.
Careful here. Please look at clause 9.4 in 754-2008.
In the case of sum or dot product you are quite correct.
But in the case of the norm operations (sum of squares &
sum of absolute value) the existence of an infinity determines
the value of the norm even if a NaN element is to be found
elsewhere in the vector.
We don't need to conform to this buggy IEEE semantics.
The exact sum 0/0+inf _may_not_ have the value inf, since it is
undefined in the theory of real numbers.
Our functions enclose the exact result, and the exact enclosure of an
undefined object can only be a (perhaps decorated) empty set or NaI.
But we must be clear in giving our functions a precise meaning,
and should explicitly mention this deviation from the IEEE semantics
of a
different, but related function.
The rules are complicated & vary a bit from operation to
operation. They are also controversial & I will not bother
justifying them again here.
They are buggy, hence controversy is highly justified.
Nobody should rely on this feature!
Arnold Neumaier