Dan Zuras Intervals wrote:
If we are to pursue this at this time, please include accurate
versions of all of sum, dot product, sum of squares, & sum of
absolute values for all supported precisions.
That the sum is needed is obvious.
The sum of squares is needed for an accurate 2-norm & is
different than calling dot product with the same argument
twice in ways that are important in our context.
The sum of absolute values is needed for a 1-norm & is pretty
cheap once you have an accurate sum.
Yes, these are useful. Perhaps also the 2-norm itself!
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.
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.