Bill, P-1788,
On 6/9/2011 10:56 AM, G. William (Bill) Walster wrote:
I believe Arnold is correct that what we require is "operations that
take a list of reals
> and return a (preferably the tightest) representable interval
enclosing the result
> of an operation with them."
However, this raises the even more fundamental question of what *IS*
the result
of any given computation, not just basic arithmetic operations?
Until this question is answered for all cases of interest, I believe
it is premature to even
consider developing a standard.
The committee has already "been there, done that," having wrestled
with expressions
versus operations, if that's what you mean. I'm not sure what you
mean by
"a given computation" or "all cases of interest". As I see it, the
scope of P-1788 is
standardization of individual operations, something for which I would
argue the result
(of a mathematical operation or function) IS known, and for which
there is broad
agreement that standardization is valuable. If you mean by
"computation," a particular
concatenated set of operations, I think we know what the result (with
point input) should
be. Otherwise, what cases of interest are not covered? If you mean
the result of a mathematical
expression evaluated with intervals, that is also well-defined, in
terms of "united extension,"
etc. It is known that computing the exact range is an NP problem,
but it is still widely
recognized that interval evaluation of such expressions is useful, and
that standardization
of the computer arithmetic for such evaluation would be a great
facilitator. Beyond that,
there was quite a bit of P-1788 work (e.g. in the "expression
evaluation" subgroup) that
you apparently missed. You may wish to review the archives.
Otherwise, rearranging
interval expressions to change the computer-generated (floating point
or interval)
results seems to be outside the scope of P-1788, and, indeed, computer
language
committees have avoided the issue. (It would, of course, be tied to
computer
algebra systems, but is that relevant to specification of basic interval
arithmetic operations? Don't we need the basic operations,
regardless, in this
context, too, and might additional tracking information associated with
individual operations also be useful?)
You may wish to clarify your statement.
Baker