Re: As simple as it is now, I am still against motion 24.03...
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