Re: Do I have a second? Re: Position: That the Standard for Computing with Intervals Have Only One Level 1 Requirement: Containment
On 08/04/2011 12:35 AM, Ralph Baker Kearfott wrote:
Nick, Dan,
On 8/3/2011 4:13 PM, N.M. Maclaren wrote:
On Aug 3 2011, Dan Zuras Intervals wrote:
.
.
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The one and only level 1 implementation requirement
must be to enclose the smallest set of values (the
containment set) that must be contained in the
interval result of any evaluated arithmetic
expression or function defined therefrom.
This says that the containment set is the hull of the range,
and the _only_ requirement for the result of an interval enclosure
should be that it _encloses_ the containment set. It cannot be equal to
it because of rounding errors, hence the only conceivable alternative
interpretation is ruled out.
Clearly, this is much less than what is needed for a dependable
high quality standard.
My understanding from corresponding with Bill is that
he actually meant that the size of the interval
is just a quality of implementation issue.
Indeed, this is what the text says.
Thus he formulated his intentions correctly.
Arnold Neumaier