Svetoslav,
On Apr 22, 2010, at 4:48 AM, Svetoslav Markov wrote:
can somebody explain what for is the line of text in 6.1 that says:
"provided that it shall be possible to retrieve the bounds of x
exactly."
My understanding:
This language prohibits mid-rad as an internal representation.
Once an interval \x has been created, it has lower and upper bounds
which are machine numbers. This language requires that accessor
functions inf(\x) and sup(\x) return the lower and upper bounds,
respectively, as the machine numbers that are stored. There is no
rounding on retrieval.
Of course, if you write them out, there may be rounding on output.
George
What is the reason and motivation for this requirement? .
I cannot think of any reason why "exactly" should be required.
One would think inclusion isotonicity is enough. Besides,
it is not clear in what sense the word "exactly" is used -
in the sense of real or machine arithmetic (that is at most
1 ulp lost)?
Regards,
Svetoslav