Dear John, Vladik, Michel, and IC members
Thank you for your kind reply.
I am writing to you regarding the previous emails about that section in Std. 1788 which deals with operations for interval arithmetic.
As I mentioned, based on the Std. 1788-2015 we may obtain results which lead to values that are not possible actually.
Michel told that it is because of dependency issue, and that
Moore's arithmetic is indeed a worst-case arithmetic -- but this allows it to *guarantee* that the computed result encloses any possible actual result.
Then, he told
When an interval programmer writes a program to compute a particular function, which could (in the point-function context) be written as an
algebraic _expression_ where certain variables may appear multiple times,
the programmer may take advantage of specific knowledge -- in particular,
monotonicity properties -- to compute a tighter enclosure than blindly
evaluating the _expression_ using Moore arithmetic.
1. Using Moore's approach leads to obtain values which may not be possible, i.e. impossible values. So, it makes us to analyze, decide, and design systems and processes with too high costs and probably too complex. That all of these are because of values which are impossible, i.e. they will not happen.
2. The standard should be based on an approach which makes us be assured in at least some future development. This is while as you can see the attachment, using advantage of specific knowledge we get to what I termed it
Restoration issue.Additionally, we are just considering very simple cases, because the
cases themselves have their own issues of obtaining
real possible results/values, let alone problems related to differential equations and defining derivatives.
I recommend to rethink about the section of Std. 1788-2015 which deals with fourth basic operations in order to avoiding what will mislead us in so many problems.