Re: Interval arithmetic in Ada?

[dewar@gnat.com (Robert Dewar)]

"Grein, Christoph" <christoph.grein@eurocopter.com> wrote in message news:<mailman.1019482382.32502.comp.lang.ada@ada.eu.org>...
> Again, this _is_ the Ada 83 model with a and b the model 
> numbers enclosing the actual value. See the Ada 83 RM.

And once again you are confused. Interval arithmetic involves a
representation where you use a pair of numbers
to represent a real, the lower and upper bounds.

You are keying off the word "interval" here, and missing
the target :-)

The answer is that the language does not specifically support interval
arithmetic. In general automatic support
for this notion is tricky. As an example, consider doing
Newton-Raphson iteration for a square root. 

If you just carry intervals through, they get wider and
wider and you don't converge. You have to realize that
the *estimate* each time is computed absolutely precisely,
with no slop, and thus the interval must be collapsed here.

The round towards +inf and round down towards -inf rounding
modes of IEEE are intended to support this model of arithmetic. See
Sam Figueroa's thesis for a further discussion of the use of these
rounding modes in Ada.

Robert Dewar