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From: dik@cwi.nl (Dik T. Winter)
Newsgroups: comp.arch
Subject: Re: IEEE arithmetic
Message-ID: <3742@charon.cwi.nl>
Date: 19 Jun 91 22:37:45 GMT
References: <9106190252.AA29755@ucbvax.Berkeley.EDU>
Sender: news@cwi.nl
Organization: CWI, Amsterdam
Lines: 31

In article <9106190252.AA29755@ucbvax.Berkeley.EDU> jbs@WATSON.IBM.COM writes:
 >          Regarding how I would implement interval arithemtic it is not
 > particularly difficult to do without the rounding modes as long as you
 > don't insist on maintaining the tightest possible intervals.  There is
 > no great loss in being a little sloppy since an extra ulp only matters
 > for narrow intervals and the main problem with interval arithmetic is
 > that the intervals don't stay narrow even if you are careful.

This is were your opinion differs from the opinion of the Karlsruhe people.
In another posting someone asked how to do pivoting when interval arithmetic
is used.  Also that misrepresents the work of the Karlsruhe people.

To reiterate what the Karlsruhe people are doing to solve a set of linear
equation:
1.	Calculate an approximate technique using your favorite solver.  No
	interval arithmetic is done in this stage!
2.	Next find an enclosing interval for the solution.
3	Narrow the interval using iterative methods with the original matrix.
So we see that *no* interval pivoting is done.
Also to succesful narrow the interval in stage 3 it is important that the
arithmetic provides the narrowest interval for every operation.
In many cases they succeed in finding solutions were each component of the
solution is pinned between two successive machine numbers.

I have my doubts about it (many people have).  But this is the most senseful
approach to interval arithmetic I know of.  Most work (finding the initial
iteration) is done without any interval arithmetic.  You use it only to squeeze
out the last few bits.
--
dik t. winter, cwi, amsterdam, nederland
dik@cwi.nl