From mboxrd@z Thu Jan  1 00:00:00 1970
From: Sylvain Pion <Sylvain.Pion@sophia.inria.fr>
To: law@cygnus.com
Cc: egcs@cygnus.com
Subject: Re: /internet
Date: Thu, 17 Dec 1998 04:43:00 -0000
Message-id: <19981217134318.C9897@rigel.inria.fr>
References: <199812161958.LAA29146@atrus.synopsys.com> <28398.913854887@hurl.cygnus.com>
X-SW-Source: 1998-12/msg00630.html

On Wed, Dec 16, 1998 at 05:34:47PM -0700, Jeffrey A Law wrote:
> [...] Though
> I believe in the case reassociating a series of multiplies we are safe.
>
> I challenge anyone to come up with a case where a reassociation of
> a * b * c * d  produces different results than ((a * b) * c) * d.

If you want that, you'd better first _prove_ that it works in every case.
But you won't be able to do so because it's false.

It might be true when the following both conditions are met:
- no intermediate overflow/underflow appears (nor denormalized numbers).
- the rounding mode is set to nearest.

I'd be interested in reading the proof in this case (if it's true).

Case if you have an intermediate overflow is easy:
DBL_MAX * DLB_MAX * DBL_MIN  gives you either Inf or DBL_MAX.
Case when rounding is set to +Infinity:
0.1 * 0.1 * -1.0  doesn't give you the same result, try it.

-- 
Sylvain