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From: roy@phri.UUCP (Roy Smith)
Newsgroups: comp.arch
Subject: Re: IEEE floating point modes (interval arithmetic and division)
Message-ID: <2774@phri.UUCP>
Date: Fri, 3-Jul-87 19:06:50 EDT
Article-I.D.: phri.2774
Posted: Fri Jul  3 19:06:50 1987
Date-Received: Sat, 4-Jul-87 15:27:14 EDT
References: <93900007@hcx1> <22630@sun.uucp>
Reply-To: roy@phri.UUCP (Roy Smith)
Organization: Public Health Research Inst. (NY, NY)
Lines: 16

In article <22630@sun.uucp> lyang@sun.UUCP (Larry Yang) writes:
> what a programmer may do is to perform a computation using 'round to
> +inf', then repeat the computation using 'round to -inf'.  Then they are
> certain that the 'true' result lies somewhere between these two bounds;
> they know the 'interval' in which the solution lies.

	Maybe I'm just exposing my ignorance of the subject, but it seems
to me that for division, i.e. if you do (a+b)/(c+d), this logic doesn't
hold.  If a+b = 1.1 and c+d = 1.9, for example, rounding both intermediate
results towards -inf gives 1.0/1.0 = 1.0; similarly, rounding both towards
+inf gives 2.0/2.0 = 1.0.  The "real" answer is 0.578..., which is *not*
within the interval (1.0,1.0).
-- 
Roy Smith, {allegra,cmcl2,philabs}!phri!roy
System Administrator, Public Health Research Institute
455 First Avenue, New York, NY 10016