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Path: utzoo!mnetor!seismo!rutgers!princeton!allegra!alice!ark
From: ark@alice.UUCP
Newsgroups: comp.arch
Subject: Re: IEEE floating point modes (interval arithmetic and division)
Message-ID: <7055@alice.UUCP>
Date: Sat, 4-Jul-87 11:00:06 EDT
Article-I.D.: alice.7055
Posted: Sat Jul  4 11:00:06 1987
Date-Received: Sat, 4-Jul-87 20:25:29 EDT
References: <93900007@hcx1> <22630@sun.uucp> <2774@phri.UUCP>
Organization: AT&T Bell Laboratories, Liberty Corner NJ
Lines: 18

In article <2774@phri.UUCP>, roy@phri.UUCP writes:
> 	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).

First of all, the rounding we're talking about is not rounding
to the nearest integer, but rounding to the nearest floating-point
number.  However, let's pretend we're rounding to the nearest
integer.  Then for division we have to round in the direction that
gives the smallest and then the largest result:

	1.0/2.0 = 0.5
	2.0/1.0 = 2.0

so we find that the result is in the interval (0.5,2.0)