Path: utzoo!mnetor!uunet!steinmetz!sunset!oconnor
From: oconnor@sunset.steinmetz (Dennis M. O'Connor)
Newsgroups: comp.arch
Subject: Re: Performance increase - a suggestion
Message-ID: <9454@steinmetz.steinmetz.UUCP>
Date: 8 Feb 88 16:38:06 GMT
References: <9408@steinmetz.steinmetz.UUCP>
Sender: news@steinmetz.steinmetz.UUCP
Reply-To: sunset!oconnor@steinmetz.UUCP
Organization: GE Corporate R&D Center
Lines: 25

An article by yuval@taux01.UUCP (Gideon Yuval) says:
>Since, under machine arithmetic, a/b is NOT equal to a*(1/b), and since the
>IEEE floating-point standard demands EXACT rounding, I don't see how Newton-
>Raphson is any use an an IEEE environment.
>-- 
>Gideon Yuval, +972-52-522255 (work), -2-690992 (home), yuval@taux01.nsc.com

Newton-Raphson does not ( neccesarily ) involve actually computing 1/b
and then multiplying by a, since as you mention this is NOT the same
as a/b. What can be done is to create a two varible function F which 
when invoked as F( 1, b ) produces 1/b, and when invoked as F( a, b )
produces a/b. This function does NOT form 1/b as part of its
algorithm. Instead it performs a series of operations that if
applied to second variable would produce 1, and performs this series
of operations to the first variable. With done in "infinite" precision
this is equivalent  to a*1/b; it is not eqivalent to a*1/b in finite
precision machines. The first use of the algorithm I'm aware of
was in the IBM 360/195, I think. I don't see how rounding is any
more a problem with this approach than with any other approach.


--
	Dennis O'Connor 	oconnor@sunset.steinmetz.UUCP ??
				ARPA: OCONNORDM@ge-crd.arpa
    "Nuclear War is NOT the worst thing people can do to this planet."