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From: ma_jpb@bath63.UUCP (Bennett)
Newsgroups: comp.arch
Subject: Re: Floating point accuracy
Message-ID: <267@bath63.UUCP>
Date: Sun, 9-Nov-86 13:48:17 EST
Article-I.D.: bath63.267
Posted: Sun Nov  9 13:48:17 1986
Date-Received: Tue, 11-Nov-86 02:21:13 EST
References: <340@euroies.UUCP> <1989@videovax.UUCP>
Organization: Bath University, England
Lines: 29
Summary: alternative floating point rounding schemes

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Reply-To: ma_jpb@ux63.bath.ac.uk (J.P. Bennett)
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Distribution: 
Organization: University of Bath, England
Keywords: floating point rounding

I recall that when I was an undergraduate being taught a novel rounding
scheme for floating point, attributed I believe to David Wheeler of Cambridge
University.

The mechanism was to add a random number in the range 0 to 1 in the last digit
and then truncate. This gives better RMS error than most other rounding
schemes. It also has the advantage that numerically unstable programs are
easy to detect (they give wildly differing results on each run).

Sadly I believe this has never been implemented. Perhaps manufacturers
couldn't face tracing hardware errors in such a system...

J.P. Bennett

Computer Group
School of Mathematical Sciences
University of Bath
Claverton Down
Bath BA2 7AY
England
Tel: +44 225 826826
ma_jpb@uk.ac.bath.ux63