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From: gnu@sun.uucp (John Gilmore)
Newsgroups: net.arch
Subject: Re: IBM 360 float
Message-ID: <2588@sun.uucp>
Date: Fri, 9-Aug-85 13:22:12 EDT
Article-I.D.: sun.2588
Posted: Fri Aug  9 13:22:12 1985
Date-Received: Mon, 12-Aug-85 06:42:30 EDT
References: <741@masscomp.UUCP> <744@masscomp.UUCP>
Organization: Sun Microsystems, Inc.
Lines: 29

I forwarded some of the discussion to a knowledgeable friend at IBM,
and he gave me permission to post his response:

Date: Wed, 24 Jul 85 11:29:58 pdt
From: ucbvax!ibmpa!lmb (Larry Breed)
Subject: 360 floating point

Hi, John.  Actually that report is a shade too kind.  You have to expect
to lose three, not one or two, bits from hex normalization.  Yes, "on the
average" you've got only one or two leading 0 bits in the fraction, but
the overall accuracy of your results is controlled by the minimum accuracy
rather than the average accuracy of intermediate results.  This blanket
statement isn't really accurate either -- leading zeros don't hurt on many
adds and subtracts, and hurt only statistically on multiplies and divides --
but it is accurate in specifying worst-case behavior.

The second overkindness was that IBM noted and corrected FP errors after first
shipment.  As I recall, it wasn't until late 1966 that the retrofitted guard
digit made its appearance, and then only because W. Kahan and other numeric
analysts outside IBM made an issue of it.  Once you can point out to IBM
that X*1.0 != X, you can usually get its attention.

Just to put things in perspective, floating point has been done wrong in 
many ways, by many people.  (1/3 == 9/27 on a 370, and not every
manufacturer can make that claim!)  This is why it's so valuable to have
the IEEE 754 standard -- it doesn't have these anomalies, it DOES have 
valuable facilities lacking in other designs, and you can tell when you've
implemented it right.  There's a test suite (driver plus about 20,000 test
cases) developed by the 754 designers and available from Berkeley.