Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84 SMI; site sun.uucp Path: utzoo!linus!philabs!prls!amdimage!amdcad!decwrl!sun!gnu 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.