Date: Wed, 6 Feb 2002 19:42:57 +0100 (CET) From: Brigitte Verdonk <verdonk@uia.ua.ac.be> To: standards@FreeBSD.org Subject: Re: Possible math problems Message-ID: <Pine.LNX.4.40.0202061857130.2895-100000@stanhope.uia.ac.be>
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The following may take away some of the confusion about the errors reported in multiplication and division on the IeeeCC754 website. As already reported, the errors only occur on extended-based platforms such as Intel, Athlon, ... and not on single-double based architectures (such as SUN). As you may also have noticed, the reported errors are always underflow cases. The cause for the errors can be traced back to a 'hole' in the IEEE 754 standard, where it is stated that extended-based architectures shall be able to mimick single or double precision, EXCEPT in the absence of underflow/overflow. What happens is that on extended based architectures, when mimicking double precision, only the precision is mimicked and not the exponent range (15 bits are allocated for the exponent, rather than 11 as in double precision). Usually this is not a problem, except in some cases of underflow where double rounding can cause "erroneous" results. Indeed, what happens on an extended-based architecture mimicking double (or single) precision, is that 1. the exact result of an operation is first rounded to 53 bits precision and exponent range represented in 15 bits 2. then this rounded result is stored in true double precision format (53 bits precision, 11 bits exponent). This entails no double rounding (53 bits precision in both cases), except when the final result needs to be denormalized due to underflow. In such cases, the extended based architectures should denormalize the 'exact' result of the operation, but instead denormalize the intermediate result (computed in 53 bits precision and extended exponent range). More details on this issue and on underflow in general can be found in ftp://wins.uia.ac.be/u/preprints/99/underflow.ps By the way, any further feedback on the testing tool IeeeCC754 is very much appreciated. Please let me know about any problems, requests for additional features, etc. Also, I would be very happy to include logfiles for additional platforms/architectures to our website. All contributions will be greatly appreciated. Best regards, Brigitte Verdonk ----------------------------Brigitte Verdonk---------------------------------- Dept. of Math. and Comp. Sc. Tel. +32 3 820.24.03 University of Antwerp (UIA) Fax. +32 3 820.24.21 Universiteitsplein 1 URL: http://www.uia.ac.be/u/verdonk B2610 Wilrijk-Antwerp (Belgium) Email: verdonk@uia.ua.ac.be ------------------------------------------------------------------------------ "Alice laughed: "There's no use trying," she said; "one can't believe impossible things." "I daresay you haven't had much practice," said the Queen. "When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast." Lewis Carroll To Unsubscribe: send mail to majordomo@FreeBSD.org with "unsubscribe freebsd-standards" in the body of the message
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