Abstract

Underflow is a floating-point phenomenon. Although the use of gradual underflow as defended in [2] and [5] is now widespread, most numerical analysts may not be aware of the fact that several implementations of the same principle are in existence, leading to different behaviour of code on different platforms, mainly with respect to exception signaling. We intend to thoroughly discuss the slight differences among these implementations. Examples will be taken from current hardware and from our own multiprecision software class library. Throughout the discussion the focus is on the analysis of the phenomenon and not on any implementation issues. Many programmers are also unaware of the fact that the IEEE 754 and 854 standards do not guarantee that a program will deliver identical results on all conforming systems. Of all the differences that can occur cross-platform, the underflow exception is just one. ? Research Director FWO-Vlaanderen ffl Supported by an NOI-grant from the Universi...

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