Editing Subnormal number (section)

== Background ==
Subnormal numbers provide the guarantee that addition and subtraction of floating-point numbers never underflows; two nearby floating-point numbers always have a representable non-zero difference. Without gradual underflow, the subtraction ''a''&nbsp;−&nbsp;''b'' can underflow and produce zero even though the values are not equal. This can, in turn, lead to [[division by zero]] errors that cannot occur when gradual underflow is used.<ref>{{cite web |url=http://grouper.ieee.org/groups/754/meeting-minutes/02-09-19.html#underflow |title=IEEE 754R meeting minutes, 2002 |author=William Kahan |access-date=29 December 2013 |archive-url=https://web.archive.org/web/20161015154158/http://grouper.ieee.org/groups/754/meeting-minutes/02-09-19.html#underflow |archive-date=15 October 2016 |url-status=dead }}</ref>

Subnormal numbers were implemented in the [[Intel 8087]] while the IEEE 754 standard was being written. They were by far the most controversial feature in the [[Kahan-Coonen-Stone format|K-C-S format]] proposal that was eventually adopted,<ref>{{cite web |url=http://www.eecs.berkeley.edu/~wkahan/ieee754status/754story.html |title=An Interview with the Old Man of Floating-Point |publisher=University of California, Berkeley}}</ref> but this implementation demonstrated that subnormal numbers could be supported in a practical implementation. Some implementations of [[floating-point unit]]s do not directly support subnormal numbers in hardware, but rather trap to some kind of software support. While this may be transparent to the user, it can result in calculations that produce or consume subnormal numbers being much slower than similar calculations on normal numbers.