Talk:Floating-point arithmetic/Archive 4: Difference between revisions

Revision as of 00:07, 23 January 2014

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:"The justification for this definition is to preserve the sign of the result in case of [[arithmetic underflow]]. For example, in the double-precision computation 1/(''x''/2), where ''x'' = ±2⁻¹⁴⁹, the computation ''x''/2 underflows and produces ±0 with sign matching ''x'', and the result will be ±∞ with sign matching ''x''. The sign will match that of the exact result ±2¹⁵⁰, but the magnitude of the exact result is too large to represent, so infinity is used to indicate overflow."

Provided this is valid, I wonder if it could also be added in some relevant ___location in the body of floating point related articles. In general I'd like to see more information on design rationales. Thanks! [[User:Dcoetzee|Dcoetzee]] 07:42, 11 September 2012 (UTC)

== Signed zero section, branch cuts ==

The section on signed zero (under Internal representation >> Special values >> Signed zero) says the following:

"The difference between +0 and −0 is mostly noticeable for complex operations at so-called [[Branch cut|branch cuts]]."

In a strictly mathematical sense, +0/-0 ''can'' be interpreted as describing the limiting behaviors of a function, but that's not actually what's happening here. Moreover, branch cuts are not the only situation where these exceptional limiting behaviors appear, one can have branch cuts without exceptional limiting behaviors of this sort, and none of the examples given in the section are actually branch cuts. As far as I can tell, there is absolutely no significance to the relationship between branch cuts in complex analysis and signed zero in floating point numerical representations, but I wanted to make sure there wasn't a good reason for this being here. Thoughts? [[Special:Contributions/71.227.119.236|71.227.119.236]] ([[User talk:71.227.119.236|talk]]) 15:25, 29 September 2012 (UTC)

:Result of a quick Google search:

:"A system with signed zero can distinguish between asin(5+0i) and asin(5-0i) and pick the appropriate branch cut continuous with quadrant I or quadrant IV, respectively. A system without signed zero cannot distinguish and, according to the choses the branch cut such that it is continuous with quadrant IV (consistent with the rule of CCC). So, for asin(5+0i) it will return the same value as a system with signed zero would for asin(5-0i)." -Richard B. Kreckel ( [ http://www.ginac.de/~kreckel/ ] [ http://lists.gnu.org/archive/html/bug-gsl/2011-12/msg00004.html ] ).

:I think that when he wrote "according to the" he meant "accordingly" (probably not a native English speaker). --[[User:Guy Macon|Guy Macon]] ([[User talk:Guy Macon|talk]]) 23:34, 29 September 2012 (UTC)

::Somewhat straying from the subject but still quite interesting; the "Signed Zero" section of "What Every Computer Scientist Should Know About Floating-Point Arithmetic" ( [ http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html ] ) --[[User:Guy Macon|Guy Macon]] ([[User talk:Guy Macon|talk]]) 23:41, 29 September 2012 (UTC)