Henning Thielemann wrote:
I wonder why Infinity has a sign in IEEE floating processing, as well as 0. To support this behaviour uniformly one would need a +0 or -0 offset for each number, which would lead straightforward to non-standard analysis ...
See "Branch Cuts for Complex Elementary Functions, or Much Ado About Nothing's Sign Bit" by William Kahan, in The State of the Art in Numerical Analysis, (eds. Iserles and Powell), Clarendon Press, Oxford, 1987. (Note that I have not read this paper. However, Kahan was the primary architect of the IEEE floating point standard, so you can be pretty sure the reasons given in the paper are also the reasons IEEE floating point has signed zero.) A good online presentation which mentions all kinds of interesting floating point pathologies, including those discussed in the above paper, is "How Java’s Floating-Point Hurts Everyone Everywhere" (http://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf).
[...] Thus (a-b) is not the same as -(b-a) for IEEE floats!
Nor is x*0 equal to 0 for every x; nor does x == y imply f(x) == f(y) for every x, y, f; nor is addition or multiplication associative. There aren't many identities that do hold of floating point numbers. -- Ben