Minimum and maximum of signed zero

Question

I am concerned about the following cases

min(-0.0,0.0)
max(-0.0,0.0)
minmag(-x,x) 
maxmag(-x,x)

According to Wikipedia IEEE 754-2008 says in

Answer 1

Why not read the standard yourself? The Wikipedia article for IEEE contains links to the standard.

Note: The C standard document is not available freely. But the final draft is (that's what I linked, search to find the pdf version). However, I've not seen the final document being cited here and AFAIK there had mostly been some typos corrected; nothing changed. IEEE is, however, available for free.

Note that a compiler need not stick to the standards (some embedded compilers/versions for instance do not implement IEEE-conforming floating point values, but are still C-conforming - just read the standard for details). So see the compiler documentation to see the compatibility. MS-VC for instance is not even compatible to C99 (and will never ben), while gcc and clang/llvm are (mostly) compatible to C11 in the current versions (gcc since 4.9.2 at least, in parts since 4.7).

In general, when using MS-VC, check if it actually does support that all standard features used. It is actually not fully compliant to the current standard, nor C99.

Answer 2

The fundamental issue in this case is the actual underlying mathematics, ignoring representational issues. There are several implications in your question that I believe are erroneous. -0.0 < 0.0 is false. -0.0 is a negative number is false. 0.0 is a positive number is false. In fact, there's no such thing as -0.0, though there is an IEEE 754 representation of zero with a sign bit set.

In addition, the behavior of min/max functions is only a small slice of legal floating-point operations that can yield zeros with different sign bits. Since floating point units are free to return (-)0.0 for expressions like -7 - -7, you'd also have to figure out what to do with that. I'd also like to point out that |0.0| could in fact return 0.0 with the sign bit set, since -0.0 is an absolute value of 0.0. Put simply, as far as mathematics is concerned 0.0 is -0.0. They are the same thing.

The only way that you can test for 0.0 with a set sign bit is to abandon mathematical expressions and instead examine the binary representation of such values. But what's the point of that? There's only one legitimate case I can think of: the generation of binary data from two different machines that are required to be bit-for-bit identical. In this case, you'll need to also worry about signaling and quiet NaN values, since there are very many more aliases of these values (10^22-1 SNaN's and 10^22 QNaN's for single-precision floats, and about 10^51 values of each for double-precision).

In these situations where binary representation is critical (it's absolutely NOT for mathematical computation), then you'll have to write code to condition all floats on write (zeros, quiet NaN's, and signaling NaN's).

For any computational purpose, it's useless to worry about whether the sign bit is set or clear when the value is zero.