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

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.