tag removed - Signed minimum?

I am looking for references to papers which might have defined a 'signed minimum' equivalent to
$$smin(x,y) ::= left(frac{textit{signum}(x)+textit{signum}(y)}{2}right)cdot min(|x|,|y|) $$
where $textit(signum)(x)$ is $-1$ for $xlt 0$, $1$ for $xgt 0$ and an arbitrary (finite) value for $x=0$. Also, any simpler expression for $smin$ would be appreciated. The above definition works for $mathbb{R}, mathbb{Q}$, and $mathbb{Z}$.

Intuition: the 'signed minimum' between x and y is the one closest to $0$ if they both have the same sign, otherwise it's 0.