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 $x\lt 0$, $1$ for $x\gt 0$ and an arbitrary (finite) value for $x=0$. Also, any simpler expression for $smin$ would be appreciated. The above definition works for $\mathbb{R}$, but actually I need to use it over $\mathbb{Z}$ in my application.

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.

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 $x\lt 0$, $1$ for $x\gt 0$ 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.