Is 'clamp' a formally recognized mathematical function?

I was surprised to find the clamp function absent from Mathworld and Wikipedia. Is this mainly a concept particular to computer programming? Is it known by another name in mathematics? I'll be editing the Wikipedia shortly to include a reference to this function but I want to make sure I'm not omitting some synonymous terms I'm currently unaware of.

$$ \operatorname{clamp}(x) = \max( a , \min( x , b ) ) \in [a,b] $$

There's no such thing as a "formally recognized" mathematical function. Some are more well known and widely used, but there is no standard defining what is a recognized function. Yes, $\mathop{\rm clamp}(x)$ is a mathematical function.

I remember using it in measure theory to show that a function $f : [a,b] \to \mathbb R$ was almost everywhere differentiable. The idea was that the clamp function was used to extend the identity $[a,b] \to [a,b]$ to the whole of $\mathbb R$, and then we could compose the clamp with $f$ to extend $f$ to the reals. This was just the first step of the proof, the clamp function had nothing to do with the rest. But I don't remember giving a name to that function ; I guess it just doesn't have enough importance in theoretical applications. It sounds more like a programmer's function.

Hope that helps,