Adjective for: algorithm that outputs its input if it is one of its outputs? Is there a well established adjective or name for an algorithm such that, given as input any of its own output, always outputs it unchanged? In other words, an algorithm such that it implements a function $f$ with the property $f\circ f=f$. What would be a reference?

My application is a cryptographic security reduction. An example would be an algorithm which on input $X\in\{0,1\}^*$, outputs $1^{|X|}$.

Besides identity, an algorithm implementing $X\mapsto|X|$ in one of $\Bbb Z$, $\Bbb Q$, $\Bbb R$, $\Bbb C$ also comes to mind.



Stationary algorithm or circular algorithm would do, but neither googles. In my experience that means quickly it will google here, bringing circularity to a new level!
In mathematics we would say $f$ is an idempotent function. It's a widely known term and I suppose most TCS people should also recognize it.