# What is the computational class of a pushdown automaton with real values?

Say there is a push-down automata, in this example I'll use a deadfish-like set:

+: increase x by 1

0: set x to 0

ln: set x to ln(x) <-- real valued result

With x being an infinite precision real-valued variable, does this allow said machine to have more power than if it was operating on integers? Or am I misunderstanding something?

Since none of your instructions can influence the behavior of the pushdown automaton (they can only influence the value of $$x$$), this does not change which languages the pushdown automaton can accept.