Are there any efficient functions to evaluate Euler's totient function $\varphi(x)$ over a explicit range $(a,b)$ where $a,b\in\mathbb{R},0\leqslant a\leqslant b$ (and potentially greater than $x$)? i.e functions that return the count of values relatively prime to $x$ over an arbitrary, positive interval.
Ideally interested in any methods that aren't limited in range by memory constraints or that take forever to compute $\geqslant\mathcal{O}(x!)$.