  We bound Kloosterman-like sums of the shape \[ \sum_{n=1}^N \exp(2\pi i (x
\lfloor f(n)\rfloor+ y \lfloor f(n)\rfloor^{-1})/p), \] with integers parts of
a real-valued, twice-differentiable function $f$ is satisfying a certain limit
condition on $f''$, and $\lfloor f(n)\rfloor^{-1}$ is meaning inversion
modulo~$p$. As an immediate application, we obtain results concerning the
distribution of modular inverses inverses $\lfloor f(n)\rfloor^{-1} \pmod{p}$.
The results apply, in particular, to Piatetski-Shapiro sequences $ \lfloor
t^c\rfloor$ with $c\in(1,\frac{4}{3})$. The proof is an adaptation of an
argument used by Banks and the first named author in a series of papers from
2006 to 2009.
