  We propose a novel class of uniformly accurate integrators for the
Klein--Gordon equation which capture classical $c=1$ as well as
highly-oscillatory non-relativistic regimes $c\gg1$ and, at the same time,
allow for low regularity approximations. In particular, the schemes converge
with order $\tau$ and $\tau^2$, respectively, under lower regularity
assumptions than classical schemes, such as splitting or exponential integrator
methods, require. The new schemes in addition preserve the nonlinear
Schr\"odinger (NLS) limit on the discrete level. More precisely, we will design
our schemes in such a way that in the limit $c\to \infty$ they converge to a
recently introduced class of low regularity integrators for NLS.
