  We introduce a family of high-order time semi-discretizations for semilinear
wave equations of Klein--Gordon type with arbitrary smooth nonlinerities that
are uniformly accurate in the non-relativistic limit where the speed of light
goes to infinity. Our schemes do not require pre-computations that are specific
to the nonlinearity and have no restrictions in step size. Instead, they rely
upon a general oscillatory quadrature rule developed in a previous paper
(Mohamad and Oliver, arXiv:1909.04616).
