  In recent years, the prospects of performing fundamental and applied studies
at the next-generation high-intensity laser facilities have greatly stimulated
the interest in performing large-scale simulations of laser interaction with
matter with the account for quantum electrodynamics (QED) processes such as
emission of high energy photons and decay of such photons into
electron-positron pairs. These processes can be modeled via probabilistic
routines that include frequent computation of synchrotron functions and can
constitute significant computational demands within accordingly extended
Particle-in-Cell (QED-PIC) algorithms. In this regard, the optimization of
these routines is of great interest. In this paper, we propose and describe two
modifications. First, we derive a more accurate upper-bound estimate for the
rate of QED events and use it to arrange local sub-stepping of the global time
step in a significantly more efficient way than done previously. Second, we
present a new high-performance implementation of synchrotron functions. Our
optimizations made it possible to speed up the computations by a factor of up
to 13.7 depending on the problem. Our implementation is integrated into the
PICADOR and Hi-Chi codes, the latter of which is distributed publicly
(https://github.com/hi-chi/pyHiChi).
