  In this article, I present a very fast and high-precision (up to 33 decimal
places) C++ implementation of the semi-global time propagation algorithm for a
system of coupled Schr\"odinger equations with a time-dependent Hamiltonian. It
can be used to describe time-dependent processes in molecular systems after
excitation by femto- and attosecond laser pulses. It also works with an
arbitrary user supplied Hamiltonian and can be used for nonlinear problems. The
semi-global algorithm is briefly presented, the C++ implementation is described
and five sample simulations are shown. The accompanying C++ source code package
is included. The high precision benchmark (long double and float128) shows the
estimated calculation costs. The presented method turns out to be faster and
more accurate than the global Chebyshev propagator.
