  We present a new special relativistic hydrodynamics (SRHD) code capable of
handling coexisting ultra-relativistically hot and non-relativistically cold
gases. We achieve this by designing a new algorithm for conversion between
primitive and conserved variables in the SRHD solver, which incorporates a
realistic ideal-gas equation of state covering both the relativistic and
non-relativistic regimes. The code can handle problems involving a Lorentz
factor as high as $10^6$ and optimally avoid the catastrophic cancellation. In
addition, we have integrated this new SRHD solver into the code GAMER
(https://github.com/gamer-project/gamer) to support adaptive mesh refinement
and hybrid OpenMP/MPI/GPU parallelization. It achieves a peak performance of
$7\times 10^{7}$ cell updates per second on a single Tesla P100 GPU and scales
well to 2048 GPUs. We apply this code to two interesting astrophysical
applications: (a) an asymmetric explosion source on the relativistic blast wave
and (b) the flow acceleration and limb-brightening of relativistic jets.
