  We introduce CAFE, a new independent code designed to solve the equations of
Relativistic ideal Magnetohydrodynamics (RMHD) in 3D. We present the standard
tests for a RMHD code and for the Relativistic Hydrodynamics (RHD) regime since
we have not reported them before. The tests include the 1D Riemann problems
related to blast waves, head-on collision of streams and states with transverse
velocities, with and without magnetic field, which is aligned or transverse,
constant or discontinuous across the initial discontinuity. Among the 2D and 3D
tests, without magnetic field we include the 2D Riemann problem, a one
dimensional shock tube along a diagonal, the high speed Emery wind tunnel, the
Kelvin-Helmholtz instability, a set of jets and a 3D spherical blast wave,
whereas in the presence of a magnetic field we show the magnetic rotor, the
cylindrical explosion, a case of Kelvin-Helmholtz instability and a 3D magnetic
field advection loop. The code uses High Resolution Shock Capturing methods and
we present the error analysis for a combination that uses the HLLE flux formula
combined with linear, PPM and fifth order WENO reconstructors. We use the
flux-CT and the divergence cleaning methods to control the divergence free
magnetic field constraint.
