  A new code for computing fully general relativistic solutions of strongly
magnetized rapidly rotating compact stars is developed as a part of the COCAL
(Compact Object CALculator) code. The full set of Einstein's equations,
Maxwell's equations and magnetohydrodynamic equations are consistently solved
assuming perfect conductivity, stationarity, and axisymmetry, and strongly
magnetized solutions associated with mixed poloidal and toroidal components of
magnetic fields are successfully obtained in generic (non-circular) spacetimes.
We introduce the formulation of the problem and the numerical method in detail,
then present examples of extremely magnetized compact star solutions and their
convergence tests. It is found that, in extremely magnetized stars, the stellar
matter can be expelled from the region of strongest toroidal fields. Hence we
conjecture that a toroidal electro-vacuum region may appear inside of the
extremely magnetized compact stars, which may seem like the neutron star
becoming the strongest toroidal solenoid coil in the universe.
