  Every numerical general relativistic investigation starts from the solution
of the initial value equations at a given time. Astrophysically relevant
initial values for different systems lead to distinct set of equations that
obey specific assumptions tied to the particular problem. Therefore a robust
and efficient solver for a variety of strongly gravitating sources is needed.
In this work we present the OpenMP version of the Compact Object CALculator
(COCAL) on shared memory processors. We performed extensive profiling of the
core COCAL modules in order to identify bottlenecks in efficiency which we
addressed. Using modest resources, the new parallel code achieves speedups
approximately one order of magnitude relative to the original serial COCAL
code, which is crucial for parameter studies of computationally expensive
systems, such as magnetized neutron stars, as well as its further development
towards more realistic scenarios. As a novel example of our new code we compute
a binary quark system where each companion has a dimensionless spin of $0.43$
aligned with the orbital angular momentum.
