  The recent fast growth of a population of millisecond pulsars with precisely
measured mass provides an excellent opportunity to characterize these compact
stars at an unprecedented level. This is because the stellar parameter values
can be accurately computed for known mass and spin rate and an assumed equation
of state (EoS) model. For each of the 16 such pulsars and for a set of EoS
models from nucleonic, hyperonic, strange quark matter and hybrid classes, we
numerically compute fast spinning stable stellar parameter values considering
the full effect of general relativity. This first detailed catalogue of the
computed parameter values of observed millisecond pulsars provides a testbed to
probe the physics of compact stars, including their formation, evolution and
EoS. We estimate uncertainties on these computed values from the uncertainty of
the measured mass, which could be useful to quantitatively constrain EoS
models. We note that the largest value of the central density $\rho_{\rm c}$ in
our catalogue is $\sim 5.8$ times the nuclear saturation density $\rho_{\rm
sat}$, which is much less than the expected maximum value $13 \rho_{\rm sat}$.
We argue that the $\rho_{\rm c}$-values of at most a small fraction of compact
stars could be much larger than $5.8 \rho_{\rm sat}$. Besides, we find that the
constraints on EoS models from accurate radius measurements could be
significantly biased for some of our pulsars, if stellar $spinning$
configurations are not used to compute the theoretical radius values.
