  We use first principles molecular dynamics simulations coupled to the
thermodynamic integration method to study the hcp-bcc transition and melting of
beryllium up to a pressure of 1600~GPa. We derive the melting line by equating
solid and liquid Gibbs free energies, and represent it by a Simon Glatzel fit
$T_m= 1564~\text{K} (1 + P/(15.6032 ~\text{GPa}))^{0.383}$, which is in good
agreement with previous two-phase simulations below 6000~K. We also derive the
hcp-bcc solid-solid phase boundary and show the quasiharmonic approximation
underestimates the stability of the hcp structure, predicting lower transition
pressures between hcp and bcc phases. However, our results are consistent with
the stability regime predicted by the phonon quasiparticle method. We also
predict that hcp-bcc-liquid triple point is located at 164.7~GPa and 4314~K. In
addition, we compute the shock Hugoniot curve, and show that it is in good
agreement with experiments, intersecting our derived melting curve at
$\sim$235~GPa at 4900~K. Finally, we show that an isentropic compression path
that intersects the melting curve at both low and high temperature in the
liquid regime, can reappear in the solid after a gap as large as 7000~K.
Therefore, we predict that a large section of the melting curve could be
sampled, in principle, by a ramp compression experiment, where solid and liquid
Be would coexist as the sample is compressed.
