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We test the performance of a recently proposed fundamental measure density functional of aligned hard cylinders by calculating the phase diagram of a monodisperse fluid of these particles. We consider all possible liquid-crystalline symmetries, namely, nematic, smectic, and columnar, as well as the crystalline phase. For this purpose we introduce a Gaussian parametrization of the density profile and use it to numerically minimize the functional. We also determine, from the analytic expression for the structure factor of the uniform fluid, the bifurcation points from the nematic to the smectic and columnar phases. The equation of state, as obtained from functional minimization, is compared to the available Monte Carlo simulation. The agreement is very good, nearly perfect in the description of the inhomogeneous phases. The columnar phase is found to be metastable with respect to the smectic or crystal phases, its free energy though being very close to that of the stable phases. This result justifies the observation of a window of stability of the columnar phase in some simulations, which disappears as the size of the system increases. The only important deviation between theory and simulations shows up in the location of the nematic-smectic transition. This is the common drawback of any fundamental measure functional of describing the uniform phase just with the accuracy of scaled particle theory.