We present an updated version of the HMcode augmented halo model that can be used to make accurate predictions of the non-linear matter power spectrum over a wide range of cosmologies. Major improvements include modelling of BAO damping in the power spectrum and an updated treatment of massive neutrinos. We fit our model to simulated power spectra and show that we can match the results with an RMS error of 2.5 per cent across a range of cosmologies, scales $k < 10,hmathrm{Mpc}^{-1}$, and redshifts $z<2$. The error rarely exceeds 5 per cent and never exceeds 16 per cent. The worst-case errors occur at $zsimeq2$, or for cosmologies with unusual dark-energy equations of state. This represents a significant improvement over previo
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