This paper presents the performance of the ATLAS muon reconstruction during the LHC run with $pp$ collisions at $\sqrt{s}=7$ –8 TeV in 2011–2012, focusing mainly on data collected in 2012. Measurements of the reconstruction efficiency and of the momentum scale and resolution, based on large reference samples of ${J/\psi \rightarrow \mu \mu }$ , $Z \rightarrow \mu \mu $ and ${\Upsilon \rightarrow \mu \mu }$ decays, are presented and compared to Monte Carlo simulations. Corrections to the simulation, to be used in physics analysis, are provided. Over most of the covered phase space (muon $|\eta |<2.7$ and $5 \lesssim p_{\mathrm{T}}\lesssim 100$ GeV) the efficiency is above $99\,\%$ and is measured with per-mille precision. The momentum resolution ranges from $1.7\,\%$ at central rapidity and for transverse momentum $p_{\mathrm{T}}\simeq 10$ GeV, to $4\,\%$ at large rapidity and $p_{\mathrm{T}}\simeq 100$ GeV. The momentum scale is known with an uncertainty of $0.05\,\%$ to $0.2\,\%$ depending on rapidity. A method for the recovery of final state radiation from the muons is also
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