We give details of our precise determination of the light quark masses mud = (mu + md)/2 and ms in 2 + 1 flavor QCD, with simulated pion masses down to 120 MeV, at five lattice spacings, and in large volumes. The details concern the action and algorithm employed, the HMC force with HEX smeared clover fermions, the choice of the scale setting procedure and of the input masses. After an overview of the simulation parameters, extensive checks of algorithmic stability, autocorrelation and (practical) ergodicity are reported. To corroborate the good scaling properties of our action, explicit tests of the scaling of hadron masses in Nf = 3 QCD are carried out. Details of how we control finite volume effects through dedicated finite volume scaling runs are reported. To check consistency with SU(2) Chiral Perturbation Theory the behavior of Mπ2/mud and Fπ as a function of mud is investigated. Details of how we use the RI/MOM procedure with a separate continuum limit of the running of the scalar density RS(μ, μ′) are given. This procedure is shown to reproduce the known value of r0ms in quenched QCD. Input from dispersion theory is used to split our value of mud into separate values of mu and md. Finally, our procedure to quantify both systematic and statistical uncertainties is discussed.
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