  We compute the Dirac spectral density of QCD in a wide range of eigenvalues
by using a stochastic method. We use 2+1 flavor lattice ensembles generated
with Mobius domain-wall fermion at three lattice spacings ($a=0.083, 0.055,
0.044$ fm) to estimate the continuum limit. The discretization effect can be
minimized by a generalization of the valence domain-wall fermion. The spectral
density at relatively high eigenvalues can be matched with perturbation theory.
We compare the lattice results with the perturbative expansion available to
$O(\alpha_s^4)$.
