  We present measurements of the cross section and double-helicity asymmetry
$A_{LL}$ of direct-photon production in $\vec{p}+\vec{p}$ collisions at
$\sqrt{s}=510$ GeV. The measurements have been performed at midrapidity
($|\eta|<0.25$) with the PHENIX detector at the Relativistic Heavy Ion
Collider. At relativistic energies, direct photons are dominantly produced from
the initial quark-gluon hard scattering and do not interact via the strong
force at leading order. Therefore, at $\sqrt{s}=510$ GeV, where
leading-order-effects dominate, these measurements provide clean and direct
access to the gluon helicity in the polarized proton in the
gluon-momentum-fraction range $0.02<x<0.08$, with direct sensitivity to the
sign of the gluon contribution.
