  Precise measurements of the single spin asymmetry, $A_N$ and the double spin
asymmetry, $A_{NN}$, in proton-proton (\textit{pp}) elastic scattering in the
region of four-momentum transfer squared $0.001 < -t < 0.032 ({\rm GeV}/c)^2$
have been performed using a polarized atomic hydrogen gas jet target and the
RHIC polarized proton beam at 24 GeV/$c$ and 100 GeV/$c$. The polarized gaseous
proton target allowed us to achieve the measurement of $A_{NN}$ in the CNI
region for the first time. Our results of $A_N$ and $A_{NN}$ provide
significant constraints to determine the magnitude of poorly known hadronic
single and double spin-flip amplitudes at this energy.
