Description of a spin-unpolarized homogeneous electron gas with the Yasuda functional applied to the exact 1-matrix gives rise to a formalism that correctly accounts for the logarithmic divergence of the correlation energy per volume at the high-density limit. The linear dependence of the on-top pair distribution function for antiparallel spins on the r(S) parameter is also correctly reproduced. A comparison of the relevant proportionality constant with its exact counterpart fixes the value of the adjustable parameter that enters the Yasuda functional.