  Quantum phases characterized by surfaces of gapless excitations are known to
violate the otherwise ubiquitous boundary law of entanglement entropy in the
form of a multiplicative log correction: $S\sim L^{d-1} \log L$. Using
variational Monte Carlo, we calculate the second R\'enyi entropy for a model
wavefunction of the $\nu=1/2$ composite Fermi liquid (CFL) state defined on the
two-dimensional triangular lattice. By carefully studying the scaling of the
total R\'enyi entropy and, crucially, its contributions from the modulus and
sign of the wavefunction on various finite-size geometries, we argue that the
prefactor of the leading $L \log L$ term is equivalent to that in the analogous
free fermion wavefunction. In contrast to the recent results of Shao et al.
[PRL 114, 206402 (2015)], we thus conclude that the "Widom formula" holds even
in this non-Fermi liquid CFL state. More generally, our results further
elucidate---and place on a more quantitative footing---the relationship between
nontrivial wavefunction sign structure and $S\sim L \log L$ entanglement
scaling in such highly entangled gapless phases.
