Function loadings 

fn loadings<R: Scalar>(rho: R) -> (R, R)

(√ρ, √(1 − ρ)), checked against [0, 1).

√ρ has an infinite slope at zero, so a correlation of exactly zero takes a passive zero rather than a NaN adjoint: the factor loading is switched off there, and the sensitivity it would carry is the one-sided limit a bump from zero reads, not a derivative. The guard is on the argument’s value, so every mode takes the same branch.