Function jacobi_elliptic 

pub fn jacobi_elliptic<P, E, V>(u: V, k: V) -> (V, V, V)
where
    E: FloatElement,
    V: FloatVector<Element = E> + SpecializedTranscendentalMath<E>,
    P: Policy,

(sn, cn, dn) at argument u and modulus k.

Only $k^2$ enters, so the sign of k is irrelevant and |k| > 1 is out of domain: $1 - k^2$ goes negative, its square root is NaN, and the NaN propagates on its own without a guard. k = 1 is the one modulus the ladder cannot walk (it starts at $k' = 0$ and never converges), and is taken by the hyperbolic limit instead.