Function binomial_coefficient_f64 

pub fn binomial_coefficient_f64(n: usize, k: usize) -> f64

Numerically stable C(n,k) = n! / (k!·(n−k)!) as f64. Uses the symmetry C(n,k) = C(n, n−k) to keep the loop count min(k, n−k) and the multiplicative recurrence C(n,j+1) = C(n,j)·(n−j)/(j+1), avoiding the overflow of separate factorial evaluations. Returns 0.0 for k > n and exact integer results within 2^53.