det(A) as sign(P) times the product of the U(k, k).

The product is unscaled, so it saturates in both directions well before n is large: a 200x200 with 0.01 on the diagonal returns 0.0 and one with 100.0 returns infinity, neither of them singular. So a returned 0.0 does not mean singular, even though a singular factorization does return it. Test F64LuDecomposition.singular for exact singularity and F64Decompositions.rcond for how close to it a matrix is; that is what LAPACK offers too, which ships dgecon and no determinant routine at all.