Fastest Executing Square Matrix Cofactor Implementation? Fastest Adjoint Implementation Which Works for Singular Matrix?

I see several cofactor functions on file exchange. Can anyone point to the fastest executing cofactor implementation, for use on n by n matrices with n in the hundreds to maybe thousands?

Alternatively, the (classical) adjoint function in MATLAB, or use of det(A)*inv(A), does not work for a singular matrix A. Is there an efficient implementation of adjoint which works even for a singular matrix? Of course, adjoint = cofactor', so fast implementation of one or the other of cofactor or adjoint can be obtained as the transpose of the other.

Thanks.