Accurate computation of the sign and the value of a matrix determinant attracts a great deal of attention. Various algebraic and geometric computations boil down to it. This includes the computation of a convex hull and a Voronoi diagram as well as the evaluation and expansion of scalar, univariate and multivariate resultants. In the present day computing environment, it is most effective to compute determinants numerically with IEEE standard double precision floating-point numbers provided rounding errors are controlled. That control is difficult where the input matrix is ill conditioned...