Evaluation of a new method to compute signs of determinants

We propose a method to evaluate signs of 2 x 2 and 3 x 3 determinants with b-bit integer entries using b and (b+ I)-bit arithmetic respectively, that N typically half the number of bits usually required. Algorithms of this kmd are very relevant to computational geometry, since most of the numerical aspects of geometric applications are reducible to evaluations of determinants. Therefore such algorithms provide a practical approach to robustness. The algorithm has been implemented and experimental results show that it slows down the computing time by only a small factor with respect to (error-prone) floating-point calculation, and compares favorably with other exact methods.