Division of Floating Point Expansions with an Application to the Computation of a Determinant

Floating point expansion is a technique for implementing multiple precision using a processor's oating point unit instead of its integer unit. Research on this subject has arised recently from the observation that the oating point unit becomes a more and more eÆcient part of modern computers. Many simple arithmetic operators and some very useful geometric operators have already been presented on expansions. Yet previous work included only a very simple division algorithm. We present in this work a new algorithm that allows us to extend the set of geometric operators with Bareiss' determinant on a matrix of size between 3 and 10. Running times with di erent determinant algorithms on di erent machines are compared with GMP, a very common multi-precision package.