Efficient multiprecision floating point multiplication with optimal directional rounding

An algorithm is described for multiplying multipre-cision oating point numbers. The algorithm produces either the smallest oating point number greater than or equal to the true product or the greatest oating point number smaller than or equal to the true product. Software implementations of multiprecision precision oating point multiplication can reduce the computing time by a factor of two if they do not compute the low order digits of the product of the two mantissas. However, these algorithms do not necessarily provide optimally rounded results. The algorithm described in this paper is guaranteed to produce optimally rounded results and typically obtains the same savings.