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Based on that we present an algorithm for calculating the rounded-to-nearest result of s := p i for a given vector of floatingpoint numbers p i , as well as algorithms for directed rounding. ... Our algorithms are fast in terms of measured computing time because they allow good instruction-level parallelism, they neither require special operations such as access to mantissa or exponent, they contain ... In Part I  of this paper we gave a fast algorithm to compute a faithfully rounded result of p i . Our methods are based on error-free transformations. ...doi:10.1137/07068816x fatcat:cle4c5osorc7nfag6d7ftfo77u