Decimal Transcendentals via Binary

Abstract

We describe the design and implementation of a comprehensive library of transcendental functions for the new IEEE decimal floating-point formats. In principle, such functions are very much analogous to their binary counterparts,though with a few additional subtleties connected with `scale' (preferred exponent). But our approach has been not to employ direct techniques, but rather to re-use existing binary functions as much as possible, both for greater efficiency and ease of implementation. For some functions the most straightforward approach (convert from decimal to binary, perform binary operation, convert back) works well. In many cases, however, these are insufficiently accurate, and subtler approaches must be used.