Decimal Transcendentals via Binary

John Harrison.

Proceedings of ARITH19, the 19th IEEE Conference on Computer Arithmetic, IEEE Computer Society Press, 2009, pp. 187-194.


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.

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Bibtex entry:

        author          = "John Harrison",
        title           = "Decimal Transcendentals via Binary",
        editor          = "Javier D. Bruguera and Marius Cornea and
                           Debjit DasSarma and John Harrison",
        booktitle       = "Proceedings of the 19th IEEE Sympoisum on
                           Computer Arithmetic",
        address         = "Portland OR",
        publisher       = "IEEE Computer Society",
        year            = 2009,
        pages           = "187--194"}