Bibliographic information

["Eric Postpischil" <stds-754+ieee.org@xxxxxxx>]

Here is information offered for the bibliography.  This is the partial
bibliography that Peter Markstein provided earlier, with a comment from me
and
a few from Peter.

                                -- edp (Eric Postpischil)
                                http://edp.org



Peter Markstein:  "Here's a short, incomplete bibliography of recent
writings
on the  correct rounding of elementary functions. These articles will also
point to other interesting works in their bibliographies."

J.M. Muller, ?Elementary Functions: Algorithms and Implementation?,
second edition, Birkhaeuser (2005), Chapter 10

D. Stehlé, V,. Lefèvre, and P. Zimmermann, ?Searching worst cases of
a one-variable function?, IEEE Transactions on Computers, 54(3):
340-346, March 2005

        Postpischil:  This shows how to search for worst cases (closest 
approaches
        to a rounding decision point) of a function f(x) in intervals where the
        exponent in the floating-point representation of x does not change, the
        exponent of f(x) does not change, and all i-th derivatives of f(x) are, 
as
        the paper writes, O(1).  (As I noted previously, I do not yet understand
        what they mean by saying a derivative is O(1).)

D. Defour, ?Fonctions élémentaires: algorithms et implémentations
efficaces pour l?arrondi correct en double précision?, PhD thesis,
Ecole Normale Supérieure de Lyon, September 2003

        From Peter Markstein, this shows a complete proof of why a specific
        double-precision exponential algorithm rounds correctly. It is done 
without
        fused multiply-add or double-extended arithmetic and is portable to all
        platforms that have IEEE-754 double-precision arithmetic.

F. de Dinechin, C. Loirat, J.M. Muller, ?A proven correctly rounded
logarithm in double precision?, Real Numbers and Computing?6, pp.
71-85, Dagstuhl, Germany (2004)

F. de Dinechin, A. Ershov, N. Gast, ?Towards the post-ultimate
libm?, Proc. Arith 17, pp 288-295, IEEE Computer Society, 2005.

        Recommended by Peter Markstein as a great article for anybody planning 
an
        implementation, with good suggestions on how to structure the code and
        exploit quad-precision routines to resolve most of the tough cases.

V. Lefèvre, "New results on the distance between a segment and Z^2.
Application to the exact rounding", Proc. Arith 17, pp 68-75, IEEE
Computer Society, 2005

V. Lefèvre, J.M. Muller, ?Worst cases for correct rounding of the
elementary functions in double precision?, Proc. Arith 15, pp.
111-118, IEEE Computer Society, 2001