Preliminary versions of the book will be published here before a commercial publication (and hopefully after if we find a commercial publisher who agrees):

Version 0.2 (June 2008), 190 pages. Previous versions: Version 0.1.1 (November 2006), 94 pages, Version 0.1 (October 2006), 91 pages. To cite this document, please use the following:

- for all operations (not just multiplication as many text books),
- for all size ranges (not just schoolbook methods or FFT-based methods),
- and including all details (for example how to properly deal with carries for integer algorithms, or a rigorous analysis of roundoff errors for floating-point algorithms).

Chapter 2 deals with modular arithmetic (representation, multiplication, division/inversion, exponentiation, conversion, applications of FFT).

Chapter 3 treats with floating-point arithmetic (addition, subtraction, comparison, multiplication, division, algebraic functions, conversion).

Chapter 4 covers Newton's method and function evaluation (Newton's method and its variants, argument reduction, power series, asymptotic expansions, continued fractions, recurrence relations, arithmetic-geometric mean, binary splitting, D-finite functions, contour integration, constants).

Finally, an appendix gives pointers to software tools, mailing-lists, and on-line documents.

*Modern Computer Algebra
*, Joachim von zur Gathen and Jürgen
Gerhard, Cambridge University Press, 2nd edition, 2003.

*The Design and Analysis of Computer Algorithms*, A. V. Aho,
J. E. Hopcroft and J. D. Ullman, Addison-Wesley, 1974 [chapters
7 and 8].

*The Computational Complexity of Algebraic and Numeric Problems*,
A. Borodin and I. Munro, Elsevier Computer Science Library, 1975.

*Handbook of Applied
Cryptography*, Alfred J. Menezes,
Paul C. van Oorschot and Scott A. Vanstone, CRC Press, 1997 [chapter 14].

*Prime Numbers: A Computational Perspective*,
Richard E. Crandall and Carl Pomerance, Springer Verlag, 2001 [chapter 9].

*Fast Algorithms, A Multitape Turing Machine Implementation*,
Arnold Schönhage and A. F. W. Grotefeld and E. Vetter,
BI-Wissenschaftsverlag, 1994 [out of print].

*Handbook of Elliptic and Hyperelliptic Curve Cryptography*,
Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange,
Kim Nguyen, Frederik Vercauteren,
Chapman & Hall/CRC, series Discrete Mathematics and its Applications, 2005
[chapters 9-12].

See also the ``Algorithms'' chapter from the GMP reference manual, and the Algorithms for programmers book in progress by Jörg Arndt.