Modern Computer Arithmetic

  • Paul Zimmermann | INRIA

This talk is about a book in progress with Richard Brent (ANU, Canberra, Australia). “Modern Computer Arithmetic” collects in the same document all state-of-the-art algorithms in multiple precision arithmetic (integers, integers modulo n, floating-point numbers). The best current reference on that topic is volume 2 from Knuth’s “The art of computer programming”, which misses some new important algorithms (divide and conquer division, other variants of FFT multiplication, floating-point algorithms, …) Our aim is to give detailed algorithms: (i) for all operations (not just multiplication as many text books), (ii) for all size ranges (not just schoolbook methods or FFT-based methods), (iii) 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).
The talk will say a few words about the history of this book, and then will focus on a few algorithms from the book, some of which are not well known.
Url of the book: http://www.loria.fr/~zimmerma/mca/pub226.html

Speaker Details

Paul Zimmermann did his PhD in 1991 on the automatic average case analysis of algorithms under the supervision of Ph. Flajolet. He then worked on the random generation of computer algebra structures, and starting from the end of the 90s his interests moved to arbitrary precision floating- point computations and computational number theory. He is the author or co-author of several computer packages, in particular the MPFR library for computing with huge floating-point numbers with correct rounding, and the GMP-ECM program for factoring integers with the Elliptic Curve Method.

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