Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
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Section: Research Program

Computer Arithmetic

Computer arithmetic is part of the common background of all team members, and is naturally ubiquitous in our application domains. However involved the mathematical objects considered may be, dealing with them first requires to master more basic objects: integers, finite fields, polynomials, and real and complex floating-point numbers. Libraries such as GNU MP, GNU MPFR, GNU MPC do an excellent job for these, both for small and large sizes (we rarely, if ever, focus on small-precision floating-point data, which explains our lack of mention of libraries relevant to it).

Most of our involvement in subjects related to computer arithmetic is to be understood in connection to our applications to the Number Field Sieve and to abelian varieties. As such, much of the research work we envision will appear as side-effects of developments in these contexts. On the topic of arithmetic work per se: