Q-adic Floating-point Transform revisited: arithmetic over small extension field via floating point routines - Laboratoire Jean Kuntzmann Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2007

Q-adic Floating-point Transform revisited: arithmetic over small extension field via floating point routines

Jean-Guillaume Dumas

Résumé

We present an algorithm to perform arithmetic operations over small extension field via numerical routines. The idea is to convert the $X$-adic representation of modular polynomials, with $X$ an indeterminate, to a $q$-adic representation where $q$ is a prime power larger than the field characteristic. With some control on the different involved sizes it is then possible to perform some of the $q$-adic arithmetic directly with floating point operators. Depending also on the number of performed numerical operations one can then convert back to the $q$-adic or $X$-adic representation and eventually mod out high residues. In this note we present a new version of both conversions: more tabulations and a way to reduce the number of divisions involved in the process are presented.
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Dates et versions

hal-00173894 , version 1 (20-09-2007)
hal-00173894 , version 2 (02-10-2007)
hal-00173894 , version 3 (26-10-2007)
hal-00173894 , version 4 (21-11-2007)
hal-00173894 , version 5 (04-04-2008)
hal-00173894 , version 6 (23-06-2008)

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Citer

Jean-Guillaume Dumas. Q-adic Floating-point Transform revisited: arithmetic over small extension field via floating point routines. 2007. ⟨hal-00173894v2⟩
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