JOHANSSON, Fredrik

doi:10.1145/3328732

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JOHANSSON, Fredrik
Lithe and fast algorithmic number theory [LFANT]

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Ce document a été publié dans

ACM Transactions on Mathematical Software. 2019-08-08, vol. 45, n° 3, p. 1-26

Association for Computing Machinery

Résumé en anglais

We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U-function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, Airy functions, Legendre functions, Jacobi polynomials, complete elliptic integrals, and other special functions. The output can be used directly for interval computations or to generate provably correct floating-point approximations in any format. Performance is competitive with earlier arbitrary-precision software, and sometimes orders of magnitude faster. We also partially cover the generalized hypergeometric function pFq and computation of high-order parameter derivatives.< Réduire

Mots clés en anglais

orthogonal polynomials

Bessel functions

arbitrary-precision arithmetic

hypergeometric functions

interval arithmetic

automatic differentiation

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194056

DOI

http://dx.doi.org/10.1145/3328732

Projet Européen

Algorithmic Number Theory in Computer Science

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251