Accuracy of Mathematical Functions in Single, Double, Double Extended, and Quadruple Precision

Brian Gladman , Vincenzo Innocente (1) , John Mather , Paul Zimmermann (2)

1 CERN [Genève]
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms

Computer users, most of whom assume they are working with reliable routines, unwittingly accept results from functions where the accuracies vary significantly from one mathematical library to another, from one library function to another, and even over different argument intervals of the same function. [...] Users are not likely to demand an improved situation because most of them, having neither the time nor the inclination to test manufacturer-supplied software, do not know the problem exists. This paper contains the results of such tests of elementary functions from several computer companies. The data (see Table I) demonstrate that the industry does not satisfy the needs of those who require accurate and efficient mathematical software.

Domaines: Algorithme et structure de données [cs.DS]

Brian Gladman, Vincenzo Innocente, John Mather, Paul Zimmermann. Accuracy of Mathematical Functions in Single, Double, Double Extended, and Quadruple Precision. 2024. ⟨hal-03141101v6⟩