On Ziv's rounding test

Florent de Dinechin 1, 2 Christoph Lauter 3 Jean-Michel Muller 1, 2 Serge Torres 1, 2
2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
3 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : A very simple test, introduced by Ziv, allows one to determine if an approximation to the value f (x) of an elementary function at a given point x suffices to return the floating-point number nearest f(x). The same test may be used when implementing floating-point operations with input and output operands of different formats, using arithmetic operators tailored for manipulating operands of the same format. That test depends on a "magic constant" e. We show how to choose that constant e to make the test reliable and efficient. Various cases are considered, depending on the availability of an fma instruction, and on the range of f (x).
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Florent de Dinechin, Christoph Lauter, Jean-Michel Muller, Serge Torres. On Ziv's rounding test. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2013, 39 (4), pp.26. ⟨ensl-00693317v2⟩

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