%0 Unpublished work %T On Ziv's rounding test %+ Laboratoire de l'Informatique du Parallélisme (LIP) %+ Arithmetic and Computing (ARIC) %+ Laboratoire d'Informatique de Paris 6 (LIP6) %A de Dinechin, Florent %A Lauter, Christoph %A Muller, Jean-Michel %A Torres, Serge %P 26 %8 2012-05 %D 2012 %K Floating-Point arithmetic %K correct rounding %K elementary functions %Z ACM G.1.0 %Z Computer Science [cs]/Other [cs.OH]Preprints, Working Papers, ... %X 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). %G English %2 https://ens-lyon.hal.science/ensl-00693317v1/document %2 https://ens-lyon.hal.science/ensl-00693317v1/file/ZivRounding_PreprintVersion.pdf %L ensl-00693317 %U https://ens-lyon.hal.science/ensl-00693317