ensl-00693317
https://ens-lyon.hal.science/ensl-00693317
https://ens-lyon.hal.science/ensl-00693317v1/document
https://ens-lyon.hal.science/ensl-00693317v1/file/ZivRounding_PreprintVersion.pdf
On Ziv's rounding test
de Dinechin, Florent
Lauter, Christoph
Muller, Jean-Michel
Torres, Serge
[INFO.INFO-OH] Computer Science [cs]/Other [cs.OH]
UNDEFINED
Floating-Point arithmetic
correct rounding
elementary functions
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).
2012-05
2012-05-02
en