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Journal Articles ACM Transactions on Mathematical Software Year : 2013

On Ziv's rounding test


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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Dates and versions

ensl-00693317 , version 1 (02-05-2012)
ensl-00693317 , version 2 (08-07-2013)


  • HAL Id : ensl-00693317 , version 2


Florent de Dinechin, Christoph Lauter, Jean-Michel Muller, Serge Torres. On Ziv's rounding test. ACM Transactions on Mathematical Software, 2013, 39 (4), pp.26. ⟨ensl-00693317v2⟩
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