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 op...

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Bibliographic Details
Published in:ACM transactions on mathematical software 2013-07, Vol.39 (4), p.1-19
Main Authors: DE DINECHIN, Florent, LAUTER, Christoph, MULLER, Jean-Michel, TORRES, Serge
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Approximation
Computer Science
Computer science
control theory
systems
Electronics
Exact sciences and technology
Integrated circuits
Integrated circuits by function (including memories and processors)
Language processing and microprogramming
Other
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
Software
Theoretical computing
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Summary: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) .
ISSN:0098-3500
1557-7295
DOI:10.1145/2491491.2491495