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Association for Computing Machinery (ACM), ACM Transactions on Mathematical Software, 4(39), p. 1-19, 2013

DOI: 10.1145/2491491.2491495

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On Ziv's Rounding Test

This paper was not found in any repository, but could be made available legally by the author.
This paper was not found in any repository, but could be made available legally by the author.

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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) .