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Journal Articles ACM Transactions on Mathematical Software Year : 2015

On the error of Computing ab + cd using Cornea, Harrison and Tang's method

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Abstract

In their book, Scientific Computing on the Itanium, Cornea et al. [2002] introduce an accurate algorithm for evaluating expressions of the form ab + cd in binary floating-point arithmetic, assuming an FMA instruction is available. They show that if p is the precision of the floating-point format and if u = 2^{−p}, the relative error of the result is of order u. We improve their proof to show that the relative error is bounded by 2u + 7u^2 + 6u^3. Furthermore, by building an example for which the relative error is asymptotically (as p → ∞ or, equivalently, as u → 0) equivalent to 2u, we show that our error bound is asymptotically optimal.
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Dates and versions

ensl-00862910 , version 1 (17-09-2013)
ensl-00862910 , version 2 (24-09-2013)

Identifiers

  • HAL Id : ensl-00862910 , version 2

Cite

Jean-Michel Muller. On the error of Computing ab + cd using Cornea, Harrison and Tang's method. ACM Transactions on Mathematical Software, 2015, 41 (2), pp.8. ⟨ensl-00862910v2⟩
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