Accurate calculation of Euclidean Norms using Double-word arithmetic
Résumé
We consider the computation of the Euclidean (or L2) norm of an n-dimensional vector in floating-point arithmetic. We review the classical solutions used to avoid spurious overflow or underflow and/or to obtain very accurate results. We modify a recently published algorithm (that uses double-word arithmetic) to allow for a very accurate solution, free of spurious overflows and underflows. To that purpose, we use a double-word square-root algorithm of which we provide a tight error analysis. The returned L2 norm will be within very slightly more than 0.5 ulp from the exact result, which means that we will almost always provide correct rounding.
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NormsandDW HaLV2.pdf (771.99 Ko)
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C_and_Julia.zip (126.7 Ko)
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en_sqrt_dw_coq.tar.gz (145.81 Ko)
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