Accurate calculation of Euclidean Norms using Double-word arithmetic
Résumé
We consider the computation of the Euclidean (a.k.a. L2) norm of an ndimensional 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 to allow for a very accurate solution, free of spurious overflows and underflows. The returned result 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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