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International audienceIn this paper, we present an efficient algorithm to compute the faithful rounding of the l2-norm of a floating-point vector. This means that the result is accurate to within one bit of the underlying floating-point type. This algorithm does not generate overflows or underflows spuriously, but does so when the final result indeed calls for such a numerical exception to be raised. Moreover, the algorithm is well suited for parallel implementation and vectorization. The implementation runs up to 3 times faster than the netlib version on current processors

Efficient Calculations of Faithfully Rounded l 2 -Norms of n -Vectors

Efficient Calculations of Faithfully Rounded l ₂ -Norms of n -Vectors