Efficient Calculations of Faithfully Rounded l2-Norms of n-Vectors

Abstract : In 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.
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Stef Graillat, Christoph Lauter, Ping Tak Peter Tang, Naoya Yamanaka, Shin’ichi Oishi. Efficient Calculations of Faithfully Rounded l2-Norms of n-Vectors. ACM Transactions on Mathematical Software, Association for Computing Machinery, 2015, 41 (4), pp.24:1. ⟨10.1145/2699469⟩. ⟨hal-01511120⟩

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