Recursive Vectorized Computation of the Vector p -norm

Recursive algorithms for computing the Frobenius norm of a real array are proposed, based on [Formula: see text], a hypotenuse function. Comparing their relative accuracy bounds with those of the BLAS routine [Formula: see text] it is shown that the proposed algorithms could in many cases be significantly more accurate. The scalar recursive algorithms are vectorized with the Intel’s vector instructions to achieve performance comparable to [Formula: see text], and are further parallelized with OpenCilk. Some scalar algorithms are unconditionally bitwise reproducible, while the reproducibility of the vector ones depends on the vector width. A modification of the proposed algorithms to compute the vector [Formula: see text]-norm is also presented.