[linalg] Discrepancy between [linalg.algs.blas1.nrm2] and reference implementation

[MattStephanson]

Hello,

[linalg.algs.blas1.nrm2]/3 specifies the return value of vector_two_norm as "The square root of the sum of the square of init and the squares of the absolute values of the elements of v." (emphasis added). But the reference implementation provides

stdBLAS/include/experimental/__p1673_bits/blas1_vector_norm2.hpp

Line 74 in 3a63e9e

return init + ssq_res.scaling_factor * sqrt(ssq_res.scaled_sum_of_squares);

which pulls init out of the square-root-of-sum-of-squares. If the purpose is to be able to calculate a two-norm in stages, then the language in [linalg] is the correct way to do it, which is why I'm filing a bug instead of an LWG issue. But LMK if I have it the other way around.

As an aside, however, the Standard language is more difficult to implement robustly because init can be complex. That is, $\sqrt{z^2 +x^2}$, with $z\in ℂ,x\in ℝ$ is harder to compute than $\sqrt{x^2+y^2}$ with $\{ x,y \} \in ℝ$.

[mhoemmen]

Thanks for reporting this! I'm working on a fix as part of the change in the Working Draft due to adoption of the proposed fix for LWG 4302.

[mhoemmen]

I've posted a fix: #321