What level of precision are users to expect of SNRM2 ?

[martin-frbg]

Over in OpenBLAS, issue OpenMathLib/OpenBLAS#5503 has showcased a (Julia) problem where the norm of a normally distributed vector, when computed in both single and double precision, is obtained with a significantly larger difference between the two computed values than expected from the precision of the input values.

This result is reproducible with the Reference BLAS, and a likely conclusion is that performing the intermediate computations at a higher precision would recover the desired result. However, this would appear to create something like an SDSNRM2 analogously to SDOT/SDSDOT, unless everybody is happy with "better than single" precision from the existing SNRM2.

I would like to solicit comments before I consider any changes on the OpenBLAS side :)

[dasergatskov]

Doing accumulation in double also avoids the issue of overflow, so one can do straight summation w/o Blue / Hammarling tricks.