(j3.2006) Fast accurate NORM2

[Van Snyder]

In ACM Transactions on Mathematical Software 41, 4 (2015) there is an
article entitled "Efficient Calculations of Faithfully Rounded l2-Norms
of n-Vectors."

>From the abstract:

"In this article, 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 1 bit of the underlying
floating-point type.  This algorithm does not generate overflows or
underflows spuriously, but does so when the final result 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 three times faster than the Netlib version on
current processors."