(j3.2006) Fast accurate NORM2

[Van Snyder]

On Mon, 2015-12-14 at 13:57 -0700, Keith Bierman wrote:
> 
> On Mon, Dec 14, 2015 at 1:49 PM, Van Snyder <Van.Snyder at jpl.nasa.gov>
> wrote:
>         Efficient Calculations of Faithfully Rounded l2-Norms
>         of n-Vectors."
> 
> ?Sounds nice. Is there a copy of the sw online?

>From page 24:16 of the article:

"The complete set of codes, together with testing and performance
measurement auxiliary sources, is available at

  http://www.christoph-lauter.org/faithfulnorm.tgz

under an open source license.
  We implemented and tested our faithfully-rounded division-free l2-norm
with faithful reporting of overflow and underflow....
  We used IEEE754 binary64 as working precision and restricted ourselves
to an SIMD environment, targeting in particular Intel SSE/AVX units,
with or without the IEEE754 FMA insruction...."

Incidentally, Jim Demmel's students have implemented Kulisch's method to
compute exact dot products.  Their implementation runs six times faster
than a floating-point dot product, let alone a correctly-rounded one
that doesn't overflow or underflow.

> A quick google peek turned up some slides which suggest that
> intermediate computations with twice the word size are required (but
> I'm not certain its the same work).
> 
> 
> If so, worked details for double-double with one and two roundings
> might be of interest for folks with platforms (e.g. POWER) that
> support it (usually much cheaper than "quad" precision). 
> 
> 
> ?
> 
> 
> Keith Bierman
> khbkhb at gmail.com
> kbiermank AIM
> 303 997 2749