Re: Arguments for supporting Motion P1788/0023.01:NoMidRad

[Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>]

Rudnei Cunha wrote:
> I strongly agree with Nate. I've seen enough evidence in the field of
> numerical linear algebra using interval arithmetic - both standard and
> mid-rad representations - that have convinced me that, in this field at
> least, mid-rad is the best choice. 

Could you please share with us enough references to that evidence
that support your conviction, so that others can check them for
their merits?

For the only evidence I have seen where midrad is preferable
is vectorized matrix-vector and matrix-matrix multiplication
of matrices with narrow entries,

But an efficient implementation of that is completely independent
from having an implementation of midrad arithmetic operations, etc.
on the level of single operations.
Indeed, it is already efficiently implemented in IntLab using
directed rounding.

Since P1788 is not about standardizing interval BLAS but about lower 
level issues, a midrad implementation on the level of the standard
could not the slightest help in making vectorized matrix products
faster than the algorithm used by IntLab.


Arnold Neumaier