middle products

[Paul Zimmermann]

> From: David Harvey <dmharvey at cims.nyu.edu>
> Date: Mon, 8 Jun 2009 23:58:34 -0400
> 
> Hi folks,
> 
> I have written up some work I've been doing on middle products,  
> please see
> 
> http://cims.nyu.edu/~harvey/mulmid/
> 
> I expect this could yield improved constants in GMP for various  
> styles of division, square root etc.
> 
> Any comments, constructive or destructive, are welcome.
> 
> david

as a first application, I suggest trying the middle product for the
inverse computation. See for example Algorithm 43 (ApproximateReciprocal)
from [1], more precisely T = A*X_h at step 5.

Paul Zimmermann

[1] Modern Computer Arithmetic, Richard Brent and Paul Zimmermann,
version 0.2.1, March 2009, http://www.loria.fr/~zimmerma/mca/mca-0.2.1.pdf.