Re: John's asinh split versus convert-to-sortable...
> Date: Fri, 23 Mar 2012 12:24:59 +0100
> From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
> To: "Kreinovich, Vladik" <vladik@xxxxxxxx>
> CC: 'Dan Zuras Intervals' <intervals08@xxxxxxxxxxxxxx>,
> "stds-1788@xxxxxxxxxxxxxxxxx" <stds-1788@xxxxxxxxxxxxxxxxx>
> Subject: Re: John's asinh split versus convert-to-sortable...
>
> On 03/22/2012 10:06 PM, Kreinovich, Vladik wrote:
> > I like this reformulation, it only used sqrt which is usually very fast.
> >
> > split(x,y):
> > u = x + sqrt(1 + x^2);
> > v = y + sqrt(1 + y^2);
> > t = sqrt(u*v);
> > return s = (t - 1/t)/2;
>
> This produces inf when x or y > 1e160, not a good splitting point.
>
Arnold,
You refer to an overflow of u*v in the formula for t.
From the list of optimizations I presented there was:
"I'll set aside problems with over/underflow in t =
sqrt(u*v) (which happen in u*v, of course) other than
to say one can always go to:
t = sqrt(u)*sqrt(v)
which is not ideal but easier to express than the
usual prescaling crap that also solves the problem."
All these things are level 2 issues for a function
which is well defined at level 1.
Dan