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Re: John's asinh split versus convert-to-sortable...

On 03/23/2012 06:37 PM, Dan Zuras Intervals wrote:

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.


No. The overflow happens when you form u.



	All these things are level 2 issues for a function
	which is well defined at level 1.
But these things should be considered before fixing something at level 1 that is complex to program at level >1.
I mention this as I think that none of these splits should belong to a standard, because how to split is a matter of algorithm design and not one of standard behavior. Any particular choice will be artificial - a very bad sign for something that should become standard.