From: Francois Charton <deef AT pobox DOT oleane DOT com>
Newsgroups: comp.os.msdos.djgpp
Subject: Re: sqrt() problem
Date: Wed, 11 Dec 1996 18:54:04 +0100
Organization: CCMSA
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John M. Aldrich wrote:
> 
> #include <math.h>
> 
>     double s;
>     s = sqrt( pow( r, 2 ) - pow( m, 2 ) );
> 

This is *very* likely to be extremely slow... Power functions are 
usually much slower than multiplies...
I'd suggest either :
       sqrt(r*r-m*m);
or, better,
	sqrt((r-m)*(r+m));
(only one multiply)

The latter formula has another advantage, it should be a less 
floating-point-error-prone : if r and m are close and very big, 
r*r - m*m will result in incorrect results

Still better, formulae like
r * sqrt((1-m/r)*(1+m/r));
(if r and m are both positive).
Which are less rounding error prone, and will overflow less easily.

Francois