%-------------------------------------------------------------
%
% For A321 course
%
%-------------------------------------------------------------
%
%    Randall Bramley
%    Department of Computer Science
%    Indiana University, Bloomington
%    bramley somewhere at cs dot indiana dot (allegedly) edu                             
%
%   Started: Mon 04 Feb 2008, 09:05 AM
%   Last Modified: Mon 16 Feb 2009, 03:46 PM
%
echo on;
%-------------------------------------------------------------
%
% This shows some effects of floating point arithmetic.
% The two expressions below are equal in exact arithmetic,
% but not in floating point.
% 
% Moral of this m-file: never test for equality between
% floating point numbers. Instead use "less than or  
% equal to" <= or greater than or equal to >=, etc.
% 
% Second moral: addition is not associative and commutative 
% on computers. The only difference below is the order in 
% which the numbers are added.
% 
%-------------------------------------------------------------

should_be_true = ( (-0.08 + 0.5 - 0.42) == (0.5 - 0.42 - 0.08))
offby = abs( (-0.08 + 0.5 - 0.42) - (0.5 - 0.42 - 0.08));

echo off;
if (should_be_true)
    disp('Woo whoo! Computation was exact.');
else
    disp('Bummer, floating point inequality here.');
    disp(['The two expressions are off by ' num2str(offby) ]);
    disp(['This should be roughly the size of eps = ' num2str(eps) ]);
end