% explore_eps.m
% k. stewart spring 1998 - written for CS 205
% we want to examine the behavior of the floating point
% number system
%
% assuming no background or familiarity with floating point
% behavior, we'll examine first a finite list of values
%
% it's dangerous to use the variable named "eps" since this is
% predefined MATLAB value which the user can reset
%

u = 1/2^15; % start the search off at an arbitrary, but exact, binary value
formax = 40;
for i=1:formax
    if (1.0 + u > 1.0) 
        fprintf('For u = %12.8g 1.0+u> 1.0 \n',u)
    else
        fprintf('Finally, after %4.0f iterations we find that\n',i)
        fprintf('  for u = %12.8g 1.0+u is NOT > 1.0 \n',u)
        fprintf('  therefore unit roundoff is %12.8g\n',2*u)
        fprintf('  Break out of the for loop\n')
        break;
    end % if-else block
    u = u/2;

    if (i == formax) 
         fprintf('Used %g loop iterations without finding u\n',formax)
    end

end % for i=1:10 loop