% unitround.m
% k stewart - spring 1998 - written for CS 205
% We will compute the Unit Round Off - now that we have a
% feeling for how the "arithmetic" works
%

u = 1.0;  % need to start somewhere - why not at 1.0?

% count how many times we go through this loop

count = 0;
while (1.0 + u > 1.0),
    count = count + 1;  % in c, you could simplify to  count += 1;
    ubig = u; % u still changed 1.0, so keep track of that value in ubig
    u = u/2.0;
end;

% we now have the first value of u so that 1.0+u <= 1.0, although
% we were searching for the value that DID change 1.0, so
% that occurred in the iteration right before the loop exit
%
% after running the "while" loop

fprintf('After %4.0f iterations of while loop, we find\n',count)
fprintf('  unitroundoff = %14.8g \n',ubig)
echo on
%
% matlab provides this value through the variable "eps"
help eps
% and we can see this value without computing our own
% version in the while loop above by simply printing it
% out by given the variables name on the MATLAB command line
format short e
eps