% given a & b such that f(a)<0 & f(b)>0
% ep is the error tolerance
% max_iterate is the maximum of the iterative 
% steps
a = 1;
b = 2;
ep = 10^-4;
max_iterate = 10000;

% check whether the interval is in the right form or not
if a >= b
    disp('a < b is not true.  Stop!')
    return
end

% check the sign of the initial boundary points
fa = f(a); fb = f(b);
if sign(fa)*sign(fb) > 0
    disp('f(a0) and f(b0) are of the same sign.  Stop!')
    return
end

% produce midpoint of boundary points
c = (a+b)/2;

% it_count is the iteration steps
it_count = 0;

while b-c > ep & it_count < max_iterate  % iteration condition
    it_count = it_count + 1;
    fc = f(c);
    
    % check the sign of the generated point
    if sign(fb)*sign(fc) <= 0
        a = c;
        fa = fc;
    else
        b = c;
        fb = fc;
    end
    c = (a+b)/2;
end

format long
root = c
format short e
error_bound = b-c
format short
it_count