function [ root ] = binarySearchV2( func, xlow, xhigh, tol )
%binarySearchV2 method to find root of a function (called func)
  % this is just like binarySearch but it evaluates func fewer times
  % it also checks that there is a root in the initial interval
  
  % Use this to solve exp(x) - 4x == 0 by running 
  % binarySearchV2( @(x) exp(x)-4*x, 0,1, 1e-7)
 
  a=xlow; 
  b=xhigh;
  
  fa = func(a);
  fb = func(b);
  
  if ( fa*fb > 0 ) 
      error('f(a).f(b) must be < 0 for bisection')
  end
  
  while abs(b - a)/2 > tol*abs(a+b)/2
    c = (a+b)/2;
    fc = func(c);  % only one evaluation of f per loop
    
    if fb*fc > 0
        b = c;
        fb = fc;
    else
        a = c;  % (fb stays the same)
    end
  end % of the "while loop"
 
  root = (a+b)/2;
end % of the function