title: 'Less than' comparison with tolerance
body: <p>I am trying to write some code that computes whether <code>a</code> is less than <code>b</code> with n-bit tolerance, where <code>a</code> and <code>b</code> are double precision variables.</p>
  
  <p>For example, <code>4.000000001 &lt; 4.00000001</code> would be <code>TRUE</code>, but <code>4.0000000001 &lt; 4.000000001</code> would be <code>FALSE</code>. <code>3.99999999 &lt; 4.00000000</code> would also be <code>FALSE</code>. Also note that <code>a</code> and <code>b</code> could be negative. </p>