title: How to perform round to even with floating point numbers
body: <p>In regards to IEEE-754 single precision floating point, how do you perform round to nearest, where ties round to the nearest even digit in the required position (the default and by far the most common mode)?</p>
  
  <p>Basically I have the guard bit, round bit, and sticky bit.
  So if we form those into a vector and call it GRS, then the following rules apply:</p>
  
  <ol>
  <li>If <code>G = 0</code>, round down (do nothing)</li>
  <li>If <code>G = 1</code>, and <code>RS == 10</code> or <code>RS == 01</code>, round up (add one to mantissa)</li>
  <li>if <code>GSR = 111</code>, round to even</li>
  </ol>
  
  <p>So I am not sure how to perform the round to nearest.  Any help is greatly appreciated.</p>