title: Floating point IEEE guarantees
body: <p>I would like to know, for the following cases, if the IEEE standard guarantees every possible case (excluding NaN and infinities) using any cpu adhering to the standard:</p>
  
  <ul>
  <li>Commutativity: x # y = y # x</li>
  <li>Associativity: (x # y) # z = x # (y # z)</li>
  <li>x - x = 0 (does x - x == 0.0f always return true?)</li>
  <li>x * 0 = 0 (does x * 0.0f == 0.0f always return true?)</li>
  <li>x * 1 = x (does x * 1.0f == x always return true?)</li>
  <li>x / x = 1.0f (does x / x == 1.0f always return true? Except for x = 0 of course)</li>
  </ul>
  
  <p>(# means all operations: + - * /)</p>