title: IEEE 754 floating point, what is the largest number < 1?
body: <p>When using IEEE 754 floating point representation (<code>double</code> type in c++), numbers that are very close to (representable) integers are rounded to their closest integer and represented exactly.  Is that true?<br>
  Exactly how close does a number have to be to the nearest representable integer before it is rounded?<br>
  Is this distance constant?<br>
  For example, given that 1 can be represented exactly, what is the largest <code>double</code> less than 1?</p>