Rounding

Sometimes, when we have a fractional or rational number, we want to get rid of the fractional part and turn it into an integer. This can be done with the floor and ceiling operators.

• floor x, also written ⌊ x ⌋, returns the largest integer which is less than or equal to x. For example:

  Disco> floor(1/2)
  0
  Disco> floor(7/2)
  3
  Disco> floor(3)
  3
  Disco> floor(-1/2)
  -1
  

  Notice that floor always rounds down, even for negative numbers. (This is how mathematicians think about floor, and is the most mathematically elegant definition; however, note that in some other programming languages, floor always rounds towards zero instead, so e.g. floor(-1/2) would be 0.)

• Likewise, ceiling x, also written ⌈ x ⌉, returns the smallest integer which is greater than or equal to x. For example:

  Disco> ceiling(1/2)
  1
  Disco> ceiling(7/2)
  4
  Disco> ceiling(3)
  3
  Disco> ceiling(-1/2)
  0