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 or natural number. 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
  

  Note

  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