## CEILING

division returning an integer by truncating toward positive infinity
Major Section: PROGRAMMING

Example Forms:
ACL2 !>(ceiling 14 3)
5
ACL2 !>(ceiling -14 3)
-4
ACL2 !>(ceiling 14 -3)
-4
ACL2 !>(ceiling -14 -3)
5
ACL2 !>(ceiling -15 -3)
5

`(Ceiling i j)`

is the result of taking the quotient of `i`

and
`j`

and returning the smallest integer that is at least as great as
that quotient. For example, the quotient of `-14`

by `3`

is `-4 2/3`

, and
the smallest integer at least that great is `-4`

.
The guard for `(ceiling i j)`

requires that `i`

and `j`

are
rational (real, in ACL2(r)) numbers and `j`

is non-zero.

`Ceiling`

is a Common Lisp function. See any Common Lisp documentation for
more information. However, note that unlike Common Lisp, the ACL2
`ceiling`

function returns only a single value,