Ceiling
Division returning an integer by truncating toward positive infinity
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,
Function: ceiling
(defun ceiling (i j)
(declare (xargs :guard (and (real/rationalp i)
(real/rationalp j)
(not (eql j 0)))))
(let* ((q (* i (/ j)))
(n (numerator q))
(d (denominator q)))
(cond ((= d 1) n)
((>= n 0)
(+ (nonnegative-integer-quotient n d)
1))
(t (- (nonnegative-integer-quotient (- n)
d))))))
