"""
https://en.wikipedia.org/wiki/Floor_and_ceiling_functions
"""


def ceil(x) -> int:
 """
 Return the ceiling of x as an Integral.

 :param x: the number
 :return: the smallest integer >= x.

 >>> import math
 >>> all(ceil(n) == math.ceil(n) for n
 ... in (1, -1, 0, -0, 1.1, -1.1, 1.0, -1.0, 1_000_000_000))
 True
 """
 return int(x) if x - int(x) <= 0 else int(x) + 1


if __name__ == "__main__":
 import doctest

 doctest.testmod()