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"""

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

"""

def floor(x: float) -> int:

"""

Return the floor of x as an Integral.

:param x: the number

:return: the largest integer <= x.

>>> import math

>>> all(floor(n) == math.floor(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()