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"""
Doctest example from the official Python documentation.
https://docs.python.org/3/library/doctest.html
"""
def factorial(n):
"""Return the factorial of n, an exact integer >= 0.
>>> [factorial(n) for n in range(6)]
[1, 1, 2, 6, 24, 120]
>>> factorial(30) # doctest: +ELLIPSIS
265252859812191058636308480000000...
>>> factorial(-1)
Traceback (most recent call last):
...
ValueError: n must be >= 0
Factorials of floats are OK, but the float must be an exact integer:
>>> factorial(30.1)
Traceback (most recent call last):
...
ValueError: n must be exact integer
>>> factorial(30.0) # doctest: +ELLIPSIS
265252859812191058636308480000000...
It must also not be ridiculously large:
>>> factorial(1e100)
Traceback (most recent call last):
...
OverflowError: n too large
"""
import math
if not n >= 0:
raise ValueError("n must be >= 0")
if math.floor(n) != n:
raise ValueError("n must be exact integer")
if n + 1 == n: # catch a value like 1e300
raise OverflowError("n too large")
result = 1
factor = 2
while factor <= n:
result *= factor
factor += 1
return result
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