def factorial(n):
"""Returns the factorial of n.
Parameters
* n: int (n >= 0)
Returns:
* prod: int
Raises:
* ValueError: If n < 0.
Examples:
>>> factorial(10)
3628800
>>> factorial(40)
815915283247897734345611269596115894272000000000L
>>> factorial(-1)
Traceback (most recent call last):
...
ValueError: factorial: Must have n >= 0.
Details:
The algorithm used is a binary splitting method. See Section 10.2.3 of
"Pi and the AGM" by Borwein and Borwein for information about this
method.
"""
if n < 0:
raise ValueError("factorial: Must have n >= 0.")
elif n in (0, 1):
return 1
prod = 1
for k in xrange(1, n.bit_length()):
lower = (n >> k) + 1
upper = (n >> (k - 1)) + 1
if lower % 2 == 0:
lower += 1
partial = 1
for j in xrange(lower, upper, 2):
partial *= j
prod *= (partial**k)
return prod << (n - bit_count(n))
def factorial(n):
"""Returns the factorial of n.
Parameters
* n: int (n >= 0)
Returns:
* prod: int
Raises:
* ValueError: If n < 0.
Examples:
>>> factorial(10)
3628800
>>> factorial(40)
815915283247897734345611269596115894272000000000L
>>> factorial(-1)
Traceback (most recent call last):
...
ValueError: factorial: Must have n >= 0.
Details:
The algorithm used is a binary splitting method. See Section 10.2.3 of
"Pi and the AGM" by Borwein and Borwein for information about this
method.
"""
if n < 0:
raise ValueError("factorial: Must have n >= 0.")
elif n in (0, 1):
return 1
prod = 1
for k in xrange(1, n.bit_length()):
lower = (n >> k) + 1
upper = (n >> (k - 1)) + 1
if lower % 2 == 0:
lower += 1
partial = 1
for j in xrange(lower, upper, 2):
partial *= j
prod *= (partial**k)
return prod << (n - bit_count(n))
def test_bit_count(self):
for k in xrange(20):
self.assertTrue(bit_count(-k) == bit_count(k) == bin(k).count('1'))
def test_bit_count(self):
for k in xrange(20):
self.assertTrue(bit_count(-k) == bit_count(k) == bin(k).count('1'))