CODE EXAMPLE FOR PYTHON

python math.factorial algorithm

# A pure Python version.

# Returns the number of bits necessary to represent an integer in binary, 
# excluding the sign and leading zeros.
# Needed only for Python version < 3.0; otherwise use n.bit_length().
def bit_length(self):
    s = bin(self)       # binary representation:  bin(-37) --> '-0b100101'
    s = s.lstrip('-0b') # remove leading zeros and minus sign
    return len(s)       # len('100101') --> 6

def num_of_set_bits(i) :
    # assert 0 <= i < 0x100000000
    i = i - ((i >> 1) & 0x55555555)
    i = (i & 0x33333333) + ((i >> 2) & 0x33333333)
    return (((i + (i >> 4) & 0xF0F0F0F) * 0x1010101) & 0xffffffff) >> 24

def rec_product(start, stop):
   """Product of integers in range(start, stop, 2), computed recursively.
      start and stop should both be odd, with start <= stop.
   """
   numfactors = (stop - start) >> 1
   if numfactors == 2 : return start * (start + 2)
   if numfactors > 1 :
       mid = (start + numfactors) | 1
       return rec_product(start, mid) * rec_product(mid, stop)
   if numfactors == 1 : return start
   return 1
 
def binsplit_factorial(n):
   """Factorial of nonnegative integer n, via binary split.
   """
   inner = outer = 1
   for i in range(n.bit_length(), -1, -1):
       inner *= rec_product((n >> i + 1) + 1 | 1, (n >> i) + 1 | 1)
       outer *= inner
   return outer << (n - num_of_set_bits(n))
 
# Test (from math import factorial).
[[n, binsplit_factorial(n) - factorial(n)] for n in range(99)]