Alexander Belopolsky <belopol...@users.sourceforge.net> added the comment:
I agree, recursive version of partial_product is much simpler to follow. While
allocation of all numbers can be avoided in iterative version, doing so would
further complicate code with little benefit.
I still believe, however that an iterative version can benefit from redefining
partial_product to be product(2*i+1 for i in range(start, stop)).
Divide and conquer algorithm for that is simply
def partial_product(start, stop):
length = stop - start
.. handle length = 1 and 2 ..
middle = start + (length >> 1)
return partial_product(start, middle) * partial_product(middle, stop)
I would also reconsider the decision of using iterative outer loop. Recursive
outer loop matching redefined partial_product() can be written as
def loop(n):
p = r = 1
if n > 2:
p, r = loop(n >> 1)
p *= partial_product((n >> 2) + (n >> 1 & 1),
(n >> 1) + (n & 1))
r *= p
return p, r
which I believe is not harder to follow than the iterative alternative and does
not require bit_length calculation.
I am replacing my python implementation, factorial.py, with the one that uses
algorithms outlined above.
If there is any interest, I can convert it to C.
----------
Added file: http://bugs.python.org/file17343/factorial.py
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