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Author belopolsky belopolsky, draghuram, mark.dickinson, rhettinger, stutzbach 2010-05-14.18:05:04 2.88214e-07 No <1273860307.82.0.964072110155.issue8692@psf.upfronthosting.co.za>
Content
```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.```
History
Date User Action Args
2010-05-14 18:05:07belopolskysetrecipients: + belopolsky, rhettinger, mark.dickinson, draghuram, stutzbach
2010-05-14 18:05:07belopolskysetmessageid: <1273860307.82.0.964072110155.issue8692@psf.upfronthosting.co.za>