How would you write a non-recursive algorithm to calculate factorials?

Question

How would you write a non-recursive algorithm to compute n!?

Answer 1

In the interests of science I ran some profiling on various implementations of algorithms to compute factorials. I created iterative, look up table, and recursive implementations of each in C# and C++. I limited the maximum input value to 12 or less, since 13! is greater than 2^32 (the maximum value capable of being held in a 32-bit int). Then, I ran each function 10 million times, cycling through the possible input values (i.e. incrementing i from 0 to 10 million, using i modulo 13 as the input parameter).

Here are the relative run-times for different implementations normalized to the iterative C++ figures:

            C++    C#
---------------------
Iterative   1.0   1.6
Lookup      .28   1.1
Recursive   2.4   2.6

And, for completeness, here are the relative run-times for implementations using 64-bit integers and allowing input values up to 20:

            C++    C#
---------------------
Iterative   1.0   2.9
Lookup      .16   .53
Recursive   1.9   3.9