# Talk:Special factorials

### Reverse factorial algorithm

I took a stab at translating the reverse factorial algorithm used in the Factor entry to Java. It should be almost as efficient as taking the factorial itself.

```public static int rf(int n) {
if (n == 1)
return 0; //1 has two answers -- return the lower one

int a = 1;
int b = 1;
while (n > a) {
b++;
a = a * b;
}
if (a == n)
return b;
else return -1; //undefined
}
```

--Chunes (talk) 17:06, 16 March 2021 (UTC)

Note that the   factorial inverse   (or  reverse factorial)   of   unity   has two possible answers:   zero   and   unity.
It is normal when searching a series   (in this case, the series of factorial products)   to use the first match found in the series.     -- Gerard Schildberger (talk) 17:37, 16 March 2021 (UTC)
Good catch. I revised the algorithm above and will make a note about it in the task description. --Chunes (talk) 17:58, 16 March 2021 (UTC)

### Why is af(0) 0?

Is it that 0 is the additive identity the way that factorial of 0 is 1 is the multiplicative identity? If so why should it be the identity anyway?

I think it's just that the formula literally produces 0 for n = 0.
First run through, i is 1, this produces -1. Second run through, i is 0, this produces 1 and their sum is 0. --Chunes (talk) 17:36, 16 March 2021 (UTC)

So the math summation notation goes backwards automatically when i > n? This may make a good task -- C will do one iteration and stop, etc. --Wherrera (talk) 21:11, 16 March 2021 (UTC)