How would I program special factorials into a calculator?

[ExplodingCaml]

By "special" I mean double factorials (n!!), hyperfactorials (H(n)), etc. I don't really want specific code so much as an idea of what I should be doing. I don't really care about what language, just the general thing I should be doing.

[Tamschi]

What's their definition?

[ExplodingCaml]

The double factorial of 6 (6!!) would be 6*4*2 as opposed to 6*5*4*3*2*1, triple would be 6*3...
The hyperfactorial of 6 (H(6)) would be (6^6)*(5^5)*(4^4)*(3*3)*(2*2)*(1^1).
The primorial regards only prime numbers, so 5 primorial would be 5*3*2*1, 7 primorial would be 7*5*3*2*1.
The superfactorial of 6 (6 $) would be 6!*5!*4!*3!*2!*1!.

[Tamschi]

That's the answer.

[ExplodingCaml]

?

[Tamschi]

You just program in the definition, using simpler operations. Remember that you can write these generally using indexed sums.

[Rìki]

Also remember that even exponential numbers will very quickly exceed the integer limit!
Depending on your inputs you need to use bigger data-types.
You said it's for a calculator, so I'd use some kind of "BigNum" data-type with (virtually) unlimited range.

For unlimited numeric data-types in .NET / C# there is BigInteger. And Java has one too.
If you need fractions you can use the BigRational class.
[url]http://bcl.codeplex.com/wikipage?title=BigRational&referringTitle=Home[/url]

[ExplodingCaml]

Oh yeah, I seem to have forgotten what a function was when I asked this question.

[editline]9th August 2014[/editline]

Except primorials look painful.

[Rìki]

I think the sieve of eratosthenes would be perfect for your concept of a 'primorial'.

With it, you can generate all primes up to some number you want.
In your case the limit is just your input-number.
Then you can just multiply the results of the sieve.

[ExplodingCaml]

Thanks!