[RFC]: add C implementation for `@stdlib/math/base/special/factorial2`

[performant23]

Description

This RFC proposes adding native C implementation for math/base/special/factorial2:

const double stdlib_base_factorial2( const double x);

Related Issues

#649

Questions

No.

Other

No.

Checklist

• I have read and understood the Code of Conduct.
• Searched for existing issues and pull requests.
• The issue name begins with RFC:.

[performant23]

Hello, working on this issue!

[performant23]

Also, just to clarify, in lib/main.js an example is given like this:

* var v = factorial2( 301 );
* // returns Infinity

Also in fixtures/integers.json, the factorials are defined from 0-300 inclusive. So since factorial2 for 301 isn't defined, won't it be invalid to use 301?
@Pranavchiku, @kgryte, @Planeshifter

var MAX_FACTORIAL2 = 301; // TODO: consider extracting as a constant
.
.
.
if ( n > MAX_FACTORIAL2 ) {
return PINF;
}

[kgryte]

I suggest implementing similar to the C implementation in fibonacci, where the C implementation accepts an integer and returns a double.

[performant23]

Got it, will do! Thanks, @kgryte! Just had a little confusion about the return value of the double factorial for 301.
Since we bound the input to 301 as MAX_FACTORIAL2, and use the comparison as above effectively returning infinity for n > 301, we are accepting 301 exactly as an input for further processing.

But the example shown above suggests that we return infinity for 301.

So, if we want to return infinity for 301, we would need something like n >= 301 or set MAX_FACTORIAL2 to 300 is what I thought, or am I missing something?

[kgryte]

The documentation is actually correct.

In [42]: base.factorial2(301)
Out[42]: Infinity

301 actually computes to infinity. So, the implementation could be updated to use greater than or equal to rather than >. Feel free to make that small tweak when adding the C implementation.