feat: add math/base/special/factorial2f

[anandkaranubc]

Progresses #649

Description

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This pull request:

• Adds the JS and C implementation of math/base/special/factorial2f.

Related Issues

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This pull request:

• progresses [RFC]: Add C implementations to base special math functions (tracking issue) #649

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• Read, understood, and followed the contributing guidelines.

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[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/factorial2f	$\color{green}203/203$ $\color{green}+100.00\%$	$\color{green}19/19$ $\color{green}+100.00\%$	$\color{green}2/2$ $\color{green}+100.00\%$	$\color{green}203/203$ $\color{green}+100.00\%$

The above coverage report was generated for the changes in this PR.

[anandkaranubc]

@kgryte Sorry if my recent comments cause any confusion. Just wanted to summarize everything I found so far.

[kgryte]

In C, this is equivalent to out = out * (float)i;.

[kgryte]

You may be able to adjust the precision here by using np.float32. np.int32 is likely to cause factorial2 to be evaluated in double-precision. NumPy is typically good about preserving float precision.

[anandkaranubc]

Thanks @kgryte for the review, and sorry for the mistakes.

Also, I tried using np.float32, which requires the factorial2 function to be called with the additional parameter extend='complex'. As the documentation mentions, this changes the values of the double factorial for even integers by reducing them by a factor of sqrt(2/π). But even if we ignore that, the results for odd integers don't match perfectly either.

After a bit of head-twisting and surfing through the source code, I found that SciPy uses the gamma function to approximate the double factorial, rather than the straightforward iterative method we typically use. They have a wrapper function that generalizes the implementation for all types of factorials.

https://github.com/scipy/scipy/blob/0f1fd4a7268b813fa2b844ca6038e4dfdf90084a/scipy/special/_basic.py#L2992-L2997

[anandkaranubc]

I could just generate the expected values locally using MATLAB.

Update: No luck with that :(

[kgryte]

No worries. Just add a note to the tests explaining why we are using approximate equality.

[Planeshifter]

All review comments have been addressed and the implementation looks good to me, so this PR should be ready to land.