feat: add math/base/special/bernoullif

[gururaj1512]

Progresses #649

Description

What is the purpose of this pull request?

• adds math/base/special/bernoullif, which would be the single-precision equivalent for math/base/special/bernoullif.

float stdlib_base_bernoullif( const int32_t n )

Related Issues

Does this pull request have any related issues?

This pull request:

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

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No.

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• Read, understood, and followed the contributing guidelines.

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@stdlib-js/reviewers

[Planeshifter]

@gunjjoshi This is not a problem exclusively with this PR, since it also applies to math/base/special/bernoulli, which you added in #1860, but I noticed that the implementation returns zero for all odd numbers. However, Wikipedia says that this is incorrect for input value 1: https://en.wikipedia.org/wiki/Bernoulli_number
Could you please take a look and confirm whether we need to handle this case separately?

[gunjjoshi]

@Planeshifter Thanks for catching this. After digging for some time, I found that there is a mix of opinions on whether B(1) = +1/2 or B(1) = -1/2. For instance, here is a discussion from sympy: sympy/sympy#23866.
While it is incorrect to use B(1) = 0, the choice that must be made is between +1/2 or -1/2.
sympy now uses +1/2 (it used -1/2 earlier). There's a discussion at sagemath too: sagemath/sage#34521.

Overall, I think, it would be better if we too, use B(1) = +1/2. I'll make this change in math/base/special/bernoulli, if this is fine.

[gunjjoshi]

But yes, NIST prescribes the convention to use B(1) = -1/2: https://en.wikipedia.org/wiki/Bernoulli_number#Notation
What should we follow, in this case?

[kgryte]

Let's go ahead and use 1/2. This will match SymPy and is also used as a convention in R. As commented elsewhere, how much the choice actually matters in practice is subject to some debate. In this case, I'm more inclined to go with Knuth.

[kgryte]

Similar to the changes proposed in #3108, we'll want to make similar changes here.

[gururaj1512]

Refactored it as suggested.

[kgryte]

/stdlib merge

[kgryte]

@gururaj1512 Looks like this PR still has failing tests. We'll need to get those resolved before further review and subsequent merge.

[stdlib-bot]

Coverage Report

Package	Statements	Branches	Functions	Lines
math/base/special/bernoullif	$\color{green}239/239$ $\color{green}+100.00\%$	$\color{green}16/16$ $\color{green}+100.00\%$	$\color{green}2/2$ $\color{green}+100.00\%$	$\color{green}239/239$ $\color{green}+100.00\%$

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

[gururaj1512]

@gururaj1512 Looks like this PR still has failing tests. We'll need to get those resolved before further review and subsequent merge.

Resolved.