RFC: Add cis(z) function, exp(iz)

[rreusser]

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Description

Description of the issue (or feature request).

Add cis function. Usage would be:

• cis(x): returns [cos(x), sin(x)]
• cis([0, 0], x): returns [cos(x), sin(x)] in-place
• cis(x, y): returns [exp(-y) cos(x), exp(-y) sin(x)]
• cis([0, 0], x, y): returns [exp(-y) cos(x), exp(-y) sin(x)] in-place

Note for the last two cases: exp(ix) is generalized to complex z, exp(iz). If z = x + iy, then this is exp(i (x + iy)) = exp(ix - y) = exp(-y) * (cos(x) + i sin(x)), hence the -y in the above formulas.

Other

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• Julia implementation
• Wikipedia entry

[kgryte]

Should we make the interface polymorphic or have two separate implementations:

@stdlib/math/base/special/cis
@stdlib/math/base/complex/cis

where the latter is aliased ccis?

[rreusser]

Yeah, it's unambiguous but I wasn't sure whether it was desirable. Perhaps base is not the place for polymorphic implementations. It feels just slightly weird to have cis in special though since it's definitely for complex numbers.

(Though really, cis(x) is just shorthand for cis(x, 0) making it slightly less polymorphic-feeling.)

[kgryte]

Then, for now, maybe we just focus on the complex use case and put in base/complex.

[rreusser]

That seems valid. If imag === 0.0, then we can avoid the exp so it's not like it's wasting too many cpu cycles.

[kgryte]

Awesome! Sounds good!