Implementation of trigonometric functions

[arbimo]

This is a proof of concept PR to gauge the interest in adding common trigonometric functions to Real.
It currently only contains a simple implementation for sin and cos to validate the approach and get early feedback before spending to much time on it.

If there is interest we should:

• cover all common ones (e.g. see the ones in spire)
• add better automated tests for differentiation (e.g. reuse the ones in Fix automated differentiation of Lookup and Abs #330)

[avi-stripe]

Interesting. Can you say something about the use cases here?

[arbimo]

Essentially, I would like to use rainier-core's features of online compilation and automated differentiation for numeric optimization. My current use case is in the control of hybrid systems where trigonometric functions are ubiquitous. Since such trigonometric functions can not be expressed in terms of anything else their absence in Rainier means I cannot use it and would need to maintain a fork.

Overall, implementations of trigo functions should not be intrusive: its mostly additional unary ops as the ones for sin and cos. With enough automated test the risks would be very low as well.

Another option would be to add an extension point to allow user-defined operations (which could also help for #227) but this would require some non-trivial refactoring and I really believe trigonometric functions have their place in the core.

[avi-stripe]

Got it, thanks for the context. I'm +1 to continuing with these. Thanks so much for the contributions!

[avi-stripe]

As a side note - I gather from this that you would probably be using the compute and ir packages but not the core package with RandomVariable and Distribution? If at some point it makes sense to split those out into a separate module I'm sure we can do that.

[arbimo]

Great, I'll start working on it.

Indeed, I am only interested in compute and ir packages. It might make sense to move them to their own module since they are very general purpose and might be useful in a lot of different contexts. However, as long as the rest of rainier-core remains small and with no additional dependencies it is more of a marketing decision with no important technical implications.

[codecov-io]

Codecov Report

Merging #331 into develop will increase coverage by 0.39%.
The diff coverage is 65.67%.

@@             Coverage Diff             @@
##           develop     #331      +/-   ##
===========================================
+ Coverage    47.89%   48.29%   +0.39%     
===========================================
  Files           80       80              
  Lines         2758     2812      +54     
  Branches       214      217       +3     
===========================================
+ Hits          1321     1358      +37     
- Misses        1437     1454      +17

Impacted Files	Coverage Δ
...ore/src/main/scala/com/stripe/rainier/ir/Ops.scala	100% <ø> (ø)	⬆️
...e/src/main/scala/com/stripe/rainier/ir/IRViz.scala	0% <0%> (ø)	⬆️
.../scala/com/stripe/rainier/ir/MethodGenerator.scala	81.6% <100%> (+1.36%)	⬆️
...c/main/scala/com/stripe/rainier/compute/Real.scala	75% <100%> (+6.25%)	⬆️
...ain/scala/com/stripe/rainier/compute/RealOps.scala	62.06% <55.55%> (-3.15%)	⬇️
...in/scala/com/stripe/rainier/compute/Gradient.scala	93.44% <85.71%> (+0.71%)	⬆️
.../scala/com/stripe/rainier/compute/LogLineOps.scala	100% <0%> (+3.44%)	⬆️

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[arbimo]

@avi-stripe This should be ready for review now.
In the end, there are only intrinsic for (a)sin, (a)cos, (a)tan. Of those only tan could have been defined in term of sin and cos.

I have also added methods on Real for hyperbolic functions that are defined in terms of the existing primitives. Those are not essential to this PR as they only introduce syntactic sugar.

[avi-stripe]

Wonderful, thank you!