Add Distributions integration tests

[mhauru]

Runs logpdf on a lot of different distributions, compares against FiniteDifferences.

Currently generating a lot of failures. Need to investigate which ones should be reported as bugs, which ones should just be marked as broken because of e.g. missing foreign calls.

Largely copied from similar tests in Tapir: https://github.com/compintell/Tapir.jl/blob/main/test/integration_testing/distributions.jl

[codecov-commenter]

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 69.41%. Comparing base (037dfed) to head (85fe94d).
Report is 179 commits behind head on main.

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Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1819      +/-   ##
==========================================
+ Coverage   67.50%   69.41%   +1.90%     
==========================================
  Files          31       35       +4     
  Lines       12668    14920    +2252     
==========================================
+ Hits         8552    10356    +1804     
- Misses       4116     4564     +448     

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[wsmoses]

@mhauru @yebai from the quadgk version incompatability, I think this should just be done in DistributionsAD.jl?

In any case, open any issues that persist and we'll get them fixed quickly

[mhauru]

This is ready for review. I've marked all failing tests as broken and opened issues for them. The univariate distributions are doing well, except for some missing foreign calls that were already known. There's still quite a lot of breakage for multivariate and matrix variate distributions.

Here are all the relevant issues:

• Missing Rmath derivatives #1620
• Implement besseli #1603
• [ForwardMode] unimplemented derivative for trtrs #1991
• Forward mode gradient error with argument of limited mutability #1821
• Missing rule for LAPACK's dgetrf_64_ #1820
• [ForwardMode] Runtime Activity not supported for BLAS calls #1995
• LLVM error: function failed verification (4) on truncated Beta distribution #1996
• Incorrect forward mode gradient for truncated normal distribution #1998
• BatchDuplicated fails with RefValues #1997
• Forward mode gradient doesn't support tuples with varying element types #1994

EDIT:
Also

• julia crash, Illegal Instruction 4, Wishart distribution #2012
• no method matching reverse with truncated Beta distribution #2010

[mhauru]

Fixed the two issues you pointed out. Tests now locally crash julia with Illegal instruction, not sure why, probably something that has changed on main. Will investigate tomorrow.

[mhauru]

Commented out the one that crashes and made an issue about it. Tests pass locally again, ready for another look, @wsmoses.