rft: make gamma_inc, gamma_inc_inv GPU-compatible

[haakon-e]

Purpose

This pull request refactors src/gamma_inc.jl to make gamma_inc and gamma_inc_inv GPU-compatible (verified on NVIDIA A100), with incidental improvements to performance and code clarity.

Summary of changes

• Replaced all constant coefficient arrays (such as acc0, big1, e0, x0, stirling_coef, auxgam_coef, and various d* arrays) with Tuples, which immutable and compatible with GPU kernels.
  • Updated type restriction in chepolsum accordingly.
• Replaced findfirst with Base.@nif in gamma_inc_asym to statically unroll the search into an if/elseif/else chain at parse time. This avoids dynamic dispatch that is unsupported in GPU kernels.
• Updated a few error messages that interpolated values into strings to use LazyString. String interpolation in error messages is not supported in GPU kernels.
• Refactored auxgam to manually inline its single recursion step. Mathematically the function recurses at most once (the x < 0 branch calls auxgam(1 + x) where 1 + x ≥ 0), but GPU compilers cannot statically prove termination of recursive call graphs, resulting in either stack overflow or illegal memory access at runtime.
• Added CI tests that verify these functions are inferable and allocation-free, as a proxy for GPU-compatibility.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.17%. Comparing base (539d6f8) to head (e0b0908).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #514   +/-   ##
=======================================
  Coverage   94.17%   94.17%           
=======================================
  Files          14       14           
  Lines        2969     2971    +2     
=======================================
+ Hits         2796     2798    +2     
  Misses        173      173           

Flag	Coverage Δ
unittests	94.17% <100.00%> (+<0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[haakon-e]

@devmotion Is there anything I can do to help get this PR merged?

[devmotion]

LGTM

[devmotion]

verified on NVIDIA A100

i wonder if we could verify this in CI to prevent regressions.

[haakon-e]

verified on NVIDIA A100

i wonder if we could verify this in CI to prevent regressions.

I agree this would be nice. In lieu of actually running CI on a GPU, a few ideas come to mind: checking type stability, and/or checking allocations

[haakon-e]

Let me know if the updated tests seem reasonable to you, and if so, feel free to merge this PR. Thanks for all your feedback, I think it greatly improved this PR!

[devmotion]

LGTM, thank you!