rft: make gamma(a,x) GPU compatible

[haakon-e]

Purpose

This pull request refactors src/expint.jl, src/gamma.jl to make the upper incomplete gamma function gamma(a, x) GPU-compatible (verified on NVIDIA A100).

Summary of changes

src/expint.jl:

• Added targeted type constraints in En_expand_origin_general, En_safe_expfact, En_expand_origin to ensure their return types are consistent with the least precise floating point type of either a or x. These functions are conditionally used by gamma(a,x) through the call chain: fn -> En_expand_origin -> _expint -> expint -> _gamma(a,x) -> gamma(a,x)
  • Note: An alternative to this approach, would be to let these inner functions remain unstable, then do type conversion at the top-level.
  • Note 2: I don't personally use gamma(a,x) with complex arguments, so would appreciate an extra pair of eyes to verify that the way I get the floating point type FT from the arguments is reasonable.
• Added condition that guarantees termination of a while loop in _expint.
  • Note: This is an ad-hoc limit, which to my understanding, should never be reached mathematically.

src/gamma.jl:

• manually inlined single recursion in _trigamma and _zeta (similar to what I did in rft: make gamma_inc, gamma_inc_inv GPU-compatible #514)
• updated gamma(n::Union{Int8,UInt8,Int16,UInt16,Int32,UInt32,Int64,UInt64}) to call gamma(Float64(n)) instead of _gamma(Float64(n)) whenever n > 20. This subtle change allows the CUDA.jl device override for gamma to work for this method.

test/gamma_inc.jl:

• Added CI tests that verify that gamma(a, x) is type stable and allocation-free.
  • Note: Additional tests would be needed to verify that all runtime paths gamma(a,x) indeed do not allocate. I haven't done that in this PR

[codecov]

Codecov Report

❌ Patch coverage is 95.45455% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 94.19%. Comparing base (d71eddb) to head (734535b).

Files with missing lines	Patch %	Lines
src/expint.jl	91.66%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #520      +/-   ##
==========================================
+ Coverage   94.17%   94.19%   +0.01%     
==========================================
  Files          14       14              
  Lines        2971     2980       +9     
==========================================
+ Hits         2798     2807       +9     
  Misses        173      173              

Flag	Coverage Δ
unittests	94.19% <95.45%> (+0.01%)	⬆️

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