Deprecate applying Gauss-Kronrod rules to surfaces

[mikeingold]

Changes

• Deprecates support for integrating (non-specialization) surfaces using GaussKronrod rules, issuing a Base.depwarn deprecation warning.
• Eliminates the _integral_gk_*d helper functions - consolidated into _integral(f, g, ::GaussKronrod) function instead.
• Minor tweaks
  • Removed explicit FP conversions inside GaussLegendre method, relying instead on automatic promotion from rational to float, resulting in a >2x performance improvement.
  • Removed obsolete QuadGK direct dependency from tests.

Discussion

Surfaces are geometries where paramdim(geometry) == 2. Use of nested GaussKronrod rules for these geometries is strictly inferior to simply using an equivalent HAdaptiveCubature rule, where generally returns results faster and with more accuracy. Earlier in the development of this package, using GaussKronrod rules on surfaces provided a workaround since HAdaptiveCubature rules didn't yet support Unitful-valued integrand functions. Since that issue has been resolved, I think we should mark this usage as deprecated in v0.16 and plan to remove support in v0.17. Support for usage on several of the specialization geometries would be unaffected for now, where there remains some justification for their usage.

[mikeingold]

@JoshuaLampert can you sanity check the _integral(f, geometry, ::GaussKronrod) function for me? For some reason the integrand symbol isn't being recognized, but I just don't see the issue. I tried commenting out the preceding depwarn in case there were any weird side effects, but saw no change.

[JoshuaLampert]

Looks mostly good to me. Please find some comments below.

[mikeingold]

Thanks!

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 95.86%. Comparing base (0cd335d) to head (f1e7d46).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #136      +/-   ##
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- Coverage   95.90%   95.86%   -0.05%     
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  Files          17       17              
  Lines         293      290       -3     
==========================================
- Hits          281      278       -3     
  Misses         12       12              

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[github-actions]

Benchmark Results

	main	f1e7d46...	main/f1e7d46fae4de3...
Differentials/Differential	0.239 ± 0.0021 μs	0.24 ± 0.001 μs	0.996
Differentials/Jacobian	0.205 ± 0.001 μs	0.205 ± 0.001 μs	1
Integrals/Meshes.BezierCurve/Scalar GaussKronrod	22.4 ± 0.04 ms	22.4 ± 0.04 ms	1
Integrals/Meshes.BezierCurve/Scalar GaussLegendre	21.4 ± 0.043 ms	21.4 ± 0.04 ms	1
Integrals/Meshes.BezierCurve/Scalar HAdaptiveCubature	22.6 ± 0.042 ms	22.6 ± 0.038 ms	1
Integrals/Meshes.BezierCurve/Vector GaussKronrod	22.4 ± 0.043 ms	22.4 ± 0.037 ms	1
Integrals/Meshes.BezierCurve/Vector GaussLegendre	21.5 ± 0.047 ms	21.4 ± 0.03 ms	1
Integrals/Meshes.BezierCurve/Vector HAdaptiveCubature	22.6 ± 0.047 ms	22.6 ± 0.053 ms	1
Integrals/Meshes.Segment/Scalar GaussKronrod	1.19 ± 0.0051 μs	1.2 ± 0.007 μs	0.992
Integrals/Meshes.Segment/Scalar GaussLegendre	0.0535 ± 0.00064 ms	8.5 ± 0.2 μs	6.3
Integrals/Meshes.Segment/Scalar HAdaptiveCubature	1.7 ± 0.045 μs	1.73 ± 0.045 μs	0.983
Integrals/Meshes.Segment/Vector GaussKronrod	3.38 ± 0.054 μs	3.41 ± 0.06 μs	0.992
Integrals/Meshes.Segment/Vector GaussLegendre	0.0638 ± 0.00086 ms	24.4 ± 0.61 μs	2.62
Integrals/Meshes.Segment/Vector HAdaptiveCubature	4.69 ± 0.09 μs	4.58 ± 0.077 μs	1.02
Integrals/Meshes.Sphere/Scalar GaussKronrod	0.0904 ± 0.00035 ms	0.0839 ± 0.00053 ms	1.08
Integrals/Meshes.Sphere/Scalar GaussLegendre	12.2 ± 0.095 ms	2.25 ± 0.0085 ms	5.42
Integrals/Meshes.Sphere/Scalar HAdaptiveCubature	0.0601 ± 0.00022 ms	0.0604 ± 0.00025 ms	0.996
Integrals/Meshes.Sphere/Vector GaussKronrod	0.117 ± 0.0012 ms	0.117 ± 0.00085 ms	0.999
Integrals/Meshes.Sphere/Vector GaussLegendre	13.5 ± 0.52 ms	3.61 ± 0.074 ms	3.75
Integrals/Meshes.Sphere/Vector HAdaptiveCubature	0.11 ± 0.0011 ms	0.11 ± 0.0011 ms	0.999
time_to_load	1.5 ± 0.011 s	1.53 ± 0.013 s	0.98

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[mikeingold]

Good to go here. Looks like the tweaks to GaussLegendre methods achieved a surprisingly big performance improvement.

[JoshuaLampert]

Good to go here. Looks like the tweaks to GaussLegendre methods achieved a surprisingly big performance improvement.

That's nice! Thanks!