Add discrete-domain benchmarks and benchmark CI workflow

[tobydriscoll]

Summary

• Add an approximate_discrete benchmark group exercising Barycentric (AAA) and Thiele construction over a 1001-point log-clustered discrete set (matching the test/discrete.jl point distribution), across three difficulty profiles: steep tanh, near-real branch-point abs, and near-pole sin(1/(1.05-x)).
• Add a GitHub Actions workflow (.github/workflows/Benchmark.yml) that runs AirspeedVelocity on PRs, comparing the PR head against the default branch and posting/updating a ratio table comment (plots uploaded as an artifact).

Notes

• The workflow uses the pull_request trigger, so it will not post comments on PRs from forks (read-only token). Fork-PR commenting would require pull_request_target, which runs untrusted code with a write token — deliberately avoided.
• The workflow only takes effect from main, so it does not run on this PR; it activates on the next PR after merge.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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[github-actions]

Benchmark Results

Ratios above 1 mean this PR is slower than main.

	main	42ce61f...	main / 42ce61f...
approximate/aaa/abs_circle	0.0469 ± 0.002 s	0.0463 ± 0.0019 s	1.01 ± 0.061
approximate/aaa/exp_interval	0.171 ± 0.029 ms	0.18 ± 0.033 ms	0.95 ± 0.24
approximate/aaa/tanh_steep	1.79 ± 0.044 ms	1.83 ± 0.055 ms	0.98 ± 0.038
approximate/thiele/abs_circle	13.4 ± 0.1 ms	13.4 ± 0.1 ms	1 ± 0.011
approximate/thiele/exp_interval	0.325 ± 0.019 ms	0.326 ± 0.019 ms	1 ± 0.083
approximate/thiele/tanh_steep	1.14 ± 0.021 ms	1.14 ± 0.023 ms	1 ± 0.028
approximate_discrete/aaa/abs_shift	4.09 ± 0.08 ms	4.12 ± 0.062 ms	0.994 ± 0.025
approximate_discrete/aaa/sin_recip	1.39 ± 0.031 ms	1.4 ± 0.03 ms	0.994 ± 0.031
approximate_discrete/aaa/tanh_steep	12.1 ± 0.68 ms	12.1 ± 0.59 ms	0.998 ± 0.074
approximate_discrete/thiele/abs_shift	3.18 ± 0.11 ms	3.2 ± 0.52 ms	0.993 ± 0.17
approximate_discrete/thiele/sin_recip	1.94 ± 0.041 ms	1.96 ± 0.032 ms	0.991 ± 0.026
approximate_discrete/thiele/tanh_steep	8.1 ± 0.78 ms	8.34 ± 0.56 ms	0.971 ± 0.11
evaluate/bary_vector	0.143 ± 0.0073 ms	0.146 ± 0.0073 ms	0.979 ± 0.07
evaluate/thiele_vector	0.138 ± 0.0098 ms	0.138 ± 0.0097 ms	0.998 ± 0.1
poles/thiele	0.423 ± 0.019 ms	0.421 ± 0.015 ms	1.01 ± 0.057
time_to_load	0.907 ± 0.00075 s	0.911 ± 0.0057 s	0.996 ± 0.0063

Benchmark Plots

Plots have been uploaded as an artifact to this workflow run
("Actions" -> this run -> "Artifacts" at the bottom).