Add discrete-domain benchmarks and benchmark CI workflow

.github/workflows/Benchmark.yml

@@ -0,0 +1,88 @@
+name: Benchmark a pull request
+
+on:
+  pull_request:
+    branches:
+      - main
+  workflow_dispatch:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
+permissions:
+  pull-requests: write
+
+jobs:
+  benchmark:
+    runs-on: ubuntu-latest
+    timeout-minutes: 60
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          ref: ${{ github.event.pull_request.head.sha }}
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: "1"
+      - uses: julia-actions/cache@v2
+      - name: Extract package name from Project.toml
+        id: extract-package-name
+        run: |
+          PACKAGE_NAME=$(grep "^name" Project.toml | sed 's/^name = "\(.*\)"$/\1/')
+          echo "package_name=$PACKAGE_NAME" >> "$GITHUB_OUTPUT"
+      - name: Install AirspeedVelocity
+        run: |
+          # Lightweight install, as the runner sometimes runs out of memory:
+          julia -e 'ENV["JULIA_PKG_PRECOMPILE_AUTO"]=0; import Pkg; Pkg.add("AirspeedVelocity")'
+          julia -e 'ENV["JULIA_PKG_PRECOMPILE_AUTO"]=0; import Pkg; Pkg.build("AirspeedVelocity")'
+          echo "$HOME/.julia/bin" >> "$GITHUB_PATH"
+      - name: Run benchmarks
+        run: |
+          mkdir -p results
+          benchpkg ${{ steps.extract-package-name.outputs.package_name }} \
+            --rev="${{ github.event.repository.default_branch }},${{ github.event.pull_request.head.sha }}" \
+            --url="${{ github.event.repository.clone_url }}" \
+            --bench-on="${{ github.event.pull_request.head.sha }}" \
+            --output-dir=results/ \
+            --tune
+      - name: Create plots from benchmarks
+        run: |
+          mkdir -p plots
+          benchpkgplot ${{ steps.extract-package-name.outputs.package_name }} \
+            --rev="${{ github.event.repository.default_branch }},${{ github.event.pull_request.head.sha }}" \
+            --npart=10 --format=png --input-dir=results/ --output-dir=plots/
+      - name: Upload plots as artifacts
+        uses: actions/upload-artifact@v4
+        with:
+          name: plots
+          path: plots
+      - name: Create markdown table from benchmarks
+        run: |
+          benchpkgtable ${{ steps.extract-package-name.outputs.package_name }} \
+            --rev="${{ github.event.repository.default_branch }},${{ github.event.pull_request.head.sha }}" \
+            --input-dir=results/ --ratio > table.md
+          {
+            echo '### Benchmark Results'
+            echo ''
+            echo 'Ratios above 1 mean this PR is slower than `${{ github.event.repository.default_branch }}`.'
+            echo ''
+            cat table.md
+            echo ''
+            echo '### Benchmark Plots'
+            echo 'Plots have been uploaded as an artifact to this workflow run'
+            echo '("Actions" -> this run -> "Artifacts" at the bottom).'
+          } > body.md
+      - name: Find existing comment
+        uses: peter-evans/find-comment@v3
+        id: fcbenchmark
+        with:
+          issue-number: ${{ github.event.pull_request.number }}
+          comment-author: 'github-actions[bot]'
+          body-includes: Benchmark Results
+      - name: Comment on PR
+        uses: peter-evans/create-or-update-comment@v4
+        with:
+          comment-id: ${{ steps.fcbenchmark.outputs.comment-id }}
+          issue-number: ${{ github.event.pull_request.number }}
+          body-path: body.md
+          edit-mode: replace

benchmark/benchmarks.jl

@@ -15,6 +15,19 @@ for (name, method) in (("aaa", Barycentric), ("thiele", Thiele))
     g["abs_circle"]   = @benchmarkable approximate(z -> abs(z - 1.0001im), $unit_circle; method = $method, allowed = true)
 end
 
+# --- construction cost on a discrete point set ---
+# log-clustered points near 0, matching the discrete-domain test setup
+let zc = 10.0 .^ range(-15, 0, 500)
+    global const DISCRETE_PTS = [-reverse(zc); 0.0; zc]
+end
+SUITE["approximate_discrete"] = BenchmarkGroup()
+for (name, method) in (("aaa", Barycentric), ("thiele", Thiele))
+    g = SUITE["approximate_discrete"][name] = BenchmarkGroup()
+    g["tanh_steep"]  = @benchmarkable approximate(x -> tanh(100x), $DISCRETE_PTS; method = $method, allowed = true)
+    g["abs_shift"]   = @benchmarkable approximate(x -> abs(x + 0.5 + 0.01im), $DISCRETE_PTS; method = $method, allowed = true)
+    g["sin_recip"]   = @benchmarkable approximate(x -> sin(1 / (1.05 - x)), $DISCRETE_PTS; method = $method, allowed = true)
+end
+
 # --- evaluation cost on a fixed approximant ---
 SUITE["evaluate"] = BenchmarkGroup()
 let r = approximate(x -> tanh(50x), unit_interval, method = Barycentric, allowed = true),
@@ -30,6 +43,6 @@ end
 
 # --- pole solve ---
 SUITE["poles"] = BenchmarkGroup()
-let r = approximate(x -> 1 / (x^2 + 0.01), unit_interval; method = Thiele)
+let r = approximate(x -> 1 / sqrt(x^2 + 0.01), unit_interval; method = Thiele)
     SUITE["poles"]["thiele"] = @benchmarkable poles($r)
 end