Add interpolation benchmarks

Author: tansongchen

examples/Project.toml

@@ -1,12 +1,16 @@
 [deps]
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
+FastInterpolations = "9ea80cae-fc13-4c00-8066-6eaedb12f34b"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 GraphMakie = "1ecd5474-83a3-4783-bb4f-06765db800d2"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 LayeredLayouts = "f4a74d36-062a-4d48-97cd-1356bad1de4e"
 NetworkLayout = "46757867-2c16-5918-afeb-47bfcb05e46a"
 NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
 ODEProblemLibrary = "fdc4e326-1af4-4b90-96e7-779fcce2daa5"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 TaylorDiff = "b36ab563-344f-407b-a36a-4f200bebf99c"

examples/interpolation.jl

@@ -0,0 +1,41 @@
+using FastInterpolations
+import ForwardDiff, TaylorDiff
+using BenchmarkTools
+
+x = 0.0:0.1:1.0
+y = sin.(π * x)
+itp = cubic_interp(x, y)
+
+x0 = 0.45
+
+function analytic(itp, x0)
+    return itp(x0; deriv = DerivOp(2))
+end
+@btime analytic($itp, $x0)
+
+function td(itp, x0)
+    t = TaylorDiff.TaylorScalar{2}(x0, one(x0))
+    v = itp(t)
+    return v.partials[2] * 2
+end
+@btime td($itp, $x0)
+
+@code_typed analytic(itp, x0)
+@code_typed td(itp, x0)
+
+z = [sin(xi) * sin(yi) for xi in x, yi in x]
+itp2d = cubic_interp((x, x), z)
+
+function analytic2(itp2d, x0)
+    return itp2d((x0, x0); deriv = DerivOp(2, 0))
+end
+@btime analytic2($itp2d, $x0)
+
+@code_native analytic2(itp2d, x0)
+
+function td2(itp2d, x0)
+    t = TaylorDiff.TaylorScalar{2}(x0, one(x0))
+    v = itp2d((t, x0))
+    return v.partials[2] * 2
+end
+@code_native td2(itp2d, x0)