Add Enzyme reverse rules

Project.toml

@@ -6,6 +6,12 @@ version = "2.9.4"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
+[weakdeps]
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+
+[extensions]
+QuadGKEnzymeExt = "Enzyme"
+
 [compat]
 DataStructures = "0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19"
 julia = "1.2"
@@ -15,3 +21,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
 test = ["Test"]
+

test/Project.toml

@@ -0,0 +1,4 @@
+[deps]
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

test/runtests.jl

@@ -1,4 +1,4 @@
-# This file contains code that was formerly part of Julia. License is MIT: http://julialang.org/license
+ # This file contains code that was formerly part of Julia. License is MIT: http://julialang.org/license
 
 using QuadGK, LinearAlgebra, Test
 
@@ -426,3 +426,17 @@ quadgk_segbuf_printnull(args...; kws...) = quadgk_segbuf_print(devnull, args...;
     @inferred QuadGK.to_segbuf([0,1])
     @inferred QuadGK.to_segbuf([(0,1+3im)])
 end
+
+# Extension package only supported in 1.9+
+@static if VERSION >= v"1.9"
+    using Enzyme
+    f1(x) = quadgk(cos, 0., x)[1]
+    f2(x) = quadgk(cos, x, 1)[1]
+    f3(x) = quadgk(y->cos(x * y), 0., 1.)[1]
+
+    @testset "Enzyme" begin
+        @test cos(0.3) ≈ Enzyme.autodiff(Reverse, f1, Active(0.3))[1][1]
+        @test -cos(0.3) ≈ Enzyme.autodiff(Reverse, f2, Active(0.3))[1][1]
+        @test (0.3 * cos(0.3) - sin(0.3))/(0.3*0.3) ≈ Enzyme.autodiff(Reverse, f3, Active(0.3))[1][1]
+    end
+end