add AD hook for abs() per DiffRules

Project.toml

@@ -5,6 +5,7 @@ version = "0.21.1"
 
 [deps]
 CRlibm = "96374032-68de-5a5b-8d9e-752f78720389"
+DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"
 EnumX = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
 FastRounding = "fa42c844-2597-5d31-933b-ebd51ab2693f"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -13,6 +14,7 @@ SetRounding = "3cc68bcd-71a2-5612-b932-767ffbe40ab0"
 
 [compat]
 CRlibm = "0.7, 0.8, 1"
+DiffRules = "1"
 EnumX = "1"
 FastRounding = "0.2, 0.3"
 RoundingEmulator = "0.2"

src/IntervalArithmetic.jl

@@ -63,6 +63,8 @@ export bisect
 include("decorations/decorations.jl")
 export decoration, DecoratedInterval, com, dac, def, trv, ill
 
+include("ad.jl")
+
 include("rand.jl")
 
 include("parsing.jl")

src/ad.jl

@@ -0,0 +1,11 @@
+function _abs_deriv(x::Interval{T}) where T 
+    if inf(x) == 0
+        return Interval{T}(1)
+    elseif sup(x) == 0
+        return Interval{T}(-1, 1)
+    else
+        return sign(x)
+    end
+end
+
+_abs_deriv(x::DecoratedInterval) = DecoratedInterval(_abs_deriv(interval(x)), decoration(x))

test/interval_tests/ad.jl

@@ -0,0 +1,16 @@
+using IntervalArithmetic, ForwardDiff
+using Test
+
+@testset "AD" begin
+    for F in (Interval, DecoratedInterval)
+        @test ForwardDiff.derivative(abs, F(-2.0 .. 2.0)) == F(-1.0 .. 1.0)
+        @test ForwardDiff.derivative(abs, F(1.0 .. 2.0)) == F(1.0 .. 1.0)
+        @test ForwardDiff.derivative(abs, F(-2.0 .. -1.0)) == F(-1.0 .. -1.0)
+        @test ForwardDiff.derivative(abs, F(0.0)) == F(1.0)
+        @test ForwardDiff.derivative(abs, F(-2.0 .. 0.0)) == F(-1.0 .. 1.0)
+        @test ForwardDiff.derivative(abs, F(0.0 .. 2.0)) == F(1.0)
+
+        # Test proper handeling at abs(0)
+        @test ForwardDiff.hessian(t -> abs(t[1])^2, [F(0.0)])[1] == F(2.0)
+    end
+end

test/runtests.jl

@@ -14,6 +14,8 @@ end
 include_test("interval_tests/intervals.jl")
 include_test("decoration_tests/decoration_tests.jl")
 
+include_test("interval_tests/ad.jl")
+
 include_test("rand.jl")
 
 # Display tests:
@@ -24,3 +26,12 @@ include_test("multidim_tests/multidim.jl")
 
 # ITF1788 tests
 include_test("test_ITF1788/run_ITF1788.jl")  # TODO fix these tests
+
+# Display tests:
+include_test("display_tests/display.jl")
+
+# Multidim tests
+include_test("multidim_tests/multidim.jl")
+
+# ITF1788 tests
+include_test("test_ITF1788/run_ITF1788.jl")  # TODO fix these tests