add AD hook for abs() per DiffRules

Project.toml

@@ -5,6 +5,7 @@ version = "0.20.9"
 
 [deps]
 CRlibm = "96374032-68de-5a5b-8d9e-752f78720389"
+DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"
 FastRounding = "fa42c844-2597-5d31-933b-ebd51ab2693f"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
@@ -16,8 +17,9 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 
 [compat]
 CRlibm = "0.7, 0.8, 1"
-IntervalContractors = "0.4"
+DiffRules = "1.0"
 FastRounding = "0.2, 0.3"
+IntervalContractors = "0.4"
 Polynomials = "0.7, 1, 2, 3"
 RecipesBase = "1.0"
 RoundingEmulator = "0.2"
@@ -26,10 +28,11 @@ StaticArrays = "0.8, 0.9, 0.10, 0.11, 0.12, 1.0"
 julia = "1.5"
 
 [extras]
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 IntervalContractors = "15111844-de3b-5229-b4ba-526f2f385dc9"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Polynomials = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["IntervalContractors", "LinearAlgebra", "Test", "Polynomials"]
+test = ["ForwardDiff", "IntervalContractors", "LinearAlgebra", "Test", "Polynomials"]

src/IntervalArithmetic.jl

@@ -47,6 +47,8 @@ import Base.MPFR: MPFRRoundUp, MPFRRoundDown, MPFRRoundNearest, MPFRRoundToZero,
 
 import .Broadcast: broadcasted
 
+import DiffRules._abs_deriv
+
 export
     AbstractInterval, Interval,
     interval,
@@ -108,6 +110,7 @@ include("intervals/intervals.jl")
 include("multidim/multidim.jl")
 include("bisect.jl")
 include("decorations/decorations.jl")
+include("ad.jl")
 
 include("rand.jl")
 include("parsing.jl")

test/runtests.jl

@@ -12,6 +12,7 @@ include("interval_tests/intervals.jl")
 include("decoration_tests/decoration_tests.jl")
 
 include("rand.jl")
+include("interval_tests/ad.jl")
 
 # Display tests:
 include("display_tests/display.jl")