add missing files

JuliaIntervals · Jun 14, 2023 · 12d5ca5 · 12d5ca5
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diff --git a/src/ad.jl b/src/ad.jl
@@ -0,0 +1,9 @@
+function _abs_deriv(x::Interval{T}) where T 
+    if inf(x) == zero(T)
+        return Interval(one(T))
+    elseif sup(x) == zero(T)
+        return -one(T) .. one(T)
+    else
+        return sign(x)
+    end
+end
diff --git a/test/interval_tests/ad.jl b/test/interval_tests/ad.jl
@@ -0,0 +1,14 @@
+using IntervalArithmetic, ForwardDiff
+using Test
+
+@testset "AD" begin
+    @test ForwardDiff.derivative(abs, -2.0 .. 2.0) == -1.0 .. 1.0
+    @test ForwardDiff.derivative(abs, 1.0 .. 2.0) == 1.0 .. 1.0
+    @test ForwardDiff.derivative(abs, -2.0 .. -1.0) == -1.0 .. -1.0
+    @test ForwardDiff.derivative(abs, Interval(0.0)) == Interval(1.0)
+    @test ForwardDiff.derivative(abs, -2.0 .. 0.0) == -1.0 .. 1.0
+    @test ForwardDiff.derivative(abs, 0.0 .. 2.0) == Interval(1.0)
+
+    # Test proper handeling at abs(0)
+    @test ForwardDiff.hessian(t -> abs(t[1])^2, [Interval(0.0)])[1] == Interval(2.0)
+end