Remove a type restriction in Base.QuadGK.Segment (#19626) (#19627)

* Remove a type restriction in Base.QuadGK.Segment (#19626)

* Test compatibility of quadgk with unitful numbers / physical quantities.

* Pare down tests.

* More test refinements.

base/quadgk.jl

@@ -40,7 +40,7 @@ immutable Segment
     a::Number
     b::Number
     I
-    E::Real
+    E
 end
 isless(i::Segment, j::Segment) = isless(i.E, j.E)
 

test/math.jl

@@ -760,6 +760,32 @@ end
     @test quadgk(cos, 0,0.7,1, norm=abs)[1] ≈ sin(1)
 end
 
+module Test19626
+    using Base.Test
+
+    # Define a mock physical quantity type
+    immutable MockQuantity <: Number
+        val::Float64
+    end
+
+    # Following definitions needed for quadgk to work with MockQuantity
+    import Base: +, -, *, abs, isnan, isinf, isless
+    +(a::MockQuantity, b::MockQuantity) = MockQuantity(a.val+b.val)
+    -(a::MockQuantity, b::MockQuantity) = MockQuantity(a.val-b.val)
+    *(a::MockQuantity, b::Number) = MockQuantity(a.val*b)
+    abs(a::MockQuantity) = MockQuantity(abs(a.val))
+    isnan(a::MockQuantity) = isnan(a.val)
+    isinf(a::MockQuantity) = isinf(a.val)
+    isless(a::MockQuantity, b::MockQuantity) = isless(a.val, b.val)
+
+    # isapprox only needed for test purposes
+    Base.isapprox(a::MockQuantity, b::MockQuantity) = isapprox(a.val, b.val)
+
+    # Test physical quantity-valued functions
+    @test quadgk(x->MockQuantity(x), 0.0, 1.0, abstol=MockQuantity(0.0))[1] ≈
+        MockQuantity(0.5)
+end
+
 @testset "subnormal flags" begin
     # Ensure subnormal flags functions don't segfault
     @test any(set_zero_subnormals(true) .== [false,true])