define isapprox (#125)

* define isapprox

* after review

Author: aplavin

src/IntervalSets.jl

@@ -1,7 +1,7 @@
 module IntervalSets
 
 using Base: @pure
-import Base: eltype, convert, show, in, length, isempty, isequal, issubset, ==, hash,
+import Base: eltype, convert, show, in, length, isempty, isequal, isapprox, issubset, ==, hash,
              union, intersect, minimum, maximum, extrema, range, clamp, mod, float, ⊇, ⊊, ⊋
 
 using Statistics
@@ -142,6 +142,16 @@ isequal(A::TypedEndpointsInterval, B::TypedEndpointsInterval) = isempty(A) & ise
 ==(A::TypedEndpointsInterval{L,R}, B::TypedEndpointsInterval{L,R}) where {L,R} = (leftendpoint(A) == leftendpoint(B) && rightendpoint(A) == rightendpoint(B)) || (isempty(A) && isempty(B))
 ==(A::TypedEndpointsInterval, B::TypedEndpointsInterval) = isempty(A) && isempty(B)
 
+function isapprox(A::AbstractInterval, B::AbstractInterval; atol=0, rtol=Base.rtoldefault(eltype(A), eltype(B), atol), kwargs...)
+    closedendpoints(A) != closedendpoints(B) && error("Comparing intervals with different closedness is not defined")
+    isempty(A) != isempty(B) && return false
+    isempty(A) && isempty(B) && return true
+    maxabs = max(maximum(abs, endpoints(A)), maximum(abs, endpoints(B)))
+    let atol = max(atol, rtol * maxabs)
+        isapprox(leftendpoint(A), leftendpoint(B); atol, rtol, kwargs...) && isapprox(rightendpoint(A), rightendpoint(B); atol, rtol, kwargs...)
+    end
+end
+
 function issubset(A::TypedEndpointsInterval, B::TypedEndpointsInterval)
     Al, Ar = endpoints(A)
     Bl, Br = endpoints(B)

test/runtests.jl

@@ -150,6 +150,20 @@ struct IncompleteInterval <: AbstractInterval{Int} end
         @test isempty(ClosedInterval(B, A))
     end
 
+    @testset "isapprox" begin
+        @test 1..2 ≈ 1..2
+        @test 1..2 ≈ (1+1e-10)..2
+        @test 1..2 ≉ 1..2.01
+        @test 10..11 ≈ 10.1..10.9  rtol=0.01
+        @test 10..11 ≈ 10.1..10.9  atol=0.1
+        @test 10..11 ≉ 10.1..10.9  rtol=0.005
+        @test 10..11 ≉ 10.1..10.9  atol=0.05
+        @test 0..1 ≈ eps()..1
+        @test 100.0..100.0 ≉ nextfloat(100.0)..100.0
+        @test 3..1 ≈ 5..1
+        @test_throws Exception OpenInterval(0, 1) ≈ ClosedInterval(0, 1)
+    end
+
     @testset "Convert" begin
         I = 0..3
         @test @inferred(convert(ClosedInterval{Float64}, I))         ===