Add n-ary intersection (#257)

* Add n-ary intersection

* add more tests

Author: mforets

src/intervals/set_operations.jl

@@ -88,6 +88,23 @@ end
 intersect(a::Interval{Complex{T}}, b::Interval{Complex{S}}) where {T,S} =
     intersect(promote(a, b)...)
 
+"""
+    intersect(a::Interval{T}...) where T
+
+Returns the n-ary intersection of its arguments.
+
+This function is applicable to any number of input intervals, as in
+`intersect(a1, a2, a3, a4)` where `ai` is an interval.
+If your use case needs to splat the input, as in `intersect(a...)`, consider
+`reduce(intersect, a)` instead, because you save the cost of splatting.
+"""
+function intersect(a::Interval{T}...) where T
+    low = maximum(broadcast(ai -> ai.lo, a))
+    high = minimum(broadcast(ai -> ai.hi, a))
+
+    !is_valid_interval(low, high) && return emptyinterval(T)
+    return Interval(low, high)
+end
 
 ## Hull
 """

test/interval_tests/consistency.jl

@@ -146,6 +146,13 @@ setprecision(Interval, Float64)
 
         @test intersect(a, hull(a,b)) == a
         @test union(a,b) == Interval(a.lo, b.hi)
+
+        # n-ary intersection
+        @test intersect(Interval(1.0, 2.0),
+                        Interval(-1.0, 5.0),
+                        Interval(1.8, 3.0)) == Interval(1.8, 2.0)
+        @test intersect(a, emptyinterval(), b) == emptyinterval()
+        @test intersect(0..1, 3..4, 0..1, 0..1) == emptyinterval()
     end
 
     @testset "Hull and union tests" begin