Improve middle(::AbstractRange) performance (#116)

* Restrict `middle(::AbstractRange)` eltype and improve performance

* Revert eltype restriction

* Apply suggestions from code review

Co-authored-by: Milan Bouchet-Valat <nalimilan@club.fr>

* Fix typo: `r` -> `a`

* Update test/runtests.jl

Co-authored-by: Milan Bouchet-Valat <nalimilan@club.fr>

* Fix CI failure

* Add `middle(0:typemax(Int))` test

Co-authored-by: Milan Bouchet-Valat <nalimilan@club.fr>

src/Statistics.jl

@@ -765,28 +765,16 @@ equivalent in both value and type to computing their mean (`(x + y) / 2`).
 middle(x::Number, y::Number) = x/2 + y/2
 
 """
-    middle(range)
+    middle(a::AbstractArray)
 
-Compute the middle of a range, which consists of computing the mean of its extrema.
-Since a range is sorted, the mean is performed with the first and last element.
+Compute the middle of an array `a`, which consists of finding its
+extrema and then computing their mean.
 
 ```jldoctest
 julia> using Statistics
 
 julia> middle(1:10)
 5.5
-```
-"""
-middle(a::AbstractRange) = middle(a[1], a[end])
-
-"""
-    middle(a)
-
-Compute the middle of an array `a`, which consists of finding its
-extrema and then computing their mean.
-
-```jldoctest
-julia> using Statistics
 
 julia> a = [1,2,3.6,10.9]
 4-element Vector{Float64}:
@@ -801,6 +789,11 @@ julia> middle(a)
 """
 middle(a::AbstractArray) = ((v1, v2) = extrema(a); middle(v1, v2))
 
+function middle(a::AbstractRange)
+    isempty(a) && throw(ArgumentError("middle of an empty range is undefined."))
+    return middle(first(a), last(a))
+end
+
 """
     median!(v)
 
@@ -997,9 +990,9 @@ end
     require_one_based_indexing(v)
 
     n = length(v)
-    
+
     @assert n > 0 # this case should never happen here
-    
+
     m = alpha + p * (one(alpha) - alpha - beta)
     aleph = n*p + oftype(p, m)
     j = clamp(trunc(Int, aleph), 1, n-1)
@@ -1012,7 +1005,7 @@ end
         a = v[j]
         b = v[j + 1]
     end
-    
+
     if isfinite(a) && isfinite(b)
         return a + γ*(b-a)
     else

test/runtests.jl

@@ -21,6 +21,15 @@ Random.seed!(123)
     for T in [Bool,Int8,Int16,Int32,Int64,Int128,UInt8,UInt16,UInt32,UInt64,UInt128,Float16,Float32,Float64]
         @test middle(one(T)) === middle(one(T), one(T))
     end
+
+    if VERSION < v"1.8.0-DEV.1343"
+        @test_throws ArgumentError middle(Int[])
+    else
+        @test_throws MethodError middle(Int[])
+    end
+    @test_throws ArgumentError middle(1:0)
+
+    @test middle(0:typemax(Int)) === typemax(Int) / 2
 end
 
 @testset "median" begin
@@ -547,16 +556,16 @@ end
         @test cor(tmp, tmp) <= 1.0
         @test cor(tmp, tmp2) <= 1.0
     end
-    
+
     @test cor(Int[]) === 1.0
     @test cor([im]) === 1.0 + 0.0im
     @test_throws MethodError cor([])
     @test_throws MethodError cor(Any[1.0])
-    
+
     @test cor([1, missing]) === 1.0
     @test ismissing(cor([missing]))
     @test_throws MethodError cor(Any[1.0, missing])
-    
+
     @test Statistics.corm([true], 1.0) === 1.0
     @test_throws MethodError Statistics.corm(Any[0.0, 1.0], 0.5)
     @test Statistics.corzm([true]) === 1.0
@@ -958,4 +967,4 @@ end
     @test isequal(cor(mx, Int[]), fill(NaN, 2, 1))
     @test isequal(cov(Int[], my), fill(-0.0, 1, 3))
     @test isequal(cor(Int[], my), fill(NaN, 1, 3))
-end
+end