fix implicit conversion of range to array

src/Statistics.jl

@@ -207,13 +207,18 @@ end
 # faster computation of real(conj(x)*y)
 realXcY(x::Real, y::Real) = x*y
 realXcY(x::Complex, y::Complex) = real(x)*real(y) + imag(x)*imag(y)
+realXcY(x::Number, y::Number) = real(conj(x) * y)
 
 var(iterable; corrected::Bool=true, mean=nothing) = _var(iterable, corrected, mean)
 
 function _var(iterable, corrected::Bool, mean)
     y = iterate(iterable)
     if y === nothing
         T = eltype(iterable)
+        # When `zero` cannot be called we throw an error
+        if T === Union{} || !(T <: Number)
+            throw(ArgumentError("cannot compute variance of an empty iterator with eltype $T"))
+        end
         return oftype((abs2(zero(T)) + abs2(zero(T)))/2, NaN)
     end
     count = 1
@@ -398,29 +403,25 @@ varm(iterable, m; corrected::Bool=true) = _var(iterable, corrected, m)
 
 ## variances over ranges
 
-varm(v::AbstractRange, m::AbstractArray) = range_varm(v, m)
-varm(v::AbstractRange, m) = range_varm(v, m)
+function varm(v::AbstractRange, m; corrected::Bool=true)
+    l = length(v)
+    l <= 1 && return _var(v, corrected, m)
+    vv = if m === nothing
+        s = step(v)
+        abs2(s) * (l + 1) * l / 12
+     else
+         range_varm(v, m)
+     end
+    return corrected ? vv : vv * (l - 1) / l
+end
 
 function range_varm(v::AbstractRange, m)
     f  = first(v) - m
     s  = step(v)
     l  = length(v)
-    vv = f^2 * l / (l - 1) + f * s * l + s^2 * l * (2 * l - 1) / 6
-    if l == 0 || l == 1
-        return typeof(vv)(NaN)
-    end
-    return vv
+    return abs2(f) * l / (l - 1) + realXcY(f, s) * l + abs2(s) * l * (2 * l - 1) / 6
 end
 
-function var(v::AbstractRange)
-    s  = step(v)
-    l  = length(v)
-    vv = abs2(s) * (l + 1) * l / 12
-    if l == 0 || l == 1
-        return typeof(vv)(NaN)
-    end
-    return vv
-end
 
 
 ##### standard deviation #####

test/runtests.jl

@@ -245,10 +245,10 @@ end
 @testset "var & std" begin
     # edge case: empty vector
     # iterable; this has to throw for type stability
-    @test_throws Exception var(())
-    @test_throws Exception var((); corrected=false)
-    @test_throws Exception var((); mean=2)
-    @test_throws Exception var((); mean=2, corrected=false)
+    @test_throws ArgumentError var(())
+    @test_throws ArgumentError var((); corrected=false)
+    @test_throws ArgumentError var((); mean=2)
+    @test_throws ArgumentError var((); mean=2, corrected=false)
     # reduction
     @test isnan(var(Int[]))
     @test isnan(var(Int[]; corrected=false))
@@ -278,10 +278,29 @@ end
     @test var([1], dims=1; mean=[2], corrected=false) ≈ [1.0]
 
     @test var(1:8) == 6.
-    @test varm(1:8,1) == varm(Vector(1:8),1)
+    @test varm(1:8, 1) == varm(Vector(1:8), 1)
+    @test var(1:8; mean=1) == var(Vector(1:8); mean=1)
+    @test var(1:8; corrected=false) == var(Vector(1:8); corrected=false)
+    @test varm(1:8, 1; corrected=false) == varm(Vector(1:8), 1; corrected=false)
+    @test var(1:8; mean=1, corrected=false) == var(Vector(1:8); mean=1, corrected=false)
     @test isnan(varm(1:1,1))
     @test isnan(var(1:1))
+    @test isnan(var(1:1; mean=1))
+    @test !isnan(var(1:1; corrected=false))
+    @test isnan(var(1:0; corrected=false))
+    @test !isnan(varm(1:1, 1; corrected=false))
+    @test isnan(varm(1:0, 1; corrected=false))
     @test isnan(var(1:-1))
+    @test isnan(varm(1:-1,1))
+    @test isnan(var(1:-1; mean=1))
+    @test isnan(var(1:-1; corrected=false))
+    @test isnan(varm(1:-1, 1; corrected=false))
+
+    let r = LinRange(1 + 2im, 3 + 4im, 11), m = mean(r)
+        @test (@inferred var(r))::Float64 ≈ var(r; mean=m)
+        @test (@inferred var(r; mean=m))::Float64 ≈ var(r)
+        @test (@inferred varm(r, m))::Float64 ≈ varm(collect(r), m)
+    end
 
     @test @inferred(var(1.0:8.0)) == 6.
     @test varm(1.0:8.0,1.0) == varm(Vector(1.0:8.0),1)
@@ -922,6 +941,14 @@ Statistics.middle(x::Furlong{p}, y::Furlong{p}) where {p} = Furlong{p}(middle(x.
     @test var(r) == var(a) == Furlong{2}(0.5)
     @test std(r) == std(a) == Furlong{1}(sqrt(0.5))
 
+    @test var(r; corrected=false) == var(a; corrected=false)
+
+    m = Furlong(100)
+    @test var(r; mean=m) == var(a; mean=m)
+    @test var(r; mean=m, corrected=false) == var(a; mean=m, corrected=false)
+    @test std(r; mean=m) == std(a; mean=m)
+    @test std(r; mean=m, corrected=false) == std(a; mean=m, corrected=false)
+
     # Issue #21786
     A = [Furlong{1}(rand(-5:5)) for i in 1:2, j in 1:2]
     @test mean(mean(A, dims=1), dims=2)[1] === mean(A)