Avoid an extra call to f in Statistic.mean(f, A)

src/Statistics.jl

@@ -165,16 +165,22 @@ mean(A::AbstractArray; dims=:) = _mean(identity, A, dims)
 
 _mean_promote(x::T, y::S) where {T,S} = convert(promote_type(T, S), y)
 
+# calls f(A[1]) twice
+_promoted_sum(f, A::AbstractArray; init, dims) = sum(x -> _mean_promote(init, f(x)), A; dims)
+ # calls f(A[1]) once
+_promoted_sum(f, A::AbstractVector; init, dims) =
+    sum(x -> _mean_promote(init, f(x)), @view A[begin+1:end]; init, dims)
+
 # ::Dims is there to force specializing on Colon (as it is a Function)
 function _mean(f, A::AbstractArray, dims::Dims=:) where Dims
-    isempty(A) && return sum(f, A, dims=dims)/0
+    isempty(A) && return sum(f, A; dims)/0
     if dims === (:)
         n = length(A)
     else
         n = mapreduce(i -> size(A, i), *, unique(dims); init=1)
     end
-    x1 = f(first(A)) / 1
-    result = sum(x -> _mean_promote(x1, f(x)), A, dims=dims)
+    init = f(first(A)) / 1
+    result = _promoted_sum(f, A; init, dims)
     if dims === (:)
         return result / n
     else
@@ -986,9 +992,9 @@ 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)
@@ -1001,7 +1007,7 @@ end
         a = v[j]
         b = v[j + 1]
     end
-    
+
     if isfinite(a) && isfinite(b)
         return a + γ*(b-a)
     else

test/runtests.jl

@@ -152,7 +152,7 @@ end
                ≈ float(typemax(Int)))
     end
     let x = rand(10000)  # mean should use sum's accurate pairwise algorithm
-        @test mean(x) == sum(x) / length(x)
+        @test mean(x) == sum((@view x[begin + 1:end]), init=x[1]) / length(x)
     end
     @test mean(Number[1, 1.5, 2+3im]) === 1.5+1im # mixed-type array
     @test mean(v for v in Number[1, 1.5, 2+3im]) === 1.5+1im
@@ -162,6 +162,15 @@ end
     @test (@inferred mean(Iterators.filter(x -> true, Int[]))) === 0/0
     @test (@inferred mean(Iterators.filter(x -> true, Float32[]))) === 0.f0/0
     @test (@inferred mean(Iterators.filter(x -> true, Float64[]))) === 0/0
+    # Check that mean does not call function argument an extra time
+    let _cnt = 0, N = 100, x = rand(Int, N)
+        f(x) = (_cnt += 1; x)
+        @test mean(1:N) == mean(f, 1:N)
+        @test _cnt == N
+        _cnt = 0
+        @test mean(x) == mean(f, x)
+        @test _cnt == N
+    end
 end
 
 @testset "mean/median for ranges" begin