Fix reduction over empty array (#780)

Author: tkf

src/mapreduce.jl

@@ -113,6 +113,17 @@ end
 @inline _mapreduce(args::Vararg{Any,N}) where N = _mapfoldl(args...)
 
 @generated function _mapfoldl(f, op, dims::Colon, init, ::Size{S}, a::StaticArray...) where {S}
+    if prod(S) == 0
+        if init === _InitialValue
+            if length(a) == 1
+                return :(Base.mapreduce_empty(f, op, $(eltype(a[1]))))
+            else
+                return :(throw(ArgumentError("reducing over an empty collection is not allowed")))
+            end
+        else
+            return :init
+        end
+    end
     tmp = [:(a[$j][1]) for j ∈ 1:length(a)]
     expr = :(f($(tmp...)))
     if init === _InitialValue

test/mapreduce.jl

@@ -58,6 +58,44 @@ using Statistics: mean
         @test mapfoldl(-, +, sv1; init=0) === mapfoldl(-, +, v1, init=0)
     end
 
+    @testset "empty array" begin
+        # issue #778
+        @test iszero(SVector{0,Int}())
+
+        @testset "$fold" for fold in [reduce, foldl]
+            @test fold(+, SVector{0,Bool}()) === 0
+            @test fold(nothing, SVector{0,Int}(), init=:INIT) === :INIT
+        end
+
+        @testset "$mapfold" for mapfold in [mapreduce, mapfoldl]
+            @test mapfold(identity, +, SVector{0,Bool}()) === 0
+            @test mapfold(abs, +, SVector{0,Bool}()) === 0
+            @test mapfold(nothing, nothing, SVector{0,Int}(), init=:INIT) === :INIT
+        end
+
+        @test mapreduce(
+            (a, b) -> a + b,
+            (a, b) -> a * b,
+            SVector{0,Int}(),
+            SVector{0,Int}();
+            init = :INIT,
+        ) == :INIT
+
+        # When there are multiple inputs, the error is thrown by
+        # StaticArrays.jl:
+        @test_throws(
+            ArgumentError("reducing over an empty collection is not allowed"),
+            mapreduce((a, b) -> a + b, (a, b) -> a * b, SVector{0,Int}(), SVector{0,Int}())
+        )
+
+        # When the mapping and/or reducing functions are unsupported,
+        # the error is thrown by `Base.mapreduce_empty`:
+        @test_throws(
+            ArgumentError("reducing over an empty collection is not allowed"),
+            mapreduce(nothing, nothing, SVector{0,Int}())
+        )
+    end
+
     @testset "implemented by [map]reduce and [map]reducedim" begin
         I, J, K = 2, 2, 2
         OSArray = SArray{Tuple{I,J,K}}  # original