Use reduce_first instead of reduce_empty

src/mapreduce.jl

@@ -299,21 +299,14 @@ _valof(::Val{D}) where D = D
  _accumulate(op, a, _maybe_val(dims), init)
 
 @inline function _accumulate(op::F, a::StaticArray, dims::Union{Val,Colon}, init) where {F}
+ # Adjoin the initial value to `op`:
+ rf(x, y) = x isa _InitialValue ? Base.reduce_first(op, y) : op(x, y)
+
  if isempty(a)
- if init isa _InitialValue
- # Deliberately not using `return_type` here, since this `eltype` is
- # exact for the singleton element case (i.e., `op` will not be called).
- return similar_type(a)()
- else
- # Using the type that _would_ be used if `size(a, dims) == 1`:
- T = return_type(op, Tuple{typeof(init), eltype(a)})
- return similar_type(a, T)()
- end
+ T = return_type(rf, Tuple{typeof(init), eltype(a)})
+ return similar_type(a, T)()
  end
 
- # Adjoin the initial value to `op`:
- rf(x, y) = x isa _InitialValue ? y : op(x, y)
-
  # StaticArrays' `reduce` is `foldl`:
  results = _reduce(
  a,
@@ -340,7 +333,5 @@ _valof(::Val{D}) where D = D
  return similar_type(a, eltype(data))(data)
 end
 
-@inline Base.cumsum(a::StaticArray; kw...) =
- accumulate(Base.add_sum, a; init = Base.reduce_empty(Base.add_sum, eltype(a)), kw...)
-@inline Base.cumprod(a::StaticArray; kw...) =
- accumulate(Base.mul_prod, a; init = Base.reduce_empty(Base.mul_prod, eltype(a)), kw...)
+@inline Base.cumsum(a::StaticArray; kw...) = accumulate(Base.add_sum, a; kw...)
+@inline Base.cumprod(a::StaticArray; kw...) = accumulate(Base.mul_prod, a; kw...)