diff --git a/base/accumulate.jl b/base/accumulate.jl
index 20363362f73c7..afe11dd97913b 100644
--- a/base/accumulate.jl
+++ b/base/accumulate.jl
@@ -416,15 +416,33 @@ function _accumulate_pairwise_small!(op, dest::AbstractArray{T}, itr, accv, w, i
     end
 end
 
+"""
+    Base.ConvertOp{T}(op)(x,y)
+
+An operator which converts `x` and `y` to type `T` before performing the `op`.
+
+The main purpose is for use in [`cumsum!`](@ref) and [`cumprod!`](@ref), where `T` is determined by the output array.
+"""
+struct ConvertOp{T,O} <: Function
+    op::O
+end
+ConvertOp{T}(op::O) where {T,O} = ConvertOp{T,O}(op)
+(c::ConvertOp{T})(x,y) where {T} = c.op(convert(T,x),convert(T,y))
+reduce_first(c::ConvertOp{T},x) where {T} = reduce_first(c.op, convert(T,x))
+
+
 
 
-function cumsum!(out, v::AbstractVector{T}) where T
+function cumsum!(out::AbstractVector, v::AbstractVector{T}) where T
     # we dispatch on the possibility of numerical accuracy issues
     cumsum!(out, v, ArithmeticStyle(T))
 end
-cumsum!(out, v::AbstractVector, ::ArithmeticRounds)  = accumulate_pairwise!(+, out, v)
-cumsum!(out, v::AbstractVector, ::ArithmeticUnknown) = accumulate_pairwise!(+, out, v)
-cumsum!(out, v::AbstractVector, ::ArithmeticStyle)   = accumulate!(+, out, v)
+cumsum!(out::AbstractVector{T}, v::AbstractVector, ::ArithmeticRounds) where {T} =
+    accumulate_pairwise!(ConvertOp{T}(+), out, v)
+cumsum!(out::AbstractVector{T}, v::AbstractVector, ::ArithmeticUnknown) where {T} =
+    accumulate_pairwise!(ConvertOp{T}(+), out, v)
+cumsum!(out::AbstractVector{T}, v::AbstractVector, ::ArithmeticStyle) where {T} =
+    accumulate!(ConvertOp{T}(+), out, v)
 
 """
     cumsum(A, dim::Integer)
@@ -488,14 +506,14 @@ cumsum(v::AbstractVector, ::ArithmeticStyle)   = accumulate(add_sum, v)
 
 Cumulative sum of `A` along the dimension `dim`, storing the result in `B`. See also [`cumsum`](@ref).
 """
-cumsum!(dest, A, dim::Integer) = accumulate!(+, dest, A, dim)
+cumsum!(dest::AbstractArray{T}, A, dim::Integer) where {T} = accumulate!(ConvertOp{T}(+), dest, A, dim)
 
 """
     cumsum!(y::AbstractVector, x::AbstractVector)
 
 Cumulative sum of a vector `x`, storing the result in `y`. See also [`cumsum`](@ref).
 """
-cumsum!(dest, itr) = accumulate!(+, dest, src)
+cumsum!(dest::AbstractArray{T}, itr) where {T} = accumulate!(ConvertOp{T}(+), dest, src)
 
 """
     cumprod(A, dim::Integer)
@@ -555,7 +573,7 @@ cumprod(x::AbstractVector) = accumulate(mul_prod, x)
 Cumulative product of `A` along the dimension `dim`, storing the result in `B`.
 See also [`cumprod`](@ref).
 """
-cumprod!(dest, A, dim::Integer) = accumulate!(*, dest, A, dim)
+cumprod!(dest::AbstractArray{T}, A, dim::Integer) where {T} = accumulate!(ConvertOp{T}(*), dest, A, dim)
 
 """
     cumprod!(y::AbstractVector, x::AbstractVector)
@@ -563,4 +581,4 @@ cumprod!(dest, A, dim::Integer) = accumulate!(*, dest, A, dim)
 Cumulative product of a vector `x`, storing the result in `y`.
 See also [`cumprod`](@ref).
 """
-cumprod!(dest, itr) = accumulate!(*, dest, itr)
+cumprod!(dest::AbstractArray{T}, itr) where {T} = accumulate!(ConvertOp{T}(*), dest, itr)
diff --git a/base/reduce.jl b/base/reduce.jl
index cb5b8fdf870d6..77e515af5c295 100644
--- a/base/reduce.jl
+++ b/base/reduce.jl
@@ -28,6 +28,7 @@ add_sum(x::SmallSigned) = Int(x)
 add_sum(x::SmallUnsigned) = UInt(x)
 add_sum(X::AbstractArray) = broadcast(add_sum, X)
 
+
 """
     Base.mul_prod(x,y)