diff --git a/base/broadcast.jl b/base/broadcast.jl
index cb470a70f6e4f..1d2c3bacb02e7 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -272,24 +272,14 @@ end
 @inline broadcast_elwise_op(f, As...) =
     broadcast!(f, similar(Array{promote_eltype_op(f, As...)}, broadcast_indices(As...)), As...)
 
-ftype(f, A) = typeof(f)
-ftype(f, A...) = typeof(a -> f(a...))
-ftype(T::Type, A...) = Type{T}
-
-typestuple(a) = (Base.@_pure_meta; Tuple{eltype(a)})
-typestuple(T::Type) = (Base.@_pure_meta; Tuple{Type{T}})
-typestuple(a, b...) = (Base.@_pure_meta; Tuple{typestuple(a).types..., typestuple(b...).types...})
-
-ziptype(A) = typestuple(A)
-ziptype(A, B) = (Base.@_pure_meta; Iterators.Zip2{typestuple(A), typestuple(B)})
-@inline ziptype(A, B, C, D...) = Iterators.Zip{typestuple(A), ziptype(B, C, D...)}
-
-_broadcast_type(f, T::Type, As...) = Base._return_type(f, typestuple(T, As...))
-_broadcast_type(f, A, Bs...) = Base._default_eltype(Base.Generator{ziptype(A, Bs...), ftype(f, A, Bs...)})
+eltypestuple(a) = (Base.@_pure_meta; Tuple{eltype(a)})
+eltypestuple(T::Type) = (Base.@_pure_meta; Tuple{Type{T}})
+eltypestuple(a, b...) = (Base.@_pure_meta; Tuple{eltypestuple(a).types..., eltypestuple(b...).types...})
+_broadcast_eltype(f, A, Bs...) = Base._return_type(f, eltypestuple(A, Bs...))
 
 # broadcast methods that dispatch on the type of the final container
 @inline function broadcast_c(f, ::Type{Array}, A, Bs...)
-    T = _broadcast_type(f, A, Bs...)
+    T = _broadcast_eltype(f, A, Bs...)
     shape = broadcast_indices(A, Bs...)
     iter = CartesianRange(shape)
     if isleaftype(T)
@@ -307,7 +297,7 @@ function broadcast_c(f, ::Type{Tuple}, As...)
 end
 @inline function broadcast_c(f, ::Type{Nullable}, a...)
     nonnull = all(hasvalue, a)
-    S = _broadcast_type(f, a...)
+    S = _broadcast_eltype(f, a...)
     if isleaftype(S) && null_safe_eltype_op(f, a...)
         Nullable{S}(f(map(unsafe_get, a)...), nonnull)
     else
diff --git a/base/promotion.jl b/base/promotion.jl
index 7edd37d309056..2d3ed42fa3bab 100644
--- a/base/promotion.jl
+++ b/base/promotion.jl
@@ -231,15 +231,13 @@ end
 promote_op(::Any...) = (@_pure_meta; Any)
 function promote_op{S}(f, ::Type{S})
     @_inline_meta
-    Z = Tuple{_default_type(S)}
-    T = _default_eltype(Generator{Z, typeof(f)})
+    T = _return_type(f, Tuple{_default_type(S)})
     isleaftype(S) && return isleaftype(T) ? T : Any
     return typejoin(S, T)
 end
 function promote_op{R,S}(f, ::Type{R}, ::Type{S})
     @_inline_meta
-    Z = Iterators.Zip2{Tuple{_default_type(R)}, Tuple{_default_type(S)}}
-    T = _default_eltype(Generator{Z, typeof(a -> f(a...))})
+    T = _return_type(f, Tuple{_default_type(R), _default_type(S)})
     isleaftype(R) && isleaftype(S) && return isleaftype(T) ? T : Any
     return typejoin(R, S, T)
 end
diff --git a/base/sparse/higherorderfns.jl b/base/sparse/higherorderfns.jl
index df4290345a0f8..8bae5a82c4043 100644
--- a/base/sparse/higherorderfns.jl
+++ b/base/sparse/higherorderfns.jl
@@ -73,7 +73,7 @@ function _noshapecheck_map{Tf,N}(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseVecO
     fofzeros = f(_zeros_eltypes(A, Bs...)...)
     fpreszeros = _iszero(fofzeros)
     maxnnzC = fpreszeros ? min(length(A), _sumnnzs(A, Bs...)) : length(A)
-    entrytypeC = Base.Broadcast._broadcast_type(f, A, Bs...)
+    entrytypeC = Base.Broadcast._broadcast_eltype(f, A, Bs...)
     indextypeC = _promote_indtype(A, Bs...)
     C = _allocres(size(A), indextypeC, entrytypeC, maxnnzC)
     return fpreszeros ? _map_zeropres!(f, C, A, Bs...) :
@@ -101,7 +101,7 @@ function _diffshape_broadcast{Tf,N}(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseV
     fofzeros = f(_zeros_eltypes(A, Bs...)...)
     fpreszeros = _iszero(fofzeros)
     indextypeC = _promote_indtype(A, Bs...)
-    entrytypeC = Base.Broadcast._broadcast_type(f, A, Bs...)
+    entrytypeC = Base.Broadcast._broadcast_eltype(f, A, Bs...)
     shapeC = to_shape(Base.Broadcast.broadcast_indices(A, Bs...))
     maxnnzC = fpreszeros ? _checked_maxnnzbcres(shapeC, A, Bs...) : _densennz(shapeC)
     C = _allocres(shapeC, indextypeC, entrytypeC, maxnnzC)
diff --git a/test/broadcast.jl b/test/broadcast.jl
index ea3152a68c685..95c5a5e69b76d 100644
--- a/test/broadcast.jl
+++ b/test/broadcast.jl
@@ -363,7 +363,7 @@ StrangeType18623(x,y) = (x,y)
 let
     f(A, n) = broadcast(x -> +(x, n), A)
     @test @inferred(f([1.0], 1)) == [2.0]
-    g() = (a = 1; Base.Broadcast._broadcast_type(x -> x + a, 1.0))
+    g() = (a = 1; Base.Broadcast._broadcast_eltype(x -> x + a, 1.0))
     @test @inferred(g()) === Float64
 end
 
@@ -418,3 +418,9 @@ let io = IOBuffer()
     broadcast(x -> print(io, x), [Nullable(1.0)])
     @test String(take!(io)) == "Nullable{Float64}(1.0)"
 end
+
+# Test that broadcast's promotion mechanism handles closures accepting more than one argument.
+# (See issue #19641 and referenced issues and pull requests.)
+let f() = (a = 1; Base.Broadcast._broadcast_eltype((x, y) -> x + y + a, 1.0, 1.0))
+    @test @inferred(f()) == Float64
+end