diff --git a/base/broadcast.jl b/base/broadcast.jl
index a4cec47b4dd6d..6af2a8a4276ef 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -282,32 +282,27 @@ 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}
 
-# nullables need to be treated like scalars sometimes and like containers
-# other times, so there are two variants of typestuple.
+# _broadcast_eltype is broadcast's primary result-eltype promotion mechanism.
+# _broadcast_eltype uses eltypestuple to construct a tuple type of the eltypes
+# of the input-array arguments passed to _broadcast_eltype (from an upstream broadcast).
+_broadcast_eltype{S}(::Type{S}, f, As...) = Base._return_type(f, eltypestuple(S, As...))
+_broadcast_eltype{S}(::Type{S}, f, T::Type, As...) = Base._return_type(f, eltypestuple(S, T, As...)) # 19419 workaround
+eltypestuple(::Type, a) = (Base.@_pure_meta; Tuple{eltype(a)})
+eltypestuple(::Type, T::Type) = (Base.@_pure_meta; Tuple{Type{T}})
+eltypestuple{S}(::Type{S}, a, b...) = (Base.@_pure_meta; Tuple{eltypestuple(S, a).types..., eltypestuple(S, b...).types...})
+# nullables need special handling: in some cases they behave like scalars, and in others
+# like containers. _broadcast_eltype and eltypestuple presently handles this via its first
+# (type) argument, through which callers provide the context in which the nullable
+# input-argument appears (and hence how it should be treated). specifically, if the
+# first argument is Any, then nullables are treated as scalars, whereas otherwise
+# (i.e. if the first argument is not Any), then nullables are treated as containers.
+eltypestuple(::Type{Any}, a::Nullable) = (Base.@_pure_meta; Tuple{typeof(a)})
 
-# if the first argument is Any, then Nullable should be treated like a
-# scalar; if the first argument is Array, then Nullable should be treated
-# like a container.
-typestuple(::Type, a) = (Base.@_pure_meta; Tuple{eltype(a)})
-typestuple(::Type{Any}, a::Nullable) = (Base.@_pure_meta; Tuple{typeof(a)})
-typestuple(::Type, T::Type) = (Base.@_pure_meta; Tuple{Type{T}})
-typestuple{T}(::Type{T}, a, b...) = (Base.@_pure_meta; Tuple{typestuple(T, a).types..., typestuple(T, b...).types...})
-
-# these functions take the variant of typestuple to be used as first argument
-ziptype{T}(::Type{T}, A) = typestuple(T, A)
-ziptype{T}(::Type{T}, A, B) = (Base.@_pure_meta; Iterators.Zip2{typestuple(T, A), typestuple(T, B)})
-@inline ziptype{T}(::Type{T}, A, B, C, D...) = Iterators.Zip{typestuple(T, A), ziptype(T, B, C, D...)}
-
-_broadcast_type{S}(::Type{S}, f, T::Type, As...) = Base._return_type(f, typestuple(S, T, As...))
-_broadcast_type{T}(::Type{T}, f, A, Bs...) = Base._default_eltype(Base.Generator{ziptype(T, A, Bs...), ftype(f, 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(Any, f, A, Bs...)
+    T = _broadcast_eltype(Any, f, A, Bs...)
     shape = broadcast_indices(A, Bs...)
     iter = CartesianRange(shape)
     if isleaftype(T)
@@ -332,7 +327,7 @@ function broadcast_c(f, ::Type{Tuple}, As...)
 end
 @inline function broadcast_c(f, ::Type{Nullable}, a...)
     nonnull = all(hasvalue, a)
-    S = _broadcast_type(Array, f, a...)
+    S = _broadcast_eltype(Array, 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 2887eec75291e..481203bff6c2b 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 = fofzeros == zero(fofzeros)
     maxnnzC = fpreszeros ? min(length(A), _sumnnzs(A, Bs...)) : length(A)
-    entrytypeC = Base.Broadcast._broadcast_type(Any, f, A, Bs...)
+    entrytypeC = Base.Broadcast._broadcast_eltype(Any, 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 = fofzeros == zero(fofzeros)
     indextypeC = _promote_indtype(A, Bs...)
-    entrytypeC = Base.Broadcast._broadcast_type(Any, f, A, Bs...)
+    entrytypeC = Base.Broadcast._broadcast_eltype(Any, 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 d92b3991e4760..a50d98b1ee906 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(Any, x -> x + a, 1.0))
+    g() = (a = 1; Base.Broadcast._broadcast_eltype(Any, x -> x + a, 1.0))
     @test @inferred(g()) === Float64
 end
 
@@ -409,3 +409,9 @@ Base.Broadcast.broadcast_c(f, ::Type{Array19745}, A, Bs...) =
     @test isa(aa .+ 1, Array19745)
     @test isa(aa .* aa', Array19745)
 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(Any, (x, y) -> x + y + a, 1.0, 1.0))
+    @test @inferred(f()) == Float64
+end