diff --git a/base/abstractarray.jl b/base/abstractarray.jl
index 9f7c01eec9fe2..eacf18ee5d287 100644
--- a/base/abstractarray.jl
+++ b/base/abstractarray.jl
@@ -1762,12 +1762,8 @@ end
 # These are needed because map(eltype, As) is not inferrable
 promote_eltype_op(::Any) = (@_pure_meta; Any)
 promote_eltype_op(op, A) = (@_pure_meta; promote_op(op, eltype(A)))
-promote_eltype_op{T}(op, ::AbstractArray{T}) = (@_pure_meta; promote_op(op, T))
-promote_eltype_op{T}(op, ::AbstractArray{T}, A) = (@_pure_meta; promote_op(op, T, eltype(A)))
-promote_eltype_op{T}(op, A, ::AbstractArray{T}) = (@_pure_meta; promote_op(op, eltype(A), T))
-promote_eltype_op{R,S}(op, ::AbstractArray{R}, ::AbstractArray{S}) = (@_pure_meta; promote_op(op, R, S))
 promote_eltype_op(op, A, B) = (@_pure_meta; promote_op(op, eltype(A), eltype(B)))
-promote_eltype_op(op, A, B, C, D...) = (@_pure_meta; promote_eltype_op(op, promote_eltype_op(op, A, B), C, D...))
+promote_eltype_op(op, A, B, C, D...) = (@_pure_meta; promote_eltype_op(op, eltype(A), promote_eltype_op(op, B, C, D...)))
 
 ## 1 argument
 
diff --git a/base/broadcast.jl b/base/broadcast.jl
index 5d49fc5f65908..fed4d06071336 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -3,7 +3,7 @@
 module Broadcast
 
 using Base.Cartesian
-using Base: promote_eltype_op, linearindices, tail, OneTo, to_shape,
+using Base: promote_eltype_op, _default_eltype, linearindices, tail, OneTo, to_shape,
             _msk_end, unsafe_bitgetindex, bitcache_chunks, bitcache_size, dumpbitcache
 import Base: .+, .-, .*, ./, .\, .//, .==, .<, .!=, .<=, .÷, .%, .<<, .>>, .^
 import Base: broadcast
@@ -16,7 +16,7 @@ export broadcast_getindex, broadcast_setindex!
 broadcast(f) = f()
 @inline broadcast(f, x::Number...) = f(x...)
 @inline broadcast{N}(f, t::NTuple{N}, ts::Vararg{NTuple{N}}) = map(f, t, ts...)
-@inline broadcast(f, As::AbstractArray...) = broadcast_t(f, promote_eltype_op(f, As...), As...)
+@inline broadcast(f, As::AbstractArray...) = broadcast_c(f, Array, As...)
 
 # special cases for "X .= ..." (broadcast!) assignments
 broadcast!(::typeof(identity), X::AbstractArray, x::Number) = fill!(X, x)
@@ -127,14 +127,14 @@ Base.@propagate_inbounds _broadcast_getindex(::Any, A, I) = A[I]
 ## Broadcasting core
 # nargs encodes the number of As arguments (which matches the number
 # of keeps). The first two type parameters are to ensure specialization.
-@generated function _broadcast!{K,ID,AT,nargs}(f, B::AbstractArray, keeps::K, Idefaults::ID, As::AT, ::Type{Val{nargs}})
+@generated function _broadcast!{K,ID,AT,nargs}(f, B::AbstractArray, keeps::K, Idefaults::ID, As::AT, ::Type{Val{nargs}}, iter)
     quote
         $(Expr(:meta, :noinline))
         # destructure the keeps and As tuples
         @nexprs $nargs i->(A_i = As[i])
         @nexprs $nargs i->(keep_i = keeps[i])
         @nexprs $nargs i->(Idefault_i = Idefaults[i])
-        @simd for I in CartesianRange(indices(B))
+        @simd for I in iter
             # reverse-broadcast the indices
             @nexprs $nargs i->(I_i = newindex(I, keep_i, Idefault_i))
             # extract array values
@@ -148,7 +148,7 @@ end
 
 # For BitArray outputs, we cache the result in a "small" Vector{Bool},
 # and then copy in chunks into the output
-@generated function _broadcast!{K,ID,AT,nargs}(f, B::BitArray, keeps::K, Idefaults::ID, As::AT, ::Type{Val{nargs}})
+@generated function _broadcast!{K,ID,AT,nargs}(f, B::BitArray, keeps::K, Idefaults::ID, As::AT, ::Type{Val{nargs}}, iter)
     quote
         $(Expr(:meta, :noinline))
         # destructure the keeps and As tuples
@@ -159,7 +159,7 @@ end
         Bc = B.chunks
         ind = 1
         cind = 1
-        @simd for I in CartesianRange(indices(B))
+        @simd for I in iter
             # reverse-broadcast the indices
             @nexprs $nargs i->(I_i = newindex(I, keep_i, Idefault_i))
             # extract array values
@@ -193,12 +193,12 @@ as in `broadcast!(f, A, A, B)` to perform `A[:] = broadcast(f, A, B)`.
     shape = indices(B)
     check_broadcast_indices(shape, As...)
     keeps, Idefaults = map_newindexer(shape, As)
-    _broadcast!(f, B, keeps, Idefaults, As, Val{nargs})
-    B
+    iter = CartesianRange(shape)
+    _broadcast!(f, B, keeps, Idefaults, As, Val{nargs}, iter)
+    return B
 end
 
 # broadcast with computed element type
-
 @generated function _broadcast!{K,ID,AT,nargs}(f, B::AbstractArray, keeps::K, Idefaults::ID, As::AT, ::Type{Val{nargs}}, iter, st, count)
     quote
         $(Expr(:meta, :noinline))
@@ -233,12 +233,8 @@ end
     end
 end
 
-function broadcast_t(f, ::Type{Any}, As...)
-    shape = broadcast_indices(As...)
-    iter = CartesianRange(shape)
-    if isempty(iter)
-        return similar(Array{Any}, shape)
-    end
+# broadcast methods that dispatch on the type found by inference
+function broadcast_t(f, ::Type{Any}, shape, iter, As...)
     nargs = length(As)
     keeps, Idefaults = map_newindexer(shape, As)
     st = start(iter)
@@ -248,17 +244,46 @@ function broadcast_t(f, ::Type{Any}, As...)
     B[I] = val
     return _broadcast!(f, B, keeps, Idefaults, As, Val{nargs}, iter, st, 1)
 end
+@inline function broadcast_t(f, T, shape, iter, As...)
+    B = similar(Array{T}, shape)
+    nargs = length(As)
+    keeps, Idefaults = map_newindexer(shape, As)
+    _broadcast!(f, B, keeps, Idefaults, As, Val{nargs}, iter)
+    return B
+end
 
-@inline broadcast_t(f, T, As...) = broadcast!(f, similar(Array{T}, broadcast_indices(As...)), As...)
-
+# broadcast method that uses inference to find the type, but preserves abstract
+# container types when possible (used by binary elementwise operators)
+@inline broadcast_elwise_op(f, As...) =
+    broadcast!(f, similar(Array{promote_eltype_op(f, As...)}, broadcast_indices(As...)), As...)
+
+ftype(f, A) = typeof(a -> f(a))
+ftype(f, A...) = typeof(a -> f(a...))
+ftype(T::DataType, A) = Type{T}
+ftype(T::DataType, A...) = Type{T}
+ziptype(A) = Tuple{eltype(A)}
+ziptype(A, B) = Iterators.Zip2{Tuple{eltype(A)}, Tuple{eltype(B)}}
+@inline ziptype(A, B, C, D...) = Iterators.Zip{Tuple{eltype(A)}, ziptype(B, C, D...)}
+
+# broadcast methods that dispatch on the type of the final container
+@inline function broadcast_c(f, ::Type{Array}, As...)
+    T = _default_eltype(Base.Generator{ziptype(As...), ftype(f, As...)})
+    shape = broadcast_indices(As...)
+    iter = CartesianRange(shape)
+    if isleaftype(T)
+        return broadcast_t(f, T, shape, iter, As...)
+    end
+    if isempty(iter)
+        return similar(Array{T}, shape)
+    end
+    return broadcast_t(f, Any, shape, iter, As...)
+end
 function broadcast_c(f, ::Type{Tuple}, As...)
     shape = broadcast_indices(As...)
-    check_broadcast_indices(shape, As...)
     n = length(shape[1])
     return ntuple(k->f((_broadcast_getindex(A, k) for A in As)...), n)
 end
 @inline broadcast_c(f, ::Type{Any}, a...) = f(a...)
-@inline broadcast_c(f, ::Type{Array}, As...) = broadcast_t(f, promote_eltype_op(f, As...), As...)
 
 """
     broadcast(f, As...)
@@ -441,10 +466,10 @@ end
 ## elementwise operators ##
 
 for op in (:÷, :%, :<<, :>>, :-, :/, :\, ://, :^)
-    @eval $(Symbol(:., op))(A::AbstractArray, B::AbstractArray) = broadcast($op, A, B)
+    @eval $(Symbol(:., op))(A::AbstractArray, B::AbstractArray) = broadcast_elwise_op($op, A, B)
 end
-.+(As::AbstractArray...) = broadcast(+, As...)
-.*(As::AbstractArray...) = broadcast(*, As...)
+.+(As::AbstractArray...) = broadcast_elwise_op(+, As...)
+.*(As::AbstractArray...) = broadcast_elwise_op(*, As...)
 
 # ## element-wise comparison operators returning BitArray ##
 
diff --git a/base/deprecated.jl b/base/deprecated.jl
index d5ca65f89b870..b54dd4339d77b 100644
--- a/base/deprecated.jl
+++ b/base/deprecated.jl
@@ -1034,6 +1034,17 @@ end))
 @deprecate_binding cycle     Iterators.cycle
 @deprecate_binding repeated  Iterators.repeated
 
+# promote_op method where the operator is also a type
+function promote_op(op::Type, Ts::Type...)
+    depwarn("promote_op(op::Type, ::Type...) is deprecated as it is no " *
+            "longer needed in Base. If you need its functionality, consider " *
+            "defining it locally.", :promote_op)
+    if isdefined(Core, :Inference)
+        return Core.Inference.return_type(op, Tuple{Ts...})
+    end
+    return op
+end
+
 # NOTE: Deprecation of Channel{T}() is implemented in channels.jl.
 # To be removed from there when 0.6 deprecations are removed.
 
diff --git a/base/nullable.jl b/base/nullable.jl
index 703713bfc52f0..3c00839a15152 100644
--- a/base/nullable.jl
+++ b/base/nullable.jl
@@ -54,6 +54,7 @@ convert(   ::Type{Nullable   }, ::Void) = Nullable{Union{}}()
 promote_rule{S,T}(::Type{Nullable{S}}, ::Type{T}) = Nullable{promote_type(S, T)}
 promote_rule{S,T}(::Type{Nullable{S}}, ::Type{Nullable{T}}) = Nullable{promote_type(S, T)}
 promote_op{S,T}(op::Any, ::Type{Nullable{S}}, ::Type{Nullable{T}}) = Nullable{promote_op(op, S, T)}
+promote_op{S,T}(op::Type, ::Type{Nullable{S}}, ::Type{Nullable{T}}) = Nullable{promote_op(op, S, T)}
 
 function show{T}(io::IO, x::Nullable{T})
     if get(io, :compact, false)
diff --git a/base/promotion.jl b/base/promotion.jl
index 37e0d6a1373ef..82c813064e344 100644
--- a/base/promotion.jl
+++ b/base/promotion.jl
@@ -217,34 +217,23 @@ max(x::Real, y::Real) = max(promote(x,y)...)
 min(x::Real, y::Real) = min(promote(x,y)...)
 minmax(x::Real, y::Real) = minmax(promote(x, y)...)
 
-# "Promotion" that takes a function into account. These are meant to be
-# used mainly by broadcast methods, so it is advised against overriding them
-if isdefined(Core, :Inference)
-    function _promote_op(op, T::ANY)
-        G = Tuple{Generator{Tuple{T},typeof(op)}}
-        return Core.Inference.return_type(first, G)
-    end
-    function _promote_op(op, R::ANY, S::ANY)
-        F = typeof(a -> op(a...))
-        G = Tuple{Generator{Iterators.Zip2{Tuple{R},Tuple{S}},F}}
-        return Core.Inference.return_type(first, G)
-    end
-else
-    _promote_op(::ANY...) = (@_pure_meta; Any)
-end
+# "Promotion" that takes a function into account and tries to preserve
+# non-concrete types. These are meant to be used mainly by elementwise
+# operations, so it is advised against overriding them
 _default_type(T::Type) = (@_pure_meta; T)
 
 promote_op(::Any...) = (@_pure_meta; Any)
-promote_op(T::Type, ::Any) = (@_pure_meta; T)
-promote_op(T::Type, ::Type) = (@_pure_meta; T) # To handle ambiguities
-# Promotion that tries to preserve non-concrete types
 function promote_op{S}(f, ::Type{S})
-    T = _promote_op(f, _default_type(S))
+    @_pure_meta
+    Z = Tuple{_default_type(S)}
+    T = _default_eltype(Generator{Z, typeof(a -> f(a))})
     isleaftype(S) && return isleaftype(T) ? T : Any
     return typejoin(S, T)
 end
 function promote_op{R,S}(f, ::Type{R}, ::Type{S})
-    T = _promote_op(f, _default_type(R), _default_type(S))
+    @_pure_meta
+    Z = Iterators.Zip2{Tuple{_default_type(R)}, Tuple{_default_type(S)}}
+    T = _default_eltype(Generator{Z, typeof(a -> f(a...))})
     isleaftype(R) && isleaftype(S) && return isleaftype(T) ? T : Any
     return typejoin(R, S, T)
 end
diff --git a/base/sparse/sparsematrix.jl b/base/sparse/sparsematrix.jl
index f7ddb3d70486d..f1bfb662f567f 100644
--- a/base/sparse/sparsematrix.jl
+++ b/base/sparse/sparsematrix.jl
@@ -1740,7 +1740,7 @@ broadcast{Tv1,Ti1,Tv2,Ti2}(f::Function, A_1::SparseMatrixCSC{Tv1,Ti1}, A_2::Spar
                  broadcast!(f, spzeros(promote_type(Tv1, Tv2), promote_type(Ti1, Ti2), to_shape(broadcast_indices(A_1, A_2))), A_1, A_2)
 
 @inline broadcast_zpreserving!(args...) = broadcast!(args...)
-@inline broadcast_zpreserving(args...) = broadcast(args...)
+@inline broadcast_zpreserving(args...) = Base.Broadcast.broadcast_elwise_op(args...)
 broadcast_zpreserving{Tv1,Ti1,Tv2,Ti2}(f::Function, A_1::SparseMatrixCSC{Tv1,Ti1}, A_2::SparseMatrixCSC{Tv2,Ti2}) =
                  broadcast_zpreserving!(f, spzeros(promote_type(Tv1, Tv2), promote_type(Ti1, Ti2), to_shape(broadcast_indices(A_1, A_2))), A_1, A_2)
 broadcast_zpreserving{Tv,Ti}(f::Function, A_1::SparseMatrixCSC{Tv,Ti}, A_2::Union{Array,BitArray,Number}) =
diff --git a/test/broadcast.jl b/test/broadcast.jl
index 7dca2095bff7e..9e1db315d8683 100644
--- a/test/broadcast.jl
+++ b/test/broadcast.jl
@@ -300,7 +300,6 @@ import Base.Meta: isexpr
 # PR 16988
 @test Base.promote_op(+, Bool) === Int
 @test isa(broadcast(+, [true]), Array{Int,1})
-@test Base.promote_op(Float64, Bool) === Float64
 
 # issue #17304
 let foo = [[1,2,3],[4,5,6],[7,8,9]]
@@ -312,7 +311,7 @@ end
 let f17314 = x -> x < 0 ? false : x
     @test eltype(broadcast(f17314, 1:3)) === Int
     @test eltype(broadcast(f17314, -1:1)) === Integer
-    @test eltype(broadcast(f17314, Int[])) === Any
+    @test eltype(broadcast(f17314, Int[])) === Union{Bool,Int}
 end
 let io = IOBuffer()
     broadcast(x->print(io,x), 1:5) # broadcast with side effects
@@ -337,3 +336,19 @@ end
 @test broadcast(+, 1.0, (0, -2.0)) == (1.0,-1.0)
 @test broadcast(+, 1.0, (0, -2.0), [1]) == [2.0, 0.0]
 @test broadcast(*, ["Hello"], ", ", ["World"], "!") == ["Hello, World!"]
+
+# Ensure that even strange constructors that break `T(x)::T` work with broadcast
+immutable StrangeType18623 end
+StrangeType18623(x) = x
+StrangeType18623(x,y) = (x,y)
+@test @inferred broadcast(StrangeType18623, 1:3) == [1,2,3]
+@test @inferred broadcast(StrangeType18623, 1:3, 4:6) == [(1,4),(2,5),(3,6)]
+
+@test typeof(Int.(Number[1, 2, 3])) === typeof((x->Int(x)).(Number[1, 2, 3]))
+
+@test @inferred broadcast(CartesianIndex, 1:2) == [CartesianIndex(1), CartesianIndex(2)]
+@test @inferred broadcast(CartesianIndex, 1:2, 3:4) == [CartesianIndex(1,3), CartesianIndex(2,4)]
+
+# Issue 18622
+@test @inferred muladd.([1.0], [2.0], [3.0])::Vector{Float64} == [5.0]
+@test @inferred tuple.(1:3, 4:6, 7:9)::Vector{Tuple{Int,Int,Int}} == [(1,4,7), (2,5,8), (3,6,9)]
diff --git a/test/numbers.jl b/test/numbers.jl
index d08c6b7a3ba97..c90a61d44fcc2 100644
--- a/test/numbers.jl
+++ b/test/numbers.jl
@@ -2814,21 +2814,21 @@ let types = (Base.BitInteger_types..., BigInt, Bool,
              Complex{Int}, Complex{UInt}, Complex32, Complex64, Complex128)
     for S in types
         for op in (+, -)
-            T = @inferred Base._promote_op(op, S)
+            T = @inferred Base.promote_op(op, S)
             t = @inferred op(one(S))
             @test T === typeof(t)
         end
 
         for R in types
             for op in (+, -, *, /, ^)
-                T = @inferred Base._promote_op(op, S, R)
+                T = @inferred Base.promote_op(op, S, R)
                 t = @inferred op(one(S), one(R))
                 @test T === typeof(t)
             end
         end
     end
 
-    @test @inferred(Base._promote_op(!, Bool)) === Bool
+    @test @inferred(Base.promote_op(!, Bool)) === Bool
 end
 
 let types = (Base.BitInteger_types..., BigInt, Bool,
@@ -2836,20 +2836,20 @@ let types = (Base.BitInteger_types..., BigInt, Bool,
              Float16, Float32, Float64, BigFloat)
     for S in types, T in types
         for op in (<, >, <=, >=, (==))
-            @test @inferred(Base._promote_op(op, S, T)) === Bool
+            @test @inferred(Base.promote_op(op, S, T)) === Bool
         end
     end
 end
 
 let types = (Base.BitInteger_types..., BigInt, Bool)
     for S in types
-        T = @inferred Base._promote_op(~, S)
+        T = @inferred Base.promote_op(~, S)
         t = @inferred ~one(S)
         @test T === typeof(t)
 
         for R in types
             for op in (&, |, <<, >>, (>>>), %, ÷)
-                T = @inferred Base._promote_op(op, S, R)
+                T = @inferred Base.promote_op(op, S, R)
                 t = @inferred op(one(S), one(R))
                 @test T === typeof(t)
             end