Make broadcasting closures inferable again

base/broadcast.jl

@@ -3,7 +3,7 @@
 module Broadcast
 
 using Base.Cartesian
-using Base: @pure, promote_eltype_op, _promote_op, linearindices, tail, OneTo, to_shape,
+using Base: promote_eltype_op, linearindices, tail, OneTo, to_shape,
             _msk_end, unsafe_bitgetindex, bitcache_chunks, bitcache_size, dumpbitcache
 import Base: .+, .-, .*, ./, .\, .//, .==, .<, .!=, .<=, .÷, .%, .<<, .>>, .^
 import Base: broadcast
@@ -257,13 +257,22 @@ end
 @inline broadcast_elwise_op(f, As...) =
     broadcast!(f, similar(Array{promote_eltype_op(f, As...)}, broadcast_indices(As...)), As...)
 
-@pure typestuple(a) = Tuple{eltype(a)}
-@pure typestuple(T::Type) = Tuple{Type{T}}
-@pure typestuple(a, b...) = Tuple{typestuple(a).types..., typestuple(b...).types...}
+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...)})
 
 # broadcast methods that dispatch on the type of the final container
 @inline function broadcast_c(f, ::Type{Array}, A, Bs...)
-    T = _promote_op(f, typestuple(A, Bs...))
+    T = _broadcast_type(f, A, Bs...)
     shape = broadcast_indices(A, Bs...)
     iter = CartesianRange(shape)
     if isleaftype(T)

base/promotion.jl

@@ -223,21 +223,23 @@ minmax(x::Real, y::Real) = minmax(promote(x, y)...)
 _default_type(T::Type) = (@_pure_meta; T)
 
 if isdefined(Core, :Inference)
-    _promote_op(f::ANY, t::ANY) = Core.Inference.return_type(f, t)
+    _return_type(f::ANY, t::ANY) = Core.Inference.return_type(f, t)
 else
-    _promote_op(f::ANY, t::ANY) = Any
+    _return_type(f::ANY, t::ANY) = Any
 end
 
 promote_op(::Any...) = (@_pure_meta; Any)
 function promote_op{S}(f, ::Type{S})
     @_inline_meta
-    T = _promote_op(f, Tuple{_default_type(S)})
+    Z = Tuple{_default_type(S)}
+    T = _default_eltype(Generator{Z, typeof(f)})
     isleaftype(S) && return isleaftype(T) ? T : Any
     return typejoin(S, T)
 end
 function promote_op{R,S}(f, ::Type{R}, ::Type{S})
     @_inline_meta
-    T = _promote_op(f, Tuple{_default_type(R), _default_type(S)})
+    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

base/sparse/sparse.jl

@@ -26,7 +26,7 @@ import Base: @get!, acos, acosd, acot, acotd, acsch, asech, asin, asind, asinh,
     rotl90, rotr90, round, scale!, setindex!, similar, size, transpose, tril,
     triu, vec, permute!, map, map!
 
-import Base.Broadcast: broadcast_indices
+import Base.Broadcast: _broadcast_type, broadcast_indices
 
 export AbstractSparseArray, AbstractSparseMatrix, AbstractSparseVector,
     SparseMatrixCSC, SparseVector, blkdiag, dense, droptol!, dropzeros!, dropzeros,

base/sparse/sparsematrix.jl

@@ -1464,7 +1464,6 @@ _maxnnzfrom(Cm, Cn, A) = nnz(A) * div(Cm, A.m) * div(Cn, A.n)
 @inline _maxnnzfrom_each(Cm, Cn, As) = (_maxnnzfrom(Cm, Cn, first(As)), _maxnnzfrom_each(Cm, Cn, tail(As))...)
 @inline _unchecked_maxnnzbcres(Cm, Cn, As) = min(Cm * Cn, sum(_maxnnzfrom_each(Cm, Cn, As)))
 @inline _checked_maxnnzbcres(Cm, Cn, As...) = Cm != 0 && Cn != 0 ? _unchecked_maxnnzbcres(Cm, Cn, As) : 0
-_broadcast_type(f, As...) = Base._promote_op(f, Base.Broadcast.typestuple(As...))
 
 # _map_zeropres!/_map_notzeropres! specialized for a single sparse matrix
 "Stores only the nonzero entries of `map(f, Matrix(A))` in `C`."

test/broadcast.jl

@@ -355,3 +355,11 @@ StrangeType18623(x,y) = (x,y)
 
 # 19419
 @test @inferred(broadcast(round, Int, [1])) == [1]
+
+# https://discourse.julialang.org/t/towards-broadcast-over-combinations-of-sparse-matrices-and-scalars/910
+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))
+    @test @inferred(g()) === Float64
+end