broadcasting not type stable

The broadcast code is not type stable, see below. The code seems quite complicated with generated functions, so I think the best would be to right special case code for the vector and matrix case.

julia>         u = BlockArray(randn(5), [2,3]);

julia>         @code_warntype copyto!(similar(u), Base.broadcasted(exp, u))
Variables
  #self#::Core.Compiler.Const(copyto!, false)
  dest::BlockArray{Float64,1,Array{Array{Float64,1},1},Tuple{BlockedUnitRange{Array{Int64,1}}}}
  bc::Base.Broadcast.Broadcasted{BlockArrays.BlockStyle{1},Nothing,typeof(exp),Tuple{BlockArray{Float64,1,Array{Array{Float64,1},1},Tuple{BlockedUnitRange{Array{Int64,1}}}}}}
  bs::Tuple{BlockedUnitRange{Array{Int64,1}}}
  @_5::Union{Nothing, Tuple{Union{Tuple{}, Tuple{Any,Vararg{Any,N} where N}},Union{Tuple{}, Tuple{Any,Vararg{Any,N} where N}}}}
  blockindexrange_0_1::Any
  blockindexrange_1_1::Any
  @_8::Int64

Body::BlockArray{Float64,1,Array{Array{Float64,1},1},Tuple{BlockedUnitRange{Array{Int64,1}}}}
1 ─       Core.NewvarNode(:(@_5))
│         (bs = BlockArrays.axes(bc))
│   %3  = BlockArrays.axes(dest)::Tuple{BlockedUnitRange{Array{Int64,1}}}
│   %4  = BlockArrays.blockisequal(%3, bs)::Bool
│   %5  = !%4::Bool
└──       goto #3 if not %5
2 ─ %7  = BlockArrays.PseudoBlockArray(dest, bs)::PseudoBlockArray{Float64,1,BlockArray{Float64,1,Array{Array{Float64,1},1},Tuple{BlockedUnitRange{Array{Int64,1}}}},Tuple{BlockedUnitRange{Array{Int64,1}}}}
│         BlockArrays.copyto!(%7, bc)
└──       return dest
3 ─ %10 = BlockArrays.subblocks(dest, bs, 1)::Union{Base.Generator{BlockRange{1,Tuple{Base.OneTo{Int64}}},BlockArrays.var"#42#43"}, BlockArrays.SubBlockIterator}
│   %11 = Core.tuple(%10)::Tuple{Union{Base.Generator{BlockRange{1,Tuple{Base.OneTo{Int64}}},BlockArrays.var"#42#43"}, BlockArrays.SubBlockIterator}}
│   %12 = Base.getproperty(bc, :args)::Tuple{BlockArray{Float64,1,Array{Array{Float64,1},1},Tuple{BlockedUnitRange{Array{Int64,1}}}}}
│   %13 = BlockArrays.Ref(bs)::Base.RefValue{Tuple{BlockedUnitRange{Array{Int64,1}}}}
│   %14 = BlockArrays.Ref(1)::Base.RefValue{Int64}
│   %15 = Base.broadcasted(BlockArrays.subblocks, %12, %13, %14)::Base.Broadcast.Broadcasted{Base.Broadcast.Style{Tuple},Nothing,typeof(BlockArrays.subblocks),Tuple{Tuple{BlockArray{Float64,1,Array{Array{Float64,1},1},Tuple{BlockedUnitRange{Array{Int64,1}}}}},Base.RefValue{Tuple{BlockedUnitRange{Array{Int64,1}}}},Base.RefValue{Int64}}}
│   %16 = Base.materialize(%15)::Tuple{Union{Base.Generator{BlockRange{1,Tuple{Base.OneTo{Int64}}},BlockArrays.var"#42#43"}, BlockArrays.SubBlockIterator}}
│   %17 = Core._apply_iterate(Base.iterate, BlockArrays.zip, %11, %16)::Base.Iterators.Zip
│         (@_5 = Base.iterate(%17))
│   %19 = (@_5 === nothing)::Bool
│   %20 = Base.not_int(%19)::Bool
└──       goto #6 if not %20
4 ┄ %22 = @_5::Tuple{Union{Tuple{}, Tuple{Any,Vararg{Any,N} where N}},Union{Tuple{}, Tuple{Any,Vararg{Any,N} where N}}}::Tuple{Union{Tuple{}, Tuple{Any,Vararg{Any,N} where N}},Union{Tuple{}, Tuple{Any,Vararg{Any,N} where N}}}
│   %23 = Core.getfield(%22, 1)::Union{Tuple{}, Tuple{Any,Vararg{Any,N} where N}}
│   %24 = Base.indexed_iterate(%23, 1)::Core.Compiler.PartialStruct(Tuple{Any,Int64}, Any[Any, Core.Compiler.Const(2, false)])
│         (blockindexrange_0_1 = Core.getfield(%24, 1))
│         (@_8 = Core.getfield(%24, 2))
│   %27 = Base.indexed_iterate(%23, 2, @_8::Core.Compiler.Const(2, false))::Core.Compiler.PartialStruct(Tuple{Any,Int64}, Any[Any, Core.Compiler.Const(3, false)])
│         (blockindexrange_1_1 = Core.getfield(%27, 1))
│   %29 = Core.getfield(%22, 2)::Union{Tuple{}, Tuple{Any,Vararg{Any,N} where N}}
│   %30 = Base.getproperty(bc, :f)::Core.Compiler.Const(exp, false)
│   %31 = BlockArrays._bview(dest, blockindexrange_0_1)::Any
│   %32 = Base.getproperty(bc, :args)::Tuple{BlockArray{Float64,1,Array{Array{Float64,1},1},Tuple{BlockedUnitRange{Array{Int64,1}}}}}
│   %33 = Base.getindex(%32, 1)::BlockArray{Float64,1,Array{Array{Float64,1},1},Tuple{BlockedUnitRange{Array{Int64,1}}}}
│   %34 = BlockArrays._bview(%33, blockindexrange_1_1)::Any
│         BlockArrays.broadcast!(%30, %31, %34)
│         (@_5 = Base.iterate(%17, %29))
│   %37 = (@_5 === nothing)::Bool
│   %38 = Base.not_int(%37)::Bool
└──       goto #6 if not %38
5 ─       goto #4
6 ┄       return dest

Start by running the Julia @code_warntype reproducer for copyto!(similar(u), Base.broadcasted(exp, u)). Read the BlockArrays broadcasting entry points shown in the output, especially copyto!, subblocks, _bview, and broadcast!. Done means the vector and matrix broadcasting paths are type stable without changing their behavior.