diff --git a/base/abstractarray.jl b/base/abstractarray.jl
index e937e9ca4208a..f4ec61de51665 100644
--- a/base/abstractarray.jl
+++ b/base/abstractarray.jl
@@ -151,7 +151,6 @@ immutable IndicesList      <: IndicesBehavior end   # indices like (:cat, :dog,
 
 indicesbehavior(A::AbstractArray) = indicesbehavior(typeof(A))
 indicesbehavior{T<:AbstractArray}(::Type{T}) = IndicesStartAt1()
-indicesbehavior(::Number) = IndicesStartAt1()
 
 abstract IndicesPerformance
 immutable IndicesFast1D <: IndicesPerformance end  # indices(A, d) is fast
@@ -412,8 +411,9 @@ end
 promote_indices(a::AbstractArray, b::AbstractArray) = _promote_indices(indicesbehavior(a), indicesbehavior(b), a, b)
 _promote_indices(::IndicesStartAt1, ::IndicesStartAt1, a, b) = a
 _promote_indices(::IndicesBehavior, ::IndicesBehavior, a, b) = throw(ArgumentError("types $(typeof(a)) and $(typeof(b)) do not have promote_indices defined"))
-promote_indices(a::Number, b::AbstractArray) = b
-promote_indices(a::AbstractArray, b::Number) = a
+promote_indices(a, b::AbstractArray) = b
+promote_indices(a::AbstractArray, b) = a
+promote_indices(a, b) = a
 
 # Strip off the index-changing container---this assumes that `parent`
 # performs such an operation. TODO: since few things in Base need this, it
@@ -1459,9 +1459,14 @@ end
 promote_eltype_op(::Any) = (@_pure_meta; Bottom)
 promote_eltype_op{T}(op, ::AbstractArray{T}) = (@_pure_meta; promote_op(op, T))
 promote_eltype_op{T}(op, ::T               ) = (@_pure_meta; promote_op(op, T))
+promote_eltype_op{T}(op, Ts::AbstractArray{DataType}, ::AbstractArray{T}) = typejoin((promote_op(op, S, T) for S in Ts)...)
+promote_eltype_op{T}(op, Ts::AbstractArray{DataType}, ::T)                = typejoin((promote_op(op, S, T) for S in Ts)...)
 promote_eltype_op{R,S}(op, ::AbstractArray{R}, ::AbstractArray{S}) = (@_pure_meta; promote_op(op, R, S))
 promote_eltype_op{R,S}(op, ::AbstractArray{R}, ::S) = (@_pure_meta; promote_op(op, R, S))
 promote_eltype_op{R,S}(op, ::R, ::AbstractArray{S}) = (@_pure_meta; promote_op(op, R, S))
+promote_eltype_op{R,S}(op, ::Type{R}, ::AbstractArray{S}) = (@_pure_meta; promote_op(op, R, S))
+promote_eltype_op{R,S}(op, ::Type{R}, ::S) = (@_pure_meta; promote_op(op, R, S))
+promote_eltype_op{R,S}(op, ::R, ::S) = (@_pure_meta; promote_op(op, R, S))
 promote_eltype_op(op, A, B, C, D...) = (@_pure_meta; promote_op(op, eltype(A), promote_eltype_op(op, B, C, D...)))
 
 ## 1 argument
diff --git a/base/broadcast.jl b/base/broadcast.jl
index 0c0165fac300e..ff7f3b0e716d4 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -13,8 +13,9 @@ export broadcast_getindex, broadcast_setindex!
 ## Calculate the broadcast shape of the arguments, or error if incompatible
 # array inputs
 broadcast_shape() = ()
-broadcast_shape(A) = shape(A)
-@inline broadcast_shape(A, B...) = broadcast_shape((), shape(A), map(shape, B)...)
+broadcast_shape(A) = ()
+broadcast_shape(A::AbstractArray) = shape(A)
+@inline broadcast_shape(A, B...) = broadcast_shape((), broadcast_shape(A), map(broadcast_shape, B)...)
 # shape inputs
 broadcast_shape(shape::Tuple) = shape
 @inline broadcast_shape(shape::Tuple, shape1::Tuple, shapes::Tuple...) = broadcast_shape(_bcs((), shape, shape1), shapes...)
@@ -40,7 +41,7 @@ _bcsm(a::Number, b::Number) = a == b || b == 1
 ## Check that all arguments are broadcast compatible with shape
 # comparing one input against a shape
 check_broadcast_shape(shp) = nothing
-check_broadcast_shape(shp, A) = check_broadcast_shape(shp, shape(A))
+check_broadcast_shape(shp, A) = check_broadcast_shape(shp, broadcast_shape(A))
 check_broadcast_shape(::Tuple{}, ::Tuple{}) = nothing
 check_broadcast_shape(shp, ::Tuple{}) = nothing
 check_broadcast_shape(::Tuple{}, Ashp::Tuple) = throw(DimensionMismatch("cannot broadcast array to have fewer dimensions"))
@@ -63,8 +64,8 @@ end
 @inline _newindex(out, I) = out  # can truncate if indexmap is shorter than I
 @inline _newindex(out, I, keep::Bool, indexmap...) = _newindex((out..., ifelse(keep, I[1], 1)), tail(I), indexmap...)
 
-newindexer(sz, x::Number) = ()
-@inline newindexer(sz, A) = _newindexer(sz, size(A))
+newindexer(sz, x) = ()
+@inline newindexer(sz, A::AbstractArray) = _newindexer(sz, size(A))
 @inline _newindexer(sz, szA::Tuple{}) = ()
 @inline _newindexer(sz, szA) = (sz[1] == szA[1], _newindexer(tail(sz), tail(szA))...)
 
@@ -79,6 +80,9 @@ const bitcache_size = 64 * bitcache_chunks # do not change this
 dumpbitcache(Bc::Vector{UInt64}, bind::Int, C::Vector{Bool}) =
     Base.copy_to_bitarray_chunks!(Bc, ((bind - 1) << 6) + 1, C, 1, min(bitcache_size, (length(Bc)-bind+1) << 6))
 
+@inline _broadcast_getvals(A, I) = A # default for non-indexable types
+@inline _broadcast_getvals(A::AbstractArray, I) = A[I]
+
 ## Broadcasting core
 # nargs encodes the number of As arguments (which matches the number
 # of indexmaps). The first two type parameters are to ensure specialization.
@@ -92,7 +96,7 @@ dumpbitcache(Bc::Vector{UInt64}, bind::Int, C::Vector{Bool}) =
             # reverse-broadcast the indices
             @nexprs $nargs i->(I_i = newindex(I, imap_i))
             # extract array values
-            @nexprs $nargs i->(@inbounds val_i = A_i[I_i])
+            @nexprs $nargs i->(@inbounds val_i = _broadcast_getvals(A_i, I_i))
             # call the function and store the result
             @inbounds B[I] = @ncall $nargs f val
         end
diff --git a/base/float.jl b/base/float.jl
index 6d507f2d6b34b..232e3fff2cf41 100644
--- a/base/float.jl
+++ b/base/float.jl
@@ -199,6 +199,13 @@ promote_rule(::Type{Float64}, ::Type{Float32}) = Float64
 widen(::Type{Float16}) = Float32
 widen(::Type{Float32}) = Float64
 
+promote_op{Op<:typeof(trunc),T<:Union{Float32,Float64}}(::Op, ::Type{Signed}, ::Type{T}) = Int
+promote_op{Op<:typeof(trunc),T<:Union{Float32,Float64}}(::Op, ::Type{Unsigned}, ::Type{T}) = UInt
+promote_op{Op<:typeof(trunc),R,S}(::Op, ::Type{R}, ::Type{S}) = R
+for f in (ceil, floor, round)
+    @eval promote_op{Op<:$(typeof(f)),R,S}(::Op, ::Type{R}, ::Type{S}) = promote_op($trunc, R, S)
+end
+
 ## floating point arithmetic ##
 -(x::Float32) = box(Float32,neg_float(unbox(Float32,x)))
 -(x::Float64) = box(Float64,neg_float(unbox(Float64,x)))
diff --git a/base/parse.jl b/base/parse.jl
index 1da9b742457e3..5387ee55d26e7 100644
--- a/base/parse.jl
+++ b/base/parse.jl
@@ -194,3 +194,5 @@ function parse(str::AbstractString; raise::Bool=true)
     end
     return ex
 end
+
+promote_op{Op<:typeof(parse),R,S}(::Op, ::Type{R}, ::Type{S}) = R
diff --git a/base/promotion.jl b/base/promotion.jl
index 7b6ebf0f406cb..2ba07567c81c2 100644
--- a/base/promotion.jl
+++ b/base/promotion.jl
@@ -221,10 +221,11 @@ minmax(x::Real, y::Real) = minmax(promote(x, y)...)
 # as needed. For example, if you need to provide a custom result type
 # for the multiplication of two types,
 #   promote_op{R<:MyType,S<:MyType}(::typeof(*), ::Type{R}, ::Type{S}) = MyType{multype(R,S)}
-promote_op(::Any)    = (@_pure_meta; Bottom)
-promote_op(::Any, T) = (@_pure_meta; T)
+promote_op(::Any)    = (@_pure_meta; Any)
+promote_op(::Any, T) = (@_pure_meta; Any)
 promote_op{T}(::Type{T}, ::Any) = (@_pure_meta; T)
 promote_op{R,S}(::Any, ::Type{R}, ::Type{S}) = (@_pure_meta; promote_type(R, S))
+promote_op{Op<:typeof(convert),R,S}(::Op, ::Type{R}, ::Type{S}) = (@_pure_meta; R)
 promote_op(op, T, S, U, V...) = (@_pure_meta; promote_op(op, T, promote_op(op, S, U, V...)))
 
 ## catch-alls to prevent infinite recursion when definitions are missing ##