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broadcast.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
module Broadcast
using Base.Cartesian
using Base: Indices, OneTo, linearindices, tail, to_shape,
_msk_end, unsafe_bitgetindex, bitcache_chunks, bitcache_size, dumpbitcache,
nullable_returntype, null_safe_op, hasvalue, isoperator
import Base: broadcast, broadcast!
export BroadcastStyle, broadcast_indices, broadcast_similar,
broadcast_getindex, broadcast_setindex!, dotview, @__dot__
### Objects with customized broadcasting behavior should declare a BroadcastStyle
"""
`BroadcastStyle` is an abstract type and trait-function used to determine behavior of
objects under broadcasting. `BroadcastStyle(typeof(x))` returns the style associated
with `x`. To customize the broadcasting behavior of a type, one can declare a style
by defining a type/method pair
struct MyContainerStyle <: BroadcastStyle end
Base.BroadcastStyle(::Type{<:MyContainer}) = MyContainerStyle()
One then writes method(s) (at least [`broadcast_similar`](@ref)) operating on
`MyContainerStyle`. There are also several pre-defined subtypes of `BroadcastStyle`
that you may be able to leverage; see the
[Interfaces chapter](@ref man-interfaces-broadcasting) for more information.
"""
abstract type BroadcastStyle end
"""
`Broadcast.Style{C}()` defines a [`BroadcastStyle`](@ref) signaling through the type
parameter `C`. You can use this as an alternative to creating custom subtypes of `BroadcastStyle`,
for example
Base.BroadcastStyle(::Type{<:MyContainer}) = Broadcast.Style{MyContainer}()
There is a pre-defined [`broadcast_similar`](@ref) method
broadcast_similar(f, ::Style{C}, ::Type{ElType}, inds, args...) =
similar(C, ElType, inds)
Naturally you can specialize this for your particular `C` (e.g., `MyContainer`).
"""
struct Style{T} <: BroadcastStyle end
BroadcastStyle(::Type{<:Tuple}) = Style{Tuple}()
BroadcastStyle(::Type{<:Nullable}) = Style{Nullable}()
struct Unknown <: BroadcastStyle end
BroadcastStyle(::Type{Union{}}) = Unknown() # ambiguity resolution
"""
`Broadcast.Scalar()` is a [`BroadcastStyle`](@ref) indicating that an object is not
treated as a container for the purposes of broadcasting. This is the default for objects
that have not customized `BroadcastStyle`.
"""
struct Scalar <: BroadcastStyle end
BroadcastStyle(::Type) = Scalar()
BroadcastStyle(::Type{<:Ptr}) = Scalar()
"""
`Broadcast.AbstractArrayStyle{N} <: BroadcastStyle` is the abstract supertype for any style
associated with an `AbstractArray` type.
The `N` parameter is the dimensionality, which can be handy for AbstractArray types
that only support specific dimensionalities:
struct SparseMatrixStyle <: Broadcast.AbstractArrayStyle{2} end
Base.BroadcastStyle(::Type{<:SparseMatrixCSC}) = SparseMatrixStyle()
For AbstractArray types that support arbitrary dimensionality, `N` can be set to `Any`:
struct MyArrayStyle <: Broadcast.AbstractArrayStyle{Any} end
Base.BroadcastStyle(::Type{<:MyArray}) = MyArrayStyle()
In cases where you want to be able to mix multiple `AbstractArrayStyle`s and keep track
of dimensionality, your style needs to support a `Val` constructor:
struct MyArrayStyleDim{N} <: Broadcast.AbstractArrayStyle{N} end
(::Type{<:MyArrayStyleDim})(::Val{N}) where N = MyArrayStyleDim{N}()
Note that if two or more `AbstractArrayStyle` subtypes conflict, broadcasting machinery
will fall back to producing `Array`s. If this is undesirable, you may need to
define binary [`BroadcastStyle`](@ref) rules to control the output type.
See also [`Broadcast.DefaultArrayStyle`](@ref).
"""
abstract type AbstractArrayStyle{N} <: BroadcastStyle end
"""
`Broadcast.ArrayStyle{MyArrayType}()` is a [`BroadcastStyle`](@ref) indicating that an object
behaves as an array for broadcasting. It presents a simple way to construct
[`Broadcast.AbstractArrayStyle`](@ref)s for specific `AbstractArray` container types.
Broadcast styles created this way lose track of dimensionality; if keeping track is important
for your type, you should create your own custom [`Broadcast.AbstractArrayStyle`](@ref).
"""
struct ArrayStyle{A<:AbstractArray} <: AbstractArrayStyle{Any} end
(::Type{<:ArrayStyle{A}})(::Val) where A = A()
"""
`Broadcast.DefaultArrayStyle{N}()` is a [`BroadcastStyle`](@ref) indicating that an object
behaves as an `N`-dimensional array for broadcasting. Specifically, `DefaultArrayStyle` is
used for any
AbstractArray type that hasn't defined a specialized style, and in the absence of
overrides from other `broadcast` arguments the resulting output type is `Array`.
When there are multiple inputs to `broadcast`, `DefaultArrayStyle` "wins" over [`Broadcast.Scalar`](@ref)
but "loses" to any other [`Broadcast.ArrayStyle`](@ref).
"""
struct DefaultArrayStyle{N} <: AbstractArrayStyle{N} end
(::Type{<:DefaultArrayStyle})(::Val{N}) where N = DefaultArrayStyle{N}()
const DefaultVectorStyle = DefaultArrayStyle{1}
const DefaultMatrixStyle = DefaultArrayStyle{2}
BroadcastStyle(::Type{<:AbstractArray{T,N}}) where {T,N} = DefaultArrayStyle{N}()
BroadcastStyle(::Type{<:Ref}) = DefaultArrayStyle{0}()
# `ArrayConflict` is an internal type signaling that two or more different `AbstractArrayStyle`
# objects were supplied as arguments, and that no rule was defined for resolving the
# conflict. The resulting output is `Array`. While this is the same output type
# produced by `DefaultArrayStyle`, `ArrayConflict` "poisons" the BroadcastStyle so that
# 3 or more arguments still return an `ArrayConflict`.
struct ArrayConflict <: AbstractArrayStyle{Any} end
### Binary BroadcastStyle rules
"""
BroadcastStyle(::Style1, ::Style2) = Style3()
Indicate how to resolve different `BroadcastStyle`s. For example,
Broadcast.rule(::Primary, ::Secondary) = Primary()
would indicate that style `Primary` has precedence over `Secondary`.
You do not have to (and generally should not) define both argument orders.
The result does not have to be one of the input arguments, it could be a third type.
Please see the [Interfaces chapter](@ref man-interfaces-broadcasting) of the manual for
more information.
"""
BroadcastStyle(::S, ::S) where S<:BroadcastStyle = S() # homogeneous types preserved
# Fall back to Unknown. This is necessary to implement argument-swapping
BroadcastStyle(::BroadcastStyle, ::BroadcastStyle) = Unknown()
# Unknown loses to everything
BroadcastStyle(::Unknown, ::Unknown) = Unknown()
BroadcastStyle(::S, ::Unknown) where S<:BroadcastStyle = S()
# Precedence rules
BroadcastStyle(::Style{Nullable}, ::Scalar) = Style{Nullable}()
BroadcastStyle(::Style{Tuple}, ::Scalar) = Style{Tuple}()
BroadcastStyle(a::AbstractArrayStyle{0}, ::Style{Tuple}) = typeof(a)(Val(1))
BroadcastStyle(a::AbstractArrayStyle, ::Style{Tuple}) = a
BroadcastStyle(a::AbstractArrayStyle, ::Scalar) = a
BroadcastStyle(::A, ::A) where A<:ArrayStyle = A()
BroadcastStyle(::ArrayStyle, ::ArrayStyle) = Unknown()
BroadcastStyle(::A, ::A) where A<:AbstractArrayStyle = A()
Base.@pure function BroadcastStyle(a::A, b::B) where {A<:AbstractArrayStyle{M},B<:AbstractArrayStyle{N}} where {M,N}
if Base.typename(A).wrapper == Base.typename(B).wrapper
return A(_max(Val(M),Val(N)))
end
Unknown()
end
# Any specific array type beats DefaultArrayStyle
BroadcastStyle(a::AbstractArrayStyle{Any}, ::DefaultArrayStyle) = a
BroadcastStyle(a::AbstractArrayStyle{N}, ::DefaultArrayStyle{N}) where N = a
BroadcastStyle(a::AbstractArrayStyle{M}, ::DefaultArrayStyle{N}) where {M,N} =
typeof(a)(_max(Val(M),Val(N)))
## Allocating the output container
"""
broadcast_similar(f, ::BroadcastStyle, ::Type{ElType}, inds, As...)
Allocate an output object for [`broadcast`](@ref), appropriate for the indicated
[`Broadcast.BroadcastStyle`](@ref). `ElType` and `inds` specify the desired element type and indices of the
container.
`f` is the broadcast operation, and `As...` are the arguments supplied to `broadcast`.
"""
broadcast_similar(f, ::DefaultArrayStyle{N}, ::Type{ElType}, inds::Indices{N}, As...) where {N,ElType} =
similar(Array{ElType}, inds)
broadcast_similar(f, ::DefaultArrayStyle{N}, ::Type{Bool}, inds::Indices{N}, As...) where {N,ElType} =
similar(BitArray, inds)
# In cases of conflict we fall back on Array
broadcast_similar(f, ::ArrayConflict, ::Type{ElType}, inds::Indices, As...) where ElType =
similar(Array{ElType}, inds)
broadcast_similar(f, ::ArrayConflict, ::Type{Bool}, inds::Indices, As...) where ElType =
similar(BitArray, inds)
## Computing the result's indices. Most types probably won't need to specialize this.
broadcast_indices() = ()
broadcast_indices(::Type{T}) where T = ()
broadcast_indices(A) = broadcast_indices(combine_styles(A), A)
broadcast_indices(::Scalar, A) = ()
broadcast_indices(::Style{Nullable}, A) = ()
broadcast_indices(::Style{Tuple}, A) = (OneTo(length(A)),)
broadcast_indices(::DefaultArrayStyle{0}, A::Ref) = ()
broadcast_indices(::AbstractArrayStyle, A) = Base.indices(A)
"""
Base.broadcast_indices(::SrcStyle, A)
Compute the indices for objects `A` with [`BroadcastStyle`](@ref) `SrcStyle`.
If needed, you can specialize this method for your styles.
You should only need to provide a custom implementation for non-AbstractArrayStyles.
"""
broadcast_indices
### End of methods that users will typically have to specialize ###
## Broadcasting utilities ##
# special cases defined for performance
broadcast(f, x::Number...) = f(x...)
@inline broadcast(f, t::NTuple{N,Any}, ts::Vararg{NTuple{N,Any}}) where {N} = map(f, t, ts...)
@inline broadcast!(::typeof(identity), x::AbstractArray{T,N}, y::AbstractArray{S,N}) where {T,S,N} =
Base.indices(x) == Base.indices(y) ? copy!(x, y) : _broadcast!(identity, x, y)
# special cases for "X .= ..." (broadcast!) assignments
broadcast!(::typeof(identity), X::AbstractArray, x::Number) = fill!(X, x)
broadcast!(f, X::AbstractArray, x::Number...) = (@inbounds for I in eachindex(X); X[I] = f(x...); end; X)
## logic for deciding the BroadcastStyle
# Dimensionality: computing max(M,N) in the type domain so we preserve inferrability
_max(V1::Val{Any}, V2::Val{Any}) = Val(Any)
_max(V1::Val{Any}, V2::Val{N}) where N = Val(Any)
_max(V1::Val{N}, V2::Val{Any}) where N = Val(Any)
_max(V1::Val, V2::Val) = __max(longest(ntuple(identity, V1), ntuple(identity, V2)))
__max(::NTuple{N,Bool}) where N = Val(N)
longest(t1::Tuple, t2::Tuple) = (true, longest(Base.tail(t1), Base.tail(t2))...)
longest(::Tuple{}, t2::Tuple) = (true, longest((), Base.tail(t2))...)
longest(t1::Tuple, ::Tuple{}) = (true, longest(Base.tail(t1), ())...)
longest(::Tuple{}, ::Tuple{}) = ()
# combine_styles operates on values (arbitrarily many)
combine_styles(c) = result_style(BroadcastStyle(typeof(c)))
combine_styles(c1, c2) = result_style(combine_styles(c1), combine_styles(c2))
combine_styles(c1, c2, cs...) = result_style(combine_styles(c1), combine_styles(c2, cs...))
# result_style works on types (singletons and pairs), and leverages `BroadcastStyle`
result_style(s::BroadcastStyle) = s
result_style(s1::S, s2::S) where S<:BroadcastStyle = S()
# Test both orders so users typically only have to declare one order
result_style(s1, s2) = result_join(s1, s2, BroadcastStyle(s1, s2), BroadcastStyle(s2, s1))
# result_join is the final arbiter. Because `BroadcastStyle` for undeclared pairs results in Unknown,
# we defer to any case where the result of `BroadcastStyle` is known.
result_join(::Any, ::Any, ::Unknown, ::Unknown) = Unknown()
result_join(::Any, ::Any, ::Unknown, s::BroadcastStyle) = s
result_join(::Any, ::Any, s::BroadcastStyle, ::Unknown) = s
# For AbstractArray types with specialized broadcasting and undefined precedence rules,
# we have to signal conflict. Because ArrayConflict is a subtype of AbstractArray,
# this will "poison" any future operations (if we instead returned `DefaultArrayStyle`, then for
# 3-array broadcasting the returned type would depend on argument order).
result_join(::AbstractArrayStyle, ::AbstractArrayStyle, ::Unknown, ::Unknown) =
ArrayConflict()
# Fallbacks in case users define `rule` for both argument-orders (not recommended)
result_join(::Any, ::Any, ::S, ::S) where S<:BroadcastStyle = S()
@noinline function result_join(::S, ::T, ::U, ::V) where {S,T,U,V}
error("""
conflicting broadcast rules defined
Broadcast.BroadcastStyle(::$S, ::$T) = $U()
Broadcast.BroadcastStyle(::$T, ::$S) = $V()
One of these should be undefined (and thus return Broadcast.Unknown).""")
end
# Indices utilities
combine_indices(A, B...) = broadcast_shape(broadcast_indices(A), combine_indices(B...))
combine_indices(A) = broadcast_indices(A)
# shape (i.e., tuple-of-indices) inputs
broadcast_shape(shape::Tuple) = shape
broadcast_shape(shape::Tuple, shape1::Tuple, shapes::Tuple...) = broadcast_shape(_bcs(shape, shape1), shapes...)
# _bcs consolidates two shapes into a single output shape
_bcs(::Tuple{}, ::Tuple{}) = ()
_bcs(::Tuple{}, newshape::Tuple) = (newshape[1], _bcs((), tail(newshape))...)
_bcs(shape::Tuple, ::Tuple{}) = (shape[1], _bcs(tail(shape), ())...)
function _bcs(shape::Tuple, newshape::Tuple)
return (_bcs1(shape[1], newshape[1]), _bcs(tail(shape), tail(newshape))...)
end
# _bcs1 handles the logic for a single dimension
_bcs1(a::Integer, b::Integer) = a == 1 ? b : (b == 1 ? a : (a == b ? a : throw(DimensionMismatch("arrays could not be broadcast to a common size"))))
_bcs1(a::Integer, b) = a == 1 ? b : (first(b) == 1 && last(b) == a ? b : throw(DimensionMismatch("arrays could not be broadcast to a common size")))
_bcs1(a, b::Integer) = _bcs1(b, a)
_bcs1(a, b) = _bcsm(b, a) ? b : (_bcsm(a, b) ? a : throw(DimensionMismatch("arrays could not be broadcast to a common size")))
# _bcsm tests whether the second index is consistent with the first
_bcsm(a, b) = a == b || length(b) == 1
_bcsm(a, b::Number) = b == 1
_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, ::Tuple{}) = nothing
check_broadcast_shape(::Tuple{}, ::Tuple{}) = nothing
check_broadcast_shape(::Tuple{}, Ashp::Tuple) = throw(DimensionMismatch("cannot broadcast array to have fewer dimensions"))
function check_broadcast_shape(shp, Ashp::Tuple)
_bcsm(shp[1], Ashp[1]) || throw(DimensionMismatch("array could not be broadcast to match destination"))
check_broadcast_shape(tail(shp), tail(Ashp))
end
check_broadcast_indices(shp, A) = check_broadcast_shape(shp, broadcast_indices(A))
# comparing many inputs
@inline function check_broadcast_indices(shp, A, As...)
check_broadcast_indices(shp, A)
check_broadcast_indices(shp, As...)
end
## Indexing manipulations
# newindex(I, keep, Idefault) replaces a CartesianIndex `I` with something that
# is appropriate for a particular broadcast array/scalar. `keep` is a
# NTuple{N,Bool}, where keep[d] == true means that one should preserve
# I[d]; if false, replace it with Idefault[d].
# If dot-broadcasting were already defined, this would be `ifelse.(keep, I, Idefault)`.
@inline newindex(I::CartesianIndex, keep, Idefault) = CartesianIndex(_newindex(I.I, keep, Idefault))
@inline _newindex(I, keep, Idefault) =
(ifelse(keep[1], I[1], Idefault[1]), _newindex(tail(I), tail(keep), tail(Idefault))...)
@inline _newindex(I, keep::Tuple{}, Idefault) = () # truncate if keep is shorter than I
# newindexer(shape, A) generates `keep` and `Idefault` (for use by
# `newindex` above) for a particular array `A`, given the
# broadcast indices `shape`
# `keep` is equivalent to map(==, indices(A), shape) (but see #17126)
@inline newindexer(shape, A) = shapeindexer(shape, broadcast_indices(A))
@inline shapeindexer(shape, indsA::Tuple{}) = (), ()
@inline function shapeindexer(shape, indsA::Tuple)
ind1 = indsA[1]
keep, Idefault = shapeindexer(tail(shape), tail(indsA))
(shape[1] == ind1, keep...), (first(ind1), Idefault...)
end
# Equivalent to map(x->newindexer(shape, x), As) (but see #17126)
map_newindexer(shape, ::Tuple{}) = (), ()
@inline function map_newindexer(shape, As)
A1 = As[1]
keeps, Idefaults = map_newindexer(shape, tail(As))
keep, Idefault = newindexer(shape, A1)
(keep, keeps...), (Idefault, Idefaults...)
end
@inline function map_newindexer(shape, A, Bs)
keeps, Idefaults = map_newindexer(shape, Bs)
keep, Idefault = newindexer(shape, A)
(keep, keeps...), (Idefault, Idefaults...)
end
Base.@propagate_inbounds _broadcast_getindex(::Type{T}, I) where T = T
Base.@propagate_inbounds _broadcast_getindex(A, I) = _broadcast_getindex(combine_styles(A), A, I)
Base.@propagate_inbounds _broadcast_getindex(::DefaultArrayStyle{0}, A::Ref, I) = A[]
Base.@propagate_inbounds _broadcast_getindex(::Union{Unknown,Scalar,Style{Nullable}}, A, I) = A
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!(f, B::AbstractArray, keeps::K, Idefaults::ID, A::AT, Bs::BT, ::Val{N}, iter) where {K,ID,AT,BT,N}
nargs = N + 1
quote
$(Expr(:meta, :inline))
# destructure the keeps and As tuples
A_1 = A
@nexprs $N i->(A_{i+1} = Bs[i])
@nexprs $nargs i->(keep_i = keeps[i])
@nexprs $nargs i->(Idefault_i = Idefaults[i])
@simd for I in iter
# reverse-broadcast the indices
@nexprs $nargs i->(I_i = newindex(I, keep_i, Idefault_i))
# extract array values
@nexprs $nargs i->(@inbounds val_i = _broadcast_getindex(A_i, I_i))
# call the function and store the result
result = @ncall $nargs f val
@inbounds B[I] = result
end
end
end
# For BitArray outputs, we cache the result in a "small" Vector{Bool},
# and then copy in chunks into the output
@generated function _broadcast!(f, B::BitArray, keeps::K, Idefaults::ID, A::AT, Bs::BT, ::Val{N}, iter) where {K,ID,AT,BT,N}
nargs = N + 1
quote
$(Expr(:meta, :inline))
# destructure the keeps and As tuples
A_1 = A
@nexprs $N i->(A_{i+1} = Bs[i])
@nexprs $nargs i->(keep_i = keeps[i])
@nexprs $nargs i->(Idefault_i = Idefaults[i])
C = Vector{Bool}(bitcache_size)
Bc = B.chunks
ind = 1
cind = 1
@simd for I in iter
# reverse-broadcast the indices
@nexprs $nargs i->(I_i = newindex(I, keep_i, Idefault_i))
# extract array values
@nexprs $nargs i->(@inbounds val_i = _broadcast_getindex(A_i, I_i))
# call the function and store the result
@inbounds C[ind] = @ncall $nargs f val
ind += 1
if ind > bitcache_size
dumpbitcache(Bc, cind, C)
cind += bitcache_chunks
ind = 1
end
end
if ind > 1
@inbounds C[ind:bitcache_size] = false
dumpbitcache(Bc, cind, C)
end
end
end
"""
broadcast!(f, dest, As...)
Like [`broadcast`](@ref), but store the result of
`broadcast(f, As...)` in the `dest` array.
Note that `dest` is only used to store the result, and does not supply
arguments to `f` unless it is also listed in the `As`,
as in `broadcast!(f, A, A, B)` to perform `A[:] = broadcast(f, A, B)`.
"""
@inline broadcast!(f, C::AbstractArray, A, Bs::Vararg{Any,N}) where {N} =
_broadcast!(f, C, A, Bs...)
# This indirection allows size-dependent implementations (e.g., see the copying `identity`
# specialization above)
@inline function _broadcast!(f, C, A, Bs::Vararg{Any,N}) where N
shape = broadcast_indices(C)
@boundscheck check_broadcast_indices(shape, A, Bs...)
keeps, Idefaults = map_newindexer(shape, A, Bs)
iter = CartesianRange(shape)
_broadcast!(f, C, keeps, Idefaults, A, Bs, Val(N), iter)
return C
end
# broadcast with element type adjusted on-the-fly. This widens the element type of
# B as needed (allocating a new container and copying previously-computed values) to
# accommodate any incompatible new elements.
@generated function _broadcast!(f, B::AbstractArray, keeps::K, Idefaults::ID, As::AT, ::Val{nargs}, iter, st, count) where {K,ID,AT,nargs}
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])
while !done(iter, st)
I, st = next(iter, st)
# reverse-broadcast the indices
@nexprs $nargs i->(I_i = newindex(I, keep_i, Idefault_i))
# extract array values
@nexprs $nargs i->(@inbounds val_i = _broadcast_getindex(A_i, I_i))
# call the function
V = @ncall $nargs f val
S = typeof(V)
# store the result
if S <: eltype(B)
@inbounds B[I] = V
else
# This element type doesn't fit in B. Allocate a new B with wider eltype,
# copy over old values, and continue
newB = Base.similar(B, typejoin(eltype(B), S))
for II in Iterators.take(iter, count)
newB[II] = B[II]
end
newB[I] = V
return _broadcast!(f, newB, keeps, Idefaults, As, Val(nargs), iter, st, count+1)
end
count += 1
end
return B
end
end
maptoTuple(f) = Tuple{}
maptoTuple(f, a, b...) = Tuple{f(a), maptoTuple(f, b...).types...}
# An element type satisfying for all A:
# broadcast_getindex(
# combine_styles(A),
# A, broadcast_indices(A)
# )::_broadcast_getindex_eltype(A)
_broadcast_getindex_eltype(A) = _broadcast_getindex_eltype(combine_styles(A), A)
_broadcast_getindex_eltype(::Scalar, ::Type{T}) where T = Type{T}
_broadcast_getindex_eltype(::Union{Unknown,Scalar,Style{Nullable}}, A) = typeof(A)
_broadcast_getindex_eltype(::BroadcastStyle, A) = eltype(A) # Tuple, Array, etc.
# An element type satisfying for all A:
# unsafe_get(A)::unsafe_get_eltype(A)
_unsafe_get_eltype(x::Nullable) = eltype(x)
_unsafe_get_eltype(::Type{T}) where T = Type{T}
_unsafe_get_eltype(x) = typeof(x)
# Inferred eltype of result of broadcast(f, xs...)
combine_eltypes(f, A, As...) =
Base._return_type(f, maptoTuple(_broadcast_getindex_eltype, A, As...))
_nullable_eltype(f, A, As...) =
Base._return_type(f, maptoTuple(_unsafe_get_eltype, A, As...))
"""
broadcast(f, As...)
Broadcasts the arrays, tuples, `Ref`s, nullables, and/or scalars `As` to a
container of the appropriate type and dimensions. In this context, anything
that is not a subtype of `AbstractArray`, `Ref` (except for `Ptr`s), `Tuple`,
or `Nullable` is considered a scalar. The resulting container is established by
the following rules:
- If all the arguments are scalars, it returns a scalar.
- If the arguments are tuples and zero or more scalars, it returns a tuple.
- If the arguments contain at least one array or `Ref`, it returns an array
(expanding singleton dimensions), and treats `Ref`s as 0-dimensional arrays,
and tuples as 1-dimensional arrays.
The following additional rule applies to `Nullable` arguments: If there is at
least one `Nullable`, and all the arguments are scalars or `Nullable`, it
returns a `Nullable` treating `Nullable`s as "containers".
A special syntax exists for broadcasting: `f.(args...)` is equivalent to
`broadcast(f, args...)`, and nested `f.(g.(args...))` calls are fused into a
single broadcast loop.
# Examples
```jldoctest
julia> A = [1, 2, 3, 4, 5]
5-element Array{Int64,1}:
1
2
3
4
5
julia> B = [1 2; 3 4; 5 6; 7 8; 9 10]
5×2 Array{Int64,2}:
1 2
3 4
5 6
7 8
9 10
julia> broadcast(+, A, B)
5×2 Array{Int64,2}:
2 3
5 6
8 9
11 12
14 15
julia> parse.(Int, ["1", "2"])
2-element Array{Int64,1}:
1
2
julia> abs.((1, -2))
(1, 2)
julia> broadcast(+, 1.0, (0, -2.0))
(1.0, -1.0)
julia> broadcast(+, 1.0, (0, -2.0), Ref(1))
2-element Array{Float64,1}:
2.0
0.0
julia> (+).([[0,2], [1,3]], Ref{Vector{Int}}([1,-1]))
2-element Array{Array{Int64,1},1}:
[1, 1]
[2, 2]
julia> string.(("one","two","three","four"), ": ", 1:4)
4-element Array{String,1}:
"one: 1"
"two: 2"
"three: 3"
"four: 4"
julia> Nullable("X") .* "Y"
Nullable{String}("XY")
julia> broadcast(/, 1.0, Nullable(2.0))
Nullable{Float64}(0.5)
julia> (1 + im) ./ Nullable{Int}()
Nullable{Complex{Float64}}()
```
"""
@inline broadcast(f, A, Bs...) =
broadcast(f, combine_styles(A, Bs...), nothing, nothing, A, Bs...)
@inline broadcast(f, s::BroadcastStyle, ::Void, ::Void, A, Bs...) =
broadcast(f, s, combine_eltypes(f, A, Bs...), combine_indices(A, Bs...),
A, Bs...)
const NonleafHandlingTypes = Union{DefaultArrayStyle,ArrayConflict}
@inline function broadcast(f, s::NonleafHandlingTypes, ::Type{ElType}, inds::Indices, As...) where ElType
if !Base._isleaftype(ElType)
return broadcast_nonleaf(f, s, ElType, inds, As...)
end
dest = broadcast_similar(f, s, ElType, inds, As...)
broadcast!(f, dest, As...)
end
@inline function broadcast(f, s::BroadcastStyle, ::Type{ElType}, inds::Indices, As...) where ElType
dest = broadcast_similar(f, s, ElType, inds, As...)
broadcast!(f, dest, As...)
end
# When ElType is not concrete, use narrowing. Use the first element of each input to determine
# the starting output eltype; the _broadcast! method will widen `dest` as needed to
# accommodate later values.
function broadcast_nonleaf(f, s::NonleafHandlingTypes, ::Type{ElType}, shape::Indices, As...) where ElType
nargs = length(As)
iter = CartesianRange(shape)
if isempty(iter)
return Base.similar(Array{ElType}, shape)
end
keeps, Idefaults = map_newindexer(shape, As)
st = start(iter)
I, st = next(iter, st)
val = f([ _broadcast_getindex(As[i], newindex(I, keeps[i], Idefaults[i])) for i=1:nargs ]...)
if val isa Bool
dest = Base.similar(BitArray, shape)
else
dest = Base.similar(Array{typeof(val)}, shape)
end
dest[I] = val
return _broadcast!(f, dest, keeps, Idefaults, As, Val(nargs), iter, st, 1)
end
@inline function broadcast(f, ::Style{Nullable}, ::Void, ::Void, a...)
nonnull = all(hasvalue, a)
S = _nullable_eltype(f, a...)
if Base._isleaftype(S) && null_safe_op(f, maptoTuple(_unsafe_get_eltype,
a...).types...)
Nullable{S}(f(map(unsafe_get, a)...), nonnull)
else
if nonnull
Nullable(f(map(unsafe_get, a)...))
else
Nullable{nullable_returntype(S)}()
end
end
end
broadcast(f, ::Union{Scalar,Unknown}, ::Void, ::Void, a...) = f(a...)
@inline broadcast(f, ::Style{Tuple}, ::Void, ::Void, A, Bs...) =
tuplebroadcast(f, first_tuple(A, Bs...), A, Bs...)
@inline tuplebroadcast(f, ::NTuple{N,Any}, As...) where {N} =
ntuple(k -> f(tuplebroadcast_getargs(As, k)...), Val(N))
@inline tuplebroadcast(f, ::NTuple{N,Any}, ::Type{T}, As...) where {N,T} =
ntuple(k -> f(T, tuplebroadcast_getargs(As, k)...), Val(N))
first_tuple(A::Tuple, Bs...) = A
first_tuple(A, Bs...) = first_tuple(Bs...)
tuplebroadcast_getargs(::Tuple{}, k) = ()
@inline tuplebroadcast_getargs(As, k) =
(_broadcast_getindex(first(As), k), tuplebroadcast_getargs(tail(As), k)...)
"""
broadcast_getindex(A, inds...)
Broadcasts the `inds` arrays to a common size like [`broadcast`](@ref)
and returns an array of the results `A[ks...]`,
where `ks` goes over the positions in the broadcast result `A`.
# Examples
```jldoctest
julia> A = [1, 2, 3, 4, 5]
5-element Array{Int64,1}:
1
2
3
4
5
julia> B = [1 2; 3 4; 5 6; 7 8; 9 10]
5×2 Array{Int64,2}:
1 2
3 4
5 6
7 8
9 10
julia> C = broadcast(+,A,B)
5×2 Array{Int64,2}:
2 3
5 6
8 9
11 12
14 15
julia> broadcast_getindex(C,[1,2,10])
3-element Array{Int64,1}:
2
5
15
```
"""
broadcast_getindex(src::AbstractArray, I::AbstractArray...) =
broadcast_getindex!(Base.similar(Array{eltype(src)}, combine_indices(I...)),
src,
I...)
@generated function broadcast_getindex!(dest::AbstractArray, src::AbstractArray, I::AbstractArray...)
N = length(I)
Isplat = Expr[:(I[$d]) for d = 1:N]
quote
@nexprs $N d->(I_d = I[d])
check_broadcast_indices(Base.indices(dest), $(Isplat...)) # unnecessary if this function is never called directly
checkbounds(src, $(Isplat...))
@nexprs $N d->(@nexprs $N k->(Ibcast_d_k = Base.indices(I_k, d) == OneTo(1)))
@nloops $N i dest d->(@nexprs $N k->(j_d_k = Ibcast_d_k ? 1 : i_d)) begin
@nexprs $N k->(@inbounds J_k = @nref $N I_k d->j_d_k)
@inbounds (@nref $N dest i) = (@nref $N src J)
end
dest
end
end
"""
broadcast_setindex!(A, X, inds...)
Broadcasts the `X` and `inds` arrays to a common size and stores the value from each
position in `X` at the indices in `A` given by the same positions in `inds`.
"""
@generated function broadcast_setindex!(A::AbstractArray, x, I::AbstractArray...)
N = length(I)
Isplat = Expr[:(I[$d]) for d = 1:N]
quote
@nexprs $N d->(I_d = I[d])
checkbounds(A, $(Isplat...))
shape = combine_indices($(Isplat...))
@nextract $N shape d->(length(shape) < d ? OneTo(1) : shape[d])
@nexprs $N d->(@nexprs $N k->(Ibcast_d_k = Base.indices(I_k, d) == 1:1))
if !isa(x, AbstractArray)
xA = convert(eltype(A), x)
@nloops $N i d->shape_d d->(@nexprs $N k->(j_d_k = Ibcast_d_k ? 1 : i_d)) begin
@nexprs $N k->(@inbounds J_k = @nref $N I_k d->j_d_k)
@inbounds (@nref $N A J) = xA
end
else
X = x
@nexprs $N d->(shapelen_d = length(shape_d))
@ncall $N Base.setindex_shape_check X shapelen
Xstate = start(X)
@inbounds @nloops $N i d->shape_d d->(@nexprs $N k->(j_d_k = Ibcast_d_k ? 1 : i_d)) begin
@nexprs $N k->(J_k = @nref $N I_k d->j_d_k)
x_el, Xstate = next(X, Xstate)
(@nref $N A J) = x_el
end
end
A
end
end
############################################################
# x[...] .= f.(y...) ---> broadcast!(f, dotview(x, ...), y...).
# The dotview function defaults to getindex, but we override it in
# a few cases to get the expected in-place behavior without affecting
# explicit calls to view. (All of this can go away if slices
# are changed to generate views by default.)
Base.@propagate_inbounds dotview(args...) = Base.maybeview(args...)
############################################################
# The parser turns @. into a call to the __dot__ macro,
# which converts all function calls and assignments into
# broadcasting "dot" calls/assignments:
dottable(x) = false # avoid dotting spliced objects (e.g. view calls inserted by @view)
dottable(x::Symbol) = !isoperator(x) || first(string(x)) != '.' || x == :.. # don't add dots to dot operators
dottable(x::Expr) = x.head != :$
undot(x) = x
function undot(x::Expr)
if x.head == :.=
Expr(:(=), x.args...)
elseif x.head == :block # occurs in for x=..., y=...
Expr(:block, map(undot, x.args)...)
else
x
end
end
__dot__(x) = x
function __dot__(x::Expr)
dotargs = map(__dot__, x.args)
if x.head == :call && dottable(x.args[1])
Expr(:., dotargs[1], Expr(:tuple, dotargs[2:end]...))
elseif x.head == :$
x.args[1]
elseif x.head == :let # don't add dots to `let x=...` assignments
Expr(:let, undot(dotargs[1]), dotargs[2])
elseif x.head == :for # don't add dots to for x=... assignments
Expr(:for, undot(dotargs[1]), dotargs[2])
elseif (x.head == :(=) || x.head == :function || x.head == :macro) &&
Meta.isexpr(x.args[1], :call) # function or macro definition
Expr(x.head, x.args[1], dotargs[2])
else
head = string(x.head)
if last(head) == '=' && first(head) != '.'
Expr(Symbol('.',head), dotargs...)
else
Expr(x.head, dotargs...)
end
end
end
"""
@. expr
Convert every function call or operator in `expr` into a "dot call"
(e.g. convert `f(x)` to `f.(x)`), and convert every assignment in `expr`
to a "dot assignment" (e.g. convert `+=` to `.+=`).
If you want to *avoid* adding dots for selected function calls in
`expr`, splice those function calls in with `\$`. For example,
`@. sqrt(abs(\$sort(x)))` is equivalent to `sqrt.(abs.(sort(x)))`
(no dot for `sort`).
(`@.` is equivalent to a call to `@__dot__`.)
# Examples
```jldoctest
julia> x = 1.0:3.0; y = similar(x);
julia> @. y = x + 3 * sin(x)
3-element Array{Float64,1}:
3.5244129544236893
4.727892280477045
3.4233600241796016
```
"""
macro __dot__(x)
esc(__dot__(x))
end
end # module