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Customizable lazy fused broadcasting in pure Julia
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This patch represents the combined efforts of four individuals, over 60
commits, and an iterated design over (at least) three pull requests that
spanned nearly an entire year (closes #22063, #23692, #25377 by superceding
them).

This introduces a pure Julia data structure that represents a fused broadcast
expression.  For example, the expression `2 .* (x .+ 1)` lowers to:

```julia
julia> Meta.@lower 2 .* (x .+ 1)
:($(Expr(:thunk, CodeInfo(:(begin
      Core.SSAValue(0) = (Base.getproperty)(Base.Broadcast, :materialize)
      Core.SSAValue(1) = (Base.getproperty)(Base.Broadcast, :make)
      Core.SSAValue(2) = (Base.getproperty)(Base.Broadcast, :make)
      Core.SSAValue(3) = (Core.SSAValue(2))(+, x, 1)
      Core.SSAValue(4) = (Core.SSAValue(1))(*, 2, Core.SSAValue(3))
      Core.SSAValue(5) = (Core.SSAValue(0))(Core.SSAValue(4))
      return Core.SSAValue(5)
  end)))))
```

Or, slightly more readably as:

```julia
using .Broadcast: materialize, make
materialize(make(*, 2, make(+, x, 1)))
```

The `Broadcast.make` function serves two purposes. Its primary purpose is to
construct the `Broadcast.Broadcasted` objects that hold onto the function, the
tuple of arguments (potentially including nested `Broadcasted` arguments), and
sometimes a set of `axes` to include knowledge of the outer shape. The
secondary purpose, however, is to allow an "out" for objects that _don't_ want
to participate in fusion. For example, if `x` is a range in the above `2 .* (x
.+ 1)` expression, it needn't allocate an array and operate elementwise — it
can just compute and return a new range. Thus custom structures are able to
specialize `Broadcast.make(f, args...)` just as they'd specialize on `f`
normally to return an immediate result.

`Broadcast.materialize` is identity for everything _except_ `Broadcasted`
objects for which it allocates an appropriate result and computes the
broadcast. It does two things: it `initialize`s the outermost `Broadcasted`
object to compute its axes and then `copy`s it.

Similarly, an in-place fused broadcast like `y .= 2 .* (x .+ 1)` uses the exact
same expression tree to compute the right-hand side of the expression as above,
and then uses `materialize!(y, make(*, 2, make(+, x, 1)))` to `instantiate` the
`Broadcasted` expression tree and then `copyto!` it into the given destination.

All-together, this forms a complete API for custom types to extend and
customize the behavior of broadcast (fixes #22060). It uses the existing
`BroadcastStyle`s throughout to simplify dispatch on many arguments:

* Custom types can opt-out of broadcast fusion by specializing
  `Broadcast.make(f, args...)` or `Broadcast.make(::BroadcastStyle, f, args...)`.

* The `Broadcasted` object computes and stores the type of the combined
  `BroadcastStyle` of its arguments as its first type parameter, allowing for
  easy dispatch and specialization.

* Custom Broadcast storage is still allocated via `broadcast_similar`, however
  instead of passing just a function as a first argument, the entire
  `Broadcasted` object is passed as a final argument. This potentially allows
  for much more runtime specialization dependent upon the exact expression
  given.

* Custom broadcast implmentations for a `CustomStyle` are defined by
  specializing `copy(bc::Broadcasted{CustomStyle})` or
  `copyto!(dest::AbstractArray, bc::Broadcasted{CustomStyle})`.

* Fallback broadcast specializations for a given output object of type `Dest`
  (for the `DefaultArrayStyle` or another such style that hasn't implemented
  assignments into such an object) are defined by specializing
  `copyto(dest::Dest, bc::Broadcasted{Nothing})`.

As it fully supports range broadcasting, this now deprecates `(1:5) + 2` to
`.+`, just as had been done for all `AbstractArray`s in general.

As a first-mover proof of concept, LinearAlgebra uses this new system to
improve broadcasting over structured arrays. Before, broadcasting over a
structured matrix would result in a sparse array. Now, broadcasting over a
structured matrix will _either_ return an appropriately structured matrix _or_
a dense array. This does incur a type instability (in the form of a
discriminated union) in some situations, but thanks to type-based introspection
of the `Broadcasted` wrapper commonly used functions can be special cased to be
type stable.  For example:

```julia
julia> f(d) = round.(Int, d)
f (generic function with 1 method)

julia> @inferred f(Diagonal(rand(3)))
3×3 Diagonal{Int64,Array{Int64,1}}:
 0  ⋅  ⋅
 ⋅  0  ⋅
 ⋅  ⋅  1

julia> @inferred Diagonal(rand(3)) .* 3
ERROR: return type Diagonal{Float64,Array{Float64,1}} does not match inferred return type Union{Array{Float64,2}, Diagonal{Float64,Array{Float64,1}}}
Stacktrace:
 [1] error(::String) at ./error.jl:33
 [2] top-level scope

julia> @inferred Diagonal(1:4) .+ Bidiagonal(rand(4), rand(3), 'U') .* Tridiagonal(1:3, 1:4, 1:3)
4×4 Tridiagonal{Float64,Array{Float64,1}}:
 1.30771  0.838589   ⋅          ⋅
 0.0      3.89109   0.0459757   ⋅
  ⋅       0.0       4.48033    2.51508
  ⋅        ⋅        0.0        6.23739
```

In addition to the issues referenced above, it fixes:

* Fixes #19313, #22053, #23445, and #24586: Literals are no longer treated
  specially in a fused broadcast; they're just arguments in a `Broadcasted`
  object like everything else.

* Fixes #21094: Since broadcasting is now represented by a pure Julia
  datastructure it can be created within `@generated` functions and serialized.

* Fixes #26097: The fallback destination-array specialization method of
  `copyto!` is specifically implemented as `Broadcasted{Nothing}` and will not
  be confused by `nothing` arguments.

* Fixes the broadcast-specific element of #25499: The default base broadcast
  implementation no longer depends upon `Base._return_type` to allocate its
  array (except in the empty or concretely-type cases). Note that the sparse
  implementation (#19595) is still dependent upon inference and is _not_ fixed.

* Fixes #25340: Functions are treated like normal values just like arguments
  and only evaluated once.

* Fixes #22255, and is performant with 12+ fused broadcasts. Okay, that one was
  fixed on master already, but this fixes it now, too.

* Fixes #25521.

* The performance of this patch has been thoroughly tested through its
  iterative development process in #25377. There remain [two classes of
  performance regressions](#25377) that Nanosoldier flagged.

* #25691: Propagation of constant literals sill lose their constant-ness upon
  going through the broadcast machinery. I believe quite a large number of
  functions would need to be marked as `@pure` to support this -- including
  functions that are intended to be specialized.

(For bookkeeping, this is the squashed version of the [teh-jn/lazydotfuse](#25377)
branch as of a1d4e7e. Squashed and separated
out to make it easier to review and commit)

Co-authored-by: Tim Holy <[email protected]>
Co-authored-by: Jameson Nash <[email protected]>
Co-authored-by: Andrew Keller <[email protected]>
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4 people committed Apr 23, 2018
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13 changes: 8 additions & 5 deletions NEWS.md
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Original file line number Diff line number Diff line change
Expand Up @@ -388,11 +388,6 @@ This section lists changes that do not have deprecation warnings.
Its return value has been removed. Use the `process_running` function
to determine if a process has already exited.

* Broadcasting has been redesigned with an extensible public interface. The new API is
documented at https://docs.julialang.org/en/latest/manual/interfaces/#Interfaces-1.
`AbstractArray` types that specialized broadcasting using the old internal API will
need to switch to the new API. ([#20740])

* The logging system has been redesigned - `info` and `warn` are deprecated
and replaced with the logging macros `@info`, `@warn`, `@debug` and
`@error`. The `logging` function is also deprecated and replaced with
Expand All @@ -418,6 +413,14 @@ This section lists changes that do not have deprecation warnings.
* `findn(x::AbstractArray)` has been deprecated in favor of `findall(!iszero, x)`, which
now returns cartesian indices for multidimensional arrays (see below, [#25532]).

* Broadcasting operations are no longer fused into a single operation by Julia's parser.
Instead, a lazy `Broadcasted` wrapper is created, and the parser will call
`copy(bc::Broadcasted)` or `copyto!(dest, bc::Broadcasted)`
to evaluate the wrapper. Consequently, package authors generally need to specialize
`copy` and `copyto!` methods rather than `broadcast` and `broadcast!`.
See the [Interfaces chapter](https://docs.julialang.org/en/latest/manual/interfaces/#Interfaces-1)
for more information.

* `find` has been renamed to `findall`. `findall`, `findfirst`, `findlast`, `findnext`
now take and/or return the same type of indices as `keys`/`pairs` for `AbstractArray`,
`AbstractDict`, `AbstractString`, `Tuple` and `NamedTuple` objects ([#24774], [#25545]).
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40 changes: 0 additions & 40 deletions base/bitarray.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -1097,19 +1097,6 @@ function (-)(B::BitArray)
end
broadcast(::typeof(sign), B::BitArray) = copy(B)

function broadcast(::typeof(~), B::BitArray)
C = similar(B)
Bc = B.chunks
if !isempty(Bc)
Cc = C.chunks
for i = 1:length(Bc)
Cc[i] = ~Bc[i]
end
Cc[end] &= _msk_end(B)
end
return C
end

"""
flipbits!(B::BitArray{N}) -> BitArray{N}
Expand Down Expand Up @@ -1166,33 +1153,6 @@ end
(/)(B::BitArray, x::Number) = (/)(Array(B), x)
(/)(x::Number, B::BitArray) = (/)(x, Array(B))

# broadcast specializations for &, |, and xor/⊻
broadcast(::typeof(&), B::BitArray, x::Bool) = x ? copy(B) : falses(size(B))
broadcast(::typeof(&), x::Bool, B::BitArray) = broadcast(&, B, x)
broadcast(::typeof(|), B::BitArray, x::Bool) = x ? trues(size(B)) : copy(B)
broadcast(::typeof(|), x::Bool, B::BitArray) = broadcast(|, B, x)
broadcast(::typeof(xor), B::BitArray, x::Bool) = x ? .~B : copy(B)
broadcast(::typeof(xor), x::Bool, B::BitArray) = broadcast(xor, B, x)
for f in (:&, :|, :xor)
@eval begin
function broadcast(::typeof($f), A::BitArray, B::BitArray)
F = BitArray(undef, promote_shape(size(A),size(B))...)
Fc = F.chunks
Ac = A.chunks
Bc = B.chunks
(isempty(Ac) || isempty(Bc)) && return F
for i = 1:length(Fc)
Fc[i] = ($f)(Ac[i], Bc[i])
end
Fc[end] &= _msk_end(F)
return F
end
broadcast(::typeof($f), A::DenseArray{Bool}, B::BitArray) = broadcast($f, BitArray(A), B)
broadcast(::typeof($f), B::BitArray, A::DenseArray{Bool}) = broadcast($f, B, BitArray(A))
end
end


## promotion to complex ##

# TODO?
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