forked from JuliaLang/julia
-
Notifications
You must be signed in to change notification settings - Fork 0
/
broadcast.jl
1370 lines (1167 loc) · 60.1 KB
/
broadcast.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
# This file is a part of Julia. License is MIT: https://julialang.org/license
"""
Base.Broadcast
Module containing the broadcasting implementation.
"""
module Broadcast
using .Base.Cartesian
using .Base: Indices, OneTo, tail, to_shape, isoperator, promote_typejoin, promote_typejoin_union,
_msk_end, unsafe_bitgetindex, bitcache_chunks, bitcache_size, dumpbitcache, unalias, negate
import .Base: copy, copyto!, axes
export broadcast, broadcast!, BroadcastStyle, broadcast_axes, broadcastable, dotview, @__dot__, BroadcastFunction
## Computing the result's axes: deprecated name
const broadcast_axes = axes
### 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 [`similar`](@ref)) operating on
`Broadcasted{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
struct Unknown <: BroadcastStyle end
BroadcastStyle(::Type{Union{}}, slurp...) = Unknown() # ambiguity resolution
"""
`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}()
"""
struct Style{T} <: BroadcastStyle end
BroadcastStyle(::Type{<:Tuple}) = Style{Tuple}()
"""
`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`](@ref) 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
ArrayStyle{A}(::Val) where A = ArrayStyle{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` "loses" to any other [`Broadcast.ArrayStyle`](@ref).
"""
struct DefaultArrayStyle{N} <: AbstractArrayStyle{N} end
DefaultArrayStyle(::Val{N}) where N = DefaultArrayStyle{N}()
DefaultArrayStyle{M}(::Val{N}) where {N,M} = DefaultArrayStyle{N}()
const DefaultVectorStyle = DefaultArrayStyle{1}
const DefaultMatrixStyle = DefaultArrayStyle{2}
BroadcastStyle(::Type{<:AbstractArray{T,N}}) where {T,N} = DefaultArrayStyle{N}()
BroadcastStyle(::Type{T}) where {T} = DefaultArrayStyle{ndims(T)}()
# `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
ArrayConflict(::Val) = ArrayConflict()
### Binary BroadcastStyle rules
"""
BroadcastStyle(::Style1, ::Style2) = Style3()
Indicate how to resolve different `BroadcastStyle`s. For example,
BroadcastStyle(::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(a::AbstractArrayStyle{0}, b::Style{Tuple}) = b
BroadcastStyle(a::AbstractArrayStyle, ::Style{Tuple}) = a
BroadcastStyle(::A, ::A) where A<:ArrayStyle = A()
BroadcastStyle(::ArrayStyle, ::ArrayStyle) = Unknown()
BroadcastStyle(::A, ::A) where A<:AbstractArrayStyle = A()
function BroadcastStyle(a::A, b::B) where {A<:AbstractArrayStyle{M},B<:AbstractArrayStyle{N}} where {M,N}
if Base.typename(A) === Base.typename(B)
return A(Val(max(M, N)))
end
return 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)(Val(max(M, N)))
### Lazy-wrapper for broadcasting
# `Broadcasted` wrap the arguments to `broadcast(f, args...)`. A statement like
# y = x .* (x .+ 1)
# will result in code that is essentially
# y = copy(Broadcasted(*, x, Broadcasted(+, x, 1)))
# `broadcast!` results in `copyto!(dest, Broadcasted(...))`.
# The use of `Nothing` in place of a `BroadcastStyle` has a different
# application, in the fallback method
# copyto!(dest, bc::Broadcasted) = copyto!(dest, convert(Broadcasted{Nothing}, bc))
# This allows methods
# copyto!(dest::DestType, bc::Broadcasted{Nothing})
# that specialize on `DestType` to be easily disambiguated from
# methods that instead specialize on `BroadcastStyle`,
# copyto!(dest::AbstractArray, bc::Broadcasted{MyStyle})
struct Broadcasted{Style<:Union{Nothing,BroadcastStyle}, Axes, F, Args<:Tuple} <: Base.AbstractBroadcasted
style::Style
f::F
args::Args
axes::Axes # the axes of the resulting object (may be bigger than implied by `args` if this is nested inside a larger `Broadcasted`)
Broadcasted(style::Union{Nothing,BroadcastStyle}, f::Tuple, args::Tuple) = error() # disambiguation: tuple is not callable
function Broadcasted(style::Union{Nothing,BroadcastStyle}, f::F, args::Tuple, axes=nothing) where {F}
# using Core.Typeof rather than F preserves inferrability when f is a type
return new{typeof(style), typeof(axes), Core.Typeof(f), typeof(args)}(style, f, args, axes)
end
function Broadcasted(f::F, args::Tuple, axes=nothing) where {F}
Broadcasted(combine_styles(args...)::BroadcastStyle, f, args, axes)
end
function Broadcasted{Style}(f::F, args, axes=nothing) where {Style, F}
return new{Style, typeof(axes), Core.Typeof(f), typeof(args)}(Style()::Style, f, args, axes)
end
function Broadcasted{Style,Axes,F,Args}(f, args, axes) where {Style,Axes,F,Args}
return new{Style, Axes, F, Args}(Style()::Style, f, args, axes)
end
end
struct AndAnd end
const andand = AndAnd()
broadcasted(::AndAnd, a, b) = broadcasted((a, b) -> a && b, a, b)
function broadcasted(::AndAnd, a, bc::Broadcasted)
bcf = flatten(bc)
broadcasted((a, args...) -> a && bcf.f(args...), a, bcf.args...)
end
struct OrOr end
const oror = OrOr()
broadcasted(::OrOr, a, b) = broadcasted((a, b) -> a || b, a, b)
function broadcasted(::OrOr, a, bc::Broadcasted)
bcf = flatten(bc)
broadcasted((a, args...) -> a || bcf.f(args...), a, bcf.args...)
end
Base.convert(::Type{Broadcasted{NewStyle}}, bc::Broadcasted{<:Any,Axes,F,Args}) where {NewStyle,Axes,F,Args} =
Broadcasted{NewStyle,Axes,F,Args}(bc.f, bc.args, bc.axes)::Broadcasted{NewStyle,Axes,F,Args}
function Base.show(io::IO, bc::Broadcasted{Style}) where {Style}
print(io, Broadcasted)
# Only show the style parameter if we have a set of axes — representing an instantiated
# "outermost" Broadcasted. The styles of nested Broadcasteds represent an intermediate
# computation that is not relevant for dispatch, confusing, and just extra line noise.
bc.axes isa Tuple && print(io, "{", Style, "}")
print(io, "(", bc.f, ", ", bc.args, ")")
nothing
end
## Allocating the output container
Base.similar(bc::Broadcasted, ::Type{T}) where {T} = similar(bc, T, axes(bc))
Base.similar(::Broadcasted{DefaultArrayStyle{N}}, ::Type{ElType}, dims) where {N,ElType} =
similar(Array{ElType}, dims)
Base.similar(::Broadcasted{DefaultArrayStyle{N}}, ::Type{Bool}, dims) where N =
similar(BitArray, dims)
# In cases of conflict we fall back on Array
Base.similar(::Broadcasted{ArrayConflict}, ::Type{ElType}, dims) where ElType =
similar(Array{ElType}, dims)
Base.similar(::Broadcasted{ArrayConflict}, ::Type{Bool}, dims) =
similar(BitArray, dims)
@inline Base.axes(bc::Broadcasted) = _axes(bc, bc.axes)
_axes(::Broadcasted, axes::Tuple) = axes
@inline _axes(bc::Broadcasted, ::Nothing) = combine_axes(bc.args...)
_axes(bc::Broadcasted{<:AbstractArrayStyle{0}}, ::Nothing) = ()
@inline Base.axes(bc::Broadcasted{<:Any, <:NTuple{N}}, d::Integer) where N =
d <= N ? axes(bc)[d] : OneTo(1)
BroadcastStyle(::Type{<:Broadcasted{Style}}) where {Style} = Style()
BroadcastStyle(::Type{<:Broadcasted{S}}) where {S<:Union{Nothing,Unknown}} =
throw(ArgumentError("Broadcasted{Unknown} wrappers do not have a style assigned"))
argtype(::Type{BC}) where {BC<:Broadcasted} = fieldtype(BC, :args)
argtype(bc::Broadcasted) = argtype(typeof(bc))
@inline Base.eachindex(bc::Broadcasted) = _eachindex(axes(bc))
_eachindex(t::Tuple{Any}) = t[1]
_eachindex(t::Tuple) = CartesianIndices(t)
Base.IndexStyle(bc::Broadcasted) = IndexStyle(typeof(bc))
Base.IndexStyle(::Type{<:Broadcasted{<:Any,<:Tuple{Any}}}) = IndexLinear()
Base.IndexStyle(::Type{<:Broadcasted{<:Any}}) = IndexCartesian()
Base.LinearIndices(bc::Broadcasted{<:Any,<:Tuple{Any}}) = LinearIndices(axes(bc))::LinearIndices{1}
Base.ndims(bc::Broadcasted) = ndims(typeof(bc))
Base.ndims(::Type{<:Broadcasted{<:Any,<:NTuple{N,Any}}}) where {N} = N
Base.size(bc::Broadcasted) = map(length, axes(bc))
Base.length(bc::Broadcasted) = prod(size(bc))
function Base.iterate(bc::Broadcasted)
iter = eachindex(bc)
iterate(bc, (iter,))
end
Base.@propagate_inbounds function Base.iterate(bc::Broadcasted, s)
y = iterate(s...)
y === nothing && return nothing
i, newstate = y
return (bc[i], (s[1], newstate))
end
Base.IteratorSize(::Type{T}) where {T<:Broadcasted} = Base.HasShape{ndims(T)}()
Base.ndims(BC::Type{<:Broadcasted{<:Any,Nothing}}) = _maxndims(fieldtype(BC, :args))
Base.ndims(::Type{<:Broadcasted{<:AbstractArrayStyle{N},Nothing}}) where {N<:Integer} = N
_maxndims(::Type{T}) where {T<:Tuple} = reduce(max, ntuple(n -> (F = fieldtype(T, n); F <: Tuple ? 1 : ndims(F)), Base._counttuple(T)))
_maxndims(::Type{<:Tuple{T}}) where {T} = T <: Tuple ? 1 : ndims(T)
function _maxndims(::Type{<:Tuple{T, S}}) where {T, S}
return max(T <: Tuple ? 1 : ndims(T), S <: Tuple ? 1 : ndims(S))
end
Base.IteratorEltype(::Type{<:Broadcasted}) = Base.EltypeUnknown()
## Instantiation fills in the "missing" fields in Broadcasted.
instantiate(x) = x
"""
Broadcast.instantiate(bc::Broadcasted)
Construct and check the axes for the lazy Broadcasted object `bc`.
Custom [`BroadcastStyle`](@ref)s may override this default in cases where it is fast and easy
to compute and verify the resulting `axes` on-demand, leaving the `axis` field
of the `Broadcasted` object empty (populated with [`nothing`](@ref)).
"""
@inline function instantiate(bc::Broadcasted)
if bc.axes isa Nothing # Not done via dispatch to make it easier to extend instantiate(::Broadcasted{Style})
axes = combine_axes(bc.args...)
else
axes = bc.axes
check_broadcast_axes(axes, bc.args...)
end
return Broadcasted(bc.style, bc.f, bc.args, axes)
end
instantiate(bc::Broadcasted{<:AbstractArrayStyle{0}}) = bc
# Tuples don't need axes, but when they have axes (for .= assignment), we need to check them (#33020)
instantiate(bc::Broadcasted{Style{Tuple}, Nothing}) = bc
function instantiate(bc::Broadcasted{Style{Tuple}})
check_broadcast_axes(bc.axes, bc.args...)
return bc
end
## Flattening
"""
bcf = flatten(bc)
Create a "flat" representation of a lazy-broadcast operation.
From
f.(a, g.(b, c), d)
we produce the equivalent of
h.(a, b, c, d)
where
h(w, x, y, z) = f(w, g(x, y), z)
In terms of its internal representation,
Broadcasted(f, a, Broadcasted(g, b, c), d)
becomes
Broadcasted(h, a, b, c, d)
This is an optional operation that may make custom implementation of broadcasting easier in
some cases.
"""
function flatten(bc::Broadcasted)
isflat(bc) && return bc
# concatenate the nested arguments into {a, b, c, d}
args = cat_nested(bc)
# build a tuple of functions `makeargs`. Its elements take
# the whole "flat" argument list and and generate the appropriate
# input arguments for the broadcasted function `f`, e.g.,
# makeargs[1] = ((w, x, y, z)) -> w
# makeargs[2] = ((w, x, y, z)) -> g(x, y)
# makeargs[3] = ((w, x, y, z)) -> z
makeargs = make_makeargs(bc.args)
f = Base.maybeconstructor(bc.f)
newf = (args...) -> (@inline; f(prepare_args(makeargs, args)...))
return Broadcasted(bc.style, newf, args, bc.axes)
end
const NestedTuple = Tuple{<:Broadcasted,Vararg{Any}}
isflat(bc::Broadcasted) = _isflat(bc.args)
_isflat(args::NestedTuple) = false
_isflat(args::Tuple) = _isflat(tail(args))
_isflat(args::Tuple{}) = true
cat_nested(bc::Broadcasted) = cat_nested_args(bc.args)
cat_nested_args(::Tuple{}) = ()
cat_nested_args(t::Tuple{Any}) = cat_nested(t[1])
cat_nested_args(t::Tuple) = (cat_nested(t[1])..., cat_nested_args(tail(t))...)
cat_nested(a) = (a,)
"""
make_makeargs(t::Tuple) -> Tuple{Vararg{Function}}
Each element of `t` is one (consecutive) node in a broadcast tree.
The returned `Tuple` are functions which take in the (whole) flattened
list and generate the inputs for the corresponding broadcasted function.
"""
make_makeargs(args::Tuple) = _make_makeargs(args, 1)[1]
# We build `makeargs` by traversing the broadcast nodes recursively.
# note: `n` indicates the flattened index of the next unused argument.
@inline function _make_makeargs(args::Tuple, n::Int)
head, n = _make_makeargs1(args[1], n)
rest, n = _make_makeargs(tail(args), n)
(head, rest...), n
end
_make_makeargs(::Tuple{}, n::Int) = (), n
# A help struct to store the flattened index statically
struct Pick{N} <: Function end
(::Pick{N})(@nospecialize(args::Tuple)) where {N} = args[N]
# For flat nodes, we just consume one argument (n += 1), and return the "Pick" function
@inline _make_makeargs1(_, n::Int) = Pick{n}(), n + 1
# For nested nodes, we form the `makeargs1` based on the child `makeargs` (n += length(cat_nested(bc)))
@inline function _make_makeargs1(bc::Broadcasted, n::Int)
makeargs, n = _make_makeargs(bc.args, n)
f = Base.maybeconstructor(bc.f)
makeargs1 = (args::Tuple) -> (@inline; f(prepare_args(makeargs, args)...))
makeargs1, n
end
@inline prepare_args(makeargs::Tuple, @nospecialize(x::Tuple)) = (makeargs[1](x), prepare_args(tail(makeargs), x)...)
@inline prepare_args(makeargs::Tuple{Any}, @nospecialize(x::Tuple)) = (makeargs[1](x),)
prepare_args(::Tuple{}, ::Tuple) = ()
## Broadcasting utilities ##
## logic for deciding the BroadcastStyle
"""
combine_styles(cs...) -> BroadcastStyle
Decides which `BroadcastStyle` to use for any number of value arguments.
Uses [`BroadcastStyle`](@ref) to get the style for each argument, and uses
[`result_style`](@ref) to combine styles.
# Examples
```jldoctest
julia> Broadcast.combine_styles([1], [1 2; 3 4])
Base.Broadcast.DefaultArrayStyle{2}()
```
"""
function combine_styles end
combine_styles() = DefaultArrayStyle{0}()
combine_styles(c) = result_style(BroadcastStyle(typeof(c)))
function combine_styles(bc::Broadcasted)
bc.style isa Union{Nothing,Unknown} || return bc.style
throw(ArgumentError("Broadcasted{Unknown} wrappers do not have a style assigned"))
end
combine_styles(c1, c2) = result_style(combine_styles(c1), combine_styles(c2))
@inline combine_styles(c1, c2, cs...) = result_style(combine_styles(c1), combine_styles(c2, cs...))
"""
result_style(s1::BroadcastStyle[, s2::BroadcastStyle]) -> BroadcastStyle
Takes one or two `BroadcastStyle`s and combines them using [`BroadcastStyle`](@ref) to
determine a common `BroadcastStyle`.
# Examples
```jldoctest
julia> Broadcast.result_style(Broadcast.DefaultArrayStyle{0}(), Broadcast.DefaultArrayStyle{3}())
Base.Broadcast.DefaultArrayStyle{3}()
julia> Broadcast.result_style(Broadcast.Unknown(), Broadcast.DefaultArrayStyle{1}())
Base.Broadcast.DefaultArrayStyle{1}()
```
"""
function result_style end
result_style(s::BroadcastStyle) = s
function result_style(s1::S, s2::S) where S<:BroadcastStyle
s1 ≡ s2 ? s1 : error("inconsistent broadcast styles, custom rule needed")
end
# 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, s1::S, s2::S) where S<:BroadcastStyle = result_style(s1, s2)
@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_axes(As...) -> Tuple
Determine the result axes for broadcasting across all values in `As`.
```jldoctest
julia> Broadcast.combine_axes([1], [1 2; 3 4; 5 6])
(Base.OneTo(3), Base.OneTo(2))
julia> Broadcast.combine_axes(1, 1, 1)
()
```
"""
@inline combine_axes(A, B...) = broadcast_shape(axes(A), combine_axes(B...))
@inline combine_axes(A, B) = broadcast_shape(axes(A), axes(B))
combine_axes(A) = axes(A)
"""
broadcast_shape(As...) -> Tuple
Determine the result axes for broadcasting across all axes (size Tuples) in `As`.
```jldoctest
julia> Broadcast.broadcast_shape((1,2), (2,1))
(2, 2)
julia> Broadcast.broadcast_shape((1,), (1,5), (4,5,3))
(4, 5, 3)
```
"""
function broadcast_shape end
# 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; got a dimension with lengths $a and $b"))))
_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; got a dimension with lengths $a and $(length(b))")))
_bcs1(a, b::Integer) = _bcs1(b, a)
_bcs1(a, b) = _bcsm(b, a) ? axistype(b, a) : (_bcsm(a, b) ? axistype(a, b) : throw(DimensionMismatch("arrays could not be broadcast to a common size; got a dimension with lengths $(length(a)) and $(length(b))")))
# _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
# Ensure inferrability when dealing with axes of different AbstractUnitRange types
# (We may not want to define general promotion rules between, say, OneTo and Slice, but if
# we get here we know the axes are at least consistent for the purposes of broadcasting)
axistype(a::T, b::T) where T = a
axistype(a::OneTo, b::OneTo) = OneTo{Int}(a)
axistype(a, b) = UnitRange{Int}(a)
## 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
function check_broadcast_shape(::Tuple{}, Ashp::Tuple)
if any(ax -> length(ax) != 1, Ashp)
throw(DimensionMismatch("cannot broadcast array to have fewer non-singleton dimensions"))
end
nothing
end
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
@inline check_broadcast_axes(shp, A) = check_broadcast_shape(shp, axes(A))
# comparing many inputs
@inline function check_broadcast_axes(shp, A, As...)
check_broadcast_axes(shp, A)
check_broadcast_axes(shp, As...)
end
## Indexing manipulations
"""
newindex(argument, I)
newindex(I, keep, default)
Recompute index `I` such that it appropriately constrains broadcasted dimensions to the source.
Two methods are supported, both allowing for `I` to be specified as either a [`CartesianIndex`](@ref) or
an `Int`.
* `newindex(argument, I)` dynamically constrains `I` based upon the axes of `argument`.
* `newindex(I, keep, default)` constrains `I` using the pre-computed tuples `keeps` and `defaults`.
* `keep` is a tuple of `Bool`s, where `keep[d] == true` means that dimension `d` in `I` should be preserved as is
* `default` is a tuple of Integers, specifying what index to use in dimension `d` when `keep[d] == false`.
Any remaining indices in `I` beyond the length of the `keep` tuple are truncated. The `keep` and `default`
tuples may be created by `newindexer(argument)`.
"""
Base.@propagate_inbounds newindex(arg, I::CartesianIndex) = to_index(_newindex(axes(arg), I.I))
Base.@propagate_inbounds newindex(arg, I::Integer) = to_index(_newindex(axes(arg), (I,)))
Base.@propagate_inbounds _newindex(ax::Tuple, I::Tuple) = (ifelse(length(ax[1]) == 1, ax[1][1], I[1]), _newindex(tail(ax), tail(I))...)
Base.@propagate_inbounds _newindex(ax::Tuple{}, I::Tuple) = ()
Base.@propagate_inbounds _newindex(ax::Tuple, I::Tuple{}) = (ax[1][1], _newindex(tail(ax), ())...)
Base.@propagate_inbounds _newindex(ax::Tuple{}, I::Tuple{}) = ()
# If dot-broadcasting were already defined, this would be `ifelse.(keep, I, Idefault)`.
@inline newindex(I::CartesianIndex, keep, Idefault) = to_index(_newindex(I.I, keep, Idefault))
@inline newindex(i::Integer, keep::Tuple, idefault) = ifelse(keep[1], i, idefault[1])
@inline newindex(i::Integer, keep::Tuple{}, idefault) = CartesianIndex(())
@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
@inline _newindex(I::Tuple{}, keep, Idefault) = () # or I is shorter
@inline _newindex(I::Tuple{}, keep::Tuple{}, Idefault) = () # or both
# newindexer(A) generates `keep` and `Idefault` (for use by `newindex` above)
# for a particular array `A`; `shapeindexer` does so for its axes.
@inline newindexer(A) = shapeindexer(axes(A))
@inline shapeindexer(ax) = _newindexer(ax)
@inline _newindexer(indsA::Tuple{}) = (), ()
@inline function _newindexer(indsA::Tuple)
ind1 = indsA[1]
keep, Idefault = _newindexer(tail(indsA))
(Base.length(ind1)::Integer != 1, keep...), (first(ind1), Idefault...)
end
@inline function Base.getindex(bc::Broadcasted, Is::Vararg{Union{Integer,CartesianIndex},N}) where {N}
I = to_index(Base.IteratorsMD.flatten(Is))
@boundscheck checkbounds(bc, I)
@inbounds _broadcast_getindex(bc, I)
end
to_index(::Tuple{}) = CartesianIndex()
to_index(Is::Tuple{Any}) = Is[1]
to_index(Is::Tuple) = CartesianIndex(Is)
@inline Base.checkbounds(bc::Broadcasted, I::Union{Integer,CartesianIndex}) =
Base.checkbounds_indices(Bool, axes(bc), (I,)) || Base.throw_boundserror(bc, (I,))
"""
_broadcast_getindex(A, I)
Index into `A` with `I`, collapsing broadcasted indices to their singleton indices as appropriate.
"""
Base.@propagate_inbounds _broadcast_getindex(A::Union{Ref,AbstractArray{<:Any,0},Number}, I) = A[] # Scalar-likes can just ignore all indices
Base.@propagate_inbounds _broadcast_getindex(::Ref{Type{T}}, I) where {T} = T
# Tuples are statically known to be singleton or vector-like
Base.@propagate_inbounds _broadcast_getindex(A::Tuple{Any}, I) = A[1]
Base.@propagate_inbounds _broadcast_getindex(A::Tuple, I) = A[I[1]]
# Everything else falls back to dynamically dropping broadcasted indices based upon its axes
Base.@propagate_inbounds _broadcast_getindex(A, I) = A[newindex(A, I)]
# In some cases, it's more efficient to sort out which dimensions should be dropped
# ahead of time (often when the size checks aren't able to be lifted out of the loop).
# The Extruded struct computes that information ahead of time and stores it as a pair
# of tuples to optimize indexing later. This is most commonly needed for `Array` and
# other `AbstractArray` subtypes that wrap `Array` and dynamically ask it for its size.
struct Extruded{T, K, D}
x::T
keeps::K # A tuple of booleans, specifying which indices should be passed normally
defaults::D # A tuple of integers, specifying the index to use when keeps[i] is false (as defaults[i])
end
@inline axes(b::Extruded) = axes(b.x)
Base.@propagate_inbounds _broadcast_getindex(b::Extruded, i) = b.x[newindex(i, b.keeps, b.defaults)]
extrude(x::AbstractArray) = Extruded(x, newindexer(x)...)
extrude(x) = x
# For Broadcasted
Base.@propagate_inbounds function _broadcast_getindex(bc::Broadcasted{<:Any,<:Any,<:Any,<:Any}, I)
args = _getindex(bc.args, I)
return _broadcast_getindex_evalf(bc.f, args...)
end
# Hack around losing Type{T} information in the final args tuple. Julia actually
# knows (in `code_typed`) the _value_ of these types, statically displaying them,
# but inference is currently skipping inferring the type of the types as they are
# transiently placed in a tuple as the argument list is lispily constructed. These
# additional methods recover type stability when a `Type` appears in one of the
# first two arguments of a function.
Base.@propagate_inbounds function _broadcast_getindex(bc::Broadcasted{<:Any,<:Any,<:Any,<:Tuple{Ref{Type{T}},Vararg{Any}}}, I) where {T}
args = _getindex(tail(bc.args), I)
return _broadcast_getindex_evalf(bc.f, T, args...)
end
Base.@propagate_inbounds function _broadcast_getindex(bc::Broadcasted{<:Any,<:Any,<:Any,<:Tuple{Any,Ref{Type{T}},Vararg{Any}}}, I) where {T}
arg1 = _broadcast_getindex(bc.args[1], I)
args = _getindex(tail(tail(bc.args)), I)
return _broadcast_getindex_evalf(bc.f, arg1, T, args...)
end
Base.@propagate_inbounds function _broadcast_getindex(bc::Broadcasted{<:Any,<:Any,<:Any,<:Tuple{Ref{Type{T}},Ref{Type{S}},Vararg{Any}}}, I) where {T,S}
args = _getindex(tail(tail(bc.args)), I)
return _broadcast_getindex_evalf(bc.f, T, S, args...)
end
# Utilities for _broadcast_getindex
Base.@propagate_inbounds _getindex(args::Tuple, I) = (_broadcast_getindex(args[1], I), _getindex(tail(args), I)...)
Base.@propagate_inbounds _getindex(args::Tuple{Any}, I) = (_broadcast_getindex(args[1], I),)
Base.@propagate_inbounds _getindex(args::Tuple{}, I) = ()
@inline _broadcast_getindex_evalf(f::Tf, args::Vararg{Any,N}) where {Tf,N} = f(args...) # not propagate_inbounds
"""
Broadcast.broadcastable(x)
Return either `x` or an object like `x` such that it supports [`axes`](@ref), indexing, and its type supports [`ndims`](@ref).
If `x` supports iteration, the returned value should have the same `axes` and indexing
behaviors as [`collect(x)`](@ref).
If `x` is not an `AbstractArray` but it supports `axes`, indexing, and its type supports
`ndims`, then `broadcastable(::typeof(x))` may be implemented to just return itself.
Further, if `x` defines its own [`BroadcastStyle`](@ref), then it must define its
`broadcastable` method to return itself for the custom style to have any effect.
# Examples
```jldoctest
julia> Broadcast.broadcastable([1,2,3]) # like `identity` since arrays already support axes and indexing
3-element Vector{Int64}:
1
2
3
julia> Broadcast.broadcastable(Int) # Types don't support axes, indexing, or iteration but are commonly used as scalars
Base.RefValue{Type{Int64}}(Int64)
julia> Broadcast.broadcastable("hello") # Strings break convention of matching iteration and act like a scalar instead
Base.RefValue{String}("hello")
```
"""
broadcastable(x::Union{Symbol,AbstractString,Function,UndefInitializer,Nothing,RoundingMode,Missing,Val,Ptr,AbstractPattern,Pair,IO,CartesianIndex}) = Ref(x)
broadcastable(::Type{T}) where {T} = Ref{Type{T}}(T)
broadcastable(x::Union{AbstractArray,Number,AbstractChar,Ref,Tuple,Broadcasted}) = x
# Default to collecting iterables — which will error for non-iterables
broadcastable(x) = collect(x)
broadcastable(::Union{AbstractDict, NamedTuple}) = throw(ArgumentError("broadcasting over dictionaries and `NamedTuple`s is reserved"))
## Computation of inferred result type, for empty and concretely inferred cases only
_broadcast_getindex_eltype(bc::Broadcasted) = combine_eltypes(bc.f, bc.args)
_broadcast_getindex_eltype(A) = eltype(A) # Tuple, Array, etc.
eltypes(::Tuple{}) = Tuple{}
eltypes(t::Tuple{Any}) = Iterators.TupleOrBottom(_broadcast_getindex_eltype(t[1]))
eltypes(t::Tuple{Any,Any}) = Iterators.TupleOrBottom(_broadcast_getindex_eltype(t[1]), _broadcast_getindex_eltype(t[2]))
eltypes(t::Tuple) = (TT = eltypes(tail(t)); TT === Union{} ? Union{} : Iterators.TupleOrBottom(_broadcast_getindex_eltype(t[1]), TT.parameters...))
# eltypes(t::Tuple) = Iterators.TupleOrBottom(ntuple(i -> _broadcast_getindex_eltype(t[i]), Val(length(t)))...)
# Inferred eltype of result of broadcast(f, args...)
function combine_eltypes(f, args::Tuple)
argT = eltypes(args)
argT === Union{} && return Union{}
return promote_typejoin_union(Base._return_type(f, argT))
end
## Broadcasting core
"""
broadcast(f, As...)
Broadcast the function `f` over the arrays, tuples, collections, [`Ref`](@ref)s and/or scalars `As`.
Broadcasting applies the function `f` over the elements of the container arguments and the
scalars themselves in `As`. Singleton and missing dimensions are expanded to match the
extents of the other arguments by virtually repeating the value. By default, only a limited
number of types are considered scalars, including `Number`s, `String`s, `Symbol`s, `Type`s,
`Function`s and some common singletons like [`missing`](@ref) and [`nothing`](@ref). All other arguments are
iterated over or indexed into elementwise.
The resulting container type is established by the following rules:
- If all the arguments are scalars or zero-dimensional arrays, it returns an unwrapped scalar.
- If at least one argument is a tuple and all others are scalars or zero-dimensional arrays,
it returns a tuple.
- All other combinations of arguments default to returning an `Array`, but
custom container types can define their own implementation and promotion-like
rules to customize the result when they appear as arguments.
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 Vector{Int64}:
1
2
3
4
5
julia> B = [1 2; 3 4; 5 6; 7 8; 9 10]
5×2 Matrix{Int64}:
1 2
3 4
5 6
7 8
9 10
julia> broadcast(+, A, B)
5×2 Matrix{Int64}:
2 3
5 6
8 9
11 12
14 15
julia> parse.(Int, ["1", "2"])
2-element Vector{Int64}:
1
2
julia> abs.((1, -2))
(1, 2)
julia> broadcast(+, 1.0, (0, -2.0))
(1.0, -1.0)
julia> (+).([[0,2], [1,3]], Ref{Vector{Int}}([1,-1]))
2-element Vector{Vector{Int64}}:
[1, 1]
[2, 2]
julia> string.(("one","two","three","four"), ": ", 1:4)
4-element Vector{String}:
"one: 1"
"two: 2"
"three: 3"
"four: 4"
```
"""
broadcast(f::Tf, As...) where {Tf} = materialize(broadcasted(f, As...))
# special cases defined for performance
@inline broadcast(f, x::Number...) = f(x...)
@inline broadcast(f, t::NTuple{N,Any}, ts::Vararg{NTuple{N,Any}}) where {N} = map(f, t, ts...)
"""
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)`.
# Examples
```jldoctest
julia> A = [1.0; 0.0]; B = [0.0; 0.0];
julia> broadcast!(+, B, A, (0, -2.0));
julia> B
2-element Vector{Float64}:
1.0
-2.0
julia> A
2-element Vector{Float64}:
1.0
0.0
julia> broadcast!(+, A, A, (0, -2.0));
julia> A
2-element Vector{Float64}:
1.0
-2.0
```
"""
broadcast!(f::Tf, dest, As::Vararg{Any,N}) where {Tf,N} = (materialize!(dest, broadcasted(f, As...)); dest)
"""
broadcast_preserving_zero_d(f, As...)
Like [`broadcast`](@ref), except in the case of a 0-dimensional result where it returns a 0-dimensional container
Broadcast automatically unwraps zero-dimensional results to be just the element itself,
but in some cases it is necessary to always return a container — even in the 0-dimensional case.
"""
@inline function broadcast_preserving_zero_d(f, As...)
bc = broadcasted(f, As...)
r = materialize(bc)
return length(axes(bc)) == 0 ? fill!(similar(bc, typeof(r)), r) : r
end
@inline broadcast_preserving_zero_d(f) = fill(f())
@inline broadcast_preserving_zero_d(f, as::Number...) = fill(f(as...))
"""
Broadcast.materialize(bc)
Take a lazy `Broadcasted` object and compute the result
"""
@inline materialize(bc::Broadcasted) = copy(instantiate(bc))
materialize(x) = x
@inline function materialize!(dest, x)
return materialize!(dest, instantiate(Broadcasted(identity, (x,), axes(dest))))
end
@inline function materialize!(dest, bc::Broadcasted{<:Any})
return materialize!(combine_styles(dest, bc), dest, bc)
end
@inline function materialize!(::BroadcastStyle, dest, bc::Broadcasted{<:Any})
return copyto!(dest, instantiate(Broadcasted(bc.style, bc.f, bc.args, axes(dest))))
end
## general `copy` methods
@inline copy(bc::Broadcasted{<:AbstractArrayStyle{0}}) = bc[CartesianIndex()]
copy(bc::Broadcasted{<:Union{Nothing,Unknown}}) =
throw(ArgumentError("broadcasting requires an assigned BroadcastStyle"))
const NonleafHandlingStyles = Union{DefaultArrayStyle,ArrayConflict}
@inline function copy(bc::Broadcasted)
ElType = combine_eltypes(bc.f, bc.args)
if Base.isconcretetype(ElType)
# We can trust it and defer to the simpler `copyto!`
return copyto!(similar(bc, ElType), bc)
end
# When ElType is not concrete, use narrowing. Use the first output
# value to determine the starting output eltype; copyto_nonleaf!
# will widen `dest` as needed to accommodate later values.
bc′ = preprocess(nothing, bc)
iter = eachindex(bc′)
y = iterate(iter)
if y === nothing
# if empty, take the ElType at face value
return similar(bc′, ElType)
end
# Initialize using the first value
I, state = y
@inbounds val = bc′[I]
dest = similar(bc′, typeof(val))
@inbounds dest[I] = val
# Now handle the remaining values
# The typeassert gives inference a helping hand on the element type and dimensionality
# (work-around for #28382)
ElType′ = ElType === Union{} ? Any : ElType <: Type ? Type : ElType
RT = dest isa AbstractArray ? AbstractArray{<:ElType′, ndims(dest)} : Any
return copyto_nonleaf!(dest, bc′, iter, state, 1)::RT
end
## general `copyto!` methods
# The most general method falls back to a method that replaces Style->Nothing
# This permits specialization on typeof(dest) without introducing ambiguities
@inline copyto!(dest::AbstractArray, bc::Broadcasted) = copyto!(dest, convert(Broadcasted{Nothing}, bc))
# Performance optimization for the common identity scalar case: dest .= val
@inline function copyto!(dest::AbstractArray, bc::Broadcasted{<:AbstractArrayStyle{0}})
# Typically, we must independently execute bc for every storage location in `dest`, but:
# IF we're in the common no-op identity case with no nested args (like `dest .= val`),
if bc.f === identity && bc.args isa Tuple{Any} && isflat(bc)
# THEN we can just extract the argument and `fill!` the destination with it
return fill!(dest, bc.args[1][])
else
# Otherwise, fall back to the default implementation like above
return copyto!(dest, convert(Broadcasted{Nothing}, bc))
end
end
# For broadcasted assignments like `broadcast!(f, A, ..., A, ...)`, where `A`
# appears on both the LHS and the RHS of the `.=`, then we know we're only
# going to make one pass through the array, and even though `A` is aliasing
# against itself, the mutations won't affect the result as the indices on the
# LHS and RHS will always match. This is not true in general, but with the `.op=`
# syntax it's fairly common for an argument to be `===` a source.
broadcast_unalias(dest, src) = dest === src ? src : unalias(dest, src)
broadcast_unalias(::Nothing, src) = src
# Preprocessing a `Broadcasted` does two things:
# * unaliases any arguments from `dest`
# * "extrudes" the arguments where it is advantageous to pre-compute the broadcasted indices
@inline preprocess(dest, bc::Broadcasted) = Broadcasted(bc.style, bc.f, preprocess_args(dest, bc.args), bc.axes)
preprocess(dest, x) = extrude(broadcast_unalias(dest, x))
@inline preprocess_args(dest, args::Tuple) = (preprocess(dest, args[1]), preprocess_args(dest, tail(args))...)
@inline preprocess_args(dest, args::Tuple{Any}) = (preprocess(dest, args[1]),)
@inline preprocess_args(dest, args::Tuple{}) = ()
# Specialize this method if all you want to do is specialize on typeof(dest)
@inline function copyto!(dest::AbstractArray, bc::Broadcasted{Nothing})
axes(dest) == axes(bc) || throwdm(axes(dest), axes(bc))
# Performance optimization: broadcast!(identity, dest, A) is equivalent to copyto!(dest, A) if indices match
if bc.f === identity && bc.args isa Tuple{AbstractArray} # only a single input argument to broadcast!
A = bc.args[1]
if axes(dest) == axes(A)
return copyto!(dest, A)
end
end
bc′ = preprocess(dest, bc)
# Performance may vary depending on whether `@inbounds` is placed outside the
# for loop or not. (cf. https://github.com/JuliaLang/julia/issues/38086)
@inbounds @simd for I in eachindex(bc′)
dest[I] = bc′[I]
end
return dest
end
# Performance optimization: for BitArray outputs, we cache the result
# in a 64-bit register before writing into memory (to bypass LSQ)
@inline function copyto!(dest::BitArray, bc::Broadcasted{Nothing})
axes(dest) == axes(bc) || throwdm(axes(dest), axes(bc))
ischunkedbroadcast(dest, bc) && return chunkedcopyto!(dest, bc)
ndims(dest) == 0 && (dest[] = bc[]; return dest)
bc′ = preprocess(dest, bc)
ax = axes(bc′)
ax1, out = ax[1], CartesianIndices(tail(ax))
destc, indc = dest.chunks, 0
bitst, remain = 0, UInt64(0)
for I in out
i = first(ax1) - 1
if ndims(bc) == 1 || bitst >= 64 - length(ax1)
if ndims(bc) > 1 && bitst != 0
@inbounds @simd for j = bitst:63
remain |= UInt64(convert(Bool, bc′[i+=1, I])) << (j & 63)
end
@inbounds destc[indc+=1] = remain
bitst, remain = 0, UInt64(0)
end
while i <= last(ax1) - 64
z = UInt64(0)
@inbounds @simd for j = 0:63
z |= UInt64(convert(Bool, bc′[i+=1, I])) << (j & 63)
end
@inbounds destc[indc+=1] = z
end