-
-
Notifications
You must be signed in to change notification settings - Fork 5.5k
/
broadcast.jl
612 lines (548 loc) · 22.1 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
# This file is a part of Julia. License is MIT: https://julialang.org/license
module Broadcast
using Base.Cartesian
using Base: linearindices, tail, OneTo, to_shape,
_msk_end, unsafe_bitgetindex, bitcache_chunks, bitcache_size, dumpbitcache,
nullable_returntype, null_safe_op, hasvalue, isoperator
import Base: broadcast, broadcast!
export broadcast_getindex, broadcast_setindex!, dotview, @__dot__
const ScalarType = Union{Type{Any}, Type{Nullable}}
## Broadcasting utilities ##
# fallbacks for some special cases
@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!(::typeof(identity), x::Array{T,N}, y::Array{S,N}) where {T,S,N} =
size(x) == size(y) ? copy!(x, y) : broadcast_c!(identity, Array, Array, 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 resulting container type
_containertype(::Type) = Any
_containertype(::Type{<:Ptr}) = Any
_containertype(::Type{<:Tuple}) = Tuple
_containertype(::Type{<:Ref}) = Array
_containertype(::Type{<:AbstractArray}) = Array
_containertype(::Type{<:Nullable}) = Nullable
containertype(x) = _containertype(typeof(x))
containertype(ct1, ct2) = promote_containertype(containertype(ct1), containertype(ct2))
@inline containertype(ct1, ct2, cts...) = promote_containertype(containertype(ct1), containertype(ct2, cts...))
promote_containertype(::Type{Array}, ::Type{Array}) = Array
promote_containertype(::Type{Array}, ct) = Array
promote_containertype(ct, ::Type{Array}) = Array
promote_containertype(::Type{Tuple}, ::ScalarType) = Tuple
promote_containertype(::ScalarType, ::Type{Tuple}) = Tuple
promote_containertype(::Type{Any}, ::Type{Nullable}) = Nullable
promote_containertype(::Type{Nullable}, ::Type{Any}) = Nullable
promote_containertype(::Type{T}, ::Type{T}) where {T} = T
## Calculate the broadcast indices of the arguments, or error if incompatible
# array inputs
broadcast_indices() = ()
broadcast_indices(A) = broadcast_indices(containertype(A), A)
@inline broadcast_indices(A, B...) = broadcast_shape(broadcast_indices(A), broadcast_indices(B...))
broadcast_indices(::ScalarType, A) = ()
broadcast_indices(::Type{Tuple}, A) = (OneTo(length(A)),)
broadcast_indices(::Type{Array}, A::Ref) = ()
broadcast_indices(::Type{Array}, A) = indices(A)
# shape (i.e., tuple-of-indices) inputs
broadcast_shape(shape::Tuple) = shape
@inline 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{}) = ()
@inline _bcs(::Tuple{}, newshape::Tuple) = (newshape[1], _bcs((), tail(newshape))...)
@inline _bcs(shape::Tuple, ::Tuple{}) = (shape[1], _bcs(tail(shape), ())...)
@inline 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].
@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(A, I) = _broadcast_getindex(containertype(A), A, I)
Base.@propagate_inbounds _broadcast_getindex(::Type{Array}, A::Ref, I) = A[]
Base.@propagate_inbounds _broadcast_getindex(::ScalarType, 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_c!(f, containertype(C), containertype(A, Bs...), C, A, Bs...)
@inline function broadcast_c!(f, ::Type, ::Type, C, A, Bs::Vararg{Any,N}) where N
shape = 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 computed element type
@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
R = typejoin(eltype(B), S)
new = similar(B, R)
for II in Iterators.take(iter, count)
new[II] = B[II]
end
new[I] = V
return _broadcast!(f, new, keeps, Idefaults, As, Val(nargs), iter, st, count+1)
end
count += 1
end
return B
end
end
# broadcast methods that dispatch on the type found by inference
function broadcast_t(f, ::Type{Any}, shape, iter, As...)
nargs = length(As)
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
B = similar(BitArray, shape)
else
B = similar(Array{typeof(val)}, shape)
end
B[I] = val
return _broadcast!(f, B, keeps, Idefaults, As, Val(nargs), iter, st, 1)
end
@inline function broadcast_t(f, T, shape, iter, A, Bs::Vararg{Any,N}) where N
C = similar(Array{T}, shape)
keeps, Idefaults = map_newindexer(shape, A, Bs)
_broadcast!(f, C, keeps, Idefaults, A, Bs, Val(N), iter)
return C
end
# default to BitArray for broadcast operations producing Bool, to save 8x space
# in the common case where this is used for logical array indexing; in
# performance-critical cases where Array{Bool} is desired, one can always
# use broadcast! instead.
@inline function broadcast_t(f, ::Type{Bool}, shape, iter, A, Bs::Vararg{Any,N}) where N
C = similar(BitArray, shape)
keeps, Idefaults = map_newindexer(shape, A, Bs)
_broadcast!(f, C, keeps, Idefaults, A, Bs, Val(N), iter)
return C
end
maptoTuple(f) = Tuple{}
maptoTuple(f, a, b...) = Tuple{f(a), maptoTuple(f, b...).types...}
# An element type satisfying for all A:
# broadcast_getindex(
# containertype(A),
# A, broadcast_indices(A)
# )::_broadcast_getindex_eltype(A)
_broadcast_getindex_eltype(A) = _broadcast_getindex_eltype(containertype(A), A)
_broadcast_getindex_eltype(::ScalarType, T::Type) = Type{T}
_broadcast_getindex_eltype(::ScalarType, A) = typeof(A)
_broadcast_getindex_eltype(::Any, 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(T::Type) = Type{T}
_unsafe_get_eltype(x) = typeof(x)
# Inferred eltype of result of broadcast(f, xs...)
_broadcast_eltype(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 methods that dispatch on the type of the final container
@inline function broadcast_c(f, ::Type{Array}, A, Bs...)
T = _broadcast_eltype(f, A, Bs...)
shape = broadcast_indices(A, Bs...)
iter = CartesianRange(shape)
if isleaftype(T)
return broadcast_t(f, T, shape, iter, A, Bs...)
end
if isempty(iter)
return similar(Array{T}, shape)
end
return broadcast_t(f, Any, shape, iter, A, Bs...)
end
@inline function broadcast_c(f, ::Type{Nullable}, a...)
nonnull = all(hasvalue, a)
S = _nullable_eltype(f, a...)
if 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
@inline broadcast_c(f, ::Type{Any}, a...) = f(a...)
@inline broadcast_c(f, ::Type{Tuple}, 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
@inline 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(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_c(f, containertype(A, Bs...), A, Bs...)
"""
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!(similar(Array{eltype(src)}, broadcast_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(indices(dest), $(Isplat...)) # unnecessary if this function is never called directly
checkbounds(src, $(Isplat...))
@nexprs $N d->(@nexprs $N k->(Ibcast_d_k = 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, $(Isplat...))
shape = broadcast_indices($(Isplat...))
@nextract $N shape d->(length(shape) < d ? OneTo(1) : shape[d])
@nexprs $N d->(@nexprs $N k->(Ibcast_d_k = 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 $N A J) = x_el
end
end
A
end
end
############################################################
# x[...] .= f.(y...) ---> broadcast!(f, dotview(x, ...), y...).
# The dotview function defaults to getindex, but we override it in
# a few cases to get the expected in-place behavior without affecting
# explicit calls to view. (All of this can go away if slices
# are changed to generate views by default.)
Base.@propagate_inbounds dotview(args...) = getindex(args...)
Base.@propagate_inbounds dotview(A::AbstractArray, args...) = view(A, args...)
Base.@propagate_inbounds dotview(A::AbstractArray{<:AbstractArray}, args::Integer...) = getindex(A, args...)
############################################################
# The parser turns @. into a call to the __dot__ macro,
# which converts all function calls and assignments into
# broadcasting "dot" calls/assignments:
dottable(x) = false # avoid dotting spliced objects (e.g. view calls inserted by @view)
dottable(x::Symbol) = !isoperator(x) || first(string(x)) != '.' || x == :.. # don't add dots to dot operators
dottable(x::Expr) = x.head != :$
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, dotargs[1], map(undot, dotargs[2:end])...)
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}:
3.52441
4.72789
3.42336
```
"""
macro __dot__(x)
esc(__dot__(x))
end
end # module