Source file owl_computation_optimiser.ml
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
# 1 "src/base/compute/owl_computation_optimiser.ml"
open Owl_graph
module Make (Operator : Owl_computation_operator_sig.Sig) = struct
module Operator = Operator
open Operator.Symbol
open Operator.Symbol.Shape.Type
open Operator.Symbol.Shape.Type.Device
let rec _optimise_term x =
Owl_log.debug "optimise %s ..." (node_to_str x);
if is_valid x = false
then (
(match get_operator x with
| Noop -> pattern_003 x
| Var -> ()
| Const -> pattern_000 x
| Empty _shape -> pattern_000 x
| Zeros _shape -> pattern_000 x
| Ones _shape -> pattern_000 x
| Create _shape -> pattern_000 x
| Sequential _shape -> pattern_000 x
| Uniform _shape -> pattern_000 x
| Gaussian _shape -> pattern_000 x
| Bernoulli _shape -> pattern_000 x
| Init (_shape, _f) -> pattern_000 x
| Get _i -> pattern_000 x
| Set _i -> pattern_000 x
| GetSlice _slice -> pattern_000 x
| SetSlice _slice -> pattern_000 x
| Copy -> pattern_018 x
| Reset -> pattern_000 x
| Reshape _shape -> pattern_022 x
| Reverse -> pattern_000 x
| Tile _repeats -> pattern_000 x
| Repeat _repeats -> pattern_023 x
| Pad (_v, _padding) -> pattern_000 x
| Concatenate _axis -> pattern_000 x
| Split (_axis, _parts) -> pattern_000 x
| Draw (_axis, _n) -> pattern_000 x
| Map _f -> pattern_000 x
| Fold (_axis, _f) -> pattern_000 x
| Scan (_axis, _f) -> pattern_000 x
| OneHot _depth -> pattern_000 x
| Delay _f -> pattern_000 x
| DelayArray (_shape, _f) -> pattern_000 x
| LazyPrint (_max_row, _max_col, _header, _fmt) -> pattern_000 x
| Abs -> pattern_000 x
| Neg -> pattern_000 x
| Floor -> pattern_000 x
| Ceil -> pattern_000 x
| Round -> pattern_000 x
| Sqr -> pattern_000 x
| Sqrt -> pattern_000 x
| Log -> pattern_000 x
| Log2 -> pattern_000 x
| Log10 -> pattern_000 x
| Exp -> pattern_000 x
| Sin -> pattern_000 x
| Cos -> pattern_000 x
| Tan -> pattern_000 x
| Sinh -> pattern_000 x
| Cosh -> pattern_000 x
| Tanh -> pattern_000 x
| Asin -> pattern_000 x
| Acos -> pattern_000 x
| Atan -> pattern_000 x
| Asinh -> pattern_000 x
| Acosh -> pattern_000 x
| Atanh -> pattern_000 x
| Min (_keep_dims, _axis) -> pattern_000 x
| Max (_keep_dims, _axis) -> pattern_000 x
| Sum (_keep_dims, _axis) -> pattern_000 x
| SumReduce _axis -> pattern_024 x
| Signum -> pattern_000 x
| Sigmoid -> pattern_000 x
| Relu -> pattern_000 x
| Min' -> pattern_000 x
| Max' -> pattern_000 x
| Sum' -> pattern_000 x
| L1norm' -> pattern_000 x
| L2norm' -> pattern_000 x
| L2NormSqr' -> pattern_000 x
| ClipByValue -> pattern_000 x
| ClipByL2norm -> pattern_000 x
| Pow -> pattern_000 x
| ScalarPow -> pattern_000 x
| PowScalar -> pattern_000 x
| Atan2 -> pattern_000 x
| ScalarAtan2 -> pattern_000 x
| Atan2Scalar -> pattern_000 x
| Add -> pattern_001 x
| Sub -> pattern_000 x
| Mul -> pattern_019 x
| Div -> pattern_007 x
| AddScalar -> pattern_015 x
| SubScalar -> pattern_000 x
| MulScalar -> pattern_000 x
| DivScalar -> pattern_000 x
| ScalarAdd -> pattern_000 x
| ScalarSub -> pattern_000 x
| ScalarMul -> pattern_014 x
| ScalarDiv -> pattern_017 x
| EltEqual -> pattern_000 x
| EltNotEqual -> pattern_000 x
| EltLess -> pattern_000 x
| EltGreater -> pattern_000 x
| EltLessEqual -> pattern_000 x
| EltGreaterEqual -> pattern_000 x
| EltEqualScalar -> pattern_000 x
| EltNotEqualScalar -> pattern_000 x
| EltLessScalar -> pattern_000 x
| EltGreaterScalar -> pattern_000 x
| EltLessEqualScalar -> pattern_000 x
| EltGreaterEqualScalar -> pattern_000 x
| Conv1d (_padding, _stride) -> pattern_000 x
| Conv2d (_padding, _stride) -> pattern_000 x
| Conv3d (_padding, _stride) -> pattern_000 x
| TransposeConv1d (_padding, _stride) -> pattern_000 x
| TransposeConv2d (_padding, _stride) -> pattern_000 x
| TransposeConv3d (_padding, _stride) -> pattern_000 x
| DilatedConv1d (_padding, _stride, _rate) -> pattern_000 x
| DilatedConv2d (_padding, _stride, _rate) -> pattern_000 x
| DilatedConv3d (_padding, _stride, _rate) -> pattern_000 x
| MaxPool1d (_padding, _kernel, _stride) -> pattern_000 x
| MaxPool2d (_padding, _kernel, _stride) -> pattern_000 x
| MaxPool3d (_padding, _kernel, _stride) -> pattern_000 x
| AvgPool1d (_padding, _kernel, _stride) -> pattern_000 x
| AvgPool2d (_padding, _kernel, _stride) -> pattern_000 x
| AvgPool3d (_padding, _kernel, _stride) -> pattern_000 x
| UpSampling2d _size -> pattern_000 x
| Conv1dBackwardInput _stride -> pattern_000 x
| Conv1dBackwardKernel _stride -> pattern_000 x
| Conv2dBackwardInput _stride -> pattern_000 x
| Conv2dBackwardKernel _stride -> pattern_000 x
| Conv3dBackwardInput _stride -> pattern_000 x
| Conv3dBackwardKernel _stride -> pattern_000 x
| TransposeConv1dBackwardInput _stride -> pattern_000 x
| TransposeConv1dBackwardKernel _stride -> pattern_000 x
| TransposeConv2dBackwardInput _stride -> pattern_000 x
| TransposeConv2dBackwardKernel _stride -> pattern_000 x
| TransposeConv3dBackwardInput _stride -> pattern_000 x
| TransposeConv3dBackwardKernel _stride -> pattern_000 x
| DilatedConv1dBackwardInput (_stride, _rate) -> pattern_000 x
| DilatedConv1dBackwardKernel (_stride, _rate) -> pattern_000 x
| DilatedConv2dBackwardInput (_stride, _rate) -> pattern_000 x
| DilatedConv2dBackwardKernel (_stride, _rate) -> pattern_000 x
| DilatedConv3dBackwardInput (_stride, _rate) -> pattern_000 x
| DilatedConv3dBackwardKernel (_stride, _rate) -> pattern_000 x
| MaxPool1dBackward (_padding, _kernel, _stride) -> pattern_000 x
| MaxPool2dBackward (_padding, _kernel, _stride) -> pattern_000 x
| MaxPool3dBackward (_padding, _kernel, _stride) -> pattern_000 x
| AvgPool1dBackward (_padding, _kernel, _stride) -> pattern_000 x
| AvgPool2dBackward (_padding, _kernel, _stride) -> pattern_000 x
| AvgPool3dBackward (_padding, _kernel, _stride) -> pattern_000 x
| UpSampling2dBackward _size -> pattern_000 x
| Row -> pattern_000 x
| Rows _i -> pattern_000 x
| CopyRowTo -> pattern_000 x
| CopyColTo -> pattern_000 x
| Dot (_transa, _transb, _alpha, _beta) -> pattern_005 x
| Inv -> pattern_000 x
| Trace -> pattern_000 x
| Transpose _axis -> pattern_000 x
| ToRows -> pattern_000 x
| OfRows -> pattern_000 x
| Scalar_Add -> pattern_010 x
| Scalar_Sub -> pattern_010 x
| Scalar_Mul -> pattern_010 x
| Scalar_Div -> pattern_010 x
| Scalar_Pow -> pattern_010 x
| Scalar_Atan2 -> pattern_010 x
| Scalar_Abs -> pattern_012 x
| Scalar_Neg -> pattern_012 x
| Scalar_Sqr -> pattern_012 x
| Scalar_Sqrt -> pattern_012 x
| Scalar_Exp -> pattern_012 x
| Scalar_Log -> pattern_012 x
| Scalar_Log2 -> pattern_012 x
| Scalar_Log10 -> pattern_012 x
| Scalar_Signum -> pattern_012 x
| Scalar_Floor -> pattern_012 x
| Scalar_Ceil -> pattern_012 x
| Scalar_Round -> pattern_012 x
| Scalar_Sin -> pattern_012 x
| Scalar_Cos -> pattern_012 x
| Scalar_Tan -> pattern_012 x
| Scalar_Sinh -> pattern_012 x
| Scalar_Cosh -> pattern_012 x
| Scalar_Tanh -> pattern_012 x
| Scalar_Asin -> pattern_012 x
| Scalar_Acos -> pattern_012 x
| Scalar_Atan -> pattern_012 x
| Scalar_Asinh -> pattern_012 x
| Scalar_Acosh -> pattern_012 x
| Scalar_Atanh -> pattern_012 x
| Scalar_Relu -> pattern_012 x
| Scalar_Sigmoid -> pattern_012 x
| Fused_Adagrad (_rate, _eps) -> pattern_000 x
| _ -> failwith "Owl_computation_optimiser:_optimise_term");
validate x)
and pattern_000 x = Array.iter _optimise_term (parents x)
and pattern_001 x =
let parents = parents x in
let a = parents.(0) in
let b = parents.(1) in
_optimise_term a;
_optimise_term b;
pattern_002 x;
pattern_004 x
and pattern_002 x =
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
if get_operator x = Add
then (
match get_operator a, get_operator b with
| Zeros _, _ ->
set_operator x Noop;
remove_edge a x;
_optimise_term x
| _, Zeros _ ->
set_operator x Noop;
remove_edge b x;
_optimise_term x
| _, _ -> ())
and pattern_003 x =
let parent = (parents x).(0) in
_optimise_term parent;
let op = get_operator x in
let reusable = get_reuse x in
if op = Noop && reusable
then (
let x_children = children x in
let parent_children = children parent in
let merged_children = Owl_utils_array.merge x_children parent_children in
set_children parent merged_children;
replace_parent x parent;
remove_node x)
and pattern_004 x =
if get_operator x = Add
then (
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
if get_operator a = Mul && refnum a = 1
then (
let new_parents = Owl_utils_array.(parents a @ [| b |]) in
set_parents x new_parents;
replace_child a x;
set_operator x FMA;
remove_node a)
else if get_operator b = Mul && refnum b = 1
then (
let new_parents = Owl_utils_array.(parents b @ [| a |]) in
set_parents x new_parents;
replace_child b x;
set_operator x FMA;
remove_node b))
and pattern_005 x =
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
_optimise_term a;
_optimise_term b;
pattern_006 x
and pattern_006 x =
match get_operator x with
| Dot (transa, transb, alpha, beta) ->
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
(match get_operator a with
| Transpose _i ->
if refnum a = 1
then (
let op = Dot (not transa, transb, alpha, beta) in
set_operator x op;
let a_parent = (parents a).(0) in
replace_child a x;
replace_parent a a_parent)
| _ -> ());
(match get_operator b with
| Transpose _i ->
if refnum b = 1
then (
let op = Dot (transa, not transb, alpha, beta) in
set_operator x op;
let b_parent = (parents b).(0) in
replace_child b x;
replace_parent b b_parent)
| _ -> ())
| _ -> ()
and pattern_007 x =
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
_optimise_term a;
_optimise_term b;
pattern_008 x
and pattern_008 x =
if get_operator x = Div
then (
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
let x_shp = node_shape x in
match get_operator a with
| Zeros _ ->
remove_edge a x;
remove_edge b x;
set_operator x (Zeros x_shp)
| _ -> ())
and pattern_009 x =
if get_operator x = Div
then (
let x_parents = parents x in
let b = x_parents.(1) in
let x_shp = node_shape x in
match get_operator b with
| Ones b_shp ->
if x_shp = b_shp
then (
remove_edge b x;
set_operator x Noop;
_optimise_term x)
| _ -> ())
and pattern_010 x =
let parents = parents x in
let a = parents.(0) in
let b = parents.(1) in
_optimise_term a;
_optimise_term b;
match get_operator a, get_operator b with
| Const, Const ->
let a_val = node_to_elt a |> elt_to_float in
let b_val = node_to_elt b |> elt_to_float in
let c_val = pattern_011 (get_operator x) a_val b_val in
set_parents x [||];
set_reuse x false;
set_operator x Const;
freeze x;
set_value x [| float_to_elt c_val |> unpack_elt |> elt_to_value |]
| _ -> ()
and pattern_011 op a b =
match op with
| Scalar_Add -> a +. b
| Scalar_Sub -> a -. b
| Scalar_Mul -> a *. b
| Scalar_Div -> a /. b
| Scalar_Pow -> a ** b
| Scalar_Atan2 -> Stdlib.atan2 a b
| _ -> failwith "pattern_011: not supported"
and pattern_012 x =
let parents = parents x in
let a = parents.(0) in
_optimise_term a;
match get_operator a with
| Const ->
let a_val = node_to_elt a |> elt_to_float in
let b_val = pattern_013 (get_operator x) a_val in
set_parents x [||];
set_reuse x false;
set_operator x Const;
freeze x;
set_value x [| float_to_elt b_val |> unpack_elt |> elt_to_value |]
| _ -> ()
and pattern_013 op x =
let open Owl_base_maths in
match op with
| Scalar_Abs -> abs x
| Scalar_Neg -> neg x
| Scalar_Sqr -> x *. x
| Scalar_Sqrt -> sqrt x
| Scalar_Exp -> exp x
| Scalar_Log -> log x
| Scalar_Log2 -> log2 x
| Scalar_Log10 -> log10 x
| Scalar_Signum -> signum x
| Scalar_Floor -> floor x
| Scalar_Ceil -> ceil x
| Scalar_Round -> round x
| Scalar_Sin -> sin x
| Scalar_Cos -> cos x
| Scalar_Tan -> tan x
| Scalar_Sinh -> sinh x
| Scalar_Cosh -> cosh x
| Scalar_Tanh -> tanh x
| Scalar_Asin -> asin x
| Scalar_Acos -> acos x
| Scalar_Atan -> atan x
| Scalar_Asinh -> asinh x
| Scalar_Acosh -> acosh x
| Scalar_Atanh -> atanh x
| Scalar_Relu -> relu x
| Scalar_Sigmoid -> sigmoid x
| _ -> failwith "pattern_013: not supported"
and pattern_014 x =
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
_optimise_term a;
_optimise_term b;
match get_operator a, get_operator b with
| _, Zeros shp ->
set_operator x (Zeros shp);
set_parents x [||];
remove_edge a x;
remove_edge b x
| _, Ones shp ->
set_parents x [| a |];
set_operator x (Create shp);
remove_edge b x
| _ -> ()
and pattern_016 x =
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
_optimise_term a;
_optimise_term b;
pattern_017 x
and pattern_017 x =
if get_operator x = ScalarDiv
then (
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
if get_operator a = Const && get_operator b = Sqrt && refnum b = 1
then (
let b_parents = parents b in
let b_a = b_parents.(0) in
if get_operator b_a = AddScalar && refnum b_a = 1
then (
let b_a_parents = parents b_a in
let b_a_a = b_a_parents.(0) in
let b_a_b = b_a_parents.(1) in
if get_operator b_a_b = Const
then (
let b_a_b_val = node_to_elt b_a_b |> elt_to_float in
if b_a_b_val = 1e-32
then (
let a_val = node_to_elt a |> elt_to_float in
set_parents x [| b_a_a |];
replace_child b_a x;
set_operator x (Fused_Adagrad (a_val, b_a_b_val)))))))
and pattern_015 x =
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
_optimise_term a;
_optimise_term b;
match get_operator a, get_operator b with
| Zeros shp, _ ->
set_parents x [| b |];
set_operator x (Create shp);
remove_edge a x
| _ -> ()
and pattern_018 x =
let a = (parents x).(0) in
_optimise_term a;
set_operator x Noop;
pattern_003 x
and pattern_019 x =
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
_optimise_term a;
_optimise_term b;
pattern_020 x
and pattern_020 x =
if get_operator x = Mul
then (
let x_parents = parents x in
let a = x_parents.(0) in
let b = x_parents.(1) in
let x_shp = node_shape x in
match get_operator a, get_operator b with
| Zeros _, _ | _, Zeros _ ->
set_operator x (Zeros x_shp);
remove_edge a x;
remove_edge b x
| _, _ -> ())
and pattern_021 _x = failwith "pattern_021: not implemented"
and pattern_022 x =
let a = (parents x).(0) in
_optimise_term a;
if refnum a = 1
then (
let x_shp = node_shape x in
match get_operator a with
| Zeros _ ->
set_operator x (Zeros x_shp);
remove_edge a x
| Ones _ ->
set_operator x (Ones x_shp);
remove_edge a x
| _ -> ())
and pattern_023 x =
let a = (parents x).(0) in
_optimise_term a;
if refnum x = 1
then (
let x_parent = (parents x).(0) in
let x_children = children x in
match get_operator x_children.(0) with
| Add | Sub | Mul | Div | Pow | Min2 | Max2 | Hypot | Atan2 ->
let reps =
match get_operator x with
| Repeat reps -> reps
| _ -> failwith "optimiser:pattern_023"
in
let optimisable = ref true in
Array.iter2
(fun d r -> if r <> 1 && d <> 1 then optimisable := false)
(node_shape x_parent)
reps;
if !optimisable = true
then (
let parent_children = children x_parent in
let merged_children = Owl_utils_array.merge x_children parent_children in
set_children x_parent merged_children;
replace_parent x x_parent;
remove_node x)
| _ -> ())
and pattern_024 x =
let x_parents = parents x in
let a = x_parents.(0) in
_optimise_term a;
match get_operator x with
| SumReduce axis ->
if Array.length axis = 1
then (
set_operator x (Sum (false, axis.(0)));
_optimise_term x)
| _ -> ()
let estimate_complexity graph =
let nodes = ref 0 in
Owl_graph.iter_ancestors (fun _ -> nodes := !nodes + 1) graph;
let edges = ref 0 in
Owl_graph.iter_in_edges (fun _ _ -> edges := !edges + 1) graph;
!nodes, !edges
let optimise_nodes xs =
let nodes, edges = estimate_complexity xs in
Owl_log.info "unoptimised graph: %i nodes, %i edges ..." nodes edges;
Array.iter _optimise_term xs;
iter_ancestors (fun v -> invalidate v) xs;
let nodes, edges = estimate_complexity xs in
Owl_log.info "optimised graph: %i nodes, %i edges ..." nodes edges
end