irreducible.ll
12.7 KB
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
; RUN: opt < %s -analyze -block-freq | FileCheck %s
; RUN: opt < %s -passes='print<block-freq>' -disable-output 2>&1 | FileCheck %s
; A loop with multiple exits isn't irreducible. It should be handled
; correctly.
;
; CHECK-LABEL: Printing analysis {{.*}} for function 'multiexit':
; CHECK-NEXT: block-frequency-info: multiexit
define void @multiexit(i1 %x) {
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
entry:
br label %loop.1
; CHECK-NEXT: loop.1: float = 2.0,
loop.1:
br i1 %x, label %exit.1, label %loop.2, !prof !0
; CHECK-NEXT: loop.2: float = 1.75,
loop.2:
br i1 %x, label %exit.2, label %loop.1, !prof !1
; CHECK-NEXT: exit.1: float = 0.25,
exit.1:
br label %return
; CHECK-NEXT: exit.2: float = 0.75,
exit.2:
br label %return
; CHECK-NEXT: return: float = 1.0, int = [[ENTRY]]
return:
ret void
}
!0 = !{!"branch_weights", i32 1, i32 7}
!1 = !{!"branch_weights", i32 3, i32 4}
; Irreducible control flow
; ========================
;
; LoopInfo defines a loop as a non-trivial SCC dominated by a single block,
; called the header. A given loop, L, can have sub-loops, which are loops
; within the subgraph of L that excludes the header.
;
; In addition to loops, -block-freq has limited support for irreducible SCCs,
; which are SCCs with multiple entry blocks. Irreducible SCCs are discovered
; on they fly, and modelled as loops with multiple headers.
;
; The headers of irreducible sub-SCCs consist of its entry blocks and all nodes
; that are targets of a backedge within it (excluding backedges within true
; sub-loops).
;
; -block-freq is currently designed to act like a block is inserted that
; intercepts all the edges to the headers. All backedges and entries point to
; this block. Its successors are the headers, which split the frequency
; evenly.
;
; There are a number of testcases below. Only the first two have detailed
; explanations.
;
; Testcase #1
; ===========
;
; In this case c1 and c2 should have frequencies of 15/7 and 13/7,
; respectively. To calculate this, consider assigning 1.0 to entry, and
; distributing frequency iteratively (to infinity). At the first iteration,
; entry gives 3/4 to c1 and 1/4 to c2. At every step after, c1 and c2 give 3/4
; of what they have to each other. Somehow, all of it comes out to exit.
;
; c1 = 3/4 + 1/4*3/4 + 3/4*3^2/4^2 + 1/4*3^3/4^3 + 3/4*3^3/4^3 + ...
; c2 = 1/4 + 3/4*3/4 + 1/4*3^2/4^2 + 3/4*3^3/4^3 + 1/4*3^3/4^3 + ...
;
; Simplify by splitting up the odd and even terms of the series and taking out
; factors so that the infite series matches:
;
; c1 = 3/4 *(9^0/16^0 + 9^1/16^1 + 9^2/16^2 + ...)
; + 3/16*(9^0/16^0 + 9^1/16^1 + 9^2/16^2 + ...)
; c2 = 1/4 *(9^0/16^0 + 9^1/16^1 + 9^2/16^2 + ...)
; + 9/16*(9^0/16^0 + 9^1/16^1 + 9^2/16^2 + ...)
;
; c1 = 15/16*(9^0/16^0 + 9^1/16^1 + 9^2/16^2 + ...)
; c2 = 13/16*(9^0/16^0 + 9^1/16^1 + 9^2/16^2 + ...)
;
; Since this geometric series sums to 16/7:
;
; c1 = 15/7
; c2 = 13/7
;
; If we treat c1 and c2 as members of the same loop, the exit frequency of the
; loop as a whole is 1/4, so the loop scale should be 4. Summing c1 and c2
; gives 28/7, or 4.0, which is nice confirmation of the math above.
;
; -block-freq currently treats the two nodes as equals.
define void @multientry(i1 %x) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'multientry':
; CHECK-NEXT: block-frequency-info: multientry
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
br i1 %x, label %c1, label %c2, !prof !2
c1:
; CHECK-NEXT: c1: float = 2.0,
; The "correct" answer is: float = 2.142857{{[0-9]*}},
br i1 %x, label %c2, label %exit, !prof !2
c2:
; CHECK-NEXT: c2: float = 2.0,
; The "correct" answer is: float = 1.857142{{[0-9]*}},
br i1 %x, label %c1, label %exit, !prof !2
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!2 = !{!"branch_weights", i32 3, i32 1}
; Testcase #2
; ===========
;
; In this case c1 and c2 should be treated as equals in a single loop. The
; exit frequency is 1/3, so the scaling factor for the loop should be 3.0. The
; loop is entered 2/3 of the time, and c1 and c2 split the total loop frequency
; evenly (1/2), so they should each have frequencies of 1.0 (3.0*2/3*1/2).
; Another way of computing this result is by assigning 1.0 to entry and showing
; that c1 and c2 should accumulate frequencies of:
;
; 1/3 + 2/9 + 4/27 + 8/81 + ...
; 2^0/3^1 + 2^1/3^2 + 2^2/3^3 + 2^3/3^4 + ...
;
; At the first step, c1 and c2 each get 1/3 of the entry. At each subsequent
; step, c1 and c2 each get 1/3 of what's left in c1 and c2 combined. This
; infinite series sums to 1.
define void @crossloops(i2 %x) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'crossloops':
; CHECK-NEXT: block-frequency-info: crossloops
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
switch i2 %x, label %exit [ i2 1, label %c1
i2 2, label %c2 ], !prof !3
c1:
; CHECK-NEXT: c1: float = 1.0,
switch i2 %x, label %exit [ i2 1, label %c1
i2 2, label %c2 ], !prof !3
c2:
; CHECK-NEXT: c2: float = 1.0,
switch i2 %x, label %exit [ i2 1, label %c1
i2 2, label %c2 ], !prof !3
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!3 = !{!"branch_weights", i32 2, i32 2, i32 2}
; A true loop with irreducible control flow inside.
define void @loop_around_irreducible(i1 %x) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'loop_around_irreducible':
; CHECK-NEXT: block-frequency-info: loop_around_irreducible
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
br label %loop
loop:
; CHECK-NEXT: loop: float = 4.0, int = [[HEAD:[0-9]+]]
br i1 %x, label %left, label %right, !prof !4
left:
; CHECK-NEXT: left: float = 8.0,
br i1 %x, label %right, label %loop.end, !prof !5
right:
; CHECK-NEXT: right: float = 8.0,
br i1 %x, label %left, label %loop.end, !prof !5
loop.end:
; CHECK-NEXT: loop.end: float = 4.0, int = [[HEAD]]
br i1 %x, label %loop, label %exit, !prof !5
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!4 = !{!"branch_weights", i32 1, i32 1}
!5 = !{!"branch_weights", i32 3, i32 1}
; Two unrelated irreducible SCCs.
define void @two_sccs(i1 %x) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'two_sccs':
; CHECK-NEXT: block-frequency-info: two_sccs
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
br i1 %x, label %a, label %b, !prof !6
a:
; CHECK-NEXT: a: float = 0.75,
br i1 %x, label %a.left, label %a.right, !prof !7
a.left:
; CHECK-NEXT: a.left: float = 1.5,
br i1 %x, label %a.right, label %exit, !prof !6
a.right:
; CHECK-NEXT: a.right: float = 1.5,
br i1 %x, label %a.left, label %exit, !prof !6
b:
; CHECK-NEXT: b: float = 0.25,
br i1 %x, label %b.left, label %b.right, !prof !7
b.left:
; CHECK-NEXT: b.left: float = 0.625,
br i1 %x, label %b.right, label %exit, !prof !8
b.right:
; CHECK-NEXT: b.right: float = 0.625,
br i1 %x, label %b.left, label %exit, !prof !8
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!6 = !{!"branch_weights", i32 3, i32 1}
!7 = !{!"branch_weights", i32 1, i32 1}
!8 = !{!"branch_weights", i32 4, i32 1}
; A true loop inside irreducible control flow.
define void @loop_inside_irreducible(i1 %x) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'loop_inside_irreducible':
; CHECK-NEXT: block-frequency-info: loop_inside_irreducible
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
br i1 %x, label %left, label %right, !prof !9
left:
; CHECK-NEXT: left: float = 2.0,
br i1 %x, label %right, label %exit, !prof !10
right:
; CHECK-NEXT: right: float = 2.0, int = [[RIGHT:[0-9]+]]
br label %loop
loop:
; CHECK-NEXT: loop: float = 6.0,
br i1 %x, label %loop, label %right.end, !prof !11
right.end:
; CHECK-NEXT: right.end: float = 2.0, int = [[RIGHT]]
br i1 %x, label %left, label %exit, !prof !10
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!9 = !{!"branch_weights", i32 1, i32 1}
!10 = !{!"branch_weights", i32 3, i32 1}
!11 = !{!"branch_weights", i32 2, i32 1}
; Irreducible control flow in a branch that's in a true loop.
define void @loop_around_branch_with_irreducible(i1 %x) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'loop_around_branch_with_irreducible':
; CHECK-NEXT: block-frequency-info: loop_around_branch_with_irreducible
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
br label %loop
loop:
; CHECK-NEXT: loop: float = 2.0, int = [[LOOP:[0-9]+]]
br i1 %x, label %normal, label %irreducible.entry, !prof !12
normal:
; CHECK-NEXT: normal: float = 1.5,
br label %loop.end
irreducible.entry:
; CHECK-NEXT: irreducible.entry: float = 0.5, int = [[IRREDUCIBLE:[0-9]+]]
br i1 %x, label %left, label %right, !prof !13
left:
; CHECK-NEXT: left: float = 1.0,
br i1 %x, label %right, label %irreducible.exit, !prof !12
right:
; CHECK-NEXT: right: float = 1.0,
br i1 %x, label %left, label %irreducible.exit, !prof !12
irreducible.exit:
; CHECK-NEXT: irreducible.exit: float = 0.5, int = [[IRREDUCIBLE]]
br label %loop.end
loop.end:
; CHECK-NEXT: loop.end: float = 2.0, int = [[LOOP]]
br i1 %x, label %loop, label %exit, !prof !13
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!12 = !{!"branch_weights", i32 3, i32 1}
!13 = !{!"branch_weights", i32 1, i32 1}
; Irreducible control flow between two true loops.
define void @loop_around_branch_with_irreducible_around_loop(i1 %x) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'loop_around_branch_with_irreducible_around_loop':
; CHECK-NEXT: block-frequency-info: loop_around_branch_with_irreducible_around_loop
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
br label %loop
loop:
; CHECK-NEXT: loop: float = 3.0, int = [[LOOP:[0-9]+]]
br i1 %x, label %normal, label %irreducible, !prof !14
normal:
; CHECK-NEXT: normal: float = 2.0,
br label %loop.end
irreducible:
; CHECK-NEXT: irreducible: float = 1.0,
br i1 %x, label %left, label %right, !prof !15
left:
; CHECK-NEXT: left: float = 2.0,
br i1 %x, label %right, label %loop.end, !prof !16
right:
; CHECK-NEXT: right: float = 2.0, int = [[RIGHT:[0-9]+]]
br label %right.loop
right.loop:
; CHECK-NEXT: right.loop: float = 10.0,
br i1 %x, label %right.loop, label %right.end, !prof !17
right.end:
; CHECK-NEXT: right.end: float = 2.0, int = [[RIGHT]]
br i1 %x, label %left, label %loop.end, !prof !16
loop.end:
; CHECK-NEXT: loop.end: float = 3.0, int = [[LOOP]]
br i1 %x, label %loop, label %exit, !prof !14
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!14 = !{!"branch_weights", i32 2, i32 1}
!15 = !{!"branch_weights", i32 1, i32 1}
!16 = !{!"branch_weights", i32 3, i32 1}
!17 = !{!"branch_weights", i32 4, i32 1}
; An irreducible SCC with a non-header.
define void @nonheader(i1 %x) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'nonheader':
; CHECK-NEXT: block-frequency-info: nonheader
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
br i1 %x, label %left, label %right, !prof !18
left:
; CHECK-NEXT: left: float = 1.0,
br i1 %x, label %bottom, label %exit, !prof !19
right:
; CHECK-NEXT: right: float = 1.0,
br i1 %x, label %bottom, label %exit, !prof !20
bottom:
; CHECK-NEXT: bottom: float = 1.0,
br i1 %x, label %left, label %right, !prof !18
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!18 = !{!"branch_weights", i32 1, i32 1}
!19 = !{!"branch_weights", i32 1, i32 3}
!20 = !{!"branch_weights", i32 3, i32 1}
; An irreducible SCC with an irreducible sub-SCC. In the current version of
; -block-freq, this means an extra header.
;
; This testcases uses non-trivial branch weights. The CHECK statements here
; will start to fail if we change -block-freq to be more accurate. Currently,
; loop headers are affected by the weight of their corresponding back edges.
define void @nonentry_header(i1 %x, i2 %y) {
; CHECK-LABEL: Printing analysis {{.*}} for function 'nonentry_header':
; CHECK-NEXT: block-frequency-info: nonentry_header
entry:
; CHECK-NEXT: entry: float = 1.0, int = [[ENTRY:[0-9]+]]
br i1 %x, label %left, label %right, !prof !21
left:
; CHECK-NEXT: left: float = 0.14
br i1 %x, label %top, label %bottom, !prof !22
right:
; CHECK-NEXT: right: float = 0.42
br i1 %x, label %top, label %bottom, !prof !22
top:
; CHECK-NEXT: top: float = 8.43
switch i2 %y, label %exit [ i2 0, label %left
i2 1, label %right
i2 2, label %bottom ], !prof !23
bottom:
; CHECK-NEXT: bottom: float = 4.5,
br label %top
exit:
; CHECK-NEXT: exit: float = 1.0, int = [[ENTRY]]
ret void
}
!21 = !{!"branch_weights", i32 2, i32 1}
!22 = !{!"branch_weights", i32 1, i32 1}
!23 = !{!"branch_weights", i32 8, i32 1, i32 3, i32 12}