aboutsummaryrefslogtreecommitdiffstats
path: root/contrib/libs/llvm16/lib/Transforms/Scalar/IndVarSimplify.cpp
blob: c834e51b5f292546c52b9c38c400ed0a9688e0db (plain) (blame)
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
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
//===- IndVarSimplify.cpp - Induction Variable Elimination ----------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// This transformation analyzes and transforms the induction variables (and
// computations derived from them) into simpler forms suitable for subsequent
// analysis and transformation.
//
// If the trip count of a loop is computable, this pass also makes the following
// changes:
//   1. The exit condition for the loop is canonicalized to compare the
//      induction value against the exit value.  This turns loops like:
//        'for (i = 7; i*i < 1000; ++i)' into 'for (i = 0; i != 25; ++i)'
//   2. Any use outside of the loop of an expression derived from the indvar
//      is changed to compute the derived value outside of the loop, eliminating
//      the dependence on the exit value of the induction variable.  If the only
//      purpose of the loop is to compute the exit value of some derived
//      expression, this transformation will make the loop dead.
//
//===----------------------------------------------------------------------===//

#include "llvm/Transforms/Scalar/IndVarSimplify.h"
#include "llvm/ADT/APFloat.h"
#include "llvm/ADT/ArrayRef.h"
#include "llvm/ADT/STLExtras.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/ADT/iterator_range.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopPass.h"
#include "llvm/Analysis/MemorySSA.h"
#include "llvm/Analysis/MemorySSAUpdater.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetLibraryInfo.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/BasicBlock.h"
#include "llvm/IR/Constant.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/DerivedTypes.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/Function.h"
#include "llvm/IR/IRBuilder.h"
#include "llvm/IR/InstrTypes.h"
#include "llvm/IR/Instruction.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/Intrinsics.h"
#include "llvm/IR/Module.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PassManager.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Type.h"
#include "llvm/IR/Use.h"
#include "llvm/IR/User.h"
#include "llvm/IR/Value.h"
#include "llvm/IR/ValueHandle.h"
#include "llvm/InitializePasses.h"
#include "llvm/Pass.h"
#include "llvm/Support/Casting.h"
#include "llvm/Support/CommandLine.h"
#include "llvm/Support/Compiler.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/MathExtras.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Scalar.h"
#include "llvm/Transforms/Utils/BasicBlockUtils.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Transforms/Utils/LoopUtils.h"
#include "llvm/Transforms/Utils/ScalarEvolutionExpander.h"
#include "llvm/Transforms/Utils/SimplifyIndVar.h"
#include <cassert>
#include <cstdint>
#include <utility>

using namespace llvm;
using namespace PatternMatch;

#define DEBUG_TYPE "indvars"

STATISTIC(NumWidened     , "Number of indvars widened");
STATISTIC(NumReplaced    , "Number of exit values replaced");
STATISTIC(NumLFTR        , "Number of loop exit tests replaced");
STATISTIC(NumElimExt     , "Number of IV sign/zero extends eliminated");
STATISTIC(NumElimIV      , "Number of congruent IVs eliminated");

// Trip count verification can be enabled by default under NDEBUG if we
// implement a strong expression equivalence checker in SCEV. Until then, we
// use the verify-indvars flag, which may assert in some cases.
static cl::opt<bool> VerifyIndvars(
    "verify-indvars", cl::Hidden,
    cl::desc("Verify the ScalarEvolution result after running indvars. Has no "
             "effect in release builds. (Note: this adds additional SCEV "
             "queries potentially changing the analysis result)"));

static cl::opt<ReplaceExitVal> ReplaceExitValue(
    "replexitval", cl::Hidden, cl::init(OnlyCheapRepl),
    cl::desc("Choose the strategy to replace exit value in IndVarSimplify"),
    cl::values(
        clEnumValN(NeverRepl, "never", "never replace exit value"),
        clEnumValN(OnlyCheapRepl, "cheap",
                   "only replace exit value when the cost is cheap"),
        clEnumValN(
            UnusedIndVarInLoop, "unusedindvarinloop",
            "only replace exit value when it is an unused "
            "induction variable in the loop and has cheap replacement cost"),
        clEnumValN(NoHardUse, "noharduse",
                   "only replace exit values when loop def likely dead"),
        clEnumValN(AlwaysRepl, "always",
                   "always replace exit value whenever possible")));

static cl::opt<bool> UsePostIncrementRanges(
  "indvars-post-increment-ranges", cl::Hidden,
  cl::desc("Use post increment control-dependent ranges in IndVarSimplify"),
  cl::init(true));

static cl::opt<bool>
DisableLFTR("disable-lftr", cl::Hidden, cl::init(false),
            cl::desc("Disable Linear Function Test Replace optimization"));

static cl::opt<bool>
LoopPredication("indvars-predicate-loops", cl::Hidden, cl::init(true),
                cl::desc("Predicate conditions in read only loops"));

static cl::opt<bool>
AllowIVWidening("indvars-widen-indvars", cl::Hidden, cl::init(true),
                cl::desc("Allow widening of indvars to eliminate s/zext"));

namespace {

class IndVarSimplify {
  LoopInfo *LI;
  ScalarEvolution *SE;
  DominatorTree *DT;
  const DataLayout &DL;
  TargetLibraryInfo *TLI;
  const TargetTransformInfo *TTI;
  std::unique_ptr<MemorySSAUpdater> MSSAU;

  SmallVector<WeakTrackingVH, 16> DeadInsts;
  bool WidenIndVars;

  bool handleFloatingPointIV(Loop *L, PHINode *PH);
  bool rewriteNonIntegerIVs(Loop *L);

  bool simplifyAndExtend(Loop *L, SCEVExpander &Rewriter, LoopInfo *LI);
  /// Try to improve our exit conditions by converting condition from signed
  /// to unsigned or rotating computation out of the loop.
  /// (See inline comment about why this is duplicated from simplifyAndExtend)
  bool canonicalizeExitCondition(Loop *L);
  /// Try to eliminate loop exits based on analyzeable exit counts
  bool optimizeLoopExits(Loop *L, SCEVExpander &Rewriter);
  /// Try to form loop invariant tests for loop exits by changing how many
  /// iterations of the loop run when that is unobservable.
  bool predicateLoopExits(Loop *L, SCEVExpander &Rewriter);

  bool rewriteFirstIterationLoopExitValues(Loop *L);

  bool linearFunctionTestReplace(Loop *L, BasicBlock *ExitingBB,
                                 const SCEV *ExitCount,
                                 PHINode *IndVar, SCEVExpander &Rewriter);

  bool sinkUnusedInvariants(Loop *L);

public:
  IndVarSimplify(LoopInfo *LI, ScalarEvolution *SE, DominatorTree *DT,
                 const DataLayout &DL, TargetLibraryInfo *TLI,
                 TargetTransformInfo *TTI, MemorySSA *MSSA, bool WidenIndVars)
      : LI(LI), SE(SE), DT(DT), DL(DL), TLI(TLI), TTI(TTI),
        WidenIndVars(WidenIndVars) {
    if (MSSA)
      MSSAU = std::make_unique<MemorySSAUpdater>(MSSA);
  }

  bool run(Loop *L);
};

} // end anonymous namespace

//===----------------------------------------------------------------------===//
// rewriteNonIntegerIVs and helpers. Prefer integer IVs.
//===----------------------------------------------------------------------===//

/// Convert APF to an integer, if possible.
static bool ConvertToSInt(const APFloat &APF, int64_t &IntVal) {
  bool isExact = false;
  // See if we can convert this to an int64_t
  uint64_t UIntVal;
  if (APF.convertToInteger(MutableArrayRef(UIntVal), 64, true,
                           APFloat::rmTowardZero, &isExact) != APFloat::opOK ||
      !isExact)
    return false;
  IntVal = UIntVal;
  return true;
}

/// If the loop has floating induction variable then insert corresponding
/// integer induction variable if possible.
/// For example,
/// for(double i = 0; i < 10000; ++i)
///   bar(i)
/// is converted into
/// for(int i = 0; i < 10000; ++i)
///   bar((double)i);
bool IndVarSimplify::handleFloatingPointIV(Loop *L, PHINode *PN) {
  unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
  unsigned BackEdge     = IncomingEdge^1;

  // Check incoming value.
  auto *InitValueVal = dyn_cast<ConstantFP>(PN->getIncomingValue(IncomingEdge));

  int64_t InitValue;
  if (!InitValueVal || !ConvertToSInt(InitValueVal->getValueAPF(), InitValue))
    return false;

  // Check IV increment. Reject this PN if increment operation is not
  // an add or increment value can not be represented by an integer.
  auto *Incr = dyn_cast<BinaryOperator>(PN->getIncomingValue(BackEdge));
  if (Incr == nullptr || Incr->getOpcode() != Instruction::FAdd) return false;

  // If this is not an add of the PHI with a constantfp, or if the constant fp
  // is not an integer, bail out.
  ConstantFP *IncValueVal = dyn_cast<ConstantFP>(Incr->getOperand(1));
  int64_t IncValue;
  if (IncValueVal == nullptr || Incr->getOperand(0) != PN ||
      !ConvertToSInt(IncValueVal->getValueAPF(), IncValue))
    return false;

  // Check Incr uses. One user is PN and the other user is an exit condition
  // used by the conditional terminator.
  Value::user_iterator IncrUse = Incr->user_begin();
  Instruction *U1 = cast<Instruction>(*IncrUse++);
  if (IncrUse == Incr->user_end()) return false;
  Instruction *U2 = cast<Instruction>(*IncrUse++);
  if (IncrUse != Incr->user_end()) return false;

  // Find exit condition, which is an fcmp.  If it doesn't exist, or if it isn't
  // only used by a branch, we can't transform it.
  FCmpInst *Compare = dyn_cast<FCmpInst>(U1);
  if (!Compare)
    Compare = dyn_cast<FCmpInst>(U2);
  if (!Compare || !Compare->hasOneUse() ||
      !isa<BranchInst>(Compare->user_back()))
    return false;

  BranchInst *TheBr = cast<BranchInst>(Compare->user_back());

  // We need to verify that the branch actually controls the iteration count
  // of the loop.  If not, the new IV can overflow and no one will notice.
  // The branch block must be in the loop and one of the successors must be out
  // of the loop.
  assert(TheBr->isConditional() && "Can't use fcmp if not conditional");
  if (!L->contains(TheBr->getParent()) ||
      (L->contains(TheBr->getSuccessor(0)) &&
       L->contains(TheBr->getSuccessor(1))))
    return false;

  // If it isn't a comparison with an integer-as-fp (the exit value), we can't
  // transform it.
  ConstantFP *ExitValueVal = dyn_cast<ConstantFP>(Compare->getOperand(1));
  int64_t ExitValue;
  if (ExitValueVal == nullptr ||
      !ConvertToSInt(ExitValueVal->getValueAPF(), ExitValue))
    return false;

  // Find new predicate for integer comparison.
  CmpInst::Predicate NewPred = CmpInst::BAD_ICMP_PREDICATE;
  switch (Compare->getPredicate()) {
  default: return false;  // Unknown comparison.
  case CmpInst::FCMP_OEQ:
  case CmpInst::FCMP_UEQ: NewPred = CmpInst::ICMP_EQ; break;
  case CmpInst::FCMP_ONE:
  case CmpInst::FCMP_UNE: NewPred = CmpInst::ICMP_NE; break;
  case CmpInst::FCMP_OGT:
  case CmpInst::FCMP_UGT: NewPred = CmpInst::ICMP_SGT; break;
  case CmpInst::FCMP_OGE:
  case CmpInst::FCMP_UGE: NewPred = CmpInst::ICMP_SGE; break;
  case CmpInst::FCMP_OLT:
  case CmpInst::FCMP_ULT: NewPred = CmpInst::ICMP_SLT; break;
  case CmpInst::FCMP_OLE:
  case CmpInst::FCMP_ULE: NewPred = CmpInst::ICMP_SLE; break;
  }

  // We convert the floating point induction variable to a signed i32 value if
  // we can.  This is only safe if the comparison will not overflow in a way
  // that won't be trapped by the integer equivalent operations.  Check for this
  // now.
  // TODO: We could use i64 if it is native and the range requires it.

  // The start/stride/exit values must all fit in signed i32.
  if (!isInt<32>(InitValue) || !isInt<32>(IncValue) || !isInt<32>(ExitValue))
    return false;

  // If not actually striding (add x, 0.0), avoid touching the code.
  if (IncValue == 0)
    return false;

  // Positive and negative strides have different safety conditions.
  if (IncValue > 0) {
    // If we have a positive stride, we require the init to be less than the
    // exit value.
    if (InitValue >= ExitValue)
      return false;

    uint32_t Range = uint32_t(ExitValue-InitValue);
    // Check for infinite loop, either:
    // while (i <= Exit) or until (i > Exit)
    if (NewPred == CmpInst::ICMP_SLE || NewPred == CmpInst::ICMP_SGT) {
      if (++Range == 0) return false;  // Range overflows.
    }

    unsigned Leftover = Range % uint32_t(IncValue);

    // If this is an equality comparison, we require that the strided value
    // exactly land on the exit value, otherwise the IV condition will wrap
    // around and do things the fp IV wouldn't.
    if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
        Leftover != 0)
      return false;

    // If the stride would wrap around the i32 before exiting, we can't
    // transform the IV.
    if (Leftover != 0 && int32_t(ExitValue+IncValue) < ExitValue)
      return false;
  } else {
    // If we have a negative stride, we require the init to be greater than the
    // exit value.
    if (InitValue <= ExitValue)
      return false;

    uint32_t Range = uint32_t(InitValue-ExitValue);
    // Check for infinite loop, either:
    // while (i >= Exit) or until (i < Exit)
    if (NewPred == CmpInst::ICMP_SGE || NewPred == CmpInst::ICMP_SLT) {
      if (++Range == 0) return false;  // Range overflows.
    }

    unsigned Leftover = Range % uint32_t(-IncValue);

    // If this is an equality comparison, we require that the strided value
    // exactly land on the exit value, otherwise the IV condition will wrap
    // around and do things the fp IV wouldn't.
    if ((NewPred == CmpInst::ICMP_EQ || NewPred == CmpInst::ICMP_NE) &&
        Leftover != 0)
      return false;

    // If the stride would wrap around the i32 before exiting, we can't
    // transform the IV.
    if (Leftover != 0 && int32_t(ExitValue+IncValue) > ExitValue)
      return false;
  }

  IntegerType *Int32Ty = Type::getInt32Ty(PN->getContext());

  // Insert new integer induction variable.
  PHINode *NewPHI = PHINode::Create(Int32Ty, 2, PN->getName()+".int", PN);
  NewPHI->addIncoming(ConstantInt::get(Int32Ty, InitValue),
                      PN->getIncomingBlock(IncomingEdge));

  Value *NewAdd =
    BinaryOperator::CreateAdd(NewPHI, ConstantInt::get(Int32Ty, IncValue),
                              Incr->getName()+".int", Incr);
  NewPHI->addIncoming(NewAdd, PN->getIncomingBlock(BackEdge));

  ICmpInst *NewCompare = new ICmpInst(TheBr, NewPred, NewAdd,
                                      ConstantInt::get(Int32Ty, ExitValue),
                                      Compare->getName());

  // In the following deletions, PN may become dead and may be deleted.
  // Use a WeakTrackingVH to observe whether this happens.
  WeakTrackingVH WeakPH = PN;

  // Delete the old floating point exit comparison.  The branch starts using the
  // new comparison.
  NewCompare->takeName(Compare);
  Compare->replaceAllUsesWith(NewCompare);
  RecursivelyDeleteTriviallyDeadInstructions(Compare, TLI, MSSAU.get());

  // Delete the old floating point increment.
  Incr->replaceAllUsesWith(PoisonValue::get(Incr->getType()));
  RecursivelyDeleteTriviallyDeadInstructions(Incr, TLI, MSSAU.get());

  // If the FP induction variable still has uses, this is because something else
  // in the loop uses its value.  In order to canonicalize the induction
  // variable, we chose to eliminate the IV and rewrite it in terms of an
  // int->fp cast.
  //
  // We give preference to sitofp over uitofp because it is faster on most
  // platforms.
  if (WeakPH) {
    Value *Conv = new SIToFPInst(NewPHI, PN->getType(), "indvar.conv",
                                 &*PN->getParent()->getFirstInsertionPt());
    PN->replaceAllUsesWith(Conv);
    RecursivelyDeleteTriviallyDeadInstructions(PN, TLI, MSSAU.get());
  }
  return true;
}

bool IndVarSimplify::rewriteNonIntegerIVs(Loop *L) {
  // First step.  Check to see if there are any floating-point recurrences.
  // If there are, change them into integer recurrences, permitting analysis by
  // the SCEV routines.
  BasicBlock *Header = L->getHeader();

  SmallVector<WeakTrackingVH, 8> PHIs;
  for (PHINode &PN : Header->phis())
    PHIs.push_back(&PN);

  bool Changed = false;
  for (unsigned i = 0, e = PHIs.size(); i != e; ++i)
    if (PHINode *PN = dyn_cast_or_null<PHINode>(&*PHIs[i]))
      Changed |= handleFloatingPointIV(L, PN);

  // If the loop previously had floating-point IV, ScalarEvolution
  // may not have been able to compute a trip count. Now that we've done some
  // re-writing, the trip count may be computable.
  if (Changed)
    SE->forgetLoop(L);
  return Changed;
}

//===---------------------------------------------------------------------===//
// rewriteFirstIterationLoopExitValues: Rewrite loop exit values if we know
// they will exit at the first iteration.
//===---------------------------------------------------------------------===//

/// Check to see if this loop has loop invariant conditions which lead to loop
/// exits. If so, we know that if the exit path is taken, it is at the first
/// loop iteration. This lets us predict exit values of PHI nodes that live in
/// loop header.
bool IndVarSimplify::rewriteFirstIterationLoopExitValues(Loop *L) {
  // Verify the input to the pass is already in LCSSA form.
  assert(L->isLCSSAForm(*DT));

  SmallVector<BasicBlock *, 8> ExitBlocks;
  L->getUniqueExitBlocks(ExitBlocks);

  bool MadeAnyChanges = false;
  for (auto *ExitBB : ExitBlocks) {
    // If there are no more PHI nodes in this exit block, then no more
    // values defined inside the loop are used on this path.
    for (PHINode &PN : ExitBB->phis()) {
      for (unsigned IncomingValIdx = 0, E = PN.getNumIncomingValues();
           IncomingValIdx != E; ++IncomingValIdx) {
        auto *IncomingBB = PN.getIncomingBlock(IncomingValIdx);

        // Can we prove that the exit must run on the first iteration if it
        // runs at all?  (i.e. early exits are fine for our purposes, but
        // traces which lead to this exit being taken on the 2nd iteration
        // aren't.)  Note that this is about whether the exit branch is
        // executed, not about whether it is taken.
        if (!L->getLoopLatch() ||
            !DT->dominates(IncomingBB, L->getLoopLatch()))
          continue;

        // Get condition that leads to the exit path.
        auto *TermInst = IncomingBB->getTerminator();

        Value *Cond = nullptr;
        if (auto *BI = dyn_cast<BranchInst>(TermInst)) {
          // Must be a conditional branch, otherwise the block
          // should not be in the loop.
          Cond = BI->getCondition();
        } else if (auto *SI = dyn_cast<SwitchInst>(TermInst))
          Cond = SI->getCondition();
        else
          continue;

        if (!L->isLoopInvariant(Cond))
          continue;

        auto *ExitVal = dyn_cast<PHINode>(PN.getIncomingValue(IncomingValIdx));

        // Only deal with PHIs in the loop header.
        if (!ExitVal || ExitVal->getParent() != L->getHeader())
          continue;

        // If ExitVal is a PHI on the loop header, then we know its
        // value along this exit because the exit can only be taken
        // on the first iteration.
        auto *LoopPreheader = L->getLoopPreheader();
        assert(LoopPreheader && "Invalid loop");
        int PreheaderIdx = ExitVal->getBasicBlockIndex(LoopPreheader);
        if (PreheaderIdx != -1) {
          assert(ExitVal->getParent() == L->getHeader() &&
                 "ExitVal must be in loop header");
          MadeAnyChanges = true;
          PN.setIncomingValue(IncomingValIdx,
                              ExitVal->getIncomingValue(PreheaderIdx));
          SE->forgetValue(&PN);
        }
      }
    }
  }
  return MadeAnyChanges;
}

//===----------------------------------------------------------------------===//
//  IV Widening - Extend the width of an IV to cover its widest uses.
//===----------------------------------------------------------------------===//

/// Update information about the induction variable that is extended by this
/// sign or zero extend operation. This is used to determine the final width of
/// the IV before actually widening it.
static void visitIVCast(CastInst *Cast, WideIVInfo &WI,
                        ScalarEvolution *SE,
                        const TargetTransformInfo *TTI) {
  bool IsSigned = Cast->getOpcode() == Instruction::SExt;
  if (!IsSigned && Cast->getOpcode() != Instruction::ZExt)
    return;

  Type *Ty = Cast->getType();
  uint64_t Width = SE->getTypeSizeInBits(Ty);
  if (!Cast->getModule()->getDataLayout().isLegalInteger(Width))
    return;

  // Check that `Cast` actually extends the induction variable (we rely on this
  // later).  This takes care of cases where `Cast` is extending a truncation of
  // the narrow induction variable, and thus can end up being narrower than the
  // "narrow" induction variable.
  uint64_t NarrowIVWidth = SE->getTypeSizeInBits(WI.NarrowIV->getType());
  if (NarrowIVWidth >= Width)
    return;

  // Cast is either an sext or zext up to this point.
  // We should not widen an indvar if arithmetics on the wider indvar are more
  // expensive than those on the narrower indvar. We check only the cost of ADD
  // because at least an ADD is required to increment the induction variable. We
  // could compute more comprehensively the cost of all instructions on the
  // induction variable when necessary.
  if (TTI &&
      TTI->getArithmeticInstrCost(Instruction::Add, Ty) >
          TTI->getArithmeticInstrCost(Instruction::Add,
                                      Cast->getOperand(0)->getType())) {
    return;
  }

  if (!WI.WidestNativeType ||
      Width > SE->getTypeSizeInBits(WI.WidestNativeType)) {
    WI.WidestNativeType = SE->getEffectiveSCEVType(Ty);
    WI.IsSigned = IsSigned;
    return;
  }

  // We extend the IV to satisfy the sign of its user(s), or 'signed'
  // if there are multiple users with both sign- and zero extensions,
  // in order not to introduce nondeterministic behaviour based on the
  // unspecified order of a PHI nodes' users-iterator.
  WI.IsSigned |= IsSigned;
}

//===----------------------------------------------------------------------===//
//  Live IV Reduction - Minimize IVs live across the loop.
//===----------------------------------------------------------------------===//

//===----------------------------------------------------------------------===//
//  Simplification of IV users based on SCEV evaluation.
//===----------------------------------------------------------------------===//

namespace {

class IndVarSimplifyVisitor : public IVVisitor {
  ScalarEvolution *SE;
  const TargetTransformInfo *TTI;
  PHINode *IVPhi;

public:
  WideIVInfo WI;

  IndVarSimplifyVisitor(PHINode *IV, ScalarEvolution *SCEV,
                        const TargetTransformInfo *TTI,
                        const DominatorTree *DTree)
    : SE(SCEV), TTI(TTI), IVPhi(IV) {
    DT = DTree;
    WI.NarrowIV = IVPhi;
  }

  // Implement the interface used by simplifyUsersOfIV.
  void visitCast(CastInst *Cast) override { visitIVCast(Cast, WI, SE, TTI); }
};

} // end anonymous namespace

/// Iteratively perform simplification on a worklist of IV users. Each
/// successive simplification may push more users which may themselves be
/// candidates for simplification.
///
/// Sign/Zero extend elimination is interleaved with IV simplification.
bool IndVarSimplify::simplifyAndExtend(Loop *L,
                                       SCEVExpander &Rewriter,
                                       LoopInfo *LI) {
  SmallVector<WideIVInfo, 8> WideIVs;

  auto *GuardDecl = L->getBlocks()[0]->getModule()->getFunction(
          Intrinsic::getName(Intrinsic::experimental_guard));
  bool HasGuards = GuardDecl && !GuardDecl->use_empty();

  SmallVector<PHINode *, 8> LoopPhis;
  for (PHINode &PN : L->getHeader()->phis())
    LoopPhis.push_back(&PN);

  // Each round of simplification iterates through the SimplifyIVUsers worklist
  // for all current phis, then determines whether any IVs can be
  // widened. Widening adds new phis to LoopPhis, inducing another round of
  // simplification on the wide IVs.
  bool Changed = false;
  while (!LoopPhis.empty()) {
    // Evaluate as many IV expressions as possible before widening any IVs. This
    // forces SCEV to set no-wrap flags before evaluating sign/zero
    // extension. The first time SCEV attempts to normalize sign/zero extension,
    // the result becomes final. So for the most predictable results, we delay
    // evaluation of sign/zero extend evaluation until needed, and avoid running
    // other SCEV based analysis prior to simplifyAndExtend.
    do {
      PHINode *CurrIV = LoopPhis.pop_back_val();

      // Information about sign/zero extensions of CurrIV.
      IndVarSimplifyVisitor Visitor(CurrIV, SE, TTI, DT);

      Changed |= simplifyUsersOfIV(CurrIV, SE, DT, LI, TTI, DeadInsts, Rewriter,
                                   &Visitor);

      if (Visitor.WI.WidestNativeType) {
        WideIVs.push_back(Visitor.WI);
      }
    } while(!LoopPhis.empty());

    // Continue if we disallowed widening.
    if (!WidenIndVars)
      continue;

    for (; !WideIVs.empty(); WideIVs.pop_back()) {
      unsigned ElimExt;
      unsigned Widened;
      if (PHINode *WidePhi = createWideIV(WideIVs.back(), LI, SE, Rewriter,
                                          DT, DeadInsts, ElimExt, Widened,
                                          HasGuards, UsePostIncrementRanges)) {
        NumElimExt += ElimExt;
        NumWidened += Widened;
        Changed = true;
        LoopPhis.push_back(WidePhi);
      }
    }
  }
  return Changed;
}

//===----------------------------------------------------------------------===//
//  linearFunctionTestReplace and its kin. Rewrite the loop exit condition.
//===----------------------------------------------------------------------===//

/// Given an Value which is hoped to be part of an add recurance in the given
/// loop, return the associated Phi node if so.  Otherwise, return null.  Note
/// that this is less general than SCEVs AddRec checking.
static PHINode *getLoopPhiForCounter(Value *IncV, Loop *L) {
  Instruction *IncI = dyn_cast<Instruction>(IncV);
  if (!IncI)
    return nullptr;

  switch (IncI->getOpcode()) {
  case Instruction::Add:
  case Instruction::Sub:
    break;
  case Instruction::GetElementPtr:
    // An IV counter must preserve its type.
    if (IncI->getNumOperands() == 2)
      break;
    [[fallthrough]];
  default:
    return nullptr;
  }

  PHINode *Phi = dyn_cast<PHINode>(IncI->getOperand(0));
  if (Phi && Phi->getParent() == L->getHeader()) {
    if (L->isLoopInvariant(IncI->getOperand(1)))
      return Phi;
    return nullptr;
  }
  if (IncI->getOpcode() == Instruction::GetElementPtr)
    return nullptr;

  // Allow add/sub to be commuted.
  Phi = dyn_cast<PHINode>(IncI->getOperand(1));
  if (Phi && Phi->getParent() == L->getHeader()) {
    if (L->isLoopInvariant(IncI->getOperand(0)))
      return Phi;
  }
  return nullptr;
}

/// Whether the current loop exit test is based on this value.  Currently this
/// is limited to a direct use in the loop condition.
static bool isLoopExitTestBasedOn(Value *V, BasicBlock *ExitingBB) {
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  ICmpInst *ICmp = dyn_cast<ICmpInst>(BI->getCondition());
  // TODO: Allow non-icmp loop test.
  if (!ICmp)
    return false;

  // TODO: Allow indirect use.
  return ICmp->getOperand(0) == V || ICmp->getOperand(1) == V;
}

/// linearFunctionTestReplace policy. Return true unless we can show that the
/// current exit test is already sufficiently canonical.
static bool needsLFTR(Loop *L, BasicBlock *ExitingBB) {
  assert(L->getLoopLatch() && "Must be in simplified form");

  // Avoid converting a constant or loop invariant test back to a runtime
  // test.  This is critical for when SCEV's cached ExitCount is less precise
  // than the current IR (such as after we've proven a particular exit is
  // actually dead and thus the BE count never reaches our ExitCount.)
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  if (L->isLoopInvariant(BI->getCondition()))
    return false;

  // Do LFTR to simplify the exit condition to an ICMP.
  ICmpInst *Cond = dyn_cast<ICmpInst>(BI->getCondition());
  if (!Cond)
    return true;

  // Do LFTR to simplify the exit ICMP to EQ/NE
  ICmpInst::Predicate Pred = Cond->getPredicate();
  if (Pred != ICmpInst::ICMP_NE && Pred != ICmpInst::ICMP_EQ)
    return true;

  // Look for a loop invariant RHS
  Value *LHS = Cond->getOperand(0);
  Value *RHS = Cond->getOperand(1);
  if (!L->isLoopInvariant(RHS)) {
    if (!L->isLoopInvariant(LHS))
      return true;
    std::swap(LHS, RHS);
  }
  // Look for a simple IV counter LHS
  PHINode *Phi = dyn_cast<PHINode>(LHS);
  if (!Phi)
    Phi = getLoopPhiForCounter(LHS, L);

  if (!Phi)
    return true;

  // Do LFTR if PHI node is defined in the loop, but is *not* a counter.
  int Idx = Phi->getBasicBlockIndex(L->getLoopLatch());
  if (Idx < 0)
    return true;

  // Do LFTR if the exit condition's IV is *not* a simple counter.
  Value *IncV = Phi->getIncomingValue(Idx);
  return Phi != getLoopPhiForCounter(IncV, L);
}

/// Return true if undefined behavior would provable be executed on the path to
/// OnPathTo if Root produced a posion result.  Note that this doesn't say
/// anything about whether OnPathTo is actually executed or whether Root is
/// actually poison.  This can be used to assess whether a new use of Root can
/// be added at a location which is control equivalent with OnPathTo (such as
/// immediately before it) without introducing UB which didn't previously
/// exist.  Note that a false result conveys no information.
static bool mustExecuteUBIfPoisonOnPathTo(Instruction *Root,
                                          Instruction *OnPathTo,
                                          DominatorTree *DT) {
  // Basic approach is to assume Root is poison, propagate poison forward
  // through all users we can easily track, and then check whether any of those
  // users are provable UB and must execute before out exiting block might
  // exit.

  // The set of all recursive users we've visited (which are assumed to all be
  // poison because of said visit)
  SmallSet<const Value *, 16> KnownPoison;
  SmallVector<const Instruction*, 16> Worklist;
  Worklist.push_back(Root);
  while (!Worklist.empty()) {
    const Instruction *I = Worklist.pop_back_val();

    // If we know this must trigger UB on a path leading our target.
    if (mustTriggerUB(I, KnownPoison) && DT->dominates(I, OnPathTo))
      return true;

    // If we can't analyze propagation through this instruction, just skip it
    // and transitive users.  Safe as false is a conservative result.
    if (I != Root && !any_of(I->operands(), [&KnownPoison](const Use &U) {
          return KnownPoison.contains(U) && propagatesPoison(U);
        }))
      continue;

    if (KnownPoison.insert(I).second)
      for (const User *User : I->users())
        Worklist.push_back(cast<Instruction>(User));
  }

  // Might be non-UB, or might have a path we couldn't prove must execute on
  // way to exiting bb.
  return false;
}

/// Recursive helper for hasConcreteDef(). Unfortunately, this currently boils
/// down to checking that all operands are constant and listing instructions
/// that may hide undef.
static bool hasConcreteDefImpl(Value *V, SmallPtrSetImpl<Value*> &Visited,
                               unsigned Depth) {
  if (isa<Constant>(V))
    return !isa<UndefValue>(V);

  if (Depth >= 6)
    return false;

  // Conservatively handle non-constant non-instructions. For example, Arguments
  // may be undef.
  Instruction *I = dyn_cast<Instruction>(V);
  if (!I)
    return false;

  // Load and return values may be undef.
  if(I->mayReadFromMemory() || isa<CallInst>(I) || isa<InvokeInst>(I))
    return false;

  // Optimistically handle other instructions.
  for (Value *Op : I->operands()) {
    if (!Visited.insert(Op).second)
      continue;
    if (!hasConcreteDefImpl(Op, Visited, Depth+1))
      return false;
  }
  return true;
}

/// Return true if the given value is concrete. We must prove that undef can
/// never reach it.
///
/// TODO: If we decide that this is a good approach to checking for undef, we
/// may factor it into a common location.
static bool hasConcreteDef(Value *V) {
  SmallPtrSet<Value*, 8> Visited;
  Visited.insert(V);
  return hasConcreteDefImpl(V, Visited, 0);
}

/// Return true if this IV has any uses other than the (soon to be rewritten)
/// loop exit test.
static bool AlmostDeadIV(PHINode *Phi, BasicBlock *LatchBlock, Value *Cond) {
  int LatchIdx = Phi->getBasicBlockIndex(LatchBlock);
  Value *IncV = Phi->getIncomingValue(LatchIdx);

  for (User *U : Phi->users())
    if (U != Cond && U != IncV) return false;

  for (User *U : IncV->users())
    if (U != Cond && U != Phi) return false;
  return true;
}

/// Return true if the given phi is a "counter" in L.  A counter is an
/// add recurance (of integer or pointer type) with an arbitrary start, and a
/// step of 1.  Note that L must have exactly one latch.
static bool isLoopCounter(PHINode* Phi, Loop *L,
                          ScalarEvolution *SE) {
  assert(Phi->getParent() == L->getHeader());
  assert(L->getLoopLatch());

  if (!SE->isSCEVable(Phi->getType()))
    return false;

  const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(SE->getSCEV(Phi));
  if (!AR || AR->getLoop() != L || !AR->isAffine())
    return false;

  const SCEV *Step = dyn_cast<SCEVConstant>(AR->getStepRecurrence(*SE));
  if (!Step || !Step->isOne())
    return false;

  int LatchIdx = Phi->getBasicBlockIndex(L->getLoopLatch());
  Value *IncV = Phi->getIncomingValue(LatchIdx);
  return (getLoopPhiForCounter(IncV, L) == Phi &&
          isa<SCEVAddRecExpr>(SE->getSCEV(IncV)));
}

/// Search the loop header for a loop counter (anadd rec w/step of one)
/// suitable for use by LFTR.  If multiple counters are available, select the
/// "best" one based profitable heuristics.
///
/// BECount may be an i8* pointer type. The pointer difference is already
/// valid count without scaling the address stride, so it remains a pointer
/// expression as far as SCEV is concerned.
static PHINode *FindLoopCounter(Loop *L, BasicBlock *ExitingBB,
                                const SCEV *BECount,
                                ScalarEvolution *SE, DominatorTree *DT) {
  uint64_t BCWidth = SE->getTypeSizeInBits(BECount->getType());

  Value *Cond = cast<BranchInst>(ExitingBB->getTerminator())->getCondition();

  // Loop over all of the PHI nodes, looking for a simple counter.
  PHINode *BestPhi = nullptr;
  const SCEV *BestInit = nullptr;
  BasicBlock *LatchBlock = L->getLoopLatch();
  assert(LatchBlock && "Must be in simplified form");
  const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();

  for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
    PHINode *Phi = cast<PHINode>(I);
    if (!isLoopCounter(Phi, L, SE))
      continue;

    // Avoid comparing an integer IV against a pointer Limit.
    if (BECount->getType()->isPointerTy() && !Phi->getType()->isPointerTy())
      continue;

    const auto *AR = cast<SCEVAddRecExpr>(SE->getSCEV(Phi));

    // AR may be a pointer type, while BECount is an integer type.
    // AR may be wider than BECount. With eq/ne tests overflow is immaterial.
    // AR may not be a narrower type, or we may never exit.
    uint64_t PhiWidth = SE->getTypeSizeInBits(AR->getType());
    if (PhiWidth < BCWidth || !DL.isLegalInteger(PhiWidth))
      continue;

    // Avoid reusing a potentially undef value to compute other values that may
    // have originally had a concrete definition.
    if (!hasConcreteDef(Phi)) {
      // We explicitly allow unknown phis as long as they are already used by
      // the loop exit test.  This is legal since performing LFTR could not
      // increase the number of undef users.
      Value *IncPhi = Phi->getIncomingValueForBlock(LatchBlock);
      if (!isLoopExitTestBasedOn(Phi, ExitingBB) &&
          !isLoopExitTestBasedOn(IncPhi, ExitingBB))
        continue;
    }

    // Avoid introducing undefined behavior due to poison which didn't exist in
    // the original program.  (Annoyingly, the rules for poison and undef
    // propagation are distinct, so this does NOT cover the undef case above.)
    // We have to ensure that we don't introduce UB by introducing a use on an
    // iteration where said IV produces poison.  Our strategy here differs for
    // pointers and integer IVs.  For integers, we strip and reinfer as needed,
    // see code in linearFunctionTestReplace.  For pointers, we restrict
    // transforms as there is no good way to reinfer inbounds once lost.
    if (!Phi->getType()->isIntegerTy() &&
        !mustExecuteUBIfPoisonOnPathTo(Phi, ExitingBB->getTerminator(), DT))
      continue;

    const SCEV *Init = AR->getStart();

    if (BestPhi && !AlmostDeadIV(BestPhi, LatchBlock, Cond)) {
      // Don't force a live loop counter if another IV can be used.
      if (AlmostDeadIV(Phi, LatchBlock, Cond))
        continue;

      // Prefer to count-from-zero. This is a more "canonical" counter form. It
      // also prefers integer to pointer IVs.
      if (BestInit->isZero() != Init->isZero()) {
        if (BestInit->isZero())
          continue;
      }
      // If two IVs both count from zero or both count from nonzero then the
      // narrower is likely a dead phi that has been widened. Use the wider phi
      // to allow the other to be eliminated.
      else if (PhiWidth <= SE->getTypeSizeInBits(BestPhi->getType()))
        continue;
    }
    BestPhi = Phi;
    BestInit = Init;
  }
  return BestPhi;
}

/// Insert an IR expression which computes the value held by the IV IndVar
/// (which must be an loop counter w/unit stride) after the backedge of loop L
/// is taken ExitCount times.
static Value *genLoopLimit(PHINode *IndVar, BasicBlock *ExitingBB,
                           const SCEV *ExitCount, bool UsePostInc, Loop *L,
                           SCEVExpander &Rewriter, ScalarEvolution *SE) {
  assert(isLoopCounter(IndVar, L, SE));
  const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(SE->getSCEV(IndVar));
  const SCEV *IVInit = AR->getStart();
  assert(AR->getStepRecurrence(*SE)->isOne() && "only handles unit stride");

  // IVInit may be a pointer while ExitCount is an integer when FindLoopCounter
  // finds a valid pointer IV. Sign extend ExitCount in order to materialize a
  // GEP. Avoid running SCEVExpander on a new pointer value, instead reusing
  // the existing GEPs whenever possible.
  if (IndVar->getType()->isPointerTy() &&
      !ExitCount->getType()->isPointerTy()) {
    // IVOffset will be the new GEP offset that is interpreted by GEP as a
    // signed value. ExitCount on the other hand represents the loop trip count,
    // which is an unsigned value. FindLoopCounter only allows induction
    // variables that have a positive unit stride of one. This means we don't
    // have to handle the case of negative offsets (yet) and just need to zero
    // extend ExitCount.
    Type *OfsTy = SE->getEffectiveSCEVType(IVInit->getType());
    const SCEV *IVOffset = SE->getTruncateOrZeroExtend(ExitCount, OfsTy);
    if (UsePostInc)
      IVOffset = SE->getAddExpr(IVOffset, SE->getOne(OfsTy));

    // Expand the code for the iteration count.
    assert(SE->isLoopInvariant(IVOffset, L) &&
           "Computed iteration count is not loop invariant!");

    const SCEV *IVLimit = SE->getAddExpr(IVInit, IVOffset);
    BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
    return Rewriter.expandCodeFor(IVLimit, IndVar->getType(), BI);
  } else {
    // In any other case, convert both IVInit and ExitCount to integers before
    // comparing. This may result in SCEV expansion of pointers, but in practice
    // SCEV will fold the pointer arithmetic away as such:
    // BECount = (IVEnd - IVInit - 1) => IVLimit = IVInit (postinc).
    //
    // Valid Cases: (1) both integers is most common; (2) both may be pointers
    // for simple memset-style loops.
    //
    // IVInit integer and ExitCount pointer would only occur if a canonical IV
    // were generated on top of case #2, which is not expected.

    // For unit stride, IVCount = Start + ExitCount with 2's complement
    // overflow.

    // For integer IVs, truncate the IV before computing IVInit + BECount,
    // unless we know apriori that the limit must be a constant when evaluated
    // in the bitwidth of the IV.  We prefer (potentially) keeping a truncate
    // of the IV in the loop over a (potentially) expensive expansion of the
    // widened exit count add(zext(add)) expression.
    if (SE->getTypeSizeInBits(IVInit->getType())
        > SE->getTypeSizeInBits(ExitCount->getType())) {
      if (isa<SCEVConstant>(IVInit) && isa<SCEVConstant>(ExitCount))
        ExitCount = SE->getZeroExtendExpr(ExitCount, IVInit->getType());
      else
        IVInit = SE->getTruncateExpr(IVInit, ExitCount->getType());
    }

    const SCEV *IVLimit = SE->getAddExpr(IVInit, ExitCount);

    if (UsePostInc)
      IVLimit = SE->getAddExpr(IVLimit, SE->getOne(IVLimit->getType()));

    // Expand the code for the iteration count.
    assert(SE->isLoopInvariant(IVLimit, L) &&
           "Computed iteration count is not loop invariant!");
    // Ensure that we generate the same type as IndVar, or a smaller integer
    // type. In the presence of null pointer values, we have an integer type
    // SCEV expression (IVInit) for a pointer type IV value (IndVar).
    Type *LimitTy = ExitCount->getType()->isPointerTy() ?
      IndVar->getType() : ExitCount->getType();
    BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
    return Rewriter.expandCodeFor(IVLimit, LimitTy, BI);
  }
}

/// This method rewrites the exit condition of the loop to be a canonical !=
/// comparison against the incremented loop induction variable.  This pass is
/// able to rewrite the exit tests of any loop where the SCEV analysis can
/// determine a loop-invariant trip count of the loop, which is actually a much
/// broader range than just linear tests.
bool IndVarSimplify::
linearFunctionTestReplace(Loop *L, BasicBlock *ExitingBB,
                          const SCEV *ExitCount,
                          PHINode *IndVar, SCEVExpander &Rewriter) {
  assert(L->getLoopLatch() && "Loop no longer in simplified form?");
  assert(isLoopCounter(IndVar, L, SE));
  Instruction * const IncVar =
    cast<Instruction>(IndVar->getIncomingValueForBlock(L->getLoopLatch()));

  // Initialize CmpIndVar to the preincremented IV.
  Value *CmpIndVar = IndVar;
  bool UsePostInc = false;

  // If the exiting block is the same as the backedge block, we prefer to
  // compare against the post-incremented value, otherwise we must compare
  // against the preincremented value.
  if (ExitingBB == L->getLoopLatch()) {
    // For pointer IVs, we chose to not strip inbounds which requires us not
    // to add a potentially UB introducing use.  We need to either a) show
    // the loop test we're modifying is already in post-inc form, or b) show
    // that adding a use must not introduce UB.
    bool SafeToPostInc =
        IndVar->getType()->isIntegerTy() ||
        isLoopExitTestBasedOn(IncVar, ExitingBB) ||
        mustExecuteUBIfPoisonOnPathTo(IncVar, ExitingBB->getTerminator(), DT);
    if (SafeToPostInc) {
      UsePostInc = true;
      CmpIndVar = IncVar;
    }
  }

  // It may be necessary to drop nowrap flags on the incrementing instruction
  // if either LFTR moves from a pre-inc check to a post-inc check (in which
  // case the increment might have previously been poison on the last iteration
  // only) or if LFTR switches to a different IV that was previously dynamically
  // dead (and as such may be arbitrarily poison). We remove any nowrap flags
  // that SCEV didn't infer for the post-inc addrec (even if we use a pre-inc
  // check), because the pre-inc addrec flags may be adopted from the original
  // instruction, while SCEV has to explicitly prove the post-inc nowrap flags.
  // TODO: This handling is inaccurate for one case: If we switch to a
  // dynamically dead IV that wraps on the first loop iteration only, which is
  // not covered by the post-inc addrec. (If the new IV was not dynamically
  // dead, it could not be poison on the first iteration in the first place.)
  if (auto *BO = dyn_cast<BinaryOperator>(IncVar)) {
    const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(SE->getSCEV(IncVar));
    if (BO->hasNoUnsignedWrap())
      BO->setHasNoUnsignedWrap(AR->hasNoUnsignedWrap());
    if (BO->hasNoSignedWrap())
      BO->setHasNoSignedWrap(AR->hasNoSignedWrap());
  }

  Value *ExitCnt = genLoopLimit(
      IndVar, ExitingBB, ExitCount, UsePostInc, L, Rewriter, SE);
  assert(ExitCnt->getType()->isPointerTy() ==
             IndVar->getType()->isPointerTy() &&
         "genLoopLimit missed a cast");

  // Insert a new icmp_ne or icmp_eq instruction before the branch.
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  ICmpInst::Predicate P;
  if (L->contains(BI->getSuccessor(0)))
    P = ICmpInst::ICMP_NE;
  else
    P = ICmpInst::ICMP_EQ;

  IRBuilder<> Builder(BI);

  // The new loop exit condition should reuse the debug location of the
  // original loop exit condition.
  if (auto *Cond = dyn_cast<Instruction>(BI->getCondition()))
    Builder.SetCurrentDebugLocation(Cond->getDebugLoc());

  // For integer IVs, if we evaluated the limit in the narrower bitwidth to
  // avoid the expensive expansion of the limit expression in the wider type,
  // emit a truncate to narrow the IV to the ExitCount type.  This is safe
  // since we know (from the exit count bitwidth), that we can't self-wrap in
  // the narrower type.
  unsigned CmpIndVarSize = SE->getTypeSizeInBits(CmpIndVar->getType());
  unsigned ExitCntSize = SE->getTypeSizeInBits(ExitCnt->getType());
  if (CmpIndVarSize > ExitCntSize) {
    assert(!CmpIndVar->getType()->isPointerTy() &&
           !ExitCnt->getType()->isPointerTy());

    // Before resorting to actually inserting the truncate, use the same
    // reasoning as from SimplifyIndvar::eliminateTrunc to see if we can extend
    // the other side of the comparison instead.  We still evaluate the limit
    // in the narrower bitwidth, we just prefer a zext/sext outside the loop to
    // a truncate within in.
    bool Extended = false;
    const SCEV *IV = SE->getSCEV(CmpIndVar);
    const SCEV *TruncatedIV = SE->getTruncateExpr(SE->getSCEV(CmpIndVar),
                                                  ExitCnt->getType());
    const SCEV *ZExtTrunc =
      SE->getZeroExtendExpr(TruncatedIV, CmpIndVar->getType());

    if (ZExtTrunc == IV) {
      Extended = true;
      ExitCnt = Builder.CreateZExt(ExitCnt, IndVar->getType(),
                                   "wide.trip.count");
    } else {
      const SCEV *SExtTrunc =
        SE->getSignExtendExpr(TruncatedIV, CmpIndVar->getType());
      if (SExtTrunc == IV) {
        Extended = true;
        ExitCnt = Builder.CreateSExt(ExitCnt, IndVar->getType(),
                                     "wide.trip.count");
      }
    }

    if (Extended) {
      bool Discard;
      L->makeLoopInvariant(ExitCnt, Discard);
    } else
      CmpIndVar = Builder.CreateTrunc(CmpIndVar, ExitCnt->getType(),
                                      "lftr.wideiv");
  }
  LLVM_DEBUG(dbgs() << "INDVARS: Rewriting loop exit condition to:\n"
                    << "      LHS:" << *CmpIndVar << '\n'
                    << "       op:\t" << (P == ICmpInst::ICMP_NE ? "!=" : "==")
                    << "\n"
                    << "      RHS:\t" << *ExitCnt << "\n"
                    << "ExitCount:\t" << *ExitCount << "\n"
                    << "  was: " << *BI->getCondition() << "\n");

  Value *Cond = Builder.CreateICmp(P, CmpIndVar, ExitCnt, "exitcond");
  Value *OrigCond = BI->getCondition();
  // It's tempting to use replaceAllUsesWith here to fully replace the old
  // comparison, but that's not immediately safe, since users of the old
  // comparison may not be dominated by the new comparison. Instead, just
  // update the branch to use the new comparison; in the common case this
  // will make old comparison dead.
  BI->setCondition(Cond);
  DeadInsts.emplace_back(OrigCond);

  ++NumLFTR;
  return true;
}

//===----------------------------------------------------------------------===//
//  sinkUnusedInvariants. A late subpass to cleanup loop preheaders.
//===----------------------------------------------------------------------===//

/// If there's a single exit block, sink any loop-invariant values that
/// were defined in the preheader but not used inside the loop into the
/// exit block to reduce register pressure in the loop.
bool IndVarSimplify::sinkUnusedInvariants(Loop *L) {
  BasicBlock *ExitBlock = L->getExitBlock();
  if (!ExitBlock) return false;

  BasicBlock *Preheader = L->getLoopPreheader();
  if (!Preheader) return false;

  bool MadeAnyChanges = false;
  BasicBlock::iterator InsertPt = ExitBlock->getFirstInsertionPt();
  BasicBlock::iterator I(Preheader->getTerminator());
  while (I != Preheader->begin()) {
    --I;
    // New instructions were inserted at the end of the preheader.
    if (isa<PHINode>(I))
      break;

    // Don't move instructions which might have side effects, since the side
    // effects need to complete before instructions inside the loop.  Also don't
    // move instructions which might read memory, since the loop may modify
    // memory. Note that it's okay if the instruction might have undefined
    // behavior: LoopSimplify guarantees that the preheader dominates the exit
    // block.
    if (I->mayHaveSideEffects() || I->mayReadFromMemory())
      continue;

    // Skip debug info intrinsics.
    if (isa<DbgInfoIntrinsic>(I))
      continue;

    // Skip eh pad instructions.
    if (I->isEHPad())
      continue;

    // Don't sink alloca: we never want to sink static alloca's out of the
    // entry block, and correctly sinking dynamic alloca's requires
    // checks for stacksave/stackrestore intrinsics.
    // FIXME: Refactor this check somehow?
    if (isa<AllocaInst>(I))
      continue;

    // Determine if there is a use in or before the loop (direct or
    // otherwise).
    bool UsedInLoop = false;
    for (Use &U : I->uses()) {
      Instruction *User = cast<Instruction>(U.getUser());
      BasicBlock *UseBB = User->getParent();
      if (PHINode *P = dyn_cast<PHINode>(User)) {
        unsigned i =
          PHINode::getIncomingValueNumForOperand(U.getOperandNo());
        UseBB = P->getIncomingBlock(i);
      }
      if (UseBB == Preheader || L->contains(UseBB)) {
        UsedInLoop = true;
        break;
      }
    }

    // If there is, the def must remain in the preheader.
    if (UsedInLoop)
      continue;

    // Otherwise, sink it to the exit block.
    Instruction *ToMove = &*I;
    bool Done = false;

    if (I != Preheader->begin()) {
      // Skip debug info intrinsics.
      do {
        --I;
      } while (I->isDebugOrPseudoInst() && I != Preheader->begin());

      if (I->isDebugOrPseudoInst() && I == Preheader->begin())
        Done = true;
    } else {
      Done = true;
    }

    MadeAnyChanges = true;
    ToMove->moveBefore(*ExitBlock, InsertPt);
    SE->forgetValue(ToMove);
    if (Done) break;
    InsertPt = ToMove->getIterator();
  }

  return MadeAnyChanges;
}

static void replaceExitCond(BranchInst *BI, Value *NewCond,
                            SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
  auto *OldCond = BI->getCondition();
  LLVM_DEBUG(dbgs() << "Replacing condition of loop-exiting branch " << *BI
                    << " with " << *NewCond << "\n");
  BI->setCondition(NewCond);
  if (OldCond->use_empty())
    DeadInsts.emplace_back(OldCond);
}

static Constant *createFoldedExitCond(const Loop *L, BasicBlock *ExitingBB,
                                      bool IsTaken) {
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  bool ExitIfTrue = !L->contains(*succ_begin(ExitingBB));
  auto *OldCond = BI->getCondition();
  return ConstantInt::get(OldCond->getType(),
                          IsTaken ? ExitIfTrue : !ExitIfTrue);
}

static void foldExit(const Loop *L, BasicBlock *ExitingBB, bool IsTaken,
                     SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  auto *NewCond = createFoldedExitCond(L, ExitingBB, IsTaken);
  replaceExitCond(BI, NewCond, DeadInsts);
}

static void replaceLoopPHINodesWithPreheaderValues(
    LoopInfo *LI, Loop *L, SmallVectorImpl<WeakTrackingVH> &DeadInsts,
    ScalarEvolution &SE) {
  assert(L->isLoopSimplifyForm() && "Should only do it in simplify form!");
  auto *LoopPreheader = L->getLoopPreheader();
  auto *LoopHeader = L->getHeader();
  SmallVector<Instruction *> Worklist;
  for (auto &PN : LoopHeader->phis()) {
    auto *PreheaderIncoming = PN.getIncomingValueForBlock(LoopPreheader);
    for (User *U : PN.users())
      Worklist.push_back(cast<Instruction>(U));
    SE.forgetValue(&PN);
    PN.replaceAllUsesWith(PreheaderIncoming);
    DeadInsts.emplace_back(&PN);
  }

  // Replacing with the preheader value will often allow IV users to simplify
  // (especially if the preheader value is a constant).
  SmallPtrSet<Instruction *, 16> Visited;
  while (!Worklist.empty()) {
    auto *I = cast<Instruction>(Worklist.pop_back_val());
    if (!Visited.insert(I).second)
      continue;

    // Don't simplify instructions outside the loop.
    if (!L->contains(I))
      continue;

    Value *Res = simplifyInstruction(I, I->getModule()->getDataLayout());
    if (Res && LI->replacementPreservesLCSSAForm(I, Res)) {
      for (User *U : I->users())
        Worklist.push_back(cast<Instruction>(U));
      I->replaceAllUsesWith(Res);
      DeadInsts.emplace_back(I);
    }
  }
}

static Value *
createInvariantCond(const Loop *L, BasicBlock *ExitingBB,
                    const ScalarEvolution::LoopInvariantPredicate &LIP,
                    SCEVExpander &Rewriter) {
  ICmpInst::Predicate InvariantPred = LIP.Pred;
  BranchInst *BI = cast<BranchInst>(ExitingBB->getTerminator());
  Rewriter.setInsertPoint(BI);
  auto *LHSV = Rewriter.expandCodeFor(LIP.LHS);
  auto *RHSV = Rewriter.expandCodeFor(LIP.RHS);
  bool ExitIfTrue = !L->contains(*succ_begin(ExitingBB));
  if (ExitIfTrue)
    InvariantPred = ICmpInst::getInversePredicate(InvariantPred);
  IRBuilder<> Builder(BI);
  return Builder.CreateICmp(InvariantPred, LHSV, RHSV,
                            BI->getCondition()->getName());
}

static std::optional<Value *>
createReplacement(ICmpInst *ICmp, const Loop *L, BasicBlock *ExitingBB,
                  const SCEV *MaxIter, bool Inverted, bool SkipLastIter,
                  ScalarEvolution *SE, SCEVExpander &Rewriter) {
  ICmpInst::Predicate Pred = ICmp->getPredicate();
  Value *LHS = ICmp->getOperand(0);
  Value *RHS = ICmp->getOperand(1);

  // 'LHS pred RHS' should now mean that we stay in loop.
  auto *BI = cast<BranchInst>(ExitingBB->getTerminator());
  if (Inverted)
    Pred = CmpInst::getInversePredicate(Pred);

  const SCEV *LHSS = SE->getSCEVAtScope(LHS, L);
  const SCEV *RHSS = SE->getSCEVAtScope(RHS, L);
  // Can we prove it to be trivially true or false?
  if (auto EV = SE->evaluatePredicateAt(Pred, LHSS, RHSS, BI))
    return createFoldedExitCond(L, ExitingBB, /*IsTaken*/ !*EV);

  auto *ARTy = LHSS->getType();
  auto *MaxIterTy = MaxIter->getType();
  // If possible, adjust types.
  if (SE->getTypeSizeInBits(ARTy) > SE->getTypeSizeInBits(MaxIterTy))
    MaxIter = SE->getZeroExtendExpr(MaxIter, ARTy);
  else if (SE->getTypeSizeInBits(ARTy) < SE->getTypeSizeInBits(MaxIterTy)) {
    const SCEV *MinusOne = SE->getMinusOne(ARTy);
    auto *MaxAllowedIter = SE->getZeroExtendExpr(MinusOne, MaxIterTy);
    if (SE->isKnownPredicateAt(ICmpInst::ICMP_ULE, MaxIter, MaxAllowedIter, BI))
      MaxIter = SE->getTruncateExpr(MaxIter, ARTy);
  }

  if (SkipLastIter) {
    // Semantically skip last iter is "subtract 1, do not bother about unsigned
    // wrap". getLoopInvariantExitCondDuringFirstIterations knows how to deal
    // with umin in a smart way, but umin(a, b) - 1 will likely not simplify.
    // So we manually construct umin(a - 1, b - 1).
    SmallVector<const SCEV *, 4> Elements;
    if (auto *UMin = dyn_cast<SCEVUMinExpr>(MaxIter)) {
      for (auto *Op : UMin->operands())
        Elements.push_back(SE->getMinusSCEV(Op, SE->getOne(Op->getType())));
      MaxIter = SE->getUMinFromMismatchedTypes(Elements);
    } else
      MaxIter = SE->getMinusSCEV(MaxIter, SE->getOne(MaxIter->getType()));
  }

  // Check if there is a loop-invariant predicate equivalent to our check.
  auto LIP = SE->getLoopInvariantExitCondDuringFirstIterations(Pred, LHSS, RHSS,
                                                               L, BI, MaxIter);
  if (!LIP)
    return std::nullopt;

  // Can we prove it to be trivially true?
  if (SE->isKnownPredicateAt(LIP->Pred, LIP->LHS, LIP->RHS, BI))
    return createFoldedExitCond(L, ExitingBB, /*IsTaken*/ false);
  else
    return createInvariantCond(L, ExitingBB, *LIP, Rewriter);
}

static bool optimizeLoopExitWithUnknownExitCount(
    const Loop *L, BranchInst *BI, BasicBlock *ExitingBB, const SCEV *MaxIter,
    bool SkipLastIter, ScalarEvolution *SE, SCEVExpander &Rewriter,
    SmallVectorImpl<WeakTrackingVH> &DeadInsts) {
  assert(
      (L->contains(BI->getSuccessor(0)) != L->contains(BI->getSuccessor(1))) &&
      "Not a loop exit!");

  // For branch that stays in loop by TRUE condition, go through AND. For branch
  // that stays in loop by FALSE condition, go through OR. Both gives the
  // similar logic: "stay in loop iff all conditions are true(false)".
  bool Inverted = L->contains(BI->getSuccessor(1));
  SmallVector<ICmpInst *, 4> LeafConditions;
  SmallVector<Value *, 4> Worklist;
  SmallPtrSet<Value *, 4> Visited;
  Value *OldCond = BI->getCondition();
  Visited.insert(OldCond);
  Worklist.push_back(OldCond);

  auto GoThrough = [&](Value *V) {
    Value *LHS = nullptr, *RHS = nullptr;
    if (Inverted) {
      if (!match(V, m_LogicalOr(m_Value(LHS), m_Value(RHS))))
        return false;
    } else {
      if (!match(V, m_LogicalAnd(m_Value(LHS), m_Value(RHS))))
        return false;
    }
    if (Visited.insert(LHS).second)
      Worklist.push_back(LHS);
    if (Visited.insert(RHS).second)
      Worklist.push_back(RHS);
    return true;
  };

  do {
    Value *Curr = Worklist.pop_back_val();
    // Go through AND/OR conditions. Collect leaf ICMPs. We only care about
    // those with one use, to avoid instruction duplication.
    if (Curr->hasOneUse())
      if (!GoThrough(Curr))
        if (auto *ICmp = dyn_cast<ICmpInst>(Curr))
          LeafConditions.push_back(ICmp);
  } while (!Worklist.empty());

  // If the current basic block has the same exit count as the whole loop, and
  // it consists of multiple icmp's, try to collect all icmp's that give exact
  // same exit count. For all other icmp's, we could use one less iteration,
  // because their value on the last iteration doesn't really matter.
  SmallPtrSet<ICmpInst *, 4> ICmpsFailingOnLastIter;
  if (!SkipLastIter && LeafConditions.size() > 1 &&
      SE->getExitCount(L, ExitingBB,
                       ScalarEvolution::ExitCountKind::SymbolicMaximum) ==
          MaxIter)
    for (auto *ICmp : LeafConditions) {
      auto EL = SE->computeExitLimitFromCond(L, ICmp, Inverted,
                                             /*ControlsExit*/ false);
      auto *ExitMax = EL.SymbolicMaxNotTaken;
      if (isa<SCEVCouldNotCompute>(ExitMax))
        continue;
      // They could be of different types (specifically this happens after
      // IV widening).
      auto *WiderType =
          SE->getWiderType(ExitMax->getType(), MaxIter->getType());
      auto *WideExitMax = SE->getNoopOrZeroExtend(ExitMax, WiderType);
      auto *WideMaxIter = SE->getNoopOrZeroExtend(MaxIter, WiderType);
      if (WideExitMax == WideMaxIter)
        ICmpsFailingOnLastIter.insert(ICmp);
    }

  bool Changed = false;
  for (auto *OldCond : LeafConditions) {
    // Skip last iteration for this icmp under one of two conditions:
    // - We do it for all conditions;
    // - There is another ICmp that would fail on last iter, so this one doesn't
    // really matter.
    bool OptimisticSkipLastIter = SkipLastIter;
    if (!OptimisticSkipLastIter) {
      if (ICmpsFailingOnLastIter.size() > 1)
        OptimisticSkipLastIter = true;
      else if (ICmpsFailingOnLastIter.size() == 1)
        OptimisticSkipLastIter = !ICmpsFailingOnLastIter.count(OldCond);
    }
    if (auto Replaced =
            createReplacement(OldCond, L, ExitingBB, MaxIter, Inverted,
                              OptimisticSkipLastIter, SE, Rewriter)) {
      Changed = true;
      auto *NewCond = *Replaced;
      if (auto *NCI = dyn_cast<Instruction>(NewCond)) {
        NCI->setName(OldCond->getName() + ".first_iter");
        NCI->moveBefore(cast<Instruction>(OldCond));
      }
      LLVM_DEBUG(dbgs() << "Unknown exit count: Replacing " << *OldCond
                        << " with " << *NewCond << "\n");
      assert(OldCond->hasOneUse() && "Must be!");
      OldCond->replaceAllUsesWith(NewCond);
      DeadInsts.push_back(OldCond);
      // Make sure we no longer consider this condition as failing on last
      // iteration.
      ICmpsFailingOnLastIter.erase(OldCond);
    }
  }
  return Changed;
}

bool IndVarSimplify::canonicalizeExitCondition(Loop *L) {
  // Note: This is duplicating a particular part on SimplifyIndVars reasoning.
  // We need to duplicate it because given icmp zext(small-iv), C, IVUsers
  // never reaches the icmp since the zext doesn't fold to an AddRec unless
  // it already has flags.  The alternative to this would be to extending the
  // set of "interesting" IV users to include the icmp, but doing that
  // regresses results in practice by querying SCEVs before trip counts which
  // rely on them which results in SCEV caching sub-optimal answers.  The
  // concern about caching sub-optimal results is why we only query SCEVs of
  // the loop invariant RHS here.
  SmallVector<BasicBlock*, 16> ExitingBlocks;
  L->getExitingBlocks(ExitingBlocks);
  bool Changed = false;
  for (auto *ExitingBB : ExitingBlocks) {
    auto *BI = dyn_cast<BranchInst>(ExitingBB->getTerminator());
    if (!BI)
      continue;
    assert(BI->isConditional() && "exit branch must be conditional");

    auto *ICmp = dyn_cast<ICmpInst>(BI->getCondition());
    if (!ICmp || !ICmp->hasOneUse())
      continue;

    auto *LHS = ICmp->getOperand(0);
    auto *RHS = ICmp->getOperand(1);
    // For the range reasoning, avoid computing SCEVs in the loop to avoid
    // poisoning cache with sub-optimal results.  For the must-execute case,
    // this is a neccessary precondition for correctness.
    if (!L->isLoopInvariant(RHS)) {
      if (!L->isLoopInvariant(LHS))
        continue;
      // Same logic applies for the inverse case
      std::swap(LHS, RHS);
    }

    // Match (icmp signed-cond zext, RHS)
    Value *LHSOp = nullptr;
    if (!match(LHS, m_ZExt(m_Value(LHSOp))) || !ICmp->isSigned())
      continue;

    const DataLayout &DL = ExitingBB->getModule()->getDataLayout();
    const unsigned InnerBitWidth = DL.getTypeSizeInBits(LHSOp->getType());
    const unsigned OuterBitWidth = DL.getTypeSizeInBits(RHS->getType());
    auto FullCR = ConstantRange::getFull(InnerBitWidth);
    FullCR = FullCR.zeroExtend(OuterBitWidth);
    auto RHSCR = SE->getUnsignedRange(SE->applyLoopGuards(SE->getSCEV(RHS), L));
    if (FullCR.contains(RHSCR)) {
      // We have now matched icmp signed-cond zext(X), zext(Y'), and can thus
      // replace the signed condition with the unsigned version.
      ICmp->setPredicate(ICmp->getUnsignedPredicate());
      Changed = true;
      // Note: No SCEV invalidation needed.  We've changed the predicate, but
      // have not changed exit counts, or the values produced by the compare.
      continue;
    }
  }

  // Now that we've canonicalized the condition to match the extend,
  // see if we can rotate the extend out of the loop.
  for (auto *ExitingBB : ExitingBlocks) {
    auto *BI = dyn_cast<BranchInst>(ExitingBB->getTerminator());
    if (!BI)
      continue;
    assert(BI->isConditional() && "exit branch must be conditional");

    auto *ICmp = dyn_cast<ICmpInst>(BI->getCondition());
    if (!ICmp || !ICmp->hasOneUse() || !ICmp->isUnsigned())
      continue;

    bool Swapped = false;
    auto *LHS = ICmp->getOperand(0);
    auto *RHS = ICmp->getOperand(1);
    if (L->isLoopInvariant(LHS) == L->isLoopInvariant(RHS))
      // Nothing to rotate
      continue;
    if (L->isLoopInvariant(LHS)) {
      // Same logic applies for the inverse case until we actually pick
      // which operand of the compare to update.
      Swapped = true;
      std::swap(LHS, RHS);
    }
    assert(!L->isLoopInvariant(LHS) && L->isLoopInvariant(RHS));

    // Match (icmp unsigned-cond zext, RHS)
    // TODO: Extend to handle corresponding sext/signed-cmp case
    // TODO: Extend to other invertible functions
    Value *LHSOp = nullptr;
    if (!match(LHS, m_ZExt(m_Value(LHSOp))))
      continue;

    // In general, we only rotate if we can do so without increasing the number
    // of instructions.  The exception is when we have an zext(add-rec).  The
    // reason for allowing this exception is that we know we need to get rid
    // of the zext for SCEV to be able to compute a trip count for said loops;
    // we consider the new trip count valuable enough to increase instruction
    // count by one.
    if (!LHS->hasOneUse() && !isa<SCEVAddRecExpr>(SE->getSCEV(LHSOp)))
      continue;

    // Given a icmp unsigned-cond zext(Op) where zext(trunc(RHS)) == RHS
    // replace with an icmp of the form icmp unsigned-cond Op, trunc(RHS)
    // when zext is loop varying and RHS is loop invariant.  This converts
    // loop varying work to loop-invariant work.
    auto doRotateTransform = [&]() {
      assert(ICmp->isUnsigned() && "must have proven unsigned already");
      auto *NewRHS =
        CastInst::Create(Instruction::Trunc, RHS, LHSOp->getType(), "",
                         L->getLoopPreheader()->getTerminator());
      ICmp->setOperand(Swapped ? 1 : 0, LHSOp);
      ICmp->setOperand(Swapped ? 0 : 1, NewRHS);
      if (LHS->use_empty())
        DeadInsts.push_back(LHS);
    };


    const DataLayout &DL = ExitingBB->getModule()->getDataLayout();
    const unsigned InnerBitWidth = DL.getTypeSizeInBits(LHSOp->getType());
    const unsigned OuterBitWidth = DL.getTypeSizeInBits(RHS->getType());
    auto FullCR = ConstantRange::getFull(InnerBitWidth);
    FullCR = FullCR.zeroExtend(OuterBitWidth);
    auto RHSCR = SE->getUnsignedRange(SE->applyLoopGuards(SE->getSCEV(RHS), L));
    if (FullCR.contains(RHSCR)) {
      doRotateTransform();
      Changed = true;
      // Note, we are leaving SCEV in an unfortunately imprecise case here
      // as rotation tends to reveal information about trip counts not
      // previously visible.
      continue;
    }
  }

  return Changed;
}

bool IndVarSimplify::optimizeLoopExits(Loop *L, SCEVExpander &Rewriter) {
  SmallVector<BasicBlock*, 16> ExitingBlocks;
  L->getExitingBlocks(ExitingBlocks);

  // Remove all exits which aren't both rewriteable and execute on every
  // iteration.
  llvm::erase_if(ExitingBlocks, [&](BasicBlock *ExitingBB) {
    // If our exitting block exits multiple loops, we can only rewrite the
    // innermost one.  Otherwise, we're changing how many times the innermost
    // loop runs before it exits.
    if (LI->getLoopFor(ExitingBB) != L)
      return true;

    // Can't rewrite non-branch yet.
    BranchInst *BI = dyn_cast<BranchInst>(ExitingBB->getTerminator());
    if (!BI)
      return true;

    // Likewise, the loop latch must be dominated by the exiting BB.
    if (!DT->dominates(ExitingBB, L->getLoopLatch()))
      return true;

    if (auto *CI = dyn_cast<ConstantInt>(BI->getCondition())) {
      // If already constant, nothing to do. However, if this is an
      // unconditional exit, we can still replace header phis with their
      // preheader value.
      if (!L->contains(BI->getSuccessor(CI->isNullValue())))
        replaceLoopPHINodesWithPreheaderValues(LI, L, DeadInsts, *SE);
      return true;
    }

    return false;
  });

  if (ExitingBlocks.empty())
    return false;

  // Get a symbolic upper bound on the loop backedge taken count.
  const SCEV *MaxBECount = SE->getSymbolicMaxBackedgeTakenCount(L);
  if (isa<SCEVCouldNotCompute>(MaxBECount))
    return false;

  // Visit our exit blocks in order of dominance. We know from the fact that
  // all exits must dominate the latch, so there is a total dominance order
  // between them.
  llvm::sort(ExitingBlocks, [&](BasicBlock *A, BasicBlock *B) {
               // std::sort sorts in ascending order, so we want the inverse of
               // the normal dominance relation.
               if (A == B) return false;
               if (DT->properlyDominates(A, B))
                 return true;
               else {
                 assert(DT->properlyDominates(B, A) &&
                        "expected total dominance order!");
                 return false;
               }
  });
#ifdef ASSERT
  for (unsigned i = 1; i < ExitingBlocks.size(); i++) {
    assert(DT->dominates(ExitingBlocks[i-1], ExitingBlocks[i]));
  }
#endif

  bool Changed = false;
  bool SkipLastIter = false;
  const SCEV *CurrMaxExit = SE->getCouldNotCompute();
  auto UpdateSkipLastIter = [&](const SCEV *MaxExitCount) {
    if (SkipLastIter || isa<SCEVCouldNotCompute>(MaxExitCount))
      return;
    if (isa<SCEVCouldNotCompute>(CurrMaxExit))
      CurrMaxExit = MaxExitCount;
    else
      CurrMaxExit = SE->getUMinFromMismatchedTypes(CurrMaxExit, MaxExitCount);
    // If the loop has more than 1 iteration, all further checks will be
    // executed 1 iteration less.
    if (CurrMaxExit == MaxBECount)
      SkipLastIter = true;
  };
  SmallSet<const SCEV *, 8> DominatingExactExitCounts;
  for (BasicBlock *ExitingBB : ExitingBlocks) {
    const SCEV *ExactExitCount = SE->getExitCount(L, ExitingBB);
    const SCEV *MaxExitCount = SE->getExitCount(
        L, ExitingBB, ScalarEvolution::ExitCountKind::SymbolicMaximum);
    if (isa<SCEVCouldNotCompute>(ExactExitCount)) {
      // Okay, we do not know the exit count here. Can we at least prove that it
      // will remain the same within iteration space?
      auto *BI = cast<BranchInst>(ExitingBB->getTerminator());
      auto OptimizeCond = [&](bool SkipLastIter) {
        return optimizeLoopExitWithUnknownExitCount(L, BI, ExitingBB,
                                                    MaxBECount, SkipLastIter,
                                                    SE, Rewriter, DeadInsts);
      };

      // TODO: We might have proved that we can skip the last iteration for
      // this check. In this case, we only want to check the condition on the
      // pre-last iteration (MaxBECount - 1). However, there is a nasty
      // corner case:
      //
      //   for (i = len; i != 0; i--) { ... check (i ult X) ... }
      //
      // If we could not prove that len != 0, then we also could not prove that
      // (len - 1) is not a UINT_MAX. If we simply query (len - 1), then
      // OptimizeCond will likely not prove anything for it, even if it could
      // prove the same fact for len.
      //
      // As a temporary solution, we query both last and pre-last iterations in
      // hope that we will be able to prove triviality for at least one of
      // them. We can stop querying MaxBECount for this case once SCEV
      // understands that (MaxBECount - 1) will not overflow here.
      if (OptimizeCond(false))
        Changed = true;
      else if (SkipLastIter && OptimizeCond(true))
        Changed = true;
      UpdateSkipLastIter(MaxExitCount);
      continue;
    }

    UpdateSkipLastIter(ExactExitCount);

    // If we know we'd exit on the first iteration, rewrite the exit to
    // reflect this.  This does not imply the loop must exit through this
    // exit; there may be an earlier one taken on the first iteration.
    // We know that the backedge can't be taken, so we replace all
    // the header PHIs with values coming from the preheader.
    if (ExactExitCount->isZero()) {
      foldExit(L, ExitingBB, true, DeadInsts);
      replaceLoopPHINodesWithPreheaderValues(LI, L, DeadInsts, *SE);
      Changed = true;
      continue;
    }

    assert(ExactExitCount->getType()->isIntegerTy() &&
           MaxBECount->getType()->isIntegerTy() &&
           "Exit counts must be integers");

    Type *WiderType =
        SE->getWiderType(MaxBECount->getType(), ExactExitCount->getType());
    ExactExitCount = SE->getNoopOrZeroExtend(ExactExitCount, WiderType);
    MaxBECount = SE->getNoopOrZeroExtend(MaxBECount, WiderType);
    assert(MaxBECount->getType() == ExactExitCount->getType());

    // Can we prove that some other exit must be taken strictly before this
    // one?
    if (SE->isLoopEntryGuardedByCond(L, CmpInst::ICMP_ULT, MaxBECount,
                                     ExactExitCount)) {
      foldExit(L, ExitingBB, false, DeadInsts);
      Changed = true;
      continue;
    }

    // As we run, keep track of which exit counts we've encountered.  If we
    // find a duplicate, we've found an exit which would have exited on the
    // exiting iteration, but (from the visit order) strictly follows another
    // which does the same and is thus dead.
    if (!DominatingExactExitCounts.insert(ExactExitCount).second) {
      foldExit(L, ExitingBB, false, DeadInsts);
      Changed = true;
      continue;
    }

    // TODO: There might be another oppurtunity to leverage SCEV's reasoning
    // here.  If we kept track of the min of dominanting exits so far, we could
    // discharge exits with EC >= MDEC. This is less powerful than the existing
    // transform (since later exits aren't considered), but potentially more
    // powerful for any case where SCEV can prove a >=u b, but neither a == b
    // or a >u b.  Such a case is not currently known.
  }
  return Changed;
}

bool IndVarSimplify::predicateLoopExits(Loop *L, SCEVExpander &Rewriter) {
  SmallVector<BasicBlock*, 16> ExitingBlocks;
  L->getExitingBlocks(ExitingBlocks);

  // Finally, see if we can rewrite our exit conditions into a loop invariant
  // form. If we have a read-only loop, and we can tell that we must exit down
  // a path which does not need any of the values computed within the loop, we
  // can rewrite the loop to exit on the first iteration.  Note that this
  // doesn't either a) tell us the loop exits on the first iteration (unless
  // *all* exits are predicateable) or b) tell us *which* exit might be taken.
  // This transformation looks a lot like a restricted form of dead loop
  // elimination, but restricted to read-only loops and without neccesssarily
  // needing to kill the loop entirely.
  if (!LoopPredication)
    return false;

  // Note: ExactBTC is the exact backedge taken count *iff* the loop exits
  // through *explicit* control flow.  We have to eliminate the possibility of
  // implicit exits (see below) before we know it's truly exact.
  const SCEV *ExactBTC = SE->getBackedgeTakenCount(L);
  if (isa<SCEVCouldNotCompute>(ExactBTC) || !Rewriter.isSafeToExpand(ExactBTC))
    return false;

  assert(SE->isLoopInvariant(ExactBTC, L) && "BTC must be loop invariant");
  assert(ExactBTC->getType()->isIntegerTy() && "BTC must be integer");

  auto BadExit = [&](BasicBlock *ExitingBB) {
    // If our exiting block exits multiple loops, we can only rewrite the
    // innermost one.  Otherwise, we're changing how many times the innermost
    // loop runs before it exits.
    if (LI->getLoopFor(ExitingBB) != L)
      return true;

    // Can't rewrite non-branch yet.
    BranchInst *BI = dyn_cast<BranchInst>(ExitingBB->getTerminator());
    if (!BI)
      return true;

    // If already constant, nothing to do.
    if (isa<Constant>(BI->getCondition()))
      return true;

    // If the exit block has phis, we need to be able to compute the values
    // within the loop which contains them.  This assumes trivially lcssa phis
    // have already been removed; TODO: generalize
    BasicBlock *ExitBlock =
    BI->getSuccessor(L->contains(BI->getSuccessor(0)) ? 1 : 0);
    if (!ExitBlock->phis().empty())
      return true;

    const SCEV *ExitCount = SE->getExitCount(L, ExitingBB);
    if (isa<SCEVCouldNotCompute>(ExitCount) ||
        !Rewriter.isSafeToExpand(ExitCount))
      return true;

    assert(SE->isLoopInvariant(ExitCount, L) &&
           "Exit count must be loop invariant");
    assert(ExitCount->getType()->isIntegerTy() && "Exit count must be integer");
    return false;
  };

  // If we have any exits which can't be predicated themselves, than we can't
  // predicate any exit which isn't guaranteed to execute before it.  Consider
  // two exits (a) and (b) which would both exit on the same iteration.  If we
  // can predicate (b), but not (a), and (a) preceeds (b) along some path, then
  // we could convert a loop from exiting through (a) to one exiting through
  // (b).  Note that this problem exists only for exits with the same exit
  // count, and we could be more aggressive when exit counts are known inequal.
  llvm::sort(ExitingBlocks,
            [&](BasicBlock *A, BasicBlock *B) {
              // std::sort sorts in ascending order, so we want the inverse of
              // the normal dominance relation, plus a tie breaker for blocks
              // unordered by dominance.
              if (DT->properlyDominates(A, B)) return true;
              if (DT->properlyDominates(B, A)) return false;
              return A->getName() < B->getName();
            });
  // Check to see if our exit blocks are a total order (i.e. a linear chain of
  // exits before the backedge).  If they aren't, reasoning about reachability
  // is complicated and we choose not to for now.
  for (unsigned i = 1; i < ExitingBlocks.size(); i++)
    if (!DT->dominates(ExitingBlocks[i-1], ExitingBlocks[i]))
      return false;

  // Given our sorted total order, we know that exit[j] must be evaluated
  // after all exit[i] such j > i.
  for (unsigned i = 0, e = ExitingBlocks.size(); i < e; i++)
    if (BadExit(ExitingBlocks[i])) {
      ExitingBlocks.resize(i);
      break;
    }

  if (ExitingBlocks.empty())
    return false;

  // We rely on not being able to reach an exiting block on a later iteration
  // then it's statically compute exit count.  The implementaton of
  // getExitCount currently has this invariant, but assert it here so that
  // breakage is obvious if this ever changes..
  assert(llvm::all_of(ExitingBlocks, [&](BasicBlock *ExitingBB) {
        return DT->dominates(ExitingBB, L->getLoopLatch());
      }));

  // At this point, ExitingBlocks consists of only those blocks which are
  // predicatable.  Given that, we know we have at least one exit we can
  // predicate if the loop is doesn't have side effects and doesn't have any
  // implicit exits (because then our exact BTC isn't actually exact).
  // @Reviewers - As structured, this is O(I^2) for loop nests.  Any
  // suggestions on how to improve this?  I can obviously bail out for outer
  // loops, but that seems less than ideal.  MemorySSA can find memory writes,
  // is that enough for *all* side effects?
  for (BasicBlock *BB : L->blocks())
    for (auto &I : *BB)
      // TODO:isGuaranteedToTransfer
      if (I.mayHaveSideEffects())
        return false;

  bool Changed = false;
  // Finally, do the actual predication for all predicatable blocks.  A couple
  // of notes here:
  // 1) We don't bother to constant fold dominated exits with identical exit
  //    counts; that's simply a form of CSE/equality propagation and we leave
  //    it for dedicated passes.
  // 2) We insert the comparison at the branch.  Hoisting introduces additional
  //    legality constraints and we leave that to dedicated logic.  We want to
  //    predicate even if we can't insert a loop invariant expression as
  //    peeling or unrolling will likely reduce the cost of the otherwise loop
  //    varying check.
  Rewriter.setInsertPoint(L->getLoopPreheader()->getTerminator());
  IRBuilder<> B(L->getLoopPreheader()->getTerminator());
  Value *ExactBTCV = nullptr; // Lazily generated if needed.
  for (BasicBlock *ExitingBB : ExitingBlocks) {
    const SCEV *ExitCount = SE->getExitCount(L, ExitingBB);

    auto *BI = cast<BranchInst>(ExitingBB->getTerminator());
    Value *NewCond;
    if (ExitCount == ExactBTC) {
      NewCond = L->contains(BI->getSuccessor(0)) ?
        B.getFalse() : B.getTrue();
    } else {
      Value *ECV = Rewriter.expandCodeFor(ExitCount);
      if (!ExactBTCV)
        ExactBTCV = Rewriter.expandCodeFor(ExactBTC);
      Value *RHS = ExactBTCV;
      if (ECV->getType() != RHS->getType()) {
        Type *WiderTy = SE->getWiderType(ECV->getType(), RHS->getType());
        ECV = B.CreateZExt(ECV, WiderTy);
        RHS = B.CreateZExt(RHS, WiderTy);
      }
      auto Pred = L->contains(BI->getSuccessor(0)) ?
        ICmpInst::ICMP_NE : ICmpInst::ICMP_EQ;
      NewCond = B.CreateICmp(Pred, ECV, RHS);
    }
    Value *OldCond = BI->getCondition();
    BI->setCondition(NewCond);
    if (OldCond->use_empty())
      DeadInsts.emplace_back(OldCond);
    Changed = true;
  }

  return Changed;
}

//===----------------------------------------------------------------------===//
//  IndVarSimplify driver. Manage several subpasses of IV simplification.
//===----------------------------------------------------------------------===//

bool IndVarSimplify::run(Loop *L) {
  // We need (and expect!) the incoming loop to be in LCSSA.
  assert(L->isRecursivelyLCSSAForm(*DT, *LI) &&
         "LCSSA required to run indvars!");

  // If LoopSimplify form is not available, stay out of trouble. Some notes:
  //  - LSR currently only supports LoopSimplify-form loops. Indvars'
  //    canonicalization can be a pessimization without LSR to "clean up"
  //    afterwards.
  //  - We depend on having a preheader; in particular,
  //    Loop::getCanonicalInductionVariable only supports loops with preheaders,
  //    and we're in trouble if we can't find the induction variable even when
  //    we've manually inserted one.
  //  - LFTR relies on having a single backedge.
  if (!L->isLoopSimplifyForm())
    return false;

#ifndef NDEBUG
  // Used below for a consistency check only
  // Note: Since the result returned by ScalarEvolution may depend on the order
  // in which previous results are added to its cache, the call to
  // getBackedgeTakenCount() may change following SCEV queries.
  const SCEV *BackedgeTakenCount;
  if (VerifyIndvars)
    BackedgeTakenCount = SE->getBackedgeTakenCount(L);
#endif

  bool Changed = false;
  // If there are any floating-point recurrences, attempt to
  // transform them to use integer recurrences.
  Changed |= rewriteNonIntegerIVs(L);

  // Create a rewriter object which we'll use to transform the code with.
  SCEVExpander Rewriter(*SE, DL, "indvars");
#ifndef NDEBUG
  Rewriter.setDebugType(DEBUG_TYPE);
#endif

  // Eliminate redundant IV users.
  //
  // Simplification works best when run before other consumers of SCEV. We
  // attempt to avoid evaluating SCEVs for sign/zero extend operations until
  // other expressions involving loop IVs have been evaluated. This helps SCEV
  // set no-wrap flags before normalizing sign/zero extension.
  Rewriter.disableCanonicalMode();
  Changed |= simplifyAndExtend(L, Rewriter, LI);

  // Check to see if we can compute the final value of any expressions
  // that are recurrent in the loop, and substitute the exit values from the
  // loop into any instructions outside of the loop that use the final values
  // of the current expressions.
  if (ReplaceExitValue != NeverRepl) {
    if (int Rewrites = rewriteLoopExitValues(L, LI, TLI, SE, TTI, Rewriter, DT,
                                             ReplaceExitValue, DeadInsts)) {
      NumReplaced += Rewrites;
      Changed = true;
    }
  }

  // Eliminate redundant IV cycles.
  NumElimIV += Rewriter.replaceCongruentIVs(L, DT, DeadInsts, TTI);

  // Try to convert exit conditions to unsigned and rotate computation
  // out of the loop.  Note: Handles invalidation internally if needed.
  Changed |= canonicalizeExitCondition(L);

  // Try to eliminate loop exits based on analyzeable exit counts
  if (optimizeLoopExits(L, Rewriter))  {
    Changed = true;
    // Given we've changed exit counts, notify SCEV
    // Some nested loops may share same folded exit basic block,
    // thus we need to notify top most loop.
    SE->forgetTopmostLoop(L);
  }

  // Try to form loop invariant tests for loop exits by changing how many
  // iterations of the loop run when that is unobservable.
  if (predicateLoopExits(L, Rewriter)) {
    Changed = true;
    // Given we've changed exit counts, notify SCEV
    SE->forgetLoop(L);
  }

  // If we have a trip count expression, rewrite the loop's exit condition
  // using it.
  if (!DisableLFTR) {
    BasicBlock *PreHeader = L->getLoopPreheader();

    SmallVector<BasicBlock*, 16> ExitingBlocks;
    L->getExitingBlocks(ExitingBlocks);
    for (BasicBlock *ExitingBB : ExitingBlocks) {
      // Can't rewrite non-branch yet.
      if (!isa<BranchInst>(ExitingBB->getTerminator()))
        continue;

      // If our exitting block exits multiple loops, we can only rewrite the
      // innermost one.  Otherwise, we're changing how many times the innermost
      // loop runs before it exits.
      if (LI->getLoopFor(ExitingBB) != L)
        continue;

      if (!needsLFTR(L, ExitingBB))
        continue;

      const SCEV *ExitCount = SE->getExitCount(L, ExitingBB);
      if (isa<SCEVCouldNotCompute>(ExitCount))
        continue;

      // This was handled above, but as we form SCEVs, we can sometimes refine
      // existing ones; this allows exit counts to be folded to zero which
      // weren't when optimizeLoopExits saw them.  Arguably, we should iterate
      // until stable to handle cases like this better.
      if (ExitCount->isZero())
        continue;

      PHINode *IndVar = FindLoopCounter(L, ExitingBB, ExitCount, SE, DT);
      if (!IndVar)
        continue;

      // Avoid high cost expansions.  Note: This heuristic is questionable in
      // that our definition of "high cost" is not exactly principled.
      if (Rewriter.isHighCostExpansion(ExitCount, L, SCEVCheapExpansionBudget,
                                       TTI, PreHeader->getTerminator()))
        continue;

      // Check preconditions for proper SCEVExpander operation. SCEV does not
      // express SCEVExpander's dependencies, such as LoopSimplify. Instead
      // any pass that uses the SCEVExpander must do it. This does not work
      // well for loop passes because SCEVExpander makes assumptions about
      // all loops, while LoopPassManager only forces the current loop to be
      // simplified.
      //
      // FIXME: SCEV expansion has no way to bail out, so the caller must
      // explicitly check any assumptions made by SCEV. Brittle.
      const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(ExitCount);
      if (!AR || AR->getLoop()->getLoopPreheader())
        Changed |= linearFunctionTestReplace(L, ExitingBB,
                                             ExitCount, IndVar,
                                             Rewriter);
    }
  }
  // Clear the rewriter cache, because values that are in the rewriter's cache
  // can be deleted in the loop below, causing the AssertingVH in the cache to
  // trigger.
  Rewriter.clear();

  // Now that we're done iterating through lists, clean up any instructions
  // which are now dead.
  while (!DeadInsts.empty()) {
    Value *V = DeadInsts.pop_back_val();

    if (PHINode *PHI = dyn_cast_or_null<PHINode>(V))
      Changed |= RecursivelyDeleteDeadPHINode(PHI, TLI, MSSAU.get());
    else if (Instruction *Inst = dyn_cast_or_null<Instruction>(V))
      Changed |=
          RecursivelyDeleteTriviallyDeadInstructions(Inst, TLI, MSSAU.get());
  }

  // The Rewriter may not be used from this point on.

  // Loop-invariant instructions in the preheader that aren't used in the
  // loop may be sunk below the loop to reduce register pressure.
  Changed |= sinkUnusedInvariants(L);

  // rewriteFirstIterationLoopExitValues does not rely on the computation of
  // trip count and therefore can further simplify exit values in addition to
  // rewriteLoopExitValues.
  Changed |= rewriteFirstIterationLoopExitValues(L);

  // Clean up dead instructions.
  Changed |= DeleteDeadPHIs(L->getHeader(), TLI, MSSAU.get());

  // Check a post-condition.
  assert(L->isRecursivelyLCSSAForm(*DT, *LI) &&
         "Indvars did not preserve LCSSA!");

  // Verify that LFTR, and any other change have not interfered with SCEV's
  // ability to compute trip count.  We may have *changed* the exit count, but
  // only by reducing it.
#ifndef NDEBUG
  if (VerifyIndvars && !isa<SCEVCouldNotCompute>(BackedgeTakenCount)) {
    SE->forgetLoop(L);
    const SCEV *NewBECount = SE->getBackedgeTakenCount(L);
    if (SE->getTypeSizeInBits(BackedgeTakenCount->getType()) <
        SE->getTypeSizeInBits(NewBECount->getType()))
      NewBECount = SE->getTruncateOrNoop(NewBECount,
                                         BackedgeTakenCount->getType());
    else
      BackedgeTakenCount = SE->getTruncateOrNoop(BackedgeTakenCount,
                                                 NewBECount->getType());
    assert(!SE->isKnownPredicate(ICmpInst::ICMP_ULT, BackedgeTakenCount,
                                 NewBECount) && "indvars must preserve SCEV");
  }
  if (VerifyMemorySSA && MSSAU)
    MSSAU->getMemorySSA()->verifyMemorySSA();
#endif

  return Changed;
}

PreservedAnalyses IndVarSimplifyPass::run(Loop &L, LoopAnalysisManager &AM,
                                          LoopStandardAnalysisResults &AR,
                                          LPMUpdater &) {
  Function *F = L.getHeader()->getParent();
  const DataLayout &DL = F->getParent()->getDataLayout();

  IndVarSimplify IVS(&AR.LI, &AR.SE, &AR.DT, DL, &AR.TLI, &AR.TTI, AR.MSSA,
                     WidenIndVars && AllowIVWidening);
  if (!IVS.run(&L))
    return PreservedAnalyses::all();

  auto PA = getLoopPassPreservedAnalyses();
  PA.preserveSet<CFGAnalyses>();
  if (AR.MSSA)
    PA.preserve<MemorySSAAnalysis>();
  return PA;
}

namespace {

struct IndVarSimplifyLegacyPass : public LoopPass {
  static char ID; // Pass identification, replacement for typeid

  IndVarSimplifyLegacyPass() : LoopPass(ID) {
    initializeIndVarSimplifyLegacyPassPass(*PassRegistry::getPassRegistry());
  }

  bool runOnLoop(Loop *L, LPPassManager &LPM) override {
    if (skipLoop(L))
      return false;

    auto *LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
    auto *SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();
    auto *DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
    auto *TLIP = getAnalysisIfAvailable<TargetLibraryInfoWrapperPass>();
    auto *TLI = TLIP ? &TLIP->getTLI(*L->getHeader()->getParent()) : nullptr;
    auto *TTIP = getAnalysisIfAvailable<TargetTransformInfoWrapperPass>();
    auto *TTI = TTIP ? &TTIP->getTTI(*L->getHeader()->getParent()) : nullptr;
    const DataLayout &DL = L->getHeader()->getModule()->getDataLayout();
    auto *MSSAAnalysis = getAnalysisIfAvailable<MemorySSAWrapperPass>();
    MemorySSA *MSSA = nullptr;
    if (MSSAAnalysis)
      MSSA = &MSSAAnalysis->getMSSA();

    IndVarSimplify IVS(LI, SE, DT, DL, TLI, TTI, MSSA, AllowIVWidening);
    return IVS.run(L);
  }

  void getAnalysisUsage(AnalysisUsage &AU) const override {
    AU.setPreservesCFG();
    AU.addPreserved<MemorySSAWrapperPass>();
    getLoopAnalysisUsage(AU);
  }
};

} // end anonymous namespace

char IndVarSimplifyLegacyPass::ID = 0;

INITIALIZE_PASS_BEGIN(IndVarSimplifyLegacyPass, "indvars",
                      "Induction Variable Simplification", false, false)
INITIALIZE_PASS_DEPENDENCY(LoopPass)
INITIALIZE_PASS_END(IndVarSimplifyLegacyPass, "indvars",
                    "Induction Variable Simplification", false, false)

Pass *llvm::createIndVarSimplifyPass() {
  return new IndVarSimplifyLegacyPass();
}