llvm.org GIT mirror llvm / 7716d65 lib / Transforms / Scalar / Reassociate.cpp
7716d65

Tree @7716d65 (Download .tar.gz)

Reassociate.cpp @7716d65raw · history · 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
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
//===- Reassociate.cpp - Reassociate binary expressions -------------------===//
//
// 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 pass reassociates commutative expressions in an order that is designed
// to promote better constant propagation, GCSE, LICM, PRE, etc.
//
// For example: 4 + (x + 5) -> x + (4 + 5)
//
// In the implementation of this algorithm, constants are assigned rank = 0,
// function arguments are rank = 1, and other values are assigned ranks
// corresponding to the reverse post order traversal of current function
// (starting at 2), which effectively gives values in deep loops higher rank
// than values not in loops.
//
//===----------------------------------------------------------------------===//

#include "llvm/Transforms/Scalar/Reassociate.h"
#include "llvm/ADT/APFloat.h"
#include "llvm/ADT/APInt.h"
#include "llvm/ADT/DenseMap.h"
#include "llvm/ADT/PostOrderIterator.h"
#include "llvm/ADT/SetVector.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/ADT/SmallSet.h"
#include "llvm/ADT/SmallVector.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/Analysis/GlobalsModRef.h"
#include "llvm/Transforms/Utils/Local.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/Argument.h"
#include "llvm/IR/BasicBlock.h"
#include "llvm/IR/CFG.h"
#include "llvm/IR/Constant.h"
#include "llvm/IR/Constants.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/Operator.h"
#include "llvm/IR/PassManager.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Type.h"
#include "llvm/IR/User.h"
#include "llvm/IR/Value.h"
#include "llvm/IR/ValueHandle.h"
#include "llvm/Pass.h"
#include "llvm/Support/Casting.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/ErrorHandling.h"
#include "llvm/Support/raw_ostream.h"
#include "llvm/Transforms/Scalar.h"
#include <algorithm>
#include <cassert>
#include <utility>

using namespace llvm;
using namespace reassociate;
using namespace PatternMatch;

#define DEBUG_TYPE "reassociate"

STATISTIC(NumChanged, "Number of insts reassociated");
STATISTIC(NumAnnihil, "Number of expr tree annihilated");
STATISTIC(NumFactor , "Number of multiplies factored");

#ifndef NDEBUG
/// Print out the expression identified in the Ops list.
static void PrintOps(Instruction *I, const SmallVectorImpl<ValueEntry> &Ops) {
  Module *M = I->getModule();
  dbgs() << Instruction::getOpcodeName(I->getOpcode()) << " "
       << *Ops[0].Op->getType() << '\t';
  for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
    dbgs() << "[ ";
    Ops[i].Op->printAsOperand(dbgs(), false, M);
    dbgs() << ", #" << Ops[i].Rank << "] ";
  }
}
#endif

/// Utility class representing a non-constant Xor-operand. We classify
/// non-constant Xor-Operands into two categories:
///  C1) The operand is in the form "X & C", where C is a constant and C != ~0
///  C2)
///    C2.1) The operand is in the form of "X | C", where C is a non-zero
///          constant.
///    C2.2) Any operand E which doesn't fall into C1 and C2.1, we view this
///          operand as "E | 0"
class llvm::reassociate::XorOpnd {
public:
  XorOpnd(Value *V);

  bool isInvalid() const { return SymbolicPart == nullptr; }
  bool isOrExpr() const { return isOr; }
  Value *getValue() const { return OrigVal; }
  Value *getSymbolicPart() const { return SymbolicPart; }
  unsigned getSymbolicRank() const { return SymbolicRank; }
  const APInt &getConstPart() const { return ConstPart; }

  void Invalidate() { SymbolicPart = OrigVal = nullptr; }
  void setSymbolicRank(unsigned R) { SymbolicRank = R; }

private:
  Value *OrigVal;
  Value *SymbolicPart;
  APInt ConstPart;
  unsigned SymbolicRank;
  bool isOr;
};

XorOpnd::XorOpnd(Value *V) {
  assert(!isa<ConstantInt>(V) && "No ConstantInt");
  OrigVal = V;
  Instruction *I = dyn_cast<Instruction>(V);
  SymbolicRank = 0;

  if (I && (I->getOpcode() == Instruction::Or ||
            I->getOpcode() == Instruction::And)) {
    Value *V0 = I->getOperand(0);
    Value *V1 = I->getOperand(1);
    const APInt *C;
    if (match(V0, m_APInt(C)))
      std::swap(V0, V1);

    if (match(V1, m_APInt(C))) {
      ConstPart = *C;
      SymbolicPart = V0;
      isOr = (I->getOpcode() == Instruction::Or);
      return;
    }
  }

  // view the operand as "V | 0"
  SymbolicPart = V;
  ConstPart = APInt::getNullValue(V->getType()->getScalarSizeInBits());
  isOr = true;
}

/// Return true if V is an instruction of the specified opcode and if it
/// only has one use.
static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode) {
  auto *I = dyn_cast<Instruction>(V);
  if (I && I->hasOneUse() && I->getOpcode() == Opcode)
    if (!isa<FPMathOperator>(I) || I->isFast())
      return cast<BinaryOperator>(I);
  return nullptr;
}

static BinaryOperator *isReassociableOp(Value *V, unsigned Opcode1,
                                        unsigned Opcode2) {
  auto *I = dyn_cast<Instruction>(V);
  if (I && I->hasOneUse() &&
      (I->getOpcode() == Opcode1 || I->getOpcode() == Opcode2))
    if (!isa<FPMathOperator>(I) || I->isFast())
      return cast<BinaryOperator>(I);
  return nullptr;
}

void ReassociatePass::BuildRankMap(Function &F,
                                   ReversePostOrderTraversal<Function*> &RPOT) {
  unsigned Rank = 2;

  // Assign distinct ranks to function arguments.
  for (auto &Arg : F.args()) {
    ValueRankMap[&Arg] = ++Rank;
    LLVM_DEBUG(dbgs() << "Calculated Rank[" << Arg.getName() << "] = " << Rank
                      << "\n");
  }

  // Traverse basic blocks in ReversePostOrder
  for (BasicBlock *BB : RPOT) {
    unsigned BBRank = RankMap[BB] = ++Rank << 16;

    // Walk the basic block, adding precomputed ranks for any instructions that
    // we cannot move.  This ensures that the ranks for these instructions are
    // all different in the block.
    for (Instruction &I : *BB)
      if (mayBeMemoryDependent(I))
        ValueRankMap[&I] = ++BBRank;
  }
}

unsigned ReassociatePass::getRank(Value *V) {
  Instruction *I = dyn_cast<Instruction>(V);
  if (!I) {
    if (isa<Argument>(V)) return ValueRankMap[V];   // Function argument.
    return 0;  // Otherwise it's a global or constant, rank 0.
  }

  if (unsigned Rank = ValueRankMap[I])
    return Rank;    // Rank already known?

  // If this is an expression, return the 1+MAX(rank(LHS), rank(RHS)) so that
  // we can reassociate expressions for code motion!  Since we do not recurse
  // for PHI nodes, we cannot have infinite recursion here, because there
  // cannot be loops in the value graph that do not go through PHI nodes.
  unsigned Rank = 0, MaxRank = RankMap[I->getParent()];
  for (unsigned i = 0, e = I->getNumOperands(); i != e && Rank != MaxRank; ++i)
    Rank = std::max(Rank, getRank(I->getOperand(i)));

  // If this is a 'not' or 'neg' instruction, do not count it for rank. This
  // assures us that X and ~X will have the same rank.
  if (!match(I, m_Not(m_Value())) && !match(I, m_Neg(m_Value())) &&
      !match(I, m_FNeg(m_Value())))
    ++Rank;

  LLVM_DEBUG(dbgs() << "Calculated Rank[" << V->getName() << "] = " << Rank
                    << "\n");

  return ValueRankMap[I] = Rank;
}

// Canonicalize constants to RHS.  Otherwise, sort the operands by rank.
void ReassociatePass::canonicalizeOperands(Instruction *I) {
  assert(isa<BinaryOperator>(I) && "Expected binary operator.");
  assert(I->isCommutative() && "Expected commutative operator.");

  Value *LHS = I->getOperand(0);
  Value *RHS = I->getOperand(1);
  if (LHS == RHS || isa<Constant>(RHS))
    return;
  if (isa<Constant>(LHS) || getRank(RHS) < getRank(LHS))
    cast<BinaryOperator>(I)->swapOperands();
}

static BinaryOperator *CreateAdd(Value *S1, Value *S2, const Twine &Name,
                                 Instruction *InsertBefore, Value *FlagsOp) {
  if (S1->getType()->isIntOrIntVectorTy())
    return BinaryOperator::CreateAdd(S1, S2, Name, InsertBefore);
  else {
    BinaryOperator *Res =
        BinaryOperator::CreateFAdd(S1, S2, Name, InsertBefore);
    Res->setFastMathFlags(cast<FPMathOperator>(FlagsOp)->getFastMathFlags());
    return Res;
  }
}

static BinaryOperator *CreateMul(Value *S1, Value *S2, const Twine &Name,
                                 Instruction *InsertBefore, Value *FlagsOp) {
  if (S1->getType()->isIntOrIntVectorTy())
    return BinaryOperator::CreateMul(S1, S2, Name, InsertBefore);
  else {
    BinaryOperator *Res =
      BinaryOperator::CreateFMul(S1, S2, Name, InsertBefore);
    Res->setFastMathFlags(cast<FPMathOperator>(FlagsOp)->getFastMathFlags());
    return Res;
  }
}

static BinaryOperator *CreateNeg(Value *S1, const Twine &Name,
                                 Instruction *InsertBefore, Value *FlagsOp) {
  if (S1->getType()->isIntOrIntVectorTy())
    return BinaryOperator::CreateNeg(S1, Name, InsertBefore);
  else {
    BinaryOperator *Res = BinaryOperator::CreateFNeg(S1, Name, InsertBefore);
    Res->setFastMathFlags(cast<FPMathOperator>(FlagsOp)->getFastMathFlags());
    return Res;
  }
}

/// Replace 0-X with X*-1.
static BinaryOperator *LowerNegateToMultiply(Instruction *Neg) {
  Type *Ty = Neg->getType();
  Constant *NegOne = Ty->isIntOrIntVectorTy() ?
    ConstantInt::getAllOnesValue(Ty) : ConstantFP::get(Ty, -1.0);

  BinaryOperator *Res = CreateMul(Neg->getOperand(1), NegOne, "", Neg, Neg);
  Neg->setOperand(1, Constant::getNullValue(Ty)); // Drop use of op.
  Res->takeName(Neg);
  Neg->replaceAllUsesWith(Res);
  Res->setDebugLoc(Neg->getDebugLoc());
  return Res;
}

/// Returns k such that lambda(2^Bitwidth) = 2^k, where lambda is the Carmichael
/// function. This means that x^(2^k) === 1 mod 2^Bitwidth for
/// every odd x, i.e. x^(2^k) = 1 for every odd x in Bitwidth-bit arithmetic.
/// Note that 0 <= k < Bitwidth, and if Bitwidth > 3 then x^(2^k) = 0 for every
/// even x in Bitwidth-bit arithmetic.
static unsigned CarmichaelShift(unsigned Bitwidth) {
  if (Bitwidth < 3)
    return Bitwidth - 1;
  return Bitwidth - 2;
}

/// Add the extra weight 'RHS' to the existing weight 'LHS',
/// reducing the combined weight using any special properties of the operation.
/// The existing weight LHS represents the computation X op X op ... op X where
/// X occurs LHS times.  The combined weight represents  X op X op ... op X with
/// X occurring LHS + RHS times.  If op is "Xor" for example then the combined
/// operation is equivalent to X if LHS + RHS is odd, or 0 if LHS + RHS is even;
/// the routine returns 1 in LHS in the first case, and 0 in LHS in the second.
static void IncorporateWeight(APInt &LHS, const APInt &RHS, unsigned Opcode) {
  // If we were working with infinite precision arithmetic then the combined
  // weight would be LHS + RHS.  But we are using finite precision arithmetic,
  // and the APInt sum LHS + RHS may not be correct if it wraps (it is correct
  // for nilpotent operations and addition, but not for idempotent operations
  // and multiplication), so it is important to correctly reduce the combined
  // weight back into range if wrapping would be wrong.

  // If RHS is zero then the weight didn't change.
  if (RHS.isMinValue())
    return;
  // If LHS is zero then the combined weight is RHS.
  if (LHS.isMinValue()) {
    LHS = RHS;
    return;
  }
  // From this point on we know that neither LHS nor RHS is zero.

  if (Instruction::isIdempotent(Opcode)) {
    // Idempotent means X op X === X, so any non-zero weight is equivalent to a
    // weight of 1.  Keeping weights at zero or one also means that wrapping is
    // not a problem.
    assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
    return; // Return a weight of 1.
  }
  if (Instruction::isNilpotent(Opcode)) {
    // Nilpotent means X op X === 0, so reduce weights modulo 2.
    assert(LHS == 1 && RHS == 1 && "Weights not reduced!");
    LHS = 0; // 1 + 1 === 0 modulo 2.
    return;
  }
  if (Opcode == Instruction::Add || Opcode == Instruction::FAdd) {
    // TODO: Reduce the weight by exploiting nsw/nuw?
    LHS += RHS;
    return;
  }

  assert((Opcode == Instruction::Mul || Opcode == Instruction::FMul) &&
         "Unknown associative operation!");
  unsigned Bitwidth = LHS.getBitWidth();
  // If CM is the Carmichael number then a weight W satisfying W >= CM+Bitwidth
  // can be replaced with W-CM.  That's because x^W=x^(W-CM) for every Bitwidth
  // bit number x, since either x is odd in which case x^CM = 1, or x is even in
  // which case both x^W and x^(W - CM) are zero.  By subtracting off multiples
  // of CM like this weights can always be reduced to the range [0, CM+Bitwidth)
  // which by a happy accident means that they can always be represented using
  // Bitwidth bits.
  // TODO: Reduce the weight by exploiting nsw/nuw?  (Could do much better than
  // the Carmichael number).
  if (Bitwidth > 3) {
    /// CM - The value of Carmichael's lambda function.
    APInt CM = APInt::getOneBitSet(Bitwidth, CarmichaelShift(Bitwidth));
    // Any weight W >= Threshold can be replaced with W - CM.
    APInt Threshold = CM + Bitwidth;
    assert(LHS.ult(Threshold) && RHS.ult(Threshold) && "Weights not reduced!");
    // For Bitwidth 4 or more the following sum does not overflow.
    LHS += RHS;
    while (LHS.uge(Threshold))
      LHS -= CM;
  } else {
    // To avoid problems with overflow do everything the same as above but using
    // a larger type.
    unsigned CM = 1U << CarmichaelShift(Bitwidth);
    unsigned Threshold = CM + Bitwidth;
    assert(LHS.getZExtValue() < Threshold && RHS.getZExtValue() < Threshold &&
           "Weights not reduced!");
    unsigned Total = LHS.getZExtValue() + RHS.getZExtValue();
    while (Total >= Threshold)
      Total -= CM;
    LHS = Total;
  }
}

using RepeatedValue = std::pair<Value*, APInt>;

/// Given an associative binary expression, return the leaf
/// nodes in Ops along with their weights (how many times the leaf occurs).  The
/// original expression is the same as
///   (Ops[0].first op Ops[0].first op ... Ops[0].first)  <- Ops[0].second times
/// op
///   (Ops[1].first op Ops[1].first op ... Ops[1].first)  <- Ops[1].second times
/// op
///   ...
/// op
///   (Ops[N].first op Ops[N].first op ... Ops[N].first)  <- Ops[N].second times
///
/// Note that the values Ops[0].first, ..., Ops[N].first are all distinct.
///
/// This routine may modify the function, in which case it returns 'true'.  The
/// changes it makes may well be destructive, changing the value computed by 'I'
/// to something completely different.  Thus if the routine returns 'true' then
/// you MUST either replace I with a new expression computed from the Ops array,
/// or use RewriteExprTree to put the values back in.
///
/// A leaf node is either not a binary operation of the same kind as the root
/// node 'I' (i.e. is not a binary operator at all, or is, but with a different
/// opcode), or is the same kind of binary operator but has a use which either
/// does not belong to the expression, or does belong to the expression but is
/// a leaf node.  Every leaf node has at least one use that is a non-leaf node
/// of the expression, while for non-leaf nodes (except for the root 'I') every
/// use is a non-leaf node of the expression.
///
/// For example:
///           expression graph        node names
///
///                     +        |        I
///                    / \       |
///                   +   +      |      A,  B
///                  / \ / \     |
///                 *   +   *    |    C,  D,  E
///                / \ / \ / \   |
///                   +   *      |      F,  G
///
/// The leaf nodes are C, E, F and G.  The Ops array will contain (maybe not in
/// that order) (C, 1), (E, 1), (F, 2), (G, 2).
///
/// The expression is maximal: if some instruction is a binary operator of the
/// same kind as 'I', and all of its uses are non-leaf nodes of the expression,
/// then the instruction also belongs to the expression, is not a leaf node of
/// it, and its operands also belong to the expression (but may be leaf nodes).
///
/// NOTE: This routine will set operands of non-leaf non-root nodes to undef in
/// order to ensure that every non-root node in the expression has *exactly one*
/// use by a non-leaf node of the expression.  This destruction means that the
/// caller MUST either replace 'I' with a new expression or use something like
/// RewriteExprTree to put the values back in if the routine indicates that it
/// made a change by returning 'true'.
///
/// In the above example either the right operand of A or the left operand of B
/// will be replaced by undef.  If it is B's operand then this gives:
///
///                     +        |        I
///                    / \       |
///                   +   +      |      A,  B - operand of B replaced with undef
///                  / \   \     |
///                 *   +   *    |    C,  D,  E
///                / \ / \ / \   |
///                   +   *      |      F,  G
///
/// Note that such undef operands can only be reached by passing through 'I'.
/// For example, if you visit operands recursively starting from a leaf node
/// then you will never see such an undef operand unless you get back to 'I',
/// which requires passing through a phi node.
///
/// Note that this routine may also mutate binary operators of the wrong type
/// that have all uses inside the expression (i.e. only used by non-leaf nodes
/// of the expression) if it can turn them into binary operators of the right
/// type and thus make the expression bigger.
static bool LinearizeExprTree(BinaryOperator *I,
                              SmallVectorImpl<RepeatedValue> &Ops) {
  LLVM_DEBUG(dbgs() << "LINEARIZE: " << *I << '\n');
  unsigned Bitwidth = I->getType()->getScalarType()->getPrimitiveSizeInBits();
  unsigned Opcode = I->getOpcode();
  assert(I->isAssociative() && I->isCommutative() &&
         "Expected an associative and commutative operation!");

  // Visit all operands of the expression, keeping track of their weight (the
  // number of paths from the expression root to the operand, or if you like
  // the number of times that operand occurs in the linearized expression).
  // For example, if I = X + A, where X = A + B, then I, X and B have weight 1
  // while A has weight two.

  // Worklist of non-leaf nodes (their operands are in the expression too) along
  // with their weights, representing a certain number of paths to the operator.
  // If an operator occurs in the worklist multiple times then we found multiple
  // ways to get to it.
  SmallVector<std::pair<BinaryOperator*, APInt>, 8> Worklist; // (Op, Weight)
  Worklist.push_back(std::make_pair(I, APInt(Bitwidth, 1)));
  bool Changed = false;

  // Leaves of the expression are values that either aren't the right kind of
  // operation (eg: a constant, or a multiply in an add tree), or are, but have
  // some uses that are not inside the expression.  For example, in I = X + X,
  // X = A + B, the value X has two uses (by I) that are in the expression.  If
  // X has any other uses, for example in a return instruction, then we consider
  // X to be a leaf, and won't analyze it further.  When we first visit a value,
  // if it has more than one use then at first we conservatively consider it to
  // be a leaf.  Later, as the expression is explored, we may discover some more
  // uses of the value from inside the expression.  If all uses turn out to be
  // from within the expression (and the value is a binary operator of the right
  // kind) then the value is no longer considered to be a leaf, and its operands
  // are explored.

  // Leaves - Keeps track of the set of putative leaves as well as the number of
  // paths to each leaf seen so far.
  using LeafMap = DenseMap<Value *, APInt>;
  LeafMap Leaves; // Leaf -> Total weight so far.
  SmallVector<Value *, 8> LeafOrder; // Ensure deterministic leaf output order.

#ifndef NDEBUG
  SmallPtrSet<Value *, 8> Visited; // For sanity checking the iteration scheme.
#endif
  while (!Worklist.empty()) {
    std::pair<BinaryOperator*, APInt> P = Worklist.pop_back_val();
    I = P.first; // We examine the operands of this binary operator.

    for (unsigned OpIdx = 0; OpIdx < 2; ++OpIdx) { // Visit operands.
      Value *Op = I->getOperand(OpIdx);
      APInt Weight = P.second; // Number of paths to this operand.
      LLVM_DEBUG(dbgs() << "OPERAND: " << *Op << " (" << Weight << ")\n");
      assert(!Op->use_empty() && "No uses, so how did we get to it?!");

      // If this is a binary operation of the right kind with only one use then
      // add its operands to the expression.
      if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
        assert(Visited.insert(Op).second && "Not first visit!");
        LLVM_DEBUG(dbgs() << "DIRECT ADD: " << *Op << " (" << Weight << ")\n");
        Worklist.push_back(std::make_pair(BO, Weight));
        continue;
      }

      // Appears to be a leaf.  Is the operand already in the set of leaves?
      LeafMap::iterator It = Leaves.find(Op);
      if (It == Leaves.end()) {
        // Not in the leaf map.  Must be the first time we saw this operand.
        assert(Visited.insert(Op).second && "Not first visit!");
        if (!Op->hasOneUse()) {
          // This value has uses not accounted for by the expression, so it is
          // not safe to modify.  Mark it as being a leaf.
          LLVM_DEBUG(dbgs()
                     << "ADD USES LEAF: " << *Op << " (" << Weight << ")\n");
          LeafOrder.push_back(Op);
          Leaves[Op] = Weight;
          continue;
        }
        // No uses outside the expression, try morphing it.
      } else {
        // Already in the leaf map.
        assert(It != Leaves.end() && Visited.count(Op) &&
               "In leaf map but not visited!");

        // Update the number of paths to the leaf.
        IncorporateWeight(It->second, Weight, Opcode);

#if 0   // TODO: Re-enable once PR13021 is fixed.
        // The leaf already has one use from inside the expression.  As we want
        // exactly one such use, drop this new use of the leaf.
        assert(!Op->hasOneUse() && "Only one use, but we got here twice!");
        I->setOperand(OpIdx, UndefValue::get(I->getType()));
        Changed = true;

        // If the leaf is a binary operation of the right kind and we now see
        // that its multiple original uses were in fact all by nodes belonging
        // to the expression, then no longer consider it to be a leaf and add
        // its operands to the expression.
        if (BinaryOperator *BO = isReassociableOp(Op, Opcode)) {
          LLVM_DEBUG(dbgs() << "UNLEAF: " << *Op << " (" << It->second << ")\n");
          Worklist.push_back(std::make_pair(BO, It->second));
          Leaves.erase(It);
          continue;
        }
#endif

        // If we still have uses that are not accounted for by the expression
        // then it is not safe to modify the value.
        if (!Op->hasOneUse())
          continue;

        // No uses outside the expression, try morphing it.
        Weight = It->second;
        Leaves.erase(It); // Since the value may be morphed below.
      }

      // At this point we have a value which, first of all, is not a binary
      // expression of the right kind, and secondly, is only used inside the
      // expression.  This means that it can safely be modified.  See if we
      // can usefully morph it into an expression of the right kind.
      assert((!isa<Instruction>(Op) ||
              cast<Instruction>(Op)->getOpcode() != Opcode
              || (isa<FPMathOperator>(Op) &&
                  !cast<Instruction>(Op)->isFast())) &&
             "Should have been handled above!");
      assert(Op->hasOneUse() && "Has uses outside the expression tree!");

      // If this is a multiply expression, turn any internal negations into
      // multiplies by -1 so they can be reassociated.
      if (BinaryOperator *BO = dyn_cast<BinaryOperator>(Op))
        if ((Opcode == Instruction::Mul && match(BO, m_Neg(m_Value()))) ||
            (Opcode == Instruction::FMul && match(BO, m_FNeg(m_Value())))) {
          LLVM_DEBUG(dbgs()
                     << "MORPH LEAF: " << *Op << " (" << Weight << ") TO ");
          BO = LowerNegateToMultiply(BO);
          LLVM_DEBUG(dbgs() << *BO << '\n');
          Worklist.push_back(std::make_pair(BO, Weight));
          Changed = true;
          continue;
        }

      // Failed to morph into an expression of the right type.  This really is
      // a leaf.
      LLVM_DEBUG(dbgs() << "ADD LEAF: " << *Op << " (" << Weight << ")\n");
      assert(!isReassociableOp(Op, Opcode) && "Value was morphed?");
      LeafOrder.push_back(Op);
      Leaves[Op] = Weight;
    }
  }

  // The leaves, repeated according to their weights, represent the linearized
  // form of the expression.
  for (unsigned i = 0, e = LeafOrder.size(); i != e; ++i) {
    Value *V = LeafOrder[i];
    LeafMap::iterator It = Leaves.find(V);
    if (It == Leaves.end())
      // Node initially thought to be a leaf wasn't.
      continue;
    assert(!isReassociableOp(V, Opcode) && "Shouldn't be a leaf!");
    APInt Weight = It->second;
    if (Weight.isMinValue())
      // Leaf already output or weight reduction eliminated it.
      continue;
    // Ensure the leaf is only output once.
    It->second = 0;
    Ops.push_back(std::make_pair(V, Weight));
  }

  // For nilpotent operations or addition there may be no operands, for example
  // because the expression was "X xor X" or consisted of 2^Bitwidth additions:
  // in both cases the weight reduces to 0 causing the value to be skipped.
  if (Ops.empty()) {
    Constant *Identity = ConstantExpr::getBinOpIdentity(Opcode, I->getType());
    assert(Identity && "Associative operation without identity!");
    Ops.emplace_back(Identity, APInt(Bitwidth, 1));
  }

  return Changed;
}

/// Now that the operands for this expression tree are
/// linearized and optimized, emit them in-order.
void ReassociatePass::RewriteExprTree(BinaryOperator *I,
                                      SmallVectorImpl<ValueEntry> &Ops) {
  assert(Ops.size() > 1 && "Single values should be used directly!");

  // Since our optimizations should never increase the number of operations, the
  // new expression can usually be written reusing the existing binary operators
  // from the original expression tree, without creating any new instructions,
  // though the rewritten expression may have a completely different topology.
  // We take care to not change anything if the new expression will be the same
  // as the original.  If more than trivial changes (like commuting operands)
  // were made then we are obliged to clear out any optional subclass data like
  // nsw flags.

  /// NodesToRewrite - Nodes from the original expression available for writing
  /// the new expression into.
  SmallVector<BinaryOperator*, 8> NodesToRewrite;
  unsigned Opcode = I->getOpcode();
  BinaryOperator *Op = I;

  /// NotRewritable - The operands being written will be the leaves of the new
  /// expression and must not be used as inner nodes (via NodesToRewrite) by
  /// mistake.  Inner nodes are always reassociable, and usually leaves are not
  /// (if they were they would have been incorporated into the expression and so
  /// would not be leaves), so most of the time there is no danger of this.  But
  /// in rare cases a leaf may become reassociable if an optimization kills uses
  /// of it, or it may momentarily become reassociable during rewriting (below)
  /// due it being removed as an operand of one of its uses.  Ensure that misuse
  /// of leaf nodes as inner nodes cannot occur by remembering all of the future
  /// leaves and refusing to reuse any of them as inner nodes.
  SmallPtrSet<Value*, 8> NotRewritable;
  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    NotRewritable.insert(Ops[i].Op);

  // ExpressionChanged - Non-null if the rewritten expression differs from the
  // original in some non-trivial way, requiring the clearing of optional flags.
  // Flags are cleared from the operator in ExpressionChanged up to I inclusive.
  BinaryOperator *ExpressionChanged = nullptr;
  for (unsigned i = 0; ; ++i) {
    // The last operation (which comes earliest in the IR) is special as both
    // operands will come from Ops, rather than just one with the other being
    // a subexpression.
    if (i+2 == Ops.size()) {
      Value *NewLHS = Ops[i].Op;
      Value *NewRHS = Ops[i+1].Op;
      Value *OldLHS = Op->getOperand(0);
      Value *OldRHS = Op->getOperand(1);

      if (NewLHS == OldLHS && NewRHS == OldRHS)
        // Nothing changed, leave it alone.
        break;

      if (NewLHS == OldRHS && NewRHS == OldLHS) {
        // The order of the operands was reversed.  Swap them.
        LLVM_DEBUG(dbgs() << "RA: " << *Op << '\n');
        Op->swapOperands();
        LLVM_DEBUG(dbgs() << "TO: " << *Op << '\n');
        MadeChange = true;
        ++NumChanged;
        break;
      }

      // The new operation differs non-trivially from the original. Overwrite
      // the old operands with the new ones.
      LLVM_DEBUG(dbgs() << "RA: " << *Op << '\n');
      if (NewLHS != OldLHS) {
        BinaryOperator *BO = isReassociableOp(OldLHS, Opcode);
        if (BO && !NotRewritable.count(BO))
          NodesToRewrite.push_back(BO);
        Op->setOperand(0, NewLHS);
      }
      if (NewRHS != OldRHS) {
        BinaryOperator *BO = isReassociableOp(OldRHS, Opcode);
        if (BO && !NotRewritable.count(BO))
          NodesToRewrite.push_back(BO);
        Op->setOperand(1, NewRHS);
      }
      LLVM_DEBUG(dbgs() << "TO: " << *Op << '\n');

      ExpressionChanged = Op;
      MadeChange = true;
      ++NumChanged;

      break;
    }

    // Not the last operation.  The left-hand side will be a sub-expression
    // while the right-hand side will be the current element of Ops.
    Value *NewRHS = Ops[i].Op;
    if (NewRHS != Op->getOperand(1)) {
      LLVM_DEBUG(dbgs() << "RA: " << *Op << '\n');
      if (NewRHS == Op->getOperand(0)) {
        // The new right-hand side was already present as the left operand.  If
        // we are lucky then swapping the operands will sort out both of them.
        Op->swapOperands();
      } else {
        // Overwrite with the new right-hand side.
        BinaryOperator *BO = isReassociableOp(Op->getOperand(1), Opcode);
        if (BO && !NotRewritable.count(BO))
          NodesToRewrite.push_back(BO);
        Op->setOperand(1, NewRHS);
        ExpressionChanged = Op;
      }
      LLVM_DEBUG(dbgs() << "TO: " << *Op << '\n');
      MadeChange = true;
      ++NumChanged;
    }

    // Now deal with the left-hand side.  If this is already an operation node
    // from the original expression then just rewrite the rest of the expression
    // into it.
    BinaryOperator *BO = isReassociableOp(Op->getOperand(0), Opcode);
    if (BO && !NotRewritable.count(BO)) {
      Op = BO;
      continue;
    }

    // Otherwise, grab a spare node from the original expression and use that as
    // the left-hand side.  If there are no nodes left then the optimizers made
    // an expression with more nodes than the original!  This usually means that
    // they did something stupid but it might mean that the problem was just too
    // hard (finding the mimimal number of multiplications needed to realize a
    // multiplication expression is NP-complete).  Whatever the reason, smart or
    // stupid, create a new node if there are none left.
    BinaryOperator *NewOp;
    if (NodesToRewrite.empty()) {
      Constant *Undef = UndefValue::get(I->getType());
      NewOp = BinaryOperator::Create(Instruction::BinaryOps(Opcode),
                                     Undef, Undef, "", I);
      if (NewOp->getType()->isFPOrFPVectorTy())
        NewOp->setFastMathFlags(I->getFastMathFlags());
    } else {
      NewOp = NodesToRewrite.pop_back_val();
    }

    LLVM_DEBUG(dbgs() << "RA: " << *Op << '\n');
    Op->setOperand(0, NewOp);
    LLVM_DEBUG(dbgs() << "TO: " << *Op << '\n');
    ExpressionChanged = Op;
    MadeChange = true;
    ++NumChanged;
    Op = NewOp;
  }

  // If the expression changed non-trivially then clear out all subclass data
  // starting from the operator specified in ExpressionChanged, and compactify
  // the operators to just before the expression root to guarantee that the
  // expression tree is dominated by all of Ops.
  if (ExpressionChanged)
    do {
      // Preserve FastMathFlags.
      if (isa<FPMathOperator>(I)) {
        FastMathFlags Flags = I->getFastMathFlags();
        ExpressionChanged->clearSubclassOptionalData();
        ExpressionChanged->setFastMathFlags(Flags);
      } else
        ExpressionChanged->clearSubclassOptionalData();

      if (ExpressionChanged == I)
        break;

      // Discard any debug info related to the expressions that has changed (we
      // can leave debug infor related to the root, since the result of the
      // expression tree should be the same even after reassociation).
      replaceDbgUsesWithUndef(ExpressionChanged);

      ExpressionChanged->moveBefore(I);
      ExpressionChanged = cast<BinaryOperator>(*ExpressionChanged->user_begin());
    } while (true);

  // Throw away any left over nodes from the original expression.
  for (unsigned i = 0, e = NodesToRewrite.size(); i != e; ++i)
    RedoInsts.insert(NodesToRewrite[i]);
}

/// Insert instructions before the instruction pointed to by BI,
/// that computes the negative version of the value specified.  The negative
/// version of the value is returned, and BI is left pointing at the instruction
/// that should be processed next by the reassociation pass.
/// Also add intermediate instructions to the redo list that are modified while
/// pushing the negates through adds.  These will be revisited to see if
/// additional opportunities have been exposed.
static Value *NegateValue(Value *V, Instruction *BI,
                          ReassociatePass::OrderedSet &ToRedo) {
  if (auto *C = dyn_cast<Constant>(V))
    return C->getType()->isFPOrFPVectorTy() ? ConstantExpr::getFNeg(C) :
                                              ConstantExpr::getNeg(C);

  // We are trying to expose opportunity for reassociation.  One of the things
  // that we want to do to achieve this is to push a negation as deep into an
  // expression chain as possible, to expose the add instructions.  In practice,
  // this means that we turn this:
  //   X = -(A+12+C+D)   into    X = -A + -12 + -C + -D = -12 + -A + -C + -D
  // so that later, a: Y = 12+X could get reassociated with the -12 to eliminate
  // the constants.  We assume that instcombine will clean up the mess later if
  // we introduce tons of unnecessary negation instructions.
  //
  if (BinaryOperator *I =
          isReassociableOp(V, Instruction::Add, Instruction::FAdd)) {
    // Push the negates through the add.
    I->setOperand(0, NegateValue(I->getOperand(0), BI, ToRedo));
    I->setOperand(1, NegateValue(I->getOperand(1), BI, ToRedo));
    if (I->getOpcode() == Instruction::Add) {
      I->setHasNoUnsignedWrap(false);
      I->setHasNoSignedWrap(false);
    }

    // We must move the add instruction here, because the neg instructions do
    // not dominate the old add instruction in general.  By moving it, we are
    // assured that the neg instructions we just inserted dominate the
    // instruction we are about to insert after them.
    //
    I->moveBefore(BI);
    I->setName(I->getName()+".neg");

    // Add the intermediate negates to the redo list as processing them later
    // could expose more reassociating opportunities.
    ToRedo.insert(I);
    return I;
  }

  // Okay, we need to materialize a negated version of V with an instruction.
  // Scan the use lists of V to see if we have one already.
  for (User *U : V->users()) {
    if (!match(U, m_Neg(m_Value())) && !match(U, m_FNeg(m_Value())))
      continue;

    // We found one!  Now we have to make sure that the definition dominates
    // this use.  We do this by moving it to the entry block (if it is a
    // non-instruction value) or right after the definition.  These negates will
    // be zapped by reassociate later, so we don't need much finesse here.
    BinaryOperator *TheNeg = cast<BinaryOperator>(U);

    // Verify that the negate is in this function, V might be a constant expr.
    if (TheNeg->getParent()->getParent() != BI->getParent()->getParent())
      continue;

    BasicBlock::iterator InsertPt;
    if (Instruction *InstInput = dyn_cast<Instruction>(V)) {
      if (InvokeInst *II = dyn_cast<InvokeInst>(InstInput)) {
        InsertPt = II->getNormalDest()->begin();
      } else {
        InsertPt = ++InstInput->getIterator();
      }
      while (isa<PHINode>(InsertPt)) ++InsertPt;
    } else {
      InsertPt = TheNeg->getParent()->getParent()->getEntryBlock().begin();
    }
    TheNeg->moveBefore(&*InsertPt);
    if (TheNeg->getOpcode() == Instruction::Sub) {
      TheNeg->setHasNoUnsignedWrap(false);
      TheNeg->setHasNoSignedWrap(false);
    } else {
      TheNeg->andIRFlags(BI);
    }
    ToRedo.insert(TheNeg);
    return TheNeg;
  }

  // Insert a 'neg' instruction that subtracts the value from zero to get the
  // negation.
  BinaryOperator *NewNeg = CreateNeg(V, V->getName() + ".neg", BI, BI);
  ToRedo.insert(NewNeg);
  return NewNeg;
}

/// Return true if we should break up this subtract of X-Y into (X + -Y).
static bool ShouldBreakUpSubtract(Instruction *Sub) {
  // If this is a negation, we can't split it up!
  if (match(Sub, m_Neg(m_Value())) || match(Sub, m_FNeg(m_Value()))) 
    return false;

  // Don't breakup X - undef.
  if (isa<UndefValue>(Sub->getOperand(1)))
    return false;

  // Don't bother to break this up unless either the LHS is an associable add or
  // subtract or if this is only used by one.
  Value *V0 = Sub->getOperand(0);
  if (isReassociableOp(V0, Instruction::Add, Instruction::FAdd) ||
      isReassociableOp(V0, Instruction::Sub, Instruction::FSub))
    return true;
  Value *V1 = Sub->getOperand(1);
  if (isReassociableOp(V1, Instruction::Add, Instruction::FAdd) ||
      isReassociableOp(V1, Instruction::Sub, Instruction::FSub))
    return true;
  Value *VB = Sub->user_back();
  if (Sub->hasOneUse() &&
      (isReassociableOp(VB, Instruction::Add, Instruction::FAdd) ||
       isReassociableOp(VB, Instruction::Sub, Instruction::FSub)))
    return true;

  return false;
}

/// If we have (X-Y), and if either X is an add, or if this is only used by an
/// add, transform this into (X+(0-Y)) to promote better reassociation.
static BinaryOperator *BreakUpSubtract(Instruction *Sub,
                                       ReassociatePass::OrderedSet &ToRedo) {
  // Convert a subtract into an add and a neg instruction. This allows sub
  // instructions to be commuted with other add instructions.
  //
  // Calculate the negative value of Operand 1 of the sub instruction,
  // and set it as the RHS of the add instruction we just made.
  Value *NegVal = NegateValue(Sub->getOperand(1), Sub, ToRedo);
  BinaryOperator *New = CreateAdd(Sub->getOperand(0), NegVal, "", Sub, Sub);
  Sub->setOperand(0, Constant::getNullValue(Sub->getType())); // Drop use of op.
  Sub->setOperand(1, Constant::getNullValue(Sub->getType())); // Drop use of op.
  New->takeName(Sub);

  // Everyone now refers to the add instruction.
  Sub->replaceAllUsesWith(New);
  New->setDebugLoc(Sub->getDebugLoc());

  LLVM_DEBUG(dbgs() << "Negated: " << *New << '\n');
  return New;
}

/// If this is a shift of a reassociable multiply or is used by one, change
/// this into a multiply by a constant to assist with further reassociation.
static BinaryOperator *ConvertShiftToMul(Instruction *Shl) {
  Constant *MulCst = ConstantInt::get(Shl->getType(), 1);
  MulCst = ConstantExpr::getShl(MulCst, cast<Constant>(Shl->getOperand(1)));

  BinaryOperator *Mul =
    BinaryOperator::CreateMul(Shl->getOperand(0), MulCst, "", Shl);
  Shl->setOperand(0, UndefValue::get(Shl->getType())); // Drop use of op.
  Mul->takeName(Shl);

  // Everyone now refers to the mul instruction.
  Shl->replaceAllUsesWith(Mul);
  Mul->setDebugLoc(Shl->getDebugLoc());

  // We can safely preserve the nuw flag in all cases.  It's also safe to turn a
  // nuw nsw shl into a nuw nsw mul.  However, nsw in isolation requires special
  // handling.
  bool NSW = cast<BinaryOperator>(Shl)->hasNoSignedWrap();
  bool NUW = cast<BinaryOperator>(Shl)->hasNoUnsignedWrap();
  if (NSW && NUW)
    Mul->setHasNoSignedWrap(true);
  Mul->setHasNoUnsignedWrap(NUW);
  return Mul;
}

/// Scan backwards and forwards among values with the same rank as element i
/// to see if X exists.  If X does not exist, return i.  This is useful when
/// scanning for 'x' when we see '-x' because they both get the same rank.
static unsigned FindInOperandList(const SmallVectorImpl<ValueEntry> &Ops,
                                  unsigned i, Value *X) {
  unsigned XRank = Ops[i].Rank;
  unsigned e = Ops.size();
  for (unsigned j = i+1; j != e && Ops[j].Rank == XRank; ++j) {
    if (Ops[j].Op == X)
      return j;
    if (Instruction *I1 = dyn_cast<Instruction>(Ops[j].Op))
      if (Instruction *I2 = dyn_cast<Instruction>(X))
        if (I1->isIdenticalTo(I2))
          return j;
  }
  // Scan backwards.
  for (unsigned j = i-1; j != ~0U && Ops[j].Rank == XRank; --j) {
    if (Ops[j].Op == X)
      return j;
    if (Instruction *I1 = dyn_cast<Instruction>(Ops[j].Op))
      if (Instruction *I2 = dyn_cast<Instruction>(X))
        if (I1->isIdenticalTo(I2))
          return j;
  }
  return i;
}

/// Emit a tree of add instructions, summing Ops together
/// and returning the result.  Insert the tree before I.
static Value *EmitAddTreeOfValues(Instruction *I,
                                  SmallVectorImpl<WeakTrackingVH> &Ops) {
  if (Ops.size() == 1) return Ops.back();

  Value *V1 = Ops.back();
  Ops.pop_back();
  Value *V2 = EmitAddTreeOfValues(I, Ops);
  return CreateAdd(V2, V1, "reass.add", I, I);
}

/// If V is an expression tree that is a multiplication sequence,
/// and if this sequence contains a multiply by Factor,
/// remove Factor from the tree and return the new tree.
Value *ReassociatePass::RemoveFactorFromExpression(Value *V, Value *Factor) {
  BinaryOperator *BO = isReassociableOp(V, Instruction::Mul, Instruction::FMul);
  if (!BO)
    return nullptr;

  SmallVector<RepeatedValue, 8> Tree;
  MadeChange |= LinearizeExprTree(BO, Tree);
  SmallVector<ValueEntry, 8> Factors;
  Factors.reserve(Tree.size());
  for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
    RepeatedValue E = Tree[i];
    Factors.append(E.second.getZExtValue(),
                   ValueEntry(getRank(E.first), E.first));
  }

  bool FoundFactor = false;
  bool NeedsNegate = false;
  for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
    if (Factors[i].Op == Factor) {
      FoundFactor = true;
      Factors.erase(Factors.begin()+i);
      break;
    }

    // If this is a negative version of this factor, remove it.
    if (ConstantInt *FC1 = dyn_cast<ConstantInt>(Factor)) {
      if (ConstantInt *FC2 = dyn_cast<ConstantInt>(Factors[i].Op))
        if (FC1->getValue() == -FC2->getValue()) {
          FoundFactor = NeedsNegate = true;
          Factors.erase(Factors.begin()+i);
          break;
        }
    } else if (ConstantFP *FC1 = dyn_cast<ConstantFP>(Factor)) {
      if (ConstantFP *FC2 = dyn_cast<ConstantFP>(Factors[i].Op)) {
        const APFloat &F1 = FC1->getValueAPF();
        APFloat F2(FC2->getValueAPF());
        F2.changeSign();
        if (F1.compare(F2) == APFloat::cmpEqual) {
          FoundFactor = NeedsNegate = true;
          Factors.erase(Factors.begin() + i);
          break;
        }
      }
    }
  }

  if (!FoundFactor) {
    // Make sure to restore the operands to the expression tree.
    RewriteExprTree(BO, Factors);
    return nullptr;
  }

  BasicBlock::iterator InsertPt = ++BO->getIterator();

  // If this was just a single multiply, remove the multiply and return the only
  // remaining operand.
  if (Factors.size() == 1) {
    RedoInsts.insert(BO);
    V = Factors[0].Op;
  } else {
    RewriteExprTree(BO, Factors);
    V = BO;
  }

  if (NeedsNegate)
    V = CreateNeg(V, "neg", &*InsertPt, BO);

  return V;
}

/// If V is a single-use multiply, recursively add its operands as factors,
/// otherwise add V to the list of factors.
///
/// Ops is the top-level list of add operands we're trying to factor.
static void FindSingleUseMultiplyFactors(Value *V,
                                         SmallVectorImpl<Value*> &Factors) {
  BinaryOperator *BO = isReassociableOp(V, Instruction::Mul, Instruction::FMul);
  if (!BO) {
    Factors.push_back(V);
    return;
  }

  // Otherwise, add the LHS and RHS to the list of factors.
  FindSingleUseMultiplyFactors(BO->getOperand(1), Factors);
  FindSingleUseMultiplyFactors(BO->getOperand(0), Factors);
}

/// Optimize a series of operands to an 'and', 'or', or 'xor' instruction.
/// This optimizes based on identities.  If it can be reduced to a single Value,
/// it is returned, otherwise the Ops list is mutated as necessary.
static Value *OptimizeAndOrXor(unsigned Opcode,
                               SmallVectorImpl<ValueEntry> &Ops) {
  // Scan the operand lists looking for X and ~X pairs, along with X,X pairs.
  // If we find any, we can simplify the expression. X&~X == 0, X|~X == -1.
  for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
    // First, check for X and ~X in the operand list.
    assert(i < Ops.size());
    Value *X;
    if (match(Ops[i].Op, m_Not(m_Value(X)))) {    // Cannot occur for ^.
      unsigned FoundX = FindInOperandList(Ops, i, X);
      if (FoundX != i) {
        if (Opcode == Instruction::And)   // ...&X&~X = 0
          return Constant::getNullValue(X->getType());

        if (Opcode == Instruction::Or)    // ...|X|~X = -1
          return Constant::getAllOnesValue(X->getType());
      }
    }

    // Next, check for duplicate pairs of values, which we assume are next to
    // each other, due to our sorting criteria.
    assert(i < Ops.size());
    if (i+1 != Ops.size() && Ops[i+1].Op == Ops[i].Op) {
      if (Opcode == Instruction::And || Opcode == Instruction::Or) {
        // Drop duplicate values for And and Or.
        Ops.erase(Ops.begin()+i);
        --i; --e;
        ++NumAnnihil;
        continue;
      }

      // Drop pairs of values for Xor.
      assert(Opcode == Instruction::Xor);
      if (e == 2)
        return Constant::getNullValue(Ops[0].Op->getType());

      // Y ^ X^X -> Y
      Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
      i -= 1; e -= 2;
      ++NumAnnihil;
    }
  }
  return nullptr;
}

/// Helper function of CombineXorOpnd(). It creates a bitwise-and
/// instruction with the given two operands, and return the resulting
/// instruction. There are two special cases: 1) if the constant operand is 0,
/// it will return NULL. 2) if the constant is ~0, the symbolic operand will
/// be returned.
static Value *createAndInstr(Instruction *InsertBefore, Value *Opnd,
                             const APInt &ConstOpnd) {
  if (ConstOpnd.isNullValue())
    return nullptr;

  if (ConstOpnd.isAllOnesValue())
    return Opnd;

  Instruction *I = BinaryOperator::CreateAnd(
      Opnd, ConstantInt::get(Opnd->getType(), ConstOpnd), "and.ra",
      InsertBefore);
  I->setDebugLoc(InsertBefore->getDebugLoc());
  return I;
}

// Helper function of OptimizeXor(). It tries to simplify "Opnd1 ^ ConstOpnd"
// into "R ^ C", where C would be 0, and R is a symbolic value.
//
// If it was successful, true is returned, and the "R" and "C" is returned
// via "Res" and "ConstOpnd", respectively; otherwise, false is returned,
// and both "Res" and "ConstOpnd" remain unchanged.
bool ReassociatePass::CombineXorOpnd(Instruction *I, XorOpnd *Opnd1,
                                     APInt &ConstOpnd, Value *&Res) {
  // Xor-Rule 1: (x | c1) ^ c2 = (x | c1) ^ (c1 ^ c1) ^ c2
  //                       = ((x | c1) ^ c1) ^ (c1 ^ c2)
  //                       = (x & ~c1) ^ (c1 ^ c2)
  // It is useful only when c1 == c2.
  if (!Opnd1->isOrExpr() || Opnd1->getConstPart().isNullValue())
    return false;

  if (!Opnd1->getValue()->hasOneUse())
    return false;

  const APInt &C1 = Opnd1->getConstPart();
  if (C1 != ConstOpnd)
    return false;

  Value *X = Opnd1->getSymbolicPart();
  Res = createAndInstr(I, X, ~C1);
  // ConstOpnd was C2, now C1 ^ C2.
  ConstOpnd ^= C1;

  if (Instruction *T = dyn_cast<Instruction>(Opnd1->getValue()))
    RedoInsts.insert(T);
  return true;
}

// Helper function of OptimizeXor(). It tries to simplify
// "Opnd1 ^ Opnd2 ^ ConstOpnd" into "R ^ C", where C would be 0, and R is a
// symbolic value.
//
// If it was successful, true is returned, and the "R" and "C" is returned
// via "Res" and "ConstOpnd", respectively (If the entire expression is
// evaluated to a constant, the Res is set to NULL); otherwise, false is
// returned, and both "Res" and "ConstOpnd" remain unchanged.
bool ReassociatePass::CombineXorOpnd(Instruction *I, XorOpnd *Opnd1,
                                     XorOpnd *Opnd2, APInt &ConstOpnd,
                                     Value *&Res) {
  Value *X = Opnd1->getSymbolicPart();
  if (X != Opnd2->getSymbolicPart())
    return false;

  // This many instruction become dead.(At least "Opnd1 ^ Opnd2" will die.)
  int DeadInstNum = 1;
  if (Opnd1->getValue()->hasOneUse())
    DeadInstNum++;
  if (Opnd2->getValue()->hasOneUse())
    DeadInstNum++;

  // Xor-Rule 2:
  //  (x | c1) ^ (x & c2)
  //   = (x|c1) ^ (x&c2) ^ (c1 ^ c1) = ((x|c1) ^ c1) ^ (x & c2) ^ c1
  //   = (x & ~c1) ^ (x & c2) ^ c1               // Xor-Rule 1
  //   = (x & c3) ^ c1, where c3 = ~c1 ^ c2      // Xor-rule 3
  //
  if (Opnd1->isOrExpr() != Opnd2->isOrExpr()) {
    if (Opnd2->isOrExpr())
      std::swap(Opnd1, Opnd2);

    const APInt &C1 = Opnd1->getConstPart();
    const APInt &C2 = Opnd2->getConstPart();
    APInt C3((~C1) ^ C2);

    // Do not increase code size!
    if (!C3.isNullValue() && !C3.isAllOnesValue()) {
      int NewInstNum = ConstOpnd.getBoolValue() ? 1 : 2;
      if (NewInstNum > DeadInstNum)
        return false;
    }

    Res = createAndInstr(I, X, C3);
    ConstOpnd ^= C1;
  } else if (Opnd1->isOrExpr()) {
    // Xor-Rule 3: (x | c1) ^ (x | c2) = (x & c3) ^ c3 where c3 = c1 ^ c2
    //
    const APInt &C1 = Opnd1->getConstPart();
    const APInt &C2 = Opnd2->getConstPart();
    APInt C3 = C1 ^ C2;

    // Do not increase code size
    if (!C3.isNullValue() && !C3.isAllOnesValue()) {
      int NewInstNum = ConstOpnd.getBoolValue() ? 1 : 2;
      if (NewInstNum > DeadInstNum)
        return false;
    }

    Res = createAndInstr(I, X, C3);
    ConstOpnd ^= C3;
  } else {
    // Xor-Rule 4: (x & c1) ^ (x & c2) = (x & (c1^c2))
    //
    const APInt &C1 = Opnd1->getConstPart();
    const APInt &C2 = Opnd2->getConstPart();
    APInt C3 = C1 ^ C2;
    Res = createAndInstr(I, X, C3);
  }

  // Put the original operands in the Redo list; hope they will be deleted
  // as dead code.
  if (Instruction *T = dyn_cast<Instruction>(Opnd1->getValue()))
    RedoInsts.insert(T);
  if (Instruction *T = dyn_cast<Instruction>(Opnd2->getValue()))
    RedoInsts.insert(T);

  return true;
}

/// Optimize a series of operands to an 'xor' instruction. If it can be reduced
/// to a single Value, it is returned, otherwise the Ops list is mutated as
/// necessary.
Value *ReassociatePass::OptimizeXor(Instruction *I,
                                    SmallVectorImpl<ValueEntry> &Ops) {
  if (Value *V = OptimizeAndOrXor(Instruction::Xor, Ops))
    return V;

  if (Ops.size() == 1)
    return nullptr;

  SmallVector<XorOpnd, 8> Opnds;
  SmallVector<XorOpnd*, 8> OpndPtrs;
  Type *Ty = Ops[0].Op->getType();
  APInt ConstOpnd(Ty->getScalarSizeInBits(), 0);

  // Step 1: Convert ValueEntry to XorOpnd
  for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
    Value *V = Ops[i].Op;
    const APInt *C;
    // TODO: Support non-splat vectors.
    if (match(V, m_APInt(C))) {
      ConstOpnd ^= *C;
    } else {
      XorOpnd O(V);
      O.setSymbolicRank(getRank(O.getSymbolicPart()));
      Opnds.push_back(O);
    }
  }

  // NOTE: From this point on, do *NOT* add/delete element to/from "Opnds".
  //  It would otherwise invalidate the "Opnds"'s iterator, and hence invalidate
  //  the "OpndPtrs" as well. For the similar reason, do not fuse this loop
  //  with the previous loop --- the iterator of the "Opnds" may be invalidated
  //  when new elements are added to the vector.
  for (unsigned i = 0, e = Opnds.size(); i != e; ++i)
    OpndPtrs.push_back(&Opnds[i]);

  // Step 2: Sort the Xor-Operands in a way such that the operands containing
  //  the same symbolic value cluster together. For instance, the input operand
  //  sequence ("x | 123", "y & 456", "x & 789") will be sorted into:
  //  ("x | 123", "x & 789", "y & 456").
  //
  //  The purpose is twofold:
  //  1) Cluster together the operands sharing the same symbolic-value.
  //  2) Operand having smaller symbolic-value-rank is permuted earlier, which
  //     could potentially shorten crital path, and expose more loop-invariants.
  //     Note that values' rank are basically defined in RPO order (FIXME).
  //     So, if Rank(X) < Rank(Y) < Rank(Z), it means X is defined earlier
  //     than Y which is defined earlier than Z. Permute "x | 1", "Y & 2",
  //     "z" in the order of X-Y-Z is better than any other orders.
  std::stable_sort(OpndPtrs.begin(), OpndPtrs.end(),
                   [](XorOpnd *LHS, XorOpnd *RHS) {
    return LHS->getSymbolicRank() < RHS->getSymbolicRank();
  });

  // Step 3: Combine adjacent operands
  XorOpnd *PrevOpnd = nullptr;
  bool Changed = false;
  for (unsigned i = 0, e = Opnds.size(); i < e; i++) {
    XorOpnd *CurrOpnd = OpndPtrs[i];
    // The combined value
    Value *CV;

    // Step 3.1: Try simplifying "CurrOpnd ^ ConstOpnd"
    if (!ConstOpnd.isNullValue() &&
        CombineXorOpnd(I, CurrOpnd, ConstOpnd, CV)) {
      Changed = true;
      if (CV)
        *CurrOpnd = XorOpnd(CV);
      else {
        CurrOpnd->Invalidate();
        continue;
      }
    }

    if (!PrevOpnd || CurrOpnd->getSymbolicPart() != PrevOpnd->getSymbolicPart()) {
      PrevOpnd = CurrOpnd;
      continue;
    }

    // step 3.2: When previous and current operands share the same symbolic
    //  value, try to simplify "PrevOpnd ^ CurrOpnd ^ ConstOpnd"
    if (CombineXorOpnd(I, CurrOpnd, PrevOpnd, ConstOpnd, CV)) {
      // Remove previous operand
      PrevOpnd->Invalidate();
      if (CV) {
        *CurrOpnd = XorOpnd(CV);
        PrevOpnd = CurrOpnd;
      } else {
        CurrOpnd->Invalidate();
        PrevOpnd = nullptr;
      }
      Changed = true;
    }
  }

  // Step 4: Reassemble the Ops
  if (Changed) {
    Ops.clear();
    for (unsigned int i = 0, e = Opnds.size(); i < e; i++) {
      XorOpnd &O = Opnds[i];
      if (O.isInvalid())
        continue;
      ValueEntry VE(getRank(O.getValue()), O.getValue());
      Ops.push_back(VE);
    }
    if (!ConstOpnd.isNullValue()) {
      Value *C = ConstantInt::get(Ty, ConstOpnd);
      ValueEntry VE(getRank(C), C);
      Ops.push_back(VE);
    }
    unsigned Sz = Ops.size();
    if (Sz == 1)
      return Ops.back().Op;
    if (Sz == 0) {
      assert(ConstOpnd.isNullValue());
      return ConstantInt::get(Ty, ConstOpnd);
    }
  }

  return nullptr;
}

/// Optimize a series of operands to an 'add' instruction.  This
/// optimizes based on identities.  If it can be reduced to a single Value, it
/// is returned, otherwise the Ops list is mutated as necessary.
Value *ReassociatePass::OptimizeAdd(Instruction *I,
                                    SmallVectorImpl<ValueEntry> &Ops) {
  // Scan the operand lists looking for X and -X pairs.  If we find any, we
  // can simplify expressions like X+-X == 0 and X+~X ==-1.  While we're at it,
  // scan for any
  // duplicates.  We want to canonicalize Y+Y+Y+Z -> 3*Y+Z.

  for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
    Value *TheOp = Ops[i].Op;
    // Check to see if we've seen this operand before.  If so, we factor all
    // instances of the operand together.  Due to our sorting criteria, we know
    // that these need to be next to each other in the vector.
    if (i+1 != Ops.size() && Ops[i+1].Op == TheOp) {
      // Rescan the list, remove all instances of this operand from the expr.
      unsigned NumFound = 0;
      do {
        Ops.erase(Ops.begin()+i);
        ++NumFound;
      } while (i != Ops.size() && Ops[i].Op == TheOp);

      LLVM_DEBUG(dbgs() << "\nFACTORING [" << NumFound << "]: " << *TheOp
                        << '\n');
      ++NumFactor;

      // Insert a new multiply.
      Type *Ty = TheOp->getType();
      Constant *C = Ty->isIntOrIntVectorTy() ?
        ConstantInt::get(Ty, NumFound) : ConstantFP::get(Ty, NumFound);
      Instruction *Mul = CreateMul(TheOp, C, "factor", I, I);

      // Now that we have inserted a multiply, optimize it. This allows us to
      // handle cases that require multiple factoring steps, such as this:
      // (X*2) + (X*2) + (X*2) -> (X*2)*3 -> X*6
      RedoInsts.insert(Mul);

      // If every add operand was a duplicate, return the multiply.
      if (Ops.empty())
        return Mul;

      // Otherwise, we had some input that didn't have the dupe, such as
      // "A + A + B" -> "A*2 + B".  Add the new multiply to the list of
      // things being added by this operation.
      Ops.insert(Ops.begin(), ValueEntry(getRank(Mul), Mul));

      --i;
      e = Ops.size();
      continue;
    }

    // Check for X and -X or X and ~X in the operand list.
    Value *X;
    if (!match(TheOp, m_Neg(m_Value(X))) && !match(TheOp, m_Not(m_Value(X))) &&
        !match(TheOp, m_FNeg(m_Value(X))))
      continue;

    unsigned FoundX = FindInOperandList(Ops, i, X);
    if (FoundX == i)
      continue;

    // Remove X and -X from the operand list.
    if (Ops.size() == 2 &&
        (match(TheOp, m_Neg(m_Value())) || match(TheOp, m_FNeg(m_Value()))))
      return Constant::getNullValue(X->getType());

    // Remove X and ~X from the operand list.
    if (Ops.size() == 2 && match(TheOp, m_Not(m_Value())))
      return Constant::getAllOnesValue(X->getType());

    Ops.erase(Ops.begin()+i);
    if (i < FoundX)
      --FoundX;
    else
      --i;   // Need to back up an extra one.
    Ops.erase(Ops.begin()+FoundX);
    ++NumAnnihil;
    --i;     // Revisit element.
    e -= 2;  // Removed two elements.

    // if X and ~X we append -1 to the operand list.
    if (match(TheOp, m_Not(m_Value()))) {
      Value *V = Constant::getAllOnesValue(X->getType());
      Ops.insert(Ops.end(), ValueEntry(getRank(V), V));
      e += 1;
    }
  }

  // Scan the operand list, checking to see if there are any common factors
  // between operands.  Consider something like A*A+A*B*C+D.  We would like to
  // reassociate this to A*(A+B*C)+D, which reduces the number of multiplies.
  // To efficiently find this, we count the number of times a factor occurs
  // for any ADD operands that are MULs.
  DenseMap<Value*, unsigned> FactorOccurrences;

  // Keep track of each multiply we see, to avoid triggering on (X*4)+(X*4)
  // where they are actually the same multiply.
  unsigned MaxOcc = 0;
  Value *MaxOccVal = nullptr;
  for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
    BinaryOperator *BOp =
        isReassociableOp(Ops[i].Op, Instruction::Mul, Instruction::FMul);
    if (!BOp)
      continue;

    // Compute all of the factors of this added value.
    SmallVector<Value*, 8> Factors;
    FindSingleUseMultiplyFactors(BOp, Factors);
    assert(Factors.size() > 1 && "Bad linearize!");

    // Add one to FactorOccurrences for each unique factor in this op.
    SmallPtrSet<Value*, 8> Duplicates;
    for (unsigned i = 0, e = Factors.size(); i != e; ++i) {
      Value *Factor = Factors[i];
      if (!Duplicates.insert(Factor).second)
        continue;

      unsigned Occ = ++FactorOccurrences[Factor];
      if (Occ > MaxOcc) {
        MaxOcc = Occ;
        MaxOccVal = Factor;
      }

      // If Factor is a negative constant, add the negated value as a factor
      // because we can percolate the negate out.  Watch for minint, which
      // cannot be positivified.
      if (ConstantInt *CI = dyn_cast<ConstantInt>(Factor)) {
        if (CI->isNegative() && !CI->isMinValue(true)) {
          Factor = ConstantInt::get(CI->getContext(), -CI->getValue());
          if (!Duplicates.insert(Factor).second)
            continue;
          unsigned Occ = ++FactorOccurrences[Factor];
          if (Occ > MaxOcc) {
            MaxOcc = Occ;
            MaxOccVal = Factor;
          }
        }
      } else if (ConstantFP *CF = dyn_cast<ConstantFP>(Factor)) {
        if (CF->isNegative()) {
          APFloat F(CF->getValueAPF());
          F.changeSign();
          Factor = ConstantFP::get(CF->getContext(), F);
          if (!Duplicates.insert(Factor).second)
            continue;
          unsigned Occ = ++FactorOccurrences[Factor];
          if (Occ > MaxOcc) {
            MaxOcc = Occ;
            MaxOccVal = Factor;
          }
        }
      }
    }
  }

  // If any factor occurred more than one time, we can pull it out.
  if (MaxOcc > 1) {
    LLVM_DEBUG(dbgs() << "\nFACTORING [" << MaxOcc << "]: " << *MaxOccVal
                      << '\n');
    ++NumFactor;

    // Create a new instruction that uses the MaxOccVal twice.  If we don't do
    // this, we could otherwise run into situations where removing a factor
    // from an expression will drop a use of maxocc, and this can cause
    // RemoveFactorFromExpression on successive values to behave differently.
    Instruction *DummyInst =
        I->getType()->isIntOrIntVectorTy()
            ? BinaryOperator::CreateAdd(MaxOccVal, MaxOccVal)
            : BinaryOperator::CreateFAdd(MaxOccVal, MaxOccVal);

    SmallVector<WeakTrackingVH, 4> NewMulOps;
    for (unsigned i = 0; i != Ops.size(); ++i) {
      // Only try to remove factors from expressions we're allowed to.
      BinaryOperator *BOp =
          isReassociableOp(Ops[i].Op, Instruction::Mul, Instruction::FMul);
      if (!BOp)
        continue;

      if (Value *V = RemoveFactorFromExpression(Ops[i].Op, MaxOccVal)) {
        // The factorized operand may occur several times.  Convert them all in
        // one fell swoop.
        for (unsigned j = Ops.size(); j != i;) {
          --j;
          if (Ops[j].Op == Ops[i].Op) {
            NewMulOps.push_back(V);
            Ops.erase(Ops.begin()+j);
          }
        }
        --i;
      }
    }

    // No need for extra uses anymore.
    DummyInst->deleteValue();

    unsigned NumAddedValues = NewMulOps.size();
    Value *V = EmitAddTreeOfValues(I, NewMulOps);

    // Now that we have inserted the add tree, optimize it. This allows us to
    // handle cases that require multiple factoring steps, such as this:
    // A*A*B + A*A*C   -->   A*(A*B+A*C)   -->   A*(A*(B+C))
    assert(NumAddedValues > 1 && "Each occurrence should contribute a value");
    (void)NumAddedValues;
    if (Instruction *VI = dyn_cast<Instruction>(V))
      RedoInsts.insert(VI);

    // Create the multiply.
    Instruction *V2 = CreateMul(V, MaxOccVal, "reass.mul", I, I);

    // Rerun associate on the multiply in case the inner expression turned into
    // a multiply.  We want to make sure that we keep things in canonical form.
    RedoInsts.insert(V2);

    // If every add operand included the factor (e.g. "A*B + A*C"), then the
    // entire result expression is just the multiply "A*(B+C)".
    if (Ops.empty())
      return V2;

    // Otherwise, we had some input that didn't have the factor, such as
    // "A*B + A*C + D" -> "A*(B+C) + D".  Add the new multiply to the list of
    // things being added by this operation.
    Ops.insert(Ops.begin(), ValueEntry(getRank(V2), V2));
  }

  return nullptr;
}

/// Build up a vector of value/power pairs factoring a product.
///
/// Given a series of multiplication operands, build a vector of factors and
/// the powers each is raised to when forming the final product. Sort them in
/// the order of descending power.
///
///      (x*x)          -> [(x, 2)]
///     ((x*x)*x)       -> [(x, 3)]
///   ((((x*y)*x)*y)*x) -> [(x, 3), (y, 2)]
///
/// \returns Whether any factors have a power greater than one.
static bool collectMultiplyFactors(SmallVectorImpl<ValueEntry> &Ops,
                                   SmallVectorImpl<Factor> &Factors) {
  // FIXME: Have Ops be (ValueEntry, Multiplicity) pairs, simplifying this.
  // Compute the sum of powers of simplifiable factors.
  unsigned FactorPowerSum = 0;
  for (unsigned Idx = 1, Size = Ops.size(); Idx < Size; ++Idx) {
    Value *Op = Ops[Idx-1].Op;

    // Count the number of occurrences of this value.
    unsigned Count = 1;
    for (; Idx < Size && Ops[Idx].Op == Op; ++Idx)
      ++Count;
    // Track for simplification all factors which occur 2 or more times.
    if (Count > 1)
      FactorPowerSum += Count;
  }

  // We can only simplify factors if the sum of the powers of our simplifiable
  // factors is 4 or higher. When that is the case, we will *always* have
  // a simplification. This is an important invariant to prevent cyclicly
  // trying to simplify already minimal formations.
  if (FactorPowerSum < 4)
    return false;

  // Now gather the simplifiable factors, removing them from Ops.
  FactorPowerSum = 0;
  for (unsigned Idx = 1; Idx < Ops.size(); ++Idx) {
    Value *Op = Ops[Idx-1].Op;

    // Count the number of occurrences of this value.
    unsigned Count = 1;
    for (; Idx < Ops.size() && Ops[Idx].Op == Op; ++Idx)
      ++Count;
    if (Count == 1)
      continue;
    // Move an even number of occurrences to Factors.
    Count &= ~1U;
    Idx -= Count;
    FactorPowerSum += Count;
    Factors.push_back(Factor(Op, Count));
    Ops.erase(Ops.begin()+Idx, Ops.begin()+Idx+Count);
  }

  // None of the adjustments above should have reduced the sum of factor powers
  // below our mininum of '4'.
  assert(FactorPowerSum >= 4);

  std::stable_sort(Factors.begin(), Factors.end(),
                   [](const Factor &LHS, const Factor &RHS) {
    return LHS.Power > RHS.Power;
  });
  return true;
}

/// Build a tree of multiplies, computing the product of Ops.
static Value *buildMultiplyTree(IRBuilder<> &Builder,
                                SmallVectorImpl<Value*> &Ops) {
  if (Ops.size() == 1)
    return Ops.back();

  Value *LHS = Ops.pop_back_val();
  do {
    if (LHS->getType()->isIntOrIntVectorTy())
      LHS = Builder.CreateMul(LHS, Ops.pop_back_val());
    else
      LHS = Builder.CreateFMul(LHS, Ops.pop_back_val());
  } while (!Ops.empty());

  return LHS;
}

/// Build a minimal multiplication DAG for (a^x)*(b^y)*(c^z)*...
///
/// Given a vector of values raised to various powers, where no two values are
/// equal and the powers are sorted in decreasing order, compute the minimal
/// DAG of multiplies to compute the final product, and return that product
/// value.
Value *
ReassociatePass::buildMinimalMultiplyDAG(IRBuilder<> &Builder,
                                         SmallVectorImpl<Factor> &Factors) {
  assert(Factors[0].Power);
  SmallVector<Value *, 4> OuterProduct;
  for (unsigned LastIdx = 0, Idx = 1, Size = Factors.size();
       Idx < Size && Factors[Idx].Power > 0; ++Idx) {
    if (Factors[Idx].Power != Factors[LastIdx].Power) {
      LastIdx = Idx;
      continue;
    }

    // We want to multiply across all the factors with the same power so that
    // we can raise them to that power as a single entity. Build a mini tree
    // for that.
    SmallVector<Value *, 4> InnerProduct;
    InnerProduct.push_back(Factors[LastIdx].Base);
    do {
      InnerProduct.push_back(Factors[Idx].Base);
      ++Idx;
    } while (Idx < Size && Factors[Idx].Power == Factors[LastIdx].Power);

    // Reset the base value of the first factor to the new expression tree.
    // We'll remove all the factors with the same power in a second pass.
    Value *M = Factors[LastIdx].Base = buildMultiplyTree(Builder, InnerProduct);
    if (Instruction *MI = dyn_cast<Instruction>(M))
      RedoInsts.insert(MI);

    LastIdx = Idx;
  }
  // Unique factors with equal powers -- we've folded them into the first one's
  // base.
  Factors.erase(std::unique(Factors.begin(), Factors.end(),
                            [](const Factor &LHS, const Factor &RHS) {
                              return LHS.Power == RHS.Power;
                            }),
                Factors.end());

  // Iteratively collect the base of each factor with an add power into the
  // outer product, and halve each power in preparation for squaring the
  // expression.
  for (unsigned Idx = 0, Size = Factors.size(); Idx != Size; ++Idx) {
    if (Factors[Idx].Power & 1)
      OuterProduct.push_back(Factors[Idx].Base);
    Factors[Idx].Power >>= 1;
  }
  if (Factors[0].Power) {
    Value *SquareRoot = buildMinimalMultiplyDAG(Builder, Factors);
    OuterProduct.push_back(SquareRoot);
    OuterProduct.push_back(SquareRoot);
  }
  if (OuterProduct.size() == 1)
    return OuterProduct.front();

  Value *V = buildMultiplyTree(Builder, OuterProduct);
  return V;
}

Value *ReassociatePass::OptimizeMul(BinaryOperator *I,
                                    SmallVectorImpl<ValueEntry> &Ops) {
  // We can only optimize the multiplies when there is a chain of more than
  // three, such that a balanced tree might require fewer total multiplies.
  if (Ops.size() < 4)
    return nullptr;

  // Try to turn linear trees of multiplies without other uses of the
  // intermediate stages into minimal multiply DAGs with perfect sub-expression
  // re-use.
  SmallVector<Factor, 4> Factors;
  if (!collectMultiplyFactors(Ops, Factors))
    return nullptr; // All distinct factors, so nothing left for us to do.

  IRBuilder<> Builder(I);
  // The reassociate transformation for FP operations is performed only
  // if unsafe algebra is permitted by FastMathFlags. Propagate those flags
  // to the newly generated operations.
  if (auto FPI = dyn_cast<FPMathOperator>(I))
    Builder.setFastMathFlags(FPI->getFastMathFlags());

  Value *V = buildMinimalMultiplyDAG(Builder, Factors);
  if (Ops.empty())
    return V;

  ValueEntry NewEntry = ValueEntry(getRank(V), V);
  Ops.insert(std::lower_bound(Ops.begin(), Ops.end(), NewEntry), NewEntry);
  return nullptr;
}

Value *ReassociatePass::OptimizeExpression(BinaryOperator *I,
                                           SmallVectorImpl<ValueEntry> &Ops) {
  // Now that we have the linearized expression tree, try to optimize it.
  // Start by folding any constants that we found.
  Constant *Cst = nullptr;
  unsigned Opcode = I->getOpcode();
  while (!Ops.empty() && isa<Constant>(Ops.back().Op)) {
    Constant *C = cast<Constant>(Ops.pop_back_val().Op);
    Cst = Cst ? ConstantExpr::get(Opcode, C, Cst) : C;
  }
  // If there was nothing but constants then we are done.
  if (Ops.empty())
    return Cst;

  // Put the combined constant back at the end of the operand list, except if
  // there is no point.  For example, an add of 0 gets dropped here, while a
  // multiplication by zero turns the whole expression into zero.
  if (Cst && Cst != ConstantExpr::getBinOpIdentity(Opcode, I->getType())) {
    if (Cst == ConstantExpr::getBinOpAbsorber(Opcode, I->getType()))
      return Cst;
    Ops.push_back(ValueEntry(0, Cst));
  }

  if (Ops.size() == 1) return Ops[0].Op;

  // Handle destructive annihilation due to identities between elements in the
  // argument list here.
  unsigned NumOps = Ops.size();
  switch (Opcode) {
  default: break;
  case Instruction::And:
  case Instruction::Or:
    if (Value *Result = OptimizeAndOrXor(Opcode, Ops))
      return Result;
    break;

  case Instruction::Xor:
    if (Value *Result = OptimizeXor(I, Ops))
      return Result;
    break;

  case Instruction::Add:
  case Instruction::FAdd:
    if (Value *Result = OptimizeAdd(I, Ops))
      return Result;
    break;

  case Instruction::Mul:
  case Instruction::FMul:
    if (Value *Result = OptimizeMul(I, Ops))
      return Result;
    break;
  }

  if (Ops.size() != NumOps)
    return OptimizeExpression(I, Ops);
  return nullptr;
}

// Remove dead instructions and if any operands are trivially dead add them to
// Insts so they will be removed as well.
void ReassociatePass::RecursivelyEraseDeadInsts(Instruction *I,
                                                OrderedSet &Insts) {
  assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!");
  SmallVector<Value *, 4> Ops(I->op_begin(), I->op_end());
  ValueRankMap.erase(I);
  Insts.remove(I);
  RedoInsts.remove(I);
  I->eraseFromParent();
  for (auto Op : Ops)
    if (Instruction *OpInst = dyn_cast<Instruction>(Op))
      if (OpInst->use_empty())
        Insts.insert(OpInst);
}

/// Zap the given instruction, adding interesting operands to the work list.
void ReassociatePass::EraseInst(Instruction *I) {
  assert(isInstructionTriviallyDead(I) && "Trivially dead instructions only!");
  LLVM_DEBUG(dbgs() << "Erasing dead inst: "; I->dump());

  SmallVector<Value*, 8> Ops(I->op_begin(), I->op_end());
  // Erase the dead instruction.
  ValueRankMap.erase(I);
  RedoInsts.remove(I);
  I->eraseFromParent();
  // Optimize its operands.
  SmallPtrSet<Instruction *, 8> Visited; // Detect self-referential nodes.
  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
    if (Instruction *Op = dyn_cast<Instruction>(Ops[i])) {
      // If this is a node in an expression tree, climb to the expression root
      // and add that since that's where optimization actually happens.
      unsigned Opcode = Op->getOpcode();
      while (Op->hasOneUse() && Op->user_back()->getOpcode() == Opcode &&
             Visited.insert(Op).second)
        Op = Op->user_back();

      // The instruction we're going to push may be coming from a
      // dead block, and Reassociate skips the processing of unreachable
      // blocks because it's a waste of time and also because it can
      // lead to infinite loop due to LLVM's non-standard definition
      // of dominance.
      if (ValueRankMap.find(Op) != ValueRankMap.end())
        RedoInsts.insert(Op);
    }

  MadeChange = true;
}

// Canonicalize expressions of the following form:
//  x + (-Constant * y) -> x - (Constant * y)
//  x - (-Constant * y) -> x + (Constant * y)
Instruction *ReassociatePass::canonicalizeNegConstExpr(Instruction *I) {
  if (!I->hasOneUse() || I->getType()->isVectorTy())
    return nullptr;

  // Must be a fmul or fdiv instruction.
  unsigned Opcode = I->getOpcode();
  if (Opcode != Instruction::FMul && Opcode != Instruction::FDiv)
    return nullptr;

  auto *C0 = dyn_cast<ConstantFP>(I->getOperand(0));
  auto *C1 = dyn_cast<ConstantFP>(I->getOperand(1));

  // Both operands are constant, let it get constant folded away.
  if (C0 && C1)
    return nullptr;

  ConstantFP *CF = C0 ? C0 : C1;

  // Must have one constant operand.
  if (!CF)
    return nullptr;

  // Must be a negative ConstantFP.
  if (!CF->isNegative())
    return nullptr;

  // User must be a binary operator with one or more uses.
  Instruction *User = I->user_back();
  if (!isa<BinaryOperator>(User) || User->use_empty())
    return nullptr;

  unsigned UserOpcode = User->getOpcode();
  if (UserOpcode != Instruction::FAdd && UserOpcode != Instruction::FSub)
    return nullptr;

  // Subtraction is not commutative. Explicitly, the following transform is
  // not valid: (-Constant * y) - x  -> x + (Constant * y)
  if (!User->isCommutative() && User->getOperand(1) != I)
    return nullptr;

  // Don't canonicalize x + (-Constant * y) -> x - (Constant * y), if the
  // resulting subtract will be broken up later.  This can get us into an
  // infinite loop during reassociation.
  if (UserOpcode == Instruction::FAdd && ShouldBreakUpSubtract(User))
    return nullptr;

  // Change the sign of the constant.
  APFloat Val = CF->getValueAPF();
  Val.changeSign();
  I->setOperand(C0 ? 0 : 1, ConstantFP::get(CF->getContext(), Val));

  // Canonicalize I to RHS to simplify the next bit of logic. E.g.,
  // ((-Const*y) + x) -> (x + (-Const*y)).
  if (User->getOperand(0) == I && User->isCommutative())
    cast<BinaryOperator>(User)->swapOperands();

  Value *Op0 = User->getOperand(0);
  Value *Op1 = User->getOperand(1);
  BinaryOperator *NI;
  switch (UserOpcode) {
  default:
    llvm_unreachable("Unexpected Opcode!");
  case Instruction::FAdd:
    NI = BinaryOperator::CreateFSub(Op0, Op1);
    NI->setFastMathFlags(cast<FPMathOperator>(User)->getFastMathFlags());
    break;
  case Instruction::FSub:
    NI = BinaryOperator::CreateFAdd(Op0, Op1);
    NI->setFastMathFlags(cast<FPMathOperator>(User)->getFastMathFlags());
    break;
  }

  NI->insertBefore(User);
  NI->setName(User->getName());
  User->replaceAllUsesWith(NI);
  NI->setDebugLoc(I->getDebugLoc());
  RedoInsts.insert(I);
  MadeChange = true;
  return NI;
}

/// Inspect and optimize the given instruction. Note that erasing
/// instructions is not allowed.
void ReassociatePass::OptimizeInst(Instruction *I) {
  // Only consider operations that we understand.
  if (!isa<BinaryOperator>(I))
    return;

  if (I->getOpcode() == Instruction::Shl && isa<ConstantInt>(I->getOperand(1)))
    // If an operand of this shift is a reassociable multiply, or if the shift
    // is used by a reassociable multiply or add, turn into a multiply.
    if (isReassociableOp(I->getOperand(0), Instruction::Mul) ||
        (I->hasOneUse() &&
         (isReassociableOp(I->user_back(), Instruction::Mul) ||
          isReassociableOp(I->user_back(), Instruction::Add)))) {
      Instruction *NI = ConvertShiftToMul(I);
      RedoInsts.insert(I);
      MadeChange = true;
      I = NI;
    }

  // Canonicalize negative constants out of expressions.
  if (Instruction *Res = canonicalizeNegConstExpr(I))
    I = Res;

  // Commute binary operators, to canonicalize the order of their operands.
  // This can potentially expose more CSE opportunities, and makes writing other
  // transformations simpler.
  if (I->isCommutative())
    canonicalizeOperands(I);

  // Don't optimize floating-point instructions unless they are 'fast'.
  if (I->getType()->isFPOrFPVectorTy() && !I->isFast())
    return;

  // Do not reassociate boolean (i1) expressions.  We want to preserve the
  // original order of evaluation for short-circuited comparisons that
  // SimplifyCFG has folded to AND/OR expressions.  If the expression
  // is not further optimized, it is likely to be transformed back to a
  // short-circuited form for code gen, and the source order may have been
  // optimized for the most likely conditions.
  if (I->getType()->isIntegerTy(1))
    return;

  // If this is a subtract instruction which is not already in negate form,
  // see if we can convert it to X+-Y.
  if (I->getOpcode() == Instruction::Sub) {
    if (ShouldBreakUpSubtract(I)) {
      Instruction *NI = BreakUpSubtract(I, RedoInsts);
      RedoInsts.insert(I);
      MadeChange = true;
      I = NI;
    } else if (match(I, m_Neg(m_Value()))) {
      // Otherwise, this is a negation.  See if the operand is a multiply tree
      // and if this is not an inner node of a multiply tree.
      if (isReassociableOp(I->getOperand(1), Instruction::Mul) &&
          (!I->hasOneUse() ||
           !isReassociableOp(I->user_back(), Instruction::Mul))) {
        Instruction *NI = LowerNegateToMultiply(I);
        // If the negate was simplified, revisit the users to see if we can
        // reassociate further.
        for (User *U : NI->users()) {
          if (BinaryOperator *Tmp = dyn_cast<BinaryOperator>(U))
            RedoInsts.insert(Tmp);
        }
        RedoInsts.insert(I);
        MadeChange = true;
        I = NI;
      }
    }
  } else if (I->getOpcode() == Instruction::FSub) {
    if (ShouldBreakUpSubtract(I)) {
      Instruction *NI = BreakUpSubtract(I, RedoInsts);
      RedoInsts.insert(I);
      MadeChange = true;
      I = NI;
    } else if (match(I, m_FNeg(m_Value()))) {
      // Otherwise, this is a negation.  See if the operand is a multiply tree
      // and if this is not an inner node of a multiply tree.
      if (isReassociableOp(I->getOperand(1), Instruction::FMul) &&
          (!I->hasOneUse() ||
           !isReassociableOp(I->user_back(), Instruction::FMul))) {
        // If the negate was simplified, revisit the users to see if we can
        // reassociate further.
        Instruction *NI = LowerNegateToMultiply(I);
        for (User *U : NI->users()) {
          if (BinaryOperator *Tmp = dyn_cast<BinaryOperator>(U))
            RedoInsts.insert(Tmp);
        }
        RedoInsts.insert(I);
        MadeChange = true;
        I = NI;
      }
    }
  }

  // If this instruction is an associative binary operator, process it.
  if (!I->isAssociative()) return;
  BinaryOperator *BO = cast<BinaryOperator>(I);

  // If this is an interior node of a reassociable tree, ignore it until we
  // get to the root of the tree, to avoid N^2 analysis.
  unsigned Opcode = BO->getOpcode();
  if (BO->hasOneUse() && BO->user_back()->getOpcode() == Opcode) {
    // During the initial run we will get to the root of the tree.
    // But if we get here while we are redoing instructions, there is no
    // guarantee that the root will be visited. So Redo later
    if (BO->user_back() != BO &&
        BO->getParent() == BO->user_back()->getParent())
      RedoInsts.insert(BO->user_back());
    return;
  }

  // If this is an add tree that is used by a sub instruction, ignore it
  // until we process the subtract.
  if (BO->hasOneUse() && BO->getOpcode() == Instruction::Add &&
      cast<Instruction>(BO->user_back())->getOpcode() == Instruction::Sub)
    return;
  if (BO->hasOneUse() && BO->getOpcode() == Instruction::FAdd &&
      cast<Instruction>(BO->user_back())->getOpcode() == Instruction::FSub)
    return;

  ReassociateExpression(BO);
}

void ReassociatePass::ReassociateExpression(BinaryOperator *I) {
  // First, walk the expression tree, linearizing the tree, collecting the
  // operand information.
  SmallVector<RepeatedValue, 8> Tree;
  MadeChange |= LinearizeExprTree(I, Tree);
  SmallVector<ValueEntry, 8> Ops;
  Ops.reserve(Tree.size());
  for (unsigned i = 0, e = Tree.size(); i != e; ++i) {
    RepeatedValue E = Tree[i];
    Ops.append(E.second.getZExtValue(),
               ValueEntry(getRank(E.first), E.first));
  }

  LLVM_DEBUG(dbgs() << "RAIn:\t"; PrintOps(I, Ops); dbgs() << '\n');

  // Now that we have linearized the tree to a list and have gathered all of
  // the operands and their ranks, sort the operands by their rank.  Use a
  // stable_sort so that values with equal ranks will have their relative
  // positions maintained (and so the compiler is deterministic).  Note that
  // this sorts so that the highest ranking values end up at the beginning of
  // the vector.
  std::stable_sort(Ops.begin(), Ops.end());

  // Now that we have the expression tree in a convenient
  // sorted form, optimize it globally if possible.
  if (Value *V = OptimizeExpression(I, Ops)) {
    if (V == I)
      // Self-referential expression in unreachable code.
      return;
    // This expression tree simplified to something that isn't a tree,
    // eliminate it.
    LLVM_DEBUG(dbgs() << "Reassoc to scalar: " << *V << '\n');
    I->replaceAllUsesWith(V);
    if (Instruction *VI = dyn_cast<Instruction>(V))
      if (I->getDebugLoc())
        VI->setDebugLoc(I->getDebugLoc());
    RedoInsts.insert(I);
    ++NumAnnihil;
    return;
  }

  // We want to sink immediates as deeply as possible except in the case where
  // this is a multiply tree used only by an add, and the immediate is a -1.
  // In this case we reassociate to put the negation on the outside so that we
  // can fold the negation into the add: (-X)*Y + Z -> Z-X*Y
  if (I->hasOneUse()) {
    if (I->getOpcode() == Instruction::Mul &&
        cast<Instruction>(I->user_back())->getOpcode() == Instruction::Add &&
        isa<ConstantInt>(Ops.back().Op) &&
        cast<ConstantInt>(Ops.back().Op)->isMinusOne()) {
      ValueEntry Tmp = Ops.pop_back_val();
      Ops.insert(Ops.begin(), Tmp);
    } else if (I->getOpcode() == Instruction::FMul &&
               cast<Instruction>(I->user_back())->getOpcode() ==
                   Instruction::FAdd &&
               isa<ConstantFP>(Ops.back().Op) &&
               cast<ConstantFP>(Ops.back().Op)->isExactlyValue(-1.0)) {
      ValueEntry Tmp = Ops.pop_back_val();
      Ops.insert(Ops.begin(), Tmp);
    }
  }

  LLVM_DEBUG(dbgs() << "RAOut:\t"; PrintOps(I, Ops); dbgs() << '\n');

  if (Ops.size() == 1) {
    if (Ops[0].Op == I)
      // Self-referential expression in unreachable code.
      return;

    // This expression tree simplified to something that isn't a tree,
    // eliminate it.
    I->replaceAllUsesWith(Ops[0].Op);
    if (Instruction *OI = dyn_cast<Instruction>(Ops[0].Op))
      OI->setDebugLoc(I->getDebugLoc());
    RedoInsts.insert(I);
    return;
  }

  if (Ops.size() > 2 && Ops.size() <= GlobalReassociateLimit) {
    // Find the pair with the highest count in the pairmap and move it to the
    // back of the list so that it can later be CSE'd.
    // example:
    //   a*b*c*d*e
    // if c*e is the most "popular" pair, we can express this as
    //   (((c*e)*d)*b)*a
    unsigned Max = 1;
    unsigned BestRank = 0;
    std::pair<unsigned, unsigned> BestPair;
    unsigned Idx = I->getOpcode() - Instruction::BinaryOpsBegin;
    for (unsigned i = 0; i < Ops.size() - 1; ++i)
      for (unsigned j = i + 1; j < Ops.size(); ++j) {
        unsigned Score = 0;
        Value *Op0 = Ops[i].Op;
        Value *Op1 = Ops[j].Op;
        if (std::less<Value *>()(Op1, Op0))
          std::swap(Op0, Op1);
        auto it = PairMap[Idx].find({Op0, Op1});
        if (it != PairMap[Idx].end()) {
          // Functions like BreakUpSubtract() can erase the Values we're using
          // as keys and create new Values after we built the PairMap. There's a
          // small chance that the new nodes can have the same address as
          // something already in the table. We shouldn't accumulate the stored
          // score in that case as it refers to the wrong Value.
          if (it->second.isValid())
            Score += it->second.Score;
        }

        unsigned MaxRank = std::max(Ops[i].Rank, Ops[j].Rank);
        if (Score > Max || (Score == Max && MaxRank < BestRank)) {
          BestPair = {i, j};
          Max = Score;
          BestRank = MaxRank;
        }
      }
    if (Max > 1) {
      auto Op0 = Ops[BestPair.first];
      auto Op1 = Ops[BestPair.second];
      Ops.erase(&Ops[BestPair.second]);
      Ops.erase(&Ops[BestPair.first]);
      Ops.push_back(Op0);
      Ops.push_back(Op1);
    }
  }
  // Now that we ordered and optimized the expressions, splat them back into
  // the expression tree, removing any unneeded nodes.
  RewriteExprTree(I, Ops);
}

void
ReassociatePass::BuildPairMap(ReversePostOrderTraversal<Function *> &RPOT) {
  // Make a "pairmap" of how often each operand pair occurs.
  for (BasicBlock *BI : RPOT) {
    for (Instruction &I : *BI) {
      if (!I.isAssociative())
        continue;

      // Ignore nodes that aren't at the root of trees.
      if (I.hasOneUse() && I.user_back()->getOpcode() == I.getOpcode())
        continue;

      // Collect all operands in a single reassociable expression.
      // Since Reassociate has already been run once, we can assume things
      // are already canonical according to Reassociation's regime.
      SmallVector<Value *, 8> Worklist = { I.getOperand(0), I.getOperand(1) };
      SmallVector<Value *, 8> Ops;
      while (!Worklist.empty() && Ops.size() <= GlobalReassociateLimit) {
        Value *Op = Worklist.pop_back_val();
        Instruction *OpI = dyn_cast<Instruction>(Op);
        if (!OpI || OpI->getOpcode() != I.getOpcode() || !OpI->hasOneUse()) {
          Ops.push_back(Op);
          continue;
        }
        // Be paranoid about self-referencing expressions in unreachable code.
        if (OpI->getOperand(0) != OpI)
          Worklist.push_back(OpI->getOperand(0));
        if (OpI->getOperand(1) != OpI)
          Worklist.push_back(OpI->getOperand(1));
      }
      // Skip extremely long expressions.
      if (Ops.size() > GlobalReassociateLimit)
        continue;

      // Add all pairwise combinations of operands to the pair map.
      unsigned BinaryIdx = I.getOpcode() - Instruction::BinaryOpsBegin;
      SmallSet<std::pair<Value *, Value*>, 32> Visited;
      for (unsigned i = 0; i < Ops.size() - 1; ++i) {
        for (unsigned j = i + 1; j < Ops.size(); ++j) {
          // Canonicalize operand orderings.
          Value *Op0 = Ops[i];
          Value *Op1 = Ops[j];
          if (std::less<Value *>()(Op1, Op0))
            std::swap(Op0, Op1);
          if (!Visited.insert({Op0, Op1}).second)
            continue;
          auto res = PairMap[BinaryIdx].insert({{Op0, Op1}, {Op0, Op1, 1}});
          if (!res.second) {
            // If either key value has been erased then we've got the same
            // address by coincidence. That can't happen here because nothing is
            // erasing values but it can happen by the time we're querying the
            // map.
            assert(res.first->second.isValid() && "WeakVH invalidated");
            ++res.first->second.Score;
          }
        }
      }
    }
  }
}

PreservedAnalyses ReassociatePass::run(Function &F, FunctionAnalysisManager &) {
  // Get the functions basic blocks in Reverse Post Order. This order is used by
  // BuildRankMap to pre calculate ranks correctly. It also excludes dead basic
  // blocks (it has been seen that the analysis in this pass could hang when
  // analysing dead basic blocks).
  ReversePostOrderTraversal<Function *> RPOT(&F);

  // Calculate the rank map for F.
  BuildRankMap(F, RPOT);

  // Build the pair map before running reassociate.
  // Technically this would be more accurate if we did it after one round
  // of reassociation, but in practice it doesn't seem to help much on
  // real-world code, so don't waste the compile time running reassociate
  // twice.
  // If a user wants, they could expicitly run reassociate twice in their
  // pass pipeline for further potential gains.
  // It might also be possible to update the pair map during runtime, but the
  // overhead of that may be large if there's many reassociable chains.
  BuildPairMap(RPOT);

  MadeChange = false;

  // Traverse the same blocks that were analysed by BuildRankMap.
  for (BasicBlock *BI : RPOT) {
    assert(RankMap.count(&*BI) && "BB should be ranked.");
    // Optimize every instruction in the basic block.
    for (BasicBlock::iterator II = BI->begin(), IE = BI->end(); II != IE;)
      if (isInstructionTriviallyDead(&*II)) {
        EraseInst(&*II++);
      } else {
        OptimizeInst(&*II);
        assert(II->getParent() == &*BI && "Moved to a different block!");
        ++II;
      }

    // Make a copy of all the instructions to be redone so we can remove dead
    // instructions.
    OrderedSet ToRedo(RedoInsts);
    // Iterate over all instructions to be reevaluated and remove trivially dead
    // instructions. If any operand of the trivially dead instruction becomes
    // dead mark it for deletion as well. Continue this process until all
    // trivially dead instructions have been removed.
    while (!ToRedo.empty()) {
      Instruction *I = ToRedo.pop_back_val();
      if (isInstructionTriviallyDead(I)) {
        RecursivelyEraseDeadInsts(I, ToRedo);
        MadeChange = true;
      }
    }

    // Now that we have removed dead instructions, we can reoptimize the
    // remaining instructions.
    while (!RedoInsts.empty()) {
      Instruction *I = RedoInsts.front();
      RedoInsts.erase(RedoInsts.begin());
      if (isInstructionTriviallyDead(I))
        EraseInst(I);
      else
        OptimizeInst(I);
    }
  }

  // We are done with the rank map and pair map.
  RankMap.clear();
  ValueRankMap.clear();
  for (auto &Entry : PairMap)
    Entry.clear();

  if (MadeChange) {
    PreservedAnalyses PA;
    PA.preserveSet<CFGAnalyses>();
    PA.preserve<GlobalsAA>();
    return PA;
  }

  return PreservedAnalyses::all();
}

namespace {

  class ReassociateLegacyPass : public FunctionPass {
    ReassociatePass Impl;

  public:
    static char ID; // Pass identification, replacement for typeid

    ReassociateLegacyPass() : FunctionPass(ID) {
      initializeReassociateLegacyPassPass(*PassRegistry::getPassRegistry());
    }

    bool runOnFunction(Function &F) override {
      if (skipFunction(F))
        return false;

      FunctionAnalysisManager DummyFAM;
      auto PA = Impl.run(F, DummyFAM);
      return !PA.areAllPreserved();
    }

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

} // end anonymous namespace

char ReassociateLegacyPass::ID = 0;

INITIALIZE_PASS(ReassociateLegacyPass, "reassociate",
                "Reassociate expressions", false, false)

// Public interface to the Reassociate pass
FunctionPass *llvm::createReassociatePass() {
  return new ReassociateLegacyPass();
}