aboutsummaryrefslogtreecommitdiffstats
path: root/lib/Analysis/ValueTracking.cpp
blob: f329e3a5084b3b7aa968ae0cb5dbe45aade0a645 (plain)
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
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
//===- ValueTracking.cpp - Walk computations to compute properties --------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file contains routines that help analyze properties that chains of
// computations have.
//
//===----------------------------------------------------------------------===//

#include "llvm/Analysis/ValueTracking.h"
#include "llvm/ADT/SmallPtrSet.h"
#include "llvm/Analysis/AssumptionCache.h"
#include "llvm/Analysis/InstructionSimplify.h"
#include "llvm/Analysis/MemoryBuiltins.h"
#include "llvm/IR/CallSite.h"
#include "llvm/IR/ConstantRange.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/DataLayout.h"
#include "llvm/IR/Dominators.h"
#include "llvm/IR/GetElementPtrTypeIterator.h"
#include "llvm/IR/GlobalAlias.h"
#include "llvm/IR/GlobalVariable.h"
#include "llvm/IR/Instructions.h"
#include "llvm/IR/IntrinsicInst.h"
#include "llvm/IR/LLVMContext.h"
#include "llvm/IR/Metadata.h"
#include "llvm/IR/Operator.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/Support/Debug.h"
#include "llvm/Support/MathExtras.h"
#include <cstring>
using namespace llvm;
using namespace llvm::PatternMatch;

const unsigned MaxDepth = 6;

/// Enable an experimental feature to leverage information about dominating
/// conditions to compute known bits.  The individual options below control how
/// hard we search.  The defaults are choosen to be fairly aggressive.  If you
/// run into compile time problems when testing, scale them back and report
/// your findings.
static cl::opt<bool> EnableDomConditions("value-tracking-dom-conditions",
                                         cl::Hidden, cl::init(false));

// This is expensive, so we only do it for the top level query value.
// (TODO: evaluate cost vs profit, consider higher thresholds)
static cl::opt<unsigned> DomConditionsMaxDepth("dom-conditions-max-depth",
                                               cl::Hidden, cl::init(1));

/// How many dominating blocks should be scanned looking for dominating
/// conditions?
static cl::opt<unsigned> DomConditionsMaxDomBlocks("dom-conditions-dom-blocks",
                                                   cl::Hidden,
                                                   cl::init(20000));

// Controls the number of uses of the value searched for possible
// dominating comparisons.
static cl::opt<unsigned> DomConditionsMaxUses("dom-conditions-max-uses",
                                              cl::Hidden, cl::init(2000));

// If true, don't consider only compares whose only use is a branch.
static cl::opt<bool> DomConditionsSingleCmpUse("dom-conditions-single-cmp-use",
                                               cl::Hidden, cl::init(false));

/// Returns the bitwidth of the given scalar or pointer type (if unknown returns
/// 0). For vector types, returns the element type's bitwidth.
static unsigned getBitWidth(Type *Ty, const DataLayout &DL) {
  if (unsigned BitWidth = Ty->getScalarSizeInBits())
    return BitWidth;

  return DL.getPointerTypeSizeInBits(Ty);
}

// Many of these functions have internal versions that take an assumption
// exclusion set. This is because of the potential for mutual recursion to
// cause computeKnownBits to repeatedly visit the same assume intrinsic. The
// classic case of this is assume(x = y), which will attempt to determine
// bits in x from bits in y, which will attempt to determine bits in y from
// bits in x, etc. Regarding the mutual recursion, computeKnownBits can call
// isKnownNonZero, which calls computeKnownBits and ComputeSignBit and
// isKnownToBeAPowerOfTwo (all of which can call computeKnownBits), and so on.
typedef SmallPtrSet<const Value *, 8> ExclInvsSet;

namespace {
// Simplifying using an assume can only be done in a particular control-flow
// context (the context instruction provides that context). If an assume and
// the context instruction are not in the same block then the DT helps in
// figuring out if we can use it.
struct Query {
  ExclInvsSet ExclInvs;
  AssumptionCache *AC;
  const Instruction *CxtI;
  const DominatorTree *DT;

  Query(AssumptionCache *AC = nullptr, const Instruction *CxtI = nullptr,
        const DominatorTree *DT = nullptr)
      : AC(AC), CxtI(CxtI), DT(DT) {}

  Query(const Query &Q, const Value *NewExcl)
      : ExclInvs(Q.ExclInvs), AC(Q.AC), CxtI(Q.CxtI), DT(Q.DT) {
    ExclInvs.insert(NewExcl);
  }
};
} // end anonymous namespace

// Given the provided Value and, potentially, a context instruction, return
// the preferred context instruction (if any).
static const Instruction *safeCxtI(const Value *V, const Instruction *CxtI) {
  // If we've been provided with a context instruction, then use that (provided
  // it has been inserted).
  if (CxtI && CxtI->getParent())
    return CxtI;

  // If the value is really an already-inserted instruction, then use that.
  CxtI = dyn_cast<Instruction>(V);
  if (CxtI && CxtI->getParent())
    return CxtI;

  return nullptr;
}

static void computeKnownBits(Value *V, APInt &KnownZero, APInt &KnownOne,
                             const DataLayout &DL, unsigned Depth,
                             const Query &Q);

void llvm::computeKnownBits(Value *V, APInt &KnownZero, APInt &KnownOne,
                            const DataLayout &DL, unsigned Depth,
                            AssumptionCache *AC, const Instruction *CxtI,
                            const DominatorTree *DT) {
  ::computeKnownBits(V, KnownZero, KnownOne, DL, Depth,
                     Query(AC, safeCxtI(V, CxtI), DT));
}

static void ComputeSignBit(Value *V, bool &KnownZero, bool &KnownOne,
                           const DataLayout &DL, unsigned Depth,
                           const Query &Q);

void llvm::ComputeSignBit(Value *V, bool &KnownZero, bool &KnownOne,
                          const DataLayout &DL, unsigned Depth,
                          AssumptionCache *AC, const Instruction *CxtI,
                          const DominatorTree *DT) {
  ::ComputeSignBit(V, KnownZero, KnownOne, DL, Depth,
                   Query(AC, safeCxtI(V, CxtI), DT));
}

static bool isKnownToBeAPowerOfTwo(Value *V, bool OrZero, unsigned Depth,
                                   const Query &Q, const DataLayout &DL);

bool llvm::isKnownToBeAPowerOfTwo(Value *V, const DataLayout &DL, bool OrZero,
                                  unsigned Depth, AssumptionCache *AC,
                                  const Instruction *CxtI,
                                  const DominatorTree *DT) {
  return ::isKnownToBeAPowerOfTwo(V, OrZero, Depth,
                                  Query(AC, safeCxtI(V, CxtI), DT), DL);
}

static bool isKnownNonZero(Value *V, const DataLayout &DL, unsigned Depth,
                           const Query &Q);

bool llvm::isKnownNonZero(Value *V, const DataLayout &DL, unsigned Depth,
                          AssumptionCache *AC, const Instruction *CxtI,
                          const DominatorTree *DT) {
  return ::isKnownNonZero(V, DL, Depth, Query(AC, safeCxtI(V, CxtI), DT));
}

static bool MaskedValueIsZero(Value *V, const APInt &Mask, const DataLayout &DL,
                              unsigned Depth, const Query &Q);

bool llvm::MaskedValueIsZero(Value *V, const APInt &Mask, const DataLayout &DL,
                             unsigned Depth, AssumptionCache *AC,
                             const Instruction *CxtI, const DominatorTree *DT) {
  return ::MaskedValueIsZero(V, Mask, DL, Depth,
                             Query(AC, safeCxtI(V, CxtI), DT));
}

static unsigned ComputeNumSignBits(Value *V, const DataLayout &DL,
                                   unsigned Depth, const Query &Q);

unsigned llvm::ComputeNumSignBits(Value *V, const DataLayout &DL,
                                  unsigned Depth, AssumptionCache *AC,
                                  const Instruction *CxtI,
                                  const DominatorTree *DT) {
  return ::ComputeNumSignBits(V, DL, Depth, Query(AC, safeCxtI(V, CxtI), DT));
}

static void computeKnownBitsAddSub(bool Add, Value *Op0, Value *Op1, bool NSW,
                                   APInt &KnownZero, APInt &KnownOne,
                                   APInt &KnownZero2, APInt &KnownOne2,
                                   const DataLayout &DL, unsigned Depth,
                                   const Query &Q) {
  if (!Add) {
    if (ConstantInt *CLHS = dyn_cast<ConstantInt>(Op0)) {
      // We know that the top bits of C-X are clear if X contains less bits
      // than C (i.e. no wrap-around can happen).  For example, 20-X is
      // positive if we can prove that X is >= 0 and < 16.
      if (!CLHS->getValue().isNegative()) {
        unsigned BitWidth = KnownZero.getBitWidth();
        unsigned NLZ = (CLHS->getValue()+1).countLeadingZeros();
        // NLZ can't be BitWidth with no sign bit
        APInt MaskV = APInt::getHighBitsSet(BitWidth, NLZ+1);
        computeKnownBits(Op1, KnownZero2, KnownOne2, DL, Depth + 1, Q);

        // If all of the MaskV bits are known to be zero, then we know the
        // output top bits are zero, because we now know that the output is
        // from [0-C].
        if ((KnownZero2 & MaskV) == MaskV) {
          unsigned NLZ2 = CLHS->getValue().countLeadingZeros();
          // Top bits known zero.
          KnownZero = APInt::getHighBitsSet(BitWidth, NLZ2);
        }
      }
    }
  }

  unsigned BitWidth = KnownZero.getBitWidth();

  // If an initial sequence of bits in the result is not needed, the
  // corresponding bits in the operands are not needed.
  APInt LHSKnownZero(BitWidth, 0), LHSKnownOne(BitWidth, 0);
  computeKnownBits(Op0, LHSKnownZero, LHSKnownOne, DL, Depth + 1, Q);
  computeKnownBits(Op1, KnownZero2, KnownOne2, DL, Depth + 1, Q);

  // Carry in a 1 for a subtract, rather than a 0.
  APInt CarryIn(BitWidth, 0);
  if (!Add) {
    // Sum = LHS + ~RHS + 1
    std::swap(KnownZero2, KnownOne2);
    CarryIn.setBit(0);
  }

  APInt PossibleSumZero = ~LHSKnownZero + ~KnownZero2 + CarryIn;
  APInt PossibleSumOne = LHSKnownOne + KnownOne2 + CarryIn;

  // Compute known bits of the carry.
  APInt CarryKnownZero = ~(PossibleSumZero ^ LHSKnownZero ^ KnownZero2);
  APInt CarryKnownOne = PossibleSumOne ^ LHSKnownOne ^ KnownOne2;

  // Compute set of known bits (where all three relevant bits are known).
  APInt LHSKnown = LHSKnownZero | LHSKnownOne;
  APInt RHSKnown = KnownZero2 | KnownOne2;
  APInt CarryKnown = CarryKnownZero | CarryKnownOne;
  APInt Known = LHSKnown & RHSKnown & CarryKnown;

  assert((PossibleSumZero & Known) == (PossibleSumOne & Known) &&
         "known bits of sum differ");

  // Compute known bits of the result.
  KnownZero = ~PossibleSumOne & Known;
  KnownOne = PossibleSumOne & Known;

  // Are we still trying to solve for the sign bit?
  if (!Known.isNegative()) {
    if (NSW) {
      // Adding two non-negative numbers, or subtracting a negative number from
      // a non-negative one, can't wrap into negative.
      if (LHSKnownZero.isNegative() && KnownZero2.isNegative())
        KnownZero |= APInt::getSignBit(BitWidth);
      // Adding two negative numbers, or subtracting a non-negative number from
      // a negative one, can't wrap into non-negative.
      else if (LHSKnownOne.isNegative() && KnownOne2.isNegative())
        KnownOne |= APInt::getSignBit(BitWidth);
    }
  }
}

static void computeKnownBitsMul(Value *Op0, Value *Op1, bool NSW,
                                APInt &KnownZero, APInt &KnownOne,
                                APInt &KnownZero2, APInt &KnownOne2,
                                const DataLayout &DL, unsigned Depth,
                                const Query &Q) {
  unsigned BitWidth = KnownZero.getBitWidth();
  computeKnownBits(Op1, KnownZero, KnownOne, DL, Depth + 1, Q);
  computeKnownBits(Op0, KnownZero2, KnownOne2, DL, Depth + 1, Q);

  bool isKnownNegative = false;
  bool isKnownNonNegative = false;
  // If the multiplication is known not to overflow, compute the sign bit.
  if (NSW) {
    if (Op0 == Op1) {
      // The product of a number with itself is non-negative.
      isKnownNonNegative = true;
    } else {
      bool isKnownNonNegativeOp1 = KnownZero.isNegative();
      bool isKnownNonNegativeOp0 = KnownZero2.isNegative();
      bool isKnownNegativeOp1 = KnownOne.isNegative();
      bool isKnownNegativeOp0 = KnownOne2.isNegative();
      // The product of two numbers with the same sign is non-negative.
      isKnownNonNegative = (isKnownNegativeOp1 && isKnownNegativeOp0) ||
        (isKnownNonNegativeOp1 && isKnownNonNegativeOp0);
      // The product of a negative number and a non-negative number is either
      // negative or zero.
      if (!isKnownNonNegative)
        isKnownNegative = (isKnownNegativeOp1 && isKnownNonNegativeOp0 &&
                           isKnownNonZero(Op0, DL, Depth, Q)) ||
                          (isKnownNegativeOp0 && isKnownNonNegativeOp1 &&
                           isKnownNonZero(Op1, DL, Depth, Q));
    }
  }

  // If low bits are zero in either operand, output low known-0 bits.
  // Also compute a conserative estimate for high known-0 bits.
  // More trickiness is possible, but this is sufficient for the
  // interesting case of alignment computation.
  KnownOne.clearAllBits();
  unsigned TrailZ = KnownZero.countTrailingOnes() +
                    KnownZero2.countTrailingOnes();
  unsigned LeadZ =  std::max(KnownZero.countLeadingOnes() +
                             KnownZero2.countLeadingOnes(),
                             BitWidth) - BitWidth;

  TrailZ = std::min(TrailZ, BitWidth);
  LeadZ = std::min(LeadZ, BitWidth);
  KnownZero = APInt::getLowBitsSet(BitWidth, TrailZ) |
              APInt::getHighBitsSet(BitWidth, LeadZ);

  // Only make use of no-wrap flags if we failed to compute the sign bit
  // directly.  This matters if the multiplication always overflows, in
  // which case we prefer to follow the result of the direct computation,
  // though as the program is invoking undefined behaviour we can choose
  // whatever we like here.
  if (isKnownNonNegative && !KnownOne.isNegative())
    KnownZero.setBit(BitWidth - 1);
  else if (isKnownNegative && !KnownZero.isNegative())
    KnownOne.setBit(BitWidth - 1);
}

void llvm::computeKnownBitsFromRangeMetadata(const MDNode &Ranges,
                                             APInt &KnownZero) {
  unsigned BitWidth = KnownZero.getBitWidth();
  unsigned NumRanges = Ranges.getNumOperands() / 2;
  assert(NumRanges >= 1);

  // Use the high end of the ranges to find leading zeros.
  unsigned MinLeadingZeros = BitWidth;
  for (unsigned i = 0; i < NumRanges; ++i) {
    ConstantInt *Lower =
        mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 0));
    ConstantInt *Upper =
        mdconst::extract<ConstantInt>(Ranges.getOperand(2 * i + 1));
    ConstantRange Range(Lower->getValue(), Upper->getValue());
    if (Range.isWrappedSet())
      MinLeadingZeros = 0; // -1 has no zeros
    unsigned LeadingZeros = (Upper->getValue() - 1).countLeadingZeros();
    MinLeadingZeros = std::min(LeadingZeros, MinLeadingZeros);
  }

  KnownZero = APInt::getHighBitsSet(BitWidth, MinLeadingZeros);
}

static bool isEphemeralValueOf(Instruction *I, const Value *E) {
  SmallVector<const Value *, 16> WorkSet(1, I);
  SmallPtrSet<const Value *, 32> Visited;
  SmallPtrSet<const Value *, 16> EphValues;

  while (!WorkSet.empty()) {
    const Value *V = WorkSet.pop_back_val();
    if (!Visited.insert(V).second)
      continue;

    // If all uses of this value are ephemeral, then so is this value.
    bool FoundNEUse = false;
    for (const User *I : V->users())
      if (!EphValues.count(I)) {
        FoundNEUse = true;
        break;
      }

    if (!FoundNEUse) {
      if (V == E)
        return true;

      EphValues.insert(V);
      if (const User *U = dyn_cast<User>(V))
        for (User::const_op_iterator J = U->op_begin(), JE = U->op_end();
             J != JE; ++J) {
          if (isSafeToSpeculativelyExecute(*J))
            WorkSet.push_back(*J);
        }
    }
  }

  return false;
}

// Is this an intrinsic that cannot be speculated but also cannot trap?
static bool isAssumeLikeIntrinsic(const Instruction *I) {
  if (const CallInst *CI = dyn_cast<CallInst>(I))
    if (Function *F = CI->getCalledFunction())
      switch (F->getIntrinsicID()) {
      default: break;
      // FIXME: This list is repeated from NoTTI::getIntrinsicCost.
      case Intrinsic::assume:
      case Intrinsic::dbg_declare:
      case Intrinsic::dbg_value:
      case Intrinsic::invariant_start:
      case Intrinsic::invariant_end:
      case Intrinsic::lifetime_start:
      case Intrinsic::lifetime_end:
      case Intrinsic::objectsize:
      case Intrinsic::ptr_annotation:
      case Intrinsic::var_annotation:
        return true;
      }

  return false;
}

static bool isValidAssumeForContext(Value *V, const Query &Q) {
  Instruction *Inv = cast<Instruction>(V);

  // There are two restrictions on the use of an assume:
  //  1. The assume must dominate the context (or the control flow must
  //     reach the assume whenever it reaches the context).
  //  2. The context must not be in the assume's set of ephemeral values
  //     (otherwise we will use the assume to prove that the condition
  //     feeding the assume is trivially true, thus causing the removal of
  //     the assume).

  if (Q.DT) {
    if (Q.DT->dominates(Inv, Q.CxtI)) {
      return true;
    } else if (Inv->getParent() == Q.CxtI->getParent()) {
      // The context comes first, but they're both in the same block. Make sure
      // there is nothing in between that might interrupt the control flow.
      for (BasicBlock::const_iterator I =
             std::next(BasicBlock::const_iterator(Q.CxtI)),
                                      IE(Inv); I != IE; ++I)
        if (!isSafeToSpeculativelyExecute(I) && !isAssumeLikeIntrinsic(I))
          return false;

      return !isEphemeralValueOf(Inv, Q.CxtI);
    }

    return false;
  }

  // When we don't have a DT, we do a limited search...
  if (Inv->getParent() == Q.CxtI->getParent()->getSinglePredecessor()) {
    return true;
  } else if (Inv->getParent() == Q.CxtI->getParent()) {
    // Search forward from the assume until we reach the context (or the end
    // of the block); the common case is that the assume will come first.
    for (BasicBlock::iterator I = std::next(BasicBlock::iterator(Inv)),
         IE = Inv->getParent()->end(); I != IE; ++I)
      if (I == Q.CxtI)
        return true;

    // The context must come first...
    for (BasicBlock::const_iterator I =
           std::next(BasicBlock::const_iterator(Q.CxtI)),
                                    IE(Inv); I != IE; ++I)
      if (!isSafeToSpeculativelyExecute(I) && !isAssumeLikeIntrinsic(I))
        return false;

    return !isEphemeralValueOf(Inv, Q.CxtI);
  }

  return false;
}

bool llvm::isValidAssumeForContext(const Instruction *I,
                                   const Instruction *CxtI,
                                   const DominatorTree *DT) {
  return ::isValidAssumeForContext(const_cast<Instruction *>(I),
                                   Query(nullptr, CxtI, DT));
}

template<typename LHS, typename RHS>
inline match_combine_or<CmpClass_match<LHS, RHS, ICmpInst, ICmpInst::Predicate>,
                        CmpClass_match<RHS, LHS, ICmpInst, ICmpInst::Predicate>>
m_c_ICmp(ICmpInst::Predicate &Pred, const LHS &L, const RHS &R) {
  return m_CombineOr(m_ICmp(Pred, L, R), m_ICmp(Pred, R, L));
}

template<typename LHS, typename RHS>
inline match_combine_or<BinaryOp_match<LHS, RHS, Instruction::And>,
                        BinaryOp_match<RHS, LHS, Instruction::And>>
m_c_And(const LHS &L, const RHS &R) {
  return m_CombineOr(m_And(L, R), m_And(R, L));
}

template<typename LHS, typename RHS>
inline match_combine_or<BinaryOp_match<LHS, RHS, Instruction::Or>,
                        BinaryOp_match<RHS, LHS, Instruction::Or>>
m_c_Or(const LHS &L, const RHS &R) {
  return m_CombineOr(m_Or(L, R), m_Or(R, L));
}

template<typename LHS, typename RHS>
inline match_combine_or<BinaryOp_match<LHS, RHS, Instruction::Xor>,
                        BinaryOp_match<RHS, LHS, Instruction::Xor>>
m_c_Xor(const LHS &L, const RHS &R) {
  return m_CombineOr(m_Xor(L, R), m_Xor(R, L));
}

/// Compute known bits in 'V' under the assumption that the condition 'Cmp' is
/// true (at the context instruction.)  This is mostly a utility function for
/// the prototype dominating conditions reasoning below.
static void computeKnownBitsFromTrueCondition(Value *V, ICmpInst *Cmp,
                                              APInt &KnownZero,
                                              APInt &KnownOne,
                                              const DataLayout &DL,
                                              unsigned Depth, const Query &Q) {
  Value *LHS = Cmp->getOperand(0);
  Value *RHS = Cmp->getOperand(1);
  // TODO: We could potentially be more aggressive here.  This would be worth
  // evaluating.  If we can, explore commoning this code with the assume
  // handling logic.
  if (LHS != V && RHS != V)
    return;

  const unsigned BitWidth = KnownZero.getBitWidth();

  switch (Cmp->getPredicate()) {
  default:
    // We know nothing from this condition
    break;
  // TODO: implement unsigned bound from below (known one bits)
  // TODO: common condition check implementations with assumes
  // TODO: implement other patterns from assume (e.g. V & B == A)
  case ICmpInst::ICMP_SGT:
    if (LHS == V) {
      APInt KnownZeroTemp(BitWidth, 0), KnownOneTemp(BitWidth, 0);
      computeKnownBits(RHS, KnownZeroTemp, KnownOneTemp, DL, Depth + 1, Q);
      if (KnownOneTemp.isAllOnesValue() || KnownZeroTemp.isNegative()) {
        // We know that the sign bit is zero.
        KnownZero |= APInt::getSignBit(BitWidth);
      }
    }
    break;
  case ICmpInst::ICMP_EQ:
    if (LHS == V)
      computeKnownBits(RHS, KnownZero, KnownOne, DL, Depth + 1, Q);
    else if (RHS == V)
      computeKnownBits(LHS, KnownZero, KnownOne, DL, Depth + 1, Q);
    else
      llvm_unreachable("missing use?");
    break;
  case ICmpInst::ICMP_ULE:
    if (LHS == V) {
      APInt KnownZeroTemp(BitWidth, 0), KnownOneTemp(BitWidth, 0);
      computeKnownBits(RHS, KnownZeroTemp, KnownOneTemp, DL, Depth + 1, Q);
      // The known zero bits carry over
      unsigned SignBits = KnownZeroTemp.countLeadingOnes();
      KnownZero |= APInt::getHighBitsSet(BitWidth, SignBits);
    }
    break;
  case ICmpInst::ICMP_ULT:
    if (LHS == V) {
      APInt KnownZeroTemp(BitWidth, 0), KnownOneTemp(BitWidth, 0);
      computeKnownBits(RHS, KnownZeroTemp, KnownOneTemp, DL, Depth + 1, Q);
      // Whatever high bits in rhs are zero are known to be zero (if rhs is a
      // power of 2, then one more).
      unsigned SignBits = KnownZeroTemp.countLeadingOnes();
      if (isKnownToBeAPowerOfTwo(RHS, false, Depth + 1, Query(Q, Cmp), DL))
        SignBits++;
      KnownZero |= APInt::getHighBitsSet(BitWidth, SignBits);
    }
    break;
  };
}

/// Compute known bits in 'V' from conditions which are known to be true along
/// all paths leading to the context instruction.  In particular, look for
/// cases where one branch of an interesting condition dominates the context
/// instruction.  This does not do general dataflow.
/// NOTE: This code is EXPERIMENTAL and currently off by default.
static void computeKnownBitsFromDominatingCondition(Value *V, APInt &KnownZero,
                                                    APInt &KnownOne,
                                                    const DataLayout &DL,
                                                    unsigned Depth,
                                                    const Query &Q) {
  // Need both the dominator tree and the query location to do anything useful
  if (!Q.DT || !Q.CxtI)
    return;
  Instruction *Cxt = const_cast<Instruction *>(Q.CxtI);

  // Avoid useless work
  if (auto VI = dyn_cast<Instruction>(V))
    if (VI->getParent() == Cxt->getParent())
      return;

  // Note: We currently implement two options.  It's not clear which of these
  // will survive long term, we need data for that.
  // Option 1 - Try walking the dominator tree looking for conditions which
  // might apply.  This works well for local conditions (loop guards, etc..),
  // but not as well for things far from the context instruction (presuming a
  // low max blocks explored).  If we can set an high enough limit, this would
  // be all we need.
  // Option 2 - We restrict out search to those conditions which are uses of
  // the value we're interested in.  This is independent of dom structure,
  // but is slightly less powerful without looking through lots of use chains.
  // It does handle conditions far from the context instruction (e.g. early
  // function exits on entry) really well though.

  // Option 1 - Search the dom tree
  unsigned NumBlocksExplored = 0;
  BasicBlock *Current = Cxt->getParent();
  while (true) {
    // Stop searching if we've gone too far up the chain
    if (NumBlocksExplored >= DomConditionsMaxDomBlocks)
      break;
    NumBlocksExplored++;

    if (!Q.DT->getNode(Current)->getIDom())
      break;
    Current = Q.DT->getNode(Current)->getIDom()->getBlock();
    if (!Current)
      // found function entry
      break;

    BranchInst *BI = dyn_cast<BranchInst>(Current->getTerminator());
    if (!BI || BI->isUnconditional())
      continue;
    ICmpInst *Cmp = dyn_cast<ICmpInst>(BI->getCondition());
    if (!Cmp)
      continue;

    // We're looking for conditions that are guaranteed to hold at the context
    // instruction.  Finding a condition where one path dominates the context
    // isn't enough because both the true and false cases could merge before
    // the context instruction we're actually interested in.  Instead, we need
    // to ensure that the taken *edge* dominates the context instruction.
    BasicBlock *BB0 = BI->getSuccessor(0);
    BasicBlockEdge Edge(BI->getParent(), BB0);
    if (!Edge.isSingleEdge() || !Q.DT->dominates(Edge, Q.CxtI->getParent()))
      continue;

    computeKnownBitsFromTrueCondition(V, Cmp, KnownZero, KnownOne, DL, Depth,
                                      Q);
  }

  // Option 2 - Search the other uses of V
  unsigned NumUsesExplored = 0;
  for (auto U : V->users()) {
    // Avoid massive lists
    if (NumUsesExplored >= DomConditionsMaxUses)
      break;
    NumUsesExplored++;
    // Consider only compare instructions uniquely controlling a branch
    ICmpInst *Cmp = dyn_cast<ICmpInst>(U);
    if (!Cmp)
      continue;

    if (DomConditionsSingleCmpUse && !Cmp->hasOneUse())
      continue;

    for (auto *CmpU : Cmp->users()) {
      BranchInst *BI = dyn_cast<BranchInst>(CmpU);
      if (!BI || BI->isUnconditional())
        continue;
      // We're looking for conditions that are guaranteed to hold at the
      // context instruction.  Finding a condition where one path dominates
      // the context isn't enough because both the true and false cases could
      // merge before the context instruction we're actually interested in.
      // Instead, we need to ensure that the taken *edge* dominates the context
      // instruction. 
      BasicBlock *BB0 = BI->getSuccessor(0);
      BasicBlockEdge Edge(BI->getParent(), BB0);
      if (!Edge.isSingleEdge() || !Q.DT->dominates(Edge, Q.CxtI->getParent()))
        continue;

      computeKnownBitsFromTrueCondition(V, Cmp, KnownZero, KnownOne, DL, Depth,
                                        Q);
    }
  }
}

static void computeKnownBitsFromAssume(Value *V, APInt &KnownZero,
                                       APInt &KnownOne, const DataLayout &DL,
                                       unsigned Depth, const Query &Q) {
  // Use of assumptions is context-sensitive. If we don't have a context, we
  // cannot use them!
  if (!Q.AC || !Q.CxtI)
    return;

  unsigned BitWidth = KnownZero.getBitWidth();

  for (auto &AssumeVH : Q.AC->assumptions()) {
    if (!AssumeVH)
      continue;
    CallInst *I = cast<CallInst>(AssumeVH);
    assert(I->getParent()->getParent() == Q.CxtI->getParent()->getParent() &&
           "Got assumption for the wrong function!");
    if (Q.ExclInvs.count(I))
      continue;

    // Warning: This loop can end up being somewhat performance sensetive.
    // We're running this loop for once for each value queried resulting in a
    // runtime of ~O(#assumes * #values).

    assert(isa<IntrinsicInst>(I) &&
           dyn_cast<IntrinsicInst>(I)->getIntrinsicID() == Intrinsic::assume &&
           "must be an assume intrinsic");
    
    Value *Arg = I->getArgOperand(0);

    if (Arg == V && isValidAssumeForContext(I, Q)) {
      assert(BitWidth == 1 && "assume operand is not i1?");
      KnownZero.clearAllBits();
      KnownOne.setAllBits();
      return;
    }

    // The remaining tests are all recursive, so bail out if we hit the limit.
    if (Depth == MaxDepth)
      continue;

    Value *A, *B;
    auto m_V = m_CombineOr(m_Specific(V),
                           m_CombineOr(m_PtrToInt(m_Specific(V)),
                           m_BitCast(m_Specific(V))));

    CmpInst::Predicate Pred;
    ConstantInt *C;
    // assume(v = a)
    if (match(Arg, m_c_ICmp(Pred, m_V, m_Value(A))) &&
        Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      KnownZero |= RHSKnownZero;
      KnownOne  |= RHSKnownOne;
    // assume(v & b = a)
    } else if (match(Arg,
                     m_c_ICmp(Pred, m_c_And(m_V, m_Value(B)), m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      APInt MaskKnownZero(BitWidth, 0), MaskKnownOne(BitWidth, 0);
      computeKnownBits(B, MaskKnownZero, MaskKnownOne, DL, Depth+1, Query(Q, I));

      // For those bits in the mask that are known to be one, we can propagate
      // known bits from the RHS to V.
      KnownZero |= RHSKnownZero & MaskKnownOne;
      KnownOne  |= RHSKnownOne  & MaskKnownOne;
    // assume(~(v & b) = a)
    } else if (match(Arg, m_c_ICmp(Pred, m_Not(m_c_And(m_V, m_Value(B))),
                                   m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      APInt MaskKnownZero(BitWidth, 0), MaskKnownOne(BitWidth, 0);
      computeKnownBits(B, MaskKnownZero, MaskKnownOne, DL, Depth+1, Query(Q, I));

      // For those bits in the mask that are known to be one, we can propagate
      // inverted known bits from the RHS to V.
      KnownZero |= RHSKnownOne  & MaskKnownOne;
      KnownOne  |= RHSKnownZero & MaskKnownOne;
    // assume(v | b = a)
    } else if (match(Arg,
                     m_c_ICmp(Pred, m_c_Or(m_V, m_Value(B)), m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      APInt BKnownZero(BitWidth, 0), BKnownOne(BitWidth, 0);
      computeKnownBits(B, BKnownZero, BKnownOne, DL, Depth+1, Query(Q, I));

      // For those bits in B that are known to be zero, we can propagate known
      // bits from the RHS to V.
      KnownZero |= RHSKnownZero & BKnownZero;
      KnownOne  |= RHSKnownOne  & BKnownZero;
    // assume(~(v | b) = a)
    } else if (match(Arg, m_c_ICmp(Pred, m_Not(m_c_Or(m_V, m_Value(B))),
                                   m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      APInt BKnownZero(BitWidth, 0), BKnownOne(BitWidth, 0);
      computeKnownBits(B, BKnownZero, BKnownOne, DL, Depth+1, Query(Q, I));

      // For those bits in B that are known to be zero, we can propagate
      // inverted known bits from the RHS to V.
      KnownZero |= RHSKnownOne  & BKnownZero;
      KnownOne  |= RHSKnownZero & BKnownZero;
    // assume(v ^ b = a)
    } else if (match(Arg,
                     m_c_ICmp(Pred, m_c_Xor(m_V, m_Value(B)), m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      APInt BKnownZero(BitWidth, 0), BKnownOne(BitWidth, 0);
      computeKnownBits(B, BKnownZero, BKnownOne, DL, Depth+1, Query(Q, I));

      // For those bits in B that are known to be zero, we can propagate known
      // bits from the RHS to V. For those bits in B that are known to be one,
      // we can propagate inverted known bits from the RHS to V.
      KnownZero |= RHSKnownZero & BKnownZero;
      KnownOne  |= RHSKnownOne  & BKnownZero;
      KnownZero |= RHSKnownOne  & BKnownOne;
      KnownOne  |= RHSKnownZero & BKnownOne;
    // assume(~(v ^ b) = a)
    } else if (match(Arg, m_c_ICmp(Pred, m_Not(m_c_Xor(m_V, m_Value(B))),
                                   m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      APInt BKnownZero(BitWidth, 0), BKnownOne(BitWidth, 0);
      computeKnownBits(B, BKnownZero, BKnownOne, DL, Depth+1, Query(Q, I));

      // For those bits in B that are known to be zero, we can propagate
      // inverted known bits from the RHS to V. For those bits in B that are
      // known to be one, we can propagate known bits from the RHS to V.
      KnownZero |= RHSKnownOne  & BKnownZero;
      KnownOne  |= RHSKnownZero & BKnownZero;
      KnownZero |= RHSKnownZero & BKnownOne;
      KnownOne  |= RHSKnownOne  & BKnownOne;
    // assume(v << c = a)
    } else if (match(Arg, m_c_ICmp(Pred, m_Shl(m_V, m_ConstantInt(C)),
                                   m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      // For those bits in RHS that are known, we can propagate them to known
      // bits in V shifted to the right by C.
      KnownZero |= RHSKnownZero.lshr(C->getZExtValue());
      KnownOne  |= RHSKnownOne.lshr(C->getZExtValue());
    // assume(~(v << c) = a)
    } else if (match(Arg, m_c_ICmp(Pred, m_Not(m_Shl(m_V, m_ConstantInt(C))),
                                   m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      // For those bits in RHS that are known, we can propagate them inverted
      // to known bits in V shifted to the right by C.
      KnownZero |= RHSKnownOne.lshr(C->getZExtValue());
      KnownOne  |= RHSKnownZero.lshr(C->getZExtValue());
    // assume(v >> c = a)
    } else if (match(Arg,
                     m_c_ICmp(Pred, m_CombineOr(m_LShr(m_V, m_ConstantInt(C)),
                                                m_AShr(m_V, m_ConstantInt(C))),
                              m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      // For those bits in RHS that are known, we can propagate them to known
      // bits in V shifted to the right by C.
      KnownZero |= RHSKnownZero << C->getZExtValue();
      KnownOne  |= RHSKnownOne  << C->getZExtValue();
    // assume(~(v >> c) = a)
    } else if (match(Arg, m_c_ICmp(Pred, m_Not(m_CombineOr(
                                             m_LShr(m_V, m_ConstantInt(C)),
                                             m_AShr(m_V, m_ConstantInt(C)))),
                                   m_Value(A))) &&
               Pred == ICmpInst::ICMP_EQ && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));
      // For those bits in RHS that are known, we can propagate them inverted
      // to known bits in V shifted to the right by C.
      KnownZero |= RHSKnownOne  << C->getZExtValue();
      KnownOne  |= RHSKnownZero << C->getZExtValue();
    // assume(v >=_s c) where c is non-negative
    } else if (match(Arg, m_ICmp(Pred, m_V, m_Value(A))) &&
               Pred == ICmpInst::ICMP_SGE && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));

      if (RHSKnownZero.isNegative()) {
        // We know that the sign bit is zero.
        KnownZero |= APInt::getSignBit(BitWidth);
      }
    // assume(v >_s c) where c is at least -1.
    } else if (match(Arg, m_ICmp(Pred, m_V, m_Value(A))) &&
               Pred == ICmpInst::ICMP_SGT && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));

      if (RHSKnownOne.isAllOnesValue() || RHSKnownZero.isNegative()) {
        // We know that the sign bit is zero.
        KnownZero |= APInt::getSignBit(BitWidth);
      }
    // assume(v <=_s c) where c is negative
    } else if (match(Arg, m_ICmp(Pred, m_V, m_Value(A))) &&
               Pred == ICmpInst::ICMP_SLE && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));

      if (RHSKnownOne.isNegative()) {
        // We know that the sign bit is one.
        KnownOne |= APInt::getSignBit(BitWidth);
      }
    // assume(v <_s c) where c is non-positive
    } else if (match(Arg, m_ICmp(Pred, m_V, m_Value(A))) &&
               Pred == ICmpInst::ICMP_SLT && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));

      if (RHSKnownZero.isAllOnesValue() || RHSKnownOne.isNegative()) {
        // We know that the sign bit is one.
        KnownOne |= APInt::getSignBit(BitWidth);
      }
    // assume(v <=_u c)
    } else if (match(Arg, m_ICmp(Pred, m_V, m_Value(A))) &&
               Pred == ICmpInst::ICMP_ULE && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));

      // Whatever high bits in c are zero are known to be zero.
      KnownZero |=
        APInt::getHighBitsSet(BitWidth, RHSKnownZero.countLeadingOnes());
    // assume(v <_u c)
    } else if (match(Arg, m_ICmp(Pred, m_V, m_Value(A))) &&
               Pred == ICmpInst::ICMP_ULT && isValidAssumeForContext(I, Q)) {
      APInt RHSKnownZero(BitWidth, 0), RHSKnownOne(BitWidth, 0);
      computeKnownBits(A, RHSKnownZero, RHSKnownOne, DL, Depth+1, Query(Q, I));

      // Whatever high bits in c are zero are known to be zero (if c is a power
      // of 2, then one more).
      if (isKnownToBeAPowerOfTwo(A, false, Depth + 1, Query(Q, I), DL))
        KnownZero |=
          APInt::getHighBitsSet(BitWidth, RHSKnownZero.countLeadingOnes()+1);
      else
        KnownZero |=
          APInt::getHighBitsSet(BitWidth, RHSKnownZero.countLeadingOnes());
    }
  }
}

/// Determine which bits of V are known to be either zero or one and return
/// them in the KnownZero/KnownOne bit sets.
///
/// NOTE: we cannot consider 'undef' to be "IsZero" here.  The problem is that
/// we cannot optimize based on the assumption that it is zero without changing
/// it to be an explicit zero.  If we don't change it to zero, other code could
/// optimized based on the contradictory assumption that it is non-zero.
/// Because instcombine aggressively folds operations with undef args anyway,
/// this won't lose us code quality.
///
/// This function is defined on values with integer type, values with pointer
/// type, and vectors of integers.  In the case
/// where V is a vector, known zero, and known one values are the
/// same width as the vector element, and the bit is set only if it is true
/// for all of the elements in the vector.
void computeKnownBits(Value *V, APInt &KnownZero, APInt &KnownOne,
                      const DataLayout &DL, unsigned Depth, const Query &Q) {
  assert(V && "No Value?");
  assert(Depth <= MaxDepth && "Limit Search Depth");
  unsigned BitWidth = KnownZero.getBitWidth();

  assert((V->getType()->isIntOrIntVectorTy() ||
          V->getType()->getScalarType()->isPointerTy()) &&
         "Not integer or pointer type!");
  assert((DL.getTypeSizeInBits(V->getType()->getScalarType()) == BitWidth) &&
         (!V->getType()->isIntOrIntVectorTy() ||
          V->getType()->getScalarSizeInBits() == BitWidth) &&
         KnownZero.getBitWidth() == BitWidth &&
         KnownOne.getBitWidth() == BitWidth &&
         "V, KnownOne and KnownZero should have same BitWidth");

  if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) {
    // We know all of the bits for a constant!
    KnownOne = CI->getValue();
    KnownZero = ~KnownOne;
    return;
  }
  // Null and aggregate-zero are all-zeros.
  if (isa<ConstantPointerNull>(V) ||
      isa<ConstantAggregateZero>(V)) {
    KnownOne.clearAllBits();
    KnownZero = APInt::getAllOnesValue(BitWidth);
    return;
  }
  // Handle a constant vector by taking the intersection of the known bits of
  // each element.  There is no real need to handle ConstantVector here, because
  // we don't handle undef in any particularly useful way.
  if (ConstantDataSequential *CDS = dyn_cast<ConstantDataSequential>(V)) {
    // We know that CDS must be a vector of integers. Take the intersection of
    // each element.
    KnownZero.setAllBits(); KnownOne.setAllBits();
    APInt Elt(KnownZero.getBitWidth(), 0);
    for (unsigned i = 0, e = CDS->getNumElements(); i != e; ++i) {
      Elt = CDS->getElementAsInteger(i);
      KnownZero &= ~Elt;
      KnownOne &= Elt;
    }
    return;
  }

  // The address of an aligned GlobalValue has trailing zeros.
  if (auto *GO = dyn_cast<GlobalObject>(V)) {
    unsigned Align = GO->getAlignment();
    if (Align == 0) {
      if (auto *GVar = dyn_cast<GlobalVariable>(GO)) {
        Type *ObjectType = GVar->getType()->getElementType();
        if (ObjectType->isSized()) {
          // If the object is defined in the current Module, we'll be giving
          // it the preferred alignment. Otherwise, we have to assume that it
          // may only have the minimum ABI alignment.
          if (!GVar->isDeclaration() && !GVar->isWeakForLinker())
            Align = DL.getPreferredAlignment(GVar);
          else
            Align = DL.getABITypeAlignment(ObjectType);
        }
      }
    }
    if (Align > 0)
      KnownZero = APInt::getLowBitsSet(BitWidth,
                                       countTrailingZeros(Align));
    else
      KnownZero.clearAllBits();
    KnownOne.clearAllBits();
    return;
  }

  if (Argument *A = dyn_cast<Argument>(V)) {
    unsigned Align = A->getType()->isPointerTy() ? A->getParamAlignment() : 0;

    if (!Align && A->hasStructRetAttr()) {
      // An sret parameter has at least the ABI alignment of the return type.
      Type *EltTy = cast<PointerType>(A->getType())->getElementType();
      if (EltTy->isSized())
        Align = DL.getABITypeAlignment(EltTy);
    }

    if (Align)
      KnownZero = APInt::getLowBitsSet(BitWidth, countTrailingZeros(Align));
    else
      KnownZero.clearAllBits();
    KnownOne.clearAllBits();

    // Don't give up yet... there might be an assumption that provides more
    // information...
    computeKnownBitsFromAssume(V, KnownZero, KnownOne, DL, Depth, Q);

    // Or a dominating condition for that matter
    if (EnableDomConditions && Depth <= DomConditionsMaxDepth)
      computeKnownBitsFromDominatingCondition(V, KnownZero, KnownOne, DL,
                                              Depth, Q);
    return;
  }

  // Start out not knowing anything.
  KnownZero.clearAllBits(); KnownOne.clearAllBits();

  // Limit search depth.
  // All recursive calls that increase depth must come after this.
  if (Depth == MaxDepth)
    return;  

  // A weak GlobalAlias is totally unknown. A non-weak GlobalAlias has
  // the bits of its aliasee.
  if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) {
    if (!GA->mayBeOverridden())
      computeKnownBits(GA->getAliasee(), KnownZero, KnownOne, DL, Depth + 1, Q);
    return;
  }

  // Check whether a nearby assume intrinsic can determine some known bits.
  computeKnownBitsFromAssume(V, KnownZero, KnownOne, DL, Depth, Q);

  // Check whether there's a dominating condition which implies something about
  // this value at the given context.
  if (EnableDomConditions && Depth <= DomConditionsMaxDepth)
    computeKnownBitsFromDominatingCondition(V, KnownZero, KnownOne, DL, Depth,
                                            Q);

  Operator *I = dyn_cast<Operator>(V);
  if (!I) return;

  APInt KnownZero2(KnownZero), KnownOne2(KnownOne);
  switch (I->getOpcode()) {
  default: break;
  case Instruction::Load:
    if (MDNode *MD = cast<LoadInst>(I)->getMetadata(LLVMContext::MD_range))
      computeKnownBitsFromRangeMetadata(*MD, KnownZero);
    break;
  case Instruction::And: {
    // If either the LHS or the RHS are Zero, the result is zero.
    computeKnownBits(I->getOperand(1), KnownZero, KnownOne, DL, Depth + 1, Q);
    computeKnownBits(I->getOperand(0), KnownZero2, KnownOne2, DL, Depth + 1, Q);

    // Output known-1 bits are only known if set in both the LHS & RHS.
    KnownOne &= KnownOne2;
    // Output known-0 are known to be clear if zero in either the LHS | RHS.
    KnownZero |= KnownZero2;
    break;
  }
  case Instruction::Or: {
    computeKnownBits(I->getOperand(1), KnownZero, KnownOne, DL, Depth + 1, Q);
    computeKnownBits(I->getOperand(0), KnownZero2, KnownOne2, DL, Depth + 1, Q);

    // Output known-0 bits are only known if clear in both the LHS & RHS.
    KnownZero &= KnownZero2;
    // Output known-1 are known to be set if set in either the LHS | RHS.
    KnownOne |= KnownOne2;
    break;
  }
  case Instruction::Xor: {
    computeKnownBits(I->getOperand(1), KnownZero, KnownOne, DL, Depth + 1, Q);
    computeKnownBits(I->getOperand(0), KnownZero2, KnownOne2, DL, Depth + 1, Q);

    // Output known-0 bits are known if clear or set in both the LHS & RHS.
    APInt KnownZeroOut = (KnownZero & KnownZero2) | (KnownOne & KnownOne2);
    // Output known-1 are known to be set if set in only one of the LHS, RHS.
    KnownOne = (KnownZero & KnownOne2) | (KnownOne & KnownZero2);
    KnownZero = KnownZeroOut;
    break;
  }
  case Instruction::Mul: {
    bool NSW = cast<OverflowingBinaryOperator>(I)->hasNoSignedWrap();
    computeKnownBitsMul(I->getOperand(0), I->getOperand(1), NSW, KnownZero,
                        KnownOne, KnownZero2, KnownOne2, DL, Depth, Q);
    break;
  }
  case Instruction::UDiv: {
    // For the purposes of computing leading zeros we can conservatively
    // treat a udiv as a logical right shift by the power of 2 known to
    // be less than the denominator.
    computeKnownBits(I->getOperand(0), KnownZero2, KnownOne2, DL, Depth + 1, Q);
    unsigned LeadZ = KnownZero2.countLeadingOnes();

    KnownOne2.clearAllBits();
    KnownZero2.clearAllBits();
    computeKnownBits(I->getOperand(1), KnownZero2, KnownOne2, DL, Depth + 1, Q);
    unsigned RHSUnknownLeadingOnes = KnownOne2.countLeadingZeros();
    if (RHSUnknownLeadingOnes != BitWidth)
      LeadZ = std::min(BitWidth,
                       LeadZ + BitWidth - RHSUnknownLeadingOnes - 1);

    KnownZero = APInt::getHighBitsSet(BitWidth, LeadZ);
    break;
  }
  case Instruction::Select:
    computeKnownBits(I->getOperand(2), KnownZero, KnownOne, DL, Depth + 1, Q);
    computeKnownBits(I->getOperand(1), KnownZero2, KnownOne2, DL, Depth + 1, Q);

    // Only known if known in both the LHS and RHS.
    KnownOne &= KnownOne2;
    KnownZero &= KnownZero2;
    break;
  case Instruction::FPTrunc:
  case Instruction::FPExt:
  case Instruction::FPToUI:
  case Instruction::FPToSI:
  case Instruction::SIToFP:
  case Instruction::UIToFP:
    break; // Can't work with floating point.
  case Instruction::PtrToInt:
  case Instruction::IntToPtr:
  case Instruction::AddrSpaceCast: // Pointers could be different sizes.
    // FALL THROUGH and handle them the same as zext/trunc.
  case Instruction::ZExt:
  case Instruction::Trunc: {
    Type *SrcTy = I->getOperand(0)->getType();

    unsigned SrcBitWidth;
    // Note that we handle pointer operands here because of inttoptr/ptrtoint
    // which fall through here.
    SrcBitWidth = DL.getTypeSizeInBits(SrcTy->getScalarType());

    assert(SrcBitWidth && "SrcBitWidth can't be zero");
    KnownZero = KnownZero.zextOrTrunc(SrcBitWidth);
    KnownOne = KnownOne.zextOrTrunc(SrcBitWidth);
    computeKnownBits(I->getOperand(0), KnownZero, KnownOne, DL, Depth + 1, Q);
    KnownZero = KnownZero.zextOrTrunc(BitWidth);
    KnownOne = KnownOne.zextOrTrunc(BitWidth);
    // Any top bits are known to be zero.
    if (BitWidth > SrcBitWidth)
      KnownZero |= APInt::getHighBitsSet(BitWidth, BitWidth - SrcBitWidth);
    break;
  }
  case Instruction::BitCast: {
    Type *SrcTy = I->getOperand(0)->getType();
    if ((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
        // TODO: For now, not handling conversions like:
        // (bitcast i64 %x to <2 x i32>)
        !I->getType()->isVectorTy()) {
      computeKnownBits(I->getOperand(0), KnownZero, KnownOne, DL, Depth + 1, Q);
      break;
    }
    break;
  }
  case Instruction::SExt: {
    // Compute the bits in the result that are not present in the input.
    unsigned SrcBitWidth = I->getOperand(0)->getType()->getScalarSizeInBits();

    KnownZero = KnownZero.trunc(SrcBitWidth);
    KnownOne = KnownOne.trunc(SrcBitWidth);
    computeKnownBits(I->getOperand(0), KnownZero, KnownOne, DL, Depth + 1, Q);
    KnownZero = KnownZero.zext(BitWidth);
    KnownOne = KnownOne.zext(BitWidth);

    // If the sign bit of the input is known set or clear, then we know the
    // top bits of the result.
    if (KnownZero[SrcBitWidth-1])             // Input sign bit known zero
      KnownZero |= APInt::getHighBitsSet(BitWidth, BitWidth - SrcBitWidth);
    else if (KnownOne[SrcBitWidth-1])           // Input sign bit known set
      KnownOne |= APInt::getHighBitsSet(BitWidth, BitWidth - SrcBitWidth);
    break;
  }
  case Instruction::Shl:
    // (shl X, C1) & C2 == 0   iff   (X & C2 >>u C1) == 0
    if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
      uint64_t ShiftAmt = SA->getLimitedValue(BitWidth);
      computeKnownBits(I->getOperand(0), KnownZero, KnownOne, DL, Depth + 1, Q);
      KnownZero <<= ShiftAmt;
      KnownOne  <<= ShiftAmt;
      KnownZero |= APInt::getLowBitsSet(BitWidth, ShiftAmt); // low bits known 0
    }
    break;
  case Instruction::LShr:
    // (ushr X, C1) & C2 == 0   iff  (-1 >> C1) & C2 == 0
    if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
      // Compute the new bits that are at the top now.
      uint64_t ShiftAmt = SA->getLimitedValue(BitWidth);

      // Unsigned shift right.
      computeKnownBits(I->getOperand(0), KnownZero, KnownOne, DL, Depth + 1, Q);
      KnownZero = APIntOps::lshr(KnownZero, ShiftAmt);
      KnownOne  = APIntOps::lshr(KnownOne, ShiftAmt);
      // high bits known zero.
      KnownZero |= APInt::getHighBitsSet(BitWidth, ShiftAmt);
    }
    break;
  case Instruction::AShr:
    // (ashr X, C1) & C2 == 0   iff  (-1 >> C1) & C2 == 0
    if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
      // Compute the new bits that are at the top now.
      uint64_t ShiftAmt = SA->getLimitedValue(BitWidth-1);

      // Signed shift right.
      computeKnownBits(I->getOperand(0), KnownZero, KnownOne, DL, Depth + 1, Q);
      KnownZero = APIntOps::lshr(KnownZero, ShiftAmt);
      KnownOne  = APIntOps::lshr(KnownOne, ShiftAmt);

      APInt HighBits(APInt::getHighBitsSet(BitWidth, ShiftAmt));
      if (KnownZero[BitWidth-ShiftAmt-1])    // New bits are known zero.
        KnownZero |= HighBits;
      else if (KnownOne[BitWidth-ShiftAmt-1])  // New bits are known one.
        KnownOne |= HighBits;
    }
    break;
  case Instruction::Sub: {
    bool NSW = cast<OverflowingBinaryOperator>(I)->hasNoSignedWrap();
    computeKnownBitsAddSub(false, I->getOperand(0), I->getOperand(1), NSW,
                           KnownZero, KnownOne, KnownZero2, KnownOne2, DL,
                           Depth, Q);
    break;
  }
  case Instruction::Add: {
    bool NSW = cast<OverflowingBinaryOperator>(I)->hasNoSignedWrap();
    computeKnownBitsAddSub(true, I->getOperand(0), I->getOperand(1), NSW,
                           KnownZero, KnownOne, KnownZero2, KnownOne2, DL,
                           Depth, Q);
    break;
  }
  case Instruction::SRem:
    if (ConstantInt *Rem = dyn_cast<ConstantInt>(I->getOperand(1))) {
      APInt RA = Rem->getValue().abs();
      if (RA.isPowerOf2()) {
        APInt LowBits = RA - 1;
        computeKnownBits(I->getOperand(0), KnownZero2, KnownOne2, DL, Depth + 1,
                         Q);

        // The low bits of the first operand are unchanged by the srem.
        KnownZero = KnownZero2 & LowBits;
        KnownOne = KnownOne2 & LowBits;

        // If the first operand is non-negative or has all low bits zero, then
        // the upper bits are all zero.
        if (KnownZero2[BitWidth-1] || ((KnownZero2 & LowBits) == LowBits))
          KnownZero |= ~LowBits;

        // If the first operand is negative and not all low bits are zero, then
        // the upper bits are all one.
        if (KnownOne2[BitWidth-1] && ((KnownOne2 & LowBits) != 0))
          KnownOne |= ~LowBits;

        assert((KnownZero & KnownOne) == 0 && "Bits known to be one AND zero?");
      }
    }

    // The sign bit is the LHS's sign bit, except when the result of the
    // remainder is zero.
    if (KnownZero.isNonNegative()) {
      APInt LHSKnownZero(BitWidth, 0), LHSKnownOne(BitWidth, 0);
      computeKnownBits(I->getOperand(0), LHSKnownZero, LHSKnownOne, DL,
                       Depth + 1, Q);
      // If it's known zero, our sign bit is also zero.
      if (LHSKnownZero.isNegative())
        KnownZero.setBit(BitWidth - 1);
    }

    break;
  case Instruction::URem: {
    if (ConstantInt *Rem = dyn_cast<ConstantInt>(I->getOperand(1))) {
      APInt RA = Rem->getValue();
      if (RA.isPowerOf2()) {
        APInt LowBits = (RA - 1);
        computeKnownBits(I->getOperand(0), KnownZero, KnownOne, DL, Depth + 1,
                         Q);
        KnownZero |= ~LowBits;
        KnownOne &= LowBits;
        break;
      }
    }

    // Since the result is less than or equal to either operand, any leading
    // zero bits in either operand must also exist in the result.
    computeKnownBits(I->getOperand(0), KnownZero, KnownOne, DL, Depth + 1, Q);
    computeKnownBits(I->getOperand(1), KnownZero2, KnownOne2, DL, Depth + 1, Q);

    unsigned Leaders = std::max(KnownZero.countLeadingOnes(),
                                KnownZero2.countLeadingOnes());
    KnownOne.clearAllBits();
    KnownZero = APInt::getHighBitsSet(BitWidth, Leaders);
    break;
  }

  case Instruction::Alloca: {
    AllocaInst *AI = cast<AllocaInst>(V);
    unsigned Align = AI->getAlignment();
    if (Align == 0)
      Align = DL.getABITypeAlignment(AI->getType()->getElementType());

    if (Align > 0)
      KnownZero = APInt::getLowBitsSet(BitWidth, countTrailingZeros(Align));
    break;
  }
  case Instruction::GetElementPtr: {
    // Analyze all of the subscripts of this getelementptr instruction
    // to determine if we can prove known low zero bits.
    APInt LocalKnownZero(BitWidth, 0), LocalKnownOne(BitWidth, 0);
    computeKnownBits(I->getOperand(0), LocalKnownZero, LocalKnownOne, DL,
                     Depth + 1, Q);
    unsigned TrailZ = LocalKnownZero.countTrailingOnes();

    gep_type_iterator GTI = gep_type_begin(I);
    for (unsigned i = 1, e = I->getNumOperands(); i != e; ++i, ++GTI) {
      Value *Index = I->getOperand(i);
      if (StructType *STy = dyn_cast<StructType>(*GTI)) {
        // Handle struct member offset arithmetic.

        // Handle case when index is vector zeroinitializer
        Constant *CIndex = cast<Constant>(Index);
        if (CIndex->isZeroValue())
          continue;

        if (CIndex->getType()->isVectorTy())
          Index = CIndex->getSplatValue();

        unsigned Idx = cast<ConstantInt>(Index)->getZExtValue();
        const StructLayout *SL = DL.getStructLayout(STy);
        uint64_t Offset = SL->getElementOffset(Idx);
        TrailZ = std::min<unsigned>(TrailZ,
                                    countTrailingZeros(Offset));
      } else {
        // Handle array index arithmetic.
        Type *IndexedTy = GTI.getIndexedType();
        if (!IndexedTy->isSized()) {
          TrailZ = 0;
          break;
        }
        unsigned GEPOpiBits = Index->getType()->getScalarSizeInBits();
        uint64_t TypeSize = DL.getTypeAllocSize(IndexedTy);
        LocalKnownZero = LocalKnownOne = APInt(GEPOpiBits, 0);
        computeKnownBits(Index, LocalKnownZero, LocalKnownOne, DL, Depth + 1,
                         Q);
        TrailZ = std::min(TrailZ,
                          unsigned(countTrailingZeros(TypeSize) +
                                   LocalKnownZero.countTrailingOnes()));
      }
    }

    KnownZero = APInt::getLowBitsSet(BitWidth, TrailZ);
    break;
  }
  case Instruction::PHI: {
    PHINode *P = cast<PHINode>(I);
    // Handle the case of a simple two-predecessor recurrence PHI.
    // There's a lot more that could theoretically be done here, but
    // this is sufficient to catch some interesting cases.
    if (P->getNumIncomingValues() == 2) {
      for (unsigned i = 0; i != 2; ++i) {
        Value *L = P->getIncomingValue(i);
        Value *R = P->getIncomingValue(!i);
        Operator *LU = dyn_cast<Operator>(L);
        if (!LU)
          continue;
        unsigned Opcode = LU->getOpcode();
        // Check for operations that have the property that if
        // both their operands have low zero bits, the result
        // will have low zero bits.
        if (Opcode == Instruction::Add ||
            Opcode == Instruction::Sub ||
            Opcode == Instruction::And ||
            Opcode == Instruction::Or ||
            Opcode == Instruction::Mul) {
          Value *LL = LU->getOperand(0);
          Value *LR = LU->getOperand(1);
          // Find a recurrence.
          if (LL == I)
            L = LR;
          else if (LR == I)
            L = LL;
          else
            break;
          // Ok, we have a PHI of the form L op= R. Check for low
          // zero bits.
          computeKnownBits(R, KnownZero2, KnownOne2, DL, Depth + 1, Q);

          // We need to take the minimum number of known bits
          APInt KnownZero3(KnownZero), KnownOne3(KnownOne);
          computeKnownBits(L, KnownZero3, KnownOne3, DL, Depth + 1, Q);

          KnownZero = APInt::getLowBitsSet(BitWidth,
                                           std::min(KnownZero2.countTrailingOnes(),
                                                    KnownZero3.countTrailingOnes()));
          break;
        }
      }
    }

    // Unreachable blocks may have zero-operand PHI nodes.
    if (P->getNumIncomingValues() == 0)
      break;

    // Otherwise take the unions of the known bit sets of the operands,
    // taking conservative care to avoid excessive recursion.
    if (Depth < MaxDepth - 1 && !KnownZero && !KnownOne) {
      // Skip if every incoming value references to ourself.
      if (dyn_cast_or_null<UndefValue>(P->hasConstantValue()))
        break;

      KnownZero = APInt::getAllOnesValue(BitWidth);
      KnownOne = APInt::getAllOnesValue(BitWidth);
      for (unsigned i = 0, e = P->getNumIncomingValues(); i != e; ++i) {
        // Skip direct self references.
        if (P->getIncomingValue(i) == P) continue;

        KnownZero2 = APInt(BitWidth, 0);
        KnownOne2 = APInt(BitWidth, 0);
        // Recurse, but cap the recursion to one level, because we don't
        // want to waste time spinning around in loops.
        computeKnownBits(P->getIncomingValue(i), KnownZero2, KnownOne2, DL,
                         MaxDepth - 1, Q);
        KnownZero &= KnownZero2;
        KnownOne &= KnownOne2;
        // If all bits have been ruled out, there's no need to check
        // more operands.
        if (!KnownZero && !KnownOne)
          break;
      }
    }
    break;
  }
  case Instruction::Call:
  case Instruction::Invoke:
    if (MDNode *MD = cast<Instruction>(I)->getMetadata(LLVMContext::MD_range))
      computeKnownBitsFromRangeMetadata(*MD, KnownZero);
    // If a range metadata is attached to this IntrinsicInst, intersect the
    // explicit range specified by the metadata and the implicit range of
    // the intrinsic.
    if (IntrinsicInst *II = dyn_cast<IntrinsicInst>(I)) {
      switch (II->getIntrinsicID()) {
      default: break;
      case Intrinsic::ctlz:
      case Intrinsic::cttz: {
        unsigned LowBits = Log2_32(BitWidth)+1;
        // If this call is undefined for 0, the result will be less than 2^n.
        if (II->getArgOperand(1) == ConstantInt::getTrue(II->getContext()))
          LowBits -= 1;
        KnownZero |= APInt::getHighBitsSet(BitWidth, BitWidth - LowBits);
        break;
      }
      case Intrinsic::ctpop: {
        unsigned LowBits = Log2_32(BitWidth)+1;
        KnownZero |= APInt::getHighBitsSet(BitWidth, BitWidth - LowBits);
        break;
      }
      case Intrinsic::x86_sse42_crc32_64_64:
        KnownZero |= APInt::getHighBitsSet(64, 32);
        break;
      }
    }
    break;
  case Instruction::ExtractValue:
    if (IntrinsicInst *II = dyn_cast<IntrinsicInst>(I->getOperand(0))) {
      ExtractValueInst *EVI = cast<ExtractValueInst>(I);
      if (EVI->getNumIndices() != 1) break;
      if (EVI->getIndices()[0] == 0) {
        switch (II->getIntrinsicID()) {
        default: break;
        case Intrinsic::uadd_with_overflow:
        case Intrinsic::sadd_with_overflow:
          computeKnownBitsAddSub(true, II->getArgOperand(0),
                                 II->getArgOperand(1), false, KnownZero,
                                 KnownOne, KnownZero2, KnownOne2, DL, Depth, Q);
          break;
        case Intrinsic::usub_with_overflow:
        case Intrinsic::ssub_with_overflow:
          computeKnownBitsAddSub(false, II->getArgOperand(0),
                                 II->getArgOperand(1), false, KnownZero,
                                 KnownOne, KnownZero2, KnownOne2, DL, Depth, Q);
          break;
        case Intrinsic::umul_with_overflow:
        case Intrinsic::smul_with_overflow:
          computeKnownBitsMul(II->getArgOperand(0), II->getArgOperand(1), false,
                              KnownZero, KnownOne, KnownZero2, KnownOne2, DL,
                              Depth, Q);
          break;
        }
      }
    }
  }

  assert((KnownZero & KnownOne) == 0 && "Bits known to be one AND zero?");
}

/// Determine whether the sign bit is known to be zero or one.
/// Convenience wrapper around computeKnownBits.
void ComputeSignBit(Value *V, bool &KnownZero, bool &KnownOne,
                    const DataLayout &DL, unsigned Depth, const Query &Q) {
  unsigned BitWidth = getBitWidth(V->getType(), DL);
  if (!BitWidth) {
    KnownZero = false;
    KnownOne = false;
    return;
  }
  APInt ZeroBits(BitWidth, 0);
  APInt OneBits(BitWidth, 0);
  computeKnownBits(V, ZeroBits, OneBits, DL, Depth, Q);
  KnownOne = OneBits[BitWidth - 1];
  KnownZero = ZeroBits[BitWidth - 1];
}

/// Return true if the given value is known to have exactly one
/// bit set when defined. For vectors return true if every element is known to
/// be a power of two when defined. Supports values with integer or pointer
/// types and vectors of integers.
bool isKnownToBeAPowerOfTwo(Value *V, bool OrZero, unsigned Depth,
                            const Query &Q, const DataLayout &DL) {
  if (Constant *C = dyn_cast<Constant>(V)) {
    if (C->isNullValue())
      return OrZero;
    if (ConstantInt *CI = dyn_cast<ConstantInt>(C))
      return CI->getValue().isPowerOf2();
    // TODO: Handle vector constants.
  }

  // 1 << X is clearly a power of two if the one is not shifted off the end.  If
  // it is shifted off the end then the result is undefined.
  if (match(V, m_Shl(m_One(), m_Value())))
    return true;

  // (signbit) >>l X is clearly a power of two if the one is not shifted off the
  // bottom.  If it is shifted off the bottom then the result is undefined.
  if (match(V, m_LShr(m_SignBit(), m_Value())))
    return true;

  // The remaining tests are all recursive, so bail out if we hit the limit.
  if (Depth++ == MaxDepth)
    return false;

  Value *X = nullptr, *Y = nullptr;
  // A shift of a power of two is a power of two or zero.
  if (OrZero && (match(V, m_Shl(m_Value(X), m_Value())) ||
                 match(V, m_Shr(m_Value(X), m_Value()))))
    return isKnownToBeAPowerOfTwo(X, /*OrZero*/ true, Depth, Q, DL);

  if (ZExtInst *ZI = dyn_cast<ZExtInst>(V))
    return isKnownToBeAPowerOfTwo(ZI->getOperand(0), OrZero, Depth, Q, DL);

  if (SelectInst *SI = dyn_cast<SelectInst>(V))
    return isKnownToBeAPowerOfTwo(SI->getTrueValue(), OrZero, Depth, Q, DL) &&
           isKnownToBeAPowerOfTwo(SI->getFalseValue(), OrZero, Depth, Q, DL);

  if (OrZero && match(V, m_And(m_Value(X), m_Value(Y)))) {
    // A power of two and'd with anything is a power of two or zero.
    if (isKnownToBeAPowerOfTwo(X, /*OrZero*/ true, Depth, Q, DL) ||
        isKnownToBeAPowerOfTwo(Y, /*OrZero*/ true, Depth, Q, DL))
      return true;
    // X & (-X) is always a power of two or zero.
    if (match(X, m_Neg(m_Specific(Y))) || match(Y, m_Neg(m_Specific(X))))
      return true;
    return false;
  }

  // Adding a power-of-two or zero to the same power-of-two or zero yields
  // either the original power-of-two, a larger power-of-two or zero.
  if (match(V, m_Add(m_Value(X), m_Value(Y)))) {
    OverflowingBinaryOperator *VOBO = cast<OverflowingBinaryOperator>(V);
    if (OrZero || VOBO->hasNoUnsignedWrap() || VOBO->hasNoSignedWrap()) {
      if (match(X, m_And(m_Specific(Y), m_Value())) ||
          match(X, m_And(m_Value(), m_Specific(Y))))
        if (isKnownToBeAPowerOfTwo(Y, OrZero, Depth, Q, DL))
          return true;
      if (match(Y, m_And(m_Specific(X), m_Value())) ||
          match(Y, m_And(m_Value(), m_Specific(X))))
        if (isKnownToBeAPowerOfTwo(X, OrZero, Depth, Q, DL))
          return true;

      unsigned BitWidth = V->getType()->getScalarSizeInBits();
      APInt LHSZeroBits(BitWidth, 0), LHSOneBits(BitWidth, 0);
      computeKnownBits(X, LHSZeroBits, LHSOneBits, DL, Depth, Q);

      APInt RHSZeroBits(BitWidth, 0), RHSOneBits(BitWidth, 0);
      computeKnownBits(Y, RHSZeroBits, RHSOneBits, DL, Depth, Q);
      // If i8 V is a power of two or zero:
      //  ZeroBits: 1 1 1 0 1 1 1 1
      // ~ZeroBits: 0 0 0 1 0 0 0 0
      if ((~(LHSZeroBits & RHSZeroBits)).isPowerOf2())
        // If OrZero isn't set, we cannot give back a zero result.
        // Make sure either the LHS or RHS has a bit set.
        if (OrZero || RHSOneBits.getBoolValue() || LHSOneBits.getBoolValue())
          return true;
    }
  }

  // An exact divide or right shift can only shift off zero bits, so the result
  // is a power of two only if the first operand is a power of two and not
  // copying a sign bit (sdiv int_min, 2).
  if (match(V, m_Exact(m_LShr(m_Value(), m_Value()))) ||
      match(V, m_Exact(m_UDiv(m_Value(), m_Value())))) {
    return isKnownToBeAPowerOfTwo(cast<Operator>(V)->getOperand(0), OrZero,
                                  Depth, Q, DL);
  }

  return false;
}

/// \brief Test whether a GEP's result is known to be non-null.
///
/// Uses properties inherent in a GEP to try to determine whether it is known
/// to be non-null.
///
/// Currently this routine does not support vector GEPs.
static bool isGEPKnownNonNull(GEPOperator *GEP, const DataLayout &DL,
                              unsigned Depth, const Query &Q) {
  if (!GEP->isInBounds() || GEP->getPointerAddressSpace() != 0)
    return false;

  // FIXME: Support vector-GEPs.
  assert(GEP->getType()->isPointerTy() && "We only support plain pointer GEP");

  // If the base pointer is non-null, we cannot walk to a null address with an
  // inbounds GEP in address space zero.
  if (isKnownNonZero(GEP->getPointerOperand(), DL, Depth, Q))
    return true;

  // Walk the GEP operands and see if any operand introduces a non-zero offset.
  // If so, then the GEP cannot produce a null pointer, as doing so would
  // inherently violate the inbounds contract within address space zero.
  for (gep_type_iterator GTI = gep_type_begin(GEP), GTE = gep_type_end(GEP);
       GTI != GTE; ++GTI) {
    // Struct types are easy -- they must always be indexed by a constant.
    if (StructType *STy = dyn_cast<StructType>(*GTI)) {
      ConstantInt *OpC = cast<ConstantInt>(GTI.getOperand());
      unsigned ElementIdx = OpC->getZExtValue();
      const StructLayout *SL = DL.getStructLayout(STy);
      uint64_t ElementOffset = SL->getElementOffset(ElementIdx);
      if (ElementOffset > 0)
        return true;
      continue;
    }

    // If we have a zero-sized type, the index doesn't matter. Keep looping.
    if (DL.getTypeAllocSize(GTI.getIndexedType()) == 0)
      continue;

    // Fast path the constant operand case both for efficiency and so we don't
    // increment Depth when just zipping down an all-constant GEP.
    if (ConstantInt *OpC = dyn_cast<ConstantInt>(GTI.getOperand())) {
      if (!OpC->isZero())
        return true;
      continue;
    }

    // We post-increment Depth here because while isKnownNonZero increments it
    // as well, when we pop back up that increment won't persist. We don't want
    // to recurse 10k times just because we have 10k GEP operands. We don't
    // bail completely out because we want to handle constant GEPs regardless
    // of depth.
    if (Depth++ >= MaxDepth)
      continue;

    if (isKnownNonZero(GTI.getOperand(), DL, Depth, Q))
      return true;
  }

  return false;
}

/// Does the 'Range' metadata (which must be a valid MD_range operand list)
/// ensure that the value it's attached to is never Value?  'RangeType' is
/// is the type of the value described by the range.
static bool rangeMetadataExcludesValue(MDNode* Ranges,
                                       const APInt& Value) {
  const unsigned NumRanges = Ranges->getNumOperands() / 2;
  assert(NumRanges >= 1);
  for (unsigned i = 0; i < NumRanges; ++i) {
    ConstantInt *Lower =
        mdconst::extract<ConstantInt>(Ranges->getOperand(2 * i + 0));
    ConstantInt *Upper =
        mdconst::extract<ConstantInt>(Ranges->getOperand(2 * i + 1));
    ConstantRange Range(Lower->getValue(), Upper->getValue());
    if (Range.contains(Value))
      return false;
  }
  return true;
}

/// Return true if the given value is known to be non-zero when defined.
/// For vectors return true if every element is known to be non-zero when
/// defined. Supports values with integer or pointer type and vectors of
/// integers.
bool isKnownNonZero(Value *V, const DataLayout &DL, unsigned Depth,
                    const Query &Q) {
  if (Constant *C = dyn_cast<Constant>(V)) {
    if (C->isNullValue())
      return false;
    if (isa<ConstantInt>(C))
      // Must be non-zero due to null test above.
      return true;
    // TODO: Handle vectors
    return false;
  }

  if (Instruction* I = dyn_cast<Instruction>(V)) {
    if (MDNode *Ranges = I->getMetadata(LLVMContext::MD_range)) {
      // If the possible ranges don't contain zero, then the value is
      // definitely non-zero.
      if (IntegerType* Ty = dyn_cast<IntegerType>(V->getType())) {
        const APInt ZeroValue(Ty->getBitWidth(), 0);
        if (rangeMetadataExcludesValue(Ranges, ZeroValue))
          return true;
      }
    }
  }

  // The remaining tests are all recursive, so bail out if we hit the limit.
  if (Depth++ >= MaxDepth)
    return false;

  // Check for pointer simplifications.
  if (V->getType()->isPointerTy()) {
    if (isKnownNonNull(V))
      return true; 
    if (GEPOperator *GEP = dyn_cast<GEPOperator>(V))
      if (isGEPKnownNonNull(GEP, DL, Depth, Q))
        return true;
  }

  unsigned BitWidth = getBitWidth(V->getType()->getScalarType(), DL);

  // X | Y != 0 if X != 0 or Y != 0.
  Value *X = nullptr, *Y = nullptr;
  if (match(V, m_Or(m_Value(X), m_Value(Y))))
    return isKnownNonZero(X, DL, Depth, Q) || isKnownNonZero(Y, DL, Depth, Q);

  // ext X != 0 if X != 0.
  if (isa<SExtInst>(V) || isa<ZExtInst>(V))
    return isKnownNonZero(cast<Instruction>(V)->getOperand(0), DL, Depth, Q);

  // shl X, Y != 0 if X is odd.  Note that the value of the shift is undefined
  // if the lowest bit is shifted off the end.
  if (BitWidth && match(V, m_Shl(m_Value(X), m_Value(Y)))) {
    // shl nuw can't remove any non-zero bits.
    OverflowingBinaryOperator *BO = cast<OverflowingBinaryOperator>(V);
    if (BO->hasNoUnsignedWrap())
      return isKnownNonZero(X, DL, Depth, Q);

    APInt KnownZero(BitWidth, 0);
    APInt KnownOne(BitWidth, 0);
    computeKnownBits(X, KnownZero, KnownOne, DL, Depth, Q);
    if (KnownOne[0])
      return true;
  }
  // shr X, Y != 0 if X is negative.  Note that the value of the shift is not
  // defined if the sign bit is shifted off the end.
  else if (match(V, m_Shr(m_Value(X), m_Value(Y)))) {
    // shr exact can only shift out zero bits.
    PossiblyExactOperator *BO = cast<PossiblyExactOperator>(V);
    if (BO->isExact())
      return isKnownNonZero(X, DL, Depth, Q);

    bool XKnownNonNegative, XKnownNegative;
    ComputeSignBit(X, XKnownNonNegative, XKnownNegative, DL, Depth, Q);
    if (XKnownNegative)
      return true;
  }
  // div exact can only produce a zero if the dividend is zero.
  else if (match(V, m_Exact(m_IDiv(m_Value(X), m_Value())))) {
    return isKnownNonZero(X, DL, Depth, Q);
  }
  // X + Y.
  else if (match(V, m_Add(m_Value(X), m_Value(Y)))) {
    bool XKnownNonNegative, XKnownNegative;
    bool YKnownNonNegative, YKnownNegative;
    ComputeSignBit(X, XKnownNonNegative, XKnownNegative, DL, Depth, Q);
    ComputeSignBit(Y, YKnownNonNegative, YKnownNegative, DL, Depth, Q);

    // If X and Y are both non-negative (as signed values) then their sum is not
    // zero unless both X and Y are zero.
    if (XKnownNonNegative && YKnownNonNegative)
      if (isKnownNonZero(X, DL, Depth, Q) || isKnownNonZero(Y, DL, Depth, Q))
        return true;

    // If X and Y are both negative (as signed values) then their sum is not
    // zero unless both X and Y equal INT_MIN.
    if (BitWidth && XKnownNegative && YKnownNegative) {
      APInt KnownZero(BitWidth, 0);
      APInt KnownOne(BitWidth, 0);
      APInt Mask = APInt::getSignedMaxValue(BitWidth);
      // The sign bit of X is set.  If some other bit is set then X is not equal
      // to INT_MIN.
      computeKnownBits(X, KnownZero, KnownOne, DL, Depth, Q);
      if ((KnownOne & Mask) != 0)
        return true;
      // The sign bit of Y is set.  If some other bit is set then Y is not equal
      // to INT_MIN.
      computeKnownBits(Y, KnownZero, KnownOne, DL, Depth, Q);
      if ((KnownOne & Mask) != 0)
        return true;
    }

    // The sum of a non-negative number and a power of two is not zero.
    if (XKnownNonNegative &&
        isKnownToBeAPowerOfTwo(Y, /*OrZero*/ false, Depth, Q, DL))
      return true;
    if (YKnownNonNegative &&
        isKnownToBeAPowerOfTwo(X, /*OrZero*/ false, Depth, Q, DL))
      return true;
  }
  // X * Y.
  else if (match(V, m_Mul(m_Value(X), m_Value(Y)))) {
    OverflowingBinaryOperator *BO = cast<OverflowingBinaryOperator>(V);
    // If X and Y are non-zero then so is X * Y as long as the multiplication
    // does not overflow.
    if ((BO->hasNoSignedWrap() || BO->hasNoUnsignedWrap()) &&
        isKnownNonZero(X, DL, Depth, Q) && isKnownNonZero(Y, DL, Depth, Q))
      return true;
  }
  // (C ? X : Y) != 0 if X != 0 and Y != 0.
  else if (SelectInst *SI = dyn_cast<SelectInst>(V)) {
    if (isKnownNonZero(SI->getTrueValue(), DL, Depth, Q) &&
        isKnownNonZero(SI->getFalseValue(), DL, Depth, Q))
      return true;
  }

  if (!BitWidth) return false;
  APInt KnownZero(BitWidth, 0);
  APInt KnownOne(BitWidth, 0);
  computeKnownBits(V, KnownZero, KnownOne, DL, Depth, Q);
  return KnownOne != 0;
}

/// Return true if 'V & Mask' is known to be zero.  We use this predicate to
/// simplify operations downstream. Mask is known to be zero for bits that V
/// cannot have.
///
/// This function is defined on values with integer type, values with pointer
/// type, and vectors of integers.  In the case
/// where V is a vector, the mask, known zero, and known one values are the
/// same width as the vector element, and the bit is set only if it is true
/// for all of the elements in the vector.
bool MaskedValueIsZero(Value *V, const APInt &Mask, const DataLayout &DL,
                       unsigned Depth, const Query &Q) {
  APInt KnownZero(Mask.getBitWidth(), 0), KnownOne(Mask.getBitWidth(), 0);
  computeKnownBits(V, KnownZero, KnownOne, DL, Depth, Q);
  return (KnownZero & Mask) == Mask;
}



/// Return the number of times the sign bit of the register is replicated into
/// the other bits. We know that at least 1 bit is always equal to the sign bit
/// (itself), but other cases can give us information. For example, immediately
/// after an "ashr X, 2", we know that the top 3 bits are all equal to each
/// other, so we return 3.
///
/// 'Op' must have a scalar integer type.
///
unsigned ComputeNumSignBits(Value *V, const DataLayout &DL, unsigned Depth,
                            const Query &Q) {
  unsigned TyBits = DL.getTypeSizeInBits(V->getType()->getScalarType());
  unsigned Tmp, Tmp2;
  unsigned FirstAnswer = 1;

  // Note that ConstantInt is handled by the general computeKnownBits case
  // below.

  if (Depth == 6)
    return 1;  // Limit search depth.

  Operator *U = dyn_cast<Operator>(V);
  switch (Operator::getOpcode(V)) {
  default: break;
  case Instruction::SExt:
    Tmp = TyBits - U->getOperand(0)->getType()->getScalarSizeInBits();
    return ComputeNumSignBits(U->getOperand(0), DL, Depth + 1, Q) + Tmp;

  case Instruction::SDiv: {
    const APInt *Denominator;
    // sdiv X, C -> adds log(C) sign bits.
    if (match(U->getOperand(1), m_APInt(Denominator))) {

      // Ignore non-positive denominator.
      if (!Denominator->isStrictlyPositive())
        break;

      // Calculate the incoming numerator bits.
      unsigned NumBits = ComputeNumSignBits(U->getOperand(0), DL, Depth + 1, Q);

      // Add floor(log(C)) bits to the numerator bits.
      return std::min(TyBits, NumBits + Denominator->logBase2());
    }
    break;
  }

  case Instruction::SRem: {
    const APInt *Denominator;
    // srem X, C -> we know that the result is within [-C+1,C) when C is a
    // positive constant.  This let us put a lower bound on the number of sign
    // bits.
    if (match(U->getOperand(1), m_APInt(Denominator))) {

      // Ignore non-positive denominator.
      if (!Denominator->isStrictlyPositive())
        break;

      // Calculate the incoming numerator bits. SRem by a positive constant
      // can't lower the number of sign bits.
      unsigned NumrBits =
          ComputeNumSignBits(U->getOperand(0), DL, Depth + 1, Q);

      // Calculate the leading sign bit constraints by examining the
      // denominator.  Given that the denominator is positive, there are two
      // cases:
      //
      //  1. the numerator is positive.  The result range is [0,C) and [0,C) u<
      //     (1 << ceilLogBase2(C)).
      //
      //  2. the numerator is negative.  Then the result range is (-C,0] and
      //     integers in (-C,0] are either 0 or >u (-1 << ceilLogBase2(C)).
      //
      // Thus a lower bound on the number of sign bits is `TyBits -
      // ceilLogBase2(C)`.

      unsigned ResBits = TyBits - Denominator->ceilLogBase2();
      return std::max(NumrBits, ResBits);
    }
    break;
  }

  case Instruction::AShr: {
    Tmp = ComputeNumSignBits(U->getOperand(0), DL, Depth + 1, Q);
    // ashr X, C   -> adds C sign bits.  Vectors too.
    const APInt *ShAmt;
    if (match(U->getOperand(1), m_APInt(ShAmt))) {
      Tmp += ShAmt->getZExtValue();
      if (Tmp > TyBits) Tmp = TyBits;
    }
    return Tmp;
  }
  case Instruction::Shl: {
    const APInt *ShAmt;
    if (match(U->getOperand(1), m_APInt(ShAmt))) {
      // shl destroys sign bits.
      Tmp = ComputeNumSignBits(U->getOperand(0), DL, Depth + 1, Q);
      Tmp2 = ShAmt->getZExtValue();
      if (Tmp2 >= TyBits ||      // Bad shift.
          Tmp2 >= Tmp) break;    // Shifted all sign bits out.
      return Tmp - Tmp2;
    }
    break;
  }
  case Instruction::And:
  case Instruction::Or:
  case Instruction::Xor:    // NOT is handled here.
    // Logical binary ops preserve the number of sign bits at the worst.
    Tmp = ComputeNumSignBits(U->getOperand(0), DL, Depth + 1, Q);
    if (Tmp != 1) {
      Tmp2 = ComputeNumSignBits(U->getOperand(1), DL, Depth + 1, Q);
      FirstAnswer = std::min(Tmp, Tmp2);
      // We computed what we know about the sign bits as our first
      // answer. Now proceed to the generic code that uses
      // computeKnownBits, and pick whichever answer is better.
    }
    break;

  case Instruction::Select:
    Tmp = ComputeNumSignBits(U->getOperand(1), DL, Depth + 1, Q);
    if (Tmp == 1) return 1;  // Early out.
    Tmp2 = ComputeNumSignBits(U->getOperand(2), DL, Depth + 1, Q);
    return std::min(Tmp, Tmp2);

  case Instruction::Add:
    // Add can have at most one carry bit.  Thus we know that the output
    // is, at worst, one more bit than the inputs.
    Tmp = ComputeNumSignBits(U->getOperand(0), DL, Depth + 1, Q);
    if (Tmp == 1) return 1;  // Early out.

    // Special case decrementing a value (ADD X, -1):
    if (const auto *CRHS = dyn_cast<Constant>(U->getOperand(1)))
      if (CRHS->isAllOnesValue()) {
        APInt KnownZero(TyBits, 0), KnownOne(TyBits, 0);
        computeKnownBits(U->getOperand(0), KnownZero, KnownOne, DL, Depth + 1,
                         Q);

        // If the input is known to be 0 or 1, the output is 0/-1, which is all
        // sign bits set.
        if ((KnownZero | APInt(TyBits, 1)).isAllOnesValue())
          return TyBits;

        // If we are subtracting one from a positive number, there is no carry
        // out of the result.
        if (KnownZero.isNegative())
          return Tmp;
      }

    Tmp2 = ComputeNumSignBits(U->getOperand(1), DL, Depth + 1, Q);
    if (Tmp2 == 1) return 1;
    return std::min(Tmp, Tmp2)-1;

  case Instruction::Sub:
    Tmp2 = ComputeNumSignBits(U->getOperand(1), DL, Depth + 1, Q);
    if (Tmp2 == 1) return 1;

    // Handle NEG.
    if (const auto *CLHS = dyn_cast<Constant>(U->getOperand(0)))
      if (CLHS->isNullValue()) {
        APInt KnownZero(TyBits, 0), KnownOne(TyBits, 0);
        computeKnownBits(U->getOperand(1), KnownZero, KnownOne, DL, Depth + 1,
                         Q);
        // If the input is known to be 0 or 1, the output is 0/-1, which is all
        // sign bits set.
        if ((KnownZero | APInt(TyBits, 1)).isAllOnesValue())
          return TyBits;

        // If the input is known to be positive (the sign bit is known clear),
        // the output of the NEG has the same number of sign bits as the input.
        if (KnownZero.isNegative())
          return Tmp2;

        // Otherwise, we treat this like a SUB.
      }

    // Sub can have at most one carry bit.  Thus we know that the output
    // is, at worst, one more bit than the inputs.
    Tmp = ComputeNumSignBits(U->getOperand(0), DL, Depth + 1, Q);
    if (Tmp == 1) return 1;  // Early out.
    return std::min(Tmp, Tmp2)-1;

  case Instruction::PHI: {
    PHINode *PN = cast<PHINode>(U);
    unsigned NumIncomingValues = PN->getNumIncomingValues();
    // Don't analyze large in-degree PHIs.
    if (NumIncomingValues > 4) break;
    // Unreachable blocks may have zero-operand PHI nodes.
    if (NumIncomingValues == 0) break;

    // Take the minimum of all incoming values.  This can't infinitely loop
    // because of our depth threshold.
    Tmp = ComputeNumSignBits(PN->getIncomingValue(0), DL, Depth + 1, Q);
    for (unsigned i = 1, e = NumIncomingValues; i != e; ++i) {
      if (Tmp == 1) return Tmp;
      Tmp = std::min(
          Tmp, ComputeNumSignBits(PN->getIncomingValue(i), DL, Depth + 1, Q));
    }
    return Tmp;
  }

  case Instruction::Trunc:
    // FIXME: it's tricky to do anything useful for this, but it is an important
    // case for targets like X86.
    break;
  }

  // Finally, if we can prove that the top bits of the result are 0's or 1's,
  // use this information.
  APInt KnownZero(TyBits, 0), KnownOne(TyBits, 0);
  APInt Mask;
  computeKnownBits(V, KnownZero, KnownOne, DL, Depth, Q);

  if (KnownZero.isNegative()) {        // sign bit is 0
    Mask = KnownZero;
  } else if (KnownOne.isNegative()) {  // sign bit is 1;
    Mask = KnownOne;
  } else {
    // Nothing known.
    return FirstAnswer;
  }

  // Okay, we know that the sign bit in Mask is set.  Use CLZ to determine
  // the number of identical bits in the top of the input value.
  Mask = ~Mask;
  Mask <<= Mask.getBitWidth()-TyBits;
  // Return # leading zeros.  We use 'min' here in case Val was zero before
  // shifting.  We don't want to return '64' as for an i32 "0".
  return std::max(FirstAnswer, std::min(TyBits, Mask.countLeadingZeros()));
}

/// This function computes the integer multiple of Base that equals V.
/// If successful, it returns true and returns the multiple in
/// Multiple. If unsuccessful, it returns false. It looks
/// through SExt instructions only if LookThroughSExt is true.
bool llvm::ComputeMultiple(Value *V, unsigned Base, Value *&Multiple,
                           bool LookThroughSExt, unsigned Depth) {
  const unsigned MaxDepth = 6;

  assert(V && "No Value?");
  assert(Depth <= MaxDepth && "Limit Search Depth");
  assert(V->getType()->isIntegerTy() && "Not integer or pointer type!");

  Type *T = V->getType();

  ConstantInt *CI = dyn_cast<ConstantInt>(V);

  if (Base == 0)
    return false;

  if (Base == 1) {
    Multiple = V;
    return true;
  }

  ConstantExpr *CO = dyn_cast<ConstantExpr>(V);
  Constant *BaseVal = ConstantInt::get(T, Base);
  if (CO && CO == BaseVal) {
    // Multiple is 1.
    Multiple = ConstantInt::get(T, 1);
    return true;
  }

  if (CI && CI->getZExtValue() % Base == 0) {
    Multiple = ConstantInt::get(T, CI->getZExtValue() / Base);
    return true;
  }

  if (Depth == MaxDepth) return false;  // Limit search depth.

  Operator *I = dyn_cast<Operator>(V);
  if (!I) return false;

  switch (I->getOpcode()) {
  default: break;
  case Instruction::SExt:
    if (!LookThroughSExt) return false;
    // otherwise fall through to ZExt
  case Instruction::ZExt:
    return ComputeMultiple(I->getOperand(0), Base, Multiple,
                           LookThroughSExt, Depth+1);
  case Instruction::Shl:
  case Instruction::Mul: {
    Value *Op0 = I->getOperand(0);
    Value *Op1 = I->getOperand(1);

    if (I->getOpcode() == Instruction::Shl) {
      ConstantInt *Op1CI = dyn_cast<ConstantInt>(Op1);
      if (!Op1CI) return false;
      // Turn Op0 << Op1 into Op0 * 2^Op1
      APInt Op1Int = Op1CI->getValue();
      uint64_t BitToSet = Op1Int.getLimitedValue(Op1Int.getBitWidth() - 1);
      APInt API(Op1Int.getBitWidth(), 0);
      API.setBit(BitToSet);
      Op1 = ConstantInt::get(V->getContext(), API);
    }

    Value *Mul0 = nullptr;
    if (ComputeMultiple(Op0, Base, Mul0, LookThroughSExt, Depth+1)) {
      if (Constant *Op1C = dyn_cast<Constant>(Op1))
        if (Constant *MulC = dyn_cast<Constant>(Mul0)) {
          if (Op1C->getType()->getPrimitiveSizeInBits() <
              MulC->getType()->getPrimitiveSizeInBits())
            Op1C = ConstantExpr::getZExt(Op1C, MulC->getType());
          if (Op1C->getType()->getPrimitiveSizeInBits() >
              MulC->getType()->getPrimitiveSizeInBits())
            MulC = ConstantExpr::getZExt(MulC, Op1C->getType());

          // V == Base * (Mul0 * Op1), so return (Mul0 * Op1)
          Multiple = ConstantExpr::getMul(MulC, Op1C);
          return true;
        }

      if (ConstantInt *Mul0CI = dyn_cast<ConstantInt>(Mul0))
        if (Mul0CI->getValue() == 1) {
          // V == Base * Op1, so return Op1
          Multiple = Op1;
          return true;
        }
    }

    Value *Mul1 = nullptr;
    if (ComputeMultiple(Op1, Base, Mul1, LookThroughSExt, Depth+1)) {
      if (Constant *Op0C = dyn_cast<Constant>(Op0))
        if (Constant *MulC = dyn_cast<Constant>(Mul1)) {
          if (Op0C->getType()->getPrimitiveSizeInBits() <
              MulC->getType()->getPrimitiveSizeInBits())
            Op0C = ConstantExpr::getZExt(Op0C, MulC->getType());
          if (Op0C->getType()->getPrimitiveSizeInBits() >
              MulC->getType()->getPrimitiveSizeInBits())
            MulC = ConstantExpr::getZExt(MulC, Op0C->getType());

          // V == Base * (Mul1 * Op0), so return (Mul1 * Op0)
          Multiple = ConstantExpr::getMul(MulC, Op0C);
          return true;
        }

      if (ConstantInt *Mul1CI = dyn_cast<ConstantInt>(Mul1))
        if (Mul1CI->getValue() == 1) {
          // V == Base * Op0, so return Op0
          Multiple = Op0;
          return true;
        }
    }
  }
  }

  // We could not determine if V is a multiple of Base.
  return false;
}

/// Return true if we can prove that the specified FP value is never equal to
/// -0.0.
///
/// NOTE: this function will need to be revisited when we support non-default
/// rounding modes!
///
bool llvm::CannotBeNegativeZero(const Value *V, unsigned Depth) {
  if (const ConstantFP *CFP = dyn_cast<ConstantFP>(V))
    return !CFP->getValueAPF().isNegZero();

  // FIXME: Magic number! At the least, this should be given a name because it's
  // used similarly in CannotBeOrderedLessThanZero(). A better fix may be to
  // expose it as a parameter, so it can be used for testing / experimenting.
  if (Depth == 6)
    return false;  // Limit search depth.

  const Operator *I = dyn_cast<Operator>(V);
  if (!I) return false;

  // Check if the nsz fast-math flag is set
  if (const FPMathOperator *FPO = dyn_cast<FPMathOperator>(I))
    if (FPO->hasNoSignedZeros())
      return true;

  // (add x, 0.0) is guaranteed to return +0.0, not -0.0.
  if (I->getOpcode() == Instruction::FAdd)
    if (ConstantFP *CFP = dyn_cast<ConstantFP>(I->getOperand(1)))
      if (CFP->isNullValue())
        return true;

  // sitofp and uitofp turn into +0.0 for zero.
  if (isa<SIToFPInst>(I) || isa<UIToFPInst>(I))
    return true;

  if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(I))
    // sqrt(-0.0) = -0.0, no other negative results are possible.
    if (II->getIntrinsicID() == Intrinsic::sqrt)
      return CannotBeNegativeZero(II->getArgOperand(0), Depth+1);

  if (const CallInst *CI = dyn_cast<CallInst>(I))
    if (const Function *F = CI->getCalledFunction()) {
      if (F->isDeclaration()) {
        // abs(x) != -0.0
        if (F->getName() == "abs") return true;
        // fabs[lf](x) != -0.0
        if (F->getName() == "fabs") return true;
        if (F->getName() == "fabsf") return true;
        if (F->getName() == "fabsl") return true;
        if (F->getName() == "sqrt" || F->getName() == "sqrtf" ||
            F->getName() == "sqrtl")
          return CannotBeNegativeZero(CI->getArgOperand(0), Depth+1);
      }
    }

  return false;
}

bool llvm::CannotBeOrderedLessThanZero(const Value *V, unsigned Depth) {
  if (const ConstantFP *CFP = dyn_cast<ConstantFP>(V))
    return !CFP->getValueAPF().isNegative() || CFP->getValueAPF().isZero();

  // FIXME: Magic number! At the least, this should be given a name because it's
  // used similarly in CannotBeNegativeZero(). A better fix may be to
  // expose it as a parameter, so it can be used for testing / experimenting.
  if (Depth == 6)
    return false;  // Limit search depth.

  const Operator *I = dyn_cast<Operator>(V);
  if (!I) return false;

  switch (I->getOpcode()) {
  default: break;
  case Instruction::FMul:
    // x*x is always non-negative or a NaN.
    if (I->getOperand(0) == I->getOperand(1)) 
      return true;
    // Fall through
  case Instruction::FAdd:
  case Instruction::FDiv:
  case Instruction::FRem:
    return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1) &&
           CannotBeOrderedLessThanZero(I->getOperand(1), Depth+1);
  case Instruction::FPExt:
  case Instruction::FPTrunc:
    // Widening/narrowing never change sign.
    return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1);
  case Instruction::Call: 
    if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(I)) 
      switch (II->getIntrinsicID()) {
      default: break;
      case Intrinsic::exp:
      case Intrinsic::exp2:
      case Intrinsic::fabs:
      case Intrinsic::sqrt:
        return true;
      case Intrinsic::powi: 
        if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
          // powi(x,n) is non-negative if n is even.
          if (CI->getBitWidth() <= 64 && CI->getSExtValue() % 2u == 0)
            return true;
        }
        return CannotBeOrderedLessThanZero(I->getOperand(0), Depth+1);
      case Intrinsic::fma:
      case Intrinsic::fmuladd:
        // x*x+y is non-negative if y is non-negative.
        return I->getOperand(0) == I->getOperand(1) && 
               CannotBeOrderedLessThanZero(I->getOperand(2), Depth+1);
      }
    break;
  }
  return false; 
}

/// If the specified value can be set by repeating the same byte in memory,
/// return the i8 value that it is represented with.  This is
/// true for all i8 values obviously, but is also true for i32 0, i32 -1,
/// i16 0xF0F0, double 0.0 etc.  If the value can't be handled with a repeated
/// byte store (e.g. i16 0x1234), return null.
Value *llvm::isBytewiseValue(Value *V) {
  // All byte-wide stores are splatable, even of arbitrary variables.
  if (V->getType()->isIntegerTy(8)) return V;

  // Handle 'null' ConstantArrayZero etc.
  if (Constant *C = dyn_cast<Constant>(V))
    if (C->isNullValue())
      return Constant::getNullValue(Type::getInt8Ty(V->getContext()));

  // Constant float and double values can be handled as integer values if the
  // corresponding integer value is "byteable".  An important case is 0.0.
  if (ConstantFP *CFP = dyn_cast<ConstantFP>(V)) {
    if (CFP->getType()->isFloatTy())
      V = ConstantExpr::getBitCast(CFP, Type::getInt32Ty(V->getContext()));
    if (CFP->getType()->isDoubleTy())
      V = ConstantExpr::getBitCast(CFP, Type::getInt64Ty(V->getContext()));
    // Don't handle long double formats, which have strange constraints.
  }

  // We can handle constant integers that are multiple of 8 bits.
  if (ConstantInt *CI = dyn_cast<ConstantInt>(V)) {
    if (CI->getBitWidth() % 8 == 0) {
      assert(CI->getBitWidth() > 8 && "8 bits should be handled above!");

      if (!CI->getValue().isSplat(8))
        return nullptr;
      return ConstantInt::get(V->getContext(), CI->getValue().trunc(8));
    }
  }

  // A ConstantDataArray/Vector is splatable if all its members are equal and
  // also splatable.
  if (ConstantDataSequential *CA = dyn_cast<ConstantDataSequential>(V)) {
    Value *Elt = CA->getElementAsConstant(0);
    Value *Val = isBytewiseValue(Elt);
    if (!Val)
      return nullptr;

    for (unsigned I = 1, E = CA->getNumElements(); I != E; ++I)
      if (CA->getElementAsConstant(I) != Elt)
        return nullptr;

    return Val;
  }

  // Conceptually, we could handle things like:
  //   %a = zext i8 %X to i16
  //   %b = shl i16 %a, 8
  //   %c = or i16 %a, %b
  // but until there is an example that actually needs this, it doesn't seem
  // worth worrying about.
  return nullptr;
}


// This is the recursive version of BuildSubAggregate. It takes a few different
// arguments. Idxs is the index within the nested struct From that we are
// looking at now (which is of type IndexedType). IdxSkip is the number of
// indices from Idxs that should be left out when inserting into the resulting
// struct. To is the result struct built so far, new insertvalue instructions
// build on that.
static Value *BuildSubAggregate(Value *From, Value* To, Type *IndexedType,
                                SmallVectorImpl<unsigned> &Idxs,
                                unsigned IdxSkip,
                                Instruction *InsertBefore) {
  llvm::StructType *STy = dyn_cast<llvm::StructType>(IndexedType);
  if (STy) {
    // Save the original To argument so we can modify it
    Value *OrigTo = To;
    // General case, the type indexed by Idxs is a struct
    for (unsigned i = 0, e = STy->getNumElements(); i != e; ++i) {
      // Process each struct element recursively
      Idxs.push_back(i);
      Value *PrevTo = To;
      To = BuildSubAggregate(From, To, STy->getElementType(i), Idxs, IdxSkip,
                             InsertBefore);
      Idxs.pop_back();
      if (!To) {
        // Couldn't find any inserted value for this index? Cleanup
        while (PrevTo != OrigTo) {
          InsertValueInst* Del = cast<InsertValueInst>(PrevTo);
          PrevTo = Del->getAggregateOperand();
          Del->eraseFromParent();
        }
        // Stop processing elements
        break;
      }
    }
    // If we successfully found a value for each of our subaggregates
    if (To)
      return To;
  }
  // Base case, the type indexed by SourceIdxs is not a struct, or not all of
  // the struct's elements had a value that was inserted directly. In the latter
  // case, perhaps we can't determine each of the subelements individually, but
  // we might be able to find the complete struct somewhere.

  // Find the value that is at that particular spot
  Value *V = FindInsertedValue(From, Idxs);

  if (!V)
    return nullptr;

  // Insert the value in the new (sub) aggregrate
  return llvm::InsertValueInst::Create(To, V, makeArrayRef(Idxs).slice(IdxSkip),
                                       "tmp", InsertBefore);
}

// This helper takes a nested struct and extracts a part of it (which is again a
// struct) into a new value. For example, given the struct:
// { a, { b, { c, d }, e } }
// and the indices "1, 1" this returns
// { c, d }.
//
// It does this by inserting an insertvalue for each element in the resulting
// struct, as opposed to just inserting a single struct. This will only work if
// each of the elements of the substruct are known (ie, inserted into From by an
// insertvalue instruction somewhere).
//
// All inserted insertvalue instructions are inserted before InsertBefore
static Value *BuildSubAggregate(Value *From, ArrayRef<unsigned> idx_range,
                                Instruction *InsertBefore) {
  assert(InsertBefore && "Must have someplace to insert!");
  Type *IndexedType = ExtractValueInst::getIndexedType(From->getType(),
                                                             idx_range);
  Value *To = UndefValue::get(IndexedType);
  SmallVector<unsigned, 10> Idxs(idx_range.begin(), idx_range.end());
  unsigned IdxSkip = Idxs.size();

  return BuildSubAggregate(From, To, IndexedType, Idxs, IdxSkip, InsertBefore);
}

/// Given an aggregrate and an sequence of indices, see if
/// the scalar value indexed is already around as a register, for example if it
/// were inserted directly into the aggregrate.
///
/// If InsertBefore is not null, this function will duplicate (modified)
/// insertvalues when a part of a nested struct is extracted.
Value *llvm::FindInsertedValue(Value *V, ArrayRef<unsigned> idx_range,
                               Instruction *InsertBefore) {
  // Nothing to index? Just return V then (this is useful at the end of our
  // recursion).
  if (idx_range.empty())
    return V;
  // We have indices, so V should have an indexable type.
  assert((V->getType()->isStructTy() || V->getType()->isArrayTy()) &&
         "Not looking at a struct or array?");
  assert(ExtractValueInst::getIndexedType(V->getType(), idx_range) &&
         "Invalid indices for type?");

  if (Constant *C = dyn_cast<Constant>(V)) {
    C = C->getAggregateElement(idx_range[0]);
    if (!C) return nullptr;
    return FindInsertedValue(C, idx_range.slice(1), InsertBefore);
  }

  if (InsertValueInst *I = dyn_cast<InsertValueInst>(V)) {
    // Loop the indices for the insertvalue instruction in parallel with the
    // requested indices
    const unsigned *req_idx = idx_range.begin();
    for (const unsigned *i = I->idx_begin(), *e = I->idx_end();
         i != e; ++i, ++req_idx) {
      if (req_idx == idx_range.end()) {
        // We can't handle this without inserting insertvalues
        if (!InsertBefore)
          return nullptr;

        // The requested index identifies a part of a nested aggregate. Handle
        // this specially. For example,
        // %A = insertvalue { i32, {i32, i32 } } undef, i32 10, 1, 0
        // %B = insertvalue { i32, {i32, i32 } } %A, i32 11, 1, 1
        // %C = extractvalue {i32, { i32, i32 } } %B, 1
        // This can be changed into
        // %A = insertvalue {i32, i32 } undef, i32 10, 0
        // %C = insertvalue {i32, i32 } %A, i32 11, 1
        // which allows the unused 0,0 element from the nested struct to be
        // removed.
        return BuildSubAggregate(V, makeArrayRef(idx_range.begin(), req_idx),
                                 InsertBefore);
      }

      // This insert value inserts something else than what we are looking for.
      // See if the (aggregrate) value inserted into has the value we are
      // looking for, then.
      if (*req_idx != *i)
        return FindInsertedValue(I->getAggregateOperand(), idx_range,
                                 InsertBefore);
    }
    // If we end up here, the indices of the insertvalue match with those
    // requested (though possibly only partially). Now we recursively look at
    // the inserted value, passing any remaining indices.
    return FindInsertedValue(I->getInsertedValueOperand(),
                             makeArrayRef(req_idx, idx_range.end()),
                             InsertBefore);
  }

  if (ExtractValueInst *I = dyn_cast<ExtractValueInst>(V)) {
    // If we're extracting a value from an aggregrate that was extracted from
    // something else, we can extract from that something else directly instead.
    // However, we will need to chain I's indices with the requested indices.

    // Calculate the number of indices required
    unsigned size = I->getNumIndices() + idx_range.size();
    // Allocate some space to put the new indices in
    SmallVector<unsigned, 5> Idxs;
    Idxs.reserve(size);
    // Add indices from the extract value instruction
    Idxs.append(I->idx_begin(), I->idx_end());

    // Add requested indices
    Idxs.append(idx_range.begin(), idx_range.end());

    assert(Idxs.size() == size
           && "Number of indices added not correct?");

    return FindInsertedValue(I->getAggregateOperand(), Idxs, InsertBefore);
  }
  // Otherwise, we don't know (such as, extracting from a function return value
  // or load instruction)
  return nullptr;
}

/// Analyze the specified pointer to see if it can be expressed as a base
/// pointer plus a constant offset. Return the base and offset to the caller.
Value *llvm::GetPointerBaseWithConstantOffset(Value *Ptr, int64_t &Offset,
                                              const DataLayout &DL) {
  unsigned BitWidth = DL.getPointerTypeSizeInBits(Ptr->getType());
  APInt ByteOffset(BitWidth, 0);
  while (1) {
    if (Ptr->getType()->isVectorTy())
      break;

    if (GEPOperator *GEP = dyn_cast<GEPOperator>(Ptr)) {
      APInt GEPOffset(BitWidth, 0);
      if (!GEP->accumulateConstantOffset(DL, GEPOffset))
        break;

      ByteOffset += GEPOffset;

      Ptr = GEP->getPointerOperand();
    } else if (Operator::getOpcode(Ptr) == Instruction::BitCast ||
               Operator::getOpcode(Ptr) == Instruction::AddrSpaceCast) {
      Ptr = cast<Operator>(Ptr)->getOperand(0);
    } else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(Ptr)) {
      if (GA->mayBeOverridden())
        break;
      Ptr = GA->getAliasee();
    } else {
      break;
    }
  }
  Offset = ByteOffset.getSExtValue();
  return Ptr;
}


/// This function computes the length of a null-terminated C string pointed to
/// by V. If successful, it returns true and returns the string in Str.
/// If unsuccessful, it returns false.
bool llvm::getConstantStringInfo(const Value *V, StringRef &Str,
                                 uint64_t Offset, bool TrimAtNul) {
  assert(V);

  // Look through bitcast instructions and geps.
  V = V->stripPointerCasts();

  // If the value is a GEP instruction or constant expression, treat it as an
  // offset.
  if (const GEPOperator *GEP = dyn_cast<GEPOperator>(V)) {
    // Make sure the GEP has exactly three arguments.
    if (GEP->getNumOperands() != 3)
      return false;

    // Make sure the index-ee is a pointer to array of i8.
    PointerType *PT = cast<PointerType>(GEP->getOperand(0)->getType());
    ArrayType *AT = dyn_cast<ArrayType>(PT->getElementType());
    if (!AT || !AT->getElementType()->isIntegerTy(8))
      return false;

    // Check to make sure that the first operand of the GEP is an integer and
    // has value 0 so that we are sure we're indexing into the initializer.
    const ConstantInt *FirstIdx = dyn_cast<ConstantInt>(GEP->getOperand(1));
    if (!FirstIdx || !FirstIdx->isZero())
      return false;

    // If the second index isn't a ConstantInt, then this is a variable index
    // into the array.  If this occurs, we can't say anything meaningful about
    // the string.
    uint64_t StartIdx = 0;
    if (const ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(2)))
      StartIdx = CI->getZExtValue();
    else
      return false;
    return getConstantStringInfo(GEP->getOperand(0), Str, StartIdx + Offset,
                                 TrimAtNul);
  }

  // The GEP instruction, constant or instruction, must reference a global
  // variable that is a constant and is initialized. The referenced constant
  // initializer is the array that we'll use for optimization.
  const GlobalVariable *GV = dyn_cast<GlobalVariable>(V);
  if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer())
    return false;

  // Handle the all-zeros case
  if (GV->getInitializer()->isNullValue()) {
    // This is a degenerate case. The initializer is constant zero so the
    // length of the string must be zero.
    Str = "";
    return true;
  }

  // Must be a Constant Array
  const ConstantDataArray *Array =
    dyn_cast<ConstantDataArray>(GV->getInitializer());
  if (!Array || !Array->isString())
    return false;

  // Get the number of elements in the array
  uint64_t NumElts = Array->getType()->getArrayNumElements();

  // Start out with the entire array in the StringRef.
  Str = Array->getAsString();

  if (Offset > NumElts)
    return false;

  // Skip over 'offset' bytes.
  Str = Str.substr(Offset);

  if (TrimAtNul) {
    // Trim off the \0 and anything after it.  If the array is not nul
    // terminated, we just return the whole end of string.  The client may know
    // some other way that the string is length-bound.
    Str = Str.substr(0, Str.find('\0'));
  }
  return true;
}

// These next two are very similar to the above, but also look through PHI
// nodes.
// TODO: See if we can integrate these two together.

/// If we can compute the length of the string pointed to by
/// the specified pointer, return 'len+1'.  If we can't, return 0.
static uint64_t GetStringLengthH(Value *V, SmallPtrSetImpl<PHINode*> &PHIs) {
  // Look through noop bitcast instructions.
  V = V->stripPointerCasts();

  // If this is a PHI node, there are two cases: either we have already seen it
  // or we haven't.
  if (PHINode *PN = dyn_cast<PHINode>(V)) {
    if (!PHIs.insert(PN).second)
      return ~0ULL;  // already in the set.

    // If it was new, see if all the input strings are the same length.
    uint64_t LenSoFar = ~0ULL;
    for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
      uint64_t Len = GetStringLengthH(PN->getIncomingValue(i), PHIs);
      if (Len == 0) return 0; // Unknown length -> unknown.

      if (Len == ~0ULL) continue;

      if (Len != LenSoFar && LenSoFar != ~0ULL)
        return 0;    // Disagree -> unknown.
      LenSoFar = Len;
    }

    // Success, all agree.
    return LenSoFar;
  }

  // strlen(select(c,x,y)) -> strlen(x) ^ strlen(y)
  if (SelectInst *SI = dyn_cast<SelectInst>(V)) {
    uint64_t Len1 = GetStringLengthH(SI->getTrueValue(), PHIs);
    if (Len1 == 0) return 0;
    uint64_t Len2 = GetStringLengthH(SI->getFalseValue(), PHIs);
    if (Len2 == 0) return 0;
    if (Len1 == ~0ULL) return Len2;
    if (Len2 == ~0ULL) return Len1;
    if (Len1 != Len2) return 0;
    return Len1;
  }

  // Otherwise, see if we can read the string.
  StringRef StrData;
  if (!getConstantStringInfo(V, StrData))
    return 0;

  return StrData.size()+1;
}

/// If we can compute the length of the string pointed to by
/// the specified pointer, return 'len+1'.  If we can't, return 0.
uint64_t llvm::GetStringLength(Value *V) {
  if (!V->getType()->isPointerTy()) return 0;

  SmallPtrSet<PHINode*, 32> PHIs;
  uint64_t Len = GetStringLengthH(V, PHIs);
  // If Len is ~0ULL, we had an infinite phi cycle: this is dead code, so return
  // an empty string as a length.
  return Len == ~0ULL ? 1 : Len;
}

Value *llvm::GetUnderlyingObject(Value *V, const DataLayout &DL,
                                 unsigned MaxLookup) {
  if (!V->getType()->isPointerTy())
    return V;
  for (unsigned Count = 0; MaxLookup == 0 || Count < MaxLookup; ++Count) {
    if (GEPOperator *GEP = dyn_cast<GEPOperator>(V)) {
      V = GEP->getPointerOperand();
    } else if (Operator::getOpcode(V) == Instruction::BitCast ||
               Operator::getOpcode(V) == Instruction::AddrSpaceCast) {
      V = cast<Operator>(V)->getOperand(0);
    } else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V)) {
      if (GA->mayBeOverridden())
        return V;
      V = GA->getAliasee();
    } else {
      // See if InstructionSimplify knows any relevant tricks.
      if (Instruction *I = dyn_cast<Instruction>(V))
        // TODO: Acquire a DominatorTree and AssumptionCache and use them.
        if (Value *Simplified = SimplifyInstruction(I, DL, nullptr)) {
          V = Simplified;
          continue;
        }

      return V;
    }
    assert(V->getType()->isPointerTy() && "Unexpected operand type!");
  }
  return V;
}

void llvm::GetUnderlyingObjects(Value *V, SmallVectorImpl<Value *> &Objects,
                                const DataLayout &DL, unsigned MaxLookup) {
  SmallPtrSet<Value *, 4> Visited;
  SmallVector<Value *, 4> Worklist;
  Worklist.push_back(V);
  do {
    Value *P = Worklist.pop_back_val();
    P = GetUnderlyingObject(P, DL, MaxLookup);

    if (!Visited.insert(P).second)
      continue;

    if (SelectInst *SI = dyn_cast<SelectInst>(P)) {
      Worklist.push_back(SI->getTrueValue());
      Worklist.push_back(SI->getFalseValue());
      continue;
    }

    if (PHINode *PN = dyn_cast<PHINode>(P)) {
      for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
        Worklist.push_back(PN->getIncomingValue(i));
      continue;
    }

    Objects.push_back(P);
  } while (!Worklist.empty());
}

/// Return true if the only users of this pointer are lifetime markers.
bool llvm::onlyUsedByLifetimeMarkers(const Value *V) {
  for (const User *U : V->users()) {
    const IntrinsicInst *II = dyn_cast<IntrinsicInst>(U);
    if (!II) return false;

    if (II->getIntrinsicID() != Intrinsic::lifetime_start &&
        II->getIntrinsicID() != Intrinsic::lifetime_end)
      return false;
  }
  return true;
}

bool llvm::isSafeToSpeculativelyExecute(const Value *V) {
  const Operator *Inst = dyn_cast<Operator>(V);
  if (!Inst)
    return false;

  for (unsigned i = 0, e = Inst->getNumOperands(); i != e; ++i)
    if (Constant *C = dyn_cast<Constant>(Inst->getOperand(i)))
      if (C->canTrap())
        return false;

  switch (Inst->getOpcode()) {
  default:
    return true;
  case Instruction::UDiv:
  case Instruction::URem: {
    // x / y is undefined if y == 0.
    const APInt *V;
    if (match(Inst->getOperand(1), m_APInt(V)))
      return *V != 0;
    return false;
  }
  case Instruction::SDiv:
  case Instruction::SRem: {
    // x / y is undefined if y == 0 or x == INT_MIN and y == -1
    const APInt *Numerator, *Denominator;
    if (!match(Inst->getOperand(1), m_APInt(Denominator)))
      return false;
    // We cannot hoist this division if the denominator is 0.
    if (*Denominator == 0)
      return false;
    // It's safe to hoist if the denominator is not 0 or -1.
    if (*Denominator != -1)
      return true;
    // At this point we know that the denominator is -1.  It is safe to hoist as
    // long we know that the numerator is not INT_MIN.
    if (match(Inst->getOperand(0), m_APInt(Numerator)))
      return !Numerator->isMinSignedValue();
    // The numerator *might* be MinSignedValue.
    return false;
  }
  case Instruction::Load: {
    const LoadInst *LI = cast<LoadInst>(Inst);
    if (!LI->isUnordered() ||
        // Speculative load may create a race that did not exist in the source.
        LI->getParent()->getParent()->hasFnAttribute(Attribute::SanitizeThread))
      return false;
    const DataLayout &DL = LI->getModule()->getDataLayout();
    return LI->getPointerOperand()->isDereferenceablePointer(DL);
  }
  case Instruction::Call: {
    if (const IntrinsicInst *II = dyn_cast<IntrinsicInst>(Inst)) {
      switch (II->getIntrinsicID()) {
      // These synthetic intrinsics have no side-effects and just mark
      // information about their operands.
      // FIXME: There are other no-op synthetic instructions that potentially
      // should be considered at least *safe* to speculate...
      case Intrinsic::dbg_declare:
      case Intrinsic::dbg_value:
        return true;

      case Intrinsic::bswap:
      case Intrinsic::ctlz:
      case Intrinsic::ctpop:
      case Intrinsic::cttz:
      case Intrinsic::objectsize:
      case Intrinsic::sadd_with_overflow:
      case Intrinsic::smul_with_overflow:
      case Intrinsic::ssub_with_overflow:
      case Intrinsic::uadd_with_overflow:
      case Intrinsic::umul_with_overflow:
      case Intrinsic::usub_with_overflow:
        return true;
      // Sqrt should be OK, since the llvm sqrt intrinsic isn't defined to set
      // errno like libm sqrt would.
      case Intrinsic::sqrt:
      case Intrinsic::fma:
      case Intrinsic::fmuladd:
      case Intrinsic::fabs:
      case Intrinsic::minnum:
      case Intrinsic::maxnum:
        return true;
      // TODO: some fp intrinsics are marked as having the same error handling
      // as libm. They're safe to speculate when they won't error.
      // TODO: are convert_{from,to}_fp16 safe?
      // TODO: can we list target-specific intrinsics here?
      default: break;
      }
    }
    return false; // The called function could have undefined behavior or
                  // side-effects, even if marked readnone nounwind.
  }
  case Instruction::VAArg:
  case Instruction::Alloca:
  case Instruction::Invoke:
  case Instruction::PHI:
  case Instruction::Store:
  case Instruction::Ret:
  case Instruction::Br:
  case Instruction::IndirectBr:
  case Instruction::Switch:
  case Instruction::Unreachable:
  case Instruction::Fence:
  case Instruction::LandingPad:
  case Instruction::AtomicRMW:
  case Instruction::AtomicCmpXchg:
  case Instruction::Resume:
    return false; // Misc instructions which have effects
  }
}

/// Return true if we know that the specified value is never null.
bool llvm::isKnownNonNull(const Value *V, const TargetLibraryInfo *TLI) {
  // Alloca never returns null, malloc might.
  if (isa<AllocaInst>(V)) return true;

  // A byval, inalloca, or nonnull argument is never null.
  if (const Argument *A = dyn_cast<Argument>(V))
    return A->hasByValOrInAllocaAttr() || A->hasNonNullAttr();

  // Global values are not null unless extern weak.
  if (const GlobalValue *GV = dyn_cast<GlobalValue>(V))
    return !GV->hasExternalWeakLinkage();

  // A Load tagged w/nonnull metadata is never null. 
  if (const LoadInst *LI = dyn_cast<LoadInst>(V))
    return LI->getMetadata(LLVMContext::MD_nonnull);

  if (ImmutableCallSite CS = V)
    if (CS.isReturnNonNull())
      return true;

  // operator new never returns null.
  if (isOperatorNewLikeFn(V, TLI, /*LookThroughBitCast=*/true))
    return true;

  return false;
}

OverflowResult llvm::computeOverflowForUnsignedMul(Value *LHS, Value *RHS,
                                                   const DataLayout &DL,
                                                   AssumptionCache *AC,
                                                   const Instruction *CxtI,
                                                   const DominatorTree *DT) {
  // Multiplying n * m significant bits yields a result of n + m significant
  // bits. If the total number of significant bits does not exceed the
  // result bit width (minus 1), there is no overflow.
  // This means if we have enough leading zero bits in the operands
  // we can guarantee that the result does not overflow.
  // Ref: "Hacker's Delight" by Henry Warren
  unsigned BitWidth = LHS->getType()->getScalarSizeInBits();
  APInt LHSKnownZero(BitWidth, 0);
  APInt LHSKnownOne(BitWidth, 0);
  APInt RHSKnownZero(BitWidth, 0);
  APInt RHSKnownOne(BitWidth, 0);
  computeKnownBits(LHS, LHSKnownZero, LHSKnownOne, DL, /*Depth=*/0, AC, CxtI,
                   DT);
  computeKnownBits(RHS, RHSKnownZero, RHSKnownOne, DL, /*Depth=*/0, AC, CxtI,
                   DT);
  // Note that underestimating the number of zero bits gives a more
  // conservative answer.
  unsigned ZeroBits = LHSKnownZero.countLeadingOnes() +
                      RHSKnownZero.countLeadingOnes();
  // First handle the easy case: if we have enough zero bits there's
  // definitely no overflow.
  if (ZeroBits >= BitWidth)
    return OverflowResult::NeverOverflows;

  // Get the largest possible values for each operand.
  APInt LHSMax = ~LHSKnownZero;
  APInt RHSMax = ~RHSKnownZero;

  // We know the multiply operation doesn't overflow if the maximum values for
  // each operand will not overflow after we multiply them together.
  bool MaxOverflow;
  LHSMax.umul_ov(RHSMax, MaxOverflow);
  if (!MaxOverflow)
    return OverflowResult::NeverOverflows;

  // We know it always overflows if multiplying the smallest possible values for
  // the operands also results in overflow.
  bool MinOverflow;
  LHSKnownOne.umul_ov(RHSKnownOne, MinOverflow);
  if (MinOverflow)
    return OverflowResult::AlwaysOverflows;

  return OverflowResult::MayOverflow;
}

OverflowResult llvm::computeOverflowForUnsignedAdd(Value *LHS, Value *RHS,
                                                   const DataLayout &DL,
                                                   AssumptionCache *AC,
                                                   const Instruction *CxtI,
                                                   const DominatorTree *DT) {
  bool LHSKnownNonNegative, LHSKnownNegative;
  ComputeSignBit(LHS, LHSKnownNonNegative, LHSKnownNegative, DL, /*Depth=*/0,
                 AC, CxtI, DT);
  if (LHSKnownNonNegative || LHSKnownNegative) {
    bool RHSKnownNonNegative, RHSKnownNegative;
    ComputeSignBit(RHS, RHSKnownNonNegative, RHSKnownNegative, DL, /*Depth=*/0,
                   AC, CxtI, DT);

    if (LHSKnownNegative && RHSKnownNegative) {
      // The sign bit is set in both cases: this MUST overflow.
      // Create a simple add instruction, and insert it into the struct.
      return OverflowResult::AlwaysOverflows;
    }

    if (LHSKnownNonNegative && RHSKnownNonNegative) {
      // The sign bit is clear in both cases: this CANNOT overflow.
      // Create a simple add instruction, and insert it into the struct.
      return OverflowResult::NeverOverflows;
    }
  }

  return OverflowResult::MayOverflow;
}