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
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
/*!
Defines a high-level intermediate (HIR) representation for regular expressions.

The HIR is represented by the [`Hir`] type, and it principally constructed via
[translation](translate) from an [`Ast`](crate::ast::Ast). Alternatively, users
may use the smart constructors defined on `Hir` to build their own by hand. The
smart constructors simultaneously simplify and "optimize" the HIR, and are also
the same routines used by translation.

Most regex engines only have an HIR like this, and usually construct it
directly from the concrete syntax. This crate however first parses the
concrete syntax into an `Ast`, and only then creates the HIR from the `Ast`,
as mentioned above. It's done this way to facilitate better error reporting,
and to have a structured representation of a regex that faithfully represents
its concrete syntax. Namely, while an `Hir` value can be converted back to an
equivalent regex pattern string, it is unlikely to look like the original due
to its simplified structure.
*/

use core::{char, cmp};

use alloc::{
    boxed::Box,
    format,
    string::{String, ToString},
    vec,
    vec::Vec,
};

use crate::{
    ast::Span,
    hir::interval::{Interval, IntervalSet, IntervalSetIter},
    unicode,
};

pub use crate::{
    hir::visitor::{visit, Visitor},
    unicode::CaseFoldError,
};

mod interval;
pub mod literal;
pub mod print;
pub mod translate;
mod visitor;

/// An error that can occur while translating an `Ast` to a `Hir`.
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct Error {
    /// The kind of error.
    kind: ErrorKind,
    /// The original pattern that the translator's Ast was parsed from. Every
    /// span in an error is a valid range into this string.
    pattern: String,
    /// The span of this error, derived from the Ast given to the translator.
    span: Span,
}

impl Error {
    /// Return the type of this error.
    pub fn kind(&self) -> &ErrorKind {
        &self.kind
    }

    /// The original pattern string in which this error occurred.
    ///
    /// Every span reported by this error is reported in terms of this string.
    pub fn pattern(&self) -> &str {
        &self.pattern
    }

    /// Return the span at which this error occurred.
    pub fn span(&self) -> &Span {
        &self.span
    }
}

/// The type of an error that occurred while building an `Hir`.
///
/// This error type is marked as `non_exhaustive`. This means that adding a
/// new variant is not considered a breaking change.
#[non_exhaustive]
#[derive(Clone, Debug, Eq, PartialEq)]
pub enum ErrorKind {
    /// This error occurs when a Unicode feature is used when Unicode
    /// support is disabled. For example `(?-u:\pL)` would trigger this error.
    UnicodeNotAllowed,
    /// This error occurs when translating a pattern that could match a byte
    /// sequence that isn't UTF-8 and `utf8` was enabled.
    InvalidUtf8,
    /// This error occurs when one uses a non-ASCII byte for a line terminator,
    /// but where Unicode mode is enabled and UTF-8 mode is disabled.
    InvalidLineTerminator,
    /// This occurs when an unrecognized Unicode property name could not
    /// be found.
    UnicodePropertyNotFound,
    /// This occurs when an unrecognized Unicode property value could not
    /// be found.
    UnicodePropertyValueNotFound,
    /// This occurs when a Unicode-aware Perl character class (`\w`, `\s` or
    /// `\d`) could not be found. This can occur when the `unicode-perl`
    /// crate feature is not enabled.
    UnicodePerlClassNotFound,
    /// This occurs when the Unicode simple case mapping tables are not
    /// available, and the regular expression required Unicode aware case
    /// insensitivity.
    UnicodeCaseUnavailable,
}

#[cfg(feature = "std")]
impl std::error::Error for Error {}

impl core::fmt::Display for Error {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        crate::error::Formatter::from(self).fmt(f)
    }
}

impl core::fmt::Display for ErrorKind {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        use self::ErrorKind::*;

        let msg = match *self {
            UnicodeNotAllowed => "Unicode not allowed here",
            InvalidUtf8 => "pattern can match invalid UTF-8",
            InvalidLineTerminator => "invalid line terminator, must be ASCII",
            UnicodePropertyNotFound => "Unicode property not found",
            UnicodePropertyValueNotFound => "Unicode property value not found",
            UnicodePerlClassNotFound => {
                "Unicode-aware Perl class not found \
                 (make sure the unicode-perl feature is enabled)"
            }
            UnicodeCaseUnavailable => {
                "Unicode-aware case insensitivity matching is not available \
                 (make sure the unicode-case feature is enabled)"
            }
        };
        f.write_str(msg)
    }
}

/// A high-level intermediate representation (HIR) for a regular expression.
///
/// An HIR value is a combination of a [`HirKind`] and a set of [`Properties`].
/// An `HirKind` indicates what kind of regular expression it is (a literal,
/// a repetition, a look-around assertion, etc.), where as a `Properties`
/// describes various facts about the regular expression. For example, whether
/// it matches UTF-8 or if it matches the empty string.
///
/// The HIR of a regular expression represents an intermediate step between
/// its abstract syntax (a structured description of the concrete syntax) and
/// an actual regex matcher. The purpose of HIR is to make regular expressions
/// easier to analyze. In particular, the AST is much more complex than the
/// HIR. For example, while an AST supports arbitrarily nested character
/// classes, the HIR will flatten all nested classes into a single set. The HIR
/// will also "compile away" every flag present in the concrete syntax. For
/// example, users of HIR expressions never need to worry about case folding;
/// it is handled automatically by the translator (e.g., by translating
/// `(?i:A)` to `[aA]`).
///
/// The specific type of an HIR expression can be accessed via its `kind`
/// or `into_kind` methods. This extra level of indirection exists for two
/// reasons:
///
/// 1. Construction of an HIR expression *must* use the constructor methods on
/// this `Hir` type instead of building the `HirKind` values directly. This
/// permits construction to enforce invariants like "concatenations always
/// consist of two or more sub-expressions."
/// 2. Every HIR expression contains attributes that are defined inductively,
/// and can be computed cheaply during the construction process. For example,
/// one such attribute is whether the expression must match at the beginning of
/// the haystack.
///
/// In particular, if you have an `HirKind` value, then there is intentionally
/// no way to build an `Hir` value from it. You instead need to do case
/// analysis on the `HirKind` value and build the `Hir` value using its smart
/// constructors.
///
/// # UTF-8
///
/// If the HIR was produced by a translator with
/// [`TranslatorBuilder::utf8`](translate::TranslatorBuilder::utf8) enabled,
/// then the HIR is guaranteed to match UTF-8 exclusively for all non-empty
/// matches.
///
/// For empty matches, those can occur at any position. It is the
/// responsibility of the regex engine to determine whether empty matches are
/// permitted between the code units of a single codepoint.
///
/// # Stack space
///
/// This type defines its own destructor that uses constant stack space and
/// heap space proportional to the size of the HIR.
///
/// Also, an `Hir`'s `fmt::Display` implementation prints an HIR as a regular
/// expression pattern string, and uses constant stack space and heap space
/// proportional to the size of the `Hir`. The regex it prints is guaranteed to
/// be _semantically_ equivalent to the original concrete syntax, but it may
/// look very different. (And potentially not practically readable by a human.)
///
/// An `Hir`'s `fmt::Debug` implementation currently does not use constant
/// stack space. The implementation will also suppress some details (such as
/// the `Properties` inlined into every `Hir` value to make it less noisy).
#[derive(Clone, Eq, PartialEq)]
pub struct Hir {
    /// The underlying HIR kind.
    kind: HirKind,
    /// Analysis info about this HIR, computed during construction.
    props: Properties,
}

/// Methods for accessing the underlying `HirKind` and `Properties`.
impl Hir {
    /// Returns a reference to the underlying HIR kind.
    pub fn kind(&self) -> &HirKind {
        &self.kind
    }

    /// Consumes ownership of this HIR expression and returns its underlying
    /// `HirKind`.
    pub fn into_kind(mut self) -> HirKind {
        core::mem::replace(&mut self.kind, HirKind::Empty)
    }

    /// Returns the properties computed for this `Hir`.
    pub fn properties(&self) -> &Properties {
        &self.props
    }

    /// Splits this HIR into its constituent parts.
    ///
    /// This is useful because `let Hir { kind, props } = hir;` does not work
    /// because of `Hir`'s custom `Drop` implementation.
    fn into_parts(mut self) -> (HirKind, Properties) {
        (
            core::mem::replace(&mut self.kind, HirKind::Empty),
            core::mem::replace(&mut self.props, Properties::empty()),
        )
    }
}

/// Smart constructors for HIR values.
///
/// These constructors are called "smart" because they do inductive work or
/// simplifications. For example, calling `Hir::repetition` with a repetition
/// like `a{0}` will actually return a `Hir` with a `HirKind::Empty` kind
/// since it is equivalent to an empty regex. Another example is calling
/// `Hir::concat(vec![expr])`. Instead of getting a `HirKind::Concat`, you'll
/// just get back the original `expr` since it's precisely equivalent.
///
/// Smart constructors enable maintaining invariants about the HIR data type
/// while also simulanteously keeping the representation as simple as possible.
impl Hir {
    /// Returns an empty HIR expression.
    ///
    /// An empty HIR expression always matches, including the empty string.
    #[inline]
    pub fn empty() -> Hir {
        let props = Properties::empty();
        Hir { kind: HirKind::Empty, props }
    }

    /// Returns an HIR expression that can never match anything. That is,
    /// the size of the set of strings in the language described by the HIR
    /// returned is `0`.
    ///
    /// This is distinct from [`Hir::empty`] in that the empty string matches
    /// the HIR returned by `Hir::empty`. That is, the set of strings in the
    /// language describe described by `Hir::empty` is non-empty.
    ///
    /// Note that currently, the HIR returned uses an empty character class to
    /// indicate that nothing can match. An equivalent expression that cannot
    /// match is an empty alternation, but all such "fail" expressions are
    /// normalized (via smart constructors) to empty character classes. This is
    /// because empty character classes can be spelled in the concrete syntax
    /// of a regex (e.g., `\P{any}` or `(?-u:[^\x00-\xFF])` or `[a&&b]`), but
    /// empty alternations cannot.
    #[inline]
    pub fn fail() -> Hir {
        let class = Class::Bytes(ClassBytes::empty());
        let props = Properties::class(&class);
        // We can't just call Hir::class here because it defers to Hir::fail
        // in order to canonicalize the Hir value used to represent "cannot
        // match."
        Hir { kind: HirKind::Class(class), props }
    }

    /// Creates a literal HIR expression.
    ///
    /// This accepts anything that can be converted into a `Box<[u8]>`.
    ///
    /// Note that there is no mechanism for storing a `char` or a `Box<str>`
    /// in an HIR. Everything is "just bytes." Whether a `Literal` (or
    /// any HIR node) matches valid UTF-8 exclusively can be queried via
    /// [`Properties::is_utf8`].
    ///
    /// # Example
    ///
    /// This example shows that concatenations of `Literal` HIR values will
    /// automatically get flattened and combined together. So for example, even
    /// if you concat multiple `Literal` values that are themselves not valid
    /// UTF-8, they might add up to valid UTF-8. This also demonstrates just
    /// how "smart" Hir's smart constructors are.
    ///
    /// ```
    /// use regex_syntax::hir::{Hir, HirKind, Literal};
    ///
    /// let literals = vec![
    ///     Hir::literal([0xE2]),
    ///     Hir::literal([0x98]),
    ///     Hir::literal([0x83]),
    /// ];
    /// // Each literal, on its own, is invalid UTF-8.
    /// assert!(literals.iter().all(|hir| !hir.properties().is_utf8()));
    ///
    /// let concat = Hir::concat(literals);
    /// // But the concatenation is valid UTF-8!
    /// assert!(concat.properties().is_utf8());
    ///
    /// // And also notice that the literals have been concatenated into a
    /// // single `Literal`, to the point where there is no explicit `Concat`!
    /// let expected = HirKind::Literal(Literal(Box::from("☃".as_bytes())));
    /// assert_eq!(&expected, concat.kind());
    /// ```
    #[inline]
    pub fn literal<B: Into<Box<[u8]>>>(lit: B) -> Hir {
        let bytes = lit.into();
        if bytes.is_empty() {
            return Hir::empty();
        }

        let lit = Literal(bytes);
        let props = Properties::literal(&lit);
        Hir { kind: HirKind::Literal(lit), props }
    }

    /// Creates a class HIR expression. The class may either be defined over
    /// ranges of Unicode codepoints or ranges of raw byte values.
    ///
    /// Note that an empty class is permitted. An empty class is equivalent to
    /// `Hir::fail()`.
    #[inline]
    pub fn class(class: Class) -> Hir {
        if class.is_empty() {
            return Hir::fail();
        } else if let Some(bytes) = class.literal() {
            return Hir::literal(bytes);
        }
        let props = Properties::class(&class);
        Hir { kind: HirKind::Class(class), props }
    }

    /// Creates a look-around assertion HIR expression.
    #[inline]
    pub fn look(look: Look) -> Hir {
        let props = Properties::look(look);
        Hir { kind: HirKind::Look(look), props }
    }

    /// Creates a repetition HIR expression.
    #[inline]
    pub fn repetition(mut rep: Repetition) -> Hir {
        // If the sub-expression of a repetition can only match the empty
        // string, then we force its maximum to be at most 1.
        if rep.sub.properties().maximum_len() == Some(0) {
            rep.min = cmp::min(rep.min, 1);
            rep.max = rep.max.map(|n| cmp::min(n, 1)).or(Some(1));
        }
        // The regex 'a{0}' is always equivalent to the empty regex. This is
        // true even when 'a' is an expression that never matches anything
        // (like '\P{any}').
        //
        // Additionally, the regex 'a{1}' is always equivalent to 'a'.
        if rep.min == 0 && rep.max == Some(0) {
            return Hir::empty();
        } else if rep.min == 1 && rep.max == Some(1) {
            return *rep.sub;
        }
        let props = Properties::repetition(&rep);
        Hir { kind: HirKind::Repetition(rep), props }
    }

    /// Creates a capture HIR expression.
    ///
    /// Note that there is no explicit HIR value for a non-capturing group.
    /// Since a non-capturing group only exists to override precedence in the
    /// concrete syntax and since an HIR already does its own grouping based on
    /// what is parsed, there is no need to explicitly represent non-capturing
    /// groups in the HIR.
    #[inline]
    pub fn capture(capture: Capture) -> Hir {
        let props = Properties::capture(&capture);
        Hir { kind: HirKind::Capture(capture), props }
    }

    /// Returns the concatenation of the given expressions.
    ///
    /// This attempts to flatten and simplify the concatenation as appropriate.
    ///
    /// # Example
    ///
    /// This shows a simple example of basic flattening of both concatenations
    /// and literals.
    ///
    /// ```
    /// use regex_syntax::hir::Hir;
    ///
    /// let hir = Hir::concat(vec![
    ///     Hir::concat(vec![
    ///         Hir::literal([b'a']),
    ///         Hir::literal([b'b']),
    ///         Hir::literal([b'c']),
    ///     ]),
    ///     Hir::concat(vec![
    ///         Hir::literal([b'x']),
    ///         Hir::literal([b'y']),
    ///         Hir::literal([b'z']),
    ///     ]),
    /// ]);
    /// let expected = Hir::literal("abcxyz".as_bytes());
    /// assert_eq!(expected, hir);
    /// ```
    pub fn concat(subs: Vec<Hir>) -> Hir {
        // We rebuild the concatenation by simplifying it. Would be nice to do
        // it in place, but that seems a little tricky?
        let mut new = vec![];
        // This gobbles up any adjacent literals in a concatenation and smushes
        // them together. Basically, when we see a literal, we add its bytes
        // to 'prior_lit', and whenever we see anything else, we first take
        // any bytes in 'prior_lit' and add it to the 'new' concatenation.
        let mut prior_lit: Option<Vec<u8>> = None;
        for sub in subs {
            let (kind, props) = sub.into_parts();
            match kind {
                HirKind::Literal(Literal(bytes)) => {
                    if let Some(ref mut prior_bytes) = prior_lit {
                        prior_bytes.extend_from_slice(&bytes);
                    } else {
                        prior_lit = Some(bytes.to_vec());
                    }
                }
                // We also flatten concats that are direct children of another
                // concat. We only need to do this one level deep since
                // Hir::concat is the only way to build concatenations, and so
                // flattening happens inductively.
                HirKind::Concat(subs2) => {
                    for sub2 in subs2 {
                        let (kind2, props2) = sub2.into_parts();
                        match kind2 {
                            HirKind::Literal(Literal(bytes)) => {
                                if let Some(ref mut prior_bytes) = prior_lit {
                                    prior_bytes.extend_from_slice(&bytes);
                                } else {
                                    prior_lit = Some(bytes.to_vec());
                                }
                            }
                            kind2 => {
                                if let Some(prior_bytes) = prior_lit.take() {
                                    new.push(Hir::literal(prior_bytes));
                                }
                                new.push(Hir { kind: kind2, props: props2 });
                            }
                        }
                    }
                }
                // We can just skip empty HIRs.
                HirKind::Empty => {}
                kind => {
                    if let Some(prior_bytes) = prior_lit.take() {
                        new.push(Hir::literal(prior_bytes));
                    }
                    new.push(Hir { kind, props });
                }
            }
        }
        if let Some(prior_bytes) = prior_lit.take() {
            new.push(Hir::literal(prior_bytes));
        }
        if new.is_empty() {
            return Hir::empty();
        } else if new.len() == 1 {
            return new.pop().unwrap();
        }
        let props = Properties::concat(&new);
        Hir { kind: HirKind::Concat(new), props }
    }

    /// Returns the alternation of the given expressions.
    ///
    /// This flattens and simplifies the alternation as appropriate. This may
    /// include factoring out common prefixes or even rewriting the alternation
    /// as a character class.
    ///
    /// Note that an empty alternation is equivalent to `Hir::fail()`. (It
    /// is not possible for one to write an empty alternation, or even an
    /// alternation with a single sub-expression, in the concrete syntax of a
    /// regex.)
    ///
    /// # Example
    ///
    /// This is a simple example showing how an alternation might get
    /// simplified.
    ///
    /// ```
    /// use regex_syntax::hir::{Hir, Class, ClassUnicode, ClassUnicodeRange};
    ///
    /// let hir = Hir::alternation(vec![
    ///     Hir::literal([b'a']),
    ///     Hir::literal([b'b']),
    ///     Hir::literal([b'c']),
    ///     Hir::literal([b'd']),
    ///     Hir::literal([b'e']),
    ///     Hir::literal([b'f']),
    /// ]);
    /// let expected = Hir::class(Class::Unicode(ClassUnicode::new([
    ///     ClassUnicodeRange::new('a', 'f'),
    /// ])));
    /// assert_eq!(expected, hir);
    /// ```
    ///
    /// And another example showing how common prefixes might get factored
    /// out.
    ///
    /// ```
    /// use regex_syntax::hir::{Hir, Class, ClassUnicode, ClassUnicodeRange};
    ///
    /// let hir = Hir::alternation(vec![
    ///     Hir::concat(vec![
    ///         Hir::literal("abc".as_bytes()),
    ///         Hir::class(Class::Unicode(ClassUnicode::new([
    ///             ClassUnicodeRange::new('A', 'Z'),
    ///         ]))),
    ///     ]),
    ///     Hir::concat(vec![
    ///         Hir::literal("abc".as_bytes()),
    ///         Hir::class(Class::Unicode(ClassUnicode::new([
    ///             ClassUnicodeRange::new('a', 'z'),
    ///         ]))),
    ///     ]),
    /// ]);
    /// let expected = Hir::concat(vec![
    ///     Hir::literal("abc".as_bytes()),
    ///     Hir::alternation(vec![
    ///         Hir::class(Class::Unicode(ClassUnicode::new([
    ///             ClassUnicodeRange::new('A', 'Z'),
    ///         ]))),
    ///         Hir::class(Class::Unicode(ClassUnicode::new([
    ///             ClassUnicodeRange::new('a', 'z'),
    ///         ]))),
    ///     ]),
    /// ]);
    /// assert_eq!(expected, hir);
    /// ```
    ///
    /// Note that these sorts of simplifications are not guaranteed.
    pub fn alternation(subs: Vec<Hir>) -> Hir {
        // We rebuild the alternation by simplifying it. We proceed similarly
        // as the concatenation case. But in this case, there's no literal
        // simplification happening. We're just flattening alternations.
        let mut new = Vec::with_capacity(subs.len());
        for sub in subs {
            let (kind, props) = sub.into_parts();
            match kind {
                HirKind::Alternation(subs2) => {
                    new.extend(subs2);
                }
                kind => {
                    new.push(Hir { kind, props });
                }
            }
        }
        if new.is_empty() {
            return Hir::fail();
        } else if new.len() == 1 {
            return new.pop().unwrap();
        }
        // Now that it's completely flattened, look for the special case of
        // 'char1|char2|...|charN' and collapse that into a class. Note that
        // we look for 'char' first and then bytes. The issue here is that if
        // we find both non-ASCII codepoints and non-ASCII singleton bytes,
        // then it isn't actually possible to smush them into a single class.
        // (Because classes are either "all codepoints" or "all bytes." You
        // can have a class that both matches non-ASCII but valid UTF-8 and
        // invalid UTF-8.) So we look for all chars and then all bytes, and
        // don't handle anything else.
        if let Some(singletons) = singleton_chars(&new) {
            let it = singletons
                .into_iter()
                .map(|ch| ClassUnicodeRange { start: ch, end: ch });
            return Hir::class(Class::Unicode(ClassUnicode::new(it)));
        }
        if let Some(singletons) = singleton_bytes(&new) {
            let it = singletons
                .into_iter()
                .map(|b| ClassBytesRange { start: b, end: b });
            return Hir::class(Class::Bytes(ClassBytes::new(it)));
        }
        // Similar to singleton chars, we can also look for alternations of
        // classes. Those can be smushed into a single class.
        if let Some(cls) = class_chars(&new) {
            return Hir::class(cls);
        }
        if let Some(cls) = class_bytes(&new) {
            return Hir::class(cls);
        }
        // Factor out a common prefix if we can, which might potentially
        // simplify the expression and unlock other optimizations downstream.
        // It also might generally make NFA matching and DFA construction
        // faster by reducing the scope of branching in the regex.
        new = match lift_common_prefix(new) {
            Ok(hir) => return hir,
            Err(unchanged) => unchanged,
        };
        let props = Properties::alternation(&new);
        Hir { kind: HirKind::Alternation(new), props }
    }

    /// Returns an HIR expression for `.`.
    ///
    /// * [`Dot::AnyChar`] maps to `(?su-R:.)`.
    /// * [`Dot::AnyByte`] maps to `(?s-Ru:.)`.
    /// * [`Dot::AnyCharExceptLF`] maps to `(?u-Rs:.)`.
    /// * [`Dot::AnyCharExceptCRLF`] maps to `(?Ru-s:.)`.
    /// * [`Dot::AnyByteExceptLF`] maps to `(?-Rsu:.)`.
    /// * [`Dot::AnyByteExceptCRLF`] maps to `(?R-su:.)`.
    ///
    /// # Example
    ///
    /// Note that this is a convenience routine for constructing the correct
    /// character class based on the value of `Dot`. There is no explicit "dot"
    /// HIR value. It is just an abbreviation for a common character class.
    ///
    /// ```
    /// use regex_syntax::hir::{Hir, Dot, Class, ClassBytes, ClassBytesRange};
    ///
    /// let hir = Hir::dot(Dot::AnyByte);
    /// let expected = Hir::class(Class::Bytes(ClassBytes::new([
    ///     ClassBytesRange::new(0x00, 0xFF),
    /// ])));
    /// assert_eq!(expected, hir);
    /// ```
    #[inline]
    pub fn dot(dot: Dot) -> Hir {
        match dot {
            Dot::AnyChar => {
                let mut cls = ClassUnicode::empty();
                cls.push(ClassUnicodeRange::new('\0', '\u{10FFFF}'));
                Hir::class(Class::Unicode(cls))
            }
            Dot::AnyByte => {
                let mut cls = ClassBytes::empty();
                cls.push(ClassBytesRange::new(b'\0', b'\xFF'));
                Hir::class(Class::Bytes(cls))
            }
            Dot::AnyCharExcept(ch) => {
                let mut cls =
                    ClassUnicode::new([ClassUnicodeRange::new(ch, ch)]);
                cls.negate();
                Hir::class(Class::Unicode(cls))
            }
            Dot::AnyCharExceptLF => {
                let mut cls = ClassUnicode::empty();
                cls.push(ClassUnicodeRange::new('\0', '\x09'));
                cls.push(ClassUnicodeRange::new('\x0B', '\u{10FFFF}'));
                Hir::class(Class::Unicode(cls))
            }
            Dot::AnyCharExceptCRLF => {
                let mut cls = ClassUnicode::empty();
                cls.push(ClassUnicodeRange::new('\0', '\x09'));
                cls.push(ClassUnicodeRange::new('\x0B', '\x0C'));
                cls.push(ClassUnicodeRange::new('\x0E', '\u{10FFFF}'));
                Hir::class(Class::Unicode(cls))
            }
            Dot::AnyByteExcept(byte) => {
                let mut cls =
                    ClassBytes::new([ClassBytesRange::new(byte, byte)]);
                cls.negate();
                Hir::class(Class::Bytes(cls))
            }
            Dot::AnyByteExceptLF => {
                let mut cls = ClassBytes::empty();
                cls.push(ClassBytesRange::new(b'\0', b'\x09'));
                cls.push(ClassBytesRange::new(b'\x0B', b'\xFF'));
                Hir::class(Class::Bytes(cls))
            }
            Dot::AnyByteExceptCRLF => {
                let mut cls = ClassBytes::empty();
                cls.push(ClassBytesRange::new(b'\0', b'\x09'));
                cls.push(ClassBytesRange::new(b'\x0B', b'\x0C'));
                cls.push(ClassBytesRange::new(b'\x0E', b'\xFF'));
                Hir::class(Class::Bytes(cls))
            }
        }
    }
}

/// The underlying kind of an arbitrary [`Hir`] expression.
///
/// An `HirKind` is principally useful for doing case analysis on the type
/// of a regular expression. If you're looking to build new `Hir` values,
/// then you _must_ use the smart constructors defined on `Hir`, like
/// [`Hir::repetition`], to build new `Hir` values. The API intentionally does
/// not expose any way of building an `Hir` directly from an `HirKind`.
#[derive(Clone, Debug, Eq, PartialEq)]
pub enum HirKind {
    /// The empty regular expression, which matches everything, including the
    /// empty string.
    Empty,
    /// A literalstring that matches exactly these bytes.
    Literal(Literal),
    /// A single character class that matches any of the characters in the
    /// class. A class can either consist of Unicode scalar values as
    /// characters, or it can use bytes.
    ///
    /// A class may be empty. In which case, it matches nothing.
    Class(Class),
    /// A look-around assertion. A look-around match always has zero length.
    Look(Look),
    /// A repetition operation applied to a sub-expression.
    Repetition(Repetition),
    /// A capturing group, which contains a sub-expression.
    Capture(Capture),
    /// A concatenation of expressions.
    ///
    /// A concatenation matches only if each of its sub-expressions match one
    /// after the other.
    ///
    /// Concatenations are guaranteed by `Hir`'s smart constructors to always
    /// have at least two sub-expressions.
    Concat(Vec<Hir>),
    /// An alternation of expressions.
    ///
    /// An alternation matches only if at least one of its sub-expressions
    /// match. If multiple sub-expressions match, then the leftmost is
    /// preferred.
    ///
    /// Alternations are guaranteed by `Hir`'s smart constructors to always
    /// have at least two sub-expressions.
    Alternation(Vec<Hir>),
}

impl HirKind {
    /// Returns a slice of this kind's sub-expressions, if any.
    pub fn subs(&self) -> &[Hir] {
        use core::slice::from_ref;

        match *self {
            HirKind::Empty
            | HirKind::Literal(_)
            | HirKind::Class(_)
            | HirKind::Look(_) => &[],
            HirKind::Repetition(Repetition { ref sub, .. }) => from_ref(sub),
            HirKind::Capture(Capture { ref sub, .. }) => from_ref(sub),
            HirKind::Concat(ref subs) => subs,
            HirKind::Alternation(ref subs) => subs,
        }
    }
}

impl core::fmt::Debug for Hir {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        self.kind.fmt(f)
    }
}

/// Print a display representation of this Hir.
///
/// The result of this is a valid regular expression pattern string.
///
/// This implementation uses constant stack space and heap space proportional
/// to the size of the `Hir`.
impl core::fmt::Display for Hir {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        crate::hir::print::Printer::new().print(self, f)
    }
}

/// The high-level intermediate representation of a literal.
///
/// A literal corresponds to `0` or more bytes that should be matched
/// literally. The smart constructors defined on `Hir` will automatically
/// concatenate adjacent literals into one literal, and will even automatically
/// replace empty literals with `Hir::empty()`.
///
/// Note that despite a literal being represented by a sequence of bytes, its
/// `Debug` implementation will attempt to print it as a normal string. (That
/// is, not a sequence of decimal numbers.)
#[derive(Clone, Eq, PartialEq)]
pub struct Literal(pub Box<[u8]>);

impl core::fmt::Debug for Literal {
    fn fmt(&self, f: &mut core::fmt::Formatter) -> core::fmt::Result {
        crate::debug::Bytes(&self.0).fmt(f)
    }
}

/// The high-level intermediate representation of a character class.
///
/// A character class corresponds to a set of characters. A character is either
/// defined by a Unicode scalar value or a byte. Unicode characters are used
/// by default, while bytes are used when Unicode mode (via the `u` flag) is
/// disabled.
///
/// A character class, regardless of its character type, is represented by a
/// sequence of non-overlapping non-adjacent ranges of characters.
///
/// Note that `Bytes` variant may be produced even when it exclusively matches
/// valid UTF-8. This is because a `Bytes` variant represents an intention by
/// the author of the regular expression to disable Unicode mode, which in turn
/// impacts the semantics of case insensitive matching. For example, `(?i)k`
/// and `(?i-u)k` will not match the same set of strings.
#[derive(Clone, Eq, PartialEq)]
pub enum Class {
    /// A set of characters represented by Unicode scalar values.
    Unicode(ClassUnicode),
    /// A set of characters represented by arbitrary bytes (one byte per
    /// character).
    Bytes(ClassBytes),
}

impl Class {
    /// Apply Unicode simple case folding to this character class, in place.
    /// The character class will be expanded to include all simple case folded
    /// character variants.
    ///
    /// If this is a byte oriented character class, then this will be limited
    /// to the ASCII ranges `A-Z` and `a-z`.
    ///
    /// # Panics
    ///
    /// This routine panics when the case mapping data necessary for this
    /// routine to complete is unavailable. This occurs when the `unicode-case`
    /// feature is not enabled and the underlying class is Unicode oriented.
    ///
    /// Callers should prefer using `try_case_fold_simple` instead, which will
    /// return an error instead of panicking.
    pub fn case_fold_simple(&mut self) {
        match *self {
            Class::Unicode(ref mut x) => x.case_fold_simple(),
            Class::Bytes(ref mut x) => x.case_fold_simple(),
        }
    }

    /// Apply Unicode simple case folding to this character class, in place.
    /// The character class will be expanded to include all simple case folded
    /// character variants.
    ///
    /// If this is a byte oriented character class, then this will be limited
    /// to the ASCII ranges `A-Z` and `a-z`.
    ///
    /// # Error
    ///
    /// This routine returns an error when the case mapping data necessary
    /// for this routine to complete is unavailable. This occurs when the
    /// `unicode-case` feature is not enabled and the underlying class is
    /// Unicode oriented.
    pub fn try_case_fold_simple(
        &mut self,
    ) -> core::result::Result<(), CaseFoldError> {
        match *self {
            Class::Unicode(ref mut x) => x.try_case_fold_simple()?,
            Class::Bytes(ref mut x) => x.case_fold_simple(),
        }
        Ok(())
    }

    /// Negate this character class in place.
    ///
    /// After completion, this character class will contain precisely the
    /// characters that weren't previously in the class.
    pub fn negate(&mut self) {
        match *self {
            Class::Unicode(ref mut x) => x.negate(),
            Class::Bytes(ref mut x) => x.negate(),
        }
    }

    /// Returns true if and only if this character class will only ever match
    /// valid UTF-8.
    ///
    /// A character class can match invalid UTF-8 only when the following
    /// conditions are met:
    ///
    /// 1. The translator was configured to permit generating an expression
    ///    that can match invalid UTF-8. (By default, this is disabled.)
    /// 2. Unicode mode (via the `u` flag) was disabled either in the concrete
    ///    syntax or in the parser builder. By default, Unicode mode is
    ///    enabled.
    pub fn is_utf8(&self) -> bool {
        match *self {
            Class::Unicode(_) => true,
            Class::Bytes(ref x) => x.is_ascii(),
        }
    }

    /// Returns the length, in bytes, of the smallest string matched by this
    /// character class.
    ///
    /// For non-empty byte oriented classes, this always returns `1`. For
    /// non-empty Unicode oriented classes, this can return `1`, `2`, `3` or
    /// `4`. For empty classes, `None` is returned. It is impossible for `0` to
    /// be returned.
    ///
    /// # Example
    ///
    /// This example shows some examples of regexes and their corresponding
    /// minimum length, if any.
    ///
    /// ```
    /// use regex_syntax::{hir::Properties, parse};
    ///
    /// // The empty string has a min length of 0.
    /// let hir = parse(r"")?;
    /// assert_eq!(Some(0), hir.properties().minimum_len());
    /// // As do other types of regexes that only match the empty string.
    /// let hir = parse(r"^$\b\B")?;
    /// assert_eq!(Some(0), hir.properties().minimum_len());
    /// // A regex that can match the empty string but match more is still 0.
    /// let hir = parse(r"a*")?;
    /// assert_eq!(Some(0), hir.properties().minimum_len());
    /// // A regex that matches nothing has no minimum defined.
    /// let hir = parse(r"[a&&b]")?;
    /// assert_eq!(None, hir.properties().minimum_len());
    /// // Character classes usually have a minimum length of 1.
    /// let hir = parse(r"\w")?;
    /// assert_eq!(Some(1), hir.properties().minimum_len());
    /// // But sometimes Unicode classes might be bigger!
    /// let hir = parse(r"\p{Cyrillic}")?;
    /// assert_eq!(Some(2), hir.properties().minimum_len());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn minimum_len(&self) -> Option<usize> {
        match *self {
            Class::Unicode(ref x) => x.minimum_len(),
            Class::Bytes(ref x) => x.minimum_len(),
        }
    }

    /// Returns the length, in bytes, of the longest string matched by this
    /// character class.
    ///
    /// For non-empty byte oriented classes, this always returns `1`. For
    /// non-empty Unicode oriented classes, this can return `1`, `2`, `3` or
    /// `4`. For empty classes, `None` is returned. It is impossible for `0` to
    /// be returned.
    ///
    /// # Example
    ///
    /// This example shows some examples of regexes and their corresponding
    /// maximum length, if any.
    ///
    /// ```
    /// use regex_syntax::{hir::Properties, parse};
    ///
    /// // The empty string has a max length of 0.
    /// let hir = parse(r"")?;
    /// assert_eq!(Some(0), hir.properties().maximum_len());
    /// // As do other types of regexes that only match the empty string.
    /// let hir = parse(r"^$\b\B")?;
    /// assert_eq!(Some(0), hir.properties().maximum_len());
    /// // A regex that matches nothing has no maximum defined.
    /// let hir = parse(r"[a&&b]")?;
    /// assert_eq!(None, hir.properties().maximum_len());
    /// // Bounded repeats work as you expect.
    /// let hir = parse(r"x{2,10}")?;
    /// assert_eq!(Some(10), hir.properties().maximum_len());
    /// // An unbounded repeat means there is no maximum.
    /// let hir = parse(r"x{2,}")?;
    /// assert_eq!(None, hir.properties().maximum_len());
    /// // With Unicode enabled, \w can match up to 4 bytes!
    /// let hir = parse(r"\w")?;
    /// assert_eq!(Some(4), hir.properties().maximum_len());
    /// // Without Unicode enabled, \w matches at most 1 byte.
    /// let hir = parse(r"(?-u)\w")?;
    /// assert_eq!(Some(1), hir.properties().maximum_len());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn maximum_len(&self) -> Option<usize> {
        match *self {
            Class::Unicode(ref x) => x.maximum_len(),
            Class::Bytes(ref x) => x.maximum_len(),
        }
    }

    /// Returns true if and only if this character class is empty. That is,
    /// it has no elements.
    ///
    /// An empty character can never match anything, including an empty string.
    pub fn is_empty(&self) -> bool {
        match *self {
            Class::Unicode(ref x) => x.ranges().is_empty(),
            Class::Bytes(ref x) => x.ranges().is_empty(),
        }
    }

    /// If this class consists of exactly one element (whether a codepoint or a
    /// byte), then return it as a literal byte string.
    ///
    /// If this class is empty or contains more than one element, then `None`
    /// is returned.
    pub fn literal(&self) -> Option<Vec<u8>> {
        match *self {
            Class::Unicode(ref x) => x.literal(),
            Class::Bytes(ref x) => x.literal(),
        }
    }
}

impl core::fmt::Debug for Class {
    fn fmt(&self, f: &mut core::fmt::Formatter) -> core::fmt::Result {
        use crate::debug::Byte;

        let mut fmter = f.debug_set();
        match *self {
            Class::Unicode(ref cls) => {
                for r in cls.ranges().iter() {
                    fmter.entry(&(r.start..=r.end));
                }
            }
            Class::Bytes(ref cls) => {
                for r in cls.ranges().iter() {
                    fmter.entry(&(Byte(r.start)..=Byte(r.end)));
                }
            }
        }
        fmter.finish()
    }
}

/// A set of characters represented by Unicode scalar values.
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct ClassUnicode {
    set: IntervalSet<ClassUnicodeRange>,
}

impl ClassUnicode {
    /// Create a new class from a sequence of ranges.
    ///
    /// The given ranges do not need to be in any specific order, and ranges
    /// may overlap. Ranges will automatically be sorted into a canonical
    /// non-overlapping order.
    pub fn new<I>(ranges: I) -> ClassUnicode
    where
        I: IntoIterator<Item = ClassUnicodeRange>,
    {
        ClassUnicode { set: IntervalSet::new(ranges) }
    }

    /// Create a new class with no ranges.
    ///
    /// An empty class matches nothing. That is, it is equivalent to
    /// [`Hir::fail`].
    pub fn empty() -> ClassUnicode {
        ClassUnicode::new(vec![])
    }

    /// Add a new range to this set.
    pub fn push(&mut self, range: ClassUnicodeRange) {
        self.set.push(range);
    }

    /// Return an iterator over all ranges in this class.
    ///
    /// The iterator yields ranges in ascending order.
    pub fn iter(&self) -> ClassUnicodeIter<'_> {
        ClassUnicodeIter(self.set.iter())
    }

    /// Return the underlying ranges as a slice.
    pub fn ranges(&self) -> &[ClassUnicodeRange] {
        self.set.intervals()
    }

    /// Expand this character class such that it contains all case folded
    /// characters, according to Unicode's "simple" mapping. For example, if
    /// this class consists of the range `a-z`, then applying case folding will
    /// result in the class containing both the ranges `a-z` and `A-Z`.
    ///
    /// # Panics
    ///
    /// This routine panics when the case mapping data necessary for this
    /// routine to complete is unavailable. This occurs when the `unicode-case`
    /// feature is not enabled.
    ///
    /// Callers should prefer using `try_case_fold_simple` instead, which will
    /// return an error instead of panicking.
    pub fn case_fold_simple(&mut self) {
        self.set
            .case_fold_simple()
            .expect("unicode-case feature must be enabled");
    }

    /// Expand this character class such that it contains all case folded
    /// characters, according to Unicode's "simple" mapping. For example, if
    /// this class consists of the range `a-z`, then applying case folding will
    /// result in the class containing both the ranges `a-z` and `A-Z`.
    ///
    /// # Error
    ///
    /// This routine returns an error when the case mapping data necessary
    /// for this routine to complete is unavailable. This occurs when the
    /// `unicode-case` feature is not enabled.
    pub fn try_case_fold_simple(
        &mut self,
    ) -> core::result::Result<(), CaseFoldError> {
        self.set.case_fold_simple()
    }

    /// Negate this character class.
    ///
    /// For all `c` where `c` is a Unicode scalar value, if `c` was in this
    /// set, then it will not be in this set after negation.
    pub fn negate(&mut self) {
        self.set.negate();
    }

    /// Union this character class with the given character class, in place.
    pub fn union(&mut self, other: &ClassUnicode) {
        self.set.union(&other.set);
    }

    /// Intersect this character class with the given character class, in
    /// place.
    pub fn intersect(&mut self, other: &ClassUnicode) {
        self.set.intersect(&other.set);
    }

    /// Subtract the given character class from this character class, in place.
    pub fn difference(&mut self, other: &ClassUnicode) {
        self.set.difference(&other.set);
    }

    /// Compute the symmetric difference of the given character classes, in
    /// place.
    ///
    /// This computes the symmetric difference of two character classes. This
    /// removes all elements in this class that are also in the given class,
    /// but all adds all elements from the given class that aren't in this
    /// class. That is, the class will contain all elements in either class,
    /// but will not contain any elements that are in both classes.
    pub fn symmetric_difference(&mut self, other: &ClassUnicode) {
        self.set.symmetric_difference(&other.set);
    }

    /// Returns true if and only if this character class will either match
    /// nothing or only ASCII bytes. Stated differently, this returns false
    /// if and only if this class contains a non-ASCII codepoint.
    pub fn is_ascii(&self) -> bool {
        self.set.intervals().last().map_or(true, |r| r.end <= '\x7F')
    }

    /// Returns the length, in bytes, of the smallest string matched by this
    /// character class.
    ///
    /// Returns `None` when the class is empty.
    pub fn minimum_len(&self) -> Option<usize> {
        let first = self.ranges().get(0)?;
        // Correct because c1 < c2 implies c1.len_utf8() < c2.len_utf8().
        Some(first.start.len_utf8())
    }

    /// Returns the length, in bytes, of the longest string matched by this
    /// character class.
    ///
    /// Returns `None` when the class is empty.
    pub fn maximum_len(&self) -> Option<usize> {
        let last = self.ranges().last()?;
        // Correct because c1 < c2 implies c1.len_utf8() < c2.len_utf8().
        Some(last.end.len_utf8())
    }

    /// If this class consists of exactly one codepoint, then return it as
    /// a literal byte string.
    ///
    /// If this class is empty or contains more than one codepoint, then `None`
    /// is returned.
    pub fn literal(&self) -> Option<Vec<u8>> {
        let rs = self.ranges();
        if rs.len() == 1 && rs[0].start == rs[0].end {
            Some(rs[0].start.encode_utf8(&mut [0; 4]).to_string().into_bytes())
        } else {
            None
        }
    }

    /// If this class consists of only ASCII ranges, then return its
    /// corresponding and equivalent byte class.
    pub fn to_byte_class(&self) -> Option<ClassBytes> {
        if !self.is_ascii() {
            return None;
        }
        Some(ClassBytes::new(self.ranges().iter().map(|r| {
            // Since we are guaranteed that our codepoint range is ASCII, the
            // 'u8::try_from' calls below are guaranteed to be correct.
            ClassBytesRange {
                start: u8::try_from(r.start).unwrap(),
                end: u8::try_from(r.end).unwrap(),
            }
        })))
    }
}

/// An iterator over all ranges in a Unicode character class.
///
/// The lifetime `'a` refers to the lifetime of the underlying class.
#[derive(Debug)]
pub struct ClassUnicodeIter<'a>(IntervalSetIter<'a, ClassUnicodeRange>);

impl<'a> Iterator for ClassUnicodeIter<'a> {
    type Item = &'a ClassUnicodeRange;

    fn next(&mut self) -> Option<&'a ClassUnicodeRange> {
        self.0.next()
    }
}

/// A single range of characters represented by Unicode scalar values.
///
/// The range is closed. That is, the start and end of the range are included
/// in the range.
#[derive(Clone, Copy, Default, Eq, PartialEq, PartialOrd, Ord)]
pub struct ClassUnicodeRange {
    start: char,
    end: char,
}

impl core::fmt::Debug for ClassUnicodeRange {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        let start = if !self.start.is_whitespace() && !self.start.is_control()
        {
            self.start.to_string()
        } else {
            format!("0x{:X}", u32::from(self.start))
        };
        let end = if !self.end.is_whitespace() && !self.end.is_control() {
            self.end.to_string()
        } else {
            format!("0x{:X}", u32::from(self.end))
        };
        f.debug_struct("ClassUnicodeRange")
            .field("start", &start)
            .field("end", &end)
            .finish()
    }
}

impl Interval for ClassUnicodeRange {
    type Bound = char;

    #[inline]
    fn lower(&self) -> char {
        self.start
    }
    #[inline]
    fn upper(&self) -> char {
        self.end
    }
    #[inline]
    fn set_lower(&mut self, bound: char) {
        self.start = bound;
    }
    #[inline]
    fn set_upper(&mut self, bound: char) {
        self.end = bound;
    }

    /// Apply simple case folding to this Unicode scalar value range.
    ///
    /// Additional ranges are appended to the given vector. Canonical ordering
    /// is *not* maintained in the given vector.
    fn case_fold_simple(
        &self,
        ranges: &mut Vec<ClassUnicodeRange>,
    ) -> Result<(), unicode::CaseFoldError> {
        let mut folder = unicode::SimpleCaseFolder::new()?;
        if !folder.overlaps(self.start, self.end) {
            return Ok(());
        }
        let (start, end) = (u32::from(self.start), u32::from(self.end));
        for cp in (start..=end).filter_map(char::from_u32) {
            for &cp_folded in folder.mapping(cp) {
                ranges.push(ClassUnicodeRange::new(cp_folded, cp_folded));
            }
        }
        Ok(())
    }
}

impl ClassUnicodeRange {
    /// Create a new Unicode scalar value range for a character class.
    ///
    /// The returned range is always in a canonical form. That is, the range
    /// returned always satisfies the invariant that `start <= end`.
    pub fn new(start: char, end: char) -> ClassUnicodeRange {
        ClassUnicodeRange::create(start, end)
    }

    /// Return the start of this range.
    ///
    /// The start of a range is always less than or equal to the end of the
    /// range.
    pub fn start(&self) -> char {
        self.start
    }

    /// Return the end of this range.
    ///
    /// The end of a range is always greater than or equal to the start of the
    /// range.
    pub fn end(&self) -> char {
        self.end
    }

    /// Returns the number of codepoints in this range.
    pub fn len(&self) -> usize {
        let diff = 1 + u32::from(self.end) - u32::from(self.start);
        // This is likely to panic in 16-bit targets since a usize can only fit
        // 2^16. It's not clear what to do here, other than to return an error
        // when building a Unicode class that contains a range whose length
        // overflows usize. (Which, to be honest, is probably quite common on
        // 16-bit targets. For example, this would imply that '.' and '\p{any}'
        // would be impossible to build.)
        usize::try_from(diff).expect("char class len fits in usize")
    }
}

/// A set of characters represented by arbitrary bytes (where one byte
/// corresponds to one character).
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct ClassBytes {
    set: IntervalSet<ClassBytesRange>,
}

impl ClassBytes {
    /// Create a new class from a sequence of ranges.
    ///
    /// The given ranges do not need to be in any specific order, and ranges
    /// may overlap. Ranges will automatically be sorted into a canonical
    /// non-overlapping order.
    pub fn new<I>(ranges: I) -> ClassBytes
    where
        I: IntoIterator<Item = ClassBytesRange>,
    {
        ClassBytes { set: IntervalSet::new(ranges) }
    }

    /// Create a new class with no ranges.
    ///
    /// An empty class matches nothing. That is, it is equivalent to
    /// [`Hir::fail`].
    pub fn empty() -> ClassBytes {
        ClassBytes::new(vec![])
    }

    /// Add a new range to this set.
    pub fn push(&mut self, range: ClassBytesRange) {
        self.set.push(range);
    }

    /// Return an iterator over all ranges in this class.
    ///
    /// The iterator yields ranges in ascending order.
    pub fn iter(&self) -> ClassBytesIter<'_> {
        ClassBytesIter(self.set.iter())
    }

    /// Return the underlying ranges as a slice.
    pub fn ranges(&self) -> &[ClassBytesRange] {
        self.set.intervals()
    }

    /// Expand this character class such that it contains all case folded
    /// characters. For example, if this class consists of the range `a-z`,
    /// then applying case folding will result in the class containing both the
    /// ranges `a-z` and `A-Z`.
    ///
    /// Note that this only applies ASCII case folding, which is limited to the
    /// characters `a-z` and `A-Z`.
    pub fn case_fold_simple(&mut self) {
        self.set.case_fold_simple().expect("ASCII case folding never fails");
    }

    /// Negate this byte class.
    ///
    /// For all `b` where `b` is a any byte, if `b` was in this set, then it
    /// will not be in this set after negation.
    pub fn negate(&mut self) {
        self.set.negate();
    }

    /// Union this byte class with the given byte class, in place.
    pub fn union(&mut self, other: &ClassBytes) {
        self.set.union(&other.set);
    }

    /// Intersect this byte class with the given byte class, in place.
    pub fn intersect(&mut self, other: &ClassBytes) {
        self.set.intersect(&other.set);
    }

    /// Subtract the given byte class from this byte class, in place.
    pub fn difference(&mut self, other: &ClassBytes) {
        self.set.difference(&other.set);
    }

    /// Compute the symmetric difference of the given byte classes, in place.
    ///
    /// This computes the symmetric difference of two byte classes. This
    /// removes all elements in this class that are also in the given class,
    /// but all adds all elements from the given class that aren't in this
    /// class. That is, the class will contain all elements in either class,
    /// but will not contain any elements that are in both classes.
    pub fn symmetric_difference(&mut self, other: &ClassBytes) {
        self.set.symmetric_difference(&other.set);
    }

    /// Returns true if and only if this character class will either match
    /// nothing or only ASCII bytes. Stated differently, this returns false
    /// if and only if this class contains a non-ASCII byte.
    pub fn is_ascii(&self) -> bool {
        self.set.intervals().last().map_or(true, |r| r.end <= 0x7F)
    }

    /// Returns the length, in bytes, of the smallest string matched by this
    /// character class.
    ///
    /// Returns `None` when the class is empty.
    pub fn minimum_len(&self) -> Option<usize> {
        if self.ranges().is_empty() {
            None
        } else {
            Some(1)
        }
    }

    /// Returns the length, in bytes, of the longest string matched by this
    /// character class.
    ///
    /// Returns `None` when the class is empty.
    pub fn maximum_len(&self) -> Option<usize> {
        if self.ranges().is_empty() {
            None
        } else {
            Some(1)
        }
    }

    /// If this class consists of exactly one byte, then return it as
    /// a literal byte string.
    ///
    /// If this class is empty or contains more than one byte, then `None`
    /// is returned.
    pub fn literal(&self) -> Option<Vec<u8>> {
        let rs = self.ranges();
        if rs.len() == 1 && rs[0].start == rs[0].end {
            Some(vec![rs[0].start])
        } else {
            None
        }
    }

    /// If this class consists of only ASCII ranges, then return its
    /// corresponding and equivalent Unicode class.
    pub fn to_unicode_class(&self) -> Option<ClassUnicode> {
        if !self.is_ascii() {
            return None;
        }
        Some(ClassUnicode::new(self.ranges().iter().map(|r| {
            // Since we are guaranteed that our byte range is ASCII, the
            // 'char::from' calls below are correct and will not erroneously
            // convert a raw byte value into its corresponding codepoint.
            ClassUnicodeRange {
                start: char::from(r.start),
                end: char::from(r.end),
            }
        })))
    }
}

/// An iterator over all ranges in a byte character class.
///
/// The lifetime `'a` refers to the lifetime of the underlying class.
#[derive(Debug)]
pub struct ClassBytesIter<'a>(IntervalSetIter<'a, ClassBytesRange>);

impl<'a> Iterator for ClassBytesIter<'a> {
    type Item = &'a ClassBytesRange;

    fn next(&mut self) -> Option<&'a ClassBytesRange> {
        self.0.next()
    }
}

/// A single range of characters represented by arbitrary bytes.
///
/// The range is closed. That is, the start and end of the range are included
/// in the range.
#[derive(Clone, Copy, Default, Eq, PartialEq, PartialOrd, Ord)]
pub struct ClassBytesRange {
    start: u8,
    end: u8,
}

impl Interval for ClassBytesRange {
    type Bound = u8;

    #[inline]
    fn lower(&self) -> u8 {
        self.start
    }
    #[inline]
    fn upper(&self) -> u8 {
        self.end
    }
    #[inline]
    fn set_lower(&mut self, bound: u8) {
        self.start = bound;
    }
    #[inline]
    fn set_upper(&mut self, bound: u8) {
        self.end = bound;
    }

    /// Apply simple case folding to this byte range. Only ASCII case mappings
    /// (for a-z) are applied.
    ///
    /// Additional ranges are appended to the given vector. Canonical ordering
    /// is *not* maintained in the given vector.
    fn case_fold_simple(
        &self,
        ranges: &mut Vec<ClassBytesRange>,
    ) -> Result<(), unicode::CaseFoldError> {
        if !ClassBytesRange::new(b'a', b'z').is_intersection_empty(self) {
            let lower = cmp::max(self.start, b'a');
            let upper = cmp::min(self.end, b'z');
            ranges.push(ClassBytesRange::new(lower - 32, upper - 32));
        }
        if !ClassBytesRange::new(b'A', b'Z').is_intersection_empty(self) {
            let lower = cmp::max(self.start, b'A');
            let upper = cmp::min(self.end, b'Z');
            ranges.push(ClassBytesRange::new(lower + 32, upper + 32));
        }
        Ok(())
    }
}

impl ClassBytesRange {
    /// Create a new byte range for a character class.
    ///
    /// The returned range is always in a canonical form. That is, the range
    /// returned always satisfies the invariant that `start <= end`.
    pub fn new(start: u8, end: u8) -> ClassBytesRange {
        ClassBytesRange::create(start, end)
    }

    /// Return the start of this range.
    ///
    /// The start of a range is always less than or equal to the end of the
    /// range.
    pub fn start(&self) -> u8 {
        self.start
    }

    /// Return the end of this range.
    ///
    /// The end of a range is always greater than or equal to the start of the
    /// range.
    pub fn end(&self) -> u8 {
        self.end
    }

    /// Returns the number of bytes in this range.
    pub fn len(&self) -> usize {
        usize::from(self.end.checked_sub(self.start).unwrap())
            .checked_add(1)
            .unwrap()
    }
}

impl core::fmt::Debug for ClassBytesRange {
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        f.debug_struct("ClassBytesRange")
            .field("start", &crate::debug::Byte(self.start))
            .field("end", &crate::debug::Byte(self.end))
            .finish()
    }
}

/// The high-level intermediate representation for a look-around assertion.
///
/// An assertion match is always zero-length. Also called an "empty match."
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub enum Look {
    /// Match the beginning of text. Specifically, this matches at the starting
    /// position of the input.
    Start = 1 << 0,
    /// Match the end of text. Specifically, this matches at the ending
    /// position of the input.
    End = 1 << 1,
    /// Match the beginning of a line or the beginning of text. Specifically,
    /// this matches at the starting position of the input, or at the position
    /// immediately following a `\n` character.
    StartLF = 1 << 2,
    /// Match the end of a line or the end of text. Specifically, this matches
    /// at the end position of the input, or at the position immediately
    /// preceding a `\n` character.
    EndLF = 1 << 3,
    /// Match the beginning of a line or the beginning of text. Specifically,
    /// this matches at the starting position of the input, or at the position
    /// immediately following either a `\r` or `\n` character, but never after
    /// a `\r` when a `\n` follows.
    StartCRLF = 1 << 4,
    /// Match the end of a line or the end of text. Specifically, this matches
    /// at the end position of the input, or at the position immediately
    /// preceding a `\r` or `\n` character, but never before a `\n` when a `\r`
    /// precedes it.
    EndCRLF = 1 << 5,
    /// Match an ASCII-only word boundary. That is, this matches a position
    /// where the left adjacent character and right adjacent character
    /// correspond to a word and non-word or a non-word and word character.
    WordAscii = 1 << 6,
    /// Match an ASCII-only negation of a word boundary.
    WordAsciiNegate = 1 << 7,
    /// Match a Unicode-aware word boundary. That is, this matches a position
    /// where the left adjacent character and right adjacent character
    /// correspond to a word and non-word or a non-word and word character.
    WordUnicode = 1 << 8,
    /// Match a Unicode-aware negation of a word boundary.
    WordUnicodeNegate = 1 << 9,
}

impl Look {
    /// Flip the look-around assertion to its equivalent for reverse searches.
    /// For example, `StartLF` gets translated to `EndLF`.
    ///
    /// Some assertions, such as `WordUnicode`, remain the same since they
    /// match the same positions regardless of the direction of the search.
    #[inline]
    pub const fn reversed(self) -> Look {
        match self {
            Look::Start => Look::End,
            Look::End => Look::Start,
            Look::StartLF => Look::EndLF,
            Look::EndLF => Look::StartLF,
            Look::StartCRLF => Look::EndCRLF,
            Look::EndCRLF => Look::StartCRLF,
            Look::WordAscii => Look::WordAscii,
            Look::WordAsciiNegate => Look::WordAsciiNegate,
            Look::WordUnicode => Look::WordUnicode,
            Look::WordUnicodeNegate => Look::WordUnicodeNegate,
        }
    }

    /// Return the underlying representation of this look-around enumeration
    /// as an integer. Giving the return value to the [`Look::from_repr`]
    /// constructor is guaranteed to return the same look-around variant that
    /// one started with within a semver compatible release of this crate.
    #[inline]
    pub const fn as_repr(self) -> u16 {
        // AFAIK, 'as' is the only way to zero-cost convert an int enum to an
        // actual int.
        self as u16
    }

    /// Given the underlying representation of a `Look` value, return the
    /// corresponding `Look` value if the representation is valid. Otherwise
    /// `None` is returned.
    #[inline]
    pub const fn from_repr(repr: u16) -> Option<Look> {
        match repr {
            0b00_0000_0001 => Some(Look::Start),
            0b00_0000_0010 => Some(Look::End),
            0b00_0000_0100 => Some(Look::StartLF),
            0b00_0000_1000 => Some(Look::EndLF),
            0b00_0001_0000 => Some(Look::StartCRLF),
            0b00_0010_0000 => Some(Look::EndCRLF),
            0b00_0100_0000 => Some(Look::WordAscii),
            0b00_1000_0000 => Some(Look::WordAsciiNegate),
            0b01_0000_0000 => Some(Look::WordUnicode),
            0b10_0000_0000 => Some(Look::WordUnicodeNegate),
            _ => None,
        }
    }

    /// Returns a convenient single codepoint representation of this
    /// look-around assertion. Each assertion is guaranteed to be represented
    /// by a distinct character.
    ///
    /// This is useful for succinctly representing a look-around assertion in
    /// human friendly but succinct output intended for a programmer working on
    /// regex internals.
    #[inline]
    pub const fn as_char(self) -> char {
        match self {
            Look::Start => 'A',
            Look::End => 'z',
            Look::StartLF => '^',
            Look::EndLF => '$',
            Look::StartCRLF => 'r',
            Look::EndCRLF => 'R',
            Look::WordAscii => 'b',
            Look::WordAsciiNegate => 'B',
            Look::WordUnicode => '𝛃',
            Look::WordUnicodeNegate => '𝚩',
        }
    }
}

/// The high-level intermediate representation for a capturing group.
///
/// A capturing group always has an index and a child expression. It may
/// also have a name associated with it (e.g., `(?P<foo>\w)`), but it's not
/// necessary.
///
/// Note that there is no explicit representation of a non-capturing group
/// in a `Hir`. Instead, non-capturing grouping is handled automatically by
/// the recursive structure of the `Hir` itself.
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct Capture {
    /// The capture index of the capture.
    pub index: u32,
    /// The name of the capture, if it exists.
    pub name: Option<Box<str>>,
    /// The expression inside the capturing group, which may be empty.
    pub sub: Box<Hir>,
}

/// The high-level intermediate representation of a repetition operator.
///
/// A repetition operator permits the repetition of an arbitrary
/// sub-expression.
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct Repetition {
    /// The minimum range of the repetition.
    ///
    /// Note that special cases like `?`, `+` and `*` all get translated into
    /// the ranges `{0,1}`, `{1,}` and `{0,}`, respectively.
    ///
    /// When `min` is zero, this expression can match the empty string
    /// regardless of what its sub-expression is.
    pub min: u32,
    /// The maximum range of the repetition.
    ///
    /// Note that when `max` is `None`, `min` acts as a lower bound but where
    /// there is no upper bound. For something like `x{5}` where the min and
    /// max are equivalent, `min` will be set to `5` and `max` will be set to
    /// `Some(5)`.
    pub max: Option<u32>,
    /// Whether this repetition operator is greedy or not. A greedy operator
    /// will match as much as it can. A non-greedy operator will match as
    /// little as it can.
    ///
    /// Typically, operators are greedy by default and are only non-greedy when
    /// a `?` suffix is used, e.g., `(expr)*` is greedy while `(expr)*?` is
    /// not. However, this can be inverted via the `U` "ungreedy" flag.
    pub greedy: bool,
    /// The expression being repeated.
    pub sub: Box<Hir>,
}

impl Repetition {
    /// Returns a new repetition with the same `min`, `max` and `greedy`
    /// values, but with its sub-expression replaced with the one given.
    pub fn with(&self, sub: Hir) -> Repetition {
        Repetition {
            min: self.min,
            max: self.max,
            greedy: self.greedy,
            sub: Box::new(sub),
        }
    }
}

/// A type describing the different flavors of `.`.
///
/// This type is meant to be used with [`Hir::dot`], which is a convenience
/// routine for building HIR values derived from the `.` regex.
#[non_exhaustive]
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
pub enum Dot {
    /// Matches the UTF-8 encoding of any Unicode scalar value.
    ///
    /// This is equivalent to `(?su:.)` and also `\p{any}`.
    AnyChar,
    /// Matches any byte value.
    ///
    /// This is equivalent to `(?s-u:.)` and also `(?-u:[\x00-\xFF])`.
    AnyByte,
    /// Matches the UTF-8 encoding of any Unicode scalar value except for the
    /// `char` given.
    ///
    /// This is equivalent to using `(?u-s:.)` with the line terminator set
    /// to a particular ASCII byte. (Because of peculiarities in the regex
    /// engines, a line terminator must be a single byte. It follows that when
    /// UTF-8 mode is enabled, this single byte must also be a Unicode scalar
    /// value. That is, ti must be ASCII.)
    ///
    /// (This and `AnyCharExceptLF` both exist because of legacy reasons.
    /// `AnyCharExceptLF` will be dropped in the next breaking change release.)
    AnyCharExcept(char),
    /// Matches the UTF-8 encoding of any Unicode scalar value except for `\n`.
    ///
    /// This is equivalent to `(?u-s:.)` and also `[\p{any}--\n]`.
    AnyCharExceptLF,
    /// Matches the UTF-8 encoding of any Unicode scalar value except for `\r`
    /// and `\n`.
    ///
    /// This is equivalent to `(?uR-s:.)` and also `[\p{any}--\r\n]`.
    AnyCharExceptCRLF,
    /// Matches any byte value except for the `u8` given.
    ///
    /// This is equivalent to using `(?-us:.)` with the line terminator set
    /// to a particular ASCII byte. (Because of peculiarities in the regex
    /// engines, a line terminator must be a single byte. It follows that when
    /// UTF-8 mode is enabled, this single byte must also be a Unicode scalar
    /// value. That is, ti must be ASCII.)
    ///
    /// (This and `AnyByteExceptLF` both exist because of legacy reasons.
    /// `AnyByteExceptLF` will be dropped in the next breaking change release.)
    AnyByteExcept(u8),
    /// Matches any byte value except for `\n`.
    ///
    /// This is equivalent to `(?-su:.)` and also `(?-u:[[\x00-\xFF]--\n])`.
    AnyByteExceptLF,
    /// Matches any byte value except for `\r` and `\n`.
    ///
    /// This is equivalent to `(?R-su:.)` and also `(?-u:[[\x00-\xFF]--\r\n])`.
    AnyByteExceptCRLF,
}

/// A custom `Drop` impl is used for `HirKind` such that it uses constant stack
/// space but heap space proportional to the depth of the total `Hir`.
impl Drop for Hir {
    fn drop(&mut self) {
        use core::mem;

        match *self.kind() {
            HirKind::Empty
            | HirKind::Literal(_)
            | HirKind::Class(_)
            | HirKind::Look(_) => return,
            HirKind::Capture(ref x) if x.sub.kind.subs().is_empty() => return,
            HirKind::Repetition(ref x) if x.sub.kind.subs().is_empty() => {
                return
            }
            HirKind::Concat(ref x) if x.is_empty() => return,
            HirKind::Alternation(ref x) if x.is_empty() => return,
            _ => {}
        }

        let mut stack = vec![mem::replace(self, Hir::empty())];
        while let Some(mut expr) = stack.pop() {
            match expr.kind {
                HirKind::Empty
                | HirKind::Literal(_)
                | HirKind::Class(_)
                | HirKind::Look(_) => {}
                HirKind::Capture(ref mut x) => {
                    stack.push(mem::replace(&mut x.sub, Hir::empty()));
                }
                HirKind::Repetition(ref mut x) => {
                    stack.push(mem::replace(&mut x.sub, Hir::empty()));
                }
                HirKind::Concat(ref mut x) => {
                    stack.extend(x.drain(..));
                }
                HirKind::Alternation(ref mut x) => {
                    stack.extend(x.drain(..));
                }
            }
        }
    }
}

/// A type that collects various properties of an HIR value.
///
/// Properties are always scalar values and represent meta data that is
/// computed inductively on an HIR value. Properties are defined for all
/// HIR values.
///
/// All methods on a `Properties` value take constant time and are meant to
/// be cheap to call.
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct Properties(Box<PropertiesI>);

/// The property definition. It is split out so that we can box it, and
/// there by make `Properties` use less stack size. This is kind-of important
/// because every HIR value has a `Properties` attached to it.
///
/// This does have the unfortunate consequence that creating any HIR value
/// always leads to at least one alloc for properties, but this is generally
/// true anyway (for pretty much all HirKinds except for look-arounds).
#[derive(Clone, Debug, Eq, PartialEq)]
struct PropertiesI {
    minimum_len: Option<usize>,
    maximum_len: Option<usize>,
    look_set: LookSet,
    look_set_prefix: LookSet,
    look_set_suffix: LookSet,
    look_set_prefix_any: LookSet,
    look_set_suffix_any: LookSet,
    utf8: bool,
    explicit_captures_len: usize,
    static_explicit_captures_len: Option<usize>,
    literal: bool,
    alternation_literal: bool,
}

impl Properties {
    /// Returns the length (in bytes) of the smallest string matched by this
    /// HIR.
    ///
    /// A return value of `0` is possible and occurs when the HIR can match an
    /// empty string.
    ///
    /// `None` is returned when there is no minimum length. This occurs in
    /// precisely the cases where the HIR matches nothing. i.e., The language
    /// the regex matches is empty. An example of such a regex is `\P{any}`.
    #[inline]
    pub fn minimum_len(&self) -> Option<usize> {
        self.0.minimum_len
    }

    /// Returns the length (in bytes) of the longest string matched by this
    /// HIR.
    ///
    /// A return value of `0` is possible and occurs when nothing longer than
    /// the empty string is in the language described by this HIR.
    ///
    /// `None` is returned when there is no longest matching string. This
    /// occurs when the HIR matches nothing or when there is no upper bound on
    /// the length of matching strings. Example of such regexes are `\P{any}`
    /// (matches nothing) and `a+` (has no upper bound).
    #[inline]
    pub fn maximum_len(&self) -> Option<usize> {
        self.0.maximum_len
    }

    /// Returns a set of all look-around assertions that appear at least once
    /// in this HIR value.
    #[inline]
    pub fn look_set(&self) -> LookSet {
        self.0.look_set
    }

    /// Returns a set of all look-around assertions that appear as a prefix for
    /// this HIR value. That is, the set returned corresponds to the set of
    /// assertions that must be passed before matching any bytes in a haystack.
    ///
    /// For example, `hir.look_set_prefix().contains(Look::Start)` returns true
    /// if and only if the HIR is fully anchored at the start.
    #[inline]
    pub fn look_set_prefix(&self) -> LookSet {
        self.0.look_set_prefix
    }

    /// Returns a set of all look-around assertions that appear as a _possible_
    /// prefix for this HIR value. That is, the set returned corresponds to the
    /// set of assertions that _may_ be passed before matching any bytes in a
    /// haystack.
    ///
    /// For example, `hir.look_set_prefix_any().contains(Look::Start)` returns
    /// true if and only if it's possible for the regex to match through a
    /// anchored assertion before consuming any input.
    #[inline]
    pub fn look_set_prefix_any(&self) -> LookSet {
        self.0.look_set_prefix_any
    }

    /// Returns a set of all look-around assertions that appear as a suffix for
    /// this HIR value. That is, the set returned corresponds to the set of
    /// assertions that must be passed in order to be considered a match after
    /// all other consuming HIR expressions.
    ///
    /// For example, `hir.look_set_suffix().contains(Look::End)` returns true
    /// if and only if the HIR is fully anchored at the end.
    #[inline]
    pub fn look_set_suffix(&self) -> LookSet {
        self.0.look_set_suffix
    }

    /// Returns a set of all look-around assertions that appear as a _possible_
    /// suffix for this HIR value. That is, the set returned corresponds to the
    /// set of assertions that _may_ be passed before matching any bytes in a
    /// haystack.
    ///
    /// For example, `hir.look_set_suffix_any().contains(Look::End)` returns
    /// true if and only if it's possible for the regex to match through a
    /// anchored assertion at the end of a match without consuming any input.
    #[inline]
    pub fn look_set_suffix_any(&self) -> LookSet {
        self.0.look_set_suffix_any
    }

    /// Return true if and only if the corresponding HIR will always match
    /// valid UTF-8.
    ///
    /// When this returns false, then it is possible for this HIR expression to
    /// match invalid UTF-8, including by matching between the code units of
    /// a single UTF-8 encoded codepoint.
    ///
    /// Note that this returns true even when the corresponding HIR can match
    /// the empty string. Since an empty string can technically appear between
    /// UTF-8 code units, it is possible for a match to be reported that splits
    /// a codepoint which could in turn be considered matching invalid UTF-8.
    /// However, it is generally assumed that such empty matches are handled
    /// specially by the search routine if it is absolutely required that
    /// matches not split a codepoint.
    ///
    /// # Example
    ///
    /// This code example shows the UTF-8 property of a variety of patterns.
    ///
    /// ```
    /// use regex_syntax::{ParserBuilder, parse};
    ///
    /// // Examples of 'is_utf8() == true'.
    /// assert!(parse(r"a")?.properties().is_utf8());
    /// assert!(parse(r"[^a]")?.properties().is_utf8());
    /// assert!(parse(r".")?.properties().is_utf8());
    /// assert!(parse(r"\W")?.properties().is_utf8());
    /// assert!(parse(r"\b")?.properties().is_utf8());
    /// assert!(parse(r"\B")?.properties().is_utf8());
    /// assert!(parse(r"(?-u)\b")?.properties().is_utf8());
    /// assert!(parse(r"(?-u)\B")?.properties().is_utf8());
    /// // Unicode mode is enabled by default, and in
    /// // that mode, all \x hex escapes are treated as
    /// // codepoints. So this actually matches the UTF-8
    /// // encoding of U+00FF.
    /// assert!(parse(r"\xFF")?.properties().is_utf8());
    ///
    /// // Now we show examples of 'is_utf8() == false'.
    /// // The only way to do this is to force the parser
    /// // to permit invalid UTF-8, otherwise all of these
    /// // would fail to parse!
    /// let parse = |pattern| {
    ///     ParserBuilder::new().utf8(false).build().parse(pattern)
    /// };
    /// assert!(!parse(r"(?-u)[^a]")?.properties().is_utf8());
    /// assert!(!parse(r"(?-u).")?.properties().is_utf8());
    /// assert!(!parse(r"(?-u)\W")?.properties().is_utf8());
    /// // Conversely to the equivalent example above,
    /// // when Unicode mode is disabled, \x hex escapes
    /// // are treated as their raw byte values.
    /// assert!(!parse(r"(?-u)\xFF")?.properties().is_utf8());
    /// // Note that just because we disabled UTF-8 in the
    /// // parser doesn't mean we still can't use Unicode.
    /// // It is enabled by default, so \xFF is still
    /// // equivalent to matching the UTF-8 encoding of
    /// // U+00FF by default.
    /// assert!(parse(r"\xFF")?.properties().is_utf8());
    /// // Even though we use raw bytes that individually
    /// // are not valid UTF-8, when combined together, the
    /// // overall expression *does* match valid UTF-8!
    /// assert!(parse(r"(?-u)\xE2\x98\x83")?.properties().is_utf8());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn is_utf8(&self) -> bool {
        self.0.utf8
    }

    /// Returns the total number of explicit capturing groups in the
    /// corresponding HIR.
    ///
    /// Note that this does not include the implicit capturing group
    /// corresponding to the entire match that is typically included by regex
    /// engines.
    ///
    /// # Example
    ///
    /// This method will return `0` for `a` and `1` for `(a)`:
    ///
    /// ```
    /// use regex_syntax::parse;
    ///
    /// assert_eq!(0, parse("a")?.properties().explicit_captures_len());
    /// assert_eq!(1, parse("(a)")?.properties().explicit_captures_len());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn explicit_captures_len(&self) -> usize {
        self.0.explicit_captures_len
    }

    /// Returns the total number of explicit capturing groups that appear in
    /// every possible match.
    ///
    /// If the number of capture groups can vary depending on the match, then
    /// this returns `None`. That is, a value is only returned when the number
    /// of matching groups is invariant or "static."
    ///
    /// Note that this does not include the implicit capturing group
    /// corresponding to the entire match.
    ///
    /// # Example
    ///
    /// This shows a few cases where a static number of capture groups is
    /// available and a few cases where it is not.
    ///
    /// ```
    /// use regex_syntax::parse;
    ///
    /// let len = |pattern| {
    ///     parse(pattern).map(|h| {
    ///         h.properties().static_explicit_captures_len()
    ///     })
    /// };
    ///
    /// assert_eq!(Some(0), len("a")?);
    /// assert_eq!(Some(1), len("(a)")?);
    /// assert_eq!(Some(1), len("(a)|(b)")?);
    /// assert_eq!(Some(2), len("(a)(b)|(c)(d)")?);
    /// assert_eq!(None, len("(a)|b")?);
    /// assert_eq!(None, len("a|(b)")?);
    /// assert_eq!(None, len("(b)*")?);
    /// assert_eq!(Some(1), len("(b)+")?);
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    #[inline]
    pub fn static_explicit_captures_len(&self) -> Option<usize> {
        self.0.static_explicit_captures_len
    }

    /// Return true if and only if this HIR is a simple literal. This is
    /// only true when this HIR expression is either itself a `Literal` or a
    /// concatenation of only `Literal`s.
    ///
    /// For example, `f` and `foo` are literals, but `f+`, `(foo)`, `foo()` and
    /// the empty string are not (even though they contain sub-expressions that
    /// are literals).
    #[inline]
    pub fn is_literal(&self) -> bool {
        self.0.literal
    }

    /// Return true if and only if this HIR is either a simple literal or an
    /// alternation of simple literals. This is only
    /// true when this HIR expression is either itself a `Literal` or a
    /// concatenation of only `Literal`s or an alternation of only `Literal`s.
    ///
    /// For example, `f`, `foo`, `a|b|c`, and `foo|bar|baz` are alternation
    /// literals, but `f+`, `(foo)`, `foo()`, and the empty pattern are not
    /// (even though that contain sub-expressions that are literals).
    #[inline]
    pub fn is_alternation_literal(&self) -> bool {
        self.0.alternation_literal
    }

    /// Returns the total amount of heap memory usage, in bytes, used by this
    /// `Properties` value.
    #[inline]
    pub fn memory_usage(&self) -> usize {
        core::mem::size_of::<PropertiesI>()
    }

    /// Returns a new set of properties that corresponds to the union of the
    /// iterator of properties given.
    ///
    /// This is useful when one has multiple `Hir` expressions and wants
    /// to combine them into a single alternation without constructing the
    /// corresponding `Hir`. This routine provides a way of combining the
    /// properties of each `Hir` expression into one set of properties
    /// representing the union of those expressions.
    ///
    /// # Example: union with HIRs that never match
    ///
    /// This example shows that unioning properties together with one that
    /// represents a regex that never matches will "poison" certain attributes,
    /// like the minimum and maximum lengths.
    ///
    /// ```
    /// use regex_syntax::{hir::Properties, parse};
    ///
    /// let hir1 = parse("ab?c?")?;
    /// assert_eq!(Some(1), hir1.properties().minimum_len());
    /// assert_eq!(Some(3), hir1.properties().maximum_len());
    ///
    /// let hir2 = parse(r"[a&&b]")?;
    /// assert_eq!(None, hir2.properties().minimum_len());
    /// assert_eq!(None, hir2.properties().maximum_len());
    ///
    /// let hir3 = parse(r"wxy?z?")?;
    /// assert_eq!(Some(2), hir3.properties().minimum_len());
    /// assert_eq!(Some(4), hir3.properties().maximum_len());
    ///
    /// let unioned = Properties::union([
    ///		hir1.properties(),
    ///		hir2.properties(),
    ///		hir3.properties(),
    ///	]);
    /// assert_eq!(None, unioned.minimum_len());
    /// assert_eq!(None, unioned.maximum_len());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    ///
    /// The maximum length can also be "poisoned" by a pattern that has no
    /// upper bound on the length of a match. The minimum length remains
    /// unaffected:
    ///
    /// ```
    /// use regex_syntax::{hir::Properties, parse};
    ///
    /// let hir1 = parse("ab?c?")?;
    /// assert_eq!(Some(1), hir1.properties().minimum_len());
    /// assert_eq!(Some(3), hir1.properties().maximum_len());
    ///
    /// let hir2 = parse(r"a+")?;
    /// assert_eq!(Some(1), hir2.properties().minimum_len());
    /// assert_eq!(None, hir2.properties().maximum_len());
    ///
    /// let hir3 = parse(r"wxy?z?")?;
    /// assert_eq!(Some(2), hir3.properties().minimum_len());
    /// assert_eq!(Some(4), hir3.properties().maximum_len());
    ///
    /// let unioned = Properties::union([
    ///		hir1.properties(),
    ///		hir2.properties(),
    ///		hir3.properties(),
    ///	]);
    /// assert_eq!(Some(1), unioned.minimum_len());
    /// assert_eq!(None, unioned.maximum_len());
    ///
    /// # Ok::<(), Box<dyn std::error::Error>>(())
    /// ```
    pub fn union<I, P>(props: I) -> Properties
    where
        I: IntoIterator<Item = P>,
        P: core::borrow::Borrow<Properties>,
    {
        let mut it = props.into_iter().peekable();
        // While empty alternations aren't possible, we still behave as if they
        // are. When we have an empty alternate, then clearly the look-around
        // prefix and suffix is empty. Otherwise, it is the intersection of all
        // prefixes and suffixes (respectively) of the branches.
        let fix = if it.peek().is_none() {
            LookSet::empty()
        } else {
            LookSet::full()
        };
        // And also, an empty alternate means we have 0 static capture groups,
        // but we otherwise start with the number corresponding to the first
        // alternate. If any subsequent alternate has a different number of
        // static capture groups, then we overall have a variation and not a
        // static number of groups.
        let static_explicit_captures_len =
            it.peek().and_then(|p| p.borrow().static_explicit_captures_len());
        // The base case is an empty alternation, which matches nothing.
        // Note though that empty alternations aren't possible, because the
        // Hir::alternation smart constructor rewrites those as empty character
        // classes.
        let mut props = PropertiesI {
            minimum_len: None,
            maximum_len: None,
            look_set: LookSet::empty(),
            look_set_prefix: fix,
            look_set_suffix: fix,
            look_set_prefix_any: LookSet::empty(),
            look_set_suffix_any: LookSet::empty(),
            utf8: true,
            explicit_captures_len: 0,
            static_explicit_captures_len,
            literal: false,
            alternation_literal: true,
        };
        let (mut min_poisoned, mut max_poisoned) = (false, false);
        // Handle properties that need to visit every child hir.
        for prop in it {
            let p = prop.borrow();
            props.look_set.set_union(p.look_set());
            props.look_set_prefix.set_intersect(p.look_set_prefix());
            props.look_set_suffix.set_intersect(p.look_set_suffix());
            props.look_set_prefix_any.set_union(p.look_set_prefix_any());
            props.look_set_suffix_any.set_union(p.look_set_suffix_any());
            props.utf8 = props.utf8 && p.is_utf8();
            props.explicit_captures_len = props
                .explicit_captures_len
                .saturating_add(p.explicit_captures_len());
            if props.static_explicit_captures_len
                != p.static_explicit_captures_len()
            {
                props.static_explicit_captures_len = None;
            }
            props.alternation_literal =
                props.alternation_literal && p.is_literal();
            if !min_poisoned {
                if let Some(xmin) = p.minimum_len() {
                    if props.minimum_len.map_or(true, |pmin| xmin < pmin) {
                        props.minimum_len = Some(xmin);
                    }
                } else {
                    props.minimum_len = None;
                    min_poisoned = true;
                }
            }
            if !max_poisoned {
                if let Some(xmax) = p.maximum_len() {
                    if props.maximum_len.map_or(true, |pmax| xmax > pmax) {
                        props.maximum_len = Some(xmax);
                    }
                } else {
                    props.maximum_len = None;
                    max_poisoned = true;
                }
            }
        }
        Properties(Box::new(props))
    }
}

impl Properties {
    /// Create a new set of HIR properties for an empty regex.
    fn empty() -> Properties {
        let inner = PropertiesI {
            minimum_len: Some(0),
            maximum_len: Some(0),
            look_set: LookSet::empty(),
            look_set_prefix: LookSet::empty(),
            look_set_suffix: LookSet::empty(),
            look_set_prefix_any: LookSet::empty(),
            look_set_suffix_any: LookSet::empty(),
            // It is debatable whether an empty regex always matches at valid
            // UTF-8 boundaries. Strictly speaking, at a byte oriented view,
            // it is clearly false. There are, for example, many empty strings
            // between the bytes encoding a '☃'.
            //
            // However, when Unicode mode is enabled, the fundamental atom
            // of matching is really a codepoint. And in that scenario, an
            // empty regex is defined to only match at valid UTF-8 boundaries
            // and to never split a codepoint. It just so happens that this
            // enforcement is somewhat tricky to do for regexes that match
            // the empty string inside regex engines themselves. It usually
            // requires some layer above the regex engine to filter out such
            // matches.
            //
            // In any case, 'true' is really the only coherent option. If it
            // were false, for example, then 'a*' would also need to be false
            // since it too can match the empty string.
            utf8: true,
            explicit_captures_len: 0,
            static_explicit_captures_len: Some(0),
            literal: false,
            alternation_literal: false,
        };
        Properties(Box::new(inner))
    }

    /// Create a new set of HIR properties for a literal regex.
    fn literal(lit: &Literal) -> Properties {
        let inner = PropertiesI {
            minimum_len: Some(lit.0.len()),
            maximum_len: Some(lit.0.len()),
            look_set: LookSet::empty(),
            look_set_prefix: LookSet::empty(),
            look_set_suffix: LookSet::empty(),
            look_set_prefix_any: LookSet::empty(),
            look_set_suffix_any: LookSet::empty(),
            utf8: core::str::from_utf8(&lit.0).is_ok(),
            explicit_captures_len: 0,
            static_explicit_captures_len: Some(0),
            literal: true,
            alternation_literal: true,
        };
        Properties(Box::new(inner))
    }

    /// Create a new set of HIR properties for a character class.
    fn class(class: &Class) -> Properties {
        let inner = PropertiesI {
            minimum_len: class.minimum_len(),
            maximum_len: class.maximum_len(),
            look_set: LookSet::empty(),
            look_set_prefix: LookSet::empty(),
            look_set_suffix: LookSet::empty(),
            look_set_prefix_any: LookSet::empty(),
            look_set_suffix_any: LookSet::empty(),
            utf8: class.is_utf8(),
            explicit_captures_len: 0,
            static_explicit_captures_len: Some(0),
            literal: false,
            alternation_literal: false,
        };
        Properties(Box::new(inner))
    }

    /// Create a new set of HIR properties for a look-around assertion.
    fn look(look: Look) -> Properties {
        let inner = PropertiesI {
            minimum_len: Some(0),
            maximum_len: Some(0),
            look_set: LookSet::singleton(look),
            look_set_prefix: LookSet::singleton(look),
            look_set_suffix: LookSet::singleton(look),
            look_set_prefix_any: LookSet::singleton(look),
            look_set_suffix_any: LookSet::singleton(look),
            // This requires a little explanation. Basically, we don't consider
            // matching an empty string to be equivalent to matching invalid
            // UTF-8, even though technically matching every empty string will
            // split the UTF-8 encoding of a single codepoint when treating a
            // UTF-8 encoded string as a sequence of bytes. Our defense here is
            // that in such a case, a codepoint should logically be treated as
            // the fundamental atom for matching, and thus the only valid match
            // points are between codepoints and not bytes.
            //
            // More practically, this is true here because it's also true
            // for 'Hir::empty()', otherwise something like 'a*' would be
            // considered to match invalid UTF-8. That in turn makes this
            // property borderline useless.
            utf8: true,
            explicit_captures_len: 0,
            static_explicit_captures_len: Some(0),
            literal: false,
            alternation_literal: false,
        };
        Properties(Box::new(inner))
    }

    /// Create a new set of HIR properties for a repetition.
    fn repetition(rep: &Repetition) -> Properties {
        let p = rep.sub.properties();
        let minimum_len = p.minimum_len().map(|child_min| {
            let rep_min = usize::try_from(rep.min).unwrap_or(usize::MAX);
            child_min.saturating_mul(rep_min)
        });
        let maximum_len = rep.max.and_then(|rep_max| {
            let rep_max = usize::try_from(rep_max).ok()?;
            let child_max = p.maximum_len()?;
            child_max.checked_mul(rep_max)
        });

        let mut inner = PropertiesI {
            minimum_len,
            maximum_len,
            look_set: p.look_set(),
            look_set_prefix: LookSet::empty(),
            look_set_suffix: LookSet::empty(),
            look_set_prefix_any: p.look_set_prefix_any(),
            look_set_suffix_any: p.look_set_suffix_any(),
            utf8: p.is_utf8(),
            explicit_captures_len: p.explicit_captures_len(),
            static_explicit_captures_len: p.static_explicit_captures_len(),
            literal: false,
            alternation_literal: false,
        };
        // If the repetition operator can match the empty string, then its
        // lookset prefix and suffixes themselves remain empty since they are
        // no longer required to match.
        if rep.min > 0 {
            inner.look_set_prefix = p.look_set_prefix();
            inner.look_set_suffix = p.look_set_suffix();
        }
        // If the static captures len of the sub-expression is not known or
        // is greater than zero, then it automatically propagates to the
        // repetition, regardless of the repetition. Otherwise, it might
        // change, but only when the repetition can match 0 times.
        if rep.min == 0
            && inner.static_explicit_captures_len.map_or(false, |len| len > 0)
        {
            // If we require a match 0 times, then our captures len is
            // guaranteed to be zero. Otherwise, if we *can* match the empty
            // string, then it's impossible to know how many captures will be
            // in the resulting match.
            if rep.max == Some(0) {
                inner.static_explicit_captures_len = Some(0);
            } else {
                inner.static_explicit_captures_len = None;
            }
        }
        Properties(Box::new(inner))
    }

    /// Create a new set of HIR properties for a capture.
    fn capture(capture: &Capture) -> Properties {
        let p = capture.sub.properties();
        Properties(Box::new(PropertiesI {
            explicit_captures_len: p.explicit_captures_len().saturating_add(1),
            static_explicit_captures_len: p
                .static_explicit_captures_len()
                .map(|len| len.saturating_add(1)),
            literal: false,
            alternation_literal: false,
            ..*p.0.clone()
        }))
    }

    /// Create a new set of HIR properties for a concatenation.
    fn concat(concat: &[Hir]) -> Properties {
        // The base case is an empty concatenation, which matches the empty
        // string. Note though that empty concatenations aren't possible,
        // because the Hir::concat smart constructor rewrites those as
        // Hir::empty.
        let mut props = PropertiesI {
            minimum_len: Some(0),
            maximum_len: Some(0),
            look_set: LookSet::empty(),
            look_set_prefix: LookSet::empty(),
            look_set_suffix: LookSet::empty(),
            look_set_prefix_any: LookSet::empty(),
            look_set_suffix_any: LookSet::empty(),
            utf8: true,
            explicit_captures_len: 0,
            static_explicit_captures_len: Some(0),
            literal: true,
            alternation_literal: true,
        };
        // Handle properties that need to visit every child hir.
        for x in concat.iter() {
            let p = x.properties();
            props.look_set.set_union(p.look_set());
            props.utf8 = props.utf8 && p.is_utf8();
            props.explicit_captures_len = props
                .explicit_captures_len
                .saturating_add(p.explicit_captures_len());
            props.static_explicit_captures_len = p
                .static_explicit_captures_len()
                .and_then(|len1| {
                    Some((len1, props.static_explicit_captures_len?))
                })
                .and_then(|(len1, len2)| Some(len1.saturating_add(len2)));
            props.literal = props.literal && p.is_literal();
            props.alternation_literal =
                props.alternation_literal && p.is_alternation_literal();
            if let Some(minimum_len) = props.minimum_len {
                match p.minimum_len() {
                    None => props.minimum_len = None,
                    Some(len) => {
                        // We use saturating arithmetic here because the
                        // minimum is just a lower bound. We can't go any
                        // higher than what our number types permit.
                        props.minimum_len =
                            Some(minimum_len.saturating_add(len));
                    }
                }
            }
            if let Some(maximum_len) = props.maximum_len {
                match p.maximum_len() {
                    None => props.maximum_len = None,
                    Some(len) => {
                        props.maximum_len = maximum_len.checked_add(len)
                    }
                }
            }
        }
        // Handle the prefix properties, which only requires visiting
        // child exprs until one matches more than the empty string.
        let mut it = concat.iter();
        while let Some(x) = it.next() {
            props.look_set_prefix.set_union(x.properties().look_set_prefix());
            props
                .look_set_prefix_any
                .set_union(x.properties().look_set_prefix_any());
            if x.properties().maximum_len().map_or(true, |x| x > 0) {
                break;
            }
        }
        // Same thing for the suffix properties, but in reverse.
        let mut it = concat.iter().rev();
        while let Some(x) = it.next() {
            props.look_set_suffix.set_union(x.properties().look_set_suffix());
            props
                .look_set_suffix_any
                .set_union(x.properties().look_set_suffix_any());
            if x.properties().maximum_len().map_or(true, |x| x > 0) {
                break;
            }
        }
        Properties(Box::new(props))
    }

    /// Create a new set of HIR properties for a concatenation.
    fn alternation(alts: &[Hir]) -> Properties {
        Properties::union(alts.iter().map(|hir| hir.properties()))
    }
}

/// A set of look-around assertions.
///
/// This is useful for efficiently tracking look-around assertions. For
/// example, an [`Hir`] provides properties that return `LookSet`s.
#[derive(Clone, Copy, Default, Eq, PartialEq)]
pub struct LookSet {
    /// The underlying representation this set is exposed to make it possible
    /// to store it somewhere efficiently. The representation is that
    /// of a bitset, where each assertion occupies bit `i` where `i =
    /// Look::as_repr()`.
    ///
    /// Note that users of this internal representation must permit the full
    /// range of `u16` values to be represented. For example, even if the
    /// current implementation only makes use of the 10 least significant bits,
    /// it may use more bits in a future semver compatible release.
    pub bits: u16,
}

impl LookSet {
    /// Create an empty set of look-around assertions.
    #[inline]
    pub fn empty() -> LookSet {
        LookSet { bits: 0 }
    }

    /// Create a full set of look-around assertions.
    ///
    /// This set contains all possible look-around assertions.
    #[inline]
    pub fn full() -> LookSet {
        LookSet { bits: !0 }
    }

    /// Create a look-around set containing the look-around assertion given.
    ///
    /// This is a convenience routine for creating an empty set and inserting
    /// one look-around assertions.
    #[inline]
    pub fn singleton(look: Look) -> LookSet {
        LookSet::empty().insert(look)
    }

    /// Returns the total number of look-around assertions in this set.
    #[inline]
    pub fn len(self) -> usize {
        // OK because max value always fits in a u8, which in turn always
        // fits in a usize, regardless of target.
        usize::try_from(self.bits.count_ones()).unwrap()
    }

    /// Returns true if and only if this set is empty.
    #[inline]
    pub fn is_empty(self) -> bool {
        self.len() == 0
    }

    /// Returns true if and only if the given look-around assertion is in this
    /// set.
    #[inline]
    pub fn contains(self, look: Look) -> bool {
        self.bits & look.as_repr() != 0
    }

    /// Returns true if and only if this set contains any anchor assertions.
    /// This includes both "start/end of haystack" and "start/end of line."
    #[inline]
    pub fn contains_anchor(&self) -> bool {
        self.contains_anchor_haystack() || self.contains_anchor_line()
    }

    /// Returns true if and only if this set contains any "start/end of
    /// haystack" anchors. This doesn't include "start/end of line" anchors.
    #[inline]
    pub fn contains_anchor_haystack(&self) -> bool {
        self.contains(Look::Start) || self.contains(Look::End)
    }

    /// Returns true if and only if this set contains any "start/end of line"
    /// anchors. This doesn't include "start/end of haystack" anchors. This
    /// includes both `\n` line anchors and CRLF (`\r\n`) aware line anchors.
    #[inline]
    pub fn contains_anchor_line(&self) -> bool {
        self.contains(Look::StartLF)
            || self.contains(Look::EndLF)
            || self.contains(Look::StartCRLF)
            || self.contains(Look::EndCRLF)
    }

    /// Returns true if and only if this set contains any "start/end of line"
    /// anchors that only treat `\n` as line terminators. This does not include
    /// haystack anchors or CRLF aware line anchors.
    #[inline]
    pub fn contains_anchor_lf(&self) -> bool {
        self.contains(Look::StartLF) || self.contains(Look::EndLF)
    }

    /// Returns true if and only if this set contains any "start/end of line"
    /// anchors that are CRLF-aware. This doesn't include "start/end of
    /// haystack" or "start/end of line-feed" anchors.
    #[inline]
    pub fn contains_anchor_crlf(&self) -> bool {
        self.contains(Look::StartCRLF) || self.contains(Look::EndCRLF)
    }

    /// Returns true if and only if this set contains any word boundary or
    /// negated word boundary assertions. This include both Unicode and ASCII
    /// word boundaries.
    #[inline]
    pub fn contains_word(self) -> bool {
        self.contains_word_unicode() || self.contains_word_ascii()
    }

    /// Returns true if and only if this set contains any Unicode word boundary
    /// or negated Unicode word boundary assertions.
    #[inline]
    pub fn contains_word_unicode(self) -> bool {
        self.contains(Look::WordUnicode)
            || self.contains(Look::WordUnicodeNegate)
    }

    /// Returns true if and only if this set contains any ASCII word boundary
    /// or negated ASCII word boundary assertions.
    #[inline]
    pub fn contains_word_ascii(self) -> bool {
        self.contains(Look::WordAscii) || self.contains(Look::WordAsciiNegate)
    }

    /// Returns an iterator over all of the look-around assertions in this set.
    #[inline]
    pub fn iter(self) -> LookSetIter {
        LookSetIter { set: self }
    }

    /// Return a new set that is equivalent to the original, but with the given
    /// assertion added to it. If the assertion is already in the set, then the
    /// returned set is equivalent to the original.
    #[inline]
    pub fn insert(self, look: Look) -> LookSet {
        LookSet { bits: self.bits | look.as_repr() }
    }

    /// Updates this set in place with the result of inserting the given
    /// assertion into this set.
    #[inline]
    pub fn set_insert(&mut self, look: Look) {
        *self = self.insert(look);
    }

    /// Return a new set that is equivalent to the original, but with the given
    /// assertion removed from it. If the assertion is not in the set, then the
    /// returned set is equivalent to the original.
    #[inline]
    pub fn remove(self, look: Look) -> LookSet {
        LookSet { bits: self.bits & !look.as_repr() }
    }

    /// Updates this set in place with the result of removing the given
    /// assertion from this set.
    #[inline]
    pub fn set_remove(&mut self, look: Look) {
        *self = self.remove(look);
    }

    /// Returns a new set that is the result of subtracting the given set from
    /// this set.
    #[inline]
    pub fn subtract(self, other: LookSet) -> LookSet {
        LookSet { bits: self.bits & !other.bits }
    }

    /// Updates this set in place with the result of subtracting the given set
    /// from this set.
    #[inline]
    pub fn set_subtract(&mut self, other: LookSet) {
        *self = self.subtract(other);
    }

    /// Returns a new set that is the union of this and the one given.
    #[inline]
    pub fn union(self, other: LookSet) -> LookSet {
        LookSet { bits: self.bits | other.bits }
    }

    /// Updates this set in place with the result of unioning it with the one
    /// given.
    #[inline]
    pub fn set_union(&mut self, other: LookSet) {
        *self = self.union(other);
    }

    /// Returns a new set that is the intersection of this and the one given.
    #[inline]
    pub fn intersect(self, other: LookSet) -> LookSet {
        LookSet { bits: self.bits & other.bits }
    }

    /// Updates this set in place with the result of intersecting it with the
    /// one given.
    #[inline]
    pub fn set_intersect(&mut self, other: LookSet) {
        *self = self.intersect(other);
    }

    /// Return a `LookSet` from the slice given as a native endian 16-bit
    /// integer.
    ///
    /// # Panics
    ///
    /// This panics if `slice.len() < 2`.
    #[inline]
    pub fn read_repr(slice: &[u8]) -> LookSet {
        let bits = u16::from_ne_bytes(slice[..2].try_into().unwrap());
        LookSet { bits }
    }

    /// Write a `LookSet` as a native endian 16-bit integer to the beginning
    /// of the slice given.
    ///
    /// # Panics
    ///
    /// This panics if `slice.len() < 2`.
    #[inline]
    pub fn write_repr(self, slice: &mut [u8]) {
        let raw = self.bits.to_ne_bytes();
        slice[0] = raw[0];
        slice[1] = raw[1];
    }
}

impl core::fmt::Debug for LookSet {
    fn fmt(&self, f: &mut core::fmt::Formatter) -> core::fmt::Result {
        if self.is_empty() {
            return write!(f, "∅");
        }
        for look in self.iter() {
            write!(f, "{}", look.as_char())?;
        }
        Ok(())
    }
}

/// An iterator over all look-around assertions in a [`LookSet`].
///
/// This iterator is created by [`LookSet::iter`].
#[derive(Clone, Debug)]
pub struct LookSetIter {
    set: LookSet,
}

impl Iterator for LookSetIter {
    type Item = Look;

    #[inline]
    fn next(&mut self) -> Option<Look> {
        if self.set.is_empty() {
            return None;
        }
        // We'll never have more than u8::MAX distinct look-around assertions,
        // so 'repr' will always fit into a u16.
        let repr = u16::try_from(self.set.bits.trailing_zeros()).unwrap();
        let look = Look::from_repr(1 << repr)?;
        self.set = self.set.remove(look);
        Some(look)
    }
}

/// Given a sequence of HIR values where each value corresponds to a Unicode
/// class (or an all-ASCII byte class), return a single Unicode class
/// corresponding to the union of the classes found.
fn class_chars(hirs: &[Hir]) -> Option<Class> {
    let mut cls = ClassUnicode::new(vec![]);
    for hir in hirs.iter() {
        match *hir.kind() {
            HirKind::Class(Class::Unicode(ref cls2)) => {
                cls.union(cls2);
            }
            HirKind::Class(Class::Bytes(ref cls2)) => {
                cls.union(&cls2.to_unicode_class()?);
            }
            _ => return None,
        };
    }
    Some(Class::Unicode(cls))
}

/// Given a sequence of HIR values where each value corresponds to a byte class
/// (or an all-ASCII Unicode class), return a single byte class corresponding
/// to the union of the classes found.
fn class_bytes(hirs: &[Hir]) -> Option<Class> {
    let mut cls = ClassBytes::new(vec![]);
    for hir in hirs.iter() {
        match *hir.kind() {
            HirKind::Class(Class::Unicode(ref cls2)) => {
                cls.union(&cls2.to_byte_class()?);
            }
            HirKind::Class(Class::Bytes(ref cls2)) => {
                cls.union(cls2);
            }
            _ => return None,
        };
    }
    Some(Class::Bytes(cls))
}

/// Given a sequence of HIR values where each value corresponds to a literal
/// that is a single `char`, return that sequence of `char`s. Otherwise return
/// None. No deduplication is done.
fn singleton_chars(hirs: &[Hir]) -> Option<Vec<char>> {
    let mut singletons = vec![];
    for hir in hirs.iter() {
        let literal = match *hir.kind() {
            HirKind::Literal(Literal(ref bytes)) => bytes,
            _ => return None,
        };
        let ch = match crate::debug::utf8_decode(literal) {
            None => return None,
            Some(Err(_)) => return None,
            Some(Ok(ch)) => ch,
        };
        if literal.len() != ch.len_utf8() {
            return None;
        }
        singletons.push(ch);
    }
    Some(singletons)
}

/// Given a sequence of HIR values where each value corresponds to a literal
/// that is a single byte, return that sequence of bytes. Otherwise return
/// None. No deduplication is done.
fn singleton_bytes(hirs: &[Hir]) -> Option<Vec<u8>> {
    let mut singletons = vec![];
    for hir in hirs.iter() {
        let literal = match *hir.kind() {
            HirKind::Literal(Literal(ref bytes)) => bytes,
            _ => return None,
        };
        if literal.len() != 1 {
            return None;
        }
        singletons.push(literal[0]);
    }
    Some(singletons)
}

/// Looks for a common prefix in the list of alternation branches given. If one
/// is found, then an equivalent but (hopefully) simplified Hir is returned.
/// Otherwise, the original given list of branches is returned unmodified.
///
/// This is not quite as good as it could be. Right now, it requires that
/// all branches are 'Concat' expressions. It also doesn't do well with
/// literals. For example, given 'foofoo|foobar', it will not refactor it to
/// 'foo(?:foo|bar)' because literals are flattened into their own special
/// concatenation. (One wonders if perhaps 'Literal' should be a single atom
/// instead of a string of bytes because of this. Otherwise, handling the
/// current representation in this routine will be pretty gnarly. Sigh.)
fn lift_common_prefix(hirs: Vec<Hir>) -> Result<Hir, Vec<Hir>> {
    if hirs.len() <= 1 {
        return Err(hirs);
    }
    let mut prefix = match hirs[0].kind() {
        HirKind::Concat(ref xs) => &**xs,
        _ => return Err(hirs),
    };
    if prefix.is_empty() {
        return Err(hirs);
    }
    for h in hirs.iter().skip(1) {
        let concat = match h.kind() {
            HirKind::Concat(ref xs) => xs,
            _ => return Err(hirs),
        };
        let common_len = prefix
            .iter()
            .zip(concat.iter())
            .take_while(|(x, y)| x == y)
            .count();
        prefix = &prefix[..common_len];
        if prefix.is_empty() {
            return Err(hirs);
        }
    }
    let len = prefix.len();
    assert_ne!(0, len);
    let mut prefix_concat = vec![];
    let mut suffix_alts = vec![];
    for h in hirs {
        let mut concat = match h.into_kind() {
            HirKind::Concat(xs) => xs,
            // We required all sub-expressions to be
            // concats above, so we're only here if we
            // have a concat.
            _ => unreachable!(),
        };
        suffix_alts.push(Hir::concat(concat.split_off(len)));
        if prefix_concat.is_empty() {
            prefix_concat = concat;
        }
    }
    let mut concat = prefix_concat;
    concat.push(Hir::alternation(suffix_alts));
    Ok(Hir::concat(concat))
}

#[cfg(test)]
mod tests {
    use super::*;

    fn uclass(ranges: &[(char, char)]) -> ClassUnicode {
        let ranges: Vec<ClassUnicodeRange> = ranges
            .iter()
            .map(|&(s, e)| ClassUnicodeRange::new(s, e))
            .collect();
        ClassUnicode::new(ranges)
    }

    fn bclass(ranges: &[(u8, u8)]) -> ClassBytes {
        let ranges: Vec<ClassBytesRange> =
            ranges.iter().map(|&(s, e)| ClassBytesRange::new(s, e)).collect();
        ClassBytes::new(ranges)
    }

    fn uranges(cls: &ClassUnicode) -> Vec<(char, char)> {
        cls.iter().map(|x| (x.start(), x.end())).collect()
    }

    #[cfg(feature = "unicode-case")]
    fn ucasefold(cls: &ClassUnicode) -> ClassUnicode {
        let mut cls_ = cls.clone();
        cls_.case_fold_simple();
        cls_
    }

    fn uunion(cls1: &ClassUnicode, cls2: &ClassUnicode) -> ClassUnicode {
        let mut cls_ = cls1.clone();
        cls_.union(cls2);
        cls_
    }

    fn uintersect(cls1: &ClassUnicode, cls2: &ClassUnicode) -> ClassUnicode {
        let mut cls_ = cls1.clone();
        cls_.intersect(cls2);
        cls_
    }

    fn udifference(cls1: &ClassUnicode, cls2: &ClassUnicode) -> ClassUnicode {
        let mut cls_ = cls1.clone();
        cls_.difference(cls2);
        cls_
    }

    fn usymdifference(
        cls1: &ClassUnicode,
        cls2: &ClassUnicode,
    ) -> ClassUnicode {
        let mut cls_ = cls1.clone();
        cls_.symmetric_difference(cls2);
        cls_
    }

    fn unegate(cls: &ClassUnicode) -> ClassUnicode {
        let mut cls_ = cls.clone();
        cls_.negate();
        cls_
    }

    fn branges(cls: &ClassBytes) -> Vec<(u8, u8)> {
        cls.iter().map(|x| (x.start(), x.end())).collect()
    }

    fn bcasefold(cls: &ClassBytes) -> ClassBytes {
        let mut cls_ = cls.clone();
        cls_.case_fold_simple();
        cls_
    }

    fn bunion(cls1: &ClassBytes, cls2: &ClassBytes) -> ClassBytes {
        let mut cls_ = cls1.clone();
        cls_.union(cls2);
        cls_
    }

    fn bintersect(cls1: &ClassBytes, cls2: &ClassBytes) -> ClassBytes {
        let mut cls_ = cls1.clone();
        cls_.intersect(cls2);
        cls_
    }

    fn bdifference(cls1: &ClassBytes, cls2: &ClassBytes) -> ClassBytes {
        let mut cls_ = cls1.clone();
        cls_.difference(cls2);
        cls_
    }

    fn bsymdifference(cls1: &ClassBytes, cls2: &ClassBytes) -> ClassBytes {
        let mut cls_ = cls1.clone();
        cls_.symmetric_difference(cls2);
        cls_
    }

    fn bnegate(cls: &ClassBytes) -> ClassBytes {
        let mut cls_ = cls.clone();
        cls_.negate();
        cls_
    }

    #[test]
    fn class_range_canonical_unicode() {
        let range = ClassUnicodeRange::new('\u{00FF}', '\0');
        assert_eq!('\0', range.start());
        assert_eq!('\u{00FF}', range.end());
    }

    #[test]
    fn class_range_canonical_bytes() {
        let range = ClassBytesRange::new(b'\xFF', b'\0');
        assert_eq!(b'\0', range.start());
        assert_eq!(b'\xFF', range.end());
    }

    #[test]
    fn class_canonicalize_unicode() {
        let cls = uclass(&[('a', 'c'), ('x', 'z')]);
        let expected = vec![('a', 'c'), ('x', 'z')];
        assert_eq!(expected, uranges(&cls));

        let cls = uclass(&[('x', 'z'), ('a', 'c')]);
        let expected = vec![('a', 'c'), ('x', 'z')];
        assert_eq!(expected, uranges(&cls));

        let cls = uclass(&[('x', 'z'), ('w', 'y')]);
        let expected = vec![('w', 'z')];
        assert_eq!(expected, uranges(&cls));

        let cls = uclass(&[
            ('c', 'f'),
            ('a', 'g'),
            ('d', 'j'),
            ('a', 'c'),
            ('m', 'p'),
            ('l', 's'),
        ]);
        let expected = vec![('a', 'j'), ('l', 's')];
        assert_eq!(expected, uranges(&cls));

        let cls = uclass(&[('x', 'z'), ('u', 'w')]);
        let expected = vec![('u', 'z')];
        assert_eq!(expected, uranges(&cls));

        let cls = uclass(&[('\x00', '\u{10FFFF}'), ('\x00', '\u{10FFFF}')]);
        let expected = vec![('\x00', '\u{10FFFF}')];
        assert_eq!(expected, uranges(&cls));

        let cls = uclass(&[('a', 'a'), ('b', 'b')]);
        let expected = vec![('a', 'b')];
        assert_eq!(expected, uranges(&cls));
    }

    #[test]
    fn class_canonicalize_bytes() {
        let cls = bclass(&[(b'a', b'c'), (b'x', b'z')]);
        let expected = vec![(b'a', b'c'), (b'x', b'z')];
        assert_eq!(expected, branges(&cls));

        let cls = bclass(&[(b'x', b'z'), (b'a', b'c')]);
        let expected = vec![(b'a', b'c'), (b'x', b'z')];
        assert_eq!(expected, branges(&cls));

        let cls = bclass(&[(b'x', b'z'), (b'w', b'y')]);
        let expected = vec![(b'w', b'z')];
        assert_eq!(expected, branges(&cls));

        let cls = bclass(&[
            (b'c', b'f'),
            (b'a', b'g'),
            (b'd', b'j'),
            (b'a', b'c'),
            (b'm', b'p'),
            (b'l', b's'),
        ]);
        let expected = vec![(b'a', b'j'), (b'l', b's')];
        assert_eq!(expected, branges(&cls));

        let cls = bclass(&[(b'x', b'z'), (b'u', b'w')]);
        let expected = vec![(b'u', b'z')];
        assert_eq!(expected, branges(&cls));

        let cls = bclass(&[(b'\x00', b'\xFF'), (b'\x00', b'\xFF')]);
        let expected = vec![(b'\x00', b'\xFF')];
        assert_eq!(expected, branges(&cls));

        let cls = bclass(&[(b'a', b'a'), (b'b', b'b')]);
        let expected = vec![(b'a', b'b')];
        assert_eq!(expected, branges(&cls));
    }

    #[test]
    #[cfg(feature = "unicode-case")]
    fn class_case_fold_unicode() {
        let cls = uclass(&[
            ('C', 'F'),
            ('A', 'G'),
            ('D', 'J'),
            ('A', 'C'),
            ('M', 'P'),
            ('L', 'S'),
            ('c', 'f'),
        ]);
        let expected = uclass(&[
            ('A', 'J'),
            ('L', 'S'),
            ('a', 'j'),
            ('l', 's'),
            ('\u{17F}', '\u{17F}'),
        ]);
        assert_eq!(expected, ucasefold(&cls));

        let cls = uclass(&[('A', 'Z')]);
        let expected = uclass(&[
            ('A', 'Z'),
            ('a', 'z'),
            ('\u{17F}', '\u{17F}'),
            ('\u{212A}', '\u{212A}'),
        ]);
        assert_eq!(expected, ucasefold(&cls));

        let cls = uclass(&[('a', 'z')]);
        let expected = uclass(&[
            ('A', 'Z'),
            ('a', 'z'),
            ('\u{17F}', '\u{17F}'),
            ('\u{212A}', '\u{212A}'),
        ]);
        assert_eq!(expected, ucasefold(&cls));

        let cls = uclass(&[('A', 'A'), ('_', '_')]);
        let expected = uclass(&[('A', 'A'), ('_', '_'), ('a', 'a')]);
        assert_eq!(expected, ucasefold(&cls));

        let cls = uclass(&[('A', 'A'), ('=', '=')]);
        let expected = uclass(&[('=', '='), ('A', 'A'), ('a', 'a')]);
        assert_eq!(expected, ucasefold(&cls));

        let cls = uclass(&[('\x00', '\x10')]);
        assert_eq!(cls, ucasefold(&cls));

        let cls = uclass(&[('k', 'k')]);
        let expected =
            uclass(&[('K', 'K'), ('k', 'k'), ('\u{212A}', '\u{212A}')]);
        assert_eq!(expected, ucasefold(&cls));

        let cls = uclass(&[('@', '@')]);
        assert_eq!(cls, ucasefold(&cls));
    }

    #[test]
    #[cfg(not(feature = "unicode-case"))]
    fn class_case_fold_unicode_disabled() {
        let mut cls = uclass(&[
            ('C', 'F'),
            ('A', 'G'),
            ('D', 'J'),
            ('A', 'C'),
            ('M', 'P'),
            ('L', 'S'),
            ('c', 'f'),
        ]);
        assert!(cls.try_case_fold_simple().is_err());
    }

    #[test]
    #[should_panic]
    #[cfg(not(feature = "unicode-case"))]
    fn class_case_fold_unicode_disabled_panics() {
        let mut cls = uclass(&[
            ('C', 'F'),
            ('A', 'G'),
            ('D', 'J'),
            ('A', 'C'),
            ('M', 'P'),
            ('L', 'S'),
            ('c', 'f'),
        ]);
        cls.case_fold_simple();
    }

    #[test]
    fn class_case_fold_bytes() {
        let cls = bclass(&[
            (b'C', b'F'),
            (b'A', b'G'),
            (b'D', b'J'),
            (b'A', b'C'),
            (b'M', b'P'),
            (b'L', b'S'),
            (b'c', b'f'),
        ]);
        let expected =
            bclass(&[(b'A', b'J'), (b'L', b'S'), (b'a', b'j'), (b'l', b's')]);
        assert_eq!(expected, bcasefold(&cls));

        let cls = bclass(&[(b'A', b'Z')]);
        let expected = bclass(&[(b'A', b'Z'), (b'a', b'z')]);
        assert_eq!(expected, bcasefold(&cls));

        let cls = bclass(&[(b'a', b'z')]);
        let expected = bclass(&[(b'A', b'Z'), (b'a', b'z')]);
        assert_eq!(expected, bcasefold(&cls));

        let cls = bclass(&[(b'A', b'A'), (b'_', b'_')]);
        let expected = bclass(&[(b'A', b'A'), (b'_', b'_'), (b'a', b'a')]);
        assert_eq!(expected, bcasefold(&cls));

        let cls = bclass(&[(b'A', b'A'), (b'=', b'=')]);
        let expected = bclass(&[(b'=', b'='), (b'A', b'A'), (b'a', b'a')]);
        assert_eq!(expected, bcasefold(&cls));

        let cls = bclass(&[(b'\x00', b'\x10')]);
        assert_eq!(cls, bcasefold(&cls));

        let cls = bclass(&[(b'k', b'k')]);
        let expected = bclass(&[(b'K', b'K'), (b'k', b'k')]);
        assert_eq!(expected, bcasefold(&cls));

        let cls = bclass(&[(b'@', b'@')]);
        assert_eq!(cls, bcasefold(&cls));
    }

    #[test]
    fn class_negate_unicode() {
        let cls = uclass(&[('a', 'a')]);
        let expected = uclass(&[('\x00', '\x60'), ('\x62', '\u{10FFFF}')]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('a', 'a'), ('b', 'b')]);
        let expected = uclass(&[('\x00', '\x60'), ('\x63', '\u{10FFFF}')]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('a', 'c'), ('x', 'z')]);
        let expected = uclass(&[
            ('\x00', '\x60'),
            ('\x64', '\x77'),
            ('\x7B', '\u{10FFFF}'),
        ]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('\x00', 'a')]);
        let expected = uclass(&[('\x62', '\u{10FFFF}')]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('a', '\u{10FFFF}')]);
        let expected = uclass(&[('\x00', '\x60')]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('\x00', '\u{10FFFF}')]);
        let expected = uclass(&[]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[]);
        let expected = uclass(&[('\x00', '\u{10FFFF}')]);
        assert_eq!(expected, unegate(&cls));

        let cls =
            uclass(&[('\x00', '\u{10FFFD}'), ('\u{10FFFF}', '\u{10FFFF}')]);
        let expected = uclass(&[('\u{10FFFE}', '\u{10FFFE}')]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('\x00', '\u{D7FF}')]);
        let expected = uclass(&[('\u{E000}', '\u{10FFFF}')]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('\x00', '\u{D7FE}')]);
        let expected = uclass(&[('\u{D7FF}', '\u{10FFFF}')]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('\u{E000}', '\u{10FFFF}')]);
        let expected = uclass(&[('\x00', '\u{D7FF}')]);
        assert_eq!(expected, unegate(&cls));

        let cls = uclass(&[('\u{E001}', '\u{10FFFF}')]);
        let expected = uclass(&[('\x00', '\u{E000}')]);
        assert_eq!(expected, unegate(&cls));
    }

    #[test]
    fn class_negate_bytes() {
        let cls = bclass(&[(b'a', b'a')]);
        let expected = bclass(&[(b'\x00', b'\x60'), (b'\x62', b'\xFF')]);
        assert_eq!(expected, bnegate(&cls));

        let cls = bclass(&[(b'a', b'a'), (b'b', b'b')]);
        let expected = bclass(&[(b'\x00', b'\x60'), (b'\x63', b'\xFF')]);
        assert_eq!(expected, bnegate(&cls));

        let cls = bclass(&[(b'a', b'c'), (b'x', b'z')]);
        let expected = bclass(&[
            (b'\x00', b'\x60'),
            (b'\x64', b'\x77'),
            (b'\x7B', b'\xFF'),
        ]);
        assert_eq!(expected, bnegate(&cls));

        let cls = bclass(&[(b'\x00', b'a')]);
        let expected = bclass(&[(b'\x62', b'\xFF')]);
        assert_eq!(expected, bnegate(&cls));

        let cls = bclass(&[(b'a', b'\xFF')]);
        let expected = bclass(&[(b'\x00', b'\x60')]);
        assert_eq!(expected, bnegate(&cls));

        let cls = bclass(&[(b'\x00', b'\xFF')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bnegate(&cls));

        let cls = bclass(&[]);
        let expected = bclass(&[(b'\x00', b'\xFF')]);
        assert_eq!(expected, bnegate(&cls));

        let cls = bclass(&[(b'\x00', b'\xFD'), (b'\xFF', b'\xFF')]);
        let expected = bclass(&[(b'\xFE', b'\xFE')]);
        assert_eq!(expected, bnegate(&cls));
    }

    #[test]
    fn class_union_unicode() {
        let cls1 = uclass(&[('a', 'g'), ('m', 't'), ('A', 'C')]);
        let cls2 = uclass(&[('a', 'z')]);
        let expected = uclass(&[('a', 'z'), ('A', 'C')]);
        assert_eq!(expected, uunion(&cls1, &cls2));
    }

    #[test]
    fn class_union_bytes() {
        let cls1 = bclass(&[(b'a', b'g'), (b'm', b't'), (b'A', b'C')]);
        let cls2 = bclass(&[(b'a', b'z')]);
        let expected = bclass(&[(b'a', b'z'), (b'A', b'C')]);
        assert_eq!(expected, bunion(&cls1, &cls2));
    }

    #[test]
    fn class_intersect_unicode() {
        let cls1 = uclass(&[]);
        let cls2 = uclass(&[('a', 'a')]);
        let expected = uclass(&[]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'a')]);
        let cls2 = uclass(&[('a', 'a')]);
        let expected = uclass(&[('a', 'a')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'a')]);
        let cls2 = uclass(&[('b', 'b')]);
        let expected = uclass(&[]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'a')]);
        let cls2 = uclass(&[('a', 'c')]);
        let expected = uclass(&[('a', 'a')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b')]);
        let cls2 = uclass(&[('a', 'c')]);
        let expected = uclass(&[('a', 'b')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b')]);
        let cls2 = uclass(&[('b', 'c')]);
        let expected = uclass(&[('b', 'b')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b')]);
        let cls2 = uclass(&[('c', 'd')]);
        let expected = uclass(&[]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('b', 'c')]);
        let cls2 = uclass(&[('a', 'd')]);
        let expected = uclass(&[('b', 'c')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b'), ('d', 'e'), ('g', 'h')]);
        let cls2 = uclass(&[('a', 'h')]);
        let expected = uclass(&[('a', 'b'), ('d', 'e'), ('g', 'h')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b'), ('d', 'e'), ('g', 'h')]);
        let cls2 = uclass(&[('a', 'b'), ('d', 'e'), ('g', 'h')]);
        let expected = uclass(&[('a', 'b'), ('d', 'e'), ('g', 'h')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b'), ('g', 'h')]);
        let cls2 = uclass(&[('d', 'e'), ('k', 'l')]);
        let expected = uclass(&[]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b'), ('d', 'e'), ('g', 'h')]);
        let cls2 = uclass(&[('h', 'h')]);
        let expected = uclass(&[('h', 'h')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b'), ('e', 'f'), ('i', 'j')]);
        let cls2 = uclass(&[('c', 'd'), ('g', 'h'), ('k', 'l')]);
        let expected = uclass(&[]);
        assert_eq!(expected, uintersect(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'b'), ('c', 'd'), ('e', 'f')]);
        let cls2 = uclass(&[('b', 'c'), ('d', 'e'), ('f', 'g')]);
        let expected = uclass(&[('b', 'f')]);
        assert_eq!(expected, uintersect(&cls1, &cls2));
    }

    #[test]
    fn class_intersect_bytes() {
        let cls1 = bclass(&[]);
        let cls2 = bclass(&[(b'a', b'a')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'a')]);
        let cls2 = bclass(&[(b'a', b'a')]);
        let expected = bclass(&[(b'a', b'a')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'a')]);
        let cls2 = bclass(&[(b'b', b'b')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'a')]);
        let cls2 = bclass(&[(b'a', b'c')]);
        let expected = bclass(&[(b'a', b'a')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b')]);
        let cls2 = bclass(&[(b'a', b'c')]);
        let expected = bclass(&[(b'a', b'b')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b')]);
        let cls2 = bclass(&[(b'b', b'c')]);
        let expected = bclass(&[(b'b', b'b')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b')]);
        let cls2 = bclass(&[(b'c', b'd')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'b', b'c')]);
        let cls2 = bclass(&[(b'a', b'd')]);
        let expected = bclass(&[(b'b', b'c')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b'), (b'd', b'e'), (b'g', b'h')]);
        let cls2 = bclass(&[(b'a', b'h')]);
        let expected = bclass(&[(b'a', b'b'), (b'd', b'e'), (b'g', b'h')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b'), (b'd', b'e'), (b'g', b'h')]);
        let cls2 = bclass(&[(b'a', b'b'), (b'd', b'e'), (b'g', b'h')]);
        let expected = bclass(&[(b'a', b'b'), (b'd', b'e'), (b'g', b'h')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b'), (b'g', b'h')]);
        let cls2 = bclass(&[(b'd', b'e'), (b'k', b'l')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b'), (b'd', b'e'), (b'g', b'h')]);
        let cls2 = bclass(&[(b'h', b'h')]);
        let expected = bclass(&[(b'h', b'h')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b'), (b'e', b'f'), (b'i', b'j')]);
        let cls2 = bclass(&[(b'c', b'd'), (b'g', b'h'), (b'k', b'l')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bintersect(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'b'), (b'c', b'd'), (b'e', b'f')]);
        let cls2 = bclass(&[(b'b', b'c'), (b'd', b'e'), (b'f', b'g')]);
        let expected = bclass(&[(b'b', b'f')]);
        assert_eq!(expected, bintersect(&cls1, &cls2));
    }

    #[test]
    fn class_difference_unicode() {
        let cls1 = uclass(&[('a', 'a')]);
        let cls2 = uclass(&[('a', 'a')]);
        let expected = uclass(&[]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'a')]);
        let cls2 = uclass(&[]);
        let expected = uclass(&[('a', 'a')]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[]);
        let cls2 = uclass(&[('a', 'a')]);
        let expected = uclass(&[]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'z')]);
        let cls2 = uclass(&[('a', 'a')]);
        let expected = uclass(&[('b', 'z')]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'z')]);
        let cls2 = uclass(&[('z', 'z')]);
        let expected = uclass(&[('a', 'y')]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'z')]);
        let cls2 = uclass(&[('m', 'm')]);
        let expected = uclass(&[('a', 'l'), ('n', 'z')]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'c'), ('g', 'i'), ('r', 't')]);
        let cls2 = uclass(&[('a', 'z')]);
        let expected = uclass(&[]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'c'), ('g', 'i'), ('r', 't')]);
        let cls2 = uclass(&[('d', 'v')]);
        let expected = uclass(&[('a', 'c')]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'c'), ('g', 'i'), ('r', 't')]);
        let cls2 = uclass(&[('b', 'g'), ('s', 'u')]);
        let expected = uclass(&[('a', 'a'), ('h', 'i'), ('r', 'r')]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'c'), ('g', 'i'), ('r', 't')]);
        let cls2 = uclass(&[('b', 'd'), ('e', 'g'), ('s', 'u')]);
        let expected = uclass(&[('a', 'a'), ('h', 'i'), ('r', 'r')]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('x', 'z')]);
        let cls2 = uclass(&[('a', 'c'), ('e', 'g'), ('s', 'u')]);
        let expected = uclass(&[('x', 'z')]);
        assert_eq!(expected, udifference(&cls1, &cls2));

        let cls1 = uclass(&[('a', 'z')]);
        let cls2 = uclass(&[('a', 'c'), ('e', 'g'), ('s', 'u')]);
        let expected = uclass(&[('d', 'd'), ('h', 'r'), ('v', 'z')]);
        assert_eq!(expected, udifference(&cls1, &cls2));
    }

    #[test]
    fn class_difference_bytes() {
        let cls1 = bclass(&[(b'a', b'a')]);
        let cls2 = bclass(&[(b'a', b'a')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'a')]);
        let cls2 = bclass(&[]);
        let expected = bclass(&[(b'a', b'a')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[]);
        let cls2 = bclass(&[(b'a', b'a')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'z')]);
        let cls2 = bclass(&[(b'a', b'a')]);
        let expected = bclass(&[(b'b', b'z')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'z')]);
        let cls2 = bclass(&[(b'z', b'z')]);
        let expected = bclass(&[(b'a', b'y')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'z')]);
        let cls2 = bclass(&[(b'm', b'm')]);
        let expected = bclass(&[(b'a', b'l'), (b'n', b'z')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'c'), (b'g', b'i'), (b'r', b't')]);
        let cls2 = bclass(&[(b'a', b'z')]);
        let expected = bclass(&[]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'c'), (b'g', b'i'), (b'r', b't')]);
        let cls2 = bclass(&[(b'd', b'v')]);
        let expected = bclass(&[(b'a', b'c')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'c'), (b'g', b'i'), (b'r', b't')]);
        let cls2 = bclass(&[(b'b', b'g'), (b's', b'u')]);
        let expected = bclass(&[(b'a', b'a'), (b'h', b'i'), (b'r', b'r')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'c'), (b'g', b'i'), (b'r', b't')]);
        let cls2 = bclass(&[(b'b', b'd'), (b'e', b'g'), (b's', b'u')]);
        let expected = bclass(&[(b'a', b'a'), (b'h', b'i'), (b'r', b'r')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'x', b'z')]);
        let cls2 = bclass(&[(b'a', b'c'), (b'e', b'g'), (b's', b'u')]);
        let expected = bclass(&[(b'x', b'z')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));

        let cls1 = bclass(&[(b'a', b'z')]);
        let cls2 = bclass(&[(b'a', b'c'), (b'e', b'g'), (b's', b'u')]);
        let expected = bclass(&[(b'd', b'd'), (b'h', b'r'), (b'v', b'z')]);
        assert_eq!(expected, bdifference(&cls1, &cls2));
    }

    #[test]
    fn class_symmetric_difference_unicode() {
        let cls1 = uclass(&[('a', 'm')]);
        let cls2 = uclass(&[('g', 't')]);
        let expected = uclass(&[('a', 'f'), ('n', 't')]);
        assert_eq!(expected, usymdifference(&cls1, &cls2));
    }

    #[test]
    fn class_symmetric_difference_bytes() {
        let cls1 = bclass(&[(b'a', b'm')]);
        let cls2 = bclass(&[(b'g', b't')]);
        let expected = bclass(&[(b'a', b'f'), (b'n', b't')]);
        assert_eq!(expected, bsymdifference(&cls1, &cls2));
    }

    // We use a thread with an explicit stack size to test that our destructor
    // for Hir can handle arbitrarily sized expressions in constant stack
    // space. In case we run on a platform without threads (WASM?), we limit
    // this test to Windows/Unix.
    #[test]
    #[cfg(any(unix, windows))]
    fn no_stack_overflow_on_drop() {
        use std::thread;

        let run = || {
            let mut expr = Hir::empty();
            for _ in 0..100 {
                expr = Hir::capture(Capture {
                    index: 1,
                    name: None,
                    sub: Box::new(expr),
                });
                expr = Hir::repetition(Repetition {
                    min: 0,
                    max: Some(1),
                    greedy: true,
                    sub: Box::new(expr),
                });

                expr = Hir {
                    kind: HirKind::Concat(vec![expr]),
                    props: Properties::empty(),
                };
                expr = Hir {
                    kind: HirKind::Alternation(vec![expr]),
                    props: Properties::empty(),
                };
            }
            assert!(!matches!(*expr.kind(), HirKind::Empty));
        };

        // We run our test on a thread with a small stack size so we can
        // force the issue more easily.
        //
        // NOTE(2023-03-21): See the corresponding test in 'crate::ast::tests'
        // for context on the specific stack size chosen here.
        thread::Builder::new()
            .stack_size(16 << 10)
            .spawn(run)
            .unwrap()
            .join()
            .unwrap();
    }

    #[test]
    fn look_set_iter() {
        let set = LookSet::empty();
        assert_eq!(0, set.iter().count());

        let set = LookSet::full();
        assert_eq!(10, set.iter().count());

        let set =
            LookSet::empty().insert(Look::StartLF).insert(Look::WordUnicode);
        assert_eq!(2, set.iter().count());

        let set = LookSet::empty().insert(Look::StartLF);
        assert_eq!(1, set.iter().count());

        let set = LookSet::empty().insert(Look::WordAsciiNegate);
        assert_eq!(1, set.iter().count());
    }

    #[test]
    fn look_set_debug() {
        let res = format!("{:?}", LookSet::empty());
        assert_eq!("∅", res);
        let res = format!("{:?}", LookSet::full());
        assert_eq!("Az^$rRbB𝛃𝚩", res);
    }
}