summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/source/latex/tools/array.dtx
blob: ff963d7f514454dc84d2b66a9c97bee8d027932e (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
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
% \iffalse meta-comment
%
% Copyright (C) 1993-2020
%
% The LaTeX3 Project and any individual authors listed elsewhere
% in this file.
%
% This file is part of the Standard LaTeX `Tools Bundle'.
% -------------------------------------------------------
%
% It may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3c
% of this license or (at your option) any later version.
% The latest version of this license is in
%    https://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% The list of all files belonging to the LaTeX `Tools Bundle' is
% given in the file `manifest.txt'.
%
% \fi
%\iffalse   % this is a METACOMMENT !
%
%% Package `array' to use with LaTeX 2e
%% Copyright (C) 1989-1998 Frank Mittelbach, all rights reserved.
%<+package>\NeedsTeXFormat{LaTeX2e}[1995/06/01]
%<+package>\providecommand\DeclareRelease[3]{}
%<+package>\providecommand\DeclareCurrentRelease[2]{}
%<+package>
%<+package>\DeclareRelease{}{2016-10-06}{array-2016-10-06.sty}
%<+package>\DeclareRelease{v2.4}{2020-02-10}{array-2020-02-10.sty}
%<+package>\DeclareCurrentRelease{}{2020-10-01}
%<+package>
%<+package>\ProvidesPackage{array}
%<+package>         [2020/10/01 v2.5c Tabular extension package (FMi)]
%
% \fi
%
%%
%
%
% \changes{v2.4g}{2018/04/07}{Renamed internal \cs{mcell@box} to
%       \cs{ar@mcellbox} and \cs{align@mcell} to \cs{ar@align@mcell}
%        to avoid conflict with makecell package}
%
% \changes{v2.4c}{2008/09/09}{(WR) Typo fix in documentation}
%
% \changes{v2.3c}{1995/11/02}{(DPC) minor doc changes}
%
% \changes{v2.3a}{1994/10/16}{Added code for \cs{firsthline} and
%                             friends}
%
% \changes{v2.2c}{1994/03/14}{removed check for \cs{@tfor} bug}
%
% \changes{v1.0b}{1987/06/04}{`@classi (faster),
%                        `@classvi (new)   A in preamble means
%                                         \&\& in `halign.}
%
% \changes{v1.1a}{1987/07/05}{New concept:
%                        preamblechar: c,l,r,C,L,R,A,p,t,{\tt !|},@,!!}
% \changes{v1.1b}{1987/09/21}{Again p like original \LaTeX{} and z for
%                        centered `parbox.}
%
% \changes{v1.2a}{1987/09/27}{Completely new implementation.}
% \changes{v1.2b}{1987/10/06}{{\tt !|} does no longer generate space at
%                        start or end of the preamble. Otherwise `hline
%                        is too long.}
% \changes{v1.2b}{1987/10/06}{Enlarged `@arstrutbox by 1pt (Test-Impl)
%                         with dimen `@strutheight.}
% \changes{v1.2c}{1987/10/22}{New dimen parameter `extrarowheight
%                        (default: 0pt).}
% \changes{v1.2c}{1987/10/22}{Enlarged `@arstrutbox by `extrarowheight.
%                        Thus you may avoid large characters to
%                        overprint a `hline.}
% \changes{v1.2c}{1987/10/22}{Introduced `m@th in `@array to allow
%                         non-zero values of `mathsurround.}
% \changes{v1.2d}{1987/11/02}{Completed the documentation.}
% \changes{v1.2e}{1987/11/03}{Bug fixed: A at start of preamble resulted
%                        in an error since `@mkpream generated
%                        `@arstrut \& ... as a preamble.}
% \changes{v1.2f}{1987/11/09}{`@testpach documented.}
%
% \changes{v1.3a}{1987/11/11}{Again a new implementation, with a new
%                        concept (cf. the documentation).}
% \changes{v1.3b}{1988/03/17}{`@decl expands now into `@empty, i.e., it
%                        disappears when the preamble is generated,
%                        except when the user specifies A\{\} or
%                        B\{\}.}
%
% \changes{v1.4a}{1988/03/18}{Test implementation of use of token
%                        registers in order to do without `protect.}
% \changes{v1.4b}{1988/03/19}{Changed erroneous class numbers:
%                        5 -!> 6
%                        6 -!> 7
%                        7 -!> 5
%                        Corresponding changes in the macros.}
% \changes{v1.4c}{1988/03/19}{Everything except p,z now works with token
%                        registers.}
%
% \changes{v1.9a}{1988/03/20}{Last (so I hope) major change: 1) Options
%                        B,A now called !>,<.  These options now point
%                        to the column they modify.}
% \changes{v1.9a}{1988/03/20}{2) `protect is no longer necessary. But
%                           still the macro `@expast needs top be
%                          modified. `multicolumn still does not work.}
% \changes{v1.9b}{1988/04/29}{inserted missing `fi in `@testpach.
%                        Corrected \LaTeX bug in `@tfor.}
% \changes{v1.9c}{1988/05/07}{Re-introduced `@endpbox.
%                        `multicolumn now works!! Version number still
%                        1.9 since the documentation is still not
%                        finished.}
% \changes{v1.9c}{1988/05/07}{1) `def `the@toks \{`the ...\} remaining
%                         only in `@mkpream.  2) Removed `@classiii and
%                        replaced by `save@decl.}
% \changes{v1.9c}{1988/05/07}{3) `insert@column contains only `@tempcnta
%                        and `count@ counters.  4) `@@startpbox and
%                        `@@endpbox now totally obsolete.}
% \changes{v1.9d}{1988/05/10}{Replaced `number by `the where the `toks
%                        registers' contents are used.}
% \changes{v1.9e}{1988/05/11}{Re-introduced `@xargarraycr and
%                        `@yargarraycr, since `endtemplate seems to
%                        be `outer.}
% \changes{v1.9f}{1988/05/20}{Small changes finally carried out:
%                        1) `par!=`@empty.
%                        2) \{..ifnum0!=!`\}...  $\to$ `bgroup and
%                           analogously `egroup.}
% \changes{v1.9g}{1988/02/24}{Inserted again \{..ifnum0!=!`\}..,
%                        c.f. Appendix D of the \protect\TeX{}book.}
% \changes{v1.9h}{1988/06/28}{No longer necessary to read in the file
%                        twice.}
% \changes{v1.9i}{1988/06/28}{Corrected typo in german version.}
% \changes{v1.9j}{1988/11/23}{In a `r' column an extra `kern`z@ is
%                        needed.}
% \changes{v1.9j}{1988/11/23}{Otherwise the `hfil on the left side
%                        will be removed by the `unskip in
%                        `insert@column if the entry is empty.}
% \changes{v1.9k}{1988/06/28}{Corrected typo in german version.}
% \changes{v1.9k}{1989/01/16}{`begin{Macro} changed to `begin{macro} in
%                        documentation.}
%
% \changes{v2.0a}{1989/05/12}{{\tt\textbackslash @thetoks} changed to
%                          {\tt\textbackslash the@toks}.}
% \changes{v2.0a}{1989/05/12}{source changed to reflect new doc.sty
%                          conventions.}
% \changes{v2.0a}{1989/05/12}{t option renamed to p to be compatible to
%                        the original.}
% \changes{v2.0a}{1989/05/12}{File renamed from arraye.sty to
%                        array.sty.}
% \changes{v2.0b}{1989/05/17}{Three forgotten end macro added.}
% \changes{v2.0b}{1989/05/17}{All lines shortened to 72 or less.}
% \changes{v2.2a}{1994/02/03}{Upgrade to \LaTeXe}
%
% \DoNotIndex{\@depth,\@ehc,\@fortmp,\@height,\@ifnextchar,\@ifstar}
% \DoNotIndex{\@ifundefined,\@ne,\@nil,\@tempa,\@tempb}
% \DoNotIndex{\@tempcnta,\@tempd,\@tempdima,\@whilenum,\@width,\\}
% \DoNotIndex{\@tforloop}
% \DoNotIndex{\advance}
% \DoNotIndex{\baselineskip,\begingroup,\bgroup}
% \DoNotIndex{\cr,\crcr,\csname}
% \DoNotIndex{\def,\do,\docdate,\dp}
% \DoNotIndex{\edef,\egroup,\else,\endcsname,\endinput,\expandafter}
% \DoNotIndex{\fi,\filedate,\fileversion}
% \DoNotIndex{\gdef}
% \DoNotIndex{\hbox,\hfil,\hsize,\hskip,\ht}
% \DoNotIndex{\if,\ifcase,\ifdim,\ifnum,\ifx,\ignorespaces}
% \DoNotIndex{\kern}
% \DoNotIndex{\leavevmode,\let,\lineskip}
% \DoNotIndex{\m@ne,\multispan}
% \DoNotIndex{\newcount,\newdimen,\noalign}
% \DoNotIndex{\or}
% \DoNotIndex{\relax}
% \DoNotIndex{\setbox,\space,\strutbox}
% \DoNotIndex{\tabskip,\thr@@,\the,\toks,\toks@,\tw@,\typeout}
% \DoNotIndex{\unhcopy,\unskip}
% \DoNotIndex{\vbox,\vcenter,\vline,\vrule,\vtop,\vskip}
% \DoNotIndex{\xdef}
% \DoNotIndex{\z@}
%
% \GetFileInfo{array.sty}
%
% \title{A new implementation of \LaTeX's \textsf{tabular}
%        and \textsf{array} environment\thanks{This file
%        has version number \fileversion, last
%        revised \filedate.}}
% \author{Frank Mittelbach
%         \and
%         David Carlisle\thanks{David kindly agreed on the inclusion
%         of the \texttt{\textbackslash{}newcolumntype} implementation,
%         formerly in
%         \texttt{newarray.sty} into this package }}
%
% \date{Printed \today}
%
% \MaintainedByLaTeXTeam{tools}
% \maketitle
%
% \MakeShortVerb{\=}
%
% \begin{abstract}
% This article describes an extended implementation of the \LaTeX\
% \textsf{array}-- and \textsf{tabular}--environments. The special
% merits of this implementation are further options to format columns
% and the fact that fragile \LaTeX--commands don't have to be
% =\protect='ed any more within those environments.
%
% The major part of the code for this package dates back to 1988---so
% does some of its documentation.
% \end{abstract}
%
%
%
% \section{Introduction}
%
% This new implementation of the \textsf{array}-- and
% \textsf{tabular}--environments is part of a larger project in which
% we are trying to improve the \LaTeX\--code in some aspects and to
% make \LaTeX\ even easier to handle.
%
% The reader should be familiar with the general structure of the
% environments
% mentioned above. Further information can be found in
% \cite{bk:lamport} and \cite{bk:GMS94}.
% The additional options which can be used in the
% preamble as well as those which now have a slightly different meaning
% are described in table~\ref{tab:opt}.
%
% \DescribeMacro\extrarowheight
% Additionally we introduce a new
% parameter called =\extrarowheight=. If it takes a positive
% length, the value of the parameter is added to the normal height of
% every row of the table, while
% the depth will remain the same. This is important for tables
% with horizontal lines because those lines normally touch the
% capital letters.
% For example, we used =\setlength{\extrarowheight}{1pt}=
% in table~\ref{tab:opt}.
%
% \begin{table}[!t]
% \begin{center}
%    \setlength{\extrarowheight}{1pt}
%    \begin{tabular}{|>{\tt}c|m{9cm}|}
%       \hline
%     \multicolumn{2}{|c|}{Unchanged options}\\
%       \hline
%       l             &  Left adjusted column. \\
%       c             &  Centered adjusted column. \\
%       r             &  Right adjusted column. \\
%       p\{width\}    &  Equivalent to =\parbox[t]{width}=. \\
%       @\{decl.\}    &  Suppresses inter-column space and inserts
%                        \texttt{decl.}\ instead. \\
%       \hline
%     \multicolumn{2}{|c|}{New options}\\
%       \hline
%       m\{width\}    &  Defines a column of width \texttt{width}.
%                        Every entry will be centered in proportion to
%                        the rest of the line. It is somewhat like
%                        =\parbox{width}=. \\
%       \hline
%       b\{width\}    &  Coincides with =\parbox[b]{width}=. \\
%       \hline
%       >\{decl.\}    &  Can be used before an \texttt{l}, \texttt{r},
%                        \texttt{c}, \texttt{p}, \texttt{m} or a
%                        \texttt{b} option. It inserts \texttt{decl.}\
%                        directly in front of the entry of the column.
%                        \\
%       \hline
%       <\{decl.\}    &  Can be used after an \texttt{l}, \texttt{r},
%                        \texttt{c}, =p{..}=, =m{..}= or a =b{..}=
%                        option.  It inserts \texttt{decl.}\ right
%                        after the entry of the column.  \\
%       \hline
%       |             &  Inserts a vertical line. The distance between
%                        two columns will be enlarged by the width of
%                        the line
%                        in contrast to the original definition of
%                        \LaTeX.  \\
%       \hline
%       !\{decl.\}    &  Can be used anywhere and corresponds with the
%                        \texttt{|} option. The difference is that
%                        \texttt{decl.} is inserted instead of a
%                        vertical line, so this option doesn't
%                        suppress the normally inserted space between
%                        columns in contrast to =@{...}=.\\
%       \hline\hline
%       w\{align\}\{width\} & Sets the cell content in a box of the
%                        specified \texttt{width} aligned according to
%                        the \texttt{align} parameter which could be
%                        either \texttt{l}, \texttt{c} or
%                        \texttt{r}. Works essentially like
%                        =\makebox[=width=][=align=]{=cell=}= so
%                        silently overprints if the cell content is
%                        wider than the specified width. If that is
%                        not desired use \texttt{W} instead.\\
%       \hline
%       W\{align\}\{width\} & Like \texttt{w} but spits out an overfull
%                        box warning (and an overfullrule marker in
%                        draft mode) when the cell content is too wide
%                        to fit. This also means that the alignment is
%                        different if there is too much material,
%                        because it then always protrudes to the right!\\
%       \hline
%    \end{tabular}
% \end{center}
% \caption{The  preamble options.} \label{tab:opt}
% \end{table}
%
%
% We will discuss a few examples using the new preamble options before
% dealing with the implementation.
% \begin{itemize}
%    \item
%       If you want to use a special font (for example =\bfseries=) in a
%       flushed left column, this can be done with =>{\bfseries}l=. You
%       do not have to begin every entry of the column with  =\bfseries=
%       any more.
%    \item
%       In columns which have been generated with \texttt{p}, \texttt{m}
%       or \texttt{b}, the default value of =\parindent= is
%       \textsf{0pt}.
%       This can be changed with \\
%       =>{\setlength{\parindent}{1cm}}p=.
%    \item
%       The \texttt{>}-- and \texttt{<}--options were originally
%       developed for the following application:
%       =>{$}c<{$}= generates a column in math
%       mode in a \textsf{tabular}--environment. If you use this type
%       of a preamble in an \textsf{array}--environment, you get a
%       column in LR mode because the additional \$'s cancel the
%       existing \$'s.
%    \item
%       One can also think of more complex applications. A problem
%       which has
%       been mentioned several times in \TeX{}hax can be solved with
%       =>{\centerdots}c=\linebreak[0]=<{\endcenterdots}=.
%       To center decimals at their
%       decimal points you (only?) have to define the following macros:
%       \begin{verbatim}
%{\catcode`\.\active\gdef.{\egroup\setbox2\hbox\bgroup}}
%\def\centerdots{\catcode`\.\active\setbox0\hbox\bgroup}
%\def\endcenterdots{\egroup\ifvoid2 \setbox2\hbox{0}\fi
%   \ifdim \wd0>\wd2 \setbox2\hbox to\wd0{\unhbox2\hfill}\else
%     \setbox0\hbox to\wd2{\hfill\unhbox0}\fi
%   \catcode`\.12 \box0.\box2}
%\end{verbatim}
%      Warning: The code is bad, it doesn't work with more than one
%      dot in a cell and doesn't work when the tabular is used in the
%      argument of some other command. A much better version is
%      provided in the \texttt{dcolumn.sty} by David Carlisle.
%    \item
%       Using =c!{\hspace{1cm}}c= you get space between two
%       columns which is enlarged by one centimeter, while
%       =c@{\hspace{1cm}}c= gives you exactly one centimeter
%       space between two columns.
%
%    \item
%       A declaration like =w{l}{3cm}= (or even shorter =wl{3cm}=)
%       works like an =l= column except that the width will always be
%       =3cm= regardless of the cell content. Same with =w{c}= or
%       =w{r}=. This means that it is easy to set up tables in which all
%       columns have predefined widths.
% \end{itemize}
%
% \subsection{Defining new column specifiers}
%
% \DeleteShortVerb{\=}
% \MakeShortVerb{\"}
% \DescribeMacro{\newcolumntype}
% Whilst it is handy to be able to type
% \begin{quote}
%   ">{"\meta{some declarations}"}{c}<{"\meta{some more
%   declarations}"}"
% \end{quote}
% if you have a one-off column in a table, it is rather inconvenient
% if you often use columns of this form. The new version allows you
% to define a new column specifier, say \texttt{x}, which will expand to
% the primitives column specifiers.\footnote{This command was named
% \texttt{\textbackslash{}newcolumn} in the \texttt{newarray.sty}.
% At the moment \texttt{\textbackslash{}newcolumn} is still supported
% (but gives a warning). In later releases it will vanish.} Thus we
% may define
% \begin{quote}
%   "\newcolumntype{x}{>{"\meta{some declarations}"}{c}<{"\meta{some
%   more declarations}"}}"\hspace*{-3cm} ^^A no overfull from this line
% \end{quote}
% One can then use the \texttt{x} column specifier in the preamble
% arguments of all \texttt{array} or \texttt{tabular} environments in
% which you want columns of this form.
%
% It is common  to need math-mode and LR-mode columns in the same
% alignment. If we define:
% \begin{quote}
%   "\newcolumntype{C}{>{$}c<{$}}" \\
%   "\newcolumntype{L}{>{$}l<{$}}" \\
%   "\newcolumntype{R}{>{$}r<{$}}"
% \end{quote}
% Then we can use \texttt{C} to get centred LR-mode in an
% \texttt{array}, or centred math-mode in a \texttt{tabular}.
%
% The example given above for `centred decimal points' could be
% assigned to a \texttt{d} specifier with the following command.
% \begin{quote}
% "\newcolumntype{d}{>{\centerdots}c<{\endcenterdots}}"
% \end{quote}
%
% The above solution always centres the dot in the
% column. This does not look too good if the column consists of large
% numbers, but to only a few decimal places. An alternative definition
% of a \texttt{d} column is
% \begin{quote}
%   "\newcolumntype{d}[1]{>{\rightdots{#1}}r<{\endrightdots}}"
% \end{quote}
% where the appropriate macros in this case are:\footnote{The package
% \texttt{dcolumn.sty} contains more robust macros based on these
% ideas.}
% \begin{verbatim}
%   \def\coldot{.}% Or if you prefer, \def\coldot{\cdot}
%   {\catcode`\.=\active
%     \gdef.{$\egroup\setbox2=\hbox to \dimen0 \bgroup$\coldot}}
%   \def\rightdots#1{%
%     \setbox0=\hbox{$1$}\dimen0=#1\wd0
%     \setbox0=\hbox{$\coldot$}\advance\dimen0 \wd0
%     \setbox2=\hbox to \dimen0 {}%
%     \setbox0=\hbox\bgroup\mathcode`\.="8000 $}
%   \def\endrightdots{$\hfil\egroup\box0\box2}
%\end{verbatim}
% Note that "\newcolumntype" takes the same optional argument as
% "\newcommand" which declares the number of arguments of the column
% specifier being defined. Now we can specify "d{2}" in our preamble
% for a column of figures to at most two decimal places.
%
% A rather different use of the "\newcolumntype" system takes
% advantage of the fact that the replacement text in the
% "\newcolumntype" command may refer to more than one column. Suppose
% that a document contains a lot of \texttt{tabular} environments that
% require the same preamble, but you wish to experiment with different
% preambles. Lamport's original definition allowed you to do the
% following (although it was probably a mis-use of the system).
% \begin{quote}
%   "\newcommand{\X}{clr}"\\
%   "\begin{tabular}{\X}" \ldots
% \end{quote}
% \texttt{array.sty} takes great care \textbf{not} to expand the
% preamble, and so the above does not work with the new scheme. With
% the new version this functionality is returned:
% \begin{quote}
% "\newcolumntype{X}{clr}"\\
% "\begin{tabular}{X}" \ldots
% \end{quote}
%
% The replacement text in a "\newcolumntype" command may refer to any of
% the primitives of \texttt{array.sty} see table \ref{tab:opt} on page
% \pageref{tab:opt}, or to any new letters defined in other
% "\newcolumntype" commands.
%
%
% \DescribeMacro{\showcols}A list of all the currently active
% "\newcolumntype" definitions is sent to the terminal and log file if
% the "\showcols" command is given.
%
%
% \subsection{Special variations of \texttt{\textbackslash hline}}
%
% The family of \texttt{tabular} environments allows
% vertical positioning with respect to the baseline of
% the text in which the environment appears.  By default the
% environment appears centered, but this can be changed to
% align with the first or last line in the environment by
% supplying a \texttt{t} or \texttt{b} value to the
% optional position argument. However, this does not work
% when the first or last element in the environment is a
% "\hline" command---in that case the environment is
% aligned at the horizontal rule.
%
% \pagebreak[3]
%
% Here is an example:
% \begin{center}
% \begin{minipage}[t]{.4\linewidth}
% Tables
% \begin{tabular}[t]{l}
%   with no\\ hline \\ commands \\ used
% \end{tabular} versus \\ tables
% \begin{tabular}[t]{|l|}
%  \hline
%   with some \\ hline \\ commands \\
%  \hline
% \end{tabular} used.
% \end{minipage}
% \begin{minipage}[t]{.5\linewidth}
% \begin{verbatim}
% Tables
% \begin{tabular}[t]{l}
%  with no\\ hline \\ commands \\ used
% \end{tabular} versus tables
% \begin{tabular}[t]{|l|}
%  \hline
%   with some \\ hline \\ commands \\
%  \hline
% \end{tabular} used.
% \end{verbatim}
% \end{minipage}
% \end{center}
%
% \DescribeMacro\firsthline
% \DescribeMacro\lasthline
% Using "\firsthline" and "\lasthline" will
% cure the problem, and the tables will align properly as long
% as their first or last line does not contain extremely large
% objects.
% \begin{center}
% \begin{minipage}[t]{.4\linewidth}
% Tables
% \begin{tabular}[t]{l}
%   with no\\ line \\ commands \\ used
% \end{tabular} versus \\ tables
% \begin{tabular}[t]{|l|}
%  \firsthline
%   with some \\ line   \\ commands \\
%  \lasthline
% \end{tabular} used.
% \end{minipage}
% \begin{minipage}[t]{.5\linewidth}
% \begin{verbatim}
% Tables
% \begin{tabular}[t]{l}
%   with no\\ line \\ commands \\ used
% \end{tabular} versus tables
% \begin{tabular}[t]{|l|}
%  \firsthline
%   with some \\ line   \\ commands \\
%  \lasthline
% \end{tabular} used.
% \end{verbatim}
% \end{minipage}
% \end{center}
% \DescribeMacro\extratabsurround
% The implementation of these two commands contains an extra
% dimension, which is called "\extratabsurround", to add some
% additional space at the top and the bottom of such an environment.
% This is useful if such tables are nested.
%
% \section{Final Comments}
%
% \subsection{Handling of rules}
%
% There are two possible approaches to the handling of horizontal and
% vertical rules in tables:
% \begin{enumerate}
%   \item rules can be placed into the available space without
%   enlarging the table, or
%   \item rules can be placed between columns or rows thereby enlarging
%   the table.
% \end{enumerate}
% For vertical rules \texttt{array.sty} implements the second
% possibility while the default implementation in the \LaTeX{} kernel
% implements the first concept.
% Both concepts have their merits but
% one has to be aware of the individual implications.
% \begin{itemize}
% \item
%   With standard \LaTeX{} adding vertical rules to a table will
%   not affect the
%   width of the table (unless double rules are used), e.g.,
%   changing a preamble from \verb=lll= to \verb=l|l|l= does not
%   affect the document other than adding rules to the table. In
%   contrast, with \texttt{array.sty} a table that just fit the
%   \verb=\textwidth= might now produce an overfull box.
% \item
%   With standard \LaTeX{} modifying the width of rules could result
%   in ugly looking tables because without adjusting the
%   \verb=\tabcolsep=, etc.\ the space between rule and column could
%   get too small (or too large). In fact even overprinting of text is
%   possible. In contrast, with  \texttt{array.sty} modifying any such
%   length usually works well as the actual visual white space (from
%   \verb=\tabcolsep=, etc.) does not depend on the width of the
%   rules.
% \item
%   With standard \LaTeX{} boxed tabulars actually have strange
%   corners because the horizontal rules end in the middle of the
%   vertical ones. This looks very unpleasant when a large
%   \verb=\arrayrulewidth= is chosen. In that case a simple table like
%\begin{verbatim}
%\setlength{\arrayrulewidth}{5pt}
%\begin{tabular}{|l|}
%  \hline  A \\  \hline
%\end{tabular}
%\end{verbatim}
%   will produce something like
%   \begin{center}
%\setlength{\arrayrulewidth}{5pt}
%\begin{tabular}{@{}l@{}}
%  \hline  \null\hskip-.5\arrayrulewidth\vline
%  \hskip\tabcolsep
%   A\hskip\tabcolsep
%  \vline\hskip-.5\arrayrulewidth\null \\  \hline
%\end{tabular}
%   \quad
%   instead of
%   \quad
%\begin{tabular}{|l|}
%  \hline  A \\  \hline
%\end{tabular}
%   \end{center}
% \end{itemize}
%
% Horizontal rules produced with \cs{hline} add to the table height in
% both implementations but they differ in handling double \cs{hline}s.
% In contrast a \cs{cline} does not change the table
% height.\footnote{All a bit inconsistent, but nothing that can be
% changed after being 30+ years in existence.}
%
% \subsection{Comparisons with older versions of \texttt{array.sty}}
%
% There are some differences in the way version 2.1 treats incorrect
% input, even if the source file does not appear to use any of the
% extra features of the new version.
% \begin{itemize}
% \item A preamble of the form "{wx*{0}{abc}yz}" was treated by
% versions prior to 2.1 as "{wx}". Version 2.1 treats it as "{wxyz}"
% \item An incorrect positional argument such as \texttt{[Q]} was
% treated as \texttt{[c]} by \texttt{array.sty}, but is now treated as
% \texttt{[t]}.
% \item A preamble such as "{cc*{2}}" with an error in
% a $*$-form will generate different errors in the new version. In
% both cases the error message is not particularly helpful to the
% casual user.
% \item Repeated \texttt{<} or \texttt{>} constructions
% generated an error in earlier versions, but are now allowed in
% this package.  ">{"\meta{decs1}"}>{"\meta{decs2}"}" is treated the
% same as ">{"\meta{decs2}\meta{decs1}"}".
% \item The "\extracolsep"
% command does not work with the old versions of \texttt{array.sty},
% see the comments in \texttt{array.bug}. With version 2.1
% "\extracolsep" may again be used in \texttt{@}-expressions as in
% standard \LaTeX, and also in \texttt{!}-expressions (but see the
% note below).
% \end{itemize}
%
% Prior to version 2.4f the space added by the optional argument to "\\"
% was added inside an m-cell if the last column was of type
% \texttt{m}. As a result that cell was vertically centered with that
% space inside, resulting in a strange offset. Since 2.4f, this space
% is now added after centering the cell.
%
% A similar problem happened when "\extrarowheight" was used. For that
% reason m-cells now manually position the cell content which
% allows to ignore this extra space request during the vertical aligment.
%
%
% \subsection{Bugs and Features}
%
% \begin{itemize}
% \item Error messages generated when parsing the column specification
%   refer to the preamble argument \textbf{after} it has been re-written
%   by the "\newcolumntype" system, not to the preamble entered by the
%   user.  This seems inevitable with any system based on
%   pre-processing and so is classed as a \textbf{feature}.
%
% \item The treatment of multiple \texttt{<} or \texttt{>}
%   declarations may seem strange at first. Earlier implementations
%   treated ">{"\meta{decs1}"}>{"\meta{decs2}"}" the same as
%   ">{"\meta{decs1}\meta{decs2}"}". However this did not give the
%   user the opportunity of overriding the settings of a
%   "\newcolumntype" defined using these declarations. For example,
%   suppose in an \texttt{array} environment we use a \texttt{C}
%   column defined as above. The \texttt{C} specifies a centred text
%   column, however ">{\bfseries}C", which re-writes to
%   ">{\bfseries}>{$}c<{$}" would not specify a bold column as might
%   be expected, as the preamble would essentially expand to
%   "\hfil$\bfseries$#$ $\hfil" and so the column entry would not be in the
%   scope of the "\bfseries"\,! The present version switches the order
%   of repeated declarations, and so the above example now produces a
%   preamble of the form "\hfil$" "$\bfseries#$" "$\hfil", and the
%   dollars cancel each other out without limiting the scope of the
%   "\bfseries".
%
% \item The use of "\extracolsep" has been subject to the following
%   two restrictions.  There must be at most one "\extracolsep"
%   command per "@", or "!" expression and the command must be
%   directly entered into the "@" expression, not as part of a macro
%   definition. Thus "\newcommand{\ef}{\extracolsep{\fill}}" \ldots
%   "@{\ef}" does not work with this package. However you can use
%   something like
%   "\newcolumntype{e}{@{\extracolsep{\fill}}" instead.
%
% \item As noted by the \LaTeX{} book, for the purpose of
%   "\multicolumn" each column with the exception of the first one
%   consists of the entry and the \emph{following} inter-column
%   material. This means that in a tabular with the preamble
%   "|l|l|l|l|" input such as "\multicolumn{2}{|c|}" in
%   anything other than the first column is incorrect.

%   In the standard array/tabular implementation this error is not so
%   noticeable as that version contains negative spacing so that each
%   "|" takes up no horizontal space. But since in this package the
%   vertical lines take up their natural width one sees two lines if
%   two are specified.
%
% \end{itemize}
%
%
%
% \changes{v2.2b}{1994/02/04}{Removed interactive prompt}
%
% \StopEventually{
%
%
% \begin{thebibliography}{1}
%    \bibitem{bk:GMS94} \textsc{M.~Goossens}, \textsc{F.~Mittelbach}
%       and \textsc{A.~Samarin}.
%       \newblock The \LaTeX{} Companion.
%       \newblock
%       Addison-Wesley, Reading, Massachusetts, 1994.
%    \bibitem{bk:knuth}  \textsc{D. E. Knuth}.
%       \newblock  The \TeX{}book (Computers \& Typesetting Volume A).
%       \newblock
%       Addison-Wesley, Reading, Massachusetts, 1986.
%    \bibitem{bk:lamport} \textsc{L. Lamport}.
%       \newblock
%       \LaTeX\ --- A Document Preparation System.
%       \newblock
%       Addison-Wesley, Reading, Massachusetts, 1986.
% \end{thebibliography}
%
% }   ^^A  end of \StopEventually
%
%
%
%
% \section{The documentation driver file}
%
% The first bit of code contains the documentation driver file for
% \TeX{}, i.e., the file that will produce the documentation you are
% currently reading. It will be extracted from this file by the
% \texttt{docstrip} program.
%    \begin{macrocode}
%<*driver>
\NeedsTeXFormat{LaTeX2e}[1995/12/01]
\documentclass{ltxdoc}

% undo the default is not used:

\IfFormatAtLeastTF {2020/10/01}
 {\AtBeginDocument[ltxdoc]{\DeleteShortVerb{\|}} } 
 {\AtBeginDocument{\DeleteShortVerb{\|}} } 

 \usepackage{array}

 % Allow large table at bottom
 \renewcommand{\bottomfraction}{0.7}

\EnableCrossrefs
 %\DisableCrossrefs   % Say \DisableCrossrefs if index is ready

\RecordChanges                  % Gather update information

\CodelineIndex                  % Index code by line number

 %\OnlyDescription    % comment out for implementation details
 %\OldMakeindex       % use if your MakeIndex is pre-v2.9

\begin{document}
   \DocInput{array.dtx}
\end{document}
%</driver>
%    \end{macrocode}
%
%
% \section{The construction of the preamble}
%
% \DeleteShortVerb{\"}
% \MakeShortVerb{\=}
%
% It is obvious that those environments will consist mainly of an
% =\halign=, because \TeX\ typesets tables using this primitive.
% That is why we will now take a look at the algorithm which determines
% a preamble for a =\halign= starting with a given user preamble
% using the options mentioned above.
%
%
%    The current version is defined at the top of the file looking
%    something like this
%    \begin{macrocode}
%<*package>
%\NeedsTeXFormat{LaTeX2e}[1994/05/13]
%\ProvidesPackage{array}[\filedate\space version\fileversion]
%    \end{macrocode}
%
% The most interesting macros of this implementation are without doubt
% those which are responsible for the construction of the preamble for
% the =\halign=. The underlying algorithm was developed by
% \textsc{Lamport} (resp.\ \textsc{Knuth}, see texhax V87\#??), and it
% has been extended and improved.
%
% The user preamble will be read \textsf{token} by \textsf{token}.  A
% \textsf{token} is a single character like \texttt{c} or a block
% enclosed in ={...}=. For example the preamble of
% =\begin{tabular}=\linebreak[0]={lc||c@{\hspace{1cm}}}= consists of
% the \textsf{token} \texttt{l}, \texttt{c}, \texttt{|}, \texttt{|},
% \texttt{@} and =\hspace{1cm}=.
%
% The currently used \textsf{token} and the one, used before, are needed
% to decide on how the construction of the preamble has to be
% continued.
% In the example mentioned above the \texttt{l} causes the preamble
% to begin with =\hskip\tabcolsep=. Furthermore
% =# \hfil= would be appended to define a flush left column.
% The next \textsf{token} is a \texttt{c}. Because it was preceded by an
% \texttt{l} it generates a new column. This is done with
% =\hskip \tabcolsep & \hskip \tabcolsep=. The column which is to
% be centered will be appended with =\hfil # \hfil=.
% The \textsf{token} \texttt{|} would then add a space of
% =\hskip \tabcolsep=
% and a vertical line because the last
% \textsf{tokens} was a \texttt{c}.
% The following \textsf{token} \texttt{|} would only add a space
% =\hskip \doublerulesep= because it was preceded by the
% \textsf{token} \texttt{|}. We will not discuss our example further but
%  rather take a look at the general case of constructing preambles.
%
% The example shows that the desired preamble for the
% =\halign= can be constructed as soon as the action of all
% combinations
% of the preamble \textsf{tokens} are specified. There are 18 such
% \textsf{tokens}
% so we have $19 \cdot 18 \string= 342$ combinations if we count the
% beginning of
% the preamble as a special \textsf{token}. Fortunately, there are many
% combinations which generate the same spaces, so we can define
% \textsf{token} classes. We will identify a
% \textsf{token} within a class with a number, so we can insert the
% formatting (for example of a column).
% Table~\ref{tab:Klassen} lists all \textsf{token} classes and
% their corresponding numbers.
% \begin{table}[ht]
% \begin{center}
%    \begin{tabular}[t]{>{\ttfamily}ccc}
%       \textsf{token} & =\@chclass= & =\@chnum= \\[2mm]
%       c   & 0  & 0 \\
%       l   & 0  & 1 \\
%       r   & 0  & 2 \\
%       p-arg    & 0  & 3 \\
%       t-arg    & 0  & 4 \\
%       b-arg    & 0  & 5 \\
%       |   & 1  & 0 \\
%       !-arg    & 1  & 1 \\
%       <-arg    & 2  & --- \\
%       >-arg    & 3  & ---
%    \end{tabular}
%    \kern3mm \vrule \kern3mm%
%    \begin{tabular}[t]{>{\ttfamily}ccc}
%       \textsf{token} & =\@chclass= & =\@chnum= \\[2mm]
%       Start    & 4  & --- \\
%       @-arg    & 5  & --- \\
%       !   & 6  & --- \\
%       @   & 7  & --- \\
%       <   & 8  & --- \\
%       >   & 9  & --- \\
%       p   & 10 & 3 \\
%       t   & 10 & 4 \\
%       b   & 10 & 5
%    \end{tabular}
% \end{center}
% \caption{Classes of preamble \textsf{tokens}}
% \label{tab:Klassen}
% \end{table}
%
%
% \begin{macro}{\@chclass}
% \begin{macro}{\@chnum}
% \begin{macro}{\@lastchclass}
%    The class and the number of the current \textsf{token} are saved in
%    the
%    \textsf{count} registers =\@chclass=
%    and =\@chnum=, while the class of the previous
%    \textsf{token} is stored in the
%    \textsf{count} register =\@lastchclass=.
%    All of the mentioned registers are already allocated in
%    \texttt{latex.tex},
%    which is the reason why the following three lines of code are
%    commented out.
%    Later throughout the text I will not mention it again explicitly
%    whenever I use a =%= sign. These parts are already defined in
%    \texttt{latex.tex}.
%    \begin{macrocode}
% \newcount \@chclass
% \newcount \@chnum
% \newcount \@lastchclass
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
%
%
% \begin{macro}{\@addtopreamble}
%    We will save the already constructed preamble for
%    the =\halign=
%    in the global macro =\@preamble=. This will then be
%     enlarged with
%    the command =\@addtopreamble=.
%    \begin{macrocode}
\def\@addtopreamble#1{\xdef\@preamble{\@preamble #1}}
%    \end{macrocode}
% \end{macro}
%
%
%
%
%
% \subsection{The character class of a \textsf{token}}
%
% \begin{macro}{\@testpach}
% \changes{v2.0a}{1989/05/12}{p option renamed to m (middle).}
% \changes{v2.0a}{1989/05/12}{t option renamed to p to be compatible to
%                         the original.}
%    With the help of =\@lastchclass= we can now define a macro
%    which determines the class and the number of a given preamble
%    \textsf{token}
%    and assigns them to the registers
%    =\@chclass= and =\@chnum=.
% \changes{v2.0f}{1992/02/29}{Argument removed since implicitly known}
%    \begin{macrocode}
\def\@testpach{\@chclass
%    \end{macrocode}
%    First we deal with the cases in which the \textsf{token}
%    (=#1=) is the argument of \texttt{!}, \texttt{@}, \texttt{<} or
%    \texttt{>}. We can see this from the value of =\@lastchclass=:
%    \begin{macrocode}
 \ifnum \@lastchclass=6 \@ne \@chnum \@ne \else
  \ifnum \@lastchclass=7 5 \else
   \ifnum \@lastchclass=8 \tw@ \else
    \ifnum \@lastchclass=9 \thr@@
%    \end{macrocode}
%    Otherwise we will assume that the \textsf{token} belongs to the
%    class $0$
%    and assign the corresponding number to =\@chnum= if our
%    assumption is correct.
%    \begin{macrocode}
   \else \z@
%    \end{macrocode}
%    If the last \textsf{token} was a \texttt{p}, \texttt{m} or a
%    \texttt{b}, =\@chnum= already has the right value. This is the
%    reason for the somewhat curious choice of the \textsf{token}
%    numbers in class $10$.
%    \begin{macrocode}
   \ifnum \@lastchclass = 10 \else
%    \end{macrocode}
%    Otherwise we will check if =\@nextchar= is either a \texttt{c},
%    \texttt{l} or an \texttt{r}.  Some applications change the
%    catcodes of certain characters like ``\texttt{@}'' in
%    \texttt{amstex.sty}. As a result the tests below would fail since
%    they assume non-active character tokens. Therefore we evaluate
%    =\@nextchar= once thereby turning the first token of its
%    replacement text into a char. At this point here this should have
%    been the only char present in =\@nextchar= which put into via a
%    =\def=.
% \changes{v2.0f}{1992/02/29}{Ensure to test a char which is not active}
%    \begin{macrocode}
   \edef\@nextchar{\expandafter\string\@nextchar}%
   \@chnum
   \if \@nextchar c\z@ \else
    \if \@nextchar l\@ne \else
     \if \@nextchar r\tw@ \else
%    \end{macrocode}
%    If it is a different \textsf{token}, we know that the class was
%    not $0$. We assign the value $0$ to =\@chnum= because this value
%    is needed for the \texttt{|}--\textsf{token}. Now we must check
%    the remaining classes.  Note that the value of =\@chnum= is
%    insignificant here for most classes.
%    \begin{macrocode}
   \z@ \@chclass
   \if\@nextchar |\@ne \else
    \if \@nextchar !6 \else
     \if \@nextchar @7 \else
      \if \@nextchar <8 \else
       \if \@nextchar >9 \else
%    \end{macrocode}
%    The remaining permitted \textsf{tokens} are \texttt{p},
%    \texttt{m} and \texttt{b} (class $10$).
%    \begin{macrocode}
  10
  \@chnum
  \if \@nextchar m\thr@@\else
   \if \@nextchar p4 \else
    \if \@nextchar b5 \else
%    \end{macrocode}
%    Now the only remaining possibility is a forbidden \textsf{token},
%    so we choose class $0$ and number $0$ and give an error message.
%    Then we finish the macro by closing all =\if='s.
%    \begin{macrocode}
   \z@ \@chclass \z@ \@preamerr \z@ \fi \fi \fi \fi
   \fi \fi  \fi  \fi  \fi  \fi  \fi \fi \fi \fi \fi \fi}
%    \end{macrocode}
% \end{macro}
%
%
%
%
%
% \subsection{Multiple columns ($*$--form)}
%
% \begin{macro}{\@xexpast}
% \begin{macro}{\the@toks}
% \begin{macro}{\the@toksz}
%    \label{@xexpast} Now we discuss the macro that deletes all forms
%    of type =*{=\textit{N\/}=}{=\textit{String\/}=}= from a user
%    preamble and replaces them with \textit{N} copies of
%    \textit{String}.  Nested $*$--expressions are dealt with
%    correctly, that means $*$--expressions are not substituted if
%    they are in explicit braces, as in =@{*}=.
%
%    This macro is called via
%    =\@xexpast=\meta{preamble}=*0x\@@=.
%    The $*$--expression =*0x= is being used to terminate the
%    recursion,
%    as we shall see later, and =\@@= serves as an argument
%    delimiter. =\@xexpast= has four arguments. The first
%    one is the part of the
%    user preamble before the first $*$--expression while the second
%    and third ones are the arguments of the first $*$--expression
%    (that is \textit{N} and \textit{String} in the notation mentioned
%    above).
%    The fourth argument is the rest of the preamble.
%    \begin{macrocode}
\def\@xexpast#1*#2#3#4\@@{%
%    \end{macrocode}
%    The number of copies of \textit{String} (=#2=) that are to be
%    produced will be saved in a \textsf{count} register.
%    \begin{macrocode}
   \@tempcnta #2
%    \end{macrocode}
%    We save the part of the preamble which does not
%    contain a $*$--form (=#1=)
%    in a \PlainTeX\ \textsf{token} register.
%    We also save \textit{String} (=#3=) using a \LaTeX\
%    \textsf{token} register.
%    \begin{macrocode}
   \toks@={#1}\@temptokena={#3}%
%    \end{macrocode}
%    Now we have to use a little trick to produce \textit{N} copies of
%    \textit{String}.
%    We could try =\def\@tempa{#1}= and then
%    \textit{N} times =\edef\@tempa{\@tempa#3}=. This would have the
%    undesired effect that all macros within =#1= and =#3=
%    would be expanded, although, for example, constructions like
%    =@{..}= are not supposed to be changed.
%    That is why we =\let= two control sequences to
%    be equivalent to =\relax=.
%    \begin{macrocode}
   \let\the@toksz\relax \let\the@toks\relax
%    \end{macrocode}
%    Then we ensure that =\@tempa= contains
%    ={\the@toksz\the@toks...\the@toks}= (the macro
%    =\the@toks= exactly \textit{N\/} times) as substitution text.
%    \begin{macrocode}
   \def\@tempa{\the@toksz}%
   \ifnum\@tempcnta >0 \@whilenum\@tempcnta >0\do
     {\edef\@tempa{\@tempa\the@toks}\advance \@tempcnta \m@ne}%
%    \end{macrocode}
%    If \textit{N\/} was greater than zero we prepare for another call
%    of =\@xexpast=. Otherwise we assume we have reached the end of
%    the user preamble, because we had appended =*0x\@@= when we first
%    called =\@xexpast=.  In other words: if the user inserts
%    =*{0}{..}= in his preamble, \LaTeX\ ignores the rest of it.
%    \begin{macrocode}
       \let \@tempb \@xexpast \else
       \let \@tempb \@xexnoop \fi
%    \end{macrocode}
%    Now we will make sure that the part of the user preamble, which
%    was already dealt with, will be saved again in =\@tempa=.
%    \begin{macrocode}
   \def\the@toksz{\the\toks@}\def\the@toks{\the\@temptokena}%
   \edef\@tempa{\@tempa}%
%    \end{macrocode}
%    We have now evaluated the first $*$--expression, and the user
%    preamble up to this point
%    is saved in =\@tempa=. We will put the contents of
%    =\@tempa= and the rest of the user preamble together and work
%    on the result with =\@tempb=. This macro either corresponds
%    to =\@xexpast=, so that the next
%    $*$--expression is handled, or to the macro =\@xexnoop=,
%    which only ends the recursion by deleting its argument.
%    \begin{macrocode}
   \expandafter \@tempb \@tempa #4\@@}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@xexnoop}
%    So the first big problem is solved. Now it is easy to
%    specify =\@xexnoop=.
%    Its argument is delimited by =\@@= and it simply expands to
%    nothing.
%    \begin{macrocode}
%  \def\@xexnoop#1\@@{}
%    \end{macrocode}
% \end{macro}
%
%
%
%
% \section{The insertion of declarations
%           (\texttt{>}, \texttt{<}, \texttt{!}, \texttt{@})}
%
%
% The preamble will be enlarged with the help of =\xdef=, but the
% arguments of \texttt{>}, \texttt{<},~\texttt{!}\ and \texttt{@} are
% not supposed to be expanded during the construction (we want an
% implementation that doesn't need a =\protect=). So we have to find a
% way to inhibit the expansion of those arguments.
%
% We will solve this problem with \textsf{token} registers. We need
% one register for every \texttt{!}\ and \texttt{@}, while we need two
% for every \texttt{c}, \texttt{l}, \texttt{r}, \texttt{m}, \texttt{p}
% or \texttt{b}. This limits the number of columns of a table because
% there are only 256 \textsf{token} registers. But then, who needs
% tables with more than 100 columns?
%
% One could also find a solution which only needs two or three
% \textsf{token} registers by proceeding similarly as in the macro
% =\@xexpast= (see page \pageref{@xexpast}). The advantage of our
% approach is the fact that we avoid some of the problems that arise
% with the other method\footnote{Maybe there are also historical
%  reasons.}.
%
% So how do we proceed? Let us assume that we had =!{foo}= in the
% user preamble and say we saved \texttt{foo} in
% \textsf{token} register $5$. Then we call
% =\@addtopreamble{\the@toks5}= where
% =\the@toks= is defined in a way that it does not expand
% (for example it could be equivalent to =\relax=). Every
% following call
% of =\@addtopreamble= leaves =\the@toks5= unchanged in
% =\@preamble=. If the construction of the preamble is completed
% we change the definition of =\the@toks= to
% =\the\toks= and expand =\@preamble= for the last time.
% During this process all parts of the form
%    =\the@toks=\meta{Number}
% will be substituted by the contents of the respective \textsf{token}
% registers.
%
% As we can see from this informal discussion the construction of the
% preamble has to take place within a group, so that the
% \textsf{token} registers we use will be freed later on. For that
% reason we keep all assignments to =\@preamble= global; therefore the
% replacement text of this macro will remain the same after we leave
% the group.
%
% \begin{macro}{\count@}
%    We further need a \textsf{count} register to remember which
%    \textsf{token} register is to be used next. This will be
%    initialized with $-1$ if we want to begin with the \textsf{token}
%    register $0$. We use the \PlainTeX\ scratch register =\count@=
%    because everything takes place locally. All we have to do is
%    insert =\the@toks= =\the= =\count@= into the preamble.
%    =\the@toks= will remain unchanged and =\the\count@= expands into
%    the saved number.
% \end{macro}
%
% \begin{macro}{\prepnext@tok}
%    The macro =\prepnext@tok= is in charge of preparing the next
%    \textsf{token} register. For that purpose we increase
%    =\count@= by $1$:
%    \begin{macrocode}
\def\prepnext@tok{\advance \count@ \@ne
%    \end{macrocode}
%    Then we locally delete any contents the
%    \textsf{token} register might have.
%    \begin{macrocode}
   \toks\count@{}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\save@decl}
%    During the construction of the preamble the current
%    \textsf{token} is always saved in the macro =\@nextchar= (see the
%    definition of =\@mkpream= on page \pageref{@mkpream}). The macro
%    =\save@decl= saves it into the next free \textsf{token} register,
%    i.e.\ in =\toks\count@=.
% \changes{v2.0c}{1990/08/14}{\cs{relax} removed and added elsewhere.}
%    \begin{macrocode}
\def\save@decl{\toks\count@ \expandafter{\@nextchar}}
%    \end{macrocode}
%    The reason for the  use of =\relax= is the following
%    hypothetical situation in the preamble:
%    \quad =..\the\toks1\the\toks2..= \quad \TeX\ expands
%    =\the\toks2= first in order to find out if the digit =1=
%    is followed by other digits. E.g.\ a =5= saved in the
%    \textsf{token} register $2$ would lead \TeX\ to insert the contents
%    of \textsf{token} register $15$ instead of $1$ later on.
%
% The example above referred to an older version of =\save@decl= which
% inserted a =\relex= inside the token register. This is now moved to
% the places where the actual token registers are inserted (look for
% =\the@toks=) because the old version would still make =@=
% expressions to moving arguments since after expanding the second
% register while looking for the end of the number the contents of the
% token register is added so that later on the whole register will be
% expanded.  This serious bug was found after nearly two years
% international use of this package  by Johannes Braams.
% \end{macro}
%
%
%
% How does the situation look like, if we want to add another column
% to the preamble, i.e.\ if we have found a \texttt{c}, \texttt{l},
% \texttt{r}, \texttt{p}, \texttt{m} or \texttt{b} in the user
% preamble?  In this case we have the problem of the \textsf{token}
% register from =>{..}= and =<{..}= having to be inserted at this
% moment because formatting instructions like =\hfil= have to be set
% around them. On the other hand it is not known yet, if any =<{..}=
% instruction will appear in the user preamble at all.
%
% We solve this problem by adding two \textsf{token} registers at a
% time.  This explains, why we have freed the \textsf{token} registers
% in =\prepnext@tok=.
%
% \begin{macro}{\insert@column}
% \begin{macro}{\@sharp}
%    We now define the macro =\insert@column= which will do
%    this work for us.
%    \begin{macrocode}
\def\insert@column{%
%    \end{macrocode}
%    Here, we assume that the \textsf{count} register
%    =\@tempcnta= has saved the value $=\count@= - 1$.
%    \begin{macrocode}
   \the@toks \the \@tempcnta
%    \end{macrocode}
%    Next follows the =#= sign which specifies the place
%    where the text of the column shall be inserted. To avoid
%    errors during the expansions in
%    =\@addtopreamble= we hide this sign in the command
%    =\@sharp= which is temporarily occupied with
%    =\relax= during the build-up of the preamble.
%    To remove unwanted spaces before and after the column text, we set
%    an =\ignorespaces=  in front and a =\unskip= afterwards.
% \changes{v2.0e}{1991/02/07}{Added \{\} around \cs{@sharp} for new ftsel}
% \changes{v2.0h}{1992/06/22}{Removed \{\} again in favour of
%                             \cs{d@llarbegin}}
%    \begin{macrocode}
   \ignorespaces \@sharp \unskip
%    \end{macrocode}
%    Then the second \textsf{token} register follows whose number should
%    be saved in =\count@=.
%    We make sure that there will be no further expansion after reading
%    the number, by finishing with =\relax=. The case above is not
%    critical since it is ended by =\ignorespaces=.
% \changes{v2.0c}{1990/08/14}{\cs{relax} added to avoid problem
%                           \cs{the}\cs{toks0}\cs{the}\cs{toks1}.}
%    \begin{macrocode}
   \the@toks \the \count@ \relax}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%
%
%
% \subsection{The separation of columns}
%
% \begin{macro}{\@addamp}
%    In the preamble a =&= has to be inserted between any two columns;
%    before the first column there should not be a =&=. As the user
%    preamble may start with a \texttt{|} we have to remember somehow
%    if we have already inserted a =#= (i.e.\ a column). This is done
%    with the boolean variable =\if@firstamp= that we test in
%    =\@addamp=, the macro that inserts the =&=.
%    \begin{macrocode}
%    \newif \@iffirstamp
%    \def\@addamp{\if@firstamp \@firstampfalse
%                 \else \@addtopreamble &\fi}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@acol}
% \begin{macro}{\@acolampacol}
% \begin{macro}{\col@sep}
%    We will now define some abbreviations for the extensions,
%    appearing most often in the preamble build-up.
%    Here =\col@sep= is a \textsf{dimen} register which is set
%    equivalent to =\arraycolsep= in an \textsf{array}--environment,
%    otherwise it is set equivalent to =\tabcolsep=.
%    \begin{macrocode}
\newdimen\col@sep
\def\@acol{\@addtopreamble{\hskip\col@sep}}
%    \def\@acolampacol{\@acol\@addamp\@acol}
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
%
% \subsection{The macro \texttt{\textbackslash @mkpream}}
%
% \begin{macro}{\@mkpream}
%    \emph{The code below has been replaced long time ago by an
%    extended version further down but the code and its documentation
%    was left here for reference. It is now commented out to avoid
%    confusion.}
% \begin{macro}{\the@toks}
%    \label{@mkpream}
%    Now we can define the macro which builds up the preamble for the
%    =\halign=.
%    First we initialize =\@preamble=, =\@lastchclass=
%    and the boolean variable =\if@firstamp=.
%    \begin{macrocode}
%\def\@mkpream#1{\gdef\@preamble{}\@lastchclass 4 \@firstamptrue
%    \end{macrocode}
%    During the build-up of the preamble we cannot directly use the
%    =#= sign; this would lead to an error message in the next
%    =\@addtopreamble= call.
%    Instead, we use the command =\@sharp= at places where later
%    a =#= will be.
%    This command is at first given the meaning =\relax=;
%    therefore it will not be expanded when the preamble
%    is extended.
%    In the macro =\@array=, shortly before the =\halign=
%    is carried out, =\@sharp= is given its final meaning.
%
%    In a similar way,
%    we deal with the commands =\@startpbox= and
%    =\@endpbox=, although the reason is different here: these
%    macros expand in many \textsf{tokens} which would delay the
%    build-up of the preamble.
%    \begin{macrocode}
%   \let\@sharp\relax\let\@startpbox\relax\let\@endpbox\relax
%    \end{macrocode}
%    Two more are needed to deal with the code that handles struts
%    for extra space after a row from =\\[<space>]=
%    (=\do@row@strut=) and code that manages m-cells depending on
%   their heights (=\ar@align@mcell=).
% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
%    \begin{macrocode}
%   \let\do@row@strut\relax
%   \let\ar@align@mcell\relax
%    \end{macrocode}
%    Now we remove possible  $*$-forms in the user preamble with the
%    command =\@xexpast=.  As we already know, this command saves
%    its result in the macro =\@tempa=.
%    \begin{macrocode}
%   \@xexpast #1*0x\@@
%    \end{macrocode}
%    Afterwards we initialize all registers and macros, that we need
%    for the build-up of the preamble.
%    Since we want to start with the \textsf{token} register $0$,
%    =\count@= has to contain the value $-1$.
%    \begin{macrocode}
%   \count@\m@ne
%   \let\the@toks\relax
%    \end{macrocode}
%    Then we call up =\prepnext@tok= in order to prepare the
%    \textsf{token} register $0$ for use.
%    \begin{macrocode}
%   \prepnext@tok
%    \end{macrocode}
%    To evaluate the user preamble (without stars) saved in
%    =\@tempa= we use the \LaTeX--macro =\@tfor=.
%    The strange appearing construction with =\expandafter= is
%    based on the fact that we have to put the replacement text of
%    =\@tempa= and not the macro =\@tempa= to this
%    \LaTeX--macro.
%    \begin{macrocode}
%   \expandafter \@tfor \expandafter \@nextchar
%    \expandafter :\expandafter =\@tempa \do
%    \end{macrocode}
%    The body of this loop (the group after the =\do=)
%    is executed for one \textsf{token} at a time, whereas
%    the current \textsf{token} is saved in =\@nextchar=.
%    At first we evaluate the current \textsf{token} with the already
%    defined macro =\@testpach=, i.e.\ we assign to
%    =\@chclass= the character class and to =\@chnum=
%    the character number of this \textsf{token}.
% \changes{v2.0f}{1992/02/29}{\cs{@testpach} now without arg}
%    \begin{macrocode}
%   {\@testpach
%    \end{macrocode}
%    Then we branch out depending on the value of =\@chclass= into
%    different macros that extend the preamble respectively.
%    \begin{macrocode}
%   \ifcase \@chclass \@classz \or \@classi \or \@classii
%     \or \save@decl \or \or \@classv \or \@classvi
%     \or \@classvii \or \@classviii  \or \@classix
%     \or \@classx \fi
%    \end{macrocode}
%    Two cases deserve our special attention: Since the current
%    \textsf{token} cannot have the character class $4$ (start) we
%    have skipped this possibility. If the character class is $3$,
%    only the content of =\@nextchar= has to be saved into the current
%    \textsf{token} register; therefore we call up =\save@decl=
%    directly and save a macro name.  After the preamble has been
%    extended we assign the value of =\@chclass= to the counter
%    =\@lastchclass= to assure that this information will be available
%    during the next run of the loop.
%    \begin{macrocode}
%   \@lastchclass\@chclass}%
%    \end{macrocode}
%    After the loop has been finished space must still be added to
%    the created preamble, depending on the last \textsf{token}.
%    Depending on the value of =\@lastchclass= we perform
%    the necessary operations.
%    \begin{macrocode}
%   \ifcase\@lastchclass
%    \end{macrocode}
%    If the last class equals $0$ we add a
%    =\hskip \col@sep=.
%    \begin{macrocode}
%   \@acol \or
%    \end{macrocode}
%    If it equals $1$ we do not add any additional space so that the
%    horizontal lines do not exceed the vertical ones.
%    \begin{macrocode}
%   \or
%    \end{macrocode}
%    Class $2$ is treated like class $0$ because a =<{...}=  can
%    only directly follow after class $0$.
%    \begin{macrocode}
%   \@acol \or
%    \end{macrocode}
%    Most of the other possibilities can only appear if the user
%    preamble was defective. Class $3$ is not allowed since after a
%    =>{..}= there must always follow a \texttt{c}, \texttt{l},
%    \texttt{r}, \texttt{p},\texttt{m} or \texttt{b}. We report an
%    error and ignore the declaration given by ={..}=.
%    \begin{macrocode}
%   \@preamerr \thr@@ \or
%    \end{macrocode}
%    If =\@lastchclass= is $4$ the user preamble has been empty.
%    To continue, we insert a =#= in the preamble.
%    \begin{macrocode}
%   \@preamerr \tw@ \@addtopreamble\@sharp \or
%    \end{macrocode}
%    Class $5$ is allowed again. In this case
%    (the user preamble ends with =@{..}=) we need not
%    do anything.
%    \begin{macrocode}
%   \or
%    \end{macrocode}
%    Any other case means that the arguments to =@=, \texttt{!},
%    \texttt{<}, \texttt{>}, \texttt{p}, \texttt{m} or \texttt{b} have
%    been forgotten. So we report an error and ignore the last
%    \textsf{token}.
%    \begin{macrocode}
%   \else  \@preamerr \@ne \fi
%    \end{macrocode}
%    Now that the build-up of the preamble is almost finished we can
%    insert the \textsf{token} registers and therefore redefine
%    =\the@toks=. The actual insertion, though, is performed
%    later.
%    \begin{macrocode}
%   \def\the@toks{\the\toks}}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%
%
%  \section{The macros \texttt{\textbackslash @classz}
%           to \texttt{\textbackslash @classx}}
%
% The preamble is extended by the macros =\@classz= to
% =\@classx= which are called by =\@mkpream=
%  depending on =\@lastchclass=
% (i.e. the character class of the last \textsf{token}).
% \begin{macro}{\@classx}
%    First we define =\@classx= because of its important r\^ole.
%    When it is called we find that the current
%    \textsf{token} is \texttt{p}, \texttt{m} or \texttt{b}.
%    That means that a new column has to start.
%    \begin{macrocode}
\def\@classx{%
%    \end{macrocode}
%    Depending on the value of =\@lastchclass= different actions
%    must take place:
%    \begin{macrocode}
  \ifcase \@lastchclass
%    \end{macrocode}
%    If the last character class was $0$ we separate the columns by
%    =\hskip\col@sep= followed by =&= and another
%    =\hskip\col@sep=.
%    \begin{macrocode}
  \@acolampacol \or
%    \end{macrocode}
%    If the last class was class $1$ --- that means that a vertical
%    line was
%    drawn, --- before this line a =\hskip\col@sep= was inserted.
%    Therefore there has to be only a =&= followed by
%    =\hskip\col@sep=. But this =&= may be inserted only
%    if this is not the first column. This process is controlled
%    by =\if@firstamp= in the macro =\addamp=.
%    \begin{macrocode}
  \@addamp \@acol \or
%    \end{macrocode}
%    Class $2$ is treated like class $0$ because =<{...}= can only
%    follow after class $0$.
%    \begin{macrocode}
  \@acolampacol \or
%    \end{macrocode}
%    Class $3$ requires no actions because all things necessary have
%    been done by the preamble \textsf{token} \texttt{>}.
%    \begin{macrocode}
  \or
%    \end{macrocode}
%    Class $4$ means that we are at the beginning of the preamble.
%    Therefore we start the preamble with =\hskip\col@sep= and
%    then call =\@firstampfalse=. This makes sure that a later
%    =\@addamp= inserts the character
%    =&= into the preamble.
%    \begin{macrocode}
  \@acol \@firstampfalse \or
%    \end{macrocode}
%    For class $5$ \textsf{tokens} only the character =&= is inserted
%    as a column separator. Therefore we call =\@addamp=.
%    \begin{macrocode}
  \@addamp
%    \end{macrocode}
%    Other cases are impossible. For an example
%    $=\@lastchclass= \string= 6$---as it might appear in a
%    preamble of the form =...!p...=---\texttt{p} would have
%    been taken as an  argument of \texttt{!}\ by =\@testpach=.
%    \begin{macrocode}
  \fi}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\@classz}
%    If the character class of the last \textsf{token} is $0$ we have
%    \texttt{c}, \texttt{l}, \texttt{r} or an argument of \texttt{m},
%    \texttt{b} or\ \texttt{p}. In the first three cases the preamble
%    must be extended the same way as if we had class $10$. The
%    remaining two cases do not require any action because the space
%    needed was generated by the last \textsf{token} (i.e.\
%    \texttt{m}, \texttt{b} or \texttt{p}). Since =\@lastchclass= has
%    the value $10$ at this point nothing happens when =\@classx= is
%    called. So the macro =\@chlassz= may start like this:
%    \begin{macrocode}
\def\@classz{\@classx
%    \end{macrocode}
%    According to the definition of =\insert@column= we must store
%    the number of the \textsf{token} register in which a preceding
%    =>{..}= might have stored its argument into
%    =\@tempcnta=.
%    \begin{macrocode}
   \@tempcnta \count@
%    \end{macrocode}
%    To have $=\count@= \string= =\@tmpcnta= + 1$ we prepare
%    the next \textsf{token} register.
%    \begin{macrocode}
   \prepnext@tok
%    \end{macrocode}
%    Now the preamble must be extended with the column whose format
%    can be determined by =\@chnum=.
%    \begin{macrocode}
   \@addtopreamble{\ifcase \@chnum
%    \end{macrocode}
%    If =\@chnum= has the value $0$ a centered column has to be
%    generated.
%    So we begin with stretchable space.
%    \begin{macrocode}
      \hfil
%    \end{macrocode}
%    We also add a space of 1sp just in case the first thing in the
%    cell is a command doing an =\unskip=.
% \changes{v2.4k}{2018/12/30}{Add extra \cs{hskip} to guard against an
%   \cs{unskip} at the start of a c-column cell (gh/102)}
%    \begin{macrocode}
      \hskip1sp%
%    \end{macrocode}
%    The command =\d@llarbegin= follows expanding into =\begingroup=
%    (in the \textsf{tabular}--environment) or into =$=.  Doing this
%    (provided an appropriate setting of =\d@llarbegin=) we achieve
%    that the contents of the columns of an \textsf{array}--environment
%    are set in math mode while those of a \textsf{tabular}--environment
%    are set in LR mode.
%    \begin{macrocode}
      \d@llarbegin
%    \end{macrocode}
%    Now we insert the contents of the two \textsf{token} registers
%    and the symbol
%    for the column entry (i.e.\ =#= or
%    more precise =\@sharp=) using =\insert@column=.
%    \begin{macrocode}
      \insert@column
%    \end{macrocode}
%    We end this case with =\d@llarend= and =\hfil= where =\d@llarend=
%    again is either =$= or =\endgroup=.
%    The strut to enforce a regular row height is placed between the two.
% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
%    \begin{macrocode}
      \d@llarend \do@row@strut \hfil \or
%    \end{macrocode}
%    The templates for \texttt{l} and \texttt{r} (i.e.\ =\@chnum= $1$
%    or $2$) are generated the same way. Since one  =\hfil= is
%    missing the text is moved to the relevant side.
%    The =\kern\z@= is needed in case of an empty column
%    entry. Otherwise
%    the =\unskip= in =\insert@column= removes the
%    =\hfil=. Changed to =\hskip1sp= so that it interacts better with
%    =\@bsphack=.
% \changes{v2.3f}{1996/04/22}
%     {(DPC) Extra \cs{kern} keeps tabcolsep in empty l columns
%             internal/2122}
% \changes{v2.3i}{1996/06/14}
%     {Change both \cs{kern}\cs{z@} to \cs{hskip}1sp for latex/2160}
% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
%    \begin{macrocode}
      \hskip1sp\d@llarbegin \insert@column \d@llarend \do@row@strut \hfil \or
      \hfil\hskip1sp\d@llarbegin \insert@column \d@llarend \do@row@strut \or
%    \end{macrocode}
%    The templates for \texttt{p}, \texttt{m} and \texttt{b} mainly
%    consist of a \textsf{box}. In case of \texttt{m} it is generated
%    by =\vcenter=.  This command is allowed only in math
%    mode. Therefore we start with a~=$=.
% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
%    \begin{macrocode}
    \setbox\ar@mcellbox\vbox
%    \end{macrocode}
%    The part of the templates which is the same in all three cases
%    (\texttt{p}, \texttt{m} and \texttt{b})
%    is built by the macros =\@startpbox= and
%    =\@endpbox=. =\@startpbox= has an argument:
%    the width of the column which is stored in the current
%    \textsf{token} (i.e.\ =\@nextchar=).
%    Between these two macros we find the well known
%    =\insert@column=.
%    The strut is places after the box
% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
%    \begin{macrocode}
    \@startpbox{\@nextchar}\insert@column \@endpbox
    \ar@align@mcell
    \do@row@strut \or
%    \end{macrocode}
%    The templates for \texttt{p} and \texttt{b} are generated in the
%    same way though we do not need the =$= characters because we use
%    =\vtop= or =\vbox=.
% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
%    \begin{macrocode}
   \vtop \@startpbox{\@nextchar}\insert@column \@endpbox\do@row@strut \or
   \vbox \@startpbox{\@nextchar}\insert@column \@endpbox\do@row@strut
%    \end{macrocode}
%    Other values for =\@chnum= are impossible. Therefore we
%    end the arguments to =\@addtopreamble= and =\ifcase=.
%    Before we come to the end of =\@classz= we have to
%    prepare the next \textsf{token} register.
%    \begin{macrocode}
  \fi}\prepnext@tok}
%    \end{macrocode}
% \end{macro}
%

%
% \begin{macro}{\ar@mcellbox}
%    When dealing with m-cells we need a box to measure the cell
%    height.
% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
%    \begin{macrocode}
\newbox\ar@mcellbox
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\ar@align@mcell}
%    M-cells are supposed to be vertically centered within the table
%    row. In the original implementation that was done using
%    =\vcenter= but the issue with that approach is that it centers
%    the material based on the math-axis. In most situations that
%    comes out quit right, but if, for example, an m-cell has only a
%    single line worth of material inside it will be positioned
%    differently to a =l=, =c= or =r= cell or to a =p= or =b= cell
%    with  the same content.
%
%    For that reason the new implementation does the centering
%    manually: First we check the height of the cell and if that is
%    less or equal to =\ht\@arstrutbox= we assume that this is a
%    single line cell. In that case  we don't do any vertical maneuvre
%    and simply output the box, i.e., make it behave like a single
%    line p-cell.
% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
%    \begin{macrocode}
\def\ar@align@mcell{%
  \ifdim \ht\ar@mcellbox > \ht\@arstrutbox
%    \end{macrocode}
%    Otherwise we realign vertically by lowering the box. The question
%    is how much do we need to move down? If there is any
%    =\arraystretch= in place then the first line will have some
%    unusual height and we don't want to consider that when finding
%    the middle point. So we substract from the cell height the height
%    of that strut. But of course we want to include the normal height
%    of the first line (which would be something like =\ht\strutbox=)
%    so we need to add that. On the other hand, when centering around
%    the mid-point of the cell, we also need to account for the depth
%    of the last line (which is nominally something like
%    =\dp\strutbox=). Both together equals =\baselineskip= so that is
%    what we add and then lower the cell by half of the resulting value.
%    \begin{macrocode}
    \begingroup
     \dimen@\ht\ar@mcellbox
     \advance\dimen@-\ht\@arstrutbox
     \advance\dimen@\baselineskip
     \lower.5\dimen@\box\ar@mcellbox
    \endgroup
  \else % assume one line and align at baseline
    \box\ar@mcellbox
  \fi}
%    \end{macrocode}
% \end{macro}
%

%
% \begin{macro}{\@classix}
%    \emph{The code below has been replaced long time ago by an
%    extended version further down but the code and its documentation
%    was left here for reference. It is now commented out to avoid
%    confusion.}
%
%    In case of class $9$ (\texttt{>}--\textsf{token}) we first check
%    if the character class of the last
%    \textsf{token} was $3$. In this case we have a
%    user preamble of the form =..>{...}>{...}..= which
%    is not allowed. We only give an error message and continue.
%    So the declarations defined by the first  =>{...}=
%    are ignored.
%    \begin{macrocode}
%\def\@classix{\ifnum \@lastchclass = \thr@@
%       \@preamerr \thr@@ \fi
%    \end{macrocode}
%    Furthermore, we call up =\@class10= because afterwards always a
%    new column is started by \texttt{c}, \texttt{l}, \texttt{r},
%    \texttt{p}, \texttt{m} or \texttt{b}.
%    \begin{macrocode}
%       \@classx}
%    \end{macrocode}
% \end{macro}
%
%
%
% \begin{macro}{\@classviii}
%    \emph{The code below has been replaced long time ago by an
%    extended version further down but the code and its documentation
%    was left here for reference. It is now commented out to avoid
%    confusion.}
%
%    If the current \textsf{token} is a \texttt{<} the last character
%    class must be $0$. In this case it is not necessary to extend the
%    preamble. Otherwise we output an error message, set =\@chclass=
%    to $6$ and call =\@classvi=.  By doing this we achieve that
%    \texttt{<} is treated like \texttt{!}.
%    \begin{macrocode}
%\def\@classviii{\ifnum \@lastchclass >\z@
%      \@preamerr 4\@chclass 6 \@classvi \fi}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@arrayrule}
%    There is only one incompatibility with the original definition:
%    the definition of =\@arrayrule=. In the original a line without
%    width\footnote{So the space between \texttt{cc} and \texttt{c|c}
%    is equal.}  is created by multiple insertions of
% =\hskip .5\arrayrulewidth=.
%    We only insert a vertical line into the
%    preamble.  This is done to prevent problems with \TeX's main
%    memory when generating tables with many vertical lines in them
%    (especially in the case of \textsf{floats}).
%    \begin{macrocode}
\def\@arrayrule{\@addtopreamble \vline}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@classvii}
%    As a consequence it follows that in case of class $7$
%    (=@= \textsf{token})  the preamble need not to be extended.
%    In the original definition $=\@lastchclass= \string= 1$
%    is treated by inserting =\hskip .5\arrayrulewidth=.
%    We only check if the last \textsf{token} was of class $3$ which is
%    forbidden.
%    \begin{macrocode}
\def\@classvii{\ifnum \@lastchclass = \thr@@
%    \end{macrocode}
%    If this is true we output an error message and
%    ignore the declarations stored
%    by the last  =>{...}=, because these are overwritten
%    by the argument of \texttt{@}.
%    \begin{macrocode}
   \@preamerr \thr@@ \fi}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\@classvi}
%    If the current \textsf{token} is a regular \texttt{!}\ and the
%    last class was $0$ or $2$ we extend the preamble with
%    =\hskip\col@sep=.  If the last \textsf{token} was of class $1$
%    (for instance \texttt{|}) we extend with =\hskip \doublerulesep=
%    because the construction =!{...}= has to be treated like
%    \texttt{|}.
%    \begin{macrocode}
\def\@classvi{\ifcase \@lastchclass
      \@acol \or
      \@addtopreamble{\hskip \doublerulesep}\or
      \@acol \or
%    \end{macrocode}
%    Now =\@preamerr...= should follow because a
%    user preamble of the form =..>{..}!.= is not allowed.
%    To save memory we call =\@classvii= instead which also
%    does what we want.
%    \begin{macrocode}
      \@classvii
%    \end{macrocode}
%    If =\@lastchclass= is $4$ or $5$ nothing has to be done.
%    Class $6$ to $10$ are not possible.
%    So we finish the macro.
%    \begin{macrocode}
      \fi}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@classii}
% \begin{macro}{\@classiii}
%    In the case of character classes $2$ and $3$ (i.e.\ the argument
%    of \texttt{<} or \texttt{>}) we only have to store the current
%    \textsf{token} (=\@nextchar=) into the corresponding
%    \textsf{token} register since the preparation and
%    insertion of these registers
%    are done by the macro =\@classz=.
%    This is equivalent to calling =\save@decl= in the case of
%    class $3$. To save command identifiers we do this call up
%     in the macro =\@mkpream=.
%
%    Class $2$ exhibits a more complicated situation: the
%    \textsf{token} registers have already been inserted by
%    =\@classz=. So the value of =\count@= is too high
%    by one. Therefore we decrease =\count@= by $1$.
%    \begin{macrocode}
\def\@classii{\advance \count@ \m@ne
%    \end{macrocode}
%    Next we store the current \textsf{token} into the correct
%    \textsf{token} register by calling =\save@decl= and then
%    increase the value of =\count@= again. At this point we
%    can save memory once more (at the cost of time) if we use the
%     macro =\prepnext@tok=.
%    \begin{macrocode}
   \save@decl\prepnext@tok}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%
% \begin{macro}{\@classv}
%    \emph{The code below has been replaced long time ago by an
%    extended version further down but the code and its documentation
%    was left here for reference. It is now commented out to avoid
%    confusion.}
%
%    If the current \textsf{token} is of class $5$ then it is an
%    argument of a \texttt{@} \textsf{token}. It must be stored into a
%    \textsf{token} register.
%    \begin{macrocode}
%\def\@classv{\save@decl
%    \end{macrocode}
%    We extend the preamble with a command which inserts this
%    \textsf{token} register into the preamble when its construction
%    is finished. The user expects that this argument is worked out in
%    math mode if it was used in an
%    \textsf{array}--environment. Therefore we surround it with
%    =\d@llar...='s.
% \changes{v2.0c}{1990/08/14}{\cs{relax} added to avoid problem
%                           `the`toks0`the`toks1.}
%    \begin{macrocode}
%   \@addtopreamble{\d@llarbegin\the@toks\the\count@\relax\d@llarend}%
%    \end{macrocode}
%    Finally we must prepare the next \textsf{token} register.
%    \begin{macrocode}
%   \prepnext@tok}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@classi}
%    In the case of class $0$ we were able to generate the necessary
%    space between columns by using the macro =\@classx=.
%    Analogously the macro =\@classvi= can be used for class $1$.
%    \begin{macrocode}
\def\@classi{\@classvi
%    \end{macrocode}
%    Depending on =\@chnum= a vertical line
%    \begin{macrocode}
   \ifcase \@chnum \@arrayrule \or
%    \end{macrocode}
%    or (in case of =!{...}=) the current \textsf{token} --- stored
%    in =\@nextchar= --- has to be inserted into the preamble.
%    This corresponds to calling =\@classv=.
%    \begin{macrocode}
      \@classv \fi}
%    \end{macrocode}
% \end{macro}
%
%
%
% \begin{macro}{\@startpbox}
%    In =\@classz=  the macro =\@startpbox= is used.
%    The width of the \textsf{parbox} is passed as an argument.
%    =\vcenter=, =\vtop= or =\vbox= are already in the
%    preamble. So we start with the braces for the wanted box.
% \changes{v2.4i}{2018/09/13}{Add group to prevent color leak (gh/72)}
%    \begin{macrocode}
\def\@startpbox#1{\bgroup
  \color@begingroup
%    \end{macrocode}
%    The argument is the width of the box. This information has to be
%    assigned to =\hsize=.
%    Then we assign default values to several parameters used in a
%    \textsf{parbox}.
% \changes{v2.3k}{1998/05/12}{Use \cs{setlength} to set \cs{hsize},
%      so that the calc package can be applied here (pr/2793)}
%    \begin{macrocode}
  \setlength\hsize{#1}\@arrayparboxrestore
%    \end{macrocode}
%    Our main problem is to obtain the same distance between succeeding
%    lines of the \textsf{parbox}.
%    We have to remember that the distance between two \textsf{parboxes}
%    should be defined by =\@arstrut=. That means that it can be
%    greater than the distance in a \textsf{parbox}.
%    Therefore it is not enough to set a =\@arstrut= at the
%    beginning and at the end of the \textsf{parbox}. This would
%    dimension the distance
%    between first and second line and the distance between the two
%    last lines of the \textsf{parbox} wrongly.
%    To prevent this we set an invisible rule of height
%    =\@arstrutbox=
%    at the beginning of the \textsf{parbox}. This has no effect on the
%    depth of the first line. At the end of the \textsf{parbox} we set
%    analogously another invisible rule which only affects the depth
%    of the last line. It is necessary to wait inserting this strut
%    until the paragraph actually starts to allow for things like
%    =\parindent= changes via =>{...}=.
% \changes{v2.1c}{1992/12/14}{Use `everypar to insert strut}
%    \begin{macrocode}
   \everypar{%
      \vrule \@height \ht\@arstrutbox \@width \z@
      \everypar{}}%
   }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@endpbox}
%    If there are any declarations defined by =>{...}=
%    and =<{...}=
%    they now follow in the macro =\@classz= --- the contents
%    of the column in between.
%    So the macro =\@endpbox= must insert the \textsf{specialstrut}
%    mentioned earlier and then close the group opened by
%    =\@startpbox=.
% \changes{v2.2d}{1994/05/16}{Use \LaTeXe \cs{@finalstrut}}
% \changes{v2.3g}{1996/05/07}{Add \cs{hfil} for tools/2120}
% \changes{v2.4i}{2018/09/13}{Add group to prevent color leak (gh/72)}
%    \begin{macrocode}
\def\@endpbox{\@finalstrut\@arstrutbox \color@endgroup \egroup\hfil}
%    \end{macrocode}
% \end{macro}
%
%
% \section{Building and calling \texttt{\textbackslash halign}}
%
% \begin{macro}{\@array}
%    After we have discussed the macros needed for the evaluation
%    of the user preamble we can define the macro =\@array=
%    which uses these macros to create a =\halign=.
%    It has two arguments. The first one is a position argument
%    which can be \texttt{t}, \texttt{b} or \texttt{c}; the
%    second one describes the wanted preamble,
%    e.g.\ it has the form =|c|c|c|=.
%    \begin{macrocode}
\def\@array[#1]#2{%
%    \end{macrocode}
%    First we define a \textsf{strut} whose size basically corresponds
%     to a normal \textsf{strut} multiplied by the factor
%    =\arraystretch=.
%    This \textsf{strut} is then  inserted into every row and enforces
%     a minimal distance between two rows.
%    Nevertheless, when using horizontal lines, large letters
%    (like accented capital letters) still collide with such lines.
%    Therefore at first we add to the height of a normal \textsf{strut}
%    the value of the parameter =\extrarowheight=.
%    \begin{macrocode}
  \@tempdima \ht \strutbox
  \advance \@tempdima by\extrarowheight
  \setbox \@arstrutbox \hbox{\vrule
             \@height \arraystretch \@tempdima
             \@depth \arraystretch \dp \strutbox
             \@width \z@}%
%    \end{macrocode}
%    Then we open a group, in which the user preamble is evaluated by
%    the macro =\@mkpream=. As we know this must happen locally.
%    This macro creates a preamble for a =\halign= and saves
%    its result globally in the control sequence =\@preamble=.
%    \begin{macrocode}
  \begingroup
  \@mkpream{#2}%
%    \end{macrocode}
%    We again redefine =\@preamble= so that a call up of =\@preamble=
%    now starts the =\halign=. Thus also the arguments of \texttt{>},
%    \texttt{<}, \texttt{@} and \texttt{!}, saved in the
%    \textsf{token} registers are inserted into the preamble.  The
%    =\tabskip= at the beginning and end of the preamble is set to
%    \textsf{0pt} (in the beginning by the use of =\ialign=). Also the
%    command =\@arstrut= is build in, which inserts the
%    =\@arstrutbox=, defined above. Of course, the opening brace after
%    =\ialign= has to be implicit as it will be closed in =\endarray=
%    or another macro.
% \changes{v2.3m}{1998/12/31}{Added \cs{noexpand} in front of \cs{ialign}
%    to guard against interesting :-) changes to \cs{halign} done to support
%    text glyphs in math}
%
%    The =\noexpand= in front of =\ialign= does no harm in standard \LaTeX{}
%    and was added since some experimental support for using text glyphs in math
%    redefines =\halign= with the result that is becomes expandable with
%    disastrous results in cases like this.
%    In the kernel definition for this macro the problem does
%    not surface because there =\protect= is set (which is not necessary in this
%    implementation as there is no arbitrary user input that can get expanded) and
%    the experimental code made the redefinition robust. Whether this is the right
%    approach is open to question; consider the =\noexpand= a courtesy to allow an
%    unsupported redefinition of a \TeX{} primitive for the moment (as people rely
%    on that experimental code).
%    \begin{macrocode}
  \xdef\@preamble{\noexpand \ialign \@halignto
                  \bgroup \@arstrut \@preamble
                          \tabskip \z@ \cr}%
%    \end{macrocode}
%    What we have not explained yet is the macro =\@halignto=
%    that was just used. Depending on its replacement text the
%    =\halign= becomes a =\halign= \texttt{to} \meta{dimen}.
%    Now we close the group again. Thus
%    =\@startpbox= and =\@endpbox= as well as all
%    \textsf{token} registers get their former meaning back.
%    \begin{macrocode}
  \endgroup
%    \end{macrocode}
%     To support the \texttt{delarray.sty} package  we include a hook
%     into this part of the code which is a no-op in the main package.
% \changes{v2.1a}{1992/07/03}{Hook for delarray added}
%    \begin{macrocode}
  \@arrayleft
%    \end{macrocode}
%    Now we decide depending on the position argument in which
%    \textsf{box} the =\halign= is to be put. (=\vcenter= may be used
%    because we are in math mode.)
% \changes{v2.1a}{1992/07/03}{Wrong spec is now equiv to [t]}
%    \begin{macrocode}
  \if #1t\vtop \else \if#1b\vbox \else \vcenter \fi \fi
%    \end{macrocode}
%    Now another implicit opening brace appears; then definitions
%    which shall stay local follow. While constructing the
%    =\@preamble= in =\@mkpream= the =#= sign must be
%    hidden in the macro =\@sharp= which is =\let= to
%    =\relax= at that moment (see definition of =\@mkpream=
%    on page~\pageref{@mkpream}).
%    All these now get their actual meaning.
%    \begin{macrocode}
  \bgroup
  \let \@sharp ##\let \protect \relax
%    \end{macrocode}
%    With the above defined \textsf{struts} we fix down the distance
%    between rows by setting =\lineskip= and =\baselineskip=
%    to \textsf{0pt}. Since there have to be set =$='s
%    around every column in the \textsf{array}--environment
%     the parameter =\mathsurround= should
%    also be set to \textsf{0pt}. This prevents additional space between
%    the rows. The
%    \PlainTeX--macro =\m@th= does this.
%    \begin{macrocode}
  \lineskip \z@
  \baselineskip \z@
  \m@th
%    \end{macrocode}
%    Beside, we have to assign a special meaning (which we still have
%    to specify) to the line separator =\\=. We also have to
%    redefine the command =\par= in such a way that empty lines in
%    =\halign= cannot do any damage. We succeed in doing  so
%    by choosing something that will disappear when expanding.
%    After that we only have to call up =\@preamble= to
%    start the wanted =\halign=.
%    \changes{1994/12/08}{v2.3b}{add \cs{tabularnewline}}
%    \begin{macrocode}
  \let\\\@arraycr \let\tabularnewline\\\let\par\@empty \@preamble}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\arraybackslash}
% \changes{v2.4a}{2003/12/17}{(DPC) Macro added (from tabularx)}
% Restore =\\= for use in array and tabular environment (after
% =\raggedright= etc.).
%    \begin{macrocode}
\def\arraybackslash{\let\\\tabularnewline}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\extrarowheight}
%    The \textsf{dimen} parameter used above also needs to be
%    allocated.  As a default value we use \textsf{0pt}, to ensure
%    compatibility with standard \LaTeX.
%    \begin{macrocode}
\newdimen \extrarowheight
\extrarowheight=0pt
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@arstrut}
%    Now the insertion of =\@arstrutbox= through =\@arstut=
%    is easy since we know exactly in which mode \TeX\ is while working
%    on the =\halign= preamble.
%    \begin{macrocode}
\def\@arstrut{\unhcopy\@arstrutbox}
%    \end{macrocode}
% \end{macro}
%
%
% \section{The line separator \texttt{\textbackslash\textbackslash}}
%
% \begin{macro}{\@arraycr}
%    In the macro =\@array= the line separator =\\= is
%    =\let= to the command =\@arraycr=.
%    Its definition starts with a special brace which I have directly
%    copied from the original definition. It is
%    necessary, because the =\futurlet= in =\@ifnextchar=
%    might
%    expand a  following =&= \textsf{token} in a construction like
%    =\\ &=. This would otherwise end the alignment template at a
%    wrong time. On the other hand we have to be careful to avoid
%    producing a real group, i.e.\ ={}=, because the command will also
%    be used for the array environment, i.e.\ in math mode. In that
%    case an extra ={}= would produce an ord atom which could mess up
%    the spacing. For this reason we use a combination that does not
%    really produce a group at all but modifies the master counter so
%    that a =&= will not be considered belonging to the current
%    =\halign= while we are looking for a =*= or =[=.
%    For further information see
%    \cite[Appendix D]{bk:knuth}.
% \changes{v2.3c}{1995/04/23}{Avoid adding an ord atom in math}
%    \begin{macrocode}
\def\@arraycr{\relax\iffalse{\fi\ifnum 0=`}\fi
%    \end{macrocode}
%    Then we test whether the user is using the star form and ignore
%    a possible star (I also disagree with this procedure, because a
%    star does not make any sense here).
%    \begin{macrocode}
  \@ifstar \@xarraycr \@xarraycr}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@xarraycr}
%    In the command =\@xarraycr= we test if an optional argument
%    exists.
%    \begin{macrocode}
\def\@xarraycr{\@ifnextchar [%
%    \end{macrocode}
%    If it does, we branch out into the macro =\@argarraycr= if
%    not we close the special brace (mentioned above) and end the row
%    of the =\halign= with a =\cr=.
% \changes{v2.3c}{1995/04/23}{Avoid adding an ord atom in math}
%    \begin{macrocode}
  \@argarraycr {\ifnum 0=`{}\fi\cr}}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\@argarraycr}
%    If additional space is requested by the user this case is treated
%    in the macro =\@argarraycr=. First we close the special brace
%    and then we test if the additional space is positive.
% \changes{v2.3c}{1995/04/23}{Avoid adding an ord atom in math}
%    \begin{macrocode}
\def\@argarraycr[#1]{\ifnum0=`{}\fi\ifdim #1>\z@
%    \end{macrocode}
%    If this is the case we create an invisible vertical rule with
%    depth =\dp\@arstutbox=${}+{}$\meta{wanted\ space}.
%    Thus we achieve that all vertical lines specified
%    in the user preamble by a \texttt{|} are now
%    generally drawn.
%    Then the row ends with a =\cr=.
%
%    If the space is negative we end the row at once with a =\cr=
%    and move back up with a =\vskip=.
%
%    While testing these macros I found out that the
%    =\endtemplate=
%    created by =\cr= and =&= is something like an
%    =\outer= primitive and therefore it should not appear in
%    incomplete =\if= statements. Thus the following solution was
%    chosen which hides the =\cr= in other macros when \TeX\
%    is skipping conditional text.
% \changes{v2.3c}{1995/04/23}{Use \cs{expandafter}'s in conditional}
%    \begin{macrocode}
  \expandafter\@xargarraycr\else
  \expandafter\@yargarraycr\fi{#1}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@xargarraycr}
% \begin{macro}{\@yargarraycr}
%    The following macros were already explained above.
% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
%    \begin{macrocode}
\def\@xargarraycr#1{\unskip\gdef\do@row@strut
 {\@tempdima #1\advance\@tempdima \dp\@arstrutbox
   \vrule \@depth\@tempdima \@width\z@\global\let\do@row@strut\relax}%
%    \end{macrocode}
%    If the last column is a =\multicolumn= cell then we need to
%    insert the row strut now as it isn't inside the template (as that
%    got =\omit=ted).
% \changes{v2.4h}{2018/04/30}{Fixing issue 42}
 %    \begin{macrocode}
   \ifnum\@multicnt >\z@ \do@row@strut \fi
   \cr}
\let\do@row@strut\relax
%    \end{macrocode}
%
%    \cs{@yargarraycr} is the same as in the \LaTeX{} kernel
%    (depending on the date of the kernel with one of the two
%    definitions below). We therefore do not define it again.
% \changes{v2.5b}{2020/04/22}{Don't define \cs{@yargarraycr} unnecessarily}
%    \begin{macrocode}
%\def\@yargarraycr#1{\cr\noalign{\@vspace@calcify{#1}}} % 2020-10-01
%\def\@yargarraycr#1{\cr\noalign{\vskip #1}}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%
%
%
% \section{Spanning several columns}
%
% \begin{macro}{\multicolumn}
%    If several columns should be held together with a special format
%    the command =\multicolumn= must be used. It has three
%    arguments: the number of columns to be covered; the format for
%    the result column and the actual column entry.
% \changes{v2.3j}{1998/01/29}{Command made \cs{long} to match
%      kernel change for pr/2180}
%    \begin{macrocode}
\long\def\multicolumn#1#2#3{%
%    \end{macrocode}
%    First we combine the given number of columns into a single one;
%    then we start a new block so that the following definition is kept
%    local.
%    \begin{macrocode}
   \multispan{#1}\begingroup
%    \end{macrocode}
%    Since a =\multicolumn= should only describe the format of a
%    result column, we redefine =\@addamp= in such a way that one gets
%    an error message if one uses more than one \texttt{c},
%    \texttt{l}, \texttt{r}, \texttt{p}, \texttt{m} or \texttt{b} in
%    the second argument. One should consider that this definition is
%    local to the build-up of the preamble; an \textsf{array}-- or
%    \textsf{tabular}--environment in the third argument of the
%    =\multicolumn= is therefore worked through correctly as well.
%    \begin{macrocode}
   \def\@addamp{\if@firstamp \@firstampfalse \else
                \@preamerr 5\fi}%
%    \end{macrocode}
%    Then we evaluate the second argument with the help of
%    =\@mkpream=.
%    Now we still have to insert the contents of the \textsf{token}
%    register into the =\@preamble=, i.e.\ we have to say
%    =\xdef\@preamble{\@preamble}=. This is achieved shorter by
%    writing:
%    \begin{macrocode}
   \@mkpream{#2}\@addtopreamble\@empty
%    \end{macrocode}
%    After the =\@preamble= is created we forget all local
%    definitions and occupations of the \textsf{token} registers.
%    \begin{macrocode}
   \endgroup
%    \end{macrocode}
%    In the special situation of  =\multicolumn= =\@preamble=
%    is not needed as preamble for a =\halign= but it is directly
%    inserted into our table. Thus instead of =\sharp=
%    there has to be the column entry (=#3=) wanted by the user.
%    \begin{macrocode}
   \def\@sharp{#3}%
%    \end{macrocode}
%    Now we can pass the =\@preamble= to \TeX\ . For safety
%    we start with an =\@arstrut=. This should usually be in the
%    template for the first column however we do not know if this
%    template was overwritten by our =\multicolumn=.
%    We also add a =\null= at the right end to prevent any following
%    =\unskip= (for example from =\\[..]=) to remove the =\tabcolsep=.
% \changes{v2.2e}{1994/06/01}{Added \cs{null}}
%    \begin{macrocode}
   \@arstrut \@preamble
   \null
   \ignorespaces}
%    \end{macrocode}
% \end{macro}
%
%
%
%   \section{The Environment Definitions}
%
% After these preparations we are able to define the environments. They
% only differ in the initialisations of =\d@llar...=, =\col@sep=
%  and =\@halignto=.
%
% \begin{macro}{\@halignto}
% \begin{macro}{\d@llarbegin}
% \begin{macro}{\d@llarend}
%    =\d@llar= has to be
%    locally asigned since otherwise nested \textsf{tabular} and \textsf{array}
%    environments (via =\multicolumn=) are impossible.
%    For 25 years or so =\@halignto= was set globally (to save space on the
%    save stack, but that was a mistake: if there is a tabular in the
%    output routine (e.g., in the running header) then that tabular is
%    able overwrite the =\@halignto=
%    setting of a tabular in the main text resulting in a very weird error.
% \changes{v2.4d}{2016/10/06}{\cs{@halignto} set locally (pr/4488)}
% \changes{v2.0g}{1992/06/18}{`d@llarbegin defined on toplevel.}
%    When the new font selection scheme is in force we have to
%    we surround all =\halign= entries
%    with braces. See remarks in TUGboat 10\#2. Actually we are going
%    to use =\begingroup= and =\endgroup=. However, this is only
%    necessary when we are in text mode. In math the surrounding
%    dollar signs will already serve as the necessary extra grouping
%    level. Therefore we switch the settings of =\d@llarbegin= and
%    =\d@llarend= between groups and dollar signs.
%    \begin{macrocode}
\let\d@llarbegin\begingroup
\let\d@llarend\endgroup
%    \end{macrocode}
% \end{macro}
% \end{macro}
% \end{macro}
%
%
% \begin{macro}{\array}
%    Our new definition of =\array= then reads:
% \changes{v2.0d}{1990/08/20}{`d@llar local to preamble.}
% \changes{v2.4d}{2016/10/06}{\cs{@halignto} set locally (pr/4488)}
%    \begin{macrocode}
\def\array{\col@sep\arraycolsep
  \def\d@llarbegin{$}\let\d@llarend\d@llarbegin\def\@halignto{}%
%    \end{macrocode}
%    Since there might be an optional argument we call another
%    macro which is also used by the other environments.
%    \begin{macrocode}
  \@tabarray}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@tabarray}
%    \emph{The code below has been replaced long time ago by an
%    extended version further down but the code and its documentation
%    was left here for reference. It is now commented out to avoid
%    confusion.}
%
%    This macro tests for a optional bracket and then calls up
%    =\@array= or =\@array[c]= (as default).
%    \begin{macrocode}
%\def\@tabarray{\@ifnextchar[{\@array}{\@array[c]}}
%    \end{macrocode}
% \end{macro}
%
%
% \begin{macro}{\tabular}
% \begin{macro}{\tabular*}
%    The environments \textsf{tabular} and \textsf{tabular$*$} differ
%    only in the initialisation of the command =\@halignto=. Therefore
%    we define
% \changes{v2.4d}{2016/10/06}{\cs{@halignto} set locally (pr/4488)}
%    \begin{macrocode}
\def\tabular{\def\@halignto{}\@tabular}
%    \end{macrocode}
%     and analogously for the star form. We evaluate the argument first
%     using =\setlength= so that users of the \texttt{calc} package can
%     write code like\\ =\begin{tabular*}{(\columnwidth-1cm)/2}...=
% \changes{v2.3l}{1998/05/13}{Use \cs{setlength} evaluate arg
%      so that the calc package can be applied here (pr/2793)}
% \changes{v2.4d}{2016/10/06}{\cs{@halignto} set locally (pr/4488)}
%     \begin{macrocode}
\expandafter\def\csname tabular*\endcsname#1{%
       \setlength\dimen@{#1}%
       \edef\@halignto{to\the\dimen@}\@tabular}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\@tabular}
%    The rest of the job is carried out by the =\@tabular= macro:
%    \begin{macrocode}
\def\@tabular{%
%    \end{macrocode}
%    First of all we have to make sure that we start out in
%    \textsf{hmode}.  Otherwise we might find our table dangling by
%    itself on a line.
%    \begin{macrocode}
  \leavevmode
%    \end{macrocode}
%    It should be taken into consideration that the macro =\@array=
%    must be called in math mode. Therefore we open a \textsf{box},
%    insert a =$= and then assign the correct values to =\col@sep= and
%    =\d@llar...=.
% \changes{v2.0d}{1990/08/20}{`d@llar local to preamble.}
%    \begin{macrocode}
  \hbox \bgroup $\col@sep\tabcolsep \let\d@llarbegin\begingroup
                                    \let\d@llarend\endgroup
%    \end{macrocode}
%    Now everything \textsf{tabular} specific is done and we are able to
%    call the =\@tabarray= macro.
%    \begin{macrocode}
  \@tabarray}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\endarray}
%    \emph{The code below has been replaced long time ago by an
%    extended version further down but the code and its documentation
%    was left here for reference. It is now commented out to avoid
%    confusion.}
%
%    When the processing of \textsf{array} is finished we have to
%    close the =\halign=
%    and afterwards the surrounding \textsf{box} selected by
%    =\@array=. To save \textsf{token} space we then redefine
%    =\@preamble=
%    because its replacement text isn't longer needed.
%    \begin{macrocode}
%\def\endarray{\crcr \egroup \egroup \gdef\@preamble{}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\endtabular}
% \begin{macro}{\endtabular*}
%    To end a \textsf{tabular} or \textsf{tabular$*$} environment we
%    call up =\endarray=, close the math mode and then the surrounding
%    =\hbox=.
%    \begin{macrocode}
\def\endtabular{\endarray $\egroup}
\expandafter\let\csname endtabular*\endcsname=\endtabular
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
%
%
%   \section{Last minute definitions}
%
%
% If this file is used as a package file we should =\let= all macros
% to =\relax= that were used in the original but are no longer
%  necessary.
%    \begin{macrocode}
\let\@ampacol=\relax        \let\@expast=\relax
\let\@arrayclassiv=\relax   \let\@arrayclassz=\relax
\let\@tabclassiv=\relax     \let\@tabclassz=\relax
\let\@arrayacol=\relax      \let\@tabacol=\relax
\let\@tabularcr=\relax      \let\@@endpbox=\relax
\let\@argtabularcr=\relax   \let\@xtabularcr=\relax
%    \end{macrocode}
%
% \begin{macro}{\@preamerr}
%    We also have to redefine the error routine =\@preamerr= since
%    new kind of errors are possible.
%    The code for this macro is not perfect yet;
%    it still needs too much memory.
%    \begin{macrocode}
\def\@preamerr#1{\def\@tempd{{..} at wrong position: }%
   \PackageError{array}{%
   \ifcase #1 Illegal pream-token (\@nextchar): `c' used\or %0
    Missing arg: token ignored\or                           %1
    Empty preamble: `l' used\or                             %2
    >\@tempd token ignored\or                               %3
    <\@tempd changed to !{..}\or                            %4
    Only one column-spec. allowed.\fi}\@ehc}                %5
%    \end{macrocode}
% \end{macro}
%
%
%
% \section
%   [Defining your own column specifiers]
%   {Defining your own column specifiers\footnotemark}
%
% \footnotetext{The code and the documentation in this section was
%   written by David. So far only the code from newarray was plugged
%   into array so that some parts of the documentation still claim
%   that this is newarray and even worse, some parts of the code are
%   unnecessarily doubled. This will go away in a future release. For
%   the moment we thought it would be more important to bring both
%   packages together.}
% \changes{v2.1a}{1992/07/03}{Newcolumn stuff added}
%
% \DeleteShortVerb{\=}
% \MakeShortVerb{\"}
%
%  \begin{macro}{\newcolumn}
%    In \texttt{newarray.sty} the macro for specifying new columns was
%    named "\newcolumn". When the functionality was added to
%    \texttt{array.sty} the command was renamed "\newcolumntype".
%    Initially both names were supported, but now (In versions of this
%    package distributed for \LaTeXe) the old name is not defined.
% \changes{v2.2a}{1994/02/03}{Now made `newcolumn an error}
% \changes{v2.2a}{1994/02/04}{Removed `newcolumn}
%    \begin{macrocode}
%<*ncols>
%    \end{macrocode}
%  \end{macro}
%
% \begin{macro}{\newcolumntype}
% \changes{v2.1b}{1992/06/07}{Macro renamed from `newcolumn} As
% described above, the "\newcolumntype" macro gives users the chance
% to define letters, to be used in the same way as the primitive
% column specifiers, `c' `p' etc.
%    \begin{macrocode}
\def\newcolumntype#1{%
%    \end{macrocode}
% "\NC@char" was added in V2.01 so that active characters, like "@" in
% AMS\LaTeX\ may be used. This trick was stolen from \texttt{array.sty}
% 2.0h. Note that we need to use the possibly active token,
% "#1", in several places, as that is the token that actually
% appears in the preamble argument.
%    \begin{macrocode}
  \edef\NC@char{\string#1}%
%    \end{macrocode}
% First we check whether there is already a definition for this column.
% Unlike "\newcommand" we give a warning rather than an error if it is
% defined. If it is a new column, add "\NC@do" \meta{column} to
% the list "\NC@list".
%    \begin{macrocode}
  \@ifundefined{NC@find@\NC@char}%
    {\@tfor\next:=<>clrmbp@!|\do
      {%
%    \end{macrocode}
%    We use \cs{noexpand} on the tokens from the list in case one or
%    the other (typically \texttt{@}, \texttt{!} or \texttt{|}) has
%    been made active.
% \changes{v2.4l}{2019/08/31}{Add a necessary \cs{expandafter} (github/148)}
%    \begin{macrocode}
        \if\expandafter\noexpand\next\NC@char
        \PackageWarning{array}%
                       {Redefining primitive column \NC@char}\fi}%
     \NC@list\expandafter{\the\NC@list\NC@do#1}}%
    {\PackageWarning{array}{Column \NC@char\space is already defined}}%
%    \end{macrocode}
% Now we define a macro with an argument delimited by the new column
% specifier, this is used to find occurrences of this specifier in the
% user preamble.
%    \begin{macrocode}
  \@namedef{NC@find@\NC@char}##1#1{\NC@{##1}}%
%    \end{macrocode}
% If an optional argument was not given, give a default argument of 0.
%    \begin{macrocode}
  \@ifnextchar[{\newcol@{\NC@char}}{\newcol@{\NC@char}[0]}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\newcol@}
% We can now define the macro which does the rewriting,
% "\@reargdef" takes the same arguments as "\newcommand", but
% does not check that the command is new. For a column, say `D' with
% one argument, define a command "\NC@rewrite@D" with one
% argument, which recursively calls "\NC@find" on the user preamble
% after replacing the first token or group with the replacement text
% specified in the "\newcolumntype" command. "\NC@find" will find the
% next occurrence of `D' as it will be "\let" equal to
% "\NC@find@D" by "\NC@do".
%    \begin{macrocode}
\def\newcol@#1[#2]#3{\expandafter\@reargdef
     \csname NC@rewrite@#1\endcsname[#2]{\NC@find#3}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@}
% Having found an occurrence of the new column, save the preamble
% before the column in "\@temptokena", then check to see if we
% are at the end of the preamble. (A dummy occurrence of the column
% specifier will be placed at the end of the preamble by "\NC@do".
%    \begin{macrocode}
\def\NC@#1{%
  \@temptokena\expandafter{\the\@temptokena#1}\futurelet\next\NC@ifend}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@ifend}
% We can tell that we are at the end as "\NC@do" will place a "\relax"
% after the dummy column.
%    \begin{macrocode}
\def\NC@ifend{%
%    \end{macrocode}
% If we are at the end, do nothing. (The whole preamble will now be in
% "\@temptokena".)
%    \begin{macrocode}
  \ifx\next\relax
%    \end{macrocode}
% Otherwise set the flag "\if@tempswa", and rewrite the column.
% "\expandafter" introduced 1n V2.01
%    \begin{macrocode}
    \else\@tempswatrue\expandafter\NC@rewrite\fi}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@do}
% If the user has specified `C' and `L' as new columns, the list of
% rewrites (in the token register "\NC@list") will look like
% "\NC@do *" "\NC@do C" "\NC@do L".
% So we need to define "\NC@do" as a one argument macro which
% initialises the rewriting of the specified column. Let us assume that
% `C' is the argument.
%    \begin{macrocode}
\def\NC@do#1{%
%    \end{macrocode}
% First we let "\NC@rewrite" and "\NC@find" be
% "\NC@rewrite@C" and "\NC@find@C" respectively.
%    \begin{macrocode}
  \expandafter\let\expandafter\NC@rewrite
    \csname NC@rewrite@\string#1\endcsname
  \expandafter\let\expandafter\NC@find
    \csname NC@find@\string#1\endcsname
%    \end{macrocode}
% Clear the token register "\@temptokena" after putting the present
% contents of the register in front of the token "\NC@find". At the
% end we place the tokens `"C\relax"' which "\NC@ifend" will use
% to detect the end of the user preamble.
%    \begin{macrocode}
  \expandafter\@temptokena\expandafter{\expandafter}%
        \expandafter\NC@find\the\@temptokena#1\relax}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\showcols}
% This macro is useful for debugging "\newcolumntype" specifications,
% it is the equivalent of the primitive "\show" command for macro
% definitions.  All we need to do is locally redefine "\NC@do" to take
% its argument (say `C') and then "\show" the (slightly modified)
% definition of "\NC@rewrite@C". Actually as the list always
% starts off with "\NC@do *" and we do not want to print the
% definition of the $*$-form, define "\NC@do" to throw away the first
% item in the list, and then redefine itself to print the rest of the
% definitions.
%    \begin{macrocode}
\def\showcols{{\def\NC@do##1{\let\NC@do\NC@show}\the\NC@list}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@show}
% If the column `C' is defined as above, then
% "\show\NC@rewrite@C" would output\\
% "\long macro: ->\NC@find >{$}c<{$}".
% We want to strip the "long macro: ->" and the "\NC@find". So first we
% use "\meaning" and then apply the macro "\NC@strip" to the tokens so
% produced and then "\typeout" the required string.
%    \begin{macrocode}
\def\NC@show#1{%
  \typeout{Column #1\expandafter\expandafter\expandafter\NC@strip
  \expandafter\meaning\csname NC@rewrite@#1\endcsname\@@}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@strip}
% Delimit the arguments to "\NC@strip" with `\texttt{:}', `\texttt{->}',
% a space, and "\@@" to pull out the required parts of the output from
% "\meaning".
%    \begin{macrocode}
\def\NC@strip#1:#2->#3 #4\@@{#2 -> #4}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\NC@list}
% Allocate the token register used for the rewrite list.
%    \begin{macrocode}
\newtoks\NC@list
%    \end{macrocode}
% \end{macro}
%
% \subsection{The $*$--form}
% We view the $*$-form as a slight generalisation of the system
% described in the previous subsection. The idea is to define a $*$
% column by a command of the form:
% \begin{verbatim}
% \newcolumntype{*}[2]{%
%    \count@=#1\ifnum\count@>0
%       \advance\count@ by -1 #2*{\count@}{#2}\fi}
% \end{verbatim}
% \begin{macro}{\NC@rewrite@*}\label{NC@rewrite@*}
% \changes{v2.4b}{2005/08/23}{Fix occasional spurious space (PR/3755)}
% This does not work however as "\newcolumntype" takes great care not
% to expand anything in the preamble, and so the "\if" is never
% expanded. "\newcolumntype" sets up various other parts of the
% rewrite correctly though so we can define:
%    \begin{macrocode}
\newcolumntype{*}[2]{}
%    \end{macrocode}
% Now we must correct the definition of "\NC@rewrite@*". The
% following is probably more efficient than a direct translation of
% the idea sketched above, we do not need to put a $*$ in the preamble
% and call the rewrite recursively, we can just put "#1" copies of
% "#2" into "\@temptokena". (Nested $*$ forms will be expanded
% when the whole rewrite list is expanded again, see "\@mkpream")
%    \begin{macrocode}
\long\@namedef{NC@rewrite@*}#1#2{%
%    \end{macrocode}
% Store the number.
%    \begin{macrocode}
  \count@#1\relax
%    \end{macrocode}
% Put "#1" copies of "#2" in the token register.
%    \begin{macrocode}
  \loop
  \ifnum\count@>\z@
  \advance\count@\m@ne
  \@temptokena\expandafter{\the\@temptokena#2}%
  \repeat
%    \end{macrocode}
% "\NC@do" will ensure that "\NC@find" is "\let" equal
% to "\NC@find@*".
%    \begin{macrocode}
  \NC@find}
%    \end{macrocode}
% \end{macro}
%
% \subsection{Modifications to internal macros of \texttt{array.sty}}
%
% \begin{macro}{\@xexpast}
% \begin{macro}{\@xexnoop}
%    These macros are used to expand $*$-forms in
%    \texttt{array.sty}. "\let" them to "\relax" to save space.
%    \begin{macrocode}
\let\@xexpast\relax
\let\@xexnoop\relax
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\save@decl}
% We do not assume that the token register is free, we add the new
% declarations to the front of the register. This is to allow user
% preambles of the form, ">{foo}>{bar}..". Users are not encouraged to
% enter such expressions directly, but they may result from the
% rewriting of "\newcolumntype"'s.
%    \begin{macrocode}
\def\save@decl{\toks \count@ = \expandafter\expandafter\expandafter
                  {\expandafter\@nextchar\the\toks\count@}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@mkpream}
%    The main modification to "\@mkpream" is to replace the call to
%    "\@xexpast" (which expanded $*$-forms) by a loop which expands
%    all "\newcolumntype" specifiers.
% \changes{v2.4e}{2016/10/07}{Fixing SX68732}
% \changes{v2.4f}{2017/11/04}{Managing m-cells without \cs{vcenter}}
%    \begin{macrocode}
\def\@mkpream#1{\gdef\@preamble{}\@lastchclass 4 \@firstamptrue
   \let\@sharp\relax
%    \end{macrocode}
%
% \changes{v2.4j}{2018/11/13}{Do not expand argument of
%    \cs{@startpbox} while building the tabular preamble (sx/459285)}
%    The "\@startpbox" (which is called for "p", "m" or "b" columns)
%    receives a user supplied argument: the width of the
%    paragraph-column. Normally that is something harmless like a length or a
%    simple length expression, but with the calc package involved it
%    could break under an "\edef" operation, which is how the preamble
%    is constructed. We now make use of "\unexpanded" here to prevent that. The
%    "\expandafter" gymnastics is necessary to expand the "#1" at least
%    once (since it will get "\@nextchar" as its value and need its
%    content!
%    \begin{macrocode}
   \def\@startpbox##1{\unexpanded\expandafter{\expandafter
                      \@startpbox\expandafter{##1}}}\let\@endpbox\relax
   \let\do@row@strut\relax
   \let\ar@align@mcell\relax
%    \end{macrocode}
%    Now we remove possible  $*$-forms and user-defined column
%    specifiers in the user preamble by repeatedly executing the list
%    "\NC@list" until the re-writes have no more effect. The
%    expanded preamble will then be in the token register
%    "\@temptokena". Actually we need to know at this point that
%    this is not "\toks0".
%    \begin{macrocode}
   \@temptokena{#1}\@tempswatrue
   \@whilesw\if@tempswa\fi{\@tempswafalse\the\NC@list}%
%    \end{macrocode}
%    Afterwards we initialize all registers and macros, that we need
%    for the build-up of the preamble.
%    \begin{macrocode}
   \count@\m@ne
   \let\the@toks\relax
   \prepnext@tok
%    \end{macrocode}
% Having expanded all tokens defined using "\newcolumntype" (including
% "*"), we evaluate the remaining tokens, which are saved in
% "\@temptokena".  We use the \LaTeX--macro "\@tfor" to inspect each
% token in turn.
%    \begin{macrocode}
   \expandafter \@tfor \expandafter \@nextchar
    \expandafter :\expandafter =\the\@temptokena \do
%    \end{macrocode}
% "\@testpatch" does not take an argument since \texttt{array.sty} 2.0h.
%    \begin{macrocode}
   {\@testpach
   \ifcase \@chclass \@classz \or \@classi \or \@classii
     \or \save@decl \or \or \@classv \or \@classvi
     \or \@classvii \or \@classviii
%    \end{macrocode}
%    In \texttt{newarray.sty} class 9 is equivalent to class 10.
%    \begin{macrocode}
     \or \@classx
     \or \@classx \fi
   \@lastchclass\@chclass}%
   \ifcase\@lastchclass
   \@acol \or
   \or
   \@acol \or
   \@preamerr \thr@@ \or
   \@preamerr \tw@ \@addtopreamble\@sharp \or
   \or
   \else  \@preamerr \@ne \fi
   \def\the@toks{\the\toks}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@classix}
%    \texttt{array.sty} does not allow repeated \texttt{>}
%    declarations for the same column. This is allowed in
%    \texttt{newarray.sty} as documented in the introduction. Removing
%    the test for this case makes class 9 equivalent to class 10, and
%    so this macro is redundant. It is "\let" to "\relax" to save
%    space.
%    \begin{macrocode}
\let\@classix\relax
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@classviii}
%    In \texttt{newarray.sty} explicitly allow class 2, as repeated
%    \texttt{<} expressions are accepted by this package.
%    \begin{macrocode}
\def\@classviii{\ifnum \@lastchclass >\z@\ifnum\@lastchclass=\tw@\else
      \@preamerr 4\@chclass 6 \@classvi \fi\fi}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\@classv}
% Class 5 is \texttt{@}-expressions (and is also called by class 1)
% This macro was incorrect in Version~1. Now we do not expand the
% "@"-expression, but instead explicitly replace an
% "\extracolsep" command by an assignment to "\tabskip" by a
% method similar to the "\newcolumntype" system described above.
% "\d@llarbegin" "\d@llarend" were introduced in V2.01 to match
% \texttt{array.sty} 2.0h.
%    \begin{macrocode}
\def\@classv{\save@decl
   \expandafter\NC@ecs\@nextchar\extracolsep{}\extracolsep\@@@
   \@addtopreamble{\d@llarbegin\the@toks\the\count@\relax\d@llarend}%
   \prepnext@tok}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\NC@ecs}
% Rewrite the first occurrence of "\extracolsep{1in}" to
% "\tabskip1in\relax". As a side effect discard any tokens after a
% second "\extracolsep", there is no point in the user entering two of
% these commands anyway, so this is not really a restriction.
%    \begin{macrocode}
\def\NC@ecs#1\extracolsep#2#3\extracolsep#4\@@@{\def\@tempa{#2}%
  \ifx\@tempa\@empty\else\toks\count@={#1\tabskip#2\relax#3}\fi}
%</ncols>
%    \end{macrocode}
% \end{macro}
%
%
% \subsection{Support for the \texttt{delarray.sty}}
%
% The \texttt{delarray.sty} package  extends the array syntax by
% supporting the notation of delimiters. To this end we extend the
% array parsing mechanism to include a hook which can be used by this
% (or another) package to do some additional parsing.
%
% \begin{macro}{\@tabarray}
%    This macro tests for an optional bracket and then calls up
%    "\@@array" or "\@@array[c]" (as default).
%    \begin{macrocode}
%<*package>
\def\@tabarray{\@ifnextchar[{\@@array}{\@@array[c]}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\@@array}
%    This macro tests could then test an optional delimiter before the
%    left brace of the main preamble argument. Here in the main package
%    it simply is let to be "\@array".
%    \begin{macrocode}
\let\@@array\@array
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\endarray}
% \begin{macro}{\@arrayright}
%    We have to declare the hook we put into "\@array" above.
%    A similar hook `"\@arrayright"' will be inserted into the
%    "\endarray" to gain control. Both defaults to empty.
%    \begin{macrocode}
\def\endarray{\crcr \egroup \egroup \@arrayright \gdef\@preamble{}}
\let\@arrayleft\@empty
\let\@arrayright\@empty
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \subsection{Support for \texttt{\textbackslash firsthline} and
%             \texttt{\textbackslash lasthline}}
%
% The Companion~\cite[p.137]{bk:GMS94} suggests two additional
% commands to control the alignments in case of tabulars with
% horizontal lines. They are now added to this package.
%
%  \begin{macro}{\extratabsurround}
%    The extra space around a table when "\firsthline" or "\lasthline"
%    are used.
%    \begin{macrocode}
\newlength{\extratabsurround}
\setlength{\extratabsurround}{2pt}
%    \end{macrocode}
%  \end{macro}
%
% \begin{macro}{\backup@length}
%    This register will be used internally by "\firsthline" and
%    "\lasthline".
%    \begin{macrocode}
\newlength{\backup@length}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\firsthline}
% \changes{v2.3h}{1996/05/25}{Complete reimplementation}
%    This code can probably be improved but for the moment it should
%    serve.
%
%    We start by producing a single tabular row without any visible
%    content that will produce the external reference point in case
%    "[t]" is used.  We need to suppress the \cs{tabcolsep} in the
%    \cs{multicolumn} in case there wasn't any in the real column.
%
% \changes{v2.5c}{2020/07/20}{Suppress all column space (gh/322)}
%    \begin{macrocode}
\newcommand{\firsthline}{%
  \multicolumn1{@{}c@{}}{%
%    \end{macrocode}
%    Within this row we calculate "\backup@length" to be the height
%    plus depth of a standard line. In addition we have to add the
%    width of the "\hline", something that was forgotten in the
%    original definition.
%    \begin{macrocode}
    \global\backup@length\ht\@arstrutbox
    \global\advance\backup@length\dp\@arstrutbox
    \global\advance\backup@length\arrayrulewidth
%    \end{macrocode}
%    Finally we do want to make the height of this first line be a bit
%    larger than usual, for this we place the standard array strut
%    into it but raised by "\extratabsurround"
%    \begin{macrocode}
     \raise\extratabsurround\copy\@arstrutbox
%    \end{macrocode}
%    And we should also cancel the guard otherwise we end up with two.
%    \begin{macrocode}
     \kern-1sp%
%    \end{macrocode}
%    Having done all this we end the line and back up by the value of
%    "\backup@length" and then finally place our "\hline". This should
%    place the line exactly at the right place but keep the reference
%    point of the whole tabular at the baseline of the first row.
%    \begin{macrocode}
    }\\[-\backup@length]\hline
}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\lasthline}
% \changes{v2.3h}{1996/05/25}{Complete reimplementation}
%    For "\lasthline" the situation is even worse and I got it
%    completely wrong initially.
%
%    The problem in this case is that if the optional argument "[b]"
%    is used we do want the reference point of the tabular be at the
%    baseline of the last row but at the same time do want the
%    depth of this last line increased by "\extratabsurround" without
%    changing the placement "\hline".
%
%    We start by placing the rule followed by an invisible row. We
%    need to suppress the \cs{tabcolsep} in the multicol in case there
%    wasn't any in the real column.
% \changes{v2.5c}{2020/07/20}{Suppress all column space (gh/322)}
%    \begin{macrocode}
\newcommand{\lasthline}{\hline\multicolumn1{@{}c@{}}{%
%    \end{macrocode}
%    We now calculate "\backup@length" to be the height and depth of
%    two lines plus the width of the rule.
%    \begin{macrocode}
    \global\backup@length2\ht\@arstrutbox
    \global\advance\backup@length2\dp\@arstrutbox
    \global\advance\backup@length\arrayrulewidth
%    \end{macrocode}
%    This will bring us back to the baseline of the second last row:
%    \begin{macrocode}
    }\\[-\backup@length]%
%    \end{macrocode}
%    Thus if we now add another invisible row the reference point of
%    that row will be at the baseline of the last row (and will be the
%    reference for the whole tabular). Since this row is invisible we
%    can enlarge its depth by the desired amount.
%    \begin{macrocode}
    \multicolumn1{@{}c@{}}{%
       \lower\extratabsurround\copy\@arstrutbox
       \kern-1sp%
       }%
}
%    \end{macrocode}
% \end{macro}
%
%
% \subsection{Getting the spacing around rules right}
%
%    Beside a larger functionality \texttt{array.sty} has one
%    important difference to the standard \texttt{tabular} and
%    \texttt{array} environments: horizontal and vertical rules make a
%    table larger or wider, e.g., \verb=\doublerulesep= really denotes
%    the space between two rules and isn't measured from the middle of
%    the rules.
%
%  \begin{macro}{\@xhline}
%    For vertical rules this is implemented by the definitions above,
%    for horizontal rules we have to take out the backspace.
% \changes{v2.3d}{1995/11/19}{fix space between double rules pr/1945}
%    \begin{macrocode}
\CheckCommand*\@xhline{\ifx\reserved@a\hline
               \vskip\doublerulesep
               \vskip-\arrayrulewidth
             \fi
      \ifnum0=`{\fi}}
\renewcommand*\@xhline{\ifx\reserved@a\hline
               \vskip\doublerulesep
             \fi
      \ifnum0=`{\fi}}
%</package>
%    \end{macrocode}
%  \end{macro}

% \subsection{Implementing column types \texttt{w} and \texttt{W}}
%
% In TugBoat 38/2 an extension was presented that implemented two
% aditional column types \texttt{w} and \texttt{W}. These have now
% been added to the package itself.
%
%
%  \begin{macro}{\ar@cellbox}
%    For \texttt{w} and \texttt{W} column types we need a box to
%    temporarily hold the cell content.
% \changes{v2.4f}{2017/11/07}{Macro added}
%    \begin{macrocode}
\newsavebox\ar@cellbox
%    \end{macrocode}
%  \end{macro}
%
%
%  \begin{macro}{\newcolumntype w}
%    The \texttt{w} column type has two arguments: the first holds the
%    alignment which is either "l", "c", or "r" and the second is the
%    nominal width of the column.
% \changes{v2.4f}{2017/11/07}{Column type added}
% \changes{v2.5a}{2020/04/06}{Use \cs{d@llarbegin} and \cs{d@llarend} so
%    that cell is typeset in math mode inside \texttt{array} (gh/297)}
%    \begin{macrocode}
\newcolumntype{w}[2]{%
%    \end{macrocode}
%    Before the cell content we start an "lrbox"-environment to
%    collect the cell material into the previously allocated box
%    "\ar@cellbox". We add \cs{d@llarbegin} (and later \cs{d@llarend})
%    so that the content is typeset in math mode if we are in an
%    \texttt{array} environment.
%    \begin{macrocode}
  >{\begin{lrbox}\ar@cellbox\d@llarbegin}%
%    \end{macrocode}
%    Then comes a specifier for the cell content.  We use "c", but
%    that doesn't matter as in the end we will always put a box of a
%    specific width ("#2") into the cells of that column, so "l" or
%    "r" would give the same result. There is only a difference if
%    there are also very wide "\multicolumn" rows overwriting the
%    setting  in which case "c" seems to be slightly better.
%    \begin{macrocode}
  c%
%    \end{macrocode}
%    At the end of the cell we end the "lrbox" environment so that all
%    of the cell content is now in box "\ar@cellbox".  As a final step we
%    put that box into a "\makebox" using the optional arguments of
%    that command to achieve the correct width and the desired
%    alignment within that width. We unbox the collected material so
%    that any stretchable glue inside can interact with the alignment.
% \changes{v2.4m}{2020/02/10}{Unbox collected material so that
%                             stretchable glue inside can act (gh/270)}
%    \begin{macrocode}
  <{\d@llarend \end{lrbox}%
    \makebox[#2][#1]{\unhbox\ar@cellbox}}}
%    \end{macrocode}
%  \end{macro}

%
%
%  \begin{macro}{\newcolumntype W}
%    The \texttt{W} is similar but in this case we want a warning if
%    the cell content is too wide.
% \changes{v2.4f}{2017/11/07}{Column type added}
% \changes{v2.5a}{2020/04/06}{Use \cs{d@llarbegin} and \cs{d@llarend} so
%    that cell is typeset in mathmode inside \texttt{array} (gh/297)}
%    \begin{macrocode}
\newcolumntype{W}[2]
  {>{\begin{lrbox}\ar@cellbox\d@llarbegin}%
   c%
   <{\d@llarend\end{lrbox}%
   \let\hss\hfil
   \makebox[#2][#1]{\unhbox\ar@cellbox}}}
%    \end{macrocode}
%    This is a bit sneaky, as it temporarily disables "\hss", but
%    given that we know what goes into that box it should be
%    sufficient.
%  \end{macro}
%
%
% \PrintIndex
% \PrintChanges
%
% \Finale
%
\endinput