summaryrefslogtreecommitdiffstats
path: root/ast/timeframe.c
blob: c3dae881db97bb1b2df2d06e90b201f1c674056d (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
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
4361
4362
4363
4364
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374
4375
4376
4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
4407
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
4428
4429
4430
4431
4432
4433
4434
4435
4436
4437
4438
4439
4440
4441
4442
4443
4444
4445
4446
4447
4448
4449
4450
4451
4452
4453
4454
4455
4456
4457
4458
4459
4460
4461
4462
4463
4464
4465
4466
4467
4468
4469
4470
4471
4472
4473
4474
4475
4476
4477
4478
4479
4480
4481
4482
4483
4484
4485
4486
4487
4488
4489
4490
4491
4492
4493
4494
4495
4496
4497
4498
4499
4500
4501
4502
4503
4504
4505
4506
4507
4508
4509
4510
4511
4512
4513
4514
4515
4516
4517
4518
4519
4520
4521
4522
4523
4524
4525
4526
4527
4528
4529
4530
4531
4532
4533
4534
4535
4536
4537
4538
4539
4540
4541
4542
4543
4544
4545
4546
4547
4548
4549
4550
4551
4552
4553
4554
4555
4556
4557
4558
4559
4560
4561
4562
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
4573
4574
4575
4576
4577
4578
4579
4580
4581
4582
4583
4584
4585
4586
4587
4588
4589
4590
4591
4592
4593
4594
4595
4596
4597
4598
4599
4600
4601
4602
4603
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
4617
4618
4619
4620
4621
4622
4623
4624
4625
4626
4627
4628
4629
4630
4631
4632
4633
4634
4635
4636
4637
4638
4639
4640
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
4654
4655
4656
4657
4658
4659
4660
4661
4662
4663
4664
4665
4666
4667
4668
4669
4670
4671
4672
4673
4674
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
4730
4731
4732
4733
4734
4735
4736
4737
4738
4739
4740
4741
4742
4743
4744
4745
4746
4747
4748
4749
4750
4751
4752
4753
4754
4755
4756
4757
4758
4759
4760
4761
4762
4763
4764
4765
4766
4767
4768
4769
4770
4771
4772
4773
4774
4775
4776
4777
4778
4779
4780
4781
4782
4783
4784
4785
4786
4787
4788
4789
4790
4791
4792
4793
4794
4795
4796
4797
4798
4799
4800
4801
4802
4803
4804
4805
4806
4807
4808
4809
4810
4811
4812
4813
4814
4815
4816
4817
4818
4819
4820
4821
4822
4823
4824
4825
4826
4827
4828
4829
4830
4831
4832
4833
4834
4835
4836
4837
4838
4839
4840
4841
4842
4843
4844
4845
4846
4847
4848
4849
4850
4851
4852
4853
4854
4855
4856
4857
4858
4859
4860
4861
4862
4863
4864
4865
4866
4867
4868
4869
4870
4871
4872
4873
4874
4875
4876
4877
4878
4879
4880
4881
4882
4883
4884
4885
4886
4887
4888
4889
4890
4891
4892
4893
4894
4895
4896
4897
4898
4899
4900
4901
4902
4903
4904
4905
4906
4907
4908
4909
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
4941
4942
4943
4944
4945
4946
4947
4948
4949
4950
4951
4952
4953
4954
4955
4956
4957
4958
4959
4960
4961
4962
4963
4964
4965
4966
4967
4968
4969
4970
4971
4972
4973
4974
4975
4976
4977
4978
4979
4980
4981
4982
4983
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
5153
5154
5155
5156
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
5172
5173
5174
5175
5176
5177
5178
5179
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
5195
5196
5197
5198
5199
5200
5201
5202
5203
5204
5205
5206
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
5232
5233
5234
5235
5236
5237
5238
5239
5240
5241
5242
5243
5244
5245
5246
5247
5248
5249
5250
5251
5252
5253
5254
5255
5256
5257
5258
5259
5260
5261
5262
5263
5264
5265
5266
5267
5268
5269
5270
5271
5272
5273
5274
5275
5276
5277
5278
5279
5280
5281
5282
5283
5284
5285
5286
5287
5288
5289
5290
5291
5292
5293
5294
5295
5296
5297
5298
5299
5300
5301
5302
5303
5304
5305
5306
5307
5308
5309
5310
5311
5312
5313
5314
5315
5316
5317
5318
5319
5320
5321
5322
5323
5324
5325
5326
5327
5328
5329
5330
5331
5332
5333
5334
5335
5336
5337
5338
5339
5340
5341
5342
5343
5344
5345
5346
5347
5348
5349
5350
5351
5352
5353
5354
5355
5356
5357
5358
5359
5360
5361
5362
5363
5364
5365
5366
5367
5368
5369
5370
5371
5372
5373
5374
5375
5376
5377
5378
5379
5380
5381
5382
5383
5384
5385
5386
5387
5388
5389
5390
5391
5392
5393
5394
5395
5396
5397
5398
5399
5400
5401
5402
5403
5404
5405
5406
5407
5408
5409
5410
5411
5412
5413
5414
5415
5416
5417
5418
5419
5420
5421
5422
5423
5424
5425
5426
5427
5428
5429
5430
5431
5432
5433
5434
5435
5436
5437
5438
5439
5440
5441
5442
5443
5444
5445
5446
5447
5448
5449
5450
5451
5452
5453
5454
5455
5456
5457
5458
5459
5460
5461
5462
5463
5464
5465
5466
5467
5468
5469
5470
5471
5472
5473
5474
5475
5476
5477
5478
5479
5480
5481
5482
5483
5484
5485
5486
5487
5488
5489
5490
5491
5492
5493
5494
5495
5496
5497
5498
5499
5500
5501
5502
5503
5504
5505
5506
5507
5508
5509
5510
5511
5512
5513
5514
5515
5516
5517
5518
5519
5520
5521
5522
5523
5524
5525
5526
5527
5528
5529
5530
5531
5532
5533
5534
5535
5536
5537
5538
5539
5540
5541
5542
5543
5544
5545
5546
5547
5548
5549
5550
5551
5552
5553
5554
5555
5556
5557
5558
5559
5560
5561
5562
5563
5564
5565
5566
5567
5568
5569
5570
5571
5572
5573
5574
5575
5576
5577
5578
5579
5580
5581
5582
5583
5584
5585
5586
5587
5588
5589
5590
5591
5592
5593
5594
5595
5596
5597
5598
5599
5600
5601
5602
5603
5604
5605
5606
5607
5608
5609
5610
5611
5612
5613
5614
5615
5616
5617
5618
5619
5620
5621
5622
5623
5624
5625
5626
5627
5628
5629
5630
5631
5632
5633
5634
5635
5636
5637
5638
5639
5640
5641
5642
5643
5644
5645
5646
5647
5648
5649
5650
5651
5652
5653
5654
5655
5656
5657
5658
5659
5660
5661
5662
5663
5664
5665
5666
5667
5668
5669
5670
5671
5672
5673
5674
5675
5676
5677
5678
5679
5680
5681
5682
5683
5684
5685
5686
5687
5688
5689
5690
5691
5692
5693
5694
5695
5696
5697
5698
5699
5700
5701
5702
5703
5704
5705
5706
5707
5708
5709
5710
5711
5712
5713
5714
5715
5716
5717
5718
5719
5720
5721
5722
5723
5724
5725
5726
5727
5728
5729
5730
5731
5732
5733
5734
5735
5736
5737
5738
5739
5740
5741
5742
5743
5744
5745
5746
5747
5748
5749
5750
5751
5752
5753
5754
5755
5756
5757
5758
5759
5760
5761
5762
5763
5764
5765
5766
5767
5768
5769
5770
5771
5772
5773
5774
5775
5776
5777
5778
5779
5780
5781
5782
5783
5784
5785
5786
5787
5788
5789
5790
5791
5792
5793
5794
5795
5796
5797
5798
5799
5800
5801
5802
5803
5804
5805
5806
5807
5808
5809
5810
5811
5812
5813
5814
5815
5816
5817
5818
5819
5820
5821
5822
5823
5824
5825
5826
5827
5828
5829
5830
5831
5832
5833
5834
5835
5836
5837
5838
5839
5840
5841
5842
5843
5844
5845
5846
5847
5848
5849
5850
5851
5852
5853
5854
5855
5856
5857
5858
5859
5860
5861
5862
5863
5864
5865
5866
5867
5868
5869
5870
5871
5872
5873
5874
5875
5876
5877
5878
5879
5880
5881
5882
5883
5884
5885
5886
5887
5888
5889
5890
5891
5892
5893
5894
5895
5896
5897
5898
5899
5900
5901
5902
5903
5904
5905
5906
5907
5908
5909
5910
5911
5912
5913
5914
5915
5916
5917
5918
5919
5920
5921
5922
5923
5924
5925
5926
5927
5928
5929
5930
5931
5932
5933
5934
5935
5936
5937
5938
5939
5940
5941
5942
5943
5944
5945
5946
5947
5948
5949
5950
5951
5952
5953
5954
5955
5956
5957
5958
5959
5960
5961
5962
5963
5964
5965
5966
5967
5968
5969
5970
5971
5972
5973
5974
5975
5976
5977
5978
5979
5980
5981
5982
5983
5984
5985
5986
5987
5988
5989
5990
5991
5992
5993
5994
5995
5996
5997
5998
5999
6000
6001
6002
6003
6004
6005
6006
6007
6008
6009
6010
6011
6012
6013
6014
6015
6016
6017
6018
6019
6020
6021
6022
6023
6024
6025
6026
6027
6028
6029
6030
6031
6032
6033
6034
6035
6036
6037
6038
6039
6040
6041
6042
6043
6044
6045
6046
6047
6048
6049
6050
6051
6052
6053
6054
6055
6056
6057
6058
6059
6060
6061
6062
6063
6064
6065
6066
6067
6068
6069
6070
6071
6072
6073
6074
6075
6076
6077
6078
6079
6080
6081
6082
6083
6084
6085
6086
6087
6088
6089
6090
6091
6092
6093
6094
6095
6096
6097
6098
6099
6100
6101
6102
6103
6104
6105
6106
6107
6108
6109
6110
6111
6112
6113
6114
6115
6116
6117
6118
6119
6120
6121
6122
6123
6124
6125
6126
6127
6128
6129
6130
6131
6132
6133
6134
6135
6136
6137
6138
6139
6140
6141
6142
6143
6144
6145
6146
6147
6148
6149
6150
6151
6152
6153
6154
6155
6156
6157
6158
6159
6160
6161
6162
6163
6164
6165
6166
6167
6168
6169
6170
6171
6172
6173
6174
6175
6176
6177
6178
6179
6180
6181
6182
6183
6184
6185
6186
6187
6188
6189
6190
6191
6192
6193
6194
6195
6196
6197
6198
6199
6200
6201
6202
6203
6204
6205
6206
6207
6208
6209
6210
6211
6212
6213
6214
6215
6216
6217
6218
6219
6220
6221
6222
6223
6224
6225
6226
6227
6228
6229
6230
6231
6232
6233
6234
6235
6236
6237
6238
6239
6240
6241
6242
6243
6244
6245
6246
6247
6248
6249
6250
6251
6252
6253
6254
6255
6256
6257
6258
6259
6260
6261
6262
6263
6264
6265
6266
6267
6268
6269
6270
6271
6272
6273
6274
6275
6276
6277
6278
6279
6280
6281
6282
6283
6284
6285
6286
6287
6288
6289
6290
6291
6292
6293
6294
6295
6296
6297
6298
6299
6300
6301
6302
6303
6304
6305
6306
6307
6308
6309
6310
6311
6312
6313
6314
6315
6316
6317
6318
6319
6320
6321
6322
6323
6324
6325
6326
6327
6328
6329
6330
6331
6332
6333
6334
6335
6336
6337
6338
6339
6340
6341
6342
6343
6344
6345
6346
6347
6348
6349
6350
6351
6352
6353
6354
6355
6356
6357
6358
6359
6360
6361
6362
6363
6364
6365
6366
6367
6368
6369
6370
6371
6372
6373
6374
6375
6376
6377
6378
6379
6380
6381
6382
6383
6384
6385
6386
6387
6388
6389
6390
6391
6392
6393
6394
6395
6396
6397
6398
6399
6400
6401
6402
6403
6404
6405
6406
6407
6408
6409
6410
6411
6412
6413
6414
6415
6416
6417
6418
6419
6420
6421
6422
6423
6424
6425
6426
6427
6428
6429
6430
6431
6432
6433
6434
6435
6436
6437
6438
6439
6440
6441
6442
6443
6444
6445
6446
6447
6448
6449
6450
6451
6452
6453
6454
6455
6456
6457
6458
6459
6460
6461
6462
6463
6464
6465
6466
6467
6468
6469
6470
6471
6472
6473
6474
6475
6476
6477
6478
6479
6480
6481
6482
6483
6484
6485
6486
6487
6488
6489
6490
6491
6492
6493
6494
6495
6496
6497
6498
6499
6500
6501
6502
6503
6504
6505
6506
6507
6508
6509
6510
6511
6512
6513
6514
6515
6516
6517
6518
6519
6520
6521
6522
6523
6524
6525
6526
6527
6528
6529
6530
6531
6532
6533
6534
6535
6536
6537
6538
6539
6540
6541
6542
6543
6544
6545
6546
6547
6548
6549
6550
6551
6552
6553
6554
6555
6556
6557
6558
6559
6560
6561
6562
6563
6564
6565
6566
6567
6568
6569
6570
6571
6572
6573
6574
6575
6576
6577
6578
6579
6580
6581
6582
6583
6584
6585
6586
6587
6588
6589
6590
6591
6592
6593
6594
6595
6596
6597
6598
6599
6600
6601
6602
6603
6604
6605
6606
6607
6608
6609
6610
6611
6612
6613
6614
6615
6616
6617
6618
6619
6620
6621
6622
6623
6624
6625
6626
6627
6628
6629
6630
6631
6632
6633
6634
6635
6636
6637
6638
6639
6640
6641
6642
6643
6644
6645
6646
6647
6648
6649
6650
6651
6652
6653
6654
6655
6656
6657
6658
6659
6660
6661
6662
6663
6664
6665
6666
6667
6668
6669
6670
6671
6672
6673
6674
6675
6676
6677
6678
6679
6680
6681
6682
6683
6684
6685
6686
6687
6688
6689
6690
6691
6692
6693
6694
6695
6696
6697
6698
6699
6700
6701
6702
6703
6704
6705
6706
6707
6708
6709
6710
6711
6712
6713
6714
6715
6716
6717
6718
6719
6720
6721
6722
6723
6724
6725
6726
6727
6728
6729
6730
6731
6732
6733
6734
6735
6736
6737
6738
6739
6740
6741
6742
6743
6744
6745
6746
6747
6748
6749
6750
6751
6752
6753
6754
6755
6756
6757
6758
6759
6760
6761
6762
6763
6764
6765
6766
6767
6768
6769
6770
6771
6772
6773
6774
6775
6776
6777
6778
6779
6780
6781
6782
6783
6784
6785
6786
6787
6788
6789
6790
6791
6792
6793
6794
6795
6796
6797
6798
6799
6800
6801
6802
6803
6804
6805
6806
6807
6808
6809
6810
6811
6812
6813
6814
6815
6816
6817
6818
6819
6820
6821
6822
6823
6824
6825
6826
6827
6828
6829
6830
6831
6832
6833
6834
6835
6836
6837
6838
6839
6840
6841
6842
6843
6844
6845
6846
6847
6848
6849
6850
6851
6852
6853
6854
6855
6856
6857
6858
6859
6860
6861
6862
6863
6864
6865
6866
6867
6868
6869
6870
6871
6872
6873
6874
6875
6876
6877
6878
6879
6880
6881
6882
6883
6884
6885
6886
6887
6888
6889
6890
6891
6892
6893
6894
6895
6896
6897
6898
6899
6900
6901
6902
6903
6904
6905
6906
6907
6908
6909
6910
6911
6912
6913
6914
6915
6916
6917
6918
6919
6920
6921
6922
6923
6924
6925
6926
6927
6928
6929
6930
6931
6932
6933
6934
6935
6936
6937
6938
6939
6940
6941
6942
6943
6944
6945
6946
6947
6948
6949
6950
6951
6952
6953
6954
6955
6956
6957
6958
6959
6960
6961
6962
6963
6964
6965
6966
6967
6968
6969
6970
6971
6972
6973
6974
6975
6976
6977
6978
6979
6980
6981
6982
6983
6984
6985
6986
6987
6988
6989
6990
6991
6992
6993
6994
6995
6996
6997
6998
6999
7000
7001
7002
7003
7004
7005
7006
7007
7008
7009
7010
7011
7012
7013
7014
7015
7016
7017
7018
7019
7020
7021
7022
7023
7024
7025
7026
7027
7028
7029
7030
7031
7032
7033
7034
7035
7036
7037
7038
7039
7040
7041
7042
7043
7044
7045
7046
7047
7048
7049
7050
7051
7052
7053
7054
7055
7056
7057
7058
7059
7060
7061
7062
7063
7064
7065
7066
7067
7068
7069
7070
7071
7072
7073
7074
7075
7076
7077
7078
7079
7080
7081
7082
7083
7084
7085
7086
7087
7088
7089
7090
7091
7092
7093
7094
7095
7096
7097
7098
7099
7100
7101
7102
7103
7104
7105
7106
7107
7108
7109
7110
7111
7112
7113
7114
7115
7116
7117
7118
7119
7120
7121
7122
7123
7124
7125
7126
7127
7128
7129
7130
7131
7132
7133
7134
7135
7136
7137
7138
7139
7140
7141
7142
7143
7144
7145
7146
7147
7148
7149
7150
7151
7152
7153
7154
7155
7156
7157
7158
7159
7160
7161
7162
7163
7164
7165
7166
7167
7168
7169
7170
7171
7172
7173
7174
7175
7176
7177
7178
7179
7180
7181
7182
7183
7184
7185
7186
7187
7188
7189
7190
7191
7192
7193
7194
7195
7196
7197
7198
7199
7200
7201
7202
7203
7204
7205
7206
7207
7208
7209
7210
7211
7212
7213
7214
7215
7216
7217
7218
7219
7220
7221
7222
7223
7224
7225
7226
7227
7228
7229
7230
7231
7232
7233
7234
7235
7236
7237
7238
7239
7240
7241
7242
7243
7244
7245
7246
7247
7248
7249
7250
7251
7252
7253
7254
7255
7256
7257
7258
7259
7260
7261
7262
7263
7264
7265
7266
7267
7268
7269
7270
7271
7272
7273
7274
7275
7276
7277
7278
7279
7280
7281
7282
7283
7284
7285
7286
7287
7288
7289
7290
7291
7292
7293
7294
7295
7296
7297
7298
7299
7300
7301
7302
7303
7304
7305
7306
7307
7308
7309
7310
7311
7312
7313
7314
7315
7316
7317
7318
7319
7320
7321
7322
7323
7324
7325
7326
7327
7328
7329
7330
7331
7332
7333
7334
7335
7336
7337
7338
7339
7340
7341
7342
7343
7344
7345
7346
7347
7348
7349
7350
7351
7352
7353
7354
7355
7356
7357
7358
7359
7360
7361
7362
7363
7364
7365
7366
7367
7368
7369
7370
7371
7372
7373
7374
7375
7376
7377
7378
7379
7380
7381
7382
7383
7384
7385
7386
7387
7388
7389
7390
7391
7392
7393
7394
7395
7396
7397
7398
7399
7400
7401
7402
7403
7404
7405
7406
7407
7408
7409
7410
7411
7412
7413
7414
7415
7416
7417
7418
7419
7420
7421
7422
7423
7424
7425
7426
7427
7428
7429
7430
7431
7432
7433
7434
7435
7436
7437
7438
7439
7440
7441
7442
7443
7444
7445
7446
7447
7448
7449
7450
7451
7452
7453
7454
7455
7456
7457
7458
7459
7460
7461
7462
7463
7464
7465
7466
7467
7468
7469
7470
7471
7472
7473
7474
7475
7476
7477
7478
7479
7480
7481
/*
*class++
*  Name:
*     TimeFrame

*  Purpose:
*     Time coordinate system description.

*  Constructor Function:
c     astTimeFrame
f     AST_TIMEFRAME

*  Description:
*     A TimeFrame is a specialised form of one-dimensional Frame which
*     represents various coordinate systems used to describe positions in
*     time.
*
*     A TimeFrame represents a moment in time as either an Modified Julian
*     Date (MJD), a Julian Date (JD), a Besselian epoch or a Julian epoch,
*     as determined by the System attribute. Optionally, a zero point can be
*     specified (using attribute TimeOrigin) which results in the TimeFrame
*     representing time offsets from the specified zero point.
*
*     Even though JD and MJD are defined as being in units of days, the
*     TimeFrame class allows other units to be used (via the Unit attribute)
*     on the basis of simple scalings (60 seconds = 1 minute, 60 minutes = 1
*     hour, 24 hours = 1 day, 365.25 days = 1 year). Likewise, Julian epochs
*     can be described in units other than the usual years. Besselian epoch
*     are always represented in units of (tropical) years.
*
*     The TimeScale attribute allows the time scale to be specified (that
*     is, the physical process used to define the rate of flow of time).
*     MJD, JD and Julian epoch can be used to represent a time in any
*     supported time scale. However, Besselian epoch may only be used with the
*     "TT" (Terrestrial Time) time scale. The list of supported time scales
*     includes universal time and siderial time. Strictly, these represent
*     angles rather than time scales, but are included in the list since
*     they are in common use and are often thought of as time scales.
*
*     When a time value is formatted it can be formated either as a simple
*     floating point value, or as a Gregorian date (see the Format
*     attribute).

*  Inheritance:
*     The TimeFrame class inherits from the Frame class.

*  Attributes:
*     In addition to those attributes common to all Frames, every
*     TimeFrame also has the following attributes:
*
*     - AlignTimeScale: Time scale in which to align TimeFrames
*     - LTOffset: The offset of Local Time from UTC, in hours.
*     - TimeOrigin: The zero point for TimeFrame axis values
*     - TimeScale: The timescale used by the TimeFrame
*
*     Several of the Frame attributes inherited by the TimeFrame class
*     refer to a specific axis of the Frame (for instance Unit(axis),
*     Label(axis), etc). Since a TimeFrame is strictly one-dimensional,
*     it allows these attributes to be specified without an axis index.
*     So for instance, "Unit" is allowed in place of "Unit(1)".

*  Functions:
c     In addition to those functions applicable to all Frames, the
c     following functions may also be applied to all TimeFrames:
f     In addition to those routines applicable to all Frames, the
f     following routines may also be applied to all TimeFrames:
*
c     - astCurrentTime: Return the current system time
f     - AST_CURRENTTIME: Return the current system time

*  Copyright:
*     Copyright (C) 1997-2006 Council for the Central Laboratory of the
*     Research Councils

*  Licence:
*     This program is free software: you can redistribute it and/or
*     modify it under the terms of the GNU Lesser General Public
*     License as published by the Free Software Foundation, either
*     version 3 of the License, or (at your option) any later
*     version.
*
*     This program is distributed in the hope that it will be useful,
*     but WITHOUT ANY WARRANTY; without even the implied warranty of
*     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
*     GNU Lesser General Public License for more details.
*
*     You should have received a copy of the GNU Lesser General
*     License along with this program.  If not, see
*     <http://www.gnu.org/licenses/>.

*  Authors:
*     NG: Norman Gray (Starlink)
*     DSB: David Berry (Starlink)

*  History:
*     XX-Aug-2003 (NG):
*        Original version, drawing heavily on specframe.c.
*     20-MAY-2005 (NG):
*        Merged into main AST system.
*     25-MAY-2005 (DSB):
*        Extensive modifications to add extra timescales, unit support,
*        support for relative times, etc, and to make it more like the
*        other AST Frame classes.
*     12-AUG-2005 (DSB):
*        Remove ClockLon and ClockLat attributes. Use the new ObsLon and
*        ObsLat attributes in the parent Frame class instead. Note, for
*        backward compatibility the public attribute accessors and the
*        astLoadTimeFrame functions still recogonise ClockLon and ClockLat,
*        but use the ObsLat/ObsLon attributes internally.
*     1-MAR-2006 (DSB):
*        Replace astSetPermMap within DEBUG blocks by astBeginPM/astEndPM.
*     29-JUN-2006 (DSB):
*        - Activate astAbbrev function for abbreviating leading fields in
*        plot labels.
*        - Include TimeOrigin in default Label.
*     30-JUN-2006 (DSB):
*        When splitting a date/time string into fields, allow each field
*        to include a decimal point.
*     30-JUN-2006 (DSB):
*        Allow astAbbrev to have a null "str1" value.
*     16-OCT-2006 (DSB):
*        Allow conversions between UTC and UT1 (using the new Frame attribute
*     1-NOV-2006 (DSB):
*        Correct sign of longitude passed to TimeMap contrutcorss in
*        function MakeMap.
*     31-JAN-2007 (DSB):
*        Modified so that a TimeFrame can be used as a template to find a
*        TimeFrame contained within a CmpFrame. This involves changes in
*        Match and the removal of the local versions of SetMaxAxes and
*        SetMinAxes.
*     3-SEP-2007 (DSB):
*        In SubFrame, since AlignSystem is extended by the TimeFrame class
*        it needs to be cleared before invoking the parent SubFrame
*        method in cases where the result Frame is not a TimeFrame.
*     2-OCT-2007 (DSB):
*        In Overlay, clear AlignSystem as well as System before calling
*        the parent overlay method.
*     2-OCT-2007 (DSB):
*        Added "LT" (Local Time) time scale.
*     9-DEC-2008 (DSB):
*        Ensure Format string pointer is used correctly.
*     19-JAN-2009 (DSB):
*        Ensure "<bad>" is returned by astFormat if the axis value is bad.
*     31-MAR-2009 (DSB):
*        Extend TimeFrame "iso" Format to allow it to specify the character to
*        place between the time and date strings.
*     15-APR-2009 (DSB):
*        Increase the number of nice calendar time axis gaps allowed by
*        the Gap function. Previously, there was a jump from 1 day to 1
*        year making it difficult to plot calendar axes covering time
*        ranges of the order of 0.5 to 2 years. Now, nice numbers of days
*        are allowed as intermediate gaps. Since months do not all have
*        the same number of days, this means that the day number at major
*        ticks will bounce around a bit.
*     29-APR-2011 (DSB):
*        Prevent astFindFrame from matching a subclass template against a
*        superclass target.
*     16-APR-2015 (DSB):
*        Add more choices when chosing gaps on time axes.
*     17-APR-2015 (DSB):
*        - Added Centre.
*        - Remove some "set but unused" variables.
*     21-APR-2016 (DSB):
*        - Over-ride astFields.
*class--
*/

/* Module Macros. */
/* ============== */
/* Set the name of the class we are implementing. This indicates to
   the header files that define class interfaces that they should make
   "protected" symbols available. */
#define astCLASS TimeFrame

/* Define the first and last acceptable System values. */
#define FIRST_SYSTEM AST__MJD
#define LAST_SYSTEM AST__BEPOCH

/* Define the first and last acceptable TimeScale values. */
#define FIRST_TS AST__TAI
#define LAST_TS AST__LT

/* The supported time scales fall into two groups. Time scales in the
   first group depend on the clock position. That is, transformation
   between a time scale in one group and a timescale in the other group
   requires the clock position, as does transformation between two time
   scales within the first group. Define a macro which tests if a given
   timescale belongs to the first group. */
#define CLOCK_SCALE(ts) \
      ( ( ts == AST__LMST || \
          ts == AST__LAST || \
          ts == AST__TDB || \
          ts == AST__TCB ) ? 1 : 0 )


/* Define a macro which tests if a given timescale requires a Dut1 value
   in order to convert from the timescale to UTC. */
#define DUT1_SCALE(ts) \
      ( ( ts == AST__LMST || \
          ts == AST__LAST || \
          ts == AST__GMST || \
          ts == AST__UT1 ) ? 1 : 0 )

/* Define a macro which tests if a given timescale requires a LTOffset value
   in order to convert from the timescale to UTC. */
#define LTOFFSET_SCALE(ts) \
      ( ( ts == AST__LT ) ? 1 : 0 )

/* The Unix epoch (00:00:00 UTC 1 January 1970 AD) as an absolute MJD in
   the UTC timescale. */
#define UNIX_EPOCH 40587.0

/* Header files. */
/* ============= */
/* Interface definitions. */
/* ---------------------- */

#include "globals.h"             /* Thread-safe global data access */
#include "error.h"               /* Error reporting facilities */
#include "memory.h"              /* Memory allocation facilities */
#include "unit.h"                /* Units management facilities */
#include "globals.h"             /* Thread-safe global data access */
#include "object.h"              /* Base Object class */
#include "timemap.h"             /* Time coordinate Mappings */
#include "frame.h"               /* Parent Frame class */
#include "timeframe.h"           /* Interface definition for this class */
#include "mapping.h"             /* Coordinate Mappings */
#include "cmpmap.h"              /* Compound Mappings */
#include "unitmap.h"             /* Unit Mappings */
#include "shiftmap.h"            /* Shift of origins */
#include "pal.h"              /* SlaLib interface */


/* Error code definitions. */
/* ----------------------- */
#include "ast_err.h"             /* AST error codes */

/* C header files. */
/* --------------- */
#include <stdarg.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#include <stddef.h>
#include <math.h>
#include <time.h>

/* Module Variables. */
/* ================= */

/* Address of this static variable is used as a unique identifier for
   member of this class. */
static int class_check;

/* Pointers to parent class methods which are used or extended by this
   class. */
static AstSystemType (* parent_getalignsystem)( AstFrame *, int * );
static AstSystemType (* parent_getsystem)( AstFrame *, int * );
static double (* parent_centre)( AstFrame *, int, double, double, int * );
static double (* parent_gap)( AstFrame *, int, double, int *, int * );
static const char *(* parent_abbrev)( AstFrame *, int, const char *, const char *, const char *, int * );
static const char *(* parent_format)( AstFrame *, int, double, int * );
static const char *(* parent_getattrib)( AstObject *, const char *, int * );
static const char *(* parent_getdomain)( AstFrame *, int * );
static const char *(* parent_getlabel)( AstFrame *, int, int * );
static const char *(* parent_getsymbol)( AstFrame *, int, int * );
static const char *(* parent_gettitle)( AstFrame *, int * );
static const char *(* parent_getunit)( AstFrame *, int, int * );
static double (* parent_getepoch)( AstFrame *, int * );
static int (* parent_fields)( AstFrame *, int, const char *, const char *, int, char **, int *, double *, int * );
static int (* parent_match)( AstFrame *, AstFrame *, int, int **, int **, AstMapping **, AstFrame **, int * );
static int (* parent_subframe)( AstFrame *, AstFrame *, int, const int *, const int *, AstMapping **, AstFrame **, int * );
static int (* parent_testattrib)( AstObject *, const char *, int * );
static int (* parent_unformat)( AstFrame *, int, const char *, double *, int * );
static void (* parent_clearattrib)( AstObject *, const char *, int * );
static void (* parent_clearsystem)( AstFrame *, int * );
static void (* parent_overlay)( AstFrame *, const int *, AstFrame *, int * );
static void (* parent_setattrib)( AstObject *, const char *, int * );
static void (* parent_setsystem)( AstFrame *, AstSystemType, int * );
static void (* parent_setunit)( AstFrame *, int, const char *, int * );

/* The Unix epoch (00:00:00 UTC 1 January 1970 AD) as an absolute MJD in
   the TAI timescale. */
static double tai_epoch;

/* Define macros for accessing each item of thread specific global data. */
#ifdef THREAD_SAFE

/* Define how to initialise thread-specific globals. */
#define GLOBAL_inits \
   globals->Class_Init = 0; \
   globals->Format_Buff[ 0 ] = 0; \
   globals->GetAttrib_Buff[ 0 ] = 0; \
   globals->GetLabel_Buff[ 0 ] = 0; \
   globals->GetSymbol_Buff[ 0 ] = 0; \
   globals->GetTitle_Buff[ 0 ] = 0; \

/* Create the function that initialises global data for this module. */
astMAKE_INITGLOBALS(TimeFrame)

/* Define macros for accessing each item of thread specific global data. */
#define class_init astGLOBAL(TimeFrame,Class_Init)
#define class_vtab astGLOBAL(TimeFrame,Class_Vtab)
#define format_buff astGLOBAL(TimeFrame,Format_Buff)
#define getattrib_buff astGLOBAL(TimeFrame,GetAttrib_Buff)
#define getlabel_buff astGLOBAL(TimeFrame,GetLabel_Buff)
#define getsymbol_buff astGLOBAL(TimeFrame,GetSymbol_Buff)
#define gettitle_buff astGLOBAL(TimeFrame,GetTitle_Buff)



static pthread_mutex_t mutex2 = PTHREAD_MUTEX_INITIALIZER;
#define LOCK_MUTEX2 pthread_mutex_lock( &mutex2 );
#define UNLOCK_MUTEX2 pthread_mutex_unlock( &mutex2 );

/* If thread safety is not needed, declare and initialise globals at static
   variables. */
#else

/* Buffers for strings returned by various functions. */
static char getattrib_buff[ AST__TIMEFRAME_GETATTRIB_BUFF_LEN + 1 ];
static char format_buff[ AST__TIMEFRAME_FORMAT_BUFF_LEN + 1 ];
static char getlabel_buff[ AST__TIMEFRAME_GETLABEL_BUFF_LEN + 1 ];
static char getsymbol_buff[ AST__TIMEFRAME_GETSYMBOL_BUFF_LEN + 1 ];
static char gettitle_buff[ AST__TIMEFRAME_GETTITLE_BUFF_LEN + 1 ];


/* Define the class virtual function table and its initialisation flag
   as static variables. */
static AstTimeFrameVtab class_vtab;   /* Virtual function table */
static int class_init = 0;       /* Virtual function table initialised? */

#define LOCK_MUTEX2
#define UNLOCK_MUTEX2

#endif


/* Prototypes for Private Member Functions. */
/* ======================================== */
static AstMapping *MakeMap( AstTimeFrame *, AstSystemType, AstSystemType, AstTimeScaleType, AstTimeScaleType, double, double, const char *, const char *, const char *, int * );
static AstSystemType GetAlignSystem( AstFrame *, int * );
static AstSystemType SystemCode( AstFrame *, const char *, int * );
static AstSystemType ValidateSystem( AstFrame *, AstSystemType, const char *, int * );
static AstTimeScaleType TimeScaleCode( const char *, int * );
static const char *DefUnit( AstSystemType, const char *, const char *, int * );
static const char *Format( AstFrame *, int, double, int * );
static const char *GetDomain( AstFrame *, int * );
static const char *GetLabel( AstFrame *, int, int * );
static const char *GetSymbol( AstFrame *, int, int * );
static const char *GetTitle( AstFrame *, int * );
static const char *GetUnit( AstFrame *, int, int * );
static const char *SystemLabel( AstSystemType, int * );
static const char *SystemString( AstFrame *, AstSystemType, int * );
static const char *TimeScaleString( AstTimeScaleType, int * );
static double CurrentTime( AstTimeFrame *, int * );
static double FromMJD( AstTimeFrame *, double, int * );
static double GetEpoch( AstFrame *, int * );
static double GetTimeOriginCur( AstTimeFrame *, int * );
static double ToMJD( AstSystemType, double, int * );
static double ToUnits( AstTimeFrame *, const char *, double, const char *, int * );
static int DateFormat( const char *, int *, char *, int * );
static int Fields( AstFrame *, int, const char *, const char *, int, char **, int *, double *, int * );
static int GetActiveUnit( AstFrame *, int * );
static int MakeTimeMapping( AstTimeFrame *, AstTimeFrame *, AstTimeFrame *, int, AstMapping **, int * );
static int Match( AstFrame *, AstFrame *, int, int **, int **, AstMapping **, AstFrame **, int * );
static int SubFrame( AstFrame *, AstFrame *, int, const int *, const int *, AstMapping **, AstFrame **, int * );
static int TestActiveUnit( AstFrame *, int * );
static void Dump( AstObject *, AstChannel *, int * );
static void OriginScale( AstTimeFrame *, AstTimeScaleType, const char *, int * );
static void OriginSystem( AstTimeFrame *, AstSystemType, const char *, int * );
static void Overlay( AstFrame *, const int *, AstFrame *, int * );
static void SetUnit( AstFrame *, int, const char *, int * );
static void VerifyAttrs( AstTimeFrame *, const char *, const char *, const char *, int * );
static AstMapping *ToMJDMap( AstSystemType, double, int * );
static int Unformat( AstFrame *, int, const char *, double *, int * );
static const char *Abbrev( AstFrame *, int, const char *, const char *, const char *, int * );
static double Centre( AstFrame *, int, double, double, int * );
static double Gap( AstFrame *, int, double, int *, int * );

static AstSystemType GetSystem( AstFrame *, int * );
static void SetSystem( AstFrame *, AstSystemType, int * );
static void ClearSystem( AstFrame *, int * );

static double GetTimeOrigin( AstTimeFrame *, int * );
static int TestTimeOrigin( AstTimeFrame *, int * );
static void ClearTimeOrigin( AstTimeFrame *, int * );
static void SetTimeOrigin( AstTimeFrame *, double, int * );

static double GetLTOffset( AstTimeFrame *, int * );
static int TestLTOffset( AstTimeFrame *, int * );
static void ClearLTOffset( AstTimeFrame *, int * );
static void SetLTOffset( AstTimeFrame *, double, int * );

static const char *GetAttrib( AstObject *, const char *, int * );
static int TestAttrib( AstObject *, const char *, int * );
static void ClearAttrib( AstObject *, const char *, int * );
static void SetAttrib( AstObject *, const char *, int * );

static AstTimeScaleType GetAlignTimeScale( AstTimeFrame *, int * );
static int TestAlignTimeScale( AstTimeFrame *, int * );
static void ClearAlignTimeScale( AstTimeFrame *, int * );
static void SetAlignTimeScale( AstTimeFrame *, AstTimeScaleType, int * );

static AstTimeScaleType GetTimeScale( AstTimeFrame *, int * );
static int TestTimeScale( AstTimeFrame *, int * );
static void ClearTimeScale( AstTimeFrame *, int * );
static void SetTimeScale( AstTimeFrame *, AstTimeScaleType, int * );

/* Member functions. */
/* ================= */
static const char *Abbrev( AstFrame *this_frame, int axis,  const char *fmt,
                           const char *str1, const char *str2, int *status ) {
/*
*  Name:
*     Abbrev

*  Purpose:
*     Abbreviate a formatted Frame axis value by skipping leading fields.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *Abbrev( AstFrame *this, int axis, const char *fmt,
*                         const char *str1, const char *str2, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astAbbrev protected
*     method inherited from the Frame class).

*  Description:
*     This function compares two Frame axis values that have been
*     formatted (using astFormat) and determines if they have any
*     redundant leading fields (i.e. leading fields in common which
*     can be suppressed when tabulating the values or plotting them on
*     the axis of a graph).

*  Parameters:
*     this
*        Pointer to the Frame.
*     axis
*        The number of the Frame axis for which the values have been
*        formatted (axis numbering starts at zero for the first axis).
*     fmt
*        Pointer to a constant null-terminated string containing the
*        format specification used to format the two values.
*     str1
*        Pointer to a constant null-terminated string containing the
*        first formatted value. If this is null, the returned pointer
*        points to the start of the final field in str2.
*     str2
*        Pointer to a constant null-terminated string containing the
*        second formatted value.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A pointer into the "str2" string which locates the first
*     character in the first field that differs between the two
*     formatted values.
*
*     If the two values have no leading fields in common, the returned
*     value will point at the start of string "str2". If the two
*     values are equal, it will point at the terminating null at the
*     end of this string.

*  Notes:
*     - This function assumes that the format specification used was
*     the same when both values were formatted and that they both
*     apply to the same Frame axis.
*     - A pointer to the start of "str2" will be returned if this
*     function is invoked with the global error status set, or if it
*     should fail for any reason.
*-
*/

/* Local Variables: */
   const char *p1;
   const char *p2;
   const char *result;
   int df;
   int nc1;
   int nc2;
   int ndp;

/* Initialise. */
   result = str2;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Validate the axis index. */
   astValidateAxis( this_frame, axis, 1, "astAbbrev" );

/* Use the parent astAbbrev function unless the Format attribute indicates
   that axis values are to be formatted as multi-field date/time strings. */
   df = DateFormat( fmt, &ndp, NULL, status );
   if( !df ) {
      result = (*parent_abbrev)( this_frame, axis,  fmt, str1, str2, status );

/* Otherwise, if no "str1" string was supplied find the start of the
   last field in "str2". */
   } else if( !str1 ){

/* Initialise a pointer to the start of the next field in the "str2" string
   (skip leading spaces). */
      p2 = str2;
      while( *p2 && isspace( *p2 ) ) p2++;

/* Check the entire string, saving the start of the next field as the
   returned pointer. */
      while( *p2 ) {
         result = p2;

/* Each field in a date/time field consists of digits only (and maybe a
   decimal point). Find the number of leading digits/dots in this field
   and increment the point to the following character (the first delimiter
   character). */
         p2 += strspn( p2, "0123456789." );

/* Skip inter-field (non-numeric) delimiters. */
         p2 += strcspn( p2, "0123456789." );
      }

/* Otherwise, if an "str1" string was supplied find the start of the
   first differing field in "str2". */
   } else {

/* Initialise pointers to the start of the next field in each string
   (skip leading spaces). */
      p1 = str1;
      p2 = str2;
      while( *p1 && isspace( *p1 ) ) p1++;
      while( *p2 && isspace( *p2 ) ) p2++;

/* Check the entire string */
      result = p2;
      while( *p1 && *p2 ) {

/* Each field in a date/time field consists of digits only (and maybe a
   decimal point). Find the number of leading digits/dots in each string */
         nc1 = strspn( p1, "0123456789." );
         nc2 = strspn( p2, "0123456789." );

/* If the next field has different lengths in the two strings, or of the
   content of the fields differ, break out of th eloop, leaving "result"
   pointing to the start of the current field. */
         if( nc1 != nc2 || strncmp( p1, p2, nc1 ) ) {
            break;

/* If the next field is identical in the two strings, skip to the
   character following the end of the field. */
         } else {
            p1 += nc1;
            p2 += nc2;

/* Skip inter-field (non-numeric) delimiters. */
            p1 += strcspn( p1, "0123456789." );
            p2 += strcspn( p2, "0123456789." );
         }

/* Prepare to check the next field. */
         result = p2;
      }
   }

/* If an error occurred, clear the returned value. */
   if ( !astOK ) result = str2;

/* Return the result. */
   return result;
}

static double Centre( AstFrame *this_frame, int axis, double value,
                      double gap, int *status ) {
/*
*  Name:
*     Centre

*  Purpose:
*     Find a "nice" central value for tabulating Frame axis values.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     double Centre( AstFrame *this_frame, int axis, double value,
*                    double gap, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the protected astCentre method
*     inherited from the Frame class).

*  Description:
*     This function returns an axis value which produces a nice formatted
*     value suitable for a major tick mark on a plot axis, close to the
*     supplied axis value.

*  Parameters:
*     this
*        Pointer to the Frame.
*     axis
*        The number of the axis (zero-based) for which a central value
*        is to be found.
*     value
*        An arbitrary axis value in the section that is being plotted.
*     gap
*        The gap size.

*  Returned Value:
*     The nice central axis value.

*  Notes:
*     - The supplied axis value is returned if the supplied gap size is
*     zero, or if this function is invoked with the global error status
*     set, or if it should fail for any reason.
*/

/* Local Variables: */
   AstTimeFrame *this;
   char *date1;
   char *date2;
   char *f1;
   char *f2;
   char *fres;
   char *p1;
   char *p2;
   char *pres;
   const char *fmt;
   const char *date;
   double result;
   int df;
   int fmod;
   int nc1;
   int nc2;
   int ndp;
   int nres;
   int v1;
   int v2;

/* Initialise. */
   result = value;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Validate the axis index. */
   astValidateAxis( this_frame, axis, 1, "astCentre" );

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* Use the parent astCentre function unless the Format attribute indicates
   that axis values are to be formatted as multi-field date/time strings. */
   fmt = astGetFormat( this, 0 );
   df = DateFormat( fmt, &ndp, NULL, status );
   if( !df ) {
      result = (*parent_centre)( this_frame, axis, value, gap, status );

/* Otherwise. */
   } else {

/* Format time values one gap above the supplied axis value and one gap below
   it. Take copies of each string since the astFormat buffer will be
   over-written by each call. */
      date = astFormat( this, 0, value - gap );
      if( date ) date1 = astStore( NULL, date, strlen( date ) + 1 );
      date = astFormat( this, 0, value + gap );
      if( date ) date2 = astStore( NULL, date, strlen( date ) + 1 );
      if( astOK ) {

/* Initialise a formatted version of the returned central value to be
   equal to "date1". */
         nres = strlen( date1 );
         fres = astStore( NULL, date1, nres + 1 );

/* Loop over all characters within the first date. */
         fmod = 0;
         nc1 = 0;
         f1 = NULL;
         p1 = date1;
         nc2 = 0;
         f2 = NULL;
         p2 = date2;
         while( 1 ) {

/* If we have not yet found the length of the next numerical field in
   date1, continue looking for it. */
            if( !nc1 ) {

/* If we are currently looking for the start of a numerical field, indicate
   we have found one if the current character is a digit. */
               if( !f1 ) {
                  if( isdigit( *p1 ) ) f1 = p1;

/* If we are currently looking for the end of a numeric field, we have
   found the end if the current character is not a digit. */
               } else {
                  if( !isdigit( *p1 ) ) {
                     nc1 = p1 - f1;
                  }
               }

/* Look at the next character */
               p1++;
            }

/* If we have not yet found the length of the next numerical field in
   date2, continue looking for it. */
            if( !nc2 ) {

/* If we are currently looking for the start of a numerical field, indicate
   we have found one if the current character is a digit. */
               if( !f2 ) {
                  if( isdigit( *p2 ) ) f2 = p2;

/* If we are currently looking for the end of a numeric field, we have
   found the end if the current character is not a digit. */
               } else {
                  if( !isdigit( *p2 ) ) {
                     nc2 = p2 - f2;
                  }
               }

/* Look at the next character */
               p2++;
            }

/* If we have found the next numerical field in both dates, convert them
   to integers. */
            if( nc1 && nc2 ) {
               v1 = atoi( f1 );
               v2 = atoi( f2 );

/* If the values are different, replace this field and all subsequent
   fields with zeros in the formatted version of the returned central
   value, and leave the loop. */
               if( v1 != v2 ) {

                  pres = fres + ( f1 - date1 ) - 1;
                  while( *(++pres) ) {
                     if( isdigit( *pres ) ) *pres = '0';
                  }
                  fmod = 1;

                  break;
               }

/* Prepare to look for the next numerical field in both strings. */
               nc1 = nc2 = 0;
               f1 = f2 = NULL;

/* If either string has been exhausted, leave the loop. */
               if( !*p1 || !*p2 ) break;
            }
         }

/* If the formatted "nice" value was changed, unformatted it to get the
   returned axis value. Otherwise we rettina the returned value set
   earlier. */
         if( fmod ) {
            if( astUnformat( this, 0, fres, &result ) != nres && astOK ) {
               astError( AST__INTER, "astCentre(%s): Error unformatting "
                         "the central time axis value '%s' (internal AST "
                         "programming error).", status, astClass( this ), fres );
            }
         }

/* Free resources. */
         fres = astFree( fres );
      }
      date1 = astFree( date1 );
      date2 = astFree( date2 );
   }

/* If an error occurred, clear the returned value. */
   if ( !astOK ) result = 0.0;

/* Return the result. */
   return result;
}

static int DateFormat( const char *fmt, int *ndp, char *sep, int *status ){
/*
*  Name:
*     DateFormat

*  Purpose:
*     Determine if TimeFrame values should be formatted as a date.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     int DateFormat( const char *fmt, int *ndp, char *sep, int *status )

*  Class Membership:
*     TimeFrame member function

*  Description:
*    This function returns a flag indicating if the supplied Format string
*    requires the TimeFrame value to be formatted as a date and/or time of
*    day.

*  Parameters:
*     fmt
*        Pointer to Format string.
*     ndp
*        A pointer to an integer in which is returned a value indicating
*        if a time is required as well as a date. A value of -1 will be
*        returned in no time is required, otherwise the returned value will
*        equal the number of decimal places required for the seconds field.
*     sep
*        A pointer to a char in which is returned the character that
*        should be used to separate the date and time fields. Ignored if
*        NULL.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Non-zero if the formatted TimeFrame value should include a date.

*/

/* Local Variables: */
   const char *c;
   int nc;
   int result;

/* Initialise  */
   result = 0;
   *ndp = -1;

/* Check the Format string */
   if( fmt ) {

/* Find the first non-white character */
      c = fmt;
      while( *c && isspace( *c ) ) c++;

/* If the first non-white character starts the string "iso"
   assume a date is required. If so see if a time is also required
   (indicated by 1 dot following) and how many seconds of precision are
   required (the interegr following the dot). */
      if( !strncmp( c, "iso", 3 ) ) {
         result = 1;
         if( astSscanf( c, "iso.%d%n", ndp, &nc ) == 1 ) {

/* Check the separate character (if any) at the end of the format string.
   Only "T" is allowed. A space is used if no separator is given. */
            if( sep ) *sep = ( c[ nc ] == 'T' || c[ nc ] == 't' ) ? 'T' : ' ';

         } else {
            *ndp = -1;
         }
      }
   }

   return result;
}

static void ClearAttrib( AstObject *this_object, const char *attrib, int *status ) {
/*
*  Name:
*     ClearAttrib

*  Purpose:
*     Clear an attribute value for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void ClearAttrib( AstObject *this, const char *attrib, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astClearAttrib protected
*     method inherited from the Frame class).

*  Description:
*     This function clears the value of a specified attribute for a
*     TimeFrame, so that the default value will subsequently be used.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     attrib
*        Pointer to a null terminated string specifying the attribute
*        name.  This should be in lower case with no surrounding white
*        space.
*     status
*        Pointer to the inherited status variable.

*  Notes:
*     - This function uses one-based axis numbering so that it is
*     suitable for external (public) use.
*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to the TimeFrame structure */
   char *new_attrib;             /* Pointer value to new attribute name */
   int len;                      /* Length of attrib string */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_object;

/* Obtain the length of the "attrib" string. */
   len = strlen( attrib );

/* Check the attribute name and clear the appropriate attribute. */

/* First look for axis attributes defined by the Frame class. Since a
   TimeFrame has only 1 axis, we allow these attributes to be specified
   without a trailing "(axis)" string. */
   if ( !strcmp( attrib, "direction" ) ||
        !strcmp( attrib, "bottom" ) ||
        !strcmp( attrib, "top" ) ||
        !strcmp( attrib, "format" ) ||
        !strcmp( attrib, "label" ) ||
        !strcmp( attrib, "symbol" ) ||
        !strcmp( attrib, "unit" ) ) {

/* Create a new attribute name from the original by appending the string
   "(1)" and then use the parent ClearAttrib method. */
      new_attrib = astMalloc( len + 4 );
      if( new_attrib ) {
         memcpy( new_attrib, attrib, len );
         memcpy( new_attrib + len, "(1)", 4 );
         (*parent_clearattrib)( this_object, new_attrib, status );
         new_attrib = astFree( new_attrib );
      }

/* AlignTimeScale. */
/* --------------- */
   } else if ( !strcmp( attrib, "aligntimescale" ) ) {
      astClearAlignTimeScale( this );

/* ClockLat. */
/* --------- */
/* Retained for backward compatibility with older versions of AST in which
   TimeFrame had ClockLon/Lat attributes (now ObsLon/Lat are used instead). */
   } else if ( !strcmp( attrib, "clocklat" ) ) {
      astClearAttrib( this, "obslat" );

/* ClockLon. */
/* --------- */
/* Retained for backward compatibility with older versions of AST in which
   TimeFrame had ClockLon/Lat attributes (now ObsLon/Lat are used instead). */
   } else if ( !strcmp( attrib, "clocklon" ) ) {
      astClearAttrib( this, "obslon" );

/* LTOffset. */
/* --------- */
   } else if ( !strcmp( attrib, "ltoffset" ) ) {
      astClearLTOffset( this );

/* TimeOrigin. */
/* ---------- */
   } else if ( !strcmp( attrib, "timeorigin" ) ) {
      astClearTimeOrigin( this );

/* TimeScale. */
/* ---------- */
   } else if ( !strcmp( attrib, "timescale" ) ) {
      astClearTimeScale( this );

/* If the attribute is not recognised, pass it on to the parent method
   for further interpretation. */
   } else {
      (*parent_clearattrib)( this_object, attrib, status );
   }
}

static void ClearSystem( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     ClearSystem

*  Purpose:
*     Clear the System attribute for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void ClearSystem( AstFrame *this_frame, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astClearSystem protected
*     method inherited from the Frame class).

*  Description:
*     This function clears the System attribute for a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*/

/* Local Variables: */
   AstSystemType oldsys;         /* System before clearing */
   AstTimeFrame *this;           /* Pointer to TimeFrame structure */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* Save the original system */
   oldsys = astGetSystem( this_frame );

/* Use the parent ClearSystem method to clear the System value. */
   (*parent_clearsystem)( this_frame, status );

/* Do nothing more if the system has not actually changed. */
   if( astGetSystem( this_frame ) != oldsys ) {

/* Modify the TimeOrigin value to use the new System */
      OriginSystem( this, oldsys, "astClearSystem", status );

/* Clear attributes which have system-specific defaults. */
      astClearLabel( this_frame, 0 );
      astClearSymbol( this_frame, 0 );
      astClearTitle( this_frame );

/* If the old system was BEPOCH also clear units and timescale. This is
   because we need to ensure that TimeScale=TT and Unit=yr will be used
   in future (these are the only acceptable values for System=BEPOCH). */
      if( oldsys == AST__BEPOCH ) {
         astClearUnit( this_frame, 0 );
         astClearTimeScale( (AstTimeFrame *) this_frame );
      }
   }
}

static void ClearTimeScale( AstTimeFrame *this, int *status ) {
/*
*+
*  Name:
*     astClearTimeScale

*  Purpose:
*     Clear the TimeScale attribute for a TimeFrame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "timeframe.h"
*     void astClearTimeScale( AstTimeFrame *this )

*  Class Membership:
*     TimeFrame virtual function

*  Description:
*     This function clears the TimeScale attribute for a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.

*-
*/

/* Check the global error status. */
   if ( !astOK ) return;

/* If the System is currently set to BEPOCH, then the TimeScale will
   either be set to TT or will be unset (since SetTimeScale will not
   allow any other value than TT if the System is BEPOCH). Therefore, if
   System is BEPOCH, we will not need to modify the TimeOrigin value,
   since it will already be appropriate. Otherwise, we modify the
   TimeOrigin value stored in the TimeFrame structure to refer to the
   default timescale (TAI or TT). */
   if( astGetSystem( this ) != AST__BEPOCH ) OriginScale( this, AST__TAI,
                                                     "astClearTimeScale", status );

/* Store a bad value for the timescale in the TimeFrame structure. */
   this->timescale = AST__BADTS;
}

static double CurrentTime( AstTimeFrame *this, int *status ){
/*
*++
*  Name:
c     astCurrentTime
f     AST_CURRENTTIME

*  Purpose:
*     Return the current system time.

*  Type:
*     Public virtual function.

*  Synopsis:
c     #include "timeframe.h"
c     double astCurrentTime( AstTimeFrame *this )
f     RESULT = AST_CURRENTTIME( THIS, STATUS )

*  Class Membership:
*     TimeFrame method.

*  Description:
c     This function
f     This routine
*     returns the current system time, represented in the form specified
*     by the supplied TimeFrame. That is, the returned floating point
*     value should be interpreted using the attribute values of the
*     TimeFrame. This includes System, TimeOrigin, LTOffset, TimeScale,
*     and Unit.

*  Parameters:
c     this
f     THIS = INTEGER (Given)
*        Pointer to the TimeFrame.
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Returned Value:
c     astCurrentTime()
f     AST_CURRENTTIME = DOUBLE
c        A TimeFrame axis value representing the current system time.

*  Notes:
*     - Values of AST__BAD will be returned if this function is
c     invoked with the AST error status set, or if it should fail for
f     invoked with STATUS set to an error value, or if it should fail for
*     any reason.
*     - It is assumes that the system time (returned by the C time()
*     function) follows the POSIX standard, representing a continuous
*     monotonic increasing count of SI seconds since the epoch 00:00:00
*     UTC 1 January 1970 AD (equivalent to TAI with a constant offset).
*     Resolution is one second.
*     - An error will be reported if the TimeFrame has a TimeScale value
*     which cannot be converted to TAI (e.g. "angular" systems such as
*     UT1, GMST, LMST and LAST).
*     - Any inaccuracy in the system clock will be reflected in the value
*     returned by this function.
*--
*/

/* Local Constants: */

/* Local Variables: */
   AstMapping *map;
   double result;
   double systime;

/* Initialise. */
   result = AST__BAD;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get a Mapping from the system time (TAI seconds relative to "tai_epoch")
   to the system represented by the supplied TimeFrame. */
   map = MakeMap( this, AST__MJD, astGetSystem( this ),
                  AST__TAI, astGetTimeScale( this ),
                  tai_epoch, astGetTimeOrigin( this ),
                  "s", astGetUnit( this, 0 ), "astCurrentTime", status );
   if( !map ) {
      astError( AST__INCTS, "astCurrentTime(%s): Cannot convert the "
                "current system time to the required timescale (%s).", status,
                astGetClass( this ),
                TimeScaleString( astGetTimeScale( this ), status ) );

/* Get the system time. The "time" function returns a "time_t" which may be
   encoded in any way. We use "difftime" to convert this into a floating
   point number of seconds by taking the difference between the current
   time and zero time. This assumes nothing about the structure of a
  "time_t" except that zero can be cast into a time_t representing
   the epoch. */
   } else {
      systime = difftime( time( NULL ), (time_t) 0 );

/* Use the Mapping to convert the time into the requied system. */
      astTran1( map, 1, &systime, 1, &result );

/* Free resources */
      map = astAnnul( map );
   }

/* Set result to AST__BAD if an error occurred. */
   if( !astOK ) result = AST__BAD;

/* Return the result. */
   return result;
}

static const char *DefUnit( AstSystemType system, const char *method,
                            const char *class, int *status ){
/*
*  Name:
*     DefUnit

*  Purpose:
*     Return the default units for a time coordinate system type.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *DefUnit( AstSystemType system, const char *method,
*                          const char *class, int *status )

*  Class Membership:
*     TimeFrame member function.

*  Description:
*     This function returns a textual representation of the default
*     units associated with the specified time coordinate system.

*  Parameters:
*     system
*        The time coordinate system.
*     method
*        Pointer to a string holding the name of the calling method.
*        This is only for use in constructing error messages.
*     class
*        Pointer to a string holding the name of the supplied object class.
*        This is only for use in constructing error messages.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A string describing the default units. This string follows the
*     units syntax described in FITS WCS paper I "Representations of world
*     coordinates in FITS" (Greisen & Calabretta).

*  Notes:
*     - A NULL pointer is returned if this function is invoked with
*     the global error status set or if it should fail for any reason.
*/

/* Local Variables: */
   const char *result;           /* Value to return */

/* Initialize */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get an identifier for the default units. */
   if( system == AST__MJD ) {
      result = "d";
   } else if( system == AST__JD ) {
      result = "d";
   } else if( system == AST__BEPOCH ) {
      result = "yr";
   } else if( system == AST__JEPOCH ) {
      result = "yr";

/* Report an error if the coordinate system was not recognised. */
   } else {
      astError( AST__SCSIN, "%s(%s): Corrupt %s contains illegal System "
                "identification code (%d).", status, method, class, class,
                (int) system );
   }

/* Return the result. */
   return result;
}

static int Fields( AstFrame *this_frame, int axis, const char *fmt,
                   const char *str, int maxfld, char **fields,
                   int *nc, double *val, int *status ) {
/*
*  Name:
*     Fields

*  Purpose:
*     Identify numerical fields within a formatted Axis value.

*  Type:
*     Protected virtual function.

*  Synopsis:
*     #include "frame.h"
*     int Fields( AstFrame *this, int axis, const char *fmt,
*                 const char *str, int maxfld, char **fields,
*                 int *nc, double *val )

*  Class Membership:
*     TimeFrame member function (over-rides the astFields protected
*     method inherited from the Frame class).

*  Description:
*     This function identifies the numerical fields within a Frame axis
*     value that has been formatted using astAxisFormat. It assumes that
*     the value was formatted using the supplied format string. It also
*     returns the equivalent floating point value.

*  Parameters:
*     this
*        Pointer to the Frame.
*     axis
*        The number of the Frame axis for which the values have been
*        formatted (axis numbering starts at zero for the first axis).
*     fmt
*        Pointer to a constant null-terminated string containing the
*        format used when creating "str".
*     str
*        Pointer to a constant null-terminated string containing the
*        formatted value.
*     maxfld
*        The maximum number of fields to identify within "str".
*     fields
*        A pointer to an array of at least "maxfld" character pointers.
*        Each element is returned holding a pointer to the start of the
*        corresponding field  in "str" (in the order in which they occur
*        within "str"), or NULL if no corresponding field can be found.
*     nc
*        A pointer to an array of at least "maxfld" integers. Each
*        element is returned holding the number of characters in the
*        corresponding field, or zero if no corresponding field can be
*        found.
*     val
*        Pointer to a location at which to store the value
*        equivalent to the returned field values. If this is NULL,
*        it is ignored.

*  Returned Value:
*     The number of fields succesfully identified and returned.

*  Notes:
*     - Leading and trailing spaces are ignored.
*     - If the formatted value is not consistent with the supplied format
*     string, then a value of zero will be returned, "fields" will be
*     returned holding NULLs, "nc" will be returned holding zeros, and
*     "val" is returned holding VAL__BAD.
*     - Fields are counted from the start of the formatted string. If the
*     string contains more than "maxfld" fields, then trailing fields are
*     ignored.
*/

/* Local Variables: */
   AstTimeFrame *this;
   char *p;
   int bad;
   int df;
   int ifld;
   int ndp;
   int result;
   int state;

/* Initialise. */
   result = 0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astFields" );

/* Call the method inherited from the parent Frame class, unless the
   format string indicates date-time formatting. */
   df = DateFormat( fmt, &ndp, NULL, status );
   if( !df ) {
      result = (*parent_fields)( this_frame, axis, fmt, str, maxfld, fields,
                                 nc, val, status );

/* Now handle date/time formats.... */
   } else {

/* Initialise. */
      for( ifld = 0; ifld < maxfld; ifld++ ) {
         fields[ ifld ] = NULL;
         nc[ ifld ] = 0;
      }
      if( val ) *val = AST__BAD;

/* The formatted string should always include a date in ISO format - three
   integer fields separated by dashes. Loop round each character until
   all characters have been read, or the max number of fields have been
   obtained, or it is shown that the string is badly formatted. */
      bad = 0;
      state = 0;
      ifld = 0;
      p = (char *) str - 1;
      while( *(++p)  && ifld < maxfld && !bad ){

/* Looking for the start of the year field. */
         if( state == 0 ) {
            if( isdigit( *p ) ) {
               fields[ ifld ] = p;
               nc[ ifld ] = 1;
               state = 1;
            } else if( !isspace( *p ) ) {
               bad = 1;
            }

/* Looking for the end of the year field. */
         } else if( state == 1 ) {
            if( isdigit( *p ) ) {
               nc[ ifld ]++;
            } else if( *p != '-' ){
               bad = 1;
            } else {
               state = 2;
               ifld++;
            }

/* Looking for the start of the month field. */
         } else if( state == 2 ) {
            if( isdigit( *p ) ) {
               fields[ ifld ] = p;
               nc[ ifld ] = 1;
               state = 3;
            } else {
               bad = 1;
            }

/* Looking for the end of the month field. */
         } else if( state == 3 ) {
            if( isdigit( *p ) ) {
               nc[ ifld ]++;
            } else if( *p != '-' ){
               bad = 1;
            } else {
               state = 4;
               ifld++;
            }

/* Looking for the start of the day field. */
         } else if( state == 4 ) {
            if( isdigit( *p ) ) {
               fields[ ifld ] = p;
               nc[ ifld ] = 1;
               state = 5;
            } else {
               bad = 1;
            }

/* Looking for the end of the day field. */
         } else if( state == 5 ) {
            if( isdigit( *p ) ) {
               nc[ ifld ]++;
            } else if( *p != ' ' && *p != 'T' ){
               bad = 1;
            } else {
               state = 6;
               ifld++;
            }

/* Looking for the start of the hour field. */
         } else if( state == 6 ) {
            if( isdigit( *p ) ) {
               fields[ ifld ] = p;
               nc[ ifld ] = 1;
               state = 7;
            } else {
               bad = 1;
            }

/* Looking for the end of the hour field. */
         } else if( state == 7 ) {
            if( isdigit( *p ) ) {
               nc[ ifld ]++;
            } else if( *p != ':' ){
               bad = 1;
            } else {
               state = 8;
               ifld++;
            }

/* Looking for the start of the minute field. */
         } else if( state == 8 ) {
            if( isdigit( *p ) ) {
               fields[ ifld ] = p;
               nc[ ifld ] = 1;
               state = 9;
            } else {
               bad = 1;
            }

/* Looking for the end of the minute field. */
         } else if( state == 9 ) {
            if( isdigit( *p ) ) {
               nc[ ifld ]++;
            } else if( *p != ':' ){
               bad = 1;
            } else {
               state = 10;
               ifld++;
            }

/* Looking for the start of the integer part of the seconds field. */
         } else if( state == 10 ) {
            if( isdigit( *p ) ) {
               fields[ ifld ] = p;
               nc[ ifld ] = 1;
               state = 11;
            } else {
               bad = 1;
            }

/* Looking for the end of the integer part of the seconds field. */
         } else if( state == 11 ) {
            if( isdigit( *p ) ) {
               nc[ ifld ]++;
            } else if( *p != '.' ){
               bad = 1;
            } else {
               state = 12;
               ifld++;
            }

/* Looking for the start of the decimal part of the seconds field. */
         } else if( state == 12 ) {
            if( isdigit( *p ) ) {
               fields[ ifld ] = p;
               nc[ ifld ] = 1;
               state = 13;
            } else {
               bad = 1;
            }

/* Looking for the end of the decimal part of the seconds field. */
         } else if( state == 13 ) {
            if( isdigit( *p ) ) {
               nc[ ifld ]++;
            } else if( !isspace( *p ) ){
               bad = 1;
            }

         } else {
            bad = 1;
         }
      }

/* If he string is badly formatted, return null values. */
      if( bad ) {
         result = 0;
         for( ifld = 0; ifld < maxfld; ifld++ ) {
            fields[ ifld ] = NULL;
            nc[ ifld ] = 0;
         }

/* Otherwise, unformat the string if required. */
      } else if( val ) {
         (void) astUnformat( this, axis, str, val );
      }
   }

/* If an error occurred, clear the returned value. */
   if ( !astOK ) result = 0;

/* Return the result. */
   return result;
}

static const char *Format( AstFrame *this_frame, int axis, double value, int *status ) {
/*
*  Name:
*     Format

*  Purpose:
*     Format a coordinate value for a TimeFrame axis.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *Format( AstFrame *this, int axis, double value, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astFormat method inherited
*     from the Frame class).

*  Description:
*     This function returns a pointer to a string containing the formatted
*     (character) version of a coordinate value for a TimeFrame axis. The
*     formatting applied is that specified by a previous invocation of the
*     astSetFormat method. A suitable default format is applied if necessary.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     axis
*        The number of the axis (zero-based) for which formatting is to be
*        performed.
*     value
*        The coordinate value to be formatted, in radians.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A pointer to a null-terminated string containing the formatted value.

*  Notes:
*     -  A NULL pointer will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.
*/

/* Local Variables: */
   astDECLARE_GLOBALS
   AstMapping *map;
   AstSystemType sys;
   AstTimeFrame *this;
   AstTimeScaleType ts;
   char *d;
   char sep;
   char tbuf[ 100 ];
   char sign[ 2 ];
   const char *fmt;
   const char *result;
   const char *u;
   double fd;
   double mjd;
   double off;
   int df;
   int id;
   int ihmsf[ 4 ];
   int im;
   int iy;
   int j;
   int ndp;

/* Initialise */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get a pointer to the structure holding thread-specific global data. */
   astGET_GLOBALS(this_frame);

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astFormat" );

/* Check if a bad coordinate value was supplied and return a pointer to an
   appropriate string if necessary. */
   if ( value == AST__BAD ) {
      result = "<bad>";
   } else {

/* If the format string does not indicate a date/time format, invoke the
   parent Format method. */
      fmt = astGetFormat( this, 0 );
      df = DateFormat( fmt, &ndp, &sep, status );
      if( !df ) {
         result = (*parent_format)( this_frame, axis, value, status );

/* Otherwise, format the value as a date/time */
      } else {

/* Convert the value to an absolute MJD in units of days. */
         ts = astGetTimeScale( this );
         sys = astGetSystem( this );
         off = astGetTimeOrigin( this );
         u = astGetUnit( this, 0 );
         map = MakeMap( this, sys, AST__MJD, ts, ts, off, 0.0, u, "d",
                        "astFormat", status );
         if( map ) {
            astTran1( map, 1, &value, 1, &mjd );
            map = astAnnul( map );

/* If no time fields will be produced, round to the nearest day. */
            if( ndp < 0 ) mjd = (int) ( mjd + 0.5 );

/* Convert the MJD into a set of numeric date fields, plus day fraction,
   and format them. */
            palDjcl( mjd, &iy, &im, &id, &fd, &j );
            d = format_buff;
            d += sprintf( d, "%4d-%2.2d-%2.2d", iy, im, id );

/* If required, convert the day fraction into a set of numerical time
   fields. */
            if( ndp >= 0 ) {
               palDd2tf( ndp, fd, sign, ihmsf );

/* Format the time fields. */
               if( ndp > 0 ) {
                  (void) sprintf( tbuf, "%c%2.2d:%2.2d:%2.2d.%*.*d", sep,
                                  ihmsf[0], ihmsf[1], ihmsf[2], ndp, ndp,
                                  ihmsf[3] );
               } else {
                  (void) sprintf( tbuf, "%c%2.2d:%2.2d:%2.2d", sep, ihmsf[0],
                                  ihmsf[1], ihmsf[2] );
               }

/* Add in the formatted time. */
               d += sprintf( d, "%s", tbuf );

            }
            result = format_buff;
         }
      }
   }

/* If an error occurred, clear the returned value. */
   if ( !astOK ) result = NULL;

/* Return the result. */
   return result;
}

static double FromMJD( AstTimeFrame *this, double oldval, int *status ){
/*
*
*  Name:
*     FromMJD

*  Purpose:
*     Convert a supplied MJD value to the System of the supplied TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     double FromMJD( AstTimeFrame *this, double oldval, int *status )

*  Class Membership:
*     TimeFrame member function

*  Description:
*     This function converts the supplied time value from an MJD to
*     the System of the supplied TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     oldval
*        The value to be converted. It is assume to be an absolute MJD
*        value (i.e. zero offset) in units of days.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The converted value (with zero offset), in the default units
*     associated with the System of "this".

*/

/* Local Variables: */
   AstTimeMap *timemap;
   AstSystemType newsys;
   double args[ 2 ];
   double result;

/* Initialise. */
   result = AST__BAD;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get the System attribute from the supplied TimeFrame. */
   newsys = astGetSystem( this );

/* If this is MJD just return the value unchanged. */
   if( newsys == AST__MJD ) {
      result = oldval;

/* Otherwise create a TimeMap wich converts from the MJD to the required
   system, and use it to transform the supplied value. */
   } else {
      timemap = astTimeMap( 0, "", status );

/* The supplied and returned values are assumed to have zero offset.*/
      args[ 0 ] = 0.0;
      args[ 1 ] = 0.0;

/* If required, add a TimeMap conversion which converts from MJD to the
   new system. */
      if( newsys == AST__JD ) {
         astTimeAdd( timemap, "MJDTOJD", args );

      } else if( newsys == AST__JEPOCH ) {
         astTimeAdd( timemap, "MJDTOJEP", args );

      } else if( newsys == AST__BEPOCH ) {
         astTimeAdd( timemap, "MJDTOBEP", args );
      }

/* Use the TimeMap to convert the supplied value. */
      astTran1( timemap, 1, &oldval, 1, &result );

/* Free resources */
      timemap = astAnnul( timemap );

   }

/* Return the result */
   return result;
}


static double Gap( AstFrame *this_frame, int axis, double gap, int *ntick, int *status ) {
/*
*  Name:
*     Gap

*  Purpose:
*     Find a "nice" gap for tabulating Frame axis values.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     double Gap( AstFrame *this, int axis, double gap, int *ntick, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGap protected
*     method inherited from the Frame class).

*  Description:
*     This function returns a gap size which produces a nicely spaced
*     series of formatted values for a Frame axis, the returned gap
*     size being as close as possible to the supplied target gap
*     size. It also returns a convenient number of divisions into
*     which the gap can be divided.

*  Parameters:
*     this
*        Pointer to the Frame.
*     axis
*        The number of the axis (zero-based) for which a gap is to be found.
*     gap
*        The target gap size.
*     ntick
*        Address of an int in which to return a convenient number of
*        divisions into which the gap can be divided.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The nice gap size.

*  Notes:
*     - A value of zero is returned if the target gap size is zero.
*     - A negative gap size is returned if the supplied gap size is negative.
*     - A value of zero will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstMapping *map;
   AstTimeFrame *this;
   AstTimeScaleType ts;
   const char *fmt;
   double mjdgap;
   double result;
   double xin[2];
   double xout[2];
   int df;
   int ndp;

/* Initialise. */
   result = 0.0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Validate the axis index. */
   astValidateAxis( this_frame, axis, 1, "astGap" );

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* Use the parent astGap function unless the Format attribute indicates
   that axis values are to be formatted as multi-field date/time strings. */
   fmt = astGetFormat( this, 0 );
   df = DateFormat( fmt, &ndp, NULL, status );
   if( !df ) {
      result = (*parent_gap)( this_frame, axis, gap, ntick, status );

/* Otherwise. */
   } else {

/* Get a Mapping which converts TimeFrame values to MJD values. */
      ts = astGetTimeScale( this );
      map = MakeMap( this, astGetSystem( this ), AST__MJD, ts, ts,
                     astGetTimeOrigin( this ), 0.0, astGetUnit( this, 0 ),
                     "d", "astGap", status );
      if( map ) {

/* Use it to transform two TimeFrame times to MJD. The first is the
   current time, and the second is the current time plus the target gap. */
         xin[ 0 ] = astCurrentTime( this );
         xin[ 1 ] = xin[ 0 ] + gap;
         astTran1( map, 2, xin, 1, xout );

/* Find the target MJD gap. */
         mjdgap = xout[ 1 ] - xout[ 0 ];

/* If it is 1 year or more, use the parent astGap method to find a nice
   number of years, and convert back to days. */
         if( mjdgap >= 365.25 ) {
            mjdgap = 365.25*(*parent_gap)( this_frame, axis, mjdgap/365.25, ntick, status );

/* If it is more than 270 days days use 1 year. */
         } else if( mjdgap > 270.0 ) {
            mjdgap = 365.25;
            *ntick = 4;

/* If it is more than 150 days days use 180 days (roughly half a year).
   Use 6 divisions (30 days each, or roughly 1 month). */
         } else if( mjdgap > 150.0 ) {
            mjdgap = 180.0;
            *ntick = 6;

/* If it is more than 90 days days use 120 days (roughly 4 months). */
         } else if( mjdgap > 90.0 ) {
            mjdgap = 120.0;
            *ntick = 4;

/* If it is more than 45 days days use 60 days (roughly 2 months). */
         } else if( mjdgap > 45.0 ) {
            mjdgap = 60.0;
            *ntick = 2;

/* If it is more than 22 days days use 30 days (roughly one month). Use 3
   ten day divisions. */
         } else if( mjdgap > 22.0 ) {
            mjdgap = 30.0;
            *ntick = 3;

/* If it is more than 12 days days use 15 days (roughly half a month). */
         } else if( mjdgap > 12.0 ) {
            mjdgap = 15.0;
            *ntick = 3;

/* If it is more than 7.5 days days use 10 days, with 5 two-day divisions. */
         } else if( mjdgap > 7.5 ) {
            mjdgap = 10.0;
            *ntick = 5;

/* If it is more than 4.5 days days use 5 days. */
         } else if( mjdgap > 4.5 ) {
            mjdgap = 5.0;
            *ntick = 5;

/* If it is more than 3 days days use 4 days. */
         } else if( mjdgap > 3.0 ) {
            mjdgap = 4.0;
            *ntick = 4;

/* If it is more than 1.5 days days use 2 days. */
         } else if( mjdgap > 1.5 ) {
            mjdgap = 2.0;
            *ntick = 2;

/* If it is more than 0.5 of a day use 1 day. */
         } else if( mjdgap > 0.5 ) {
            mjdgap = 1.0;
            *ntick = 4;

/* Otherwise, if the format indicates that no time field is allowed,
   use 1 day. */
         } else if( ndp < 0 ) {
            mjdgap = 1.0;
            *ntick = 2;

/* Otherwise (i.e. if the target gap is 0.5 day or less and the format
   indicates that a time field is allowed), choose a value which looks
   nice. */
         } else if( mjdgap >= 6.0/24.0 ) {    /* 12 hours */
            mjdgap = 12.0/24.0;
            *ntick = 4;

         } else if( mjdgap >= 3.0/24.0 ) {     /* 6 hours */
            mjdgap = 6.0/24.0;
            *ntick = 3;

         } else if( mjdgap >= 1.0/24.0 ) {     /* 2 hours */
            mjdgap = 2.0/24.0;
            *ntick = 4;

         } else if( mjdgap >= 30.0/1440.0 ) {     /* 1 hour */
            mjdgap = 60.0/1440.0;
            *ntick = 4;

         } else if( mjdgap >= 15.0/1440.0 ) {  /* 30 minutes */
            mjdgap = 30.0/1440.0;
            *ntick = 3;

         } else if( mjdgap >= 5.0/1440.0 ) {  /* 10 minutes */
            mjdgap = 10.0/1440.0;
            *ntick = 5;

         } else if( mjdgap >= 2.5/1440.0 ) {  /* 5 minutes */
            mjdgap = 5.0/1440.0;
            *ntick = 5;

         } else if( mjdgap >= 1.0/1440.0 ) {  /* 2 minutes */
            mjdgap = 2.0/1440.0;
            *ntick = 4;

         } else if( mjdgap >= 0.5/1440.0 ) {   /* 1 minute */
            mjdgap = 1.0/1440.0;
            *ntick = 4;

         } else if( mjdgap >= 15.0/86400.0 ) { /* 30 seconds */
            mjdgap = 30.0/86400.0;
            *ntick = 3;

         } else if( mjdgap >= 5.0/86400.0 ) { /* 10 seconds */
            mjdgap = 10.0/86400.0;
            *ntick = 5;

         } else if( mjdgap >= 2.5/86400.0 ) { /* 5 seconds */
            mjdgap = 5.0/86400.0;
            *ntick = 5;

         } else if( mjdgap >= 1.0/86400.0 ) { /* 2 seconds */
            mjdgap = 2.0/86400.0;
            *ntick = 4;

         } else if( mjdgap >= 0.5/86400.0 ) {  /* 1 second */
            mjdgap = 1.0/86400.0;
            *ntick = 4;

         } else {                              /* Less than 1 second */
            mjdgap = 86400.0*(*parent_gap)( this_frame, axis, mjdgap/86400.0, ntick, status );

         }

/* Convert the MJD gap back into the system of the supplied TimeFrame. */
         xout[ 1 ] = xout[ 0 ] + mjdgap;
         astTran1( map, 2, xout, 0, xin );
         result = xin[ 1 ] - xin[ 0 ];

/* Free resources */
         map = astAnnul( map );

/* If no Mapping could be found, use the parent astGap method. */
      } else {
         result = (*parent_gap)( this_frame, axis, gap, ntick, status );
      }
   }

/* If an error occurred, clear the returned value. */
   if ( !astOK ) result = 0.0;

/* Return the result. */
   return result;
}

static int GetActiveUnit( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     GetActiveUnit

*  Purpose:
*     Obtain the value of the ActiveUnit flag for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     int GetActiveUnit( AstFrame *this_frame, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetActiveUnit protected
*     method inherited from the Frame class).

*  Description:
*    This function returns the value of the ActiveUnit flag for a
*    TimeFrame, which is always 1.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The value to use for the ActiveUnit flag (1).

*/
   return 1;
}

static const char *GetAttrib( AstObject *this_object, const char *attrib, int *status ) {
/*
*  Name:
*     GetAttrib

*  Purpose:
*     Get the value of a specified attribute for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *GetAttrib( AstObject *this, const char *attrib, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the protected astGetAttrib
*     method inherited from the Frame class).

*  Description:
*     This function returns a pointer to the value of a specified
*     attribute for a TimeFrame, formatted as a character string.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     attrib
*        Pointer to a null-terminated string containing the name of
*        the attribute whose value is required. This name should be in
*        lower case, with all white space removed.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     - Pointer to a null-terminated string containing the attribute
*     value.

*  Notes:
*     - This function uses one-based axis numbering so that it is
*     suitable for external (public) use.
*     - The returned string pointer may point at memory allocated
*     within the TimeFrame, or at static memory. The contents of the
*     string may be over-written or the pointer may become invalid
*     following a further invocation of the same function or any
*     modification of the TimeFrame. A copy of the string should
*     therefore be made if necessary.
*     - A NULL pointer will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to the TimeFrame structure */
   AstTimeScaleType ts;          /* Time scale */
   astDECLARE_GLOBALS            /* Declare the thread specific global data */
   char *new_attrib;             /* Pointer value to new attribute name */
   const char *result;           /* Pointer value to return */
   double dval;                  /* Attribute value */
   int len;                      /* Length of attrib string */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get a pointer to the structure holding thread-specific global data. */
   astGET_GLOBALS(this_object);

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_object;

/* Obtain the length of the attrib string. */
   len = strlen( attrib );

/* Compare "attrib" with each recognised attribute name in turn,
   obtaining the value of the required attribute. If necessary, write
   the value into "getattrib_buff" as a null-terminated string in an appropriate
   format.  Set "result" to point at the result string. */

/* First look for axis attributes defined by the Frame class. Since a
   TimeFrame has only 1 axis, we allow these attributes to be specified
   without a trailing "(axis)" string. */
   if ( !strcmp( attrib, "direction" ) ||
        !strcmp( attrib, "bottom" ) ||
        !strcmp( attrib, "top" ) ||
        !strcmp( attrib, "format" ) ||
        !strcmp( attrib, "label" ) ||
        !strcmp( attrib, "symbol" ) ||
        !strcmp( attrib, "unit" ) ) {

/* Create a new attribute name from the original by appending the string
   "(1)" and then use the parent GetAttrib method. */
      new_attrib = astMalloc( len + 4 );
      if( new_attrib ) {
         memcpy( new_attrib, attrib, len );
         memcpy( new_attrib + len, "(1)", 4 );
         result = (*parent_getattrib)( this_object, new_attrib, status );
         new_attrib = astFree( new_attrib );
      }

/* AlignTimeScale. */
/* --------------- */
/* Obtain the AlignTimeScale code and convert to a string. */
   } else if ( !strcmp( attrib, "aligntimescale" ) ) {
      ts = astGetAlignTimeScale( this );
      if ( astOK ) {
         result = TimeScaleString( ts, status );

/* Report an error if the value was not recognised. */
         if ( !result ) {
            astError( AST__SCSIN,
                     "astGetAttrib(%s): Corrupt %s contains invalid AlignTimeScale "
                     "identification code (%d).", status, astGetClass( this ),
                     astGetClass( this ), (int) ts );
         }
      }

/* ClockLat. */
/* ------- */
   } else if ( !strcmp( attrib, "clocklat" ) ) {
      result = astGetAttrib( this, "obslat" );

/* ClockLon. */
/* ------- */
   } else if ( !strcmp( attrib, "clocklon" ) ) {
      result = astGetAttrib( this, "obslon" );

/* TimeOrigin. */
/* ----------- */
   } else if ( !strcmp( attrib, "timeorigin" ) ) {
      dval = GetTimeOriginCur( this, status );
      if( astOK ) {
         (void) sprintf( getattrib_buff, "%.*g", DBL_DIG, dval );
         result = getattrib_buff;
      }

/* LTOffset. */
/* --------- */
   } else if ( !strcmp( attrib, "ltoffset" ) ) {
      dval = astGetLTOffset( this );
      if( astOK ) {
         (void) sprintf( getattrib_buff, "%.*g", DBL_DIG, dval );
         result = getattrib_buff;
      }

/* TimeScale. */
/* ---------- */
/* Obtain the TimeScale code and convert to a string. */
   } else if ( !strcmp( attrib, "timescale" ) ) {
      ts = astGetTimeScale( this );
      if ( astOK ) {
         result = TimeScaleString( ts, status );

/* Report an error if the value was not recognised. */
         if ( !result ) {
            astError( AST__SCSIN,
                     "astGetAttrib(%s): Corrupt %s contains invalid TimeScale "
                     "identification code (%d).", status, astGetClass( this ),
                     astGetClass( this ), (int) ts );
         }
      }

/* If the attribute name was not recognised, pass it on to the parent
   method for further interpretation. */
   } else {
      result = (*parent_getattrib)( this_object, attrib, status );
   }

/* Return the result. */
   return result;
}

static double GetTimeOriginCur( AstTimeFrame *this, int *status ) {
/*
*  Name:
*     GetTimeOriginCur

*  Purpose:
*     Obtain the TimeOrigin attribute for a TimeFrame in current units.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     double GetTimeOriginCur( AstTimeFrame *this, int *status )

*  Class Membership:
*     TimeFrame virtual function

*  Description:
*     This function returns the TimeOrigin attribute for a TimeFrame, in
*     the current units of the TimeFrame. The protected astGetTimeOrigin
*     method can be used to obtain the time origin in the default units of
*     the TimeFrame's System.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The TimeOrigin value, in the units, system and timescale specified
*     by the current values of the Unit, System and TimeScale attributes
*     within "this".

*  Notes:
*     - AST__BAD is returned if this function is invoked with
*     the global error status set or if it should fail for any reason.
*/

/* Local Variables: */
   AstMapping *map;
   const char *cur;
   const char *def;
   double result;
   double defval;

/* Initialise. */
   result = AST__BAD;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get the value in the default units */
   result = astGetTimeOrigin( this );

/* If non-zero we convert to the current units.*/
   if( result != 0.0 && result != AST__BAD ) {

/* Get the default units for the TimeFrame's System. */
      def = DefUnit( astGetSystem( this ), "astGetTimeOrigin", "TimeFrame", status );

/* Get the current units from the TimeFrame. */
      cur = astGetUnit( this, 0 );

/* If the units differ, get a Mapping from default to current units. */
      if( cur && def ){
         if( strcmp( cur, def ) ) {
            map = astUnitMapper( def, cur, NULL, NULL );

/* Report an error if the units are incompatible. */
            if( !map ) {
               astError( AST__BADUN, "%s(%s): The current units (%s) are not suitable "
                         "for a TimeFrame.", status, "astGetTimeOrigin", astGetClass( this ),
                         cur );

/* Otherwise, transform the stored origin value.*/
            } else {
               defval = result;
               astTran1( map, 1, &defval, 1, &result );
               map = astAnnul( map );
            }
         }
      }
   }

/* Return the result. */
   return result;
}

static const char *GetDomain( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     GetDomain

*  Purpose:
*     Obtain a pointer to the Domain attribute string for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *GetDomain( AstFrame *this, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetDomain protected
*     method inherited from the Frame class).

*  Description:
*    This function returns a pointer to the Domain attribute string
*    for a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A pointer to a constant null-terminated string containing the
*     Domain value.

*  Notes:
*     - The returned pointer or the string it refers to may become
*     invalid following further invocation of this function or
*     modification of the TimeFrame.
*     - A NULL pointer is returned if this function is invoked with
*     the global error status set or if it should fail for any reason.
*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to TimeFrame structure */
   const char *result;           /* Pointer value to return */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* If a Domain attribute string has been set, invoke the parent method
   to obtain a pointer to it. */
   if ( astTestDomain( this ) ) {
      result = (*parent_getdomain)( this_frame, status );

/* Otherwise, provide a pointer to a suitable default string. */
   } else {
      result = "TIME";
   }

/* Return the result. */
   return result;
}

static double GetEpoch( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     GetEpoch

*  Purpose:
*     Get a value for the Epoch attribute of a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     double GetEpoch( AstFrame *this, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetEpoch method
*     inherited from the Frame class).

*  Description:
*     This function returns a value for the Epoch attribute of a
*     TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The Epoch attribute value.

*  Notes:
*     - A value of AST__BAD will be returned if this function is invoked
*     with the global error status set or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstMapping *map;
   AstSystemType sys;
   AstTimeFrame *this;
   AstTimeScaleType ts;
   const char *u;
   double oldval;
   double result;

/* Initialise. */
   result = AST__BAD;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* If an Epoch attribute value has been set, invoke the parent method
   to obtain it. */
   if ( astTestEpoch( this ) ) {
      result = (*parent_getepoch)( this_frame, status );

/* Otherwise, if the TimeOrigin value is set in the TimeFrame,
   return it, converted to an absolute TDB MJD. */
   } else if( astTestTimeOrigin( this ) ){

/* Get the required properties of the TimeFrame. */
      oldval = astGetTimeOrigin( this );
      ts = astGetTimeScale( this );
      sys = astGetSystem( this );
      u = DefUnit( sys, "astGetEpoch", "TimeFrame", status );

/* Epoch is defined as a TDB value. If the timescale is stored in an angular
   timescale such as UT1, then we would not normally be able to convert it
   to TDB since knowledge of DUT1 is required (the difference between UTC
   and UT1). Since the default Epoch value is not critical we assume a DUT1
   value of zero in this case. We first map the stored value to UT1 then
   from UTC to TDB (using the approximation UT1 == UTC). */
      if( ts == AST__UT1 || ts == AST__GMST ||
          ts == AST__LAST || ts == AST__LMST ) {
         map = MakeMap( this, sys, AST__MJD, ts, AST__UT1, 0.0, 0.0, u,
                        "d", "astGetEpoch", status );
         if( map ) {
            astTran1( map, 1, &oldval, 1, &result );
            map = astAnnul( map );

/* Update the values to use when converting to TBD. */
            oldval = result;
            ts = AST__UTC;
            sys = AST__MJD;
            u = "d";

         } else if( astOK ) {
            astError( AST__INTER, "astGetEpoch(%s): No Mapping from %s to "
                      "UT1 (AST internal programming error).", status,
                      astGetClass( this ), TimeScaleString(  ts, status ) );
         }
      }

/* Now convert to TDB */
      map = MakeMap( this, sys, AST__MJD, ts, AST__TDB, 0.0, 0.0, u,
                     "d", "astGetEpoch", status );
      if( map ) {
         oldval = astGetTimeOrigin( this );
         astTran1( map, 1, &oldval, 1, &result );
         map = astAnnul( map );

      } else if( astOK ) {
         astError( AST__INTER, "astGetEpoch(%s): No Mapping from %s to "
                   "TDB (AST internal programming error).", status,
                   astGetClass( this ), TimeScaleString(  ts, status ) );
      }

/* Otherwise, return the default Epoch value from the parent Frame. */
   } else {
      result =  (*parent_getepoch)( this_frame, status );
   }

/* Return the result. */
   return result;
}

static const char *GetLabel( AstFrame *this, int axis, int *status ) {
/*
*  Name:
*     GetLabel

*  Purpose:
*     Access the Label string for a TimeFrame axis.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *GetLabel( AstFrame *this, int axis, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetLabel method inherited
*     from the Frame class).

*  Description:
*     This function returns a pointer to the Label string for a specified axis
*     of a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     axis
*        Axis index (zero-based) identifying the axis for which information is
*        required.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to a constant null-terminated character string containing the
*     requested information.

*  Notes:
*     -  A NULL pointer will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.
*/

/* Local Variables: */
   astDECLARE_GLOBALS            /* Declare the thread specific global data */
   AstMapping *map;              /* Mapping between units */
   AstSystemType system;         /* Code identifying type of time coordinates */
   char *new_lab;                /* Modified label string */
   const char *fmt;              /* Pointer to original Format string */
   const char *result;           /* Pointer to label string */
   double ltoff;                 /* Local Time offset from UTC (hours) */
   double orig;                  /* Time origin (seconds) */
   int fmtSet;                   /* Was Format attribute set? */
   int ndp;                      /* Number of decimal places for seconds field */

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Get a pointer to the structure holding thread-specific global data. */
   astGET_GLOBALS(this);

/* Initialise. */
   result = NULL;

/* Validate the axis index. */
   astValidateAxis( this, axis, 1, "astGetLabel" );

/* Check if a value has been set for the required axis label string. If so,
   invoke the parent astGetLabel method to obtain a pointer to it. */
   if ( astTestLabel( this, axis ) ) {
      result = (*parent_getlabel)( this, axis, status );

/* Otherwise, provide a suitable default label. */
   } else {

/* If the Format attribute indicates that time values will be formatted
   as dates, then choose a suitable label. */
      fmt = astGetFormat( this, 0 );
      if( DateFormat( fmt, &ndp, NULL, status ) ) {
         result = ( ndp >= 0 ) ? "Date/Time" : "Date";

/* Otherwise, identify the time coordinate system described by the
   TimeFrame. */
      } else {
         system = astGetSystem( this );

/* If OK, supply a pointer to a suitable default label string. */
         if ( astOK ) {
            result = strcpy( getlabel_buff, SystemLabel( system, status ) );
            getlabel_buff[ 0 ] = toupper( getlabel_buff[ 0 ] );

/* If a non-zero TimeOrigin has been specified, include the offset now as a
   date/time string. */
            orig = astGetTimeOrigin( this );
            if( orig != 0.0 ) {

/* Save the Format attribute, and then temporarily set it to give a date/time
   string. */
               fmt = astStore( NULL, fmt, strlen( fmt ) + 1 );
               fmtSet = astTestFormat( this, 0 );
               astSetFormat( this, 0, "iso.0" );

/* Format the origin value as an absolute time and append it to the
   returned label string. Note, the origin always corresponds to a
   TimeFrame axis value of zero. */
               sprintf( getlabel_buff + strlen( getlabel_buff ), " offset from %s",
                        astFormat( this, 0, 0.0 ) );

/* Re-instate the original Format value. */
               if( fmtSet ) {
                  astSetFormat( this, 0, fmt );
               } else {
                  astClearFormat( this, 0 );
               }

/* Free the memory holding the copy of the format string. */
               fmt = astFree( (char *) fmt );

/* If the time of day is "00:00:00", remove it. */
               if( !strcmp( getlabel_buff + strlen( getlabel_buff ) - 8, "00:00:00" ) ) {
                  getlabel_buff[ strlen( getlabel_buff ) - 8 ] = 0;
               }
            }

/* Modify this default to take account of the current value of the Unit
   attribute, if set. */
            if( astTestUnit( this, axis ) ) {

/* Find a Mapping from the default Units for the current System, to the
   units indicated by the Unit attribute. This Mapping is used to modify
   the existing default label appropriately. For instance, if the default
   units is "yr" and the actual units is "log(yr)", then the default label
   of "Julian epoch" is changed to "log( Julian epoch )". */
               map = astUnitMapper( DefUnit( system, "astGetLabel",
                                             astGetClass( this ), status ),
                                    astGetUnit( this, axis ), result,
                                    &new_lab );
               if( new_lab ) {
                  result = strcpy( getlabel_buff, new_lab );
                  new_lab = astFree( new_lab );
               }

/* Annul the unused Mapping. */
               if( map ) map = astAnnul( map );
            }
         }
      }

/* If the time is a Local Time, indicate the offset from UTC. */
      if( astGetTimeScale( this ) == AST__LT ) {
         ltoff = astGetLTOffset( this );
         if( ltoff >= 0.0 ) {
            sprintf( getlabel_buff, "%s (UTC+%g)", result, ltoff );
         } else {
            sprintf( getlabel_buff, "%s (UTC-%g)", result, -ltoff );
         }
         result = getlabel_buff;
      }
   }

/* Return the result. */
   return result;
}

static const char *GetSymbol( AstFrame *this, int axis, int *status ) {
/*
*  Name:
*     GetSymbol

*  Purpose:
*     Obtain a pointer to the Symbol string for a TimeFrame axis.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *GetSymbol( AstFrame *this, int axis, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetSymbol method inherited
*     from the Frame class).

*  Description:
*     This function returns a pointer to the Symbol string for a specified axis
*     of a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     axis
*        Axis index (zero-based) identifying the axis for which information is
*        required.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to a constant null-terminated character string containing the
*     requested information.

*  Notes:
*     -  A NULL pointer will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.
*/

/* Local Variables: */
   astDECLARE_GLOBALS            /* Declare the thread specific global data */
   AstMapping *map;              /* Mapping between units */
   AstSystemType system;         /* Code identifying type of sky coordinates */
   char *new_sym;                /* Modified symbol string */
   const char *result;           /* Pointer to symbol string */

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Get a pointer to the structure holding thread-specific global data. */
   astGET_GLOBALS(this);

/* Initialise. */
   result = NULL;

/* Validate the axis index. */
   astValidateAxis( this, axis, 1, "astGetSymbol" );

/* Check if a value has been set for the required axis symbol string. If so,
   invoke the parent astGetSymbol method to obtain a pointer to it. */
   if ( astTestSymbol( this, axis ) ) {
      result = (*parent_getsymbol)( this, axis, status );

/* Otherwise, identify the sky coordinate system described by the TimeFrame. */
   } else {
      system = astGetSystem( this );

/* If OK, supply a pointer to a suitable default Symbol string. */
      if ( astOK ) {

         if( system == AST__MJD ) {
	    result = "MJD";
         } else if( system == AST__JD ) {
	    result = "JD";
         } else if( system == AST__BEPOCH ) {
	    result = "BEP";
         } else if( system == AST__JEPOCH ) {
	    result = "JEP";

/* Report an error if the coordinate system was not recognised. */
         } else {
	    astError( AST__SCSIN, "astGetSymbol(%s): Corrupt %s contains "
		      "invalid System identification code (%d).", status,
                      astGetClass( this ), astGetClass( this ), (int) system );
         }

/* Modify this default to take account of the current value of the Unit
   attribute, if set. */
         if( astTestUnit( this, axis ) ) {

/* Find a Mapping from the default Units for the current System, to the
   units indicated by the Unit attribute. This Mapping is used to modify
   the existing default symbol appropriately. For instance, if the default
   units is "yr" and the actual units is "log(yr)", then the default symbol
   of "JEP" is changed to "log( JEP )". */
            map = astUnitMapper( DefUnit( system, "astGetSymbol",
                                          astGetClass( this ), status ),
                                 astGetUnit( this, axis ), result,
                                 &new_sym );
            if( new_sym ) {
               result = strcpy( getsymbol_buff, new_sym );
               new_sym = astFree( new_sym );
            }

/* Annul the unused Mapping. */
            if( map ) map = astAnnul( map );

         }
      }
   }

/* Return the result. */
   return result;
}

static AstSystemType GetAlignSystem( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     GetAlignSystem

*  Purpose:
*     Obtain the AlignSystem attribute for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "Specframe.h"
*     AstSystemType GetAlignSystem( AstFrame *this_frame, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetAlignSystem protected
*     method inherited from the Frame class).

*  Description:
*     This function returns the AlignSystem attribute for a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The AlignSystem value.

*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to TimeFrame structure */
   AstSystemType result;         /* Value to return */

/* Initialise. */
   result = AST__BADSYSTEM;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* If a AlignSystem attribute has been set, invoke the parent method to obtain
   it. */
   if ( astTestAlignSystem( this ) ) {
      result = (*parent_getalignsystem)( this_frame, status );

/* Otherwise, provide a suitable default. */
   } else {
      result = AST__MJD;
   }

/* Return the result. */
   return result;
}

static AstTimeScaleType GetAlignTimeScale( AstTimeFrame *this, int *status ) {
/*
*+
*  Name:
*     astGetAlignTimeScale

*  Purpose:
*     Obtain the AlignTimeScale attribute for a TimeFrame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "timeframe.h"
*     AstTimeScaleType GetAlignTimeScale( AstTimeFrame *this )

*  Class Membership:
*     TimeFrame virtual function

*  Description:
*     This function returns the System attribute for a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.

*  Returned Value:
*     The System value.

*  Notes:
*     - AST__BADTS is returned if this function is invoked with
*     the global error status set or if it should fail for any reason.
*-
*/

/* Local Variables: */
   AstTimeScaleType result;
   AstTimeScaleType ts;

/* Initialise. */
   result = AST__BADTS;

/* Check the global error status. */
   if ( !astOK ) return result;

/* If a value has been set, return it. */
   if( this->aligntimescale != AST__BADTS ) {
      result = this->aligntimescale;

/* Otherwise, return a default depending on the current TimeScale value */
   } else {
      ts = astGetTimeScale( this );
      if ( ts == AST__UT1 || ts == AST__LAST || ts == AST__LMST || ts == AST__GMST ) {
         result = AST__UT1;
      } else {
         result = AST__TAI;
      }

   }

/* Return the result. */
   return result;
}

static AstSystemType GetSystem( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     GetSystem

*  Purpose:
*     Obtain the System attribute for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     AstSystemType GetSystem( AstFrame *this_frame, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetSystem protected
*     method inherited from the Frame class).

*  Description:
*     This function returns the System attribute for a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The System value.

*  Notes:
*     - AST__BADSYSTEM is returned if this function is invoked with
*     the global error status set or if it should fail for any reason.
*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to TimeFrame structure */
   AstSystemType result;         /* Value to return */

/* Initialise. */
   result = AST__BADSYSTEM;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* If a System attribute has been set, invoke the parent method to obtain
   it. */
   if ( astTestSystem( this ) ) {
      result = (*parent_getsystem)( this_frame, status );

/* Otherwise, provide a suitable default. */
   } else {
      result = AST__MJD;
   }

/* Return the result. */
   return result;
}

static AstTimeScaleType GetTimeScale( AstTimeFrame *this, int *status ) {
/*
*+
*  Name:
*     astGetTimeScale

*  Purpose:
*     Obtain the TimeScale attribute for a TimeFrame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "timeframe.h"
*     AstTimeScaleType GetTimeScale( AstTimeFrame *this )

*  Class Membership:
*     TimeFrame virtual function

*  Description:
*     This function returns the System attribute for a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.

*  Returned Value:
*     The System value.

*  Notes:
*     - AST__BADTS is returned if this function is invoked with
*     the global error status set or if it should fail for any reason.
*-
*/

/* Local Variables: */
   AstTimeScaleType result;

/* Initialise. */
   result = AST__BADTS;

/* Check the global error status. */
   if ( !astOK ) return result;

/* If a value has been set, return it. */
   if( this->timescale != AST__BADTS ) {
      result = this->timescale;

/* Otherwise, return a default depending on the current System value. */
   } else {
      if ( astGetSystem( this ) == AST__BEPOCH ) {
         result = AST__TT;
      } else {
         result = AST__TAI;
      }

   }

/* Return the result. */
   return result;
}

static const char *GetTitle( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     GetTitle

*  Purpose:
*     Obtain a pointer to the Title string for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *GetTitle( AstFrame *this_frame, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetTitle method inherited
*     from the Frame class).

*  Description:
*     This function returns a pointer to the Title string for a TimeFrame.
*     A pointer to a suitable default string is returned if no Title value has
*     previously been set.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to a null-terminated character string containing the requested
*     information.

*  Notes:
*     -  A NULL pointer will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.
*/

/* Local Variables: */
   astDECLARE_GLOBALS            /* Declare the thread specific global data */
   AstSystemType system;         /* Code identifying type of coordinates */
   AstTimeScaleType ts;          /* Time scale value */
   AstTimeFrame *this;           /* Pointer to TimeFrame structure */
   const char *fmt;              /* Pointer to original Format string */
   const char *result;           /* Pointer to result string */
   double ltoff;                 /* Local Time offset from UTC (hours) */
   double orig;                  /* Time origin (seconds) */
   int fmtSet;                   /* Was Format attribute set? */
   int nc;                       /* No. of characters added */
   int ndp;                      /* Number of decimal places */
   int pos;                      /* Buffer position to enter text */

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Get a pointer to the structure holding thread-specific global data. */
   astGET_GLOBALS(this_frame);

/* Initialise. */
   result = NULL;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* See if a Title string has been set. If so, use the parent astGetTitle
   method to obtain a pointer to it. */
   if ( astTestTitle( this ) ) {
      result = (*parent_gettitle)( this_frame, status );

/* Otherwise, we will generate a default Title string. Obtain the values of the
   TimeFrame's attributes that determine what this string will be. */
   } else {
      system = astGetSystem( this );
      orig = GetTimeOriginCur( this, status );
      ts = astGetTimeScale( this );
      if ( astOK ) {
         result = gettitle_buff;

/* Begin with the system's default label. */
         pos = sprintf( gettitle_buff, "%s", SystemLabel( system, status ) );
         gettitle_buff[ 0 ] = toupper( gettitle_buff[ 0 ] );

/* Append the time scale code, if a value has been set for the timescale.
   Do not do this if the system is BEPOCH since BEPOCH can only be used
   with the TT timescale. */
         if( system != AST__BEPOCH && astTestTimeScale( this ) ) {
            nc = sprintf( gettitle_buff + pos, " [%s", TimeScaleString( ts, status ) );
            pos += nc;

/* For Local Time, include the offset from UTC. */
            if( ts == AST__LT ) {
               ltoff = astGetLTOffset( this );
               if( ltoff >= 0.0 ) {
                  nc = sprintf( gettitle_buff + pos, " (UTC+%g)", ltoff );
               } else {
                  nc = sprintf( gettitle_buff + pos, " (UTC-%g)", -ltoff );
               }
               pos += nc;
            }

/* Close the brackets. */
            nc = sprintf( gettitle_buff + pos, "]" );
            pos += nc;
         }

/* If a non-zero offset has been specified, and the Format attribute does
   not indicate a date string (which is always absolute), include the
   offset now as a date/time string. */
         fmt = astGetFormat( this, 0 );
         if( orig != 0.0 && !DateFormat( fmt, &ndp, NULL, status ) ) {

/* Save the Format attribute, and then temporarily set it to give a date/time
   string. */
            fmt = astStore( NULL, fmt, strlen( fmt ) + 1 );
            fmtSet = astTestFormat( this, 0 );
            astSetFormat( this, 0, "iso.0" );

/* Format the origin value as an absolute time and append it to the
   returned title string. Note, the origin always corresponds to a
   TimeFrame axis value of zero. */
            nc = sprintf( gettitle_buff+pos, " offset from %s",
                          astFormat( this, 0, 0.0 ) );
            pos += nc;

/* Re-instate the original Format value. */
            if( fmtSet ) {
               astSetFormat( this, 0, fmt );
            } else {
               astClearFormat( this, 0 );
            }

/* Free the Format string copy. */
            fmt = astFree( (char *) fmt );

         }
      }
   }

/* If an error occurred, clear the returned pointer value. */
   if ( !astOK ) result = NULL;

/* Return the result. */
   return result;
}

static const char *GetUnit( AstFrame *this_frame, int axis, int *status ) {
/*
*  Name:
*     GetUnit

*  Purpose:
*     Obtain a pointer to the Unit string for a TimeFrame's axis.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *GetUnit( AstFrame *this_frame, int axis )

*  Class Membership:
*     TimeFrame member function (over-rides the astGetUnit method inherited
*     from the Frame class).

*  Description:
*     This function returns a pointer to the Unit string for a specified axis
*     of a TimeFrame. If the Unit attribute has not been set for the axis, a
*     pointer to a suitable default string is returned instead.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     axis
*        The number of the axis (zero-based) for which information is required.

*  Returned Value:
*     A pointer to a null-terminated string containing the Unit value.

*  Notes:
*     -  A NULL pointer will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.
*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to the TimeFrame structure */
   AstSystemType system;         /* The TimeFrame's System value */
   const char *result;           /* Pointer value to return */

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* Validate the axis index. */
   astValidateAxis( this, axis, 1, "astGetUnit" );

/* If a value has been set for the Unit attribute, use the parent
   GetUnit method to return a pointer to the required Unit string. */
   if( astTestUnit( this, axis ) ){
      result = (*parent_getunit)( this_frame, axis, status );

/* Otherwise, identify the time coordinate system described by the
   TimeFrame. */
   } else {
      system = astGetSystem( this );

/* Return a string describing the default units. */
      result = DefUnit( system, "astGetUnit", astGetClass( this ), status );
   }

/* If an error occurred, clear the returned value. */
   if ( !astOK ) result = NULL;

/* Return the result. */
   return result;
}

void astInitTimeFrameVtab_(  AstTimeFrameVtab *vtab, const char *name, int *status ) {
/*
*+
*  Name:
*     astInitTimeFrameVtab

*  Purpose:
*     Initialise a virtual function table for a TimeFrame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "timeframe.h"
*     void astInitTimeFrameVtab( AstTimeFrameVtab *vtab, const char *name )

*  Class Membership:
*     TimeFrame vtab initialiser.

*  Description:
*     This function initialises the component of a virtual function
*     table which is used by the TimeFrame class.

*  Parameters:
*     vtab
*        Pointer to the virtual function table. The components used by
*        all ancestral classes will be initialised if they have not already
*        been initialised.
*     name
*        Pointer to a constant null-terminated character string which contains
*        the name of the class to which the virtual function table belongs (it
*        is this pointer value that will subsequently be returned by the Object
*        astClass function).
*-
*/

/* Local Variables: */
   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
   AstFrameVtab *frame;          /* Pointer to Frame component of Vtab */
   AstMapping *map;              /* Temporary Maping */
   AstObjectVtab *object;        /* Pointer to Object component of Vtab */
   double utc_epoch;             /* Unix epoch as a UTC MJD */

/* Check the local error status. */
   if ( !astOK ) return;

/* Get a pointer to the thread specific global data structure. */
   astGET_GLOBALS(NULL);

/* Initialize the component of the virtual function table used by the
   parent class. */
   astInitFrameVtab( (AstFrameVtab *) vtab, name );

/* Store a unique "magic" value in the virtual function table. This
   will be used (by astIsATimeFrame) to determine if an object belongs
   to this class.  We can conveniently use the address of the (static)
   class_check variable to generate this unique value. */
   vtab->id.check = &class_check;
   vtab->id.parent = &(((AstFrameVtab *) vtab)->id);

/* Initialise member function pointers. */
/* ------------------------------------ */
/* Store pointers to the member functions (implemented here) that
   provide virtual methods for this class. */

   vtab->ClearAlignTimeScale = ClearAlignTimeScale;
   vtab->TestAlignTimeScale = TestAlignTimeScale;
   vtab->GetAlignTimeScale = GetAlignTimeScale;
   vtab->SetAlignTimeScale = SetAlignTimeScale;

   vtab->ClearTimeOrigin = ClearTimeOrigin;
   vtab->TestTimeOrigin = TestTimeOrigin;
   vtab->GetTimeOrigin = GetTimeOrigin;
   vtab->SetTimeOrigin = SetTimeOrigin;

   vtab->ClearLTOffset = ClearLTOffset;
   vtab->TestLTOffset = TestLTOffset;
   vtab->GetLTOffset = GetLTOffset;
   vtab->SetLTOffset = SetLTOffset;

   vtab->ClearTimeScale = ClearTimeScale;
   vtab->TestTimeScale = TestTimeScale;
   vtab->GetTimeScale = GetTimeScale;
   vtab->SetTimeScale = SetTimeScale;

   vtab->CurrentTime = CurrentTime;

/* Save the inherited pointers to methods that will be extended, and
   replace them with pointers to the new member functions. */
   object = (AstObjectVtab *) vtab;
   frame = (AstFrameVtab *) vtab;

   parent_clearattrib = object->ClearAttrib;
   object->ClearAttrib = ClearAttrib;
   parent_getattrib = object->GetAttrib;
   object->GetAttrib = GetAttrib;
   parent_setattrib = object->SetAttrib;
   object->SetAttrib = SetAttrib;
   parent_testattrib = object->TestAttrib;
   object->TestAttrib = TestAttrib;

   parent_getdomain = frame->GetDomain;
   frame->GetDomain = GetDomain;

   parent_getsystem = frame->GetSystem;
   frame->GetSystem = GetSystem;
   parent_setsystem = frame->SetSystem;
   frame->SetSystem = SetSystem;
   parent_clearsystem = frame->ClearSystem;
   frame->ClearSystem = ClearSystem;

   parent_getalignsystem = frame->GetAlignSystem;
   frame->GetAlignSystem = GetAlignSystem;

   parent_getlabel = frame->GetLabel;
   frame->GetLabel = GetLabel;

   parent_getsymbol = frame->GetSymbol;
   frame->GetSymbol = GetSymbol;

   parent_gettitle = frame->GetTitle;
   frame->GetTitle = GetTitle;

   parent_getepoch = frame->GetEpoch;
   frame->GetEpoch = GetEpoch;

   parent_getunit = frame->GetUnit;
   frame->GetUnit = GetUnit;

   parent_setunit = frame->SetUnit;
   frame->SetUnit = SetUnit;

   parent_match = frame->Match;
   frame->Match = Match;

   parent_overlay = frame->Overlay;
   frame->Overlay = Overlay;

   parent_subframe = frame->SubFrame;
   frame->SubFrame = SubFrame;

   parent_format = frame->Format;
   frame->Format = Format;

   parent_unformat = frame->Unformat;
   frame->Unformat = Unformat;

   parent_abbrev = frame->Abbrev;
   frame->Abbrev = Abbrev;

   parent_fields = frame->Fields;
   frame->Fields = Fields;

   parent_gap = frame->Gap;
   frame->Gap = Gap;

   parent_centre = frame->Centre;
   frame->Centre = Centre;

/* Store replacement pointers for methods which will be over-ridden by new
   member functions implemented here. */
   frame->GetActiveUnit = GetActiveUnit;
   frame->TestActiveUnit = TestActiveUnit;
   frame->ValidateSystem = ValidateSystem;
   frame->SystemString = SystemString;
   frame->SystemCode = SystemCode;

/* Declare the copy constructor, destructor and class dump
   function. */
   astSetDump( vtab, Dump, "TimeFrame",
               "Description of time coordinate system" );

/* Convert the Unix Epoch (00:00:00 UTC 1 January 1970 AD) from UTC to TAI. */
   LOCK_MUTEX2
   map = MakeMap( NULL, AST__MJD, AST__MJD, AST__UTC, AST__TAI,
                  0.0, 0.0, "d", "d", "astInitTimeFrameVtab", status );
   utc_epoch = UNIX_EPOCH;
   astTran1( map, 1, &utc_epoch, 1, &tai_epoch );
   map = astAnnul( map );
   UNLOCK_MUTEX2

/* If we have just initialised the vtab for the current class, indicate
   that the vtab is now initialised, and store a pointer to the class
   identifier in the base "object" level of the vtab. */
   if( vtab == &class_vtab ) {
      class_init = 1;
      astSetVtabClassIdentifier( vtab, &(vtab->id) );
   }
}

static AstMapping *MakeMap( AstTimeFrame *this, AstSystemType sys1,
                            AstSystemType sys2, AstTimeScaleType ts1,
                            AstTimeScaleType ts2, double off1, double off2,
                            const char *unit1, const char *unit2,
                            const char *method, int *status ){
/*
*  Name:
*     MakeMap

*  Purpose:
*     Make a Mapping between stated timescales and systems.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     AstMapping *MakeMap( AstTimeFrame *this, AstSystemType sys1,
*                          AstSystemType sys2, AstTimeScaleType ts1,
*                          AstTimeScaleType ts2, double off1, double off2,
*                          const char *unit1, const char unit2,
*                          const char *method, int *status )

*  Class Membership:
*     TimeFrame member function

*  Description:
*     This function creates a Mapping from a stated pair of System and
*     TimeScale to another stated pair.

*  Parameters:
*     this
*        A TimeFrame which specifies extra attributes (the clock position,
*        time zone, etc) for both input and output.
*     sys1
*        The input System.
*     sys2
*        The output System.
*     ts1
*        The input System.
*     ts2
*        The output System.
*     off1
*        The axis offset used with the input, in the defaults units
*        associated with "sys1".
*     off2
*        The axis offset used with the output, in the defaults units
*        associated with "sys2".
*     unit1
*        The input units.
*     unit2
*        The output units.
*     method
*        A string containing the method name to include in error messages.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A pointer to the new Mapping. NULL if the timescales were
*     incompatible.

*/


/* Local Variables: */
   AstMapping *result;
   AstMapping *tmap;
   AstMapping *tmap2;
   AstMapping *umap;
   AstMapping *umap1;
   AstMapping *umap2;
   AstTimeMap *timemap;
   const char *du;
   double args[ 4 ];
   double args_lt[ 1 ];
   double args_ut[ 1 ];
   double shift;

/* Check the global error status. */
   result = NULL;
   if ( !astOK ) return result;

/* If the timescales are equal... */
   if( ts1 == ts2 ) {

/* and the time systems are equal... */
      if( sys1 == sys2 ) {

/* and the time offsets are equal... */
         if( astEQUALS( off1, off2, 1.0E3 ) ) {

/* and the units are equal, return a UnitMap. */
            if( !strcmp( unit1, unit2 ) ) {
               result = (AstMapping *) astUnitMap( 1, "", status );

/* If only the units differ, return the appropriate units Mapping. */
            } else {
               result = astUnitMapper( unit1, unit2, NULL, NULL );
            }

/* If the time offsets differ... */
         } else {

/* Transform the difference in offsets from the default units associated
   with the (common) system, to the units associated with the output. */
            shift = off1 - off2;
            du = DefUnit( sys1, method, "TimeFrame", status );
            if( du && strcmp( du, unit2 ) && shift != 0.0 ) {
               umap = astUnitMapper( DefUnit( sys1, method, "TimeFrame", status ),
                                     unit2, NULL, NULL );
               astTran1( umap, 1, &shift, 1, &shift );
               umap = astAnnul( umap );
            }

/* Create a ShiftMap to apply the shift. */
            result = (AstMapping *) astShiftMap( 1, &shift, "", status );

/* If the input and output units also differ, include the appropriate units
   Mapping. */
            if( strcmp( unit1, unit2 ) ) {
               umap = astUnitMapper( unit1, unit2, NULL, NULL );
               tmap = (AstMapping *) astCmpMap( umap, result, 1, "", status );
               umap = astAnnul( umap );
               (void) astAnnul( result );
               result = tmap;
            }
         }
      }
   }

/* If the systems and/or timescales differ, we convert first from the
   input frame to a common frame, then from the common frame to the output
   frame. */
   if( !result ) {

/* First, a Mapping from the input units to the default units for the
   input System (these are the units expected by the TimeMap conversions). */
      umap1 = astUnitMapper( unit1, DefUnit( sys1, method, "TimeFrame", status ),
                             NULL, NULL );

/* Now create a null TimeMap. */
      timemap = astTimeMap( 0, "", status );

/* Store the input time offsets to use. They correspond to the same moment in
   time (the second is the MJD equivalent of the first). */
      args[ 0 ] = off1;
      args[ 1 ] = ToMJD( sys1, off1, status );

/* Add a conversion from the input System to MJD. */
      if( sys1 == AST__JD ) {
         astTimeAdd( timemap, "JDTOMJD", args );

      } else if( sys1 == AST__JEPOCH ) {
         astTimeAdd( timemap, "JEPTOMJD", args );

      } else if( sys1 == AST__BEPOCH ) {
         astTimeAdd( timemap, "BEPTOMJD", args );
      }

/* All timescale conversions except UTTOUTC and UTCTOUT require the input (MJD)
   offset as the first argument. In general, the observers longitude, latitude
   and altitude are also needed. The Frame class stores longitude values in a
   +ve eastwards sense, but the TimeMap class needs +ve westwards, so negate
   the longitude. */
      args[ 0 ] = args[ 1 ];
      args[ 1 ] = this ? -astGetObsLon( this ) : 0.0;
      args[ 2 ] = this ? astGetObsLat( this ) : 0.0;
      args[ 3 ] = this ? astGetObsAlt( this ) : 0.0;

/* The UTTOUTC and UTCTOUT conversions required just the DUT1 value. */
      args_ut[ 0 ] = this ? astGetDut1( this ) : 0.0;

/* The LTTOUTC and UTCTOLT conversions required just the time zone
   correction. */
      args_lt[ 0 ] = this ? astGetLTOffset( this ) : 0.0;

/* If the input and output timescales differ, now add a conversion from the
   input timescale to TAI. */
      if( ts1 != ts2 ) {
         if( ts1 == AST__TAI ) {

         } else if( ts1 == AST__UTC ) {
            astTimeAdd( timemap, "UTCTOTAI", args );

         } else if( ts1 == AST__TT ) {
            astTimeAdd( timemap, "TTTOTAI", args );

         } else if( ts1 == AST__TDB ) {
            astTimeAdd( timemap, "TDBTOTT", args );
            astTimeAdd( timemap, "TTTOTAI", args );

         } else if( ts1 == AST__TCG ) {
            astTimeAdd( timemap, "TCGTOTT", args );
            astTimeAdd( timemap, "TTTOTAI", args );

         } else if( ts1 == AST__LT ) {
            astTimeAdd( timemap, "LTTOUTC", args_lt );
            astTimeAdd( timemap, "UTCTOTAI", args );

         } else if( ts1 == AST__TCB ) {
            astTimeAdd( timemap, "TCBTOTDB", args );
            astTimeAdd( timemap, "TDBTOTT", args );
            astTimeAdd( timemap, "TTTOTAI", args );

         } else if( ts1 == AST__UT1 ) {
            astTimeAdd( timemap, "UTTOUTC", args_ut );
            astTimeAdd( timemap, "UTCTOTAI", args );

         } else if( ts1 == AST__GMST ) {
            astTimeAdd( timemap, "GMSTTOUT", args );
            astTimeAdd( timemap, "UTTOUTC", args_ut );
            astTimeAdd( timemap, "UTCTOTAI", args );

         } else if( ts1 == AST__LAST ) {
            astTimeAdd( timemap, "LASTTOLMST", args );
            astTimeAdd( timemap, "LMSTTOGMST", args );
            astTimeAdd( timemap, "GMSTTOUT", args );
            astTimeAdd( timemap, "UTTOUTC", args_ut );
            astTimeAdd( timemap, "UTCTOTAI", args );

         } else if( ts1 == AST__LMST ) {
            astTimeAdd( timemap, "LMSTTOGMST", args );
            astTimeAdd( timemap, "GMSTTOUT", args );
            astTimeAdd( timemap, "UTTOUTC", args_ut );
            astTimeAdd( timemap, "UTCTOTAI", args );
         }

/* Now add a conversion from TAI to the output timescale. */
         if( ts2 == AST__TAI ) {

         } else if( ts2 == AST__UTC ) {
            astTimeAdd( timemap, "TAITOUTC", args );

         } else if( ts2 == AST__TT ) {
            astTimeAdd( timemap, "TAITOTT", args );

         } else if( ts2 == AST__TDB ) {
            astTimeAdd( timemap, "TAITOTT", args );
            astTimeAdd( timemap, "TTTOTDB", args );

         } else if( ts2 == AST__TCG ) {
            astTimeAdd( timemap, "TAITOTT", args );
            astTimeAdd( timemap, "TTTOTCG", args );

         } else if( ts2 == AST__TCB ) {
            astTimeAdd( timemap, "TAITOTT", args );
            astTimeAdd( timemap, "TTTOTDB", args );
            astTimeAdd( timemap, "TDBTOTCB", args );

         } else if( ts2 == AST__UT1 ) {
            astTimeAdd( timemap, "TAITOUTC", args );
            astTimeAdd( timemap, "UTCTOUT", args_ut );

         } else if( ts2 == AST__GMST ) {
            astTimeAdd( timemap, "TAITOUTC", args );
            astTimeAdd( timemap, "UTCTOUT", args_ut );
            astTimeAdd( timemap, "UTTOGMST", args );

         } else if( ts2 == AST__LAST ) {
            astTimeAdd( timemap, "TAITOUTC", args );
            astTimeAdd( timemap, "UTCTOUT", args_ut );
            astTimeAdd( timemap, "UTTOGMST", args );
            astTimeAdd( timemap, "GMSTTOLMST", args );
            astTimeAdd( timemap, "LMSTTOLAST", args );

         } else if( ts2 == AST__LMST ) {
            astTimeAdd( timemap, "TAITOUTC", args );
            astTimeAdd( timemap, "UTCTOUT", args_ut );
            astTimeAdd( timemap, "UTTOGMST", args );
            astTimeAdd( timemap, "GMSTTOLMST", args );

         } else if( ts2 == AST__LT ) {
            astTimeAdd( timemap, "TAITOUTC", args );
            astTimeAdd( timemap, "UTCTOLT", args_lt );

         }
      }

/* Add a conversion from MJD to the output System, if needed. */
      args[ 1 ] = off2;
      if( sys2 == AST__MJD ) {
         if( args[ 0 ] != off2 ) astTimeAdd( timemap, "MJDTOMJD", args );

      } else if( sys2 == AST__JD ) {
         astTimeAdd( timemap, "MJDTOJD", args );

      } else if( sys2 == AST__JEPOCH ) {
         astTimeAdd( timemap, "MJDTOJEP", args );

      } else if( sys2 == AST__BEPOCH ) {
         astTimeAdd( timemap, "MJDTOBEP", args );
      }

/* Now, create a Mapping from the default units for the output System (these
   are the units produced by the TimeMap conversions) to the requested
   output units. */
      umap2 = astUnitMapper( DefUnit( sys2, method, "TimeFrame", status ), unit2,
                             NULL, NULL );

/* If OK, combine the Mappings in series. Note, umap1 and umap2 should
   always be non-NULL because the suitablity of units strings is checked
   within OriginSystem - called from within SetSystem. */
      if( umap1 && umap2 ) {
         tmap = (AstMapping *) astCmpMap( umap1, timemap, 1, "", status );
         tmap2 = (AstMapping *) astCmpMap( tmap, umap2, 1, "", status );
         tmap = astAnnul( tmap );
         result = astSimplify( tmap2 );
         tmap2 = astAnnul( tmap2 );
      }

/* Free remaining resources */
      if( umap1 ) umap1 = astAnnul( umap1 );
      if( umap2 ) umap2 = astAnnul( umap2 );
      timemap = astAnnul( timemap );
   }

/* Return NULL if an error has occurred. */
   if( !astOK ) result = astAnnul( result );

/* Return the result. */
   return result;

}

static int MakeTimeMapping( AstTimeFrame *target, AstTimeFrame *result,
                            AstTimeFrame *align_frm, int report,
                            AstMapping **map, int *status ) {
/*
*  Name:
*     MakeTimeMapping

*  Purpose:
*     Generate a Mapping between two TimeFrames.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     int MakeTimeMapping( AstTimeFrame *target, AstTimeFrame *result,
*                          AstTimeFrame *align_frm, int report,
*                          AstMapping **map, int *status ) {

*  Class Membership:
*     TimeFrame member function.

*  Description:
*     This function takes two TimeFrames and generates a Mapping that
*     converts between them, taking account of differences in their
*     coordinate systems, offsets, timescales, units, etc.

*  Parameters:
*     target
*        Pointer to the first TimeFrame.
*     result
*        Pointer to the second TimeFrame.
*     align_frm
*        A TimeFrame defining the system and time scale in which to
*        align the target and result TimeFrames. The AlignSystem and
*        AlignTimeScale attributes are used for this purpose.
*     report
*        Should errors be reported if no match is possible? These reports
*        will describe why no match was possible.
*     map
*        Pointer to a location which is to receive a pointer to the
*        returned Mapping. The forward transformation of this Mapping
*        will convert from "target" coordinates to "result"
*        coordinates, and the inverse transformation will convert in
*        the opposite direction (all coordinate values in radians).
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Non-zero if the Mapping could be generated, or zero if the two
*     TimeFrames are sufficiently un-related that no meaningful Mapping
*     can be produced (albeit an "unmeaningful" Mapping will be returned
*     in this case, which will need to be annulled).

*  Notes:
*     A value of zero is returned if this function is invoked with the
*     global error status set or if it should fail for any reason.
*/

/* Local Variables: */
   AstMapping *map1;             /* Intermediate Mapping */
   AstMapping *map2;             /* Intermediate Mapping */
   AstMapping *tmap;             /* Intermediate Mapping */
   AstSystemType sys1;           /* Code to identify input system */
   AstSystemType sys2;           /* Code to identify output system */
   AstTimeScaleType align_ts;    /* Alignment time scale */
   AstTimeScaleType ts1;         /* Input time scale */
   AstTimeScaleType ts2;         /* Output time scale */
   const char *align_unit;       /* Units used for alignment */
   const char *u1;               /* Input target units */
   const char *u2;               /* Output target units */
   double align_off;             /* Axis offset */
   double ltoff1;                /* Input axis Local Time offset */
   double ltoff2;                /* Output axis Local Time offset */
   double off1;                  /* Input axis offset */
   double off2;                  /* Output axis offset */
   int arclk;                    /* Align->result depends on clock position? */
   int ardut;                    /* Align->result depends on Dut1? */
   int arlto;                    /* Align->result depends on LT offset? */
   int clkdiff;                  /* Do target and result clock positions differ? */
   int dut1diff;                 /* Do target and result Dut1 values differ? */
   int ltodiff;                  /* Do target and result LTOffset values differ? */
   int match;                    /* Mapping can be generated? */
   int taclk;                    /* Target->align depends on clock position? */
   int tadut;                    /* Target->align depends on Dut1? */
   int talto;                    /* Target->align depends on LT offset? */

/* Check the global error status. */
   if ( !astOK ) return 0;

/* Initialise the returned values. */
   match = 0;
   *map = NULL;

/* Get the required properties of the input (target) TimeFrame */
   sys1 = astGetSystem( target );
   ts1 = astGetTimeScale( target );
   off1 = astGetTimeOrigin( target );
   u1 = astGetUnit( target, 0 );
   ltoff1= astGetLTOffset( target );

/* Get the required properties of the output (result) TimeFrame */
   sys2 = astGetSystem( result );
   ts2 = astGetTimeScale( result );
   off2 = astGetTimeOrigin( result );
   u2 = astGetUnit( result, 0 );
   ltoff2= astGetLTOffset( result );

/* Get the timescale in which alignment is to be performed. The alignment
   System does not matter since they all supported time systems are linearly
   related, and so the choice of alignment System has no effect on the total
   Mapping. We arbitrarily choose MJD as the alignment System (if needed). */
   align_ts = astGetAlignTimeScale( align_frm );

/* The main difference between this function and the MakeMap function is
   that this function takes account of the requested alignment frame. But
   the alignment Frame only makes a difference to the overall Mapping if
   1) the observer's positions are different in the target and result Frame,
   and 2) one or both of the Mappings to or from the alignment frame depends
   on the observer's position. If either of these 2 conditions is not met,
   then the alignment frame can be ignored, and the simpler MakeMap function
   can be called. See if the observer's positions differ. */
   clkdiff = ( astGetObsLon( target ) != astGetObsLon( result ) ||
               astGetObsLat( target ) != astGetObsLat( result ) ||
               astGetObsAlt( target ) != astGetObsAlt( result ) );

/* See if the Mapping from target to alignment frame depends on the
   observer's position. */
   taclk = CLOCK_SCALE( ts1 ) || CLOCK_SCALE( align_ts );

/* See if the Mapping from alignment to result frame depends on the
   observer's position. */
   arclk = CLOCK_SCALE( align_ts ) || CLOCK_SCALE( ts2 );

/* In addition, the alignment frame is significant if either of the Mappings
   depends on DUT1 and the values of the DUT1 attribute are different for the
   two TimeFrames. */
   dut1diff = ( astGetDut1( target ) != astGetDut1( result ) );
   tadut = DUT1_SCALE( ts1 ) != DUT1_SCALE( align_ts );
   ardut = DUT1_SCALE( align_ts ) != DUT1_SCALE( ts2 );

/* In addition, the alignment frame is significant if either of the Mappings
   depends on LTOffset and the values of the LTOffset attribute are different
   for the two TimeFrames. */
   ltodiff = ( ltoff1 != ltoff2 );
   talto = LTOFFSET_SCALE( ts1 ) != LTOFFSET_SCALE( align_ts );
   arlto = LTOFFSET_SCALE( align_ts ) != LTOFFSET_SCALE( ts2 );

/* If the alignment frame can be ignored, use MakeMap */
   if( ( !clkdiff || !( taclk || arclk ) ) &&
       ( !ltodiff || !( talto || arlto ) ) &&
       ( !dut1diff || !( tadut || ardut ) ) ) {
      *map = MakeMap( target, sys1, sys2, ts1, ts2, off1, off2, u1, u2,
                      "astSubFrame", status );
      if( *map ) match = 1;

/* Otherwise, we create the Mapping in two parts; first a Mapping from
   the target Frame to the alignment Frame (using the target clock, dut1
   and ltoffset), then a Mapping from the alignment Frame to the results
   Frame (using the result clock, dut1 and ltoffset). */
   } else {

/* Create a Mapping from target units/system/timescale/offset to MJD in
   the alignment timescale with default units and offset equal to the MJD
   equivalent of the target offset. */
      align_off = ToMJD( sys1, off1, status );
      align_unit = DefUnit( AST__MJD, "MakeTimeMap", "TimeFrame", status );
      map1 = MakeMap( target, sys1, AST__MJD, ts1, align_ts, off1, align_off,
                      u1, align_unit, "MakeTimeMap", status );

/* Report an error if the timescales were incompatible. */
      if( !map1 ){
         match = 0;
         if( report && astOK ) {
            astError( AST__INCTS, "astMatch(%s): Alignment in requested "
                   "timescale (%s) is not possible since one or both of the "
                   "TimeFrames being aligned refer to the %s timescale.", status,
                   astGetClass( target ), TimeScaleString( align_ts, status ),
                   TimeScaleString( ts1, status ) );
         }
      }

/* We now create a Mapping that converts from the alignment System (MJD),
   TimeScale and offset to the result coordinate system. */
      map2 = MakeMap( result, AST__MJD, sys2, align_ts, ts2, align_off, off2,
                      align_unit, u2, "MakeTimeMap", status );

/* Report an error if the timescales were incompatible. */
      if( !map2 ){
         match = 0;
         if( report && astOK ) {
            astError( AST__INCTS, "astMatch(%s): Alignment in requested "
                   "timescale (%s) is not possible since one or both of the "
                   "TimeFrames being aligned refer to the %s timescale.", status,
                   astGetClass( result ), TimeScaleString( align_ts, status ),
                   TimeScaleString( ts2, status ) );
         }
      }

/* Combine these two Mappings. */
      if( map1 && map2 ) {
         match = 1;
         tmap = (AstMapping *) astCmpMap( map1, map2, 1, "", status );
         *map = astSimplify( tmap );
         tmap = astAnnul( tmap );
      }

/* Free resources. */
      if( map1 ) map1 = astAnnul( map1 );
      if( map2 ) map2 = astAnnul( map2 );
   }

/* If an error occurred, annul the returned Mapping and clear the returned
   values. */
   if ( !astOK ) {
      *map = astAnnul( *map );
      match = 0;
   }

/* Return the result. */
   return match;
}

static int Match( AstFrame *template_frame, AstFrame *target, int matchsub,
                  int **template_axes, int **target_axes, AstMapping **map,
                  AstFrame **result, int *status ) {
/*
*  Name:
*     Match

*  Purpose:
*     Determine if conversion is possible between two coordinate systems.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     int Match( AstFrame *template, AstFrame *target, int matchsub,
*                int **template_axes, int **target_axes,
*                AstMapping **map, AstFrame **result, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the protected astMatch method
*     inherited from the Frame class).

*  Description:
*     This function matches a "template" TimeFrame to a "target" Frame and
*     determines whether it is possible to convert coordinates between them.
*     If it is, a mapping that performs the transformation is returned along
*     with a new Frame that describes the coordinate system that results when
*     this mapping is applied to the "target" coordinate system. In addition,
*     information is returned to allow the axes in this "result" Frame to be
*     associated with the corresponding axes in the "target" and "template"
*     Frames from which they are derived.

*  Parameters:
*     template
*        Pointer to the template TimeFrame. This describes the coordinate
*        system (or set of possible coordinate systems) into which we wish to
*        convert our coordinates.
*     target
*        Pointer to the target Frame. This describes the coordinate system in
*        which we already have coordinates.
*     matchsub
*        If zero then a match only occurs if the template is of the same
*        class as the target, or of a more specialised class. If non-zero
*        then a match can occur even if this is not the case.
*     template_axes
*        Address of a location where a pointer to int will be returned if the
*        requested coordinate conversion is possible. This pointer will point
*        at a dynamically allocated array of integers with one element for each
*        axis of the "result" Frame (see below). It must be freed by the caller
*        (using astFree) when no longer required.
*
*        For each axis in the result Frame, the corresponding element of this
*        array will return the index of the template TimeFrame axis from
*        which it is derived. If it is not derived from any template
*        TimeFrame axis, a value of -1 will be returned instead.
*     target_axes
*        Address of a location where a pointer to int will be returned if the
*        requested coordinate conversion is possible. This pointer will point
*        at a dynamically allocated array of integers with one element for each
*        axis of the "result" Frame (see below). It must be freed by the caller
*        (using astFree) when no longer required.
*
*        For each axis in the result Frame, the corresponding element of this
*        array will return the index of the target Frame axis from which it
*        is derived. If it is not derived from any target Frame axis, a value
*        of -1 will be returned instead.
*     map
*        Address of a location where a pointer to a new Mapping will be
*        returned if the requested coordinate conversion is possible. If
*        returned, the forward transformation of this Mapping may be used to
*        convert coordinates between the "target" Frame and the "result"
*        Frame (see below) and the inverse transformation will convert in the
*        opposite direction.
*     result
*        Address of a location where a pointer to a new Frame will be returned
*        if the requested coordinate conversion is possible. If returned, this
*        Frame describes the coordinate system that results from applying the
*        returned Mapping (above) to the "target" coordinate system. In
*        general, this Frame will combine attributes from (and will therefore
*        be more specific than) both the target and the template Frames. In
*        particular, when the template allows the possibility of transformaing
*        to any one of a set of alternative coordinate systems, the "result"
*        Frame will indicate which of the alternatives was used.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A non-zero value is returned if the requested coordinate conversion is
*     possible. Otherwise zero is returned (this will not in itself result in
*     an error condition).

*  Notes:
*     -  A value of zero will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.

*  Implementation Notes:
*     This implementation addresses the matching of a TimeFrame class
*     object to any other class of Frame. A TimeFrame will match any class
*     of TimeFrame (i.e. possibly from a derived class) but will not match
*     a less specialised class of Frame.
*/

   AstFrame *frame0;             /* Pointer to Frame underlying axis 0 */
   AstTimeFrame *template;       /* Pointer to template TimeFrame structure */
   int iaxis0;                   /* Axis index underlying axis 0 */
   int iaxis;                    /* Axis index */
   int match;                    /* Coordinate conversion possible? */
   int target_axis0;             /* Index of TimeFrame axis in the target */
   int target_naxes;             /* Number of target axes */

/* Initialise the returned values. */
   *template_axes = NULL;
   *target_axes = NULL;
   *map = NULL;
   *result = NULL;
   match = 0;

/* Check the global error status. */
   if ( !astOK ) return match;

/* Obtain a pointer to the template TimeFrame structure. */
   template = (AstTimeFrame *) template_frame;

/* Obtain the number of axes in the target Frame. */
   target_naxes = astGetNaxes( target );

/* The first criterion for a match is that the template matches as a
   Frame class object. This ensures that the number of axes (1) and
   domain, etc. of the target Frame are suitable. Invoke the parent
   "astMatch" method to verify this. */
   match = (*parent_match)( template_frame, target, matchsub,
                            template_axes, target_axes, map, result, status );

/* If a match was found, annul the returned objects, which are not
   needed, but keep the memory allocated for the axis association
   arrays, which we will re-use. */
   if ( astOK && match ) {
      *map = astAnnul( *map );
      *result = astAnnul( *result );
   }

/* If OK so far, obtain pointers to the primary Frames which underlie
   all target axes. Stop when a TimeFrame axis is found. */
   if ( match && astOK ) {
      match = 0;
      for( iaxis = 0; iaxis < target_naxes; iaxis++ ) {
         astPrimaryFrame( target, iaxis, &frame0, &iaxis0 );
         if( astIsATimeFrame( frame0 ) ) {
            frame0 = astAnnul( frame0 );
            target_axis0 = iaxis;
            match = 1;
            break;
         } else {
            frame0 = astAnnul( frame0 );
         }
      }
   }

/* Check at least one TimeFrame axis was found it the target. Store the
   axis associataions. */
   if( match && astOK ) {
      (*template_axes)[ 0 ] = 0;
      (*target_axes)[ 0 ] = target_axis0;

/* Use the target's "astSubFrame" method to create a new Frame (the
   result Frame) with copies of the target axes in the required
   order. This process also overlays the template attributes on to the
   target Frame and returns a Mapping between the target and result
   Frames which effects the required coordinate conversion. */
      match = astSubFrame( target, template, 1, *target_axes, *template_axes,
                           map, result );
   }

/* If an error occurred, or conversion to the result Frame's coordinate
   system was not possible, then free all memory, annul the returned
   objects, and reset the returned value. */
   if ( !astOK || !match ) {
      *template_axes = astFree( *template_axes );
      *target_axes = astFree( *target_axes );
      if( *map ) *map = astAnnul( *map );
      if( *result ) *result = astAnnul( *result );
      match = 0;
   }

/* Return the result. */
   return match;
}

static void OriginScale( AstTimeFrame *this, AstTimeScaleType newts,
                         const char *method, int *status ){
/*
*  Name:
*     OriginScale

*  Purpose:
*     Convert the TimeOrigin in a TimeFrame to a new timescale.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void OriginScale( AstTimeFrame *this, AstTimeScaleType newts,
*                       const char *method, int *status )

*  Class Membership:
*     TimeFrame member function

*  Description:
*     This function converts the value of the TimeOrigin attribute stored
*     within a supplied TimeFrame from the timescale currently associated
*     with the TimeFrame, to the new timescale indicated by "newts".

*  Parameters:
*     this
*        Point to the TimeFrame. On entry, the TimeOrigin value is
*        assumed to refer to the timescale given by the astGetTimeScale
*        method. On exit, the TimeOrigin value refers to the timescale
*        supplied in "newts". The TimeScale attribute of the TimeFrame
*        should then be modified in order to keep things consistent.
*     newts
*        The timescale to which the TimeOrigin value stored within "this"
*        should refer on exit.
*     method
*        Pointer to a string holding the name of the method to be
*        included in any error messages.
*     status
*        Pointer to the inherited status variable.

*/


/* Local Variables: */
   AstMapping *map;
   AstSystemType sys;
   AstTimeScaleType oldts;
   const char *u;
   double newval;
   double oldval;

/* Check the global error status. */
   if ( !astOK ) return;

/* Do nothing if the TimeOrigin attribute has not been assigned a value. */
   if( astTestTimeOrigin( this ) ) {

/* Do nothing if the Scale will not change. */
      oldts = astGetTimeScale( this );
      if( newts != oldts ) {

/* Create a Mapping to perform the TimeScale change. */
         sys = astGetSystem( this );
         u = DefUnit( sys, method, "TimeFrame", status ),
         map = MakeMap( this, sys, sys, oldts, newts, 0.0, 0.0, u, u,
                        method, status );

/* Use the Mapping to convert the stored TimeOrigin value. */
         if( map ) {
            oldval = astGetTimeOrigin( this );
            astTran1( map, 1, &oldval, 1, &newval );

/* Store the new value */
            astSetTimeOrigin( this, newval );

/* Free resources */
            map = astAnnul( map );

         } else if( astOK ) {
            astError( AST__INCTS, "%s(%s): Cannot convert the TimeOrigin "
                      "value to a different timescale because of "
                      "incompatible time scales.", status, method,
                      astGetClass( this ) );
         }
      }
   }
}

static void OriginSystem( AstTimeFrame *this, AstSystemType oldsys,
                          const char *method, int *status ){
/*
*  Name:
*     OriginSystem

*  Purpose:
*     Convert the TimeOrigin in a TimeFrame to a new System.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void OriginSystem( AstTimeFrame *this, AstSystemType oldsys,
*                        const char *method, int *status )

*  Class Membership:
*     TimeFrame member function

*  Description:
*     This function converts the value of the TimeOrigin attribute stored
*     within a supplied TimeFrame from its original System, etc, to the
*     System, etc, currently associated with the TimeFrame.

*  Parameters:
*     this
*        Point to the TimeFrame. On entry, the TimeOrigin value is
*        assumed to refer to the System given by "oldsys", etc. On exit, the
*        TimeOrigin value refers to the System returned by the astGetSystem
*        method, etc.
*     oldsys
*        The System to which the TimeOrigin value stored within "this"
*        refers on entry.
*     method
*        A string containing the method name for error messages.
*     status
*        Pointer to the inherited status variable.

*/

/* Local Variables: */
   AstMapping *map;
   AstSystemType newsys;
   AstTimeScaleType ts;
   const char *oldu;
   const char *newu;
   double newval;
   double oldval;

/* Check the global error status. */
   if ( !astOK ) return;

/* Do nothing if the TimeOrigin attribute has not been assigned a value. */
   if( astTestTimeOrigin( this ) ) {

/* Do nothing if the System has not changed. */
      newsys = astGetSystem( this );
      if( oldsys != newsys ) {

/* Create a Mapping to perform the System change. */
         ts = astGetTimeScale( this );
         oldu = DefUnit( oldsys, method, "TimeFrame", status ),
         newu = DefUnit( newsys, method, "TimeFrame", status ),
         map = MakeMap( this, oldsys, newsys, ts, ts, 0.0, 0.0, oldu, newu,
                        method, status );

/* Use the Mapping to convert the stored TimeOrigin value. */
         if( map ) {
            oldval = astGetTimeOrigin( this );
            astTran1( map, 1, &oldval, 1, &newval );

/* Store the new value */
            astSetTimeOrigin( this, newval );

/* Free resources */
            map = astAnnul( map );

         } else if( astOK ) {
            astError( AST__INCTS, "%s(%s): Cannot convert the TimeOrigin "
                      "value to a different System because of incompatible "
                      "time scales.", status, method, astGetClass( this ) );
         }
      }
   }
}

static void Overlay( AstFrame *template, const int *template_axes,
                     AstFrame *result, int *status ) {
/*
*  Name:
*     Overlay

*  Purpose:
*     Overlay the attributes of a template TimeFrame on to another Frame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void Overlay( AstFrame *template, const int *template_axes,
*                   AstFrame *result, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the protected astOverlay method
*     inherited from the Frame class).

*  Description:
*     This function overlays attributes of a TimeFrame (the "template") on to
*     another Frame, so as to over-ride selected attributes of that second
*     Frame. Normally only those attributes which have been specifically set
*     in the template will be transferred. This implements a form of
*     defaulting, in which a Frame acquires attributes from the template, but
*     retains its original attributes (as the default) if new values have not
*     previously been explicitly set in the template.
*
*     Note that if the result Frame is a TimeFrame and a change of time
*     coordinate system occurs as a result of overlaying its System
*     attribute, then some of its original attribute values may no
*     longer be appropriate (e.g. the Title, or attributes describing
*     its axes). In this case, these will be cleared before overlaying
*     any new values.

*  Parameters:
*     template
*        Pointer to the template TimeFrame, for which values should have been
*        explicitly set for any attribute which is to be transferred.
*     template_axes
*        Pointer to an array of int, with one element for each axis of the
*        "result" Frame (see below). For each axis in the result frame, the
*        corresponding element of this array should contain the (zero-based)
*        index of the template axis to which it corresponds. This array is used
*        to establish from which template axis any axis-dependent attributes
*        should be obtained.
*
*        If any axis in the result Frame is not associated with a template
*        axis, the corresponding element of this array should be set to -1.
*
*        If a NULL pointer is supplied, the template and result axis
*        indices are assumed to be identical.
*     result
*        Pointer to the Frame which is to receive the new attribute values.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     void

*  Notes:
*     -  In general, if the result Frame is not from the same class as the
*     template TimeFrame, or from a class derived from it, then attributes may
*     exist in the template TimeFrame which do not exist in the result Frame.
*     In this case, these attributes will not be transferred.
*/


/* Local Variables: */
   AstSystemType new_alignsystem;/* Code identifying new alignment coords */
   AstSystemType new_system;     /* Code identifying new cordinates */
   AstSystemType old_system;     /* Code identifying old coordinates */
   int resetSystem;              /* Was the template System value cleared? */
   int timeframe;                /* Result Frame is a TimeFrame? */

/* Check the global error status. */
   if ( !astOK ) return;

/* Get the old and new systems. */
   old_system = astGetSystem( result );
   new_system = astGetSystem( template );

/* If the result Frame is a TimeFrame, we must test to see if overlaying its
   System attribute will change the type of coordinate system it describes.
   Determine the value of this attribute for the result and template
   TimeFrames. */
   resetSystem = 0;
   timeframe = astIsATimeFrame( result );
   if( timeframe ) {

/* If the coordinate system will change, any value already set for the result
   TimeFrame's Title, etc,  will no longer be appropriate, so clear it. */
      if ( new_system != old_system ) {
         astClearTitle( result );
         astClearLabel( result, 0 );
         astClearSymbol( result, 0 );
      }

/* If the result Frame is not a TimeFrame, we must temporarily clear the
   System and AlignSystem values since the values used by this class are only
   appropriate to this class. */
   } else {
      if( astTestSystem( template ) ) {
         astClearSystem( template );

         new_alignsystem = astGetAlignSystem( template );
         astClearAlignSystem( template );

         resetSystem = 1;
      }
   }

/* Invoke the parent class astOverlay method to transfer attributes inherited
   from the parent class. */
   (*parent_overlay)( template, template_axes, result, status );

/* Reset the System and AlignSystem values if necessary */
   if( resetSystem ) {
      astSetSystem( template, new_system );
      astSetAlignSystem( template, new_alignsystem );
   }

/* Check if the result Frame is a TimeFrame or from a class derived from
   TimeFrame. If not, we cannot transfer TimeFrame attributes to it as it is
   insufficiently specialised. In this case simply omit these attributes. */
   if ( timeframe && astOK ) {

/* Define macros that test whether an attribute is set in the template and,
   if so, transfers its value to the result. */
#define OVERLAY(attribute) \
   if ( astTest##attribute( template ) ) { \
      astSet##attribute( result, astGet##attribute( template ) ); \
   }

/* Use the macro to transfer each TimeFrame attribute in turn. Note,
   SourceVRF must be overlayed before SourceVel. Otherwise the stored value
   for SourceVel would be changed from the default SourceVRF to the specified
   SourceVRF when SourceVRF was overlayed. */
      OVERLAY(AlignTimeScale)
      OVERLAY(LTOffset)
      OVERLAY(TimeOrigin)
      OVERLAY(TimeScale)
   }

/* Undefine macros local to this function. */
#undef OVERLAY
}

static void SetAttrib( AstObject *this_object, const char *setting, int *status ) {
/*
*  Name:
*     SetAttrib

*  Purpose:
*     Set an attribute value for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void SetAttrib( AstObject *this, const char *setting, int *status )

*  Class Membership:
*     TimeFrame member function (extends the astSetAttrib method inherited from
*     the Mapping class).

*  Description:
*     This function assigns an attribute value for a TimeFrame, the attribute
*     and its value being specified by means of a string of the form:
*
*        "attribute= value "
*
*     Here, "attribute" specifies the attribute name and should be in lower
*     case with no white space present. The value to the right of the "="
*     should be a suitable textual representation of the value to be assigned
*     and this will be interpreted according to the attribute's data type.
*     White space surrounding the value is only significant for string
*     attributes.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     setting
*        Pointer to a null terminated string specifying the new attribute
*        value.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     void

*  Notes:
*     This protected method is intended to be invoked by the Object astSet
*     method and makes additional attributes accessible to it.
*/

/* Local Vaiables: */
   AstTimeFrame *this;           /* Pointer to the TimeFrame structure */
   AstTimeScaleType ts;          /* time scale type code */
   char *a;                      /* Pointer to next character */
   char *new_setting;            /* Pointer value to new attribute setting */
   double dval;                  /* Double atribute value */
   double mjd;                   /* MJD read from setting */
   double origin;                /* TimeOrigin value */
   int len;                      /* Length of setting string */
   int namelen;                  /* Length of attribute name in setting */
   int nc;                       /* Number of characters read by astSscanf */
   int off;                      /* Offset of attribute value */
   int rep;                      /* Original error reporting state */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_object;

/* Obtain the length of the setting string. */
   len = strlen( setting );

/* Test for each recognised attribute in turn, using "astSscanf" to parse the
   setting string and extract the attribute value (or an offset to it in the
   case of string values). In each case, use the value set in "nc" to check
   that the entire string was matched. Once a value has been obtained, use the
   appropriate method to set it. */

/* First look for axis attributes defined by the Frame class. Since a
   TimeFrame has only 1 axis, we allow these attributes to be specified
   without a trailing "(axis)" string. */
   if ( !strncmp( setting, "direction=", 10 ) ||
        !strncmp( setting, "bottom=", 7 ) ||
        !strncmp( setting, "top=", 4 ) ||
        !strncmp( setting, "format=", 7 ) ||
        !strncmp( setting, "label=", 6 ) ||
        !strncmp( setting, "symbol=", 7 ) ||
        !strncmp( setting, "unit=", 5 ) ) {

/* Create a new setting string from the original by appending the string
   "(1)" to the end of the attribute name and then use the parent SetAttrib
   method. */
      new_setting = astMalloc( len + 4 );
      if( new_setting ) {
         memcpy( new_setting, setting, len + 1 );
         a = strchr( new_setting, '=' );
         namelen = a - new_setting;
         memcpy( a, "(1)", 4 );
         a += 3;
         strcpy( a, setting + namelen );
         (*parent_setattrib)( this_object, new_setting, status );
         new_setting = astFree( new_setting );
      }

/* AlignTimeScale. */
/* --------------- */
   } else if ( nc = 0,
        ( 0 == astSscanf( setting, "aligntimescale=%n%*s %n", &off, &nc ) )
        && ( nc >= len ) ) {

/* Convert the string to a TimeScale code before use. */
      ts = TimeScaleCode( setting + off, status );
      if ( ts != AST__BADTS ) {
         astSetAlignTimeScale( this, ts );

/* Report an error if the string value wasn't recognised. */
      } else {
         astError( AST__ATTIN, "astSetAttrib(%s): Invalid time scale "
                   "description \"%s\".", status, astGetClass( this ), setting+off );
      }

/* ClockLat. */
/* ------- */
   } else if ( nc = 0,
              ( 0 == astSscanf( setting, "clocklat=%n%*s %n", &off, &nc ) )
              && ( nc >= 7 ) ) {
      new_setting = astMalloc( sizeof( char )*(size_t) len + 1 );
      new_setting[ 0 ] = 'o';
      new_setting[ 1 ] = 'b';
      new_setting[ 2 ] = 's';
      strcpy( new_setting + 3, setting + 5 );
      astSetAttrib( this, new_setting );
      new_setting = astFree( new_setting );

/* ClockLon. */
/* ------- */
   } else if ( nc = 0,
              ( 0 == astSscanf( setting, "clocklon=%n%*s %n", &off, &nc ) )
              && ( nc >= 7 ) ) {
      new_setting = astMalloc( sizeof( char )*(size_t) len + 1 );
      new_setting[ 0 ] = 'o';
      new_setting[ 1 ] = 'b';
      new_setting[ 2 ] = 's';
      strcpy( new_setting + 3, setting + 5 );
      astSetAttrib( this, new_setting );
      new_setting = astFree( new_setting );

/* LTOffset */
/* -------- */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "ltoffset= %lg %n", &dval, &nc ) )
        && ( nc >= len ) ) {
      astSetLTOffset( this, dval );

/* TimeOrigin */
/* ---------- */

/* Floating-point without any units indication - assume the current Unit
   value. */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "timeorigin= %lg %n", &dval, &nc ) )
        && ( nc >= len ) ) {

      astSetTimeOrigin( this, ToUnits( this, astGetUnit( this, 0 ), dval,
                                       "astSetTimeOrigin", status ) );

/* Floating-point with units. */
   } else if ( nc = 0,
        ( 1 == astSscanf( setting, "timeorigin= %lg %n%*s %n", &dval, &off, &nc ) )
        && ( nc >= len ) ) {

/* Defer error reporting in case a date string was given which starts
   with a floating point number, then convert the supplied value to the
   default units for the TimeFrame's System. */
      rep = astReporting( 0 );
      origin = ToUnits( this, setting + off, dval, "astSetTimeOrigin", status );
      if( !astOK ) astClearStatus;
      astReporting( rep );

/* If the origin was converted, store it. */
      if( origin != AST__BAD ) {
         astSetTimeOrigin( this, origin );

/* Otherwise, interpret the string as a date. Convert first to MJD then to
   default system. */
      } else if ( nc = 0,
           ( 0 == astSscanf( setting, "timeorigin=%n%*[^\n]%n", &off, &nc ) )
           && ( nc >= len ) ) {
         mjd = astReadDateTime( setting + off );
         if ( astOK ) {
            astSetTimeOrigin( this, FromMJD( this, mjd, status ) );

/* Report contextual information if the conversion failed. */
         } else {
            astError( AST__ATTIN, "astSetAttrib(%s): Invalid TimeOrigin value "
                      "\"%s\" given.", status, astGetClass( this ), setting + off );
         }
      }

/* String (assumed to be a date). Convert first to MJD then to default
   system. */
   } else if ( nc = 0,
        ( 0 == astSscanf( setting, "timeorigin=%n%*[^\n]%n", &off, &nc ) )
        && ( nc >= len ) ) {
      mjd = astReadDateTime( setting + off );
      if ( astOK ) {
         astSetTimeOrigin( this, FromMJD( this, mjd, status ) );

/* Report contextual information if the conversion failed. */
      } else {
         astError( AST__ATTIN, "astSetAttrib(%s): Invalid TimeOrigin value "
                   "\"%s\" given.", status, astGetClass( this ), setting + off );
      }

/* TimeScale. */
/* ---------- */
   } else if ( nc = 0,
              ( 0 == astSscanf( setting, "timescale=%n%*s %n", &off, &nc ) )
              && ( nc >= len ) ) {

/* Convert the string to a TimeScale code before use. */
      ts = TimeScaleCode( setting + off, status );
      if ( ts != AST__BADTS ) {
         astSetTimeScale( this, ts );

/* Report an error if the string value wasn't recognised. */
      } else {
         astError( AST__ATTIN, "astSetAttrib(%s): Invalid time scale "
                   "description \"%s\".", status, astGetClass( this ), setting + off );
      }

/* Pass any unrecognised setting to the parent method for further
   interpretation. */
   } else {
      (*parent_setattrib)( this_object, setting, status );
   }
}

static void SetSystem( AstFrame *this_frame, AstSystemType newsys, int *status ) {
/*
*  Name:
*     SetSystem

*  Purpose:
*     Set the System attribute for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void SetSystem( AstFrame *this_frame, AstSystemType newsys, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astSetSystem protected
*     method inherited from the Frame class).

*  Description:
*     This function sets the System attribute for a TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     newsys
*        The new System value to be stored.
*     status
*        Pointer to the inherited status variable.

*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to TimeFrame structure */
   AstSystemType oldsys;         /* Original System value */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* If we are changing the System to BEPOCH, set the Unit attribute to
   "yr" and TimeScale to "TT". */
   if( newsys == AST__BEPOCH ) {
      astSetUnit( this_frame, 0, "yr" );
      astSetTimeScale( (AstTimeFrame *) this_frame, AST__TT );
   }

/* Save the original System value */
   oldsys = astGetSystem( this_frame );

/* Use the parent SetSystem method to store the new System value. */
   (*parent_setsystem)( this_frame, newsys, status );

/* If the system has changed... */
   if( oldsys != newsys ) {

/* Modify the stored TimeOrigin. */
      OriginSystem( this, oldsys, "astSetSystem", status );

/* Clear all attributes which have system-specific defaults. */
      astClearLabel( this_frame, 0 );
      astClearSymbol( this_frame, 0 );
      astClearTitle( this_frame );
   }
}

static void SetTimeScale( AstTimeFrame *this, AstTimeScaleType value, int *status ) {
/*
*+
*  Name:
*     astSetTimeScale

*  Purpose:
*     Set the TimeScale attribute for a TimeFrame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "timeframe.h"
*     void astSetTimeScale( AstTimeFrame *this, AstTimeScaleType value )

*  Class Membership:
*     TimeFrame virtual function

*  Description:
*     This function set a new value for the TimeScale attribute for a
*     TimeFrame.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     value
*        The new value.

*-
*/

/* Check the global error status. */
   if ( !astOK ) return;

/* Verify the supplied timescale value */
   if( value < FIRST_TS || value > LAST_TS ) {
      astError( AST__ATTIN, "%s(%s): Bad value (%d) given for TimeScale "
                "attribute.", status, "astSetTimeScale", astGetClass( this ),
                (int) value );

/* Report an error if System is set to BEPOCH and an in appropriate
   TimeScale was supplied. */
   } else if( astGetSystem( this ) == AST__BEPOCH &&
              value != AST__TT ) {
      astError( AST__ATTIN, "%s(%s): Supplied TimeScale (%s) cannot be "
                "used because the %s represents Besselian Epoch which "
                "is defined in terms of TT.", status, "astSetTimeScale",
                astGetClass( this ), TimeScaleString( value, status ),
                astGetClass( this ) );

/* Otherwise set the new TimeScale */
   } else {

/* Modify the TimeOrigin value stored in the TimeFrame structure to refer
   to the new timescale. */
      OriginScale( this, value, "astSetTimeScale", status );

/* Store the new value for the timescale in the TimeFrame structure. */
      this->timescale = value;

   }
}

static void SetUnit( AstFrame *this_frame, int axis, const char *value, int *status ) {
/*
*  Name:
*     SetUnit

*  Purpose:
*     Set a pointer to the Unit string for a TimeFrame's axis.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void SetUnit( AstFrame *this_frame, int axis, const char *value )

*  Class Membership:
*     TimeFrame member function (over-rides the astSetUnit method inherited
*     from the Frame class).

*  Description:
*     This function stores a pointer to the Unit string for a specified axis
*     of a TimeFrame. It also stores the string in the "usedunits" array
*     in the TimeFrame structure, in the element associated with the
*     current System.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     axis
*        The number of the axis (zero-based) for which information is required.
*     unit
*        The new string to store.
*/

/* Local Variables: */
   AstTimeFrame *this;

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* Validate the axis index. */
   astValidateAxis( this, axis, 1, "astSetUnit" );

/* Report an error if System is set to BEPOCH and an in appropriate
   Unit was supplied. */
   if( astGetSystem( this ) == AST__BEPOCH && strcmp( "yr", value ) ) {
      astError( AST__ATTIN, "astSetUnit(%s): Supplied Unit (%s) cannot "
                "be used because the %s represents Besselian Epoch which "
                "is defined in units of years (yr).", status, astGetClass( this ),
                value, astGetClass( this ) );

/* Otherwise use the parent SetUnit method to store the value in the Axis
   structure */
   } else {
      (*parent_setunit)( this_frame, axis, value, status );
   }
}

static AstTimeScaleType TimeScaleCode( const char *ts, int *status ) {
/*
*  Name:
*     TimeScaleCode

*  Purpose:
*     Convert a string into a time scale type code.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     AstTimeScaleType TimeScaleCode( const char *ts )

*  Class Membership:
*     TimeFrame member function.

*  Description:
*     This function converts a string used for the external description of
*     a time scale into a TimeFrame time scale type code  (TimeScale attribute
*     value). It is the inverse of the TimeScaleString function.

*  Parameters:
*     ts
*        Pointer to a constant null-terminated string containing the
*        external description of the time scale.

*  Returned Value:
*     The TimeScale type code.

*  Notes:
*     - A value of AST__BADTS is returned if the time scale
*     description was not recognised. This does not produce an error.
*     - A value of AST__BADTS is also returned if this function
*     is invoked with the global error status set or if it should fail
*     for any reason.
*/

/* Local Variables: */
   AstTimeScaleType result;      /* Result value to return */

/* Initialise. */
   result = AST__BADTS;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Match the timescale string against each possibility and assign the
   result. */
   if ( astChrMatch( "TAI", ts ) ) {
      result = AST__TAI;

   } else if ( astChrMatch( "UTC", ts ) ) {
      result = AST__UTC;

   } else if ( astChrMatch( "UT1", ts ) ) {
      result = AST__UT1;

   } else if ( astChrMatch( "GMST", ts ) ) {
      result = AST__GMST;

   } else if ( astChrMatch( "LAST", ts ) ) {
      result = AST__LAST;

   } else if ( astChrMatch( "LMST", ts ) ) {
      result = AST__LMST;

   } else if ( astChrMatch( "TT", ts ) ) {
      result = AST__TT;

   } else if ( astChrMatch( "TDB", ts ) ) {
      result = AST__TDB;

   } else if ( astChrMatch( "TCG", ts ) ) {
      result = AST__TCG;

   } else if ( astChrMatch( "TCB", ts ) ) {
      result = AST__TCB;

   } else if ( astChrMatch( "LT", ts ) ) {
      result = AST__LT;

   }

/* Return the result. */
   return result;
}

static const char *TimeScaleString( AstTimeScaleType ts, int *status ) {
/*
*  Name:
*     TimeScaleString

*  Purpose:
*     Convert a time scale type code into a string.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *TimeScaleString( AstTimeScaleType ts, int *status )

*  Class Membership:
*     TimeFrame member function.

*  Description:
*     This function converts a TimeFrame time scale type code (TimeScale
*     attribute value) into a string suitable for use as an external
*     representation of the time scale type.

*  Parameters:
*     ts
*        The time scale type code.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to a constant null-terminated string containing the
*     textual equivalent of the type code supplied.

*  Notes:
*     - A NULL pointer value is returned if the time scale
*     code was not recognised. This does not produce an error.
*     - A NULL pointer value is also returned if this function is
*     invoked with the global error status set or if it should fail
*     for any reason.
*/

/* Local Variables: */
   const char *result;           /* Pointer value to return */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Match the timescale value against each possibility and convert to a
   string pointer. */
   switch ( ts ) {

   case AST__TAI:
      result = "TAI";
      break;

   case AST__UTC:
      result = "UTC";
      break;

   case AST__UT1:
      result = "UT1";
      break;

   case AST__GMST:
      result = "GMST";
      break;

   case AST__LAST:
      result = "LAST";
      break;

   case AST__LMST:
      result = "LMST";
      break;

   case AST__TT:
      result = "TT";
      break;

   case AST__TDB:
      result = "TDB";
      break;

   case AST__TCB:
      result = "TCB";
      break;

   case AST__TCG:
      result = "TCG";
      break;

   case AST__LT:
      result = "LT";
      break;

   }

/* Return the result pointer. */
   return result;
}

static int SubFrame( AstFrame *target_frame, AstFrame *template,
                     int result_naxes, const int *target_axes,
                     const int *template_axes, AstMapping **map,
                     AstFrame **result, int *status ) {
/*
*  Name:
*     SubFrame

*  Purpose:
*     Select axes from a TimeFrame and convert to the new coordinate
*     system.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     int SubFrame( AstFrame *target, AstFrame *template,
*                   int result_naxes, const int *target_axes,
*                   const int *template_axes, AstMapping **map,
*                   AstFrame **result, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the protected astSubFrame
*     method inherited from the Frame class).

*  Description:
*     This function selects a requested sub-set (or super-set) of the axes
*     from a "target" TimeFrame and creates a new Frame with copies of
*     the selected axes assembled in the requested order. It then
*     optionally overlays the attributes of a "template" Frame on to the
*     result. It returns both the resulting Frame and a Mapping that
*     describes how to convert between the coordinate systems described by
*     the target and result Frames. If necessary, this Mapping takes
*     account of any differences in the Frames' attributes due to the
*     influence of the template.

*  Parameters:
*     target
*        Pointer to the target TimeFrame, from which axes are to be
*        selected.
*     template
*        Pointer to the template Frame, from which new attributes for the
*        result Frame are to be obtained. Optionally, this may be NULL, in
*        which case no overlaying of template attributes will be performed.
*     result_naxes
*        Number of axes to be selected from the target Frame. This number may
*        be greater than or less than the number of axes in this Frame (or
*        equal).
*     target_axes
*        Pointer to an array of int with result_naxes elements, giving a list
*        of the (zero-based) axis indices of the axes to be selected from the
*        target TimeFrame. The order in which these are given determines
*        the order in which the axes appear in the result Frame. If any of the
*        values in this array is set to -1, the corresponding result axis will
*        not be derived from the target Frame, but will be assigned default
*        attributes instead.
*     template_axes
*        Pointer to an array of int with result_naxes elements. This should
*        contain a list of the template axes (given as zero-based axis indices)
*        with which the axes of the result Frame are to be associated. This
*        array determines which axes are used when overlaying axis-dependent
*        attributes of the template on to the result. If any element of this
*        array is set to -1, the corresponding result axis will not receive any
*        template attributes.
*
*        If the template argument is given as NULL, this array is not used and
*        a NULL pointer may also be supplied here.
*     map
*        Address of a location to receive a pointer to the returned Mapping.
*        The forward transformation of this Mapping will describe how to
*        convert coordinates from the coordinate system described by the target
*        TimeFrame to that described by the result Frame. The inverse
*        transformation will convert in the opposite direction.
*     result
*        Address of a location to receive a pointer to the result Frame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     A non-zero value is returned if coordinate conversion is possible
*     between the target and the result Frame. Otherwise zero is returned and
*     *map and *result are returned as NULL (but this will not in itself
*     result in an error condition). In general, coordinate conversion should
*     always be possible if no template Frame is supplied but may not always
*     be possible otherwise.

*  Notes:
*     -  A value of zero will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.

*  Implementation Notes:
*     -  This implementation addresses the selection of axes from a
*     TimeFrame object. This results in another object of the same class
*     only if the single TimeFrame axis is selected exactly once.
*     Otherwise, the result is a Frame class object which inherits the
*     TimeFrame's axis information (if appropriate) but none of the other
*     properties of a TimeFrame.
*     -  In the event that a TimeFrame results, the returned Mapping will
*     take proper account of the relationship between the target and result
*     coordinate systems.
*     -  In the event that a Frame class object results, the returned Mapping
*     will only represent a selection/permutation of axes.

*  Implementation Deficiencies:
*     -  Any axis selection is currently permitted. Probably this should be
*     restricted so that each axis can only be selected once. The
*     astValidateAxisSelection method will do this but currently there are bugs
*     in the CmpFrame class that cause axis selections which will not pass this
*     test. Install the validation when these are fixed.
*/

/* Local Variables: */
   AstTimeFrame *target;      /* Pointer to the TimeFrame structure */
   AstTimeFrame *temp;        /* Pointer to copy of target TimeFrame */
   AstTimeFrame *align_frm;   /* Frame in which to align the TimeFrames */
   int match;                 /* Coordinate conversion is possible? */

/* Initialise the returned values. */
   *map = NULL;
   *result = NULL;
   match = 0;

/* Check the global error status. */
   if ( !astOK ) return match;

/* Obtain a pointer to the target TimeFrame structure. */
   target = (AstTimeFrame *) target_frame;

/* Result is a TimeFrame. */
/* -------------------------- */
/* Check if the result Frame is to have one axis obtained by selecting
   the single target TimeFrame axis. If so, the result will also be
   a TimeFrame. */
   if ( ( result_naxes == 1 ) && ( target_axes[ 0 ] == 0 ) ) {

/* Form the result from a copy of the target. */
      *result = astCopy( target );

/* If required, overlay the template attributes on to the result TimeFrame.
   Also choose the Frame which defined the alignment system and time scale
   (via its AlignSystem and AlignTimeScale attributes) in which to align the
   two TimeFrames. This is the template (if there is a template). */
      if ( template ) {
         astOverlay( template, template_axes, *result );
         if( astIsATimeFrame( template ) ) {
            align_frm = astClone( template );
         } else {
            align_frm = astClone( target );
         }

/* If no template was supplied, align in the System and TimeScale of the
   target. */
      } else {
         VerifyAttrs( target, "convert between different time systems",
                      "TimeScale", "astMatch", status );
         align_frm = astClone( target );
      }

/* Generate a Mapping that takes account of changes in the sky coordinate
   system (equinox, epoch, etc.) between the target TimeFrame and the result
   TimeFrame. If this Mapping can be generated, set "match" to indicate that
   coordinate conversion is possible. */
      match = ( MakeTimeMapping( target, (AstTimeFrame *) *result,
                align_frm, 0, map, status ) != 0 );

/* Free resources. */
      align_frm = astAnnul( align_frm );

/* Result is not a TimeFrame. */
/* ------------------------------ */
/* In this case, we select axes as if the target were from the Frame
   class.  However, since the resulting data will then be separated
   from their enclosing TimeFrame, default attribute values may differ
   if the methods for obtaining them were over-ridden by the TimeFrame
   class. To overcome this, we ensure that these values are explicitly
   set for the result Frame (rather than relying on their defaults). */
   } else {

/* Make a temporary copy of the target TimeFrame. We will explicitly
   set the attribute values in this copy so as not to modify the original. */
      temp = astCopy( target );

/* Define a macro to test if an attribute is set. If not, set it
   explicitly to its default value. */
#define SET(attribute) \
   if ( !astTest##attribute( temp ) ) { \
      astSet##attribute( temp, astGet##attribute( temp ) ); \
   }

/* Set attribute values which apply to the Frame as a whole and which
   we want to retain, but whose defaults are over-ridden by the
   TimeFrame class. */
      SET(Domain)
      SET(Title)

/* Define a macro to test if an attribute is set for axis zero (the only
   axis of a TimeFrame). If not, set it explicitly to its default value. */
#define SET_AXIS(attribute) \
   if ( !astTest##attribute( temp, 0 ) ) { \
      astSet##attribute( temp, 0, \
                         astGet##attribute( temp, 0 ) ); \
   }

/* Use this macro to set explicit values for all the axis attributes
   for which the TimeFrame class over-rides the default value. */
      SET_AXIS(Label)
      SET_AXIS(Symbol)
      SET_AXIS(Unit)

/* Clear attributes which have an extended range of values allowed by
   this class. */
      astClearSystem( temp );
      astClearAlignSystem( temp );

/* Invoke the astSubFrame method inherited from the Frame class to
   produce the result Frame by selecting the required set of axes and
   overlaying the template Frame's attributes. */
      match = (*parent_subframe)( (AstFrame *) temp, template,
                                  result_naxes, target_axes, template_axes,
                                  map, result, status );

/* Delete the temporary copy of the target TimeFrame. */
      temp = astDelete( temp );
   }

/* If an error occurred or no match was found, annul the returned
   objects and reset the returned result. */
   if ( !astOK || !match ) {
      if( *map ) *map = astAnnul( *map );
      if( *result ) *result = astAnnul( *result );
      match = 0;
   }

/* Return the result. */
   return match;

/* Undefine macros local to this function. */
#undef SET
#undef SET_AXIS
}

static AstSystemType SystemCode( AstFrame *this, const char *system, int *status ) {
/*
*  Name:
*     SystemCode

*  Purpose:
*     Convert a string into a coordinate system type code.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     AstSystemType SystemCode( AstFrame *this, const char *system, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astSystemCode method
*     inherited from the Frame class).

*  Description:
*     This function converts a string used for the external description of
*     a coordinate system into a TimeFrame coordinate system type code
*     (System attribute value). It is the inverse of the astSystemString
*     function.

*  Parameters:
*     this
*        The Frame.
*     system
*        Pointer to a constant null-terminated string containing the
*        external description of the sky coordinate system.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The System type code.

*  Notes:
*     - A value of AST__BADSYSTEM is returned if the sky coordinate
*     system description was not recognised. This does not produce an
*     error.
*     - A value of AST__BADSYSTEM is also returned if this function
*     is invoked with the global error status set or if it should fail
*     for any reason.
*/

/* Local Variables: */
   AstSystemType result;      /* Result value to return */

/* Initialise. */
   result = AST__BADSYSTEM;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Match the "system" string against each possibility and assign the
   result. */
   if ( astChrMatch( "MJD", system ) || astChrMatch( "Modified Julian Date", system ) ) {
      result = AST__MJD;

   } else if ( astChrMatch( "JD", system ) || astChrMatch( "Julian Date", system ) ) {
      result = AST__JD;

   } else if ( astChrMatch( "BEPOCH", system ) || astChrMatch( "Besselian Epoch", system ) ) {
      result = AST__BEPOCH;

   } else if ( astChrMatch( "JEPOCH", system ) || astChrMatch( "Julian Epoch", system ) ) {
      result = AST__JEPOCH;

   }

/* Return the result. */
   return result;
}

static const char *SystemLabel( AstSystemType system, int *status ) {
/*
*  Name:
*     SystemLabel

*  Purpose:
*     Return a label for a coordinate system type code.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *SystemLabel( AstSystemType system, int *status )

*  Class Membership:
*     TimeFrame member function.

*  Description:
*     This function converts a TimeFrame coordinate system type code
*     (System attribute value) into a descriptive string for human readers.

*  Parameters:
*     system
*        The coordinate system type code.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to a constant null-terminated string containing the
*     textual equivalent of the type code supplied.

*  Notes:
*     - A NULL pointer value is returned if the sky coordinate system
*     code was not recognised. This does not produce an error.
*     - A NULL pointer value is also returned if this function is
*     invoked with the global error status set or if it should fail
*     for any reason.
*/

/* Local Variables: */
   const char *result;           /* Pointer value to return */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Match the "system" value against each possibility and convert to a
   string pointer. */
   switch ( system ) {

   case AST__MJD:
      result = "Modified Julian Date";
      break;

   case AST__JD:
      result = "Julian Date";
      break;

   case AST__JEPOCH:
      result = "Julian Epoch";
      break;

   case AST__BEPOCH:
      result = "Besselian Epoch";
      break;

   }

/* Return the result pointer. */
   return result;
}

static const char *SystemString( AstFrame *this, AstSystemType system, int *status ) {
/*
*  Name:
*     SystemString

*  Purpose:
*     Convert a coordinate system type code into a string.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     const char *SystemString( AstFrame *this, AstSystemType system, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astSystemString method
*     inherited from the Frame class).

*  Description:
*     This function converts a TimeFrame coordinate system type code
*     (System attribute value) into a string suitable for use as an
*     external representation of the coordinate system type.

*  Parameters:
*     this
*        The Frame.
*     system
*        The coordinate system type code.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     Pointer to a constant null-terminated string containing the
*     textual equivalent of the type code supplied.

*  Notes:
*     - A NULL pointer value is returned if the sky coordinate system
*     code was not recognised. This does not produce an error.
*     - A NULL pointer value is also returned if this function is
*     invoked with the global error status set or if it should fail
*     for any reason.
*/

/* Local Variables: */
   const char *result;           /* Pointer value to return */

/* Initialise. */
   result = NULL;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Match the "system" value against each possibility and convert to a
   string pointer. (Where possible, return the same string as would be
   used in the FITS WCS representation of the coordinate system). */
   switch ( system ) {

   case AST__MJD:
      result = "MJD";
      break;

   case AST__JD:
      result = "JD";
      break;

   case AST__JEPOCH:
      result = "JEPOCH";
      break;

   case AST__BEPOCH:
      result = "BEPOCH";
      break;
   }

/* Return the result pointer. */
   return result;
}

static int TestActiveUnit( AstFrame *this_frame, int *status ) {
/*
*  Name:
*     TestActiveUnit

*  Purpose:
*     Test the ActiveUnit flag for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     int TestActiveUnit( AstFrame *this_frame, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astTestActiveUnit protected
*     method inherited from the Frame class).

*  Description:
*    This function test the value of the ActiveUnit flag for a TimeFrame,
*    which is always "unset".

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The result of the test (0).

*/
   return 0;
}

static int TestAttrib( AstObject *this_object, const char *attrib, int *status ) {
/*
*  Name:
*     TestAttrib

*  Purpose:
*     Test if a specified attribute value is set for a TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     int TestAttrib( AstObject *this, const char *attrib, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astTestAttrib protected
*     method inherited from the Frame class).

*  Description:
*     This function returns a boolean result (0 or 1) to indicate whether
*     a value has been set for one of a TimeFrame's attributes.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     attrib
*        Pointer to a null terminated string specifying the attribute
*        name.  This should be in lower case with no surrounding white
*        space.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     One if a value has been set, otherwise zero.

*  Notes:
*     - This function uses one-based axis numbering so that it is
*     suitable for external (public) use.
*     - A value of zero will be returned if this function is invoked
*     with the global status set, or if it should fail for any reason.
*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to the TimeFrame structure */
   char *new_attrib;             /* Pointer value to new attribute name */
   int len;                      /* Length of attrib string */
   int result;                   /* Result value to return */

/* Initialise. */
   result = 0;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_object;

/* Obtain the length of the attrib string. */
   len = strlen( attrib );

/* Check the attribute name and test the appropriate attribute. */

/* First look for axis attributes defined by the Frame class. Since a
   TimeFrame has only 1 axis, we allow these attributes to be specified
   without a trailing "(axis)" string. */
   if ( !strcmp( attrib, "direction" ) ||
        !strcmp( attrib, "bottom" ) ||
        !strcmp( attrib, "top" ) ||
        !strcmp( attrib, "format" ) ||
        !strcmp( attrib, "label" ) ||
        !strcmp( attrib, "symbol" ) ||
        !strcmp( attrib, "unit" ) ) {

/* Create a new attribute name from the original by appending the string
   "(1)" and then use the parent TestAttrib method. */
      new_attrib = astMalloc( len + 4 );
      if( new_attrib ) {
         memcpy( new_attrib, attrib, len );
         memcpy( new_attrib + len, "(1)", 4 );
         result = (*parent_testattrib)( this_object, new_attrib, status );
         new_attrib = astFree( new_attrib );
      }

/* AlignTimeScale. */
/* --------------- */
   } else if ( !strcmp( attrib, "aligntimescale" ) ) {
      result = astTestAlignTimeScale( this );

/* ClockLat. */
/* ------- */
   } else if ( !strcmp( attrib, "clocklat" ) ) {
      result = astTestAttrib( this, "obslat" );

/* ClockLon. */
/* ------- */
   } else if ( !strcmp( attrib, "clocklon" ) ) {
      result = astTestAttrib( this, "obslon" );

/* LTOffset. */
/* --------- */
   } else if ( !strcmp( attrib, "ltoffset" ) ) {
      result = astTestLTOffset( this );

/* TimeOrigin. */
/* --------- */
   } else if ( !strcmp( attrib, "timeorigin" ) ) {
      result = astTestTimeOrigin( this );

/* TimeScale. */
/* ---------- */
   } else if ( !strcmp( attrib, "timescale" ) ) {
      result = astTestTimeScale( this );

/* If the attribute is not recognised, pass it on to the parent method
   for further interpretation. */
   } else {
      result = (*parent_testattrib)( this_object, attrib, status );
   }

/* Return the result, */
   return result;
}

static double ToMJD( AstSystemType oldsys, double oldval, int *status ){
/*
*  Name:
*     ToMJD

*  Purpose:
*     Convert a time value from TimeFrame's System to MJD.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     double ToMJD( AstSystemType oldsys, double oldval, int *status ){

*  Class Membership:
*     TimeFrame member function

*  Description:
*     This function converts the supplied value from the supplied System
*     to an MJD.

*  Parameters:
*     oldsys
*        The System in which the oldval is supplied.
*     oldval
*        The value to convert, assumed to be in the default units
*        associated with "oldsys".
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The MJD value corresponding to "oldval"

*  Notes:
*     - Both old and new value are assumed to be absolute (i.e. have zero
*     offset).

*/

/* Local Variables; */
   AstMapping *map;
   double result;

/* Initialise. */
   result = AST__BAD;

/* Check the global error status. */
   if ( !astOK ) return result;

/* If the old system is MJD just return the value unchanged. */
   if( oldsys == AST__MJD ) {
      result = oldval;

/* Otherwise create a TimeMap wich converts from the TimeFrame system to
   MJD, and use it to transform the supplied value. */
   } else {
      map = ToMJDMap( oldsys, 0.0, status );

/* Use the TimeMap to convert the supplied value. */
      astTran1( map, 1, &oldval, 1, &result );

/* Free resources */
      map = astAnnul( map );

   }

/* Return the result */
   return result;
}

static AstMapping *ToMJDMap( AstSystemType oldsys, double off, int *status ){
/*
*  Name:
*     ToMJDMap

*  Purpose:
*     Create a Mapping from a specified System to MJD.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     AstMapping *ToMJDMap( AstSystemType oldsys, double off, int *status ){

*  Class Membership:
*     TimeFrame member function

*  Description:
*     This function creates a Mapping which converts from the supplied
*     system and offset to absolute MJD.

*  Parameters:
*     oldsys
*        The System in which the oldval is supplied.
*     off
*        The axis offset used with the old System, assumed to be in the
*        default system associated with oldsys.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The Mapping.

*/

/* Local Variables; */
   AstTimeMap *timemap;
   double args[ 2 ];

/* Check the global error status. */
   if ( !astOK ) return NULL;

/* Create a null TimeMap */
   timemap = astTimeMap( 0, "", status );

/* Set the offsets for the supplied and returned values. */
   args[ 0 ] = off;
   args[ 1 ] = 0.0;

/* If required, add a TimeMap conversion which converts from the TimeFrame
   system to MJD. */
   if( oldsys == AST__MJD ) {
/*      if( off != 0.0 ) astTimeAdd( timemap, "MJDTOMJD", args ); */
      astTimeAdd( timemap, "MJDTOMJD", args );

   } else if( oldsys == AST__JD ) {
      astTimeAdd( timemap, "JDTOMJD", args );

   } else if( oldsys == AST__JEPOCH ) {
      astTimeAdd( timemap, "JEPTOMJD", args );

   } else if( oldsys == AST__BEPOCH ) {
      astTimeAdd( timemap, "BEPTOMJD", args );
   }

/* Return the result */
   return (AstMapping *) timemap;
}

static double ToUnits( AstTimeFrame *this, const char *oldunit, double oldval,
                       const char *method, int *status ){
/*
*
*  Name:
*     ToUnits

*  Purpose:
*     Convert a supplied time value to the default units of the supplied TimeFrame.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     double ToUnits( AstTimeFrame *this, const char *oldunit, double oldval,
*                     const char *method, int *status )

*  Class Membership:
*     TimeFrame member function

*  Description:
*     This function converts the supplied time value from the supplied
*     units to the default units associated with the supplied TimeFrame's
*     System.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     oldunit
*        The units in which "oldval" is supplied.
*     oldval
*        The value to be converted.
*     method
*        Pointer to a string holding the name of the method to be
*        included in any error messages.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The converted value.

*/

/* Local Variables: */
   AstMapping *map;
   const char *defunit;
   double result;

/* Initialise. */
   result = AST__BAD;

/* Check the global error status. */
   if ( !astOK ) return result;

/* Get default units associated with the System attribute of the supplied
   TimeFrame, and find a Mapping from the old units to the default. */
   defunit = DefUnit( astGetSystem( this ), method, "TimeFrame", status );
   map = astUnitMapper( oldunit, defunit, NULL, NULL );
   if( map ) {

/* Use the Mapping to convert the supplied value. */
      astTran1( map, 1, &oldval, 1, &result );

/* Free resources. */
      map = astAnnul( map );

/* Report an error if no conversion is possible. */
   } else if( astOK ){
      astError( AST__BADUN, "%s(%s): Cannot convert the supplied attribute "
                "value from units of %s to %s.", status, method, astGetClass( this ),
                 oldunit, defunit );
   }

/* Return the result */
   return result;
}

static int Unformat( AstFrame *this_frame, int axis, const char *string,
                     double *value, int *status ) {
/*
*  Name:
*     Unformat

*  Purpose:
*     Read a formatted coordinate value for a TimeFrame axis.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     int Unformat( AstFrame *this, int axis, const char *string,
*                   double *value, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the public astUnformat
*     method inherited from the Frame class).

*  Description:
*     This function reads a formatted coordinate value for a TimeFrame
*     axis (supplied as a string) and returns the equivalent numerical
*     value as a double. It also returns the number of characters read
*     from the string.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     axis
*        The number of the TimeFrame axis for which the coordinate
*        value is to be read (axis numbering starts at zero for the
*        first axis).
*     string
*        Pointer to a constant null-terminated string containing the
*        formatted coordinate value.
*     value
*        Pointer to a double in which the coordinate value read will
*        be returned.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The number of characters read from the string to obtain the
*     coordinate value.

*  Notes:
*     - Any white space at the beginning of the string will be
*     skipped, as also will any trailing white space following the
*     coordinate value read. The function's return value will reflect
*     this.
*     - A function value of zero (and no coordinate value) will be
*     returned, without error, if the string supplied does not contain
*     a suitably formatted value.
*     - The string "<bad>" is recognised as a special case and will
*     generate the value AST__BAD, without error. The test for this
*     string is case-insensitive and permits embedded white space.
*     - A function result of zero will be returned and no coordinate
*     value will be returned via the "value" pointer if this function
*     is invoked with the global error status set, or if it should
*     fail for any reason.
*/

/* Local Variables: */
   AstMapping *map;
   AstTimeFrame *this;
   AstTimeScaleType ts1;
   AstTimeScaleType ts2;
   const char *c;
   char *old_fmt;
   char *str;
   const char *txt;
   double mjd;
   double val1;
   int l;
   int lt;
   int nc1;
   int nc;
   int ndp;
   int rep;

/* Initialise. */
   nc = 0;

/* Check the global error status. */
   if ( !astOK ) return nc;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_frame;

/* Validate the axis index. */
   (void) astValidateAxis( this, axis, 1, "astUnformat" );

/* First attempt to read the value using the parent unformat method, and
   note how many characters were used. We temporarily clear the Format
   attribute if it has been set to a date format, since the parent Frame
   class does not understand date format.*/
   txt = astGetFormat( this, axis );
   if( DateFormat( txt, &ndp, NULL, status ) ) {
       old_fmt = astStore( NULL, txt, strlen( txt ) + 1 );
       astClearFormat( this, axis );
   } else {
       old_fmt = NULL;
   }

   nc1 = (*parent_unformat)( this_frame, axis, string, &val1, status );

/* Re-instate the original Format */
   if( old_fmt ) {
      astSetFormat( this,axis, old_fmt );
      old_fmt = astFree( old_fmt );
   }

/* The astReadDateTime function (defined within frame.c) does not allow
   for any extra text to be appended to the end of the formatted date/time
   (AST__BAD is returned if any such extra text is present). But astUnformat
   is contracted to allow such text. So we need to make multiple attempts
   at reading the date/time in order to find the longest leading string
   which gives a non-bad value. First take a copy of the supplied string
   si we can terminate it at any point we wish. */
   l = astChrLen( string );
   str = astStore( NULL, string, l + 1 );

/* Now attempt to read an ISO date from the start of the string. We
   switch off error reporting to avoid reports of unsuitable syntax. */
   rep = astReporting( 0 );

/* Attempt to read a date/time from the whol string. If this fails
   terminate the string in order to make it one character shorter and try
   again. */
   for( lt = l; lt > 0; lt-- ) {
      str[ lt ] = 0;
      mjd = astReadDateTime( str );
      if( !astOK ) astClearStatus;
      if( mjd != AST__BAD ) break;
   }

/* Re-instate error reporting. */
   astReporting( rep );

/* Free resources. */
   str = astFree( str );

/* If the whole non-blank start of the string was consumed, add on any
   trailing white space. */
   if( lt >= l ) lt = strlen( string );

/* If no date/time could be read, or if reading the value as a
   floating point value was at least as good, return the floating point
   value (assumed to be in the system and units of the TimeFrame. */
   if( mjd == AST__BAD || nc1 >= l ) {
      *value = val1;
      nc = nc1;

/* Otherwise, if a date/time was read convert it to the TimeFrame system,
   etc. */
   } else if( mjd != AST__BAD ) {

/* Save the number of character read from the supplied string. */
      nc = lt;

/* We require a value in the timescale of the supplied TimeFrame. Get
   this TimeScale. */
      ts2 = astGetTimeScale( this );

/* If the supplied string gave the date/time as a Besselian epoch, the
   input timescale is TT, otherwise it is assumed to be the TimeScale of
   the TimeFrame. Locate the first non-space character. */
      c = string;
      while( *c && isspace( *c ) ) c++;

/* If the first non-space is a "B", assuming a TT timescale. Otherwise
   assume the timescale of the supplied TimeFrame. */
      ts1 = ( *c == 'B' || *c == 'b' ) ? AST__TT : ts2;

/* Create the Mapping and use it to transform the mjd value. */
      map = MakeMap( this, AST__MJD, astGetSystem( this ), ts1, ts2,
                     0.0, astGetTimeOrigin( this ), "d",
                     astGetUnit( this, 0 ), "astFormat", status );
      if( map ) {
         astTran1( map, 1, &mjd, 1, value );
         map = astAnnul( map );
      } else {
         astError( AST__INCTS, "astUnformat(%s): Cannot convert the "
                "supplied date/time string (%s) to the required "
                "timescale (%s).", status, astGetClass( this ), string,
                TimeScaleString( ts2, status ) );
      }
   }

/* Return the number of characters read. */
   return nc;
}

static int ValidateSystem( AstFrame *this, AstSystemType system, const char *method, int *status ) {
/*
*
*  Name:
*     ValidateSystem

*  Purpose:
*     Validate a value for a Frame's System attribute.

*  Type:
*     Protected virtual function.

*  Synopsis:
*     #include "timeframe.h"
*     int ValidateSystem( AstFrame *this, AstSystemType system,
*                         const char *method, int *status )

*  Class Membership:
*     TimeFrame member function (over-rides the astValidateSystem method
*     inherited from the Frame class).

*  Description:
*     This function checks the validity of the supplied system value.
*     If the value is valid, it is returned unchanged. Otherwise, an
*     error is reported and a value of AST__BADSYSTEM is returned.

*  Parameters:
*     this
*        Pointer to the Frame.
*     system
*        The system value to be checked.
*     method
*        Pointer to a constant null-terminated character string
*        containing the name of the method that invoked this function
*        to validate an axis index. This method name is used solely
*        for constructing error messages.
*     status
*        Pointer to the inherited status variable.

*  Returned Value:
*     The validated system value.

*  Notes:
*     - A value of AST__BADSYSTEM will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*/

/* Local Variables: */
   AstSystemType result;              /* Validated system value */

/* Initialise. */
   result = AST__BADSYSTEM;

/* Check the global error status. */
   if ( !astOK ) return result;

/* If the value is out of bounds, report an error. */
   if ( system < FIRST_SYSTEM || system > LAST_SYSTEM ) {
         astError( AST__AXIIN, "%s(%s): Bad value (%d) given for the System "
                   "or AlignSystem attribute of a %s.", status, method,
                   astGetClass( this ), (int) system, astGetClass( this ) );

/* Otherwise, return the supplied value. */
   } else {
      result = system;
   }

/* Return the result. */
   return result;
}

static void VerifyAttrs( AstTimeFrame *this, const char *purp,
                         const char *attrs, const char *method, int *status ) {
/*
*  Name:
*     VerifyAttrs

*  Purpose:
*     Verify that usable attribute values are available.

*  Type:
*     Private function.

*  Synopsis:
*     #include "timeframe.h"
*     void VerifyAttrs( AstTimeFrame *this, const char *purp,
*                       const char *attrs, const char *method, int *status  )

*  Class Membership:
*     TimeFrame member function

*  Description:
*     This function tests each attribute listed in "attrs". It returns
*     without action if 1) an explicit value has been set for each attribute
*     or 2) the UseDefs attribute of the supplied TimeFrame is non-zero.
*
*     If UseDefs is zero (indicating that default values should not be
*     used for attributes), and any of the named attributes does not have
*     an explicitly set value, then an error is reported.

*  Parameters:
*     this
*        Pointer to the TimeFrame.
*     purp
*        Pointer to a text string containing a message which will be
*        included in any error report. This shouldindicate the purpose
*        for which the attribute value is required.
*     attrs
*        A string holding a space separated list of attribute names.
*     method
*        A string holding the name of the calling method for use in error
*        messages.
*     status
*        Pointer to the inherited status variable.

*/

/* Local Variables: */
   const char *a;
   const char *desc;
   const char *p;
   int len;
   int set;
   int state;

/* Check inherited status */
   if( !astOK ) return;

/* Stop compiler warnings about uninitialised variables */
   a = NULL;
   desc = NULL;
   len = 0;
   set = 0;

/* If the TimeFrame has a non-zero value for its UseDefs attribute, then
   all attributes are assumed to have usable values, since the defaults
   will be used if no explicit value has been set. So we only need to do
   any checks if UseDefs is zero. */
   if( !astGetUseDefs( this ) ) {

/* Loop round the "attrs" string identifying the start and length of each
   non-blank word in the string. */
      state = 0;
      p = attrs;
      while( 1 ) {
         if( state == 0 ) {
            if( !isspace( *p ) ) {
               a = p;
               len = 1;
               state = 1;
            }
         } else {
            if( isspace( *p ) || !*p ) {

/* The end of a word has just been reached. Compare it to each known
   attribute value. Get a flag indicating if the attribute has a set
   value, and a string describing the attribute.*/
               if( len > 0 ) {

                  if( !strncmp( "ObsLat", a, len ) ) {
                     set = astTestObsLat( this );
                     desc = "observer latitude";

                  } else if( !strncmp( "ObsLon", a, len ) ) {
                     set = astTestObsLon( this );
                     desc = "observer longitude";

                  } else if( !strncmp( "ObsAlt", a, len ) ) {
                     set = astTestObsAlt( this );
                     desc = "observer altitude";

                  } else if( !strncmp( "Dut1", a, len ) ) {
                     set = astTestDut1( this );
                     desc = "UT1-UTC correction";

                  } else if( !strncmp( "TimeOrigin", a, len ) ) {
                     set = astTestTimeOrigin( this );
                     desc = "time offset";

                  } else if( !strncmp( "LTOffset", a, len ) ) {
                     set = astTestLTOffset( this );
                     desc = "local time offset";

                  } else if( !strncmp( "TimeScale", a, len ) ) {
                     set = astTestTimeScale( this );
                     desc = "time scale";

                  } else {
                     astError( AST__INTER, "VerifyAttrs(TimeFrame): "
                               "Unknown attribute name \"%.*s\" supplied (AST "
                               "internal programming error).", status, len, a );
                  }

/* If the attribute does not have a set value, report an error. */
                  if( !set && astOK ) {
                     astError( AST__NOVAL, "%s(%s): Cannot %s.", status, method,
                               astGetClass( this ), purp );
                     astError( AST__NOVAL, "No value has been set for "
                               "the AST \"%.*s\" attribute (%s).", status, len, a,
                               desc );
                  }

/* Continue the word search algorithm. */
               }
               len = 0;
               state = 0;
            } else {
               len++;
            }
         }
         if( !*(p++) ) break;
      }
   }
}

/* Functions which access class attributes. */
/* ---------------------------------------- */

/*
*att++
*  Name:
*     TimeOrigin

*  Purpose:
*     The zero point for TimeFrame axis values

*  Type:
*     Public attribute.

*  Synopsis:
*     Floating point.

*  Description:
*     This specifies the origin from which all time values are measured.
*     The default value (zero) results in the TimeFrame describing
*     absolute time values in the system given by the System attribute
*     (e.g. MJD, Julian epoch, etc). If a TimeFrame is to be used to
*     describe elapsed time since some origin, the TimeOrigin attribute
*     should be set to hold the required origin value. The TimeOrigin value
*     stored inside the TimeFrame structure is modified whenever TimeFrame
*     attribute values are changed so that it refers to the original moment
*     in time.
*
*  Input Formats:
*     The formats accepted when setting a TimeOrigin value are listed
*     below. They are all case-insensitive and are generally tolerant
*     of extra white space and alternative field delimiters:
*
*     - Besselian Epoch: Expressed in decimal years, with or without
*     decimal places ("B1950" or "B1976.13" for example).
*
*     - Julian Epoch: Expressed in decimal years, with or without
*     decimal places ("J2000" or "J2100.9" for example).
*
*     - Units: An unqualified decimal value is interpreted as a value in
*     the system specified by the TimeFrame's System attribute, in the
*     units given by the TimeFrame's Unit attribute. Alternatively, an
*     appropriate unit string can be appended to the end of the floating
*     point value ("123.4 d" for example), in which case the supplied value
*     is scaled into the units specified by the Unit attribute.
*
*     - Julian Date: With or without decimal places ("JD 2454321.9" for
*     example).
*
*     - Modified Julian Date: With or without decimal places
*     ("MJD 54321.4" for example).
*
*     - Gregorian Calendar Date: With the month expressed either as an
*     integer or a 3-character abbreviation, and with optional decimal
*     places to represent a fraction of a day ("1996-10-2" or
*     "1996-Oct-2.6" for example). If no fractional part of a day is
*     given, the time refers to the start of the day (zero hours).
*
*     - Gregorian Date and Time: Any calendar date (as above) but with
*     a fraction of a day expressed as hours, minutes and seconds
*     ("1996-Oct-2 12:13:56.985" for example). The date and time can be
*     separated by a space or by a "T" (as used by ISO8601 format).

*  Output Format:
*     When enquiring TimeOrigin values, the returned formatted floating
*     point value represents a value in the TimeFrame's System, in the unit
*     specified by the TimeFrame's Unit attribute.

*  Applicability:
*     TimeFrame
*        All TimeFrames have this attribute.

*att--
*/
/* The time origin, stored internally in the default units associated
   with the current System value. Clear the TimeOrigin value  by setting it
   to AST__BAD, which gives 0.0 as the default value. Any value is acceptable. */
astMAKE_CLEAR(TimeFrame,TimeOrigin,timeorigin,AST__BAD)
astMAKE_GET(TimeFrame,TimeOrigin,double,0.0,((this->timeorigin!=AST__BAD)?this->timeorigin:0.0))
astMAKE_SET(TimeFrame,TimeOrigin,double,timeorigin,value)
astMAKE_TEST(TimeFrame,TimeOrigin,( this->timeorigin != AST__BAD ))

/*
*att++
*  Name:
*     LTOffset

*  Purpose:
*     The offset from UTC to Local Time, in hours.

*  Type:
*     Public attribute.

*  Synopsis:
*     Floating point.

*  Description:
*     This specifies the offset from UTC to Local Time, in hours (fractional
*     hours can be supplied). It is positive for time zones east of Greenwich.
*     AST uses the figure as given, without making any attempt to correct for
*     daylight saving. The default value is zero.

*  Applicability:
*     TimeFrame
*        All TimeFrames have this attribute.

*att--
*/
astMAKE_CLEAR(TimeFrame,LTOffset,ltoffset,AST__BAD)
astMAKE_GET(TimeFrame,LTOffset,double,0.0,((this->ltoffset!=AST__BAD)?this->ltoffset:0.0))
astMAKE_SET(TimeFrame,LTOffset,double,ltoffset,value)
astMAKE_TEST(TimeFrame,LTOffset,( this->ltoffset != AST__BAD ))

/*
*att++
*  Name:
*     AlignTimeScale

*  Purpose:
*     Time scale to use when aligning TimeFrames.

*  Type:
*     Public attribute.

*  Synopsis:
*     String.

*  Description:
*     This attribute controls how a TimeFrame behaves when it is used (by
c     astFindFrame or astConvert) as a template to match another (target)
f     AST_FINDFRAME or AST_CONVERT) as a template to match another (target)
*     TimeFrame. It identifies the time scale in which alignment is
*     to occur. See the TimeScale attribute for a desription of the values
*     which may be assigned to this attribute. The default AlignTimeScale
*     value depends on the current value of TimeScale: if TimeScale is
*     UT1, GMST, LMST or LAST, the default for AlignTimeScale is UT1, for all
*     other TimeScales the default is TAI.
*
c     When astFindFrame or astConvert is used on two TimeFrames (potentially
f     When AST_FindFrame or AST_CONVERT is used on two TimeFrames (potentially
*     describing different time coordinate systems), it returns a Mapping
*     which can be used to transform a position in one TimeFrame into the
*     corresponding position in the other. The Mapping is made up of the
*     following steps in the indicated order:
*
*     - Map values from the system used by the target (MJD, JD, etc) to the
*     system specified by the AlignSystem attribute.
*
*     - Map these values from the target's time scale to the time scale
*     specified by the AlignTimeScale attribute.
*
*     - Map these values from the time scale specified by the AlignTimeScale
*     attribute, to the template's time scale.
*
*     - Map these values from the system specified by the AlignSystem
*     attribute, to the system used by the template.

*  Applicability:
*     TimeFrame
*        All TimeFrames have this attribute.

*att--
*/
astMAKE_TEST(TimeFrame,AlignTimeScale,( this->aligntimescale != AST__BADTS ))
astMAKE_CLEAR(TimeFrame,AlignTimeScale,aligntimescale,AST__BADTS)
astMAKE_SET(TimeFrame,AlignTimeScale,AstTimeScaleType,aligntimescale,(
            ( ( value >= FIRST_TS ) && ( value <= LAST_TS ) ) ?
                 value :
                 ( astError( AST__ATTIN, "%s(%s): Bad value (%d) "
                             "given for AlignTimeScale attribute.", status,
                             "astSetAlignTimeScale", astGetClass( this ), (int) value ),

/* Leave the value unchanged on error. */
                                            this->aligntimescale ) ) )

/*
*att++
*  Name:
*     TimeScale

*  Purpose:
*     Time scale.

*  Type:
*     Public attribute.

*  Synopsis:
*     String.

*  Description:
*     This attribute identifies the time scale to which the time axis values
*     of a TimeFrame refer, and may take any of the values listed in the
*     "Time Scales" section (below).
*
*     The default TimeScale value depends on the current System value; if
*     the current TimeFrame system is "Besselian epoch" the default is
*     "TT", otherwise it is "TAI". Note, if the System attribute is set
*     so that the TimeFrame represents Besselian Epoch, then an error
*     will be reported if an attempt is made to set the TimeScale to
*     anything other than TT.
*
*     Note, the supported time scales fall into two groups. The first group
*     containing  UT1, GMST, LAST and LMST define time in terms of the
*     orientation of the earth. The second group (containing all the remaining
*     time scales) define time in terms of an atomic process. Since the rate of
*     rotation of the earth varies in an unpredictable way, conversion between
*     two timescales in different groups relies on a value being supplied for
*     the Dut1 attribute (defined by the parent Frame class). This attribute
*     specifies the difference between the UT1 and UTC time scales, in seconds,
*     and defaults to zero. See the documentation for the Dut1 attribute for
*     further details.

*  Applicability:
*     TimeFrame
*        All TimeFrames have this attribute.

*  Time Scales:
*     The TimeFrame class supports the following TimeScale values (all are
*     case-insensitive):
*
*     - "TAI" - International Atomic Time
*     - "UTC" - Coordinated Universal Time
*     - "UT1" - Universal Time
*     - "GMST" - Greenwich Mean Sidereal Time
*     - "LAST" - Local Apparent Sidereal Time
*     - "LMST" - Local Mean Sidereal Time
*     - "TT" - Terrestrial Time
*     - "TDB" - Barycentric Dynamical Time
*     - "TCB" - Barycentric Coordinate Time
*     - "TCG" - Geocentric Coordinate Time
*     - "LT" - Local Time (the offset from UTC is given by attribute LTOffset)
*
*     An very informative description of these and other time scales is
*     available at http://www.ucolick.org/~sla/leapsecs/timescales.html.

*  UTC Warnings:
*     UTC should ideally be expressed using separate hours, minutes and
*     seconds fields (or at least in seconds for a given date) if leap seconds
*     are to be taken into account. Since the TimeFrame class represents
*     each moment in time using a single floating point number (the axis value)
*     there will be an ambiguity during a leap second. Thus an error of up to
*     1 second can result when using AST to convert a UTC time to another
*     time scale if the time occurs within a leap second. Leap seconds
*     occur at most twice a year, and are introduced to take account of
*     variation in the rotation of the earth. The most recent leap second
*     occurred on 1st January 1999. Although in the vast majority of cases
*     leap second ambiguities won't matter, there are potential problems in
*     on-line data acquisition systems and in critical applications involving
*     taking the difference between two times.

*att--
*/
astMAKE_TEST(TimeFrame,TimeScale,( this->timescale != AST__BADTS ))

/* Copy constructor. */
/* ----------------- */

/* Destructor. */
/* ----------- */

/* Dump function. */
/* -------------- */
static void Dump( AstObject *this_object, AstChannel *channel, int *status ) {
/*
*  Name:
*     Dump

*  Purpose:
*     Dump function for TimeFrame objects.

*  Type:
*     Private function.

*  Synopsis:
*     void Dump( AstObject *this, AstChannel *channel, int *status )

*  Description:
*     This function implements the Dump function which writes out data
*     for the TimeFrame class to an output Channel.

*  Parameters:
*     this
*        Pointer to the TimeFrame whose data are being written.
*     channel
*        Pointer to the Channel to which the data are being written.
*     status
*        Pointer to the inherited status variable.
*/

/* Local Variables: */
   AstTimeFrame *this;           /* Pointer to the TimeFrame structure */
   AstTimeScaleType ts;          /* TimeScale attribute value */
   const char *sval;             /* Pointer to string value */
   double dval;                  /* Double value */
   int set;                      /* Attribute value set? */

/* Check the global error status. */
   if ( !astOK ) return;

/* Obtain a pointer to the TimeFrame structure. */
   this = (AstTimeFrame *) this_object;

/* Write out values representing the instance variables for the
   TimeFrame class.  Accompany these with appropriate comment strings,
   possibly depending on the values being written.*/

/* In the case of attributes, we first use the appropriate (private)
   Test...  member function to see if they are set. If so, we then use
   the (private) Get... function to obtain the value to be written
   out.

   For attributes which are not set, we use the astGet... method to
   obtain the value instead. This will supply a default value
   (possibly provided by a derived class which over-rides this method)
   which is more useful to a human reader as it corresponds to the
   actual default attribute value.  Since "set" will be zero, these
   values are for information only and will not be read back. */

/* TimeScale. */
/* ---------- */
   set = TestTimeScale( this, status );
   ts = set ? GetTimeScale( this, status ) : astGetTimeScale( this );

/* If set, convert explicitly to a string for the external
   representation. */
   sval = "";
   if ( set ) {
      if ( astOK ) {
         sval = TimeScaleString( ts, status );

/* Report an error if the TimeScale value was not recognised. */
         if ( !sval ) {
            astError( AST__SCSIN,
                     "%s(%s): Corrupt %s contains invalid time scale "
                     "identification code (%d).", status, "astWrite",
                     astGetClass( channel ), astGetClass( this ), (int) ts );
         }
      }

/* If not set, use astGetAttrib which returns a string value using
   (possibly over-ridden) methods. */
   } else {
      sval = astGetAttrib( this_object, "timescale" );
   }

/* Write out the value. */
   astWriteString( channel, "TmScl", set, 1, sval, "Time scale" );

/* AlignTimeScale. */
/* --------------- */
   set = TestAlignTimeScale( this, status );
   ts = set ? GetAlignTimeScale( this, status ) : astGetAlignTimeScale( this );

/* If set, convert explicitly to a string for the external representation. */
   if ( set ) {
      if ( astOK ) {
         sval = TimeScaleString( ts, status );

/* Report an error if the TimeScale value was not recognised. */
         if ( !sval ) {
            astError( AST__SCSIN,
                     "%s(%s): Corrupt %s contains invalid alignment time "
                     "scale identification code (%d).", status, "astWrite",
                     astGetClass( channel ), astGetClass( this ), (int) ts );
         }
      }

/* If not set, use astGetAttrib which returns a string value using
   (possibly over-ridden) methods. */
   } else {
      sval = astGetAttrib( this_object, "aligntimescale" );
   }

/* Write out the value. */
   astWriteString( channel, "ATmScl", set, 0, sval, "Alignment time scale" );

/* TimeOrigin. */
/* ----------- */
   set = TestTimeOrigin( this, status );
   dval = set ? GetTimeOrigin( this, status ) : astGetTimeOrigin( this );
   astWriteDouble( channel, "TmOrg", set, 0, dval, "Time offset" );

/* LTOffset. */
/* --------- */
   set = TestLTOffset( this, status );
   dval = set ? GetLTOffset( this, status ) : astGetLTOffset( this );
   astWriteDouble( channel, "LTOff", set, 0, dval, "Local Time offset from UTC" );

}

/* Standard class functions. */
/* ========================= */
/* Implement the astIsATimeFrame and astCheckTimeFrame functions using the
   macros defined for this purpose in the "object.h" header file. */
astMAKE_ISA(TimeFrame,Frame)
astMAKE_CHECK(TimeFrame)

AstTimeFrame *astTimeFrame_( const char *options, int *status, ...) {
/*
*+
*  Name:
*     astTimeFrame

*  Purpose:
*     Create a TimeFrame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "timeframe.h"
*     AstTimeFrame *astTimeFrame( const char *options, int *status, ... )

*  Class Membership:
*     TimeFrame constructor.

*  Description:
*     This function creates a new TimeFrame and optionally initialises its
*     attributes.

*  Parameters:
*     options
*        Pointer to a null terminated string containing an optional
*        comma-separated list of attribute assignments to be used for
*        initialising the new TimeFrame. The syntax used is the same as for the
*        astSet method and may include "printf" format specifiers identified
*        by "%" symbols in the normal way.
*     status
*        Pointer to the inherited status variable.
*     ...
*        If the "options" string contains "%" format specifiers, then an
*        optional list of arguments may follow it in order to supply values to
*        be substituted for these specifiers. The rules for supplying these
*        are identical to those for the astSet method (and for the C "printf"
*        function).

*  Returned Value:
*     A pointer to the new TimeFrame.

*  Notes:
*     -  A NULL pointer will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.
*-

*  Implementation Notes:
*     - This function implements the basic TimeFrame constructor which
*     is available via the protected interface to the TimeFrame class.
*     A public interface is provided by the astTimeFrameId_ function.
*/

/* Local Variables: */
   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
   AstMapping *um;               /* Mapping from default to actual units */
   AstTimeFrame *new;            /* Pointer to new TimeFrame */
   AstSystemType s;              /* System */
   const char *u;                /* Units string */
   va_list args;                 /* Variable argument list */

/* Get a pointer to the thread specific global data structure. */
   astGET_GLOBALS(NULL);

/* Check the global status. */
   if ( !astOK ) return NULL;

/* Initialise the TimeFrame, allocating memory and initialising the virtual
   function table as well if necessary. */
   new = astInitTimeFrame( NULL, sizeof( AstTimeFrame ), !class_init,
                           &class_vtab, "TimeFrame" );

/* If successful, note that the virtual function table has been initialised. */
   if ( astOK ) {
      class_init = 1;

/* Obtain the variable argument list and pass it along with the options string
   to the astVSet method to initialise the new TimeFrame's attributes. */
      va_start( args, status );
      astVSet( new, options, NULL, args );
      va_end( args );

/* Check the Units are appropriate for the System. */
      u = astGetUnit( new, 0 );
      s = astGetSystem( new );
      um = astUnitMapper( DefUnit( s, "astTimeFrame", "TimeFrame", status ),
                          u, NULL, NULL );
      if( um ) {
         um = astAnnul( um );
      } else {
         astError( AST__BADUN, "astTimeFrame: Inappropriate units (%s) "
                   "specified for a %s axis.", status, u, SystemLabel( s, status ) );
      }

/* If an error occurred, clean up by deleting the new object. */
      if ( !astOK ) new = astDelete( new );
   }

/* Return a pointer to the new TimeFrame. */
   return new;
}

AstTimeFrame *astInitTimeFrame_( void *mem, size_t size, int init,
                                 AstTimeFrameVtab *vtab, const char *name, int *status ) {
/*
*+
*  Name:
*     astInitTimeFrame

*  Purpose:
*     Initialise a TimeFrame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "timeframe.h"
*     AstTimeFrame *astInitTimeFrame( void *mem, size_t size, int init,
*                                     AstFrameVtab *vtab, const char *name )

*  Class Membership:
*     TimeFrame initialiser.

*  Description:
*     This function is provided for use by class implementations to
*     initialise a new TimeFrame object. It allocates memory (if
*     necessary) to accommodate the TimeFrame plus any additional data
*     associated with the derived class. It then initialises a
*     TimeFrame structure at the start of this memory. If the "init"
*     flag is set, it also initialises the contents of a virtual function
*     table for a TimeFrame at the start of the memory passed via the
*     "vtab" parameter.

*  Parameters:
*     mem
*        A pointer to the memory in which the TimeFrame is to be
*	created. This must be of sufficient size to accommodate the
*	TimeFrame data (sizeof(TimeFrame)) plus any data used by
*	the derived class. If a value of NULL is given, this function
*	will allocate the memory itself using the "size" parameter to
*	determine its size.
*     size
*        The amount of memory used by the TimeFrame (plus derived
*	class data). This will be used to allocate memory if a value of
*	NULL is given for the "mem" parameter. This value is also stored
*	in the TimeFrame structure, so a valid value must be supplied
*	even if not required for allocating memory.
*     init
*        A logical flag indicating if the TimeFrame's virtual function
*	table is to be initialised. If this value is non-zero, the
*	virtual function table will be initialised by this function.
*     vtab
*        Pointer to the start of the virtual function table to be
*	associated with the new TimeFrame.
*     name
*        Pointer to a constant null-terminated character string which
*	contains the name of the class to which the new object belongs
*	(it is this pointer value that will subsequently be returned by
*	the astGetClass method).

*  Returned Value:
*     A pointer to the new TimeFrame.

*  Notes:
*     -  A null pointer will be returned if this function is invoked with the
*     global error status set, or if it should fail for any reason.
*-
*/

/* Local Variables: */
   AstTimeFrame *new;        /* Pointer to the new TimeFrame */

/* Check the global status. */
   if ( !astOK ) return NULL;

/* If necessary, initialise the virtual function table. */
   if ( init ) astInitTimeFrameVtab( vtab, name );

/* Initialise a 1D Frame structure (the parent class) as the first component
   within the TimeFrame structure, allocating memory if necessary. */
   new = (AstTimeFrame *) astInitFrame( mem, size, 0,
                                        (AstFrameVtab *) vtab, name, 1 );

   if ( astOK ) {

/* Initialise the TimeFrame data. */
/* ----------------------------- */
/* Initialise all attributes to their "undefined" values. */
      new->timeorigin = AST__BAD;
      new->ltoffset = AST__BAD;
      new->timescale = AST__BADTS;
      new->aligntimescale = AST__BADTS;

/* If an error occurred, clean up by deleting the new object. */
      if ( !astOK ) new = astDelete( new );

   }

/* Return a pointer to the new object. */
   return new;
}

AstTimeFrame *astLoadTimeFrame_( void *mem, size_t size,
                                 AstTimeFrameVtab *vtab,
                                 const char *name, AstChannel *channel, int *status ) {
/*
*+
*  Name:
*     astLoadTimeFrame

*  Purpose:
*     Load a TimeFrame.

*  Type:
*     Protected function.

*  Synopsis:
*     #include "timeframe.h"
*     AstTimeFrame *astLoadTimeFrame( void *mem, size_t size,
*                                      AstTimeFrameVtab *vtab,
*                                      const char *name, AstChannel *channel )

*  Class Membership:
*     TimeFrame loader.

*  Description:
*     This function is provided to load a new TimeFrame using data read
*     from a Channel. It first loads the data used by the parent class
*     (which allocates memory if necessary) and then initialises a
*     TimeFrame structure in this memory, using data read from the
*     input Channel.

*  Parameters:
*     mem
*        A pointer to the memory into which the TimeFrame is to be
*        loaded.  This must be of sufficient size to accommodate the
*        TimeFrame data (sizeof(TimeFrame)) plus any data used by
*        derived classes. If a value of NULL is given, this function
*        will allocate the memory itself using the "size" parameter to
*        determine its size.
*     size
*        The amount of memory used by the TimeFrame (plus derived class
*        data).  This will be used to allocate memory if a value of
*        NULL is given for the "mem" parameter. This value is also
*        stored in the TimeFrame structure, so a valid value must be
*        supplied even if not required for allocating memory.
*
*        If the "vtab" parameter is NULL, the "size" value is ignored
*        and sizeof(AstTimeFrame) is used instead.
*     vtab
*        Pointer to the start of the virtual function table to be
*        associated with the new TimeFrame. If this is NULL, a pointer
*        to the (static) virtual function table for the TimeFrame class
*        is used instead.
*     name
*        Pointer to a constant null-terminated character string which
*        contains the name of the class to which the new object
*        belongs (it is this pointer value that will subsequently be
*        returned by the astGetClass method).
*
*        If the "vtab" parameter is NULL, the "name" value is ignored
*        and a pointer to the string "TimeFrame" is used instead.

*  Returned Value:
*     A pointer to the new TimeFrame.

*  Notes:
*     - A null pointer will be returned if this function is invoked
*     with the global error status set, or if it should fail for any
*     reason.
*-
*/

/* Local Variables: */
   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
   AstTimeFrame *new;            /* Pointer to the new TimeFrame */
   char *sval;                   /* Pointer to string value */
   double obslat;                /* Value for ObsLat attribute */
   double obslon;                /* Value for ObsLon attribute */

/* Get a pointer to the thread specific global data structure. */
   astGET_GLOBALS(channel);

/* Initialise. */
   new = NULL;

/* Check the global error status. */
   if ( !astOK ) return new;

/* If a NULL virtual function table has been supplied, then this is
   the first loader to be invoked for this TimeFrame. In this case the
   TimeFrame belongs to this class, so supply appropriate values to be
   passed to the parent class loader (and its parent, etc.). */
   if ( !vtab ) {
      size = sizeof( AstTimeFrame );
      vtab = &class_vtab;
      name = "TimeFrame";

/* If required, initialise the virtual function table for this class. */
      if ( !class_init ) {
         astInitTimeFrameVtab( vtab, name );
         class_init = 1;
      }
   }

/* Invoke the parent class loader to load data for all the ancestral
   classes of the current one, returning a pointer to the resulting
   partly-built TimeFrame. */
   new = astLoadFrame( mem, size, (AstFrameVtab *) vtab, name,
                       channel );
   if ( astOK ) {

/* Read input data. */
/* ================ */
/* Request the input Channel to read all the input data appropriate to
   this class into the internal "values list". */
       astReadClassData( channel, "TimeFrame" );

/* Now read each individual data item from this list and use it to
   initialise the appropriate instance variable(s) for this class. */

/* In the case of attributes, we first read the "raw" input value,
   supplying the "unset" value as the default. If a "set" value is
   obtained, we then use the appropriate (private) Set... member
   function to validate and set the value properly. */

/* TimeScale. */
/* ---------- */
/* Set the default and read the external representation as a string. */
       new->timescale = AST__BADTS;
       sval = astReadString( channel, "tmscl", NULL );

/* If a value was read, convert from a string to a TimeScale code. */
       if ( sval ) {
          if ( astOK ) {
             new->timescale = TimeScaleCode( sval, status );

/* Report an error if the value wasn't recognised. */
             if ( new->timescale == AST__BADTS ) {
                astError( AST__ATTIN,
                          "astRead(%s): Invalid time scale description "
                          "\"%s\".", status, astGetClass( channel ), sval );
             }
          }

/* Free the string value. */
          sval = astFree( sval );
       }

/* AlignTimeScale. */
/* --------------- */
/* Set the default and read the external representation as a string. */
       new->aligntimescale = AST__BADTS;
       sval = astReadString( channel, "atmscl", NULL );

/* If a value was read, convert from a string to a TimeScale code. */
       if ( sval ) {
          if ( astOK ) {
             new->aligntimescale = TimeScaleCode( sval, status );

/* Report an error if the value wasn't recognised. */
             if ( new->aligntimescale == AST__BADTS ) {
                astError( AST__ATTIN,
                          "astRead(%s): Invalid alignment time scale "
                          "description \"%s\".", status, astGetClass( channel ), sval );
             }
          }

/* Free the string value. */
          sval = astFree( sval );
       }

/* ClockLat. */
/* --------- */
/* Retained for backward compatibility with older versions of AST in
   which TimeFrame had a ClockLat attribute (now ObsLat is used instead). */
      if( !astTestObsLat( new ) ) {
         obslat = astReadDouble( channel, "cllat", AST__BAD );
         if ( obslat != AST__BAD ) astSetObsLat( new, obslat );
      }

/* ClockLon. */
/* ------- */
/* Retained for backward compatibility with older versions of AST in
   which TimeFrame had a ClockLon attribute (now ObsLon is used instead). */
      if( !astTestObsLon( new ) ) {
         obslon = astReadDouble( channel, "cllon", AST__BAD );
         if ( obslon != AST__BAD ) astSetObsLon( new, obslon );
      }

/* TimeOrigin. */
/* --------- */
      new->timeorigin = astReadDouble( channel, "tmorg", AST__BAD );
      if ( TestTimeOrigin( new, status ) ) SetTimeOrigin( new, new->timeorigin, status );

/* LTOffset. */
/* --------- */
      new->ltoffset = astReadDouble( channel, "ltoff", AST__BAD );
      if ( TestLTOffset( new, status ) ) SetLTOffset( new, new->ltoffset, status );

/* If an error occurred, clean up by deleting the new TimeFrame. */
      if ( !astOK ) new = astDelete( new );
   }

/* Return the new TimeFrame pointer. */
   return new;
}

/* Virtual function interfaces. */
/* ============================ */
/* These provide the external interface to the virtual functions defined by
   this class. Each simply checks the global error status and then locates and
   executes the appropriate member function, using the function pointer stored
   in the object's virtual function table (this pointer is located using the
   astMEMBER macro defined in "object.h").

   Note that the member function may not be the one defined here, as it may
   have been over-ridden by a derived class. However, it should still have the
   same interface. */

void astSetTimeScale_( AstTimeFrame *this, AstTimeScaleType value, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,TimeFrame,SetTimeScale))(this,value, status );
}

void astClearTimeScale_( AstTimeFrame *this, int *status ){
   if ( !astOK ) return;
   (**astMEMBER(this,TimeFrame,ClearTimeScale))(this, status );
}

AstTimeScaleType astGetAlignTimeScale_( AstTimeFrame *this, int *status ) {
   if ( !astOK ) return AST__BADTS;
   return (**astMEMBER(this,TimeFrame,GetAlignTimeScale))(this, status );
}

AstTimeScaleType astGetTimeScale_( AstTimeFrame *this, int *status ) {
   if ( !astOK ) return AST__BADTS;
   return (**astMEMBER(this,TimeFrame,GetTimeScale))(this, status );
}

double astCurrentTime_( AstTimeFrame *this, int *status ){
   if ( !astOK ) return AST__BAD;
   return (**astMEMBER(this,TimeFrame,CurrentTime))(this, status );
}



/* Special public interface functions. */
/* =================================== */
/* These provide the public interface to certain special functions
   whose public interface cannot be handled using macros (such as
   astINVOKE) alone. In general, they are named after the
   corresponding protected version of the function, but with "Id"
   appended to the name. */

/* Public Interface Function Prototypes. */
/* ------------------------------------- */
/* The following functions have public prototypes only (i.e. no
   protected prototypes), so we must provide local prototypes for use
   within this module. */
AstTimeFrame *astTimeFrameId_( const char *, ... );

/* Special interface function implementations. */
/* ------------------------------------------- */
AstTimeFrame *astTimeFrameId_( const char *options, ... ) {
/*
*++
*  Name:
c     astTimeFrame
f     AST_TIMEFRAME

*  Purpose:
*     Create a TimeFrame.

*  Type:
*     Public function.

*  Synopsis:
c     #include "timeframe.h"
c     AstTimeFrame *astTimeFrame( const char *options, ... )
f     RESULT = AST_TIMEFRAME( OPTIONS, STATUS )

*  Class Membership:
*     TimeFrame constructor.

*  Description:
*     This function creates a new TimeFrame and optionally initialises
*     its attributes.
*
*     A TimeFrame is a specialised form of one-dimensional Frame which
*     represents various coordinate systems used to describe positions in
*     time.
*
*     A TimeFrame represents a moment in time as either an Modified Julian
*     Date (MJD), a Julian Date (JD), a Besselian epoch or a Julian epoch,
*     as determined by the System attribute. Optionally, a zero point can be
*     specified (using attribute TimeOrigin) which results in the TimeFrame
*     representing time offsets from the specified zero point.
*
*     Even though JD and MJD are defined as being in units of days, the
*     TimeFrame class allows other units to be used (via the Unit attribute)
*     on the basis of simple scalings (60 seconds = 1 minute, 60 minutes = 1
*     hour, 24 hours = 1 day, 365.25 days = 1 year). Likewise, Julian epochs
*     can be described in units other than the usual years. Besselian epoch
*     are always represented in units of (tropical) years.
*
*     The TimeScale attribute allows the time scale to be specified (that
*     is, the physical proces used to define the rate of flow of time).
*     MJD, JD and Julian epoch can be used to represent a time in any
*     supported time scale. However, Besselian epoch may only be used with the
*     "TT" (Terrestrial Time) time scale. The list of supported time scales
*     includes universal time and siderial time. Strictly, these represent
*     angles rather than time scales, but are included in the list since
*     they are in common use and are often thought of as time scales.
*
*     When a time value is formatted it can be formated either as a simple
*     floating point value, or as a Gregorian date (see the Format
*     attribute).

*  Parameters:
c     options
f     OPTIONS = CHARACTER * ( * ) (Given)
c        Pointer to a null-terminated string containing an optional
c        comma-separated list of attribute assignments to be used for
c        initialising the new TimeFrame. The syntax used is identical to
c        that for the astSet function and may include "printf" format
c        specifiers identified by "%" symbols in the normal way.
c        If no initialisation is required, a zero-length string may be
c        supplied.
f        A character string containing an optional comma-separated
f        list of attribute assignments to be used for initialising the
f        new TimeFrame. The syntax used is identical to that for the
f        AST_SET routine. If no initialisation is required, a blank
f        value may be supplied.
c     ...
c        If the "options" string contains "%" format specifiers, then
c        an optional list of additional arguments may follow it in
c        order to supply values to be substituted for these
c        specifiers. The rules for supplying these are identical to
c        those for the astSet function (and for the C "printf"
c        function).
f     STATUS = INTEGER (Given and Returned)
f        The global status.

*  Returned Value:
c     astTimeFrame()
f     AST_TIMEFRAME = INTEGER
*        A pointer to the new TimeFrame.

*  Notes:
*     - When conversion between two TimeFrames is requested (as when
c     supplying TimeFrames to astConvert),
f     supplying TimeFrames AST_CONVERT),
*     account will be taken of the nature of the time coordinate systems
*     they represent, together with any qualifying time scale, offset,
*     unit, etc. The AlignSystem and AlignTimeScale attributes will also be
*     taken into account.
*     - A null Object pointer (AST__NULL) will be returned if this
c     function is invoked with the AST error status set, or if it
f     function is invoked with STATUS set to an error value, or if it
*     should fail for any reason.
*--

*  Implementation Notes:
*     - This function implements the external (public) interface to
*     the astTimeFrame constructor function. It returns an ID value
*     (instead of a true C pointer) to external users, and must be
*     provided because astTimeFrame_ has a variable argument list which
*     cannot be encapsulated in a macro (where this conversion would
*     otherwise occur).
*     - The variable argument list also prevents this function from
*     invoking astTimeFrame_ directly, so it must be a
*     re-implementation of it in all respects, except for the final
*     conversion of the result to an ID value.
*/

/* Local Variables: */
   astDECLARE_GLOBALS            /* Pointer to thread-specific global data */
   AstMapping *um;               /* Mapping from default to actual units */
   AstTimeFrame *new;            /* Pointer to new TimeFrame */
   AstSystemType s;              /* System */
   const char *u;                /* Units string */
   va_list args;                 /* Variable argument list */

   int *status;                  /* Pointer to inherited status value */

/* Get a pointer to the thread specific global data structure. */
   astGET_GLOBALS(NULL);

/* Get a pointer to the inherited status value. */
   status = astGetStatusPtr;

/* Check the global status. */
   if ( !astOK ) return NULL;

/* Initialise the TimeFrame, allocating memory and initialising the virtual
   function table as well if necessary. */
   new = astInitTimeFrame( NULL, sizeof( AstTimeFrame ), !class_init,
                           &class_vtab, "TimeFrame" );

/* If successful, note that the virtual function table has been initialised. */
   if ( astOK ) {
      class_init = 1;

/* Obtain the variable argument list and pass it along with the options string
   to the astVSet method to initialise the new TimeFrame's attributes. */
      va_start( args, options );
      astVSet( new, options, NULL, args );
      va_end( args );

/* Check the Units are appropriate for the System. */
      u = astGetUnit( new, 0 );
      s = astGetSystem( new );
      um = astUnitMapper( DefUnit( s, "astTimeFrame", "TimeFrame", status ),
                          u, NULL, NULL );
      if( um ) {
         um = astAnnul( um );
      } else {
         astError( AST__BADUN, "astTimeFrame: Inappropriate units (%s) "
                   "specified for a %s axis.", status, u, SystemLabel( s, status ) );
      }

/* If an error occurred, clean up by deleting the new object. */
      if ( !astOK ) new = astDelete( new );
   }

/* Return an ID value for the new TimeFrame. */
   return astMakeId( new );
}