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
7482
7483
7484
7485
7486
7487
7488
7489
7490
7491
7492
7493
7494
7495
7496
7497
7498
7499
7500
7501
7502
7503
7504
7505
7506
7507
7508
7509
7510
7511
7512
7513
7514
7515
7516
7517
7518
7519
7520
7521
7522
7523
7524
7525
7526
7527
7528
7529
7530
7531
7532
7533
7534
7535
7536
7537
7538
7539
7540
7541
7542
7543
7544
7545
7546
7547
7548
7549
7550
7551
7552
7553
7554
7555
7556
7557
7558
7559
7560
7561
7562
7563
7564
7565
7566
7567
7568
7569
7570
7571
7572
7573
7574
7575
7576
7577
7578
7579
7580
7581
7582
7583
7584
7585
7586
7587
7588
7589
7590
7591
7592
7593
7594
7595
7596
7597
7598
7599
7600
7601
7602
7603
7604
7605
7606
7607
7608
7609
7610
7611
7612
7613
7614
7615
7616
7617
7618
7619
7620
7621
7622
7623
7624
7625
7626
7627
7628
7629
7630
7631
7632
7633
7634
7635
7636
7637
7638
7639
7640
7641
7642
7643
7644
7645
7646
7647
7648
7649
7650
7651
7652
7653
7654
7655
7656
7657
7658
7659
7660
7661
7662
7663
7664
7665
7666
7667
7668
7669
7670
7671
7672
7673
7674
7675
7676
7677
7678
7679
7680
7681
7682
7683
7684
7685
7686
7687
7688
7689
7690
7691
7692
7693
7694
7695
7696
7697
7698
7699
7700
7701
7702
7703
7704
7705
7706
7707
7708
7709
7710
7711
7712
7713
7714
7715
7716
7717
7718
7719
7720
7721
7722
7723
7724
7725
7726
7727
7728
7729
7730
7731
7732
7733
7734
7735
7736
7737
7738
7739
7740
7741
7742
7743
7744
7745
7746
7747
7748
7749
7750
7751
7752
7753
7754
7755
7756
7757
7758
7759
7760
7761
7762
7763
7764
7765
7766
7767
7768
7769
7770
7771
7772
7773
7774
7775
7776
7777
7778
7779
7780
7781
7782
7783
7784
7785
7786
7787
7788
7789
7790
7791
7792
7793
7794
7795
7796
7797
7798
7799
7800
7801
7802
7803
7804
7805
7806
7807
7808
7809
7810
7811
7812
7813
7814
7815
7816
7817
7818
7819
7820
7821
7822
7823
7824
7825
7826
7827
7828
7829
7830
7831
7832
7833
7834
7835
7836
7837
7838
7839
7840
7841
7842
7843
7844
7845
7846
7847
7848
7849
7850
7851
7852
7853
7854
7855
7856
7857
7858
7859
7860
7861
7862
7863
7864
7865
7866
7867
7868
7869
7870
7871
7872
7873
7874
7875
7876
7877
7878
7879
7880
7881
7882
7883
7884
7885
7886
7887
7888
7889
7890
7891
7892
7893
7894
7895
7896
7897
7898
7899
7900
7901
7902
7903
7904
7905
7906
7907
7908
7909
7910
7911
7912
7913
7914
7915
7916
7917
7918
7919
7920
7921
7922
7923
7924
7925
7926
7927
7928
7929
7930
7931
7932
7933
7934
7935
7936
7937
7938
7939
7940
7941
7942
7943
7944
7945
7946
7947
7948
7949
7950
7951
7952
7953
7954
7955
7956
7957
7958
7959
7960
7961
7962
7963
7964
7965
7966
7967
7968
7969
7970
7971
7972
7973
7974
7975
7976
7977
7978
7979
7980
7981
7982
7983
7984
7985
7986
7987
7988
7989
7990
7991
7992
7993
7994
7995
7996
7997
7998
7999
8000
8001
8002
8003
8004
8005
8006
8007
8008
8009
8010
8011
8012
8013
8014
8015
8016
8017
8018
8019
8020
8021
8022
8023
8024
8025
8026
8027
8028
8029
8030
8031
8032
8033
8034
8035
8036
8037
8038
8039
8040
8041
8042
8043
8044
8045
8046
8047
8048
8049
8050
8051
8052
8053
8054
8055
8056
8057
8058
8059
8060
8061
8062
8063
8064
8065
8066
8067
8068
8069
8070
8071
8072
8073
8074
8075
8076
8077
8078
8079
8080
8081
8082
8083
8084
8085
8086
8087
8088
8089
8090
8091
8092
8093
8094
8095
8096
8097
8098
8099
8100
8101
8102
8103
8104
8105
8106
8107
8108
8109
8110
8111
8112
8113
8114
8115
8116
8117
8118
8119
8120
8121
8122
8123
8124
8125
8126
8127
8128
8129
8130
8131
8132
8133
8134
8135
8136
8137
8138
8139
8140
8141
8142
8143
8144
8145
8146
8147
8148
8149
8150
8151
8152
8153
8154
8155
8156
8157
8158
8159
8160
8161
8162
8163
8164
8165
8166
8167
8168
8169
8170
8171
8172
8173
8174
8175
8176
8177
8178
8179
8180
8181
8182
8183
8184
8185
8186
8187
8188
8189
8190
8191
8192
8193
8194
8195
8196
8197
8198
8199
8200
8201
8202
8203
8204
8205
8206
8207
8208
8209
8210
8211
8212
8213
8214
8215
8216
8217
8218
8219
8220
8221
8222
8223
8224
8225
8226
8227
8228
8229
8230
8231
8232
8233
8234
8235
8236
8237
8238
8239
8240
8241
8242
8243
8244
8245
8246
8247
8248
8249
8250
8251
8252
8253
8254
8255
8256
8257
8258
8259
8260
8261
8262
8263
8264
8265
8266
8267
8268
8269
8270
8271
8272
8273
8274
8275
8276
8277
8278
8279
8280
8281
8282
8283
8284
8285
8286
8287
8288
8289
8290
8291
8292
8293
8294
8295
8296
8297
8298
8299
8300
8301
8302
8303
8304
8305
8306
8307
8308
8309
8310
8311
8312
8313
8314
8315
8316
8317
8318
8319
8320
8321
8322
8323
8324
8325
8326
8327
8328
8329
8330
8331
8332
8333
8334
8335
8336
8337
8338
8339
8340
8341
8342
8343
8344
8345
8346
8347
8348
8349
8350
8351
8352
8353
8354
8355
8356
8357
8358
8359
8360
8361
8362
8363
8364
8365
8366
8367
8368
8369
8370
8371
8372
8373
8374
8375
8376
8377
8378
8379
8380
8381
8382
8383
8384
8385
8386
8387
8388
8389
8390
8391
8392
8393
8394
8395
8396
8397
8398
8399
8400
8401
8402
8403
8404
8405
8406
8407
8408
8409
8410
8411
8412
8413
8414
8415
8416
8417
8418
8419
8420
8421
8422
8423
8424
8425
8426
8427
8428
8429
8430
8431
8432
8433
8434
8435
8436
8437
8438
8439
8440
8441
8442
8443
8444
8445
8446
8447
8448
8449
8450
8451
8452
8453
8454
8455
8456
8457
8458
8459
8460
8461
8462
8463
8464
8465
8466
8467
8468
8469
8470
8471
8472
8473
8474
8475
8476
8477
8478
8479
8480
8481
8482
8483
8484
8485
8486
8487
8488
8489
8490
8491
8492
8493
8494
8495
8496
8497
8498
8499
8500
8501
8502
8503
8504
8505
8506
8507
8508
8509
8510
8511
8512
8513
8514
8515
8516
8517
8518
8519
8520
8521
8522
8523
8524
8525
8526
8527
8528
8529
8530
8531
8532
8533
8534
8535
8536
8537
8538
8539
8540
8541
8542
8543
8544
8545
8546
8547
8548
8549
8550
8551
8552
8553
8554
8555
8556
8557
8558
8559
8560
8561
8562
8563
8564
8565
8566
8567
8568
8569
8570
8571
8572
8573
8574
8575
8576
8577
8578
8579
8580
8581
8582
8583
8584
8585
8586
8587
8588
8589
8590
8591
8592
8593
8594
8595
8596
8597
8598
8599
8600
8601
8602
8603
8604
8605
8606
8607
8608
8609
8610
8611
8612
8613
8614
8615
8616
8617
8618
8619
8620
8621
8622
8623
8624
8625
8626
8627
8628
8629
8630
8631
8632
8633
8634
8635
8636
8637
8638
8639
8640
8641
8642
8643
8644
8645
8646
8647
8648
8649
8650
8651
8652
8653
8654
8655
8656
8657
8658
8659
8660
8661
8662
8663
8664
8665
8666
8667
8668
8669
8670
8671
8672
8673
8674
8675
8676
8677
8678
8679
8680
8681
8682
8683
8684
8685
8686
8687
8688
8689
8690
8691
8692
8693
8694
8695
8696
8697
8698
8699
8700
8701
8702
8703
8704
8705
8706
8707
8708
8709
8710
8711
8712
8713
8714
8715
8716
8717
8718
8719
8720
8721
8722
8723
8724
8725
8726
8727
8728
8729
8730
8731
8732
8733
8734
8735
8736
8737
8738
8739
8740
8741
8742
8743
8744
8745
8746
8747
8748
8749
8750
8751
8752
8753
8754
8755
8756
8757
8758
8759
8760
8761
8762
8763
8764
8765
8766
8767
8768
8769
8770
8771
8772
8773
8774
8775
8776
8777
8778
8779
8780
8781
8782
8783
8784
8785
8786
8787
8788
8789
8790
8791
8792
8793
8794
8795
8796
8797
8798
8799
8800
8801
8802
8803
8804
8805
8806
8807
8808
8809
8810
8811
8812
8813
8814
8815
8816
8817
8818
8819
8820
8821
8822
8823
8824
8825
8826
8827
8828
8829
8830
8831
8832
8833
8834
8835
8836
8837
8838
8839
8840
8841
8842
8843
8844
8845
8846
8847
8848
8849
8850
8851
8852
8853
8854
8855
8856
8857
8858
8859
8860
8861
8862
8863
8864
8865
8866
8867
8868
8869
8870
8871
8872
8873
8874
8875
8876
8877
8878
8879
8880
8881
8882
8883
8884
8885
8886
8887
8888
8889
8890
8891
8892
8893
8894
8895
8896
8897
8898
8899
8900
8901
8902
8903
8904
8905
8906
8907
8908
8909
8910
8911
8912
8913
8914
8915
8916
8917
8918
8919
8920
8921
8922
8923
8924
8925
8926
8927
8928
8929
8930
8931
8932
8933
8934
8935
8936
8937
8938
8939
8940
8941
8942
8943
8944
8945
8946
8947
8948
8949
8950
8951
8952
8953
8954
8955
8956
8957
8958
8959
8960
8961
8962
8963
8964
8965
8966
8967
8968
8969
8970
8971
8972
8973
8974
8975
8976
8977
8978
8979
8980
8981
8982
8983
8984
8985
8986
8987
8988
8989
8990
8991
8992
8993
8994
8995
8996
8997
8998
8999
9000
9001
9002
9003
9004
9005
9006
9007
9008
9009
9010
9011
9012
9013
9014
9015
9016
9017
9018
9019
9020
9021
9022
9023
9024
9025
9026
9027
9028
9029
9030
9031
9032
9033
9034
9035
9036
9037
9038
9039
9040
9041
9042
9043
9044
9045
9046
9047
9048
9049
9050
9051
9052
9053
9054
9055
9056
9057
9058
9059
9060
9061
9062
9063
9064
9065
9066
9067
9068
9069
9070
9071
9072
9073
9074
9075
9076
9077
9078
9079
9080
9081
9082
9083
9084
9085
9086
9087
9088
9089
9090
9091
9092
9093
9094
9095
9096
9097
9098
9099
9100
9101
9102
9103
9104
9105
9106
9107
9108
9109
9110
9111
9112
9113
9114
9115
9116
9117
9118
9119
9120
9121
9122
9123
9124
9125
9126
9127
9128
9129
9130
9131
9132
9133
9134
9135
9136
9137
9138
9139
9140
9141
9142
9143
9144
9145
9146
9147
9148
9149
9150
9151
9152
9153
9154
9155
9156
9157
9158
9159
9160
9161
9162
9163
9164
9165
9166
9167
9168
9169
9170
9171
9172
9173
9174
9175
9176
9177
9178
9179
9180
9181
9182
9183
9184
9185
9186
9187
9188
9189
9190
9191
9192
9193
9194
9195
9196
9197
9198
9199
9200
9201
9202
9203
9204
9205
9206
9207
9208
9209
9210
9211
9212
9213
9214
9215
9216
9217
9218
9219
9220
9221
9222
9223
9224
9225
9226
9227
9228
9229
9230
9231
9232
9233
9234
9235
9236
9237
9238
9239
9240
9241
9242
9243
9244
9245
9246
9247
9248
9249
9250
9251
9252
9253
9254
9255
9256
9257
9258
9259
9260
9261
9262
9263
9264
9265
9266
9267
9268
9269
9270
9271
9272
9273
9274
9275
9276
9277
9278
9279
9280
9281
9282
9283
9284
9285
9286
9287
9288
9289
9290
9291
9292
9293
9294
9295
9296
9297
9298
9299
9300
9301
9302
9303
9304
9305
9306
9307
9308
9309
9310
9311
9312
9313
9314
9315
9316
9317
9318
9319
9320
9321
9322
9323
9324
9325
9326
9327
9328
9329
9330
9331
9332
9333
9334
9335
9336
9337
9338
9339
9340
9341
9342
9343
9344
9345
9346
9347
9348
9349
9350
9351
9352
9353
9354
9355
9356
9357
9358
9359
9360
9361
9362
9363
9364
9365
9366
9367
9368
9369
9370
9371
9372
9373
9374
9375
9376
9377
9378
9379
9380
9381
9382
9383
9384
9385
9386
9387
9388
9389
9390
9391
9392
9393
9394
9395
9396
9397
9398
9399
9400
9401
9402
9403
9404
9405
9406
9407
9408
9409
9410
9411
9412
9413
9414
9415
9416
9417
9418
9419
9420
9421
9422
9423
9424
9425
9426
9427
9428
9429
9430
9431
9432
9433
9434
9435
9436
9437
9438
9439
9440
9441
9442
9443
9444
9445
9446
9447
9448
9449
9450
9451
9452
9453
9454
9455
9456
9457
9458
9459
9460
9461
9462
9463
9464
9465
9466
9467
9468
9469
9470
9471
9472
9473
9474
9475
9476
9477
9478
9479
9480
9481
9482
9483
9484
9485
9486
9487
9488
9489
9490
9491
9492
9493
9494
9495
9496
9497
9498
9499
9500
9501
9502
9503
9504
9505
9506
9507
9508
9509
9510
9511
9512
9513
9514
9515
9516
9517
9518
9519
9520
9521
9522
9523
9524
9525
9526
9527
9528
9529
9530
9531
9532
9533
9534
9535
9536
9537
9538
9539
9540
9541
9542
9543
9544
9545
9546
9547
9548
9549
9550
9551
9552
9553
9554
9555
9556
9557
9558
9559
9560
9561
9562
9563
9564
9565
9566
9567
9568
9569
9570
9571
9572
9573
9574
9575
9576
9577
9578
9579
9580
9581
9582
9583
9584
9585
9586
9587
9588
9589
9590
9591
9592
9593
9594
9595
9596
9597
9598
9599
9600
9601
9602
9603
9604
9605
9606
9607
9608
9609
9610
9611
9612
9613
9614
9615
9616
9617
9618
9619
9620
9621
9622
9623
9624
9625
9626
9627
9628
9629
9630
9631
9632
9633
9634
9635
9636
9637
9638
9639
9640
9641
9642
9643
9644
9645
9646
9647
9648
9649
9650
9651
9652
9653
9654
9655
9656
9657
9658
9659
9660
9661
9662
9663
9664
9665
9666
9667
9668
9669
9670
9671
9672
9673
9674
9675
9676
9677
9678
9679
9680
9681
9682
9683
9684
9685
9686
9687
9688
9689
9690
9691
9692
9693
9694
9695
9696
9697
9698
9699
9700
9701
9702
9703
9704
9705
9706
9707
9708
9709
9710
9711
9712
9713
9714
9715
9716
9717
9718
9719
9720
9721
9722
9723
9724
9725
9726
9727
9728
9729
9730
9731
9732
9733
9734
9735
9736
9737
9738
9739
9740
9741
9742
9743
9744
9745
9746
9747
9748
9749
9750
9751
9752
9753
9754
9755
9756
9757
9758
9759
9760
9761
9762
9763
9764
9765
9766
9767
9768
9769
9770
9771
9772
9773
9774
9775
9776
9777
9778
9779
9780
9781
9782
9783
9784
9785
9786
9787
9788
9789
9790
9791
9792
9793
9794
9795
9796
9797
9798
9799
9800
9801
9802
9803
9804
9805
9806
9807
9808
9809
9810
9811
9812
9813
9814
9815
9816
9817
9818
9819
9820
9821
9822
9823
9824
9825
9826
9827
9828
9829
9830
9831
9832
9833
9834
9835
9836
9837
9838
9839
9840
9841
9842
9843
9844
9845
9846
9847
9848
9849
9850
9851
9852
9853
9854
9855
9856
9857
9858
9859
9860
9861
9862
9863
9864
9865
9866
9867
9868
9869
9870
9871
9872
9873
9874
9875
9876
9877
9878
9879
9880
9881
9882
9883
9884
9885
9886
9887
9888
9889
9890
9891
9892
9893
9894
9895
9896
9897
9898
9899
9900
9901
9902
9903
9904
9905
9906
9907
9908
9909
9910
9911
9912
9913
9914
9915
9916
9917
9918
9919
9920
9921
9922
9923
9924
9925
9926
9927
9928
9929
9930
9931
9932
9933
9934
9935
9936
9937
9938
9939
9940
9941
9942
9943
9944
9945
9946
9947
9948
9949
9950
9951
9952
9953
9954
9955
9956
9957
9958
9959
9960
9961
9962
9963
9964
9965
9966
9967
9968
9969
9970
9971
9972
9973
9974
9975
9976
9977
9978
9979
9980
9981
9982
9983
9984
9985
9986
9987
9988
9989
9990
9991
9992
9993
9994
9995
9996
9997
9998
9999
10000
10001
10002
10003
10004
10005
10006
10007
10008
10009
10010
10011
10012
10013
10014
10015
10016
10017
10018
10019
10020
10021
10022
10023
10024
10025
10026
10027
10028
10029
10030
10031
10032
10033
10034
10035
10036
10037
10038
10039
10040
10041
10042
10043
10044
10045
10046
10047
10048
10049
10050
10051
10052
10053
10054
10055
10056
10057
10058
10059
10060
10061
10062
10063
10064
10065
10066
10067
10068
10069
10070
10071
10072
10073
10074
10075
10076
10077
10078
10079
10080
10081
10082
10083
10084
10085
10086
10087
10088
10089
10090
10091
10092
10093
10094
10095
10096
10097
10098
10099
10100
10101
10102
10103
10104
10105
10106
10107
10108
10109
10110
10111
10112
10113
10114
10115
10116
10117
10118
10119
10120
10121
10122
10123
10124
10125
10126
10127
10128
10129
10130
10131
10132
10133
10134
10135
10136
10137
10138
10139
10140
10141
10142
10143
10144
10145
10146
10147
10148
10149
10150
10151
10152
10153
10154
10155
10156
10157
10158
10159
10160
10161
10162
10163
10164
10165
10166
10167
10168
10169
10170
10171
10172
10173
10174
10175
10176
10177
10178
10179
10180
10181
10182
10183
10184
10185
10186
10187
10188
10189
10190
10191
10192
10193
10194
10195
10196
10197
10198
10199
10200
10201
10202
10203
10204
10205
10206
10207
10208
10209
10210
10211
10212
10213
10214
10215
10216
10217
10218
10219
10220
10221
10222
10223
10224
10225
10226
10227
10228
10229
10230
10231
10232
10233
10234
10235
10236
10237
10238
10239
10240
10241
10242
10243
10244
10245
10246
10247
10248
10249
10250
10251
10252
10253
10254
10255
10256
10257
10258
10259
10260
10261
10262
10263
10264
10265
10266
10267
10268
10269
10270
10271
10272
10273
10274
10275
10276
10277
10278
10279
10280
10281
10282
10283
10284
10285
10286
10287
10288
10289
10290
10291
10292
10293
10294
10295
10296
10297
10298
10299
10300
10301
10302
10303
10304
10305
10306
10307
10308
10309
10310
10311
10312
10313
10314
10315
10316
10317
10318
10319
10320
10321
10322
10323
10324
10325
10326
10327
10328
10329
10330
10331
10332
10333
10334
10335
10336
10337
10338
10339
10340
10341
10342
10343
10344
10345
10346
10347
10348
10349
10350
10351
10352
10353
10354
10355
10356
10357
10358
10359
10360
10361
10362
10363
10364
10365
10366
10367
10368
10369
10370
10371
10372
10373
10374
10375
10376
10377
10378
10379
10380
10381
10382
10383
10384
10385
10386
10387
10388
10389
10390
10391
10392
10393
10394
10395
10396
10397
10398
10399
10400
10401
10402
10403
10404
10405
10406
10407
10408
10409
10410
10411
10412
10413
10414
10415
10416
10417
10418
10419
10420
10421
10422
10423
10424
10425
10426
10427
10428
10429
10430
10431
10432
10433
10434
10435
10436
10437
10438
10439
10440
10441
10442
10443
10444
10445
10446
10447
10448
10449
10450
10451
10452
10453
10454
10455
10456
10457
10458
10459
10460
10461
10462
10463
10464
10465
10466
10467
10468
10469
10470
10471
10472
10473
10474
10475
10476
10477
10478
10479
10480
10481
10482
10483
10484
10485
10486
10487
10488
10489
10490
10491
10492
10493
10494
10495
10496
10497
10498
10499
10500
10501
10502
10503
10504
10505
10506
10507
10508
10509
10510
10511
10512
10513
10514
10515
10516
10517
10518
10519
10520
10521
10522
10523
10524
10525
10526
10527
10528
10529
10530
10531
10532
10533
10534
10535
10536
10537
10538
10539
10540
10541
10542
10543
10544
10545
10546
10547
10548
10549
10550
10551
10552
10553
10554
10555
10556
10557
10558
10559
10560
10561
10562
10563
10564
10565
10566
10567
10568
10569
10570
10571
10572
10573
10574
10575
10576
10577
10578
10579
10580
10581
10582
10583
10584
10585
10586
10587
10588
10589
10590
10591
10592
10593
10594
10595
10596
10597
10598
10599
10600
10601
10602
10603
10604
10605
10606
10607
10608
10609
10610
10611
10612
10613
10614
10615
10616
10617
10618
10619
10620
10621
10622
10623
10624
10625
10626
10627
10628
10629
10630
10631
10632
10633
10634
10635
10636
10637
10638
10639
10640
10641
10642
10643
10644
10645
10646
10647
10648
10649
10650
10651
10652
10653
10654
10655
10656
10657
10658
10659
10660
10661
10662
10663
10664
10665
10666
10667
10668
10669
10670
10671
10672
10673
10674
10675
10676
10677
10678
10679
10680
10681
10682
10683
10684
10685
10686
10687
10688
10689
10690
10691
10692
10693
10694
10695
10696
10697
10698
10699
10700
10701
10702
10703
10704
10705
10706
10707
10708
10709
10710
10711
10712
10713
10714
10715
10716
10717
10718
10719
10720
10721
10722
10723
10724
10725
10726
10727
10728
10729
10730
10731
10732
10733
10734
10735
10736
10737
10738
10739
10740
10741
10742
10743
10744
10745
10746
10747
10748
10749
10750
10751
10752
10753
10754
10755
10756
10757
10758
10759
10760
10761
10762
10763
10764
10765
10766
10767
10768
10769
10770
10771
10772
10773
10774
10775
10776
10777
10778
10779
10780
10781
10782
10783
10784
10785
10786
10787
10788
10789
10790
10791
10792
10793
10794
10795
10796
10797
10798
10799
10800
10801
10802
10803
10804
10805
10806
10807
10808
10809
10810
10811
10812
10813
10814
10815
10816
10817
10818
10819
10820
10821
10822
10823
10824
10825
10826
10827
10828
10829
10830
10831
10832
10833
10834
10835
10836
10837
10838
10839
10840
10841
10842
10843
10844
10845
10846
10847
10848
10849
10850
10851
10852
10853
10854
10855
10856
10857
10858
10859
10860
10861
10862
10863
10864
10865
10866
10867
10868
10869
10870
10871
10872
10873
10874
10875
10876
10877
10878
10879
10880
10881
10882
10883
10884
10885
10886
10887
10888
10889
10890
10891
10892
10893
10894
10895
10896
10897
10898
10899
10900
10901
10902
10903
10904
10905
10906
10907
10908
10909
10910
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<HTML>
<HEAD>
<TITLE>Lua 5.3 Reference Manual</TITLE>
<LINK REL="stylesheet" TYPE="text/css" HREF="lua.css">
<LINK REL="stylesheet" TYPE="text/css" HREF="manual.css">
<META HTTP-EQUIV="content-type" CONTENT="text/html; charset=iso-8859-1">
</HEAD>
<BODY>
<H1>
<A HREF="http://www.lua.org/"><IMG SRC="logo.gif" ALT="Lua"></A>
Lua 5.3 Reference Manual
</H1>
<P>
by Roberto Ierusalimschy, Luiz Henrique de Figueiredo, Waldemar Celes
<P>
<SMALL>
Copyright © 2015–2016 Lua.org, PUC-Rio.
Freely available under the terms of the
<a href="http://www.lua.org/license.html">Lua license</a>.
</SMALL>
<DIV CLASS="menubar">
<A HREF="contents.html#contents">contents</A>
·
<A HREF="contents.html#index">index</A>
·
<A HREF="http://www.lua.org/manual/">other versions</A>
</DIV>
<!-- ====================================================================== -->
<p>
<!-- $Id: manual.of,v 1.162 2016/05/30 15:57:03 roberto Exp $ -->
<h1>1 – <a name="1">Introduction</a></h1>
<p>
Lua is a powerful, efficient, lightweight, embeddable scripting language.
It supports procedural programming,
object-oriented programming, functional programming,
data-driven programming, and data description.
<p>
Lua combines simple procedural syntax with powerful data description
constructs based on associative arrays and extensible semantics.
Lua is dynamically typed,
runs by interpreting bytecode with a register-based
virtual machine,
and has automatic memory management with
incremental garbage collection,
making it ideal for configuration, scripting,
and rapid prototyping.
<p>
Lua is implemented as a library, written in <em>clean C</em>,
the common subset of Standard C and C++.
The Lua distribution includes a host program called <code>lua</code>,
which uses the Lua library to offer a complete,
standalone Lua interpreter,
for interactive or batch use.
Lua is intended to be used both as a powerful, lightweight,
embeddable scripting language for any program that needs one,
and as a powerful but lightweight and efficient stand-alone language.
<p>
As an extension language, Lua has no notion of a "main" program:
it works <em>embedded</em> in a host client,
called the <em>embedding program</em> or simply the <em>host</em>.
(Frequently, this host is the stand-alone <code>lua</code> program.)
The host program can invoke functions to execute a piece of Lua code,
can write and read Lua variables,
and can register C functions to be called by Lua code.
Through the use of C functions, Lua can be augmented to cope with
a wide range of different domains,
thus creating customized programming languages sharing a syntactical framework.
<p>
Lua is free software,
and is provided as usual with no guarantees,
as stated in its license.
The implementation described in this manual is available
at Lua's official web site, <code>www.lua.org</code>.
<p>
Like any other reference manual,
this document is dry in places.
For a discussion of the decisions behind the design of Lua,
see the technical papers available at Lua's web site.
For a detailed introduction to programming in Lua,
see Roberto's book, <em>Programming in Lua</em>.
<h1>2 – <a name="2">Basic Concepts</a></h1>
<p>
This section describes the basic concepts of the language.
<h2>2.1 – <a name="2.1">Values and Types</a></h2>
<p>
Lua is a <em>dynamically typed language</em>.
This means that
variables do not have types; only values do.
There are no type definitions in the language.
All values carry their own type.
<p>
All values in Lua are <em>first-class values</em>.
This means that all values can be stored in variables,
passed as arguments to other functions, and returned as results.
<p>
There are eight basic types in Lua:
<em>nil</em>, <em>boolean</em>, <em>number</em>,
<em>string</em>, <em>function</em>, <em>userdata</em>,
<em>thread</em>, and <em>table</em>.
The type <em>nil</em> has one single value, <b>nil</b>,
whose main property is to be different from any other value;
it usually represents the absence of a useful value.
The type <em>boolean</em> has two values, <b>false</b> and <b>true</b>.
Both <b>nil</b> and <b>false</b> make a condition false;
any other value makes it true.
The type <em>number</em> represents both
integer numbers and real (floating-point) numbers.
The type <em>string</em> represents immutable sequences of bytes.
Lua is 8-bit clean:
strings can contain any 8-bit value,
including embedded zeros ('<code>\0</code>').
Lua is also encoding-agnostic;
it makes no assumptions about the contents of a string.
<p>
The type <em>number</em> uses two internal representations,
or two subtypes,
one called <em>integer</em> and the other called <em>float</em>.
Lua has explicit rules about when each representation is used,
but it also converts between them automatically as needed (see <a href="#3.4.3">§3.4.3</a>).
Therefore,
the programmer may choose to mostly ignore the difference
between integers and floats
or to assume complete control over the representation of each number.
Standard Lua uses 64-bit integers and double-precision (64-bit) floats,
but you can also compile Lua so that it
uses 32-bit integers and/or single-precision (32-bit) floats.
The option with 32 bits for both integers and floats
is particularly attractive
for small machines and embedded systems.
(See macro <code>LUA_32BITS</code> in file <code>luaconf.h</code>.)
<p>
Lua can call (and manipulate) functions written in Lua and
functions written in C (see <a href="#3.4.10">§3.4.10</a>).
Both are represented by the type <em>function</em>.
<p>
The type <em>userdata</em> is provided to allow arbitrary C data to
be stored in Lua variables.
A userdata value represents a block of raw memory.
There are two kinds of userdata:
<em>full userdata</em>,
which is an object with a block of memory managed by Lua,
and <em>light userdata</em>,
which is simply a C pointer value.
Userdata has no predefined operations in Lua,
except assignment and identity test.
By using <em>metatables</em>,
the programmer can define operations for full userdata values
(see <a href="#2.4">§2.4</a>).
Userdata values cannot be created or modified in Lua,
only through the C API.
This guarantees the integrity of data owned by the host program.
<p>
The type <em>thread</em> represents independent threads of execution
and it is used to implement coroutines (see <a href="#2.6">§2.6</a>).
Lua threads are not related to operating-system threads.
Lua supports coroutines on all systems,
even those that do not support threads natively.
<p>
The type <em>table</em> implements associative arrays,
that is, arrays that can be indexed not only with numbers,
but with any Lua value except <b>nil</b> and NaN.
(<em>Not a Number</em> is a special value used to represent
undefined or unrepresentable numerical results, such as <code>0/0</code>.)
Tables can be <em>heterogeneous</em>;
that is, they can contain values of all types (except <b>nil</b>).
Any key with value <b>nil</b> is not considered part of the table.
Conversely, any key that is not part of a table has
an associated value <b>nil</b>.
<p>
Tables are the sole data-structuring mechanism in Lua;
they can be used to represent ordinary arrays, sequences,
symbol tables, sets, records, graphs, trees, etc.
To represent records, Lua uses the field name as an index.
The language supports this representation by
providing <code>a.name</code> as syntactic sugar for <code>a["name"]</code>.
There are several convenient ways to create tables in Lua
(see <a href="#3.4.9">§3.4.9</a>).
<p>
We use the term <em>sequence</em> to denote a table where
the set of all positive numeric keys is equal to {1..<em>n</em>}
for some non-negative integer <em>n</em>,
which is called the length of the sequence (see <a href="#3.4.7">§3.4.7</a>).
<p>
Like indices,
the values of table fields can be of any type.
In particular,
because functions are first-class values,
table fields can contain functions.
Thus tables can also carry <em>methods</em> (see <a href="#3.4.11">§3.4.11</a>).
<p>
The indexing of tables follows
the definition of raw equality in the language.
The expressions <code>a[i]</code> and <code>a[j]</code>
denote the same table element
if and only if <code>i</code> and <code>j</code> are raw equal
(that is, equal without metamethods).
In particular, floats with integral values
are equal to their respective integers
(e.g., <code>1.0 == 1</code>).
To avoid ambiguities,
any float with integral value used as a key
is converted to its respective integer.
For instance, if you write <code>a[2.0] = true</code>,
the actual key inserted into the table will be the
integer <code>2</code>.
(On the other hand,
2 and "<code>2</code>" are different Lua values and therefore
denote different table entries.)
<p>
Tables, functions, threads, and (full) userdata values are <em>objects</em>:
variables do not actually <em>contain</em> these values,
only <em>references</em> to them.
Assignment, parameter passing, and function returns
always manipulate references to such values;
these operations do not imply any kind of copy.
<p>
The library function <a href="#pdf-type"><code>type</code></a> returns a string describing the type
of a given value (see <a href="#6.1">§6.1</a>).
<h2>2.2 – <a name="2.2">Environments and the Global Environment</a></h2>
<p>
As will be discussed in <a href="#3.2">§3.2</a> and <a href="#3.3.3">§3.3.3</a>,
any reference to a free name
(that is, a name not bound to any declaration) <code>var</code>
is syntactically translated to <code>_ENV.var</code>.
Moreover, every chunk is compiled in the scope of
an external local variable named <code>_ENV</code> (see <a href="#3.3.2">§3.3.2</a>),
so <code>_ENV</code> itself is never a free name in a chunk.
<p>
Despite the existence of this external <code>_ENV</code> variable and
the translation of free names,
<code>_ENV</code> is a completely regular name.
In particular,
you can define new variables and parameters with that name.
Each reference to a free name uses the <code>_ENV</code> that is
visible at that point in the program,
following the usual visibility rules of Lua (see <a href="#3.5">§3.5</a>).
<p>
Any table used as the value of <code>_ENV</code> is called an <em>environment</em>.
<p>
Lua keeps a distinguished environment called the <em>global environment</em>.
This value is kept at a special index in the C registry (see <a href="#4.5">§4.5</a>).
In Lua, the global variable <a href="#pdf-_G"><code>_G</code></a> is initialized with this same value.
(<a href="#pdf-_G"><code>_G</code></a> is never used internally.)
<p>
When Lua loads a chunk,
the default value for its <code>_ENV</code> upvalue
is the global environment (see <a href="#pdf-load"><code>load</code></a>).
Therefore, by default,
free names in Lua code refer to entries in the global environment
(and, therefore, they are also called <em>global variables</em>).
Moreover, all standard libraries are loaded in the global environment
and some functions there operate on that environment.
You can use <a href="#pdf-load"><code>load</code></a> (or <a href="#pdf-loadfile"><code>loadfile</code></a>)
to load a chunk with a different environment.
(In C, you have to load the chunk and then change the value
of its first upvalue.)
<h2>2.3 – <a name="2.3">Error Handling</a></h2>
<p>
Because Lua is an embedded extension language,
all Lua actions start from C code in the host program
calling a function from the Lua library.
(When you use Lua standalone,
the <code>lua</code> application is the host program.)
Whenever an error occurs during
the compilation or execution of a Lua chunk,
control returns to the host,
which can take appropriate measures
(such as printing an error message).
<p>
Lua code can explicitly generate an error by calling the
<a href="#pdf-error"><code>error</code></a> function.
If you need to catch errors in Lua,
you can use <a href="#pdf-pcall"><code>pcall</code></a> or <a href="#pdf-xpcall"><code>xpcall</code></a>
to call a given function in <em>protected mode</em>.
<p>
Whenever there is an error,
an <em>error object</em> (also called an <em>error message</em>)
is propagated with information about the error.
Lua itself only generates errors whose error object is a string,
but programs may generate errors with
any value as the error object.
It is up to the Lua program or its host to handle such error objects.
<p>
When you use <a href="#pdf-xpcall"><code>xpcall</code></a> or <a href="#lua_pcall"><code>lua_pcall</code></a>,
you may give a <em>message handler</em>
to be called in case of errors.
This function is called with the original error object
and returns a new error object.
It is called before the error unwinds the stack,
so that it can gather more information about the error,
for instance by inspecting the stack and creating a stack traceback.
This message handler is still protected by the protected call;
so, an error inside the message handler
will call the message handler again.
If this loop goes on for too long,
Lua breaks it and returns an appropriate message.
<h2>2.4 – <a name="2.4">Metatables and Metamethods</a></h2>
<p>
Every value in Lua can have a <em>metatable</em>.
This <em>metatable</em> is an ordinary Lua table
that defines the behavior of the original value
under certain special operations.
You can change several aspects of the behavior
of operations over a value by setting specific fields in its metatable.
For instance, when a non-numeric value is the operand of an addition,
Lua checks for a function in the field "<code>__add</code>" of the value's metatable.
If it finds one,
Lua calls this function to perform the addition.
<p>
The key for each event in a metatable is a string
with the event name prefixed by two underscores;
the corresponding values are called <em>metamethods</em>.
In the previous example, the key is "<code>__add</code>"
and the metamethod is the function that performs the addition.
<p>
You can query the metatable of any value
using the <a href="#pdf-getmetatable"><code>getmetatable</code></a> function.
Lua queries metamethods in metatables using a raw access (see <a href="#pdf-rawget"><code>rawget</code></a>).
So, to retrieve the metamethod for event <code>ev</code> in object <code>o</code>,
Lua does the equivalent to the following code:
<pre>
rawget(getmetatable(<em>o</em>) or {}, "__<em>ev</em>")
</pre>
<p>
You can replace the metatable of tables
using the <a href="#pdf-setmetatable"><code>setmetatable</code></a> function.
You cannot change the metatable of other types from Lua code
(except by using the debug library (<a href="#6.10">§6.10</a>));
you should use the C API for that.
<p>
Tables and full userdata have individual metatables
(although multiple tables and userdata can share their metatables).
Values of all other types share one single metatable per type;
that is, there is one single metatable for all numbers,
one for all strings, etc.
By default, a value has no metatable,
but the string library sets a metatable for the string type (see <a href="#6.4">§6.4</a>).
<p>
A metatable controls how an object behaves in
arithmetic operations, bitwise operations,
order comparisons, concatenation, length operation, calls, and indexing.
A metatable also can define a function to be called
when a userdata or a table is garbage collected (<a href="#2.5">§2.5</a>).
<p>
For the unary operators (negation, length, and bitwise NOT),
the metamethod is computed and called with a dummy second operand,
equal to the first one.
This extra operand is only to simplify Lua's internals
(by making these operators behave like a binary operation)
and may be removed in future versions.
(For most uses this extra operand is irrelevant.)
<p>
A detailed list of events controlled by metatables is given next.
Each operation is identified by its corresponding key.
<ul>
<li><b><code>__add</code>: </b>
the addition (<code>+</code>) operation.
If any operand for an addition is not a number
(nor a string coercible to a number),
Lua will try to call a metamethod.
First, Lua will check the first operand (even if it is valid).
If that operand does not define a metamethod for <code>__add</code>,
then Lua will check the second operand.
If Lua can find a metamethod,
it calls the metamethod with the two operands as arguments,
and the result of the call
(adjusted to one value)
is the result of the operation.
Otherwise,
it raises an error.
</li>
<li><b><code>__sub</code>: </b>
the subtraction (<code>-</code>) operation.
Behavior similar to the addition operation.
</li>
<li><b><code>__mul</code>: </b>
the multiplication (<code>*</code>) operation.
Behavior similar to the addition operation.
</li>
<li><b><code>__div</code>: </b>
the division (<code>/</code>) operation.
Behavior similar to the addition operation.
</li>
<li><b><code>__mod</code>: </b>
the modulo (<code>%</code>) operation.
Behavior similar to the addition operation.
</li>
<li><b><code>__pow</code>: </b>
the exponentiation (<code>^</code>) operation.
Behavior similar to the addition operation.
</li>
<li><b><code>__unm</code>: </b>
the negation (unary <code>-</code>) operation.
Behavior similar to the addition operation.
</li>
<li><b><code>__idiv</code>: </b>
the floor division (<code>//</code>) operation.
Behavior similar to the addition operation.
</li>
<li><b><code>__band</code>: </b>
the bitwise AND (<code>&</code>) operation.
Behavior similar to the addition operation,
except that Lua will try a metamethod
if any operand is neither an integer
nor a value coercible to an integer (see <a href="#3.4.3">§3.4.3</a>).
</li>
<li><b><code>__bor</code>: </b>
the bitwise OR (<code>|</code>) operation.
Behavior similar to the bitwise AND operation.
</li>
<li><b><code>__bxor</code>: </b>
the bitwise exclusive OR (binary <code>~</code>) operation.
Behavior similar to the bitwise AND operation.
</li>
<li><b><code>__bnot</code>: </b>
the bitwise NOT (unary <code>~</code>) operation.
Behavior similar to the bitwise AND operation.
</li>
<li><b><code>__shl</code>: </b>
the bitwise left shift (<code><<</code>) operation.
Behavior similar to the bitwise AND operation.
</li>
<li><b><code>__shr</code>: </b>
the bitwise right shift (<code>>></code>) operation.
Behavior similar to the bitwise AND operation.
</li>
<li><b><code>__concat</code>: </b>
the concatenation (<code>..</code>) operation.
Behavior similar to the addition operation,
except that Lua will try a metamethod
if any operand is neither a string nor a number
(which is always coercible to a string).
</li>
<li><b><code>__len</code>: </b>
the length (<code>#</code>) operation.
If the object is not a string,
Lua will try its metamethod.
If there is a metamethod,
Lua calls it with the object as argument,
and the result of the call
(always adjusted to one value)
is the result of the operation.
If there is no metamethod but the object is a table,
then Lua uses the table length operation (see <a href="#3.4.7">§3.4.7</a>).
Otherwise, Lua raises an error.
</li>
<li><b><code>__eq</code>: </b>
the equal (<code>==</code>) operation.
Behavior similar to the addition operation,
except that Lua will try a metamethod only when the values
being compared are either both tables or both full userdata
and they are not primitively equal.
The result of the call is always converted to a boolean.
</li>
<li><b><code>__lt</code>: </b>
the less than (<code><</code>) operation.
Behavior similar to the addition operation,
except that Lua will try a metamethod only when the values
being compared are neither both numbers nor both strings.
The result of the call is always converted to a boolean.
</li>
<li><b><code>__le</code>: </b>
the less equal (<code><=</code>) operation.
Unlike other operations,
the less-equal operation can use two different events.
First, Lua looks for the <code>__le</code> metamethod in both operands,
like in the less than operation.
If it cannot find such a metamethod,
then it will try the <code>__lt</code> metamethod,
assuming that <code>a <= b</code> is equivalent to <code>not (b < a)</code>.
As with the other comparison operators,
the result is always a boolean.
(This use of the <code>__lt</code> event can be removed in future versions;
it is also slower than a real <code>__le</code> metamethod.)
</li>
<li><b><code>__index</code>: </b>
The indexing access <code>table[key]</code>.
This event happens when <code>table</code> is not a table or
when <code>key</code> is not present in <code>table</code>.
The metamethod is looked up in <code>table</code>.
<p>
Despite the name,
the metamethod for this event can be either a function or a table.
If it is a function,
it is called with <code>table</code> and <code>key</code> as arguments,
and the result of the call
(adjusted to one value)
is the result of the operation.
If it is a table,
the final result is the result of indexing this table with <code>key</code>.
(This indexing is regular, not raw,
and therefore can trigger another metamethod.)
</li>
<li><b><code>__newindex</code>: </b>
The indexing assignment <code>table[key] = value</code>.
Like the index event,
this event happens when <code>table</code> is not a table or
when <code>key</code> is not present in <code>table</code>.
The metamethod is looked up in <code>table</code>.
<p>
Like with indexing,
the metamethod for this event can be either a function or a table.
If it is a function,
it is called with <code>table</code>, <code>key</code>, and <code>value</code> as arguments.
If it is a table,
Lua does an indexing assignment to this table with the same key and value.
(This assignment is regular, not raw,
and therefore can trigger another metamethod.)
<p>
Whenever there is a <code>__newindex</code> metamethod,
Lua does not perform the primitive assignment.
(If necessary,
the metamethod itself can call <a href="#pdf-rawset"><code>rawset</code></a>
to do the assignment.)
</li>
<li><b><code>__call</code>: </b>
The call operation <code>func(args)</code>.
This event happens when Lua tries to call a non-function value
(that is, <code>func</code> is not a function).
The metamethod is looked up in <code>func</code>.
If present,
the metamethod is called with <code>func</code> as its first argument,
followed by the arguments of the original call (<code>args</code>).
All results of the call
are the result of the operation.
(This is the only metamethod that allows multiple results.)
</li>
</ul>
<p>
It is a good practice to add all needed metamethods to a table
before setting it as a metatable of some object.
In particular, the <code>__gc</code> metamethod works only when this order
is followed (see <a href="#2.5.1">§2.5.1</a>).
<p>
Because metatables are regular tables,
they can contain arbitrary fields,
not only the event names defined above.
Some functions in the standard library
(e.g., <a href="#pdf-tostring"><code>tostring</code></a>)
use other fields in metatables for their own purposes.
<h2>2.5 – <a name="2.5">Garbage Collection</a></h2>
<p>
Lua performs automatic memory management.
This means that
you do not have to worry about allocating memory for new objects
or freeing it when the objects are no longer needed.
Lua manages memory automatically by running
a <em>garbage collector</em> to collect all <em>dead objects</em>
(that is, objects that are no longer accessible from Lua).
All memory used by Lua is subject to automatic management:
strings, tables, userdata, functions, threads, internal structures, etc.
<p>
Lua implements an incremental mark-and-sweep collector.
It uses two numbers to control its garbage-collection cycles:
the <em>garbage-collector pause</em> and
the <em>garbage-collector step multiplier</em>.
Both use percentage points as units
(e.g., a value of 100 means an internal value of 1).
<p>
The garbage-collector pause
controls how long the collector waits before starting a new cycle.
Larger values make the collector less aggressive.
Values smaller than 100 mean the collector will not wait to
start a new cycle.
A value of 200 means that the collector waits for the total memory in use
to double before starting a new cycle.
<p>
The garbage-collector step multiplier
controls the relative speed of the collector relative to
memory allocation.
Larger values make the collector more aggressive but also increase
the size of each incremental step.
You should not use values smaller than 100,
because they make the collector too slow and
can result in the collector never finishing a cycle.
The default is 200,
which means that the collector runs at "twice"
the speed of memory allocation.
<p>
If you set the step multiplier to a very large number
(larger than 10% of the maximum number of
bytes that the program may use),
the collector behaves like a stop-the-world collector.
If you then set the pause to 200,
the collector behaves as in old Lua versions,
doing a complete collection every time Lua doubles its
memory usage.
<p>
You can change these numbers by calling <a href="#lua_gc"><code>lua_gc</code></a> in C
or <a href="#pdf-collectgarbage"><code>collectgarbage</code></a> in Lua.
You can also use these functions to control
the collector directly (e.g., stop and restart it).
<h3>2.5.1 – <a name="2.5.1">Garbage-Collection Metamethods</a></h3>
<p>
You can set garbage-collector metamethods for tables
and, using the C API,
for full userdata (see <a href="#2.4">§2.4</a>).
These metamethods are also called <em>finalizers</em>.
Finalizers allow you to coordinate Lua's garbage collection
with external resource management
(such as closing files, network or database connections,
or freeing your own memory).
<p>
For an object (table or userdata) to be finalized when collected,
you must <em>mark</em> it for finalization.
You mark an object for finalization when you set its metatable
and the metatable has a field indexed by the string "<code>__gc</code>".
Note that if you set a metatable without a <code>__gc</code> field
and later create that field in the metatable,
the object will not be marked for finalization.
<p>
When a marked object becomes garbage,
it is not collected immediately by the garbage collector.
Instead, Lua puts it in a list.
After the collection,
Lua goes through that list.
For each object in the list,
it checks the object's <code>__gc</code> metamethod:
If it is a function,
Lua calls it with the object as its single argument;
if the metamethod is not a function,
Lua simply ignores it.
<p>
At the end of each garbage-collection cycle,
the finalizers for objects are called in
the reverse order that the objects were marked for finalization,
among those collected in that cycle;
that is, the first finalizer to be called is the one associated
with the object marked last in the program.
The execution of each finalizer may occur at any point during
the execution of the regular code.
<p>
Because the object being collected must still be used by the finalizer,
that object (and other objects accessible only through it)
must be <em>resurrected</em> by Lua.
Usually, this resurrection is transient,
and the object memory is freed in the next garbage-collection cycle.
However, if the finalizer stores the object in some global place
(e.g., a global variable),
then the resurrection is permanent.
Moreover, if the finalizer marks a finalizing object for finalization again,
its finalizer will be called again in the next cycle where the
object is unreachable.
In any case,
the object memory is freed only in a GC cycle where
the object is unreachable and not marked for finalization.
<p>
When you close a state (see <a href="#lua_close"><code>lua_close</code></a>),
Lua calls the finalizers of all objects marked for finalization,
following the reverse order that they were marked.
If any finalizer marks objects for collection during that phase,
these marks have no effect.
<h3>2.5.2 – <a name="2.5.2">Weak Tables</a></h3>
<p>
A <em>weak table</em> is a table whose elements are
<em>weak references</em>.
A weak reference is ignored by the garbage collector.
In other words,
if the only references to an object are weak references,
then the garbage collector will collect that object.
<p>
A weak table can have weak keys, weak values, or both.
A table with weak values allows the collection of its values,
but prevents the collection of its keys.
A table with both weak keys and weak values allows the collection of
both keys and values.
In any case, if either the key or the value is collected,
the whole pair is removed from the table.
The weakness of a table is controlled by the
<code>__mode</code> field of its metatable.
If the <code>__mode</code> field is a string containing the character '<code>k</code>',
the keys in the table are weak.
If <code>__mode</code> contains '<code>v</code>',
the values in the table are weak.
<p>
A table with weak keys and strong values
is also called an <em>ephemeron table</em>.
In an ephemeron table,
a value is considered reachable only if its key is reachable.
In particular,
if the only reference to a key comes through its value,
the pair is removed.
<p>
Any change in the weakness of a table may take effect only
at the next collect cycle.
In particular, if you change the weakness to a stronger mode,
Lua may still collect some items from that table
before the change takes effect.
<p>
Only objects that have an explicit construction
are removed from weak tables.
Values, such as numbers and light C functions,
are not subject to garbage collection,
and therefore are not removed from weak tables
(unless their associated values are collected).
Although strings are subject to garbage collection,
they do not have an explicit construction,
and therefore are not removed from weak tables.
<p>
Resurrected objects
(that is, objects being finalized
and objects accessible only through objects being finalized)
have a special behavior in weak tables.
They are removed from weak values before running their finalizers,
but are removed from weak keys only in the next collection
after running their finalizers, when such objects are actually freed.
This behavior allows the finalizer to access properties
associated with the object through weak tables.
<p>
If a weak table is among the resurrected objects in a collection cycle,
it may not be properly cleared until the next cycle.
<h2>2.6 – <a name="2.6">Coroutines</a></h2>
<p>
Lua supports coroutines,
also called <em>collaborative multithreading</em>.
A coroutine in Lua represents an independent thread of execution.
Unlike threads in multithread systems, however,
a coroutine only suspends its execution by explicitly calling
a yield function.
<p>
You create a coroutine by calling <a href="#pdf-coroutine.create"><code>coroutine.create</code></a>.
Its sole argument is a function
that is the main function of the coroutine.
The <code>create</code> function only creates a new coroutine and
returns a handle to it (an object of type <em>thread</em>);
it does not start the coroutine.
<p>
You execute a coroutine by calling <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a>.
When you first call <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a>,
passing as its first argument
a thread returned by <a href="#pdf-coroutine.create"><code>coroutine.create</code></a>,
the coroutine starts its execution by
calling its main function.
Extra arguments passed to <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a> are passed
as arguments to that function.
After the coroutine starts running,
it runs until it terminates or <em>yields</em>.
<p>
A coroutine can terminate its execution in two ways:
normally, when its main function returns
(explicitly or implicitly, after the last instruction);
and abnormally, if there is an unprotected error.
In case of normal termination,
<a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a> returns <b>true</b>,
plus any values returned by the coroutine main function.
In case of errors, <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a> returns <b>false</b>
plus an error object.
<p>
A coroutine yields by calling <a href="#pdf-coroutine.yield"><code>coroutine.yield</code></a>.
When a coroutine yields,
the corresponding <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a> returns immediately,
even if the yield happens inside nested function calls
(that is, not in the main function,
but in a function directly or indirectly called by the main function).
In the case of a yield, <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a> also returns <b>true</b>,
plus any values passed to <a href="#pdf-coroutine.yield"><code>coroutine.yield</code></a>.
The next time you resume the same coroutine,
it continues its execution from the point where it yielded,
with the call to <a href="#pdf-coroutine.yield"><code>coroutine.yield</code></a> returning any extra
arguments passed to <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a>.
<p>
Like <a href="#pdf-coroutine.create"><code>coroutine.create</code></a>,
the <a href="#pdf-coroutine.wrap"><code>coroutine.wrap</code></a> function also creates a coroutine,
but instead of returning the coroutine itself,
it returns a function that, when called, resumes the coroutine.
Any arguments passed to this function
go as extra arguments to <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a>.
<a href="#pdf-coroutine.wrap"><code>coroutine.wrap</code></a> returns all the values returned by <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a>,
except the first one (the boolean error code).
Unlike <a href="#pdf-coroutine.resume"><code>coroutine.resume</code></a>,
<a href="#pdf-coroutine.wrap"><code>coroutine.wrap</code></a> does not catch errors;
any error is propagated to the caller.
<p>
As an example of how coroutines work,
consider the following code:
<pre>
function foo (a)
print("foo", a)
return coroutine.yield(2*a)
end
co = coroutine.create(function (a,b)
print("co-body", a, b)
local r = foo(a+1)
print("co-body", r)
local r, s = coroutine.yield(a+b, a-b)
print("co-body", r, s)
return b, "end"
end)
print("main", coroutine.resume(co, 1, 10))
print("main", coroutine.resume(co, "r"))
print("main", coroutine.resume(co, "x", "y"))
print("main", coroutine.resume(co, "x", "y"))
</pre><p>
When you run it, it produces the following output:
<pre>
co-body 1 10
foo 2
main true 4
co-body r
main true 11 -9
co-body x y
main true 10 end
main false cannot resume dead coroutine
</pre>
<p>
You can also create and manipulate coroutines through the C API:
see functions <a href="#lua_newthread"><code>lua_newthread</code></a>, <a href="#lua_resume"><code>lua_resume</code></a>,
and <a href="#lua_yield"><code>lua_yield</code></a>.
<h1>3 – <a name="3">The Language</a></h1>
<p>
This section describes the lexis, the syntax, and the semantics of Lua.
In other words,
this section describes
which tokens are valid,
how they can be combined,
and what their combinations mean.
<p>
Language constructs will be explained using the usual extended BNF notation,
in which
{<em>a</em>} means 0 or more <em>a</em>'s, and
[<em>a</em>] means an optional <em>a</em>.
Non-terminals are shown like non-terminal,
keywords are shown like <b>kword</b>,
and other terminal symbols are shown like ‘<b>=</b>’.
The complete syntax of Lua can be found in <a href="#9">§9</a>
at the end of this manual.
<h2>3.1 – <a name="3.1">Lexical Conventions</a></h2>
<p>
Lua is a free-form language.
It ignores spaces (including new lines) and comments
between lexical elements (tokens),
except as delimiters between names and keywords.
<p>
<em>Names</em>
(also called <em>identifiers</em>)
in Lua can be any string of letters,
digits, and underscores,
not beginning with a digit and
not being a reserved word.
Identifiers are used to name variables, table fields, and labels.
<p>
The following <em>keywords</em> are reserved
and cannot be used as names:
<pre>
and break do else elseif end
false for function goto if in
local nil not or repeat return
then true until while
</pre>
<p>
Lua is a case-sensitive language:
<code>and</code> is a reserved word, but <code>And</code> and <code>AND</code>
are two different, valid names.
As a convention,
programs should avoid creating
names that start with an underscore followed by
one or more uppercase letters (such as <a href="#pdf-_VERSION"><code>_VERSION</code></a>).
<p>
The following strings denote other tokens:
<pre>
+ - * / % ^ #
& ~ | << >> //
== ~= <= >= < > =
( ) { } [ ] ::
; : , . .. ...
</pre>
<p>
<em>Literal strings</em>
can be delimited by matching single or double quotes,
and can contain the following C-like escape sequences:
'<code>\a</code>' (bell),
'<code>\b</code>' (backspace),
'<code>\f</code>' (form feed),
'<code>\n</code>' (newline),
'<code>\r</code>' (carriage return),
'<code>\t</code>' (horizontal tab),
'<code>\v</code>' (vertical tab),
'<code>\\</code>' (backslash),
'<code>\"</code>' (quotation mark [double quote]),
and '<code>\'</code>' (apostrophe [single quote]).
A backslash followed by a real newline
results in a newline in the string.
The escape sequence '<code>\z</code>' skips the following span
of white-space characters,
including line breaks;
it is particularly useful to break and indent a long literal string
into multiple lines without adding the newlines and spaces
into the string contents.
<p>
Strings in Lua can contain any 8-bit value, including embedded zeros,
which can be specified as '<code>\0</code>'.
More generally,
we can specify any byte in a literal string by its numeric value.
This can be done
with the escape sequence <code>\x<em>XX</em></code>,
where <em>XX</em> is a sequence of exactly two hexadecimal digits,
or with the escape sequence <code>\<em>ddd</em></code>,
where <em>ddd</em> is a sequence of up to three decimal digits.
(Note that if a decimal escape sequence is to be followed by a digit,
it must be expressed using exactly three digits.)
<p>
The UTF-8 encoding of a Unicode character
can be inserted in a literal string with
the escape sequence <code>\u{<em>XXX</em>}</code>
(note the mandatory enclosing brackets),
where <em>XXX</em> is a sequence of one or more hexadecimal digits
representing the character code point.
<p>
Literal strings can also be defined using a long format
enclosed by <em>long brackets</em>.
We define an <em>opening long bracket of level <em>n</em></em> as an opening
square bracket followed by <em>n</em> equal signs followed by another
opening square bracket.
So, an opening long bracket of level 0 is written as <code>[[</code>,
an opening long bracket of level 1 is written as <code>[=[</code>,
and so on.
A <em>closing long bracket</em> is defined similarly;
for instance,
a closing long bracket of level 4 is written as <code>]====]</code>.
A <em>long literal</em> starts with an opening long bracket of any level and
ends at the first closing long bracket of the same level.
It can contain any text except a closing bracket of the same level.
Literals in this bracketed form can run for several lines,
do not interpret any escape sequences,
and ignore long brackets of any other level.
Any kind of end-of-line sequence
(carriage return, newline, carriage return followed by newline,
or newline followed by carriage return)
is converted to a simple newline.
<p>
Any byte in a literal string not
explicitly affected by the previous rules represents itself.
However, Lua opens files for parsing in text mode,
and the system file functions may have problems with
some control characters.
So, it is safer to represent
non-text data as a quoted literal with
explicit escape sequences for the non-text characters.
<p>
For convenience,
when the opening long bracket is immediately followed by a newline,
the newline is not included in the string.
As an example, in a system using ASCII
(in which '<code>a</code>' is coded as 97,
newline is coded as 10, and '<code>1</code>' is coded as 49),
the five literal strings below denote the same string:
<pre>
a = 'alo\n123"'
a = "alo\n123\""
a = '\97lo\10\04923"'
a = [[alo
123"]]
a = [==[
alo
123"]==]
</pre>
<p>
A <em>numeric constant</em> (or <em>numeral</em>)
can be written with an optional fractional part
and an optional decimal exponent,
marked by a letter '<code>e</code>' or '<code>E</code>'.
Lua also accepts hexadecimal constants,
which start with <code>0x</code> or <code>0X</code>.
Hexadecimal constants also accept an optional fractional part
plus an optional binary exponent,
marked by a letter '<code>p</code>' or '<code>P</code>'.
A numeric constant with a radix point or an exponent
denotes a float;
otherwise,
if its value fits in an integer,
it denotes an integer.
Examples of valid integer constants are
<pre>
3 345 0xff 0xBEBADA
</pre><p>
Examples of valid float constants are
<pre>
3.0 3.1416 314.16e-2 0.31416E1 34e1
0x0.1E 0xA23p-4 0X1.921FB54442D18P+1
</pre>
<p>
A <em>comment</em> starts with a double hyphen (<code>--</code>)
anywhere outside a string.
If the text immediately after <code>--</code> is not an opening long bracket,
the comment is a <em>short comment</em>,
which runs until the end of the line.
Otherwise, it is a <em>long comment</em>,
which runs until the corresponding closing long bracket.
Long comments are frequently used to disable code temporarily.
<h2>3.2 – <a name="3.2">Variables</a></h2>
<p>
Variables are places that store values.
There are three kinds of variables in Lua:
global variables, local variables, and table fields.
<p>
A single name can denote a global variable or a local variable
(or a function's formal parameter,
which is a particular kind of local variable):
<pre>
var ::= Name
</pre><p>
Name denotes identifiers, as defined in <a href="#3.1">§3.1</a>.
<p>
Any variable name is assumed to be global unless explicitly declared
as a local (see <a href="#3.3.7">§3.3.7</a>).
Local variables are <em>lexically scoped</em>:
local variables can be freely accessed by functions
defined inside their scope (see <a href="#3.5">§3.5</a>).
<p>
Before the first assignment to a variable, its value is <b>nil</b>.
<p>
Square brackets are used to index a table:
<pre>
var ::= prefixexp ‘<b>[</b>’ exp ‘<b>]</b>’
</pre><p>
The meaning of accesses to table fields can be changed via metatables.
An access to an indexed variable <code>t[i]</code> is equivalent to
a call <code>gettable_event(t,i)</code>.
(See <a href="#2.4">§2.4</a> for a complete description of the
<code>gettable_event</code> function.
This function is not defined or callable in Lua.
We use it here only for explanatory purposes.)
<p>
The syntax <code>var.Name</code> is just syntactic sugar for
<code>var["Name"]</code>:
<pre>
var ::= prefixexp ‘<b>.</b>’ Name
</pre>
<p>
An access to a global variable <code>x</code>
is equivalent to <code>_ENV.x</code>.
Due to the way that chunks are compiled,
<code>_ENV</code> is never a global name (see <a href="#2.2">§2.2</a>).
<h2>3.3 – <a name="3.3">Statements</a></h2>
<p>
Lua supports an almost conventional set of statements,
similar to those in Pascal or C.
This set includes
assignments, control structures, function calls,
and variable declarations.
<h3>3.3.1 – <a name="3.3.1">Blocks</a></h3>
<p>
A block is a list of statements,
which are executed sequentially:
<pre>
block ::= {stat}
</pre><p>
Lua has <em>empty statements</em>
that allow you to separate statements with semicolons,
start a block with a semicolon
or write two semicolons in sequence:
<pre>
stat ::= ‘<b>;</b>’
</pre>
<p>
Function calls and assignments
can start with an open parenthesis.
This possibility leads to an ambiguity in Lua's grammar.
Consider the following fragment:
<pre>
a = b + c
(print or io.write)('done')
</pre><p>
The grammar could see it in two ways:
<pre>
a = b + c(print or io.write)('done')
a = b + c; (print or io.write)('done')
</pre><p>
The current parser always sees such constructions
in the first way,
interpreting the open parenthesis
as the start of the arguments to a call.
To avoid this ambiguity,
it is a good practice to always precede with a semicolon
statements that start with a parenthesis:
<pre>
;(print or io.write)('done')
</pre>
<p>
A block can be explicitly delimited to produce a single statement:
<pre>
stat ::= <b>do</b> block <b>end</b>
</pre><p>
Explicit blocks are useful
to control the scope of variable declarations.
Explicit blocks are also sometimes used to
add a <b>return</b> statement in the middle
of another block (see <a href="#3.3.4">§3.3.4</a>).
<h3>3.3.2 – <a name="3.3.2">Chunks</a></h3>
<p>
The unit of compilation of Lua is called a <em>chunk</em>.
Syntactically,
a chunk is simply a block:
<pre>
chunk ::= block
</pre>
<p>
Lua handles a chunk as the body of an anonymous function
with a variable number of arguments
(see <a href="#3.4.11">§3.4.11</a>).
As such, chunks can define local variables,
receive arguments, and return values.
Moreover, such anonymous function is compiled as in the
scope of an external local variable called <code>_ENV</code> (see <a href="#2.2">§2.2</a>).
The resulting function always has <code>_ENV</code> as its only upvalue,
even if it does not use that variable.
<p>
A chunk can be stored in a file or in a string inside the host program.
To execute a chunk,
Lua first <em>loads</em> it,
precompiling the chunk's code into instructions for a virtual machine,
and then Lua executes the compiled code
with an interpreter for the virtual machine.
<p>
Chunks can also be precompiled into binary form;
see program <code>luac</code> and function <a href="#pdf-string.dump"><code>string.dump</code></a> for details.
Programs in source and compiled forms are interchangeable;
Lua automatically detects the file type and acts accordingly (see <a href="#pdf-load"><code>load</code></a>).
<h3>3.3.3 – <a name="3.3.3">Assignment</a></h3>
<p>
Lua allows multiple assignments.
Therefore, the syntax for assignment
defines a list of variables on the left side
and a list of expressions on the right side.
The elements in both lists are separated by commas:
<pre>
stat ::= varlist ‘<b>=</b>’ explist
varlist ::= var {‘<b>,</b>’ var}
explist ::= exp {‘<b>,</b>’ exp}
</pre><p>
Expressions are discussed in <a href="#3.4">§3.4</a>.
<p>
Before the assignment,
the list of values is <em>adjusted</em> to the length of
the list of variables.
If there are more values than needed,
the excess values are thrown away.
If there are fewer values than needed,
the list is extended with as many <b>nil</b>'s as needed.
If the list of expressions ends with a function call,
then all values returned by that call enter the list of values,
before the adjustment
(except when the call is enclosed in parentheses; see <a href="#3.4">§3.4</a>).
<p>
The assignment statement first evaluates all its expressions
and only then the assignments are performed.
Thus the code
<pre>
i = 3
i, a[i] = i+1, 20
</pre><p>
sets <code>a[3]</code> to 20, without affecting <code>a[4]</code>
because the <code>i</code> in <code>a[i]</code> is evaluated (to 3)
before it is assigned 4.
Similarly, the line
<pre>
x, y = y, x
</pre><p>
exchanges the values of <code>x</code> and <code>y</code>,
and
<pre>
x, y, z = y, z, x
</pre><p>
cyclically permutes the values of <code>x</code>, <code>y</code>, and <code>z</code>.
<p>
The meaning of assignments to global variables
and table fields can be changed via metatables.
An assignment to an indexed variable <code>t[i] = val</code> is equivalent to
<code>settable_event(t,i,val)</code>.
(See <a href="#2.4">§2.4</a> for a complete description of the
<code>settable_event</code> function.
This function is not defined or callable in Lua.
We use it here only for explanatory purposes.)
<p>
An assignment to a global name <code>x = val</code>
is equivalent to the assignment
<code>_ENV.x = val</code> (see <a href="#2.2">§2.2</a>).
<h3>3.3.4 – <a name="3.3.4">Control Structures</a></h3><p>
The control structures
<b>if</b>, <b>while</b>, and <b>repeat</b> have the usual meaning and
familiar syntax:
<pre>
stat ::= <b>while</b> exp <b>do</b> block <b>end</b>
stat ::= <b>repeat</b> block <b>until</b> exp
stat ::= <b>if</b> exp <b>then</b> block {<b>elseif</b> exp <b>then</b> block} [<b>else</b> block] <b>end</b>
</pre><p>
Lua also has a <b>for</b> statement, in two flavors (see <a href="#3.3.5">§3.3.5</a>).
<p>
The condition expression of a
control structure can return any value.
Both <b>false</b> and <b>nil</b> are considered false.
All values different from <b>nil</b> and <b>false</b> are considered true
(in particular, the number 0 and the empty string are also true).
<p>
In the <b>repeat</b>–<b>until</b> loop,
the inner block does not end at the <b>until</b> keyword,
but only after the condition.
So, the condition can refer to local variables
declared inside the loop block.
<p>
The <b>goto</b> statement transfers the program control to a label.
For syntactical reasons,
labels in Lua are considered statements too:
<pre>
stat ::= <b>goto</b> Name
stat ::= label
label ::= ‘<b>::</b>’ Name ‘<b>::</b>’
</pre>
<p>
A label is visible in the entire block where it is defined,
except
inside nested blocks where a label with the same name is defined and
inside nested functions.
A goto may jump to any visible label as long as it does not
enter into the scope of a local variable.
<p>
Labels and empty statements are called <em>void statements</em>,
as they perform no actions.
<p>
The <b>break</b> statement terminates the execution of a
<b>while</b>, <b>repeat</b>, or <b>for</b> loop,
skipping to the next statement after the loop:
<pre>
stat ::= <b>break</b>
</pre><p>
A <b>break</b> ends the innermost enclosing loop.
<p>
The <b>return</b> statement is used to return values
from a function or a chunk
(which is an anonymous function).
Functions can return more than one value,
so the syntax for the <b>return</b> statement is
<pre>
stat ::= <b>return</b> [explist] [‘<b>;</b>’]
</pre>
<p>
The <b>return</b> statement can only be written
as the last statement of a block.
If it is really necessary to <b>return</b> in the middle of a block,
then an explicit inner block can be used,
as in the idiom <code>do return end</code>,
because now <b>return</b> is the last statement in its (inner) block.
<h3>3.3.5 – <a name="3.3.5">For Statement</a></h3>
<p>
The <b>for</b> statement has two forms:
one numerical and one generic.
<p>
The numerical <b>for</b> loop repeats a block of code while a
control variable runs through an arithmetic progression.
It has the following syntax:
<pre>
stat ::= <b>for</b> Name ‘<b>=</b>’ exp ‘<b>,</b>’ exp [‘<b>,</b>’ exp] <b>do</b> block <b>end</b>
</pre><p>
The <em>block</em> is repeated for <em>name</em> starting at the value of
the first <em>exp</em>, until it passes the second <em>exp</em> by steps of the
third <em>exp</em>.
More precisely, a <b>for</b> statement like
<pre>
for v = <em>e1</em>, <em>e2</em>, <em>e3</em> do <em>block</em> end
</pre><p>
is equivalent to the code:
<pre>
do
local <em>var</em>, <em>limit</em>, <em>step</em> = tonumber(<em>e1</em>), tonumber(<em>e2</em>), tonumber(<em>e3</em>)
if not (<em>var</em> and <em>limit</em> and <em>step</em>) then error() end
<em>var</em> = <em>var</em> - <em>step</em>
while true do
<em>var</em> = <em>var</em> + <em>step</em>
if (<em>step</em> >= 0 and <em>var</em> > <em>limit</em>) or (<em>step</em> < 0 and <em>var</em> < <em>limit</em>) then
break
end
local v = <em>var</em>
<em>block</em>
end
end
</pre>
<p>
Note the following:
<ul>
<li>
All three control expressions are evaluated only once,
before the loop starts.
They must all result in numbers.
</li>
<li>
<code><em>var</em></code>, <code><em>limit</em></code>, and <code><em>step</em></code> are invisible variables.
The names shown here are for explanatory purposes only.
</li>
<li>
If the third expression (the step) is absent,
then a step of 1 is used.
</li>
<li>
You can use <b>break</b> and <b>goto</b> to exit a <b>for</b> loop.
</li>
<li>
The loop variable <code>v</code> is local to the loop body.
If you need its value after the loop,
assign it to another variable before exiting the loop.
</li>
</ul>
<p>
The generic <b>for</b> statement works over functions,
called <em>iterators</em>.
On each iteration, the iterator function is called to produce a new value,
stopping when this new value is <b>nil</b>.
The generic <b>for</b> loop has the following syntax:
<pre>
stat ::= <b>for</b> namelist <b>in</b> explist <b>do</b> block <b>end</b>
namelist ::= Name {‘<b>,</b>’ Name}
</pre><p>
A <b>for</b> statement like
<pre>
for <em>var_1</em>, ···, <em>var_n</em> in <em>explist</em> do <em>block</em> end
</pre><p>
is equivalent to the code:
<pre>
do
local <em>f</em>, <em>s</em>, <em>var</em> = <em>explist</em>
while true do
local <em>var_1</em>, ···, <em>var_n</em> = <em>f</em>(<em>s</em>, <em>var</em>)
if <em>var_1</em> == nil then break end
<em>var</em> = <em>var_1</em>
<em>block</em>
end
end
</pre><p>
Note the following:
<ul>
<li>
<code><em>explist</em></code> is evaluated only once.
Its results are an <em>iterator</em> function,
a <em>state</em>,
and an initial value for the first <em>iterator variable</em>.
</li>
<li>
<code><em>f</em></code>, <code><em>s</em></code>, and <code><em>var</em></code> are invisible variables.
The names are here for explanatory purposes only.
</li>
<li>
You can use <b>break</b> to exit a <b>for</b> loop.
</li>
<li>
The loop variables <code><em>var_i</em></code> are local to the loop;
you cannot use their values after the <b>for</b> ends.
If you need these values,
then assign them to other variables before breaking or exiting the loop.
</li>
</ul>
<h3>3.3.6 – <a name="3.3.6">Function Calls as Statements</a></h3><p>
To allow possible side-effects,
function calls can be executed as statements:
<pre>
stat ::= functioncall
</pre><p>
In this case, all returned values are thrown away.
Function calls are explained in <a href="#3.4.10">§3.4.10</a>.
<h3>3.3.7 – <a name="3.3.7">Local Declarations</a></h3><p>
Local variables can be declared anywhere inside a block.
The declaration can include an initial assignment:
<pre>
stat ::= <b>local</b> namelist [‘<b>=</b>’ explist]
</pre><p>
If present, an initial assignment has the same semantics
of a multiple assignment (see <a href="#3.3.3">§3.3.3</a>).
Otherwise, all variables are initialized with <b>nil</b>.
<p>
A chunk is also a block (see <a href="#3.3.2">§3.3.2</a>),
and so local variables can be declared in a chunk outside any explicit block.
<p>
The visibility rules for local variables are explained in <a href="#3.5">§3.5</a>.
<h2>3.4 – <a name="3.4">Expressions</a></h2>
<p>
The basic expressions in Lua are the following:
<pre>
exp ::= prefixexp
exp ::= <b>nil</b> | <b>false</b> | <b>true</b>
exp ::= Numeral
exp ::= LiteralString
exp ::= functiondef
exp ::= tableconstructor
exp ::= ‘<b>...</b>’
exp ::= exp binop exp
exp ::= unop exp
prefixexp ::= var | functioncall | ‘<b>(</b>’ exp ‘<b>)</b>’
</pre>
<p>
Numerals and literal strings are explained in <a href="#3.1">§3.1</a>;
variables are explained in <a href="#3.2">§3.2</a>;
function definitions are explained in <a href="#3.4.11">§3.4.11</a>;
function calls are explained in <a href="#3.4.10">§3.4.10</a>;
table constructors are explained in <a href="#3.4.9">§3.4.9</a>.
Vararg expressions,
denoted by three dots ('<code>...</code>'), can only be used when
directly inside a vararg function;
they are explained in <a href="#3.4.11">§3.4.11</a>.
<p>
Binary operators comprise arithmetic operators (see <a href="#3.4.1">§3.4.1</a>),
bitwise operators (see <a href="#3.4.2">§3.4.2</a>),
relational operators (see <a href="#3.4.4">§3.4.4</a>), logical operators (see <a href="#3.4.5">§3.4.5</a>),
and the concatenation operator (see <a href="#3.4.6">§3.4.6</a>).
Unary operators comprise the unary minus (see <a href="#3.4.1">§3.4.1</a>),
the unary bitwise NOT (see <a href="#3.4.2">§3.4.2</a>),
the unary logical <b>not</b> (see <a href="#3.4.5">§3.4.5</a>),
and the unary <em>length operator</em> (see <a href="#3.4.7">§3.4.7</a>).
<p>
Both function calls and vararg expressions can result in multiple values.
If a function call is used as a statement (see <a href="#3.3.6">§3.3.6</a>),
then its return list is adjusted to zero elements,
thus discarding all returned values.
If an expression is used as the last (or the only) element
of a list of expressions,
then no adjustment is made
(unless the expression is enclosed in parentheses).
In all other contexts,
Lua adjusts the result list to one element,
either discarding all values except the first one
or adding a single <b>nil</b> if there are no values.
<p>
Here are some examples:
<pre>
f() -- adjusted to 0 results
g(f(), x) -- f() is adjusted to 1 result
g(x, f()) -- g gets x plus all results from f()
a,b,c = f(), x -- f() is adjusted to 1 result (c gets nil)
a,b = ... -- a gets the first vararg parameter, b gets
-- the second (both a and b can get nil if there
-- is no corresponding vararg parameter)
a,b,c = x, f() -- f() is adjusted to 2 results
a,b,c = f() -- f() is adjusted to 3 results
return f() -- returns all results from f()
return ... -- returns all received vararg parameters
return x,y,f() -- returns x, y, and all results from f()
{f()} -- creates a list with all results from f()
{...} -- creates a list with all vararg parameters
{f(), nil} -- f() is adjusted to 1 result
</pre>
<p>
Any expression enclosed in parentheses always results in only one value.
Thus,
<code>(f(x,y,z))</code> is always a single value,
even if <code>f</code> returns several values.
(The value of <code>(f(x,y,z))</code> is the first value returned by <code>f</code>
or <b>nil</b> if <code>f</code> does not return any values.)
<h3>3.4.1 – <a name="3.4.1">Arithmetic Operators</a></h3><p>
Lua supports the following arithmetic operators:
<ul>
<li><b><code>+</code>: </b>addition</li>
<li><b><code>-</code>: </b>subtraction</li>
<li><b><code>*</code>: </b>multiplication</li>
<li><b><code>/</code>: </b>float division</li>
<li><b><code>//</code>: </b>floor division</li>
<li><b><code>%</code>: </b>modulo</li>
<li><b><code>^</code>: </b>exponentiation</li>
<li><b><code>-</code>: </b>unary minus</li>
</ul>
<p>
With the exception of exponentiation and float division,
the arithmetic operators work as follows:
If both operands are integers,
the operation is performed over integers and the result is an integer.
Otherwise, if both operands are numbers
or strings that can be converted to
numbers (see <a href="#3.4.3">§3.4.3</a>),
then they are converted to floats,
the operation is performed following the usual rules
for floating-point arithmetic
(usually the IEEE 754 standard),
and the result is a float.
<p>
Exponentiation and float division (<code>/</code>)
always convert their operands to floats
and the result is always a float.
Exponentiation uses the ISO C function <code>pow</code>,
so that it works for non-integer exponents too.
<p>
Floor division (<code>//</code>) is a division
that rounds the quotient towards minus infinity,
that is, the floor of the division of its operands.
<p>
Modulo is defined as the remainder of a division
that rounds the quotient towards minus infinity (floor division).
<p>
In case of overflows in integer arithmetic,
all operations <em>wrap around</em>,
according to the usual rules of two-complement arithmetic.
(In other words,
they return the unique representable integer
that is equal modulo <em>2<sup>64</sup></em> to the mathematical result.)
<h3>3.4.2 – <a name="3.4.2">Bitwise Operators</a></h3><p>
Lua supports the following bitwise operators:
<ul>
<li><b><code>&</code>: </b>bitwise AND</li>
<li><b><code>|</code>: </b>bitwise OR</li>
<li><b><code>~</code>: </b>bitwise exclusive OR</li>
<li><b><code>>></code>: </b>right shift</li>
<li><b><code><<</code>: </b>left shift</li>
<li><b><code>~</code>: </b>unary bitwise NOT</li>
</ul>
<p>
All bitwise operations convert its operands to integers
(see <a href="#3.4.3">§3.4.3</a>),
operate on all bits of those integers,
and result in an integer.
<p>
Both right and left shifts fill the vacant bits with zeros.
Negative displacements shift to the other direction;
displacements with absolute values equal to or higher than
the number of bits in an integer
result in zero (as all bits are shifted out).
<h3>3.4.3 – <a name="3.4.3">Coercions and Conversions</a></h3><p>
Lua provides some automatic conversions between some
types and representations at run time.
Bitwise operators always convert float operands to integers.
Exponentiation and float division
always convert integer operands to floats.
All other arithmetic operations applied to mixed numbers
(integers and floats) convert the integer operand to a float;
this is called the <em>usual rule</em>.
The C API also converts both integers to floats and
floats to integers, as needed.
Moreover, string concatenation accepts numbers as arguments,
besides strings.
<p>
Lua also converts strings to numbers,
whenever a number is expected.
<p>
In a conversion from integer to float,
if the integer value has an exact representation as a float,
that is the result.
Otherwise,
the conversion gets the nearest higher or
the nearest lower representable value.
This kind of conversion never fails.
<p>
The conversion from float to integer
checks whether the float has an exact representation as an integer
(that is, the float has an integral value and
it is in the range of integer representation).
If it does, that representation is the result.
Otherwise, the conversion fails.
<p>
The conversion from strings to numbers goes as follows:
First, the string is converted to an integer or a float,
following its syntax and the rules of the Lua lexer.
(The string may have also leading and trailing spaces and a sign.)
Then, the resulting number (float or integer)
is converted to the type (float or integer) required by the context
(e.g., the operation that forced the conversion).
<p>
All conversions from strings to numbers
accept both a dot and the current locale mark
as the radix character.
(The Lua lexer, however, accepts only a dot.)
<p>
The conversion from numbers to strings uses a
non-specified human-readable format.
For complete control over how numbers are converted to strings,
use the <code>format</code> function from the string library
(see <a href="#pdf-string.format"><code>string.format</code></a>).
<h3>3.4.4 – <a name="3.4.4">Relational Operators</a></h3><p>
Lua supports the following relational operators:
<ul>
<li><b><code>==</code>: </b>equality</li>
<li><b><code>~=</code>: </b>inequality</li>
<li><b><code><</code>: </b>less than</li>
<li><b><code>></code>: </b>greater than</li>
<li><b><code><=</code>: </b>less or equal</li>
<li><b><code>>=</code>: </b>greater or equal</li>
</ul><p>
These operators always result in <b>false</b> or <b>true</b>.
<p>
Equality (<code>==</code>) first compares the type of its operands.
If the types are different, then the result is <b>false</b>.
Otherwise, the values of the operands are compared.
Strings are compared in the obvious way.
Numbers are equal if they denote the same mathematical value.
<p>
Tables, userdata, and threads
are compared by reference:
two objects are considered equal only if they are the same object.
Every time you create a new object
(a table, userdata, or thread),
this new object is different from any previously existing object.
Closures with the same reference are always equal.
Closures with any detectable difference
(different behavior, different definition) are always different.
<p>
You can change the way that Lua compares tables and userdata
by using the "eq" metamethod (see <a href="#2.4">§2.4</a>).
<p>
Equality comparisons do not convert strings to numbers
or vice versa.
Thus, <code>"0"==0</code> evaluates to <b>false</b>,
and <code>t[0]</code> and <code>t["0"]</code> denote different
entries in a table.
<p>
The operator <code>~=</code> is exactly the negation of equality (<code>==</code>).
<p>
The order operators work as follows.
If both arguments are numbers,
then they are compared according to their mathematical values
(regardless of their subtypes).
Otherwise, if both arguments are strings,
then their values are compared according to the current locale.
Otherwise, Lua tries to call the "lt" or the "le"
metamethod (see <a href="#2.4">§2.4</a>).
A comparison <code>a > b</code> is translated to <code>b < a</code>
and <code>a >= b</code> is translated to <code>b <= a</code>.
<p>
Following the IEEE 754 standard,
NaN is considered neither smaller than,
nor equal to, nor greater than any value (including itself).
<h3>3.4.5 – <a name="3.4.5">Logical Operators</a></h3><p>
The logical operators in Lua are
<b>and</b>, <b>or</b>, and <b>not</b>.
Like the control structures (see <a href="#3.3.4">§3.3.4</a>),
all logical operators consider both <b>false</b> and <b>nil</b> as false
and anything else as true.
<p>
The negation operator <b>not</b> always returns <b>false</b> or <b>true</b>.
The conjunction operator <b>and</b> returns its first argument
if this value is <b>false</b> or <b>nil</b>;
otherwise, <b>and</b> returns its second argument.
The disjunction operator <b>or</b> returns its first argument
if this value is different from <b>nil</b> and <b>false</b>;
otherwise, <b>or</b> returns its second argument.
Both <b>and</b> and <b>or</b> use short-circuit evaluation;
that is,
the second operand is evaluated only if necessary.
Here are some examples:
<pre>
10 or 20 --> 10
10 or error() --> 10
nil or "a" --> "a"
nil and 10 --> nil
false and error() --> false
false and nil --> false
false or nil --> nil
10 and 20 --> 20
</pre><p>
(In this manual,
<code>--></code> indicates the result of the preceding expression.)
<h3>3.4.6 – <a name="3.4.6">Concatenation</a></h3><p>
The string concatenation operator in Lua is
denoted by two dots ('<code>..</code>').
If both operands are strings or numbers, then they are converted to
strings according to the rules described in <a href="#3.4.3">§3.4.3</a>.
Otherwise, the <code>__concat</code> metamethod is called (see <a href="#2.4">§2.4</a>).
<h3>3.4.7 – <a name="3.4.7">The Length Operator</a></h3>
<p>
The length operator is denoted by the unary prefix operator <code>#</code>.
The length of a string is its number of bytes
(that is, the usual meaning of string length when each
character is one byte).
<p>
A program can modify the behavior of the length operator for
any value but strings through the <code>__len</code> metamethod (see <a href="#2.4">§2.4</a>).
<p>
Unless a <code>__len</code> metamethod is given,
the length of a table <code>t</code> is only defined if the
table is a <em>sequence</em>,
that is,
the set of its positive numeric keys is equal to <em>{1..n}</em>
for some non-negative integer <em>n</em>.
In that case, <em>n</em> is its length.
Note that a table like
<pre>
{10, 20, nil, 40}
</pre><p>
is not a sequence, because it has the key <code>4</code>
but does not have the key <code>3</code>.
(So, there is no <em>n</em> such that the set <em>{1..n}</em> is equal
to the set of positive numeric keys of that table.)
Note, however, that non-numeric keys do not interfere
with whether a table is a sequence.
<h3>3.4.8 – <a name="3.4.8">Precedence</a></h3><p>
Operator precedence in Lua follows the table below,
from lower to higher priority:
<pre>
or
and
< > <= >= ~= ==
|
~
&
<< >>
..
+ -
* / // %
unary operators (not # - ~)
^
</pre><p>
As usual,
you can use parentheses to change the precedences of an expression.
The concatenation ('<code>..</code>') and exponentiation ('<code>^</code>')
operators are right associative.
All other binary operators are left associative.
<h3>3.4.9 – <a name="3.4.9">Table Constructors</a></h3><p>
Table constructors are expressions that create tables.
Every time a constructor is evaluated, a new table is created.
A constructor can be used to create an empty table
or to create a table and initialize some of its fields.
The general syntax for constructors is
<pre>
tableconstructor ::= ‘<b>{</b>’ [fieldlist] ‘<b>}</b>’
fieldlist ::= field {fieldsep field} [fieldsep]
field ::= ‘<b>[</b>’ exp ‘<b>]</b>’ ‘<b>=</b>’ exp | Name ‘<b>=</b>’ exp | exp
fieldsep ::= ‘<b>,</b>’ | ‘<b>;</b>’
</pre>
<p>
Each field of the form <code>[exp1] = exp2</code> adds to the new table an entry
with key <code>exp1</code> and value <code>exp2</code>.
A field of the form <code>name = exp</code> is equivalent to
<code>["name"] = exp</code>.
Finally, fields of the form <code>exp</code> are equivalent to
<code>[i] = exp</code>, where <code>i</code> are consecutive integers
starting with 1.
Fields in the other formats do not affect this counting.
For example,
<pre>
a = { [f(1)] = g; "x", "y"; x = 1, f(x), [30] = 23; 45 }
</pre><p>
is equivalent to
<pre>
do
local t = {}
t[f(1)] = g
t[1] = "x" -- 1st exp
t[2] = "y" -- 2nd exp
t.x = 1 -- t["x"] = 1
t[3] = f(x) -- 3rd exp
t[30] = 23
t[4] = 45 -- 4th exp
a = t
end
</pre>
<p>
The order of the assignments in a constructor is undefined.
(This order would be relevant only when there are repeated keys.)
<p>
If the last field in the list has the form <code>exp</code>
and the expression is a function call or a vararg expression,
then all values returned by this expression enter the list consecutively
(see <a href="#3.4.10">§3.4.10</a>).
<p>
The field list can have an optional trailing separator,
as a convenience for machine-generated code.
<h3>3.4.10 – <a name="3.4.10">Function Calls</a></h3><p>
A function call in Lua has the following syntax:
<pre>
functioncall ::= prefixexp args
</pre><p>
In a function call,
first prefixexp and args are evaluated.
If the value of prefixexp has type <em>function</em>,
then this function is called
with the given arguments.
Otherwise, the prefixexp "call" metamethod is called,
having as first parameter the value of prefixexp,
followed by the original call arguments
(see <a href="#2.4">§2.4</a>).
<p>
The form
<pre>
functioncall ::= prefixexp ‘<b>:</b>’ Name args
</pre><p>
can be used to call "methods".
A call <code>v:name(<em>args</em>)</code>
is syntactic sugar for <code>v.name(v,<em>args</em>)</code>,
except that <code>v</code> is evaluated only once.
<p>
Arguments have the following syntax:
<pre>
args ::= ‘<b>(</b>’ [explist] ‘<b>)</b>’
args ::= tableconstructor
args ::= LiteralString
</pre><p>
All argument expressions are evaluated before the call.
A call of the form <code>f{<em>fields</em>}</code> is
syntactic sugar for <code>f({<em>fields</em>})</code>;
that is, the argument list is a single new table.
A call of the form <code>f'<em>string</em>'</code>
(or <code>f"<em>string</em>"</code> or <code>f[[<em>string</em>]]</code>)
is syntactic sugar for <code>f('<em>string</em>')</code>;
that is, the argument list is a single literal string.
<p>
A call of the form <code>return <em>functioncall</em></code> is called
a <em>tail call</em>.
Lua implements <em>proper tail calls</em>
(or <em>proper tail recursion</em>):
in a tail call,
the called function reuses the stack entry of the calling function.
Therefore, there is no limit on the number of nested tail calls that
a program can execute.
However, a tail call erases any debug information about the
calling function.
Note that a tail call only happens with a particular syntax,
where the <b>return</b> has one single function call as argument;
this syntax makes the calling function return exactly
the returns of the called function.
So, none of the following examples are tail calls:
<pre>
return (f(x)) -- results adjusted to 1
return 2 * f(x)
return x, f(x) -- additional results
f(x); return -- results discarded
return x or f(x) -- results adjusted to 1
</pre>
<h3>3.4.11 – <a name="3.4.11">Function Definitions</a></h3>
<p>
The syntax for function definition is
<pre>
functiondef ::= <b>function</b> funcbody
funcbody ::= ‘<b>(</b>’ [parlist] ‘<b>)</b>’ block <b>end</b>
</pre>
<p>
The following syntactic sugar simplifies function definitions:
<pre>
stat ::= <b>function</b> funcname funcbody
stat ::= <b>local</b> <b>function</b> Name funcbody
funcname ::= Name {‘<b>.</b>’ Name} [‘<b>:</b>’ Name]
</pre><p>
The statement
<pre>
function f () <em>body</em> end
</pre><p>
translates to
<pre>
f = function () <em>body</em> end
</pre><p>
The statement
<pre>
function t.a.b.c.f () <em>body</em> end
</pre><p>
translates to
<pre>
t.a.b.c.f = function () <em>body</em> end
</pre><p>
The statement
<pre>
local function f () <em>body</em> end
</pre><p>
translates to
<pre>
local f; f = function () <em>body</em> end
</pre><p>
not to
<pre>
local f = function () <em>body</em> end
</pre><p>
(This only makes a difference when the body of the function
contains references to <code>f</code>.)
<p>
A function definition is an executable expression,
whose value has type <em>function</em>.
When Lua precompiles a chunk,
all its function bodies are precompiled too.
Then, whenever Lua executes the function definition,
the function is <em>instantiated</em> (or <em>closed</em>).
This function instance (or <em>closure</em>)
is the final value of the expression.
<p>
Parameters act as local variables that are
initialized with the argument values:
<pre>
parlist ::= namelist [‘<b>,</b>’ ‘<b>...</b>’] | ‘<b>...</b>’
</pre><p>
When a function is called,
the list of arguments is adjusted to
the length of the list of parameters,
unless the function is a <em>vararg function</em>,
which is indicated by three dots ('<code>...</code>')
at the end of its parameter list.
A vararg function does not adjust its argument list;
instead, it collects all extra arguments and supplies them
to the function through a <em>vararg expression</em>,
which is also written as three dots.
The value of this expression is a list of all actual extra arguments,
similar to a function with multiple results.
If a vararg expression is used inside another expression
or in the middle of a list of expressions,
then its return list is adjusted to one element.
If the expression is used as the last element of a list of expressions,
then no adjustment is made
(unless that last expression is enclosed in parentheses).
<p>
As an example, consider the following definitions:
<pre>
function f(a, b) end
function g(a, b, ...) end
function r() return 1,2,3 end
</pre><p>
Then, we have the following mapping from arguments to parameters and
to the vararg expression:
<pre>
CALL PARAMETERS
f(3) a=3, b=nil
f(3, 4) a=3, b=4
f(3, 4, 5) a=3, b=4
f(r(), 10) a=1, b=10
f(r()) a=1, b=2
g(3) a=3, b=nil, ... --> (nothing)
g(3, 4) a=3, b=4, ... --> (nothing)
g(3, 4, 5, 8) a=3, b=4, ... --> 5 8
g(5, r()) a=5, b=1, ... --> 2 3
</pre>
<p>
Results are returned using the <b>return</b> statement (see <a href="#3.3.4">§3.3.4</a>).
If control reaches the end of a function
without encountering a <b>return</b> statement,
then the function returns with no results.
<p>
There is a system-dependent limit on the number of values
that a function may return.
This limit is guaranteed to be larger than 1000.
<p>
The <em>colon</em> syntax
is used for defining <em>methods</em>,
that is, functions that have an implicit extra parameter <code>self</code>.
Thus, the statement
<pre>
function t.a.b.c:f (<em>params</em>) <em>body</em> end
</pre><p>
is syntactic sugar for
<pre>
t.a.b.c.f = function (self, <em>params</em>) <em>body</em> end
</pre>
<h2>3.5 – <a name="3.5">Visibility Rules</a></h2>
<p>
Lua is a lexically scoped language.
The scope of a local variable begins at the first statement after
its declaration and lasts until the last non-void statement
of the innermost block that includes the declaration.
Consider the following example:
<pre>
x = 10 -- global variable
do -- new block
local x = x -- new 'x', with value 10
print(x) --> 10
x = x+1
do -- another block
local x = x+1 -- another 'x'
print(x) --> 12
end
print(x) --> 11
end
print(x) --> 10 (the global one)
</pre>
<p>
Notice that, in a declaration like <code>local x = x</code>,
the new <code>x</code> being declared is not in scope yet,
and so the second <code>x</code> refers to the outside variable.
<p>
Because of the lexical scoping rules,
local variables can be freely accessed by functions
defined inside their scope.
A local variable used by an inner function is called
an <em>upvalue</em>, or <em>external local variable</em>,
inside the inner function.
<p>
Notice that each execution of a <b>local</b> statement
defines new local variables.
Consider the following example:
<pre>
a = {}
local x = 20
for i=1,10 do
local y = 0
a[i] = function () y=y+1; return x+y end
end
</pre><p>
The loop creates ten closures
(that is, ten instances of the anonymous function).
Each of these closures uses a different <code>y</code> variable,
while all of them share the same <code>x</code>.
<h1>4 – <a name="4">The Application Program Interface</a></h1>
<p>
This section describes the C API for Lua, that is,
the set of C functions available to the host program to communicate
with Lua.
All API functions and related types and constants
are declared in the header file <a name="pdf-lua.h"><code>lua.h</code></a>.
<p>
Even when we use the term "function",
any facility in the API may be provided as a macro instead.
Except where stated otherwise,
all such macros use each of their arguments exactly once
(except for the first argument, which is always a Lua state),
and so do not generate any hidden side-effects.
<p>
As in most C libraries,
the Lua API functions do not check their arguments for validity or consistency.
However, you can change this behavior by compiling Lua
with the macro <a name="pdf-LUA_USE_APICHECK"><code>LUA_USE_APICHECK</code></a> defined.
<h2>4.1 – <a name="4.1">The Stack</a></h2>
<p>
Lua uses a <em>virtual stack</em> to pass values to and from C.
Each element in this stack represents a Lua value
(<b>nil</b>, number, string, etc.).
<p>
Whenever Lua calls C, the called function gets a new stack,
which is independent of previous stacks and of stacks of
C functions that are still active.
This stack initially contains any arguments to the C function
and it is where the C function pushes its results
to be returned to the caller (see <a href="#lua_CFunction"><code>lua_CFunction</code></a>).
<p>
For convenience,
most query operations in the API do not follow a strict stack discipline.
Instead, they can refer to any element in the stack
by using an <em>index</em>:
A positive index represents an absolute stack position
(starting at 1);
a negative index represents an offset relative to the top of the stack.
More specifically, if the stack has <em>n</em> elements,
then index 1 represents the first element
(that is, the element that was pushed onto the stack first)
and
index <em>n</em> represents the last element;
index -1 also represents the last element
(that is, the element at the top)
and index <em>-n</em> represents the first element.
<h2>4.2 – <a name="4.2">Stack Size</a></h2>
<p>
When you interact with the Lua API,
you are responsible for ensuring consistency.
In particular,
<em>you are responsible for controlling stack overflow</em>.
You can use the function <a href="#lua_checkstack"><code>lua_checkstack</code></a>
to ensure that the stack has enough space for pushing new elements.
<p>
Whenever Lua calls C,
it ensures that the stack has space for
at least <a name="pdf-LUA_MINSTACK"><code>LUA_MINSTACK</code></a> extra slots.
<code>LUA_MINSTACK</code> is defined as 20,
so that usually you do not have to worry about stack space
unless your code has loops pushing elements onto the stack.
<p>
When you call a Lua function
without a fixed number of results (see <a href="#lua_call"><code>lua_call</code></a>),
Lua ensures that the stack has enough space for all results,
but it does not ensure any extra space.
So, before pushing anything in the stack after such a call
you should use <a href="#lua_checkstack"><code>lua_checkstack</code></a>.
<h2>4.3 – <a name="4.3">Valid and Acceptable Indices</a></h2>
<p>
Any function in the API that receives stack indices
works only with <em>valid indices</em> or <em>acceptable indices</em>.
<p>
A <em>valid index</em> is an index that refers to a
position that stores a modifiable Lua value.
It comprises stack indices between 1 and the stack top
(<code>1 ≤ abs(index) ≤ top</code>)
plus <em>pseudo-indices</em>,
which represent some positions that are accessible to C code
but that are not in the stack.
Pseudo-indices are used to access the registry (see <a href="#4.5">§4.5</a>)
and the upvalues of a C function (see <a href="#4.4">§4.4</a>).
<p>
Functions that do not need a specific mutable position,
but only a value (e.g., query functions),
can be called with acceptable indices.
An <em>acceptable index</em> can be any valid index,
but it also can be any positive index after the stack top
within the space allocated for the stack,
that is, indices up to the stack size.
(Note that 0 is never an acceptable index.)
Except when noted otherwise,
functions in the API work with acceptable indices.
<p>
Acceptable indices serve to avoid extra tests
against the stack top when querying the stack.
For instance, a C function can query its third argument
without the need to first check whether there is a third argument,
that is, without the need to check whether 3 is a valid index.
<p>
For functions that can be called with acceptable indices,
any non-valid index is treated as if it
contains a value of a virtual type <a name="pdf-LUA_TNONE"><code>LUA_TNONE</code></a>,
which behaves like a nil value.
<h2>4.4 – <a name="4.4">C Closures</a></h2>
<p>
When a C function is created,
it is possible to associate some values with it,
thus creating a <em>C closure</em>
(see <a href="#lua_pushcclosure"><code>lua_pushcclosure</code></a>);
these values are called <em>upvalues</em> and are
accessible to the function whenever it is called.
<p>
Whenever a C function is called,
its upvalues are located at specific pseudo-indices.
These pseudo-indices are produced by the macro
<a href="#lua_upvalueindex"><code>lua_upvalueindex</code></a>.
The first upvalue associated with a function is at index
<code>lua_upvalueindex(1)</code>, and so on.
Any access to <code>lua_upvalueindex(<em>n</em>)</code>,
where <em>n</em> is greater than the number of upvalues of the
current function
(but not greater than 256,
which is one plus the maximum number of upvalues in a closure),
produces an acceptable but invalid index.
<h2>4.5 – <a name="4.5">Registry</a></h2>
<p>
Lua provides a <em>registry</em>,
a predefined table that can be used by any C code to
store whatever Lua values it needs to store.
The registry table is always located at pseudo-index
<a name="pdf-LUA_REGISTRYINDEX"><code>LUA_REGISTRYINDEX</code></a>.
Any C library can store data into this table,
but it must take care to choose keys
that are different from those used
by other libraries, to avoid collisions.
Typically, you should use as key a string containing your library name,
or a light userdata with the address of a C object in your code,
or any Lua object created by your code.
As with variable names,
string keys starting with an underscore followed by
uppercase letters are reserved for Lua.
<p>
The integer keys in the registry are used
by the reference mechanism (see <a href="#luaL_ref"><code>luaL_ref</code></a>)
and by some predefined values.
Therefore, integer keys must not be used for other purposes.
<p>
When you create a new Lua state,
its registry comes with some predefined values.
These predefined values are indexed with integer keys
defined as constants in <code>lua.h</code>.
The following constants are defined:
<ul>
<li><b><a name="pdf-LUA_RIDX_MAINTHREAD"><code>LUA_RIDX_MAINTHREAD</code></a>: </b> At this index the registry has
the main thread of the state.
(The main thread is the one created together with the state.)
</li>
<li><b><a name="pdf-LUA_RIDX_GLOBALS"><code>LUA_RIDX_GLOBALS</code></a>: </b> At this index the registry has
the global environment.
</li>
</ul>
<h2>4.6 – <a name="4.6">Error Handling in C</a></h2>
<p>
Internally, Lua uses the C <code>longjmp</code> facility to handle errors.
(Lua will use exceptions if you compile it as C++;
search for <code>LUAI_THROW</code> in the source code for details.)
When Lua faces any error
(such as a memory allocation error, type errors, syntax errors,
and runtime errors)
it <em>raises</em> an error;
that is, it does a long jump.
A <em>protected environment</em> uses <code>setjmp</code>
to set a recovery point;
any error jumps to the most recent active recovery point.
<p>
If an error happens outside any protected environment,
Lua calls a <em>panic function</em> (see <a href="#lua_atpanic"><code>lua_atpanic</code></a>)
and then calls <code>abort</code>,
thus exiting the host application.
Your panic function can avoid this exit by
never returning
(e.g., doing a long jump to your own recovery point outside Lua).
<p>
The panic function runs as if it were a message handler (see <a href="#2.3">§2.3</a>);
in particular, the error object is at the top of the stack.
However, there is no guarantee about stack space.
To push anything on the stack,
the panic function must first check the available space (see <a href="#4.2">§4.2</a>).
<p>
Most functions in the API can raise an error,
for instance due to a memory allocation error.
The documentation for each function indicates whether
it can raise errors.
<p>
Inside a C function you can raise an error by calling <a href="#lua_error"><code>lua_error</code></a>.
<h2>4.7 – <a name="4.7">Handling Yields in C</a></h2>
<p>
Internally, Lua uses the C <code>longjmp</code> facility to yield a coroutine.
Therefore, if a C function <code>foo</code> calls an API function
and this API function yields
(directly or indirectly by calling another function that yields),
Lua cannot return to <code>foo</code> any more,
because the <code>longjmp</code> removes its frame from the C stack.
<p>
To avoid this kind of problem,
Lua raises an error whenever it tries to yield across an API call,
except for three functions:
<a href="#lua_yieldk"><code>lua_yieldk</code></a>, <a href="#lua_callk"><code>lua_callk</code></a>, and <a href="#lua_pcallk"><code>lua_pcallk</code></a>.
All those functions receive a <em>continuation function</em>
(as a parameter named <code>k</code>) to continue execution after a yield.
<p>
We need to set some terminology to explain continuations.
We have a C function called from Lua which we will call
the <em>original function</em>.
This original function then calls one of those three functions in the C API,
which we will call the <em>callee function</em>,
that then yields the current thread.
(This can happen when the callee function is <a href="#lua_yieldk"><code>lua_yieldk</code></a>,
or when the callee function is either <a href="#lua_callk"><code>lua_callk</code></a> or <a href="#lua_pcallk"><code>lua_pcallk</code></a>
and the function called by them yields.)
<p>
Suppose the running thread yields while executing the callee function.
After the thread resumes,
it eventually will finish running the callee function.
However,
the callee function cannot return to the original function,
because its frame in the C stack was destroyed by the yield.
Instead, Lua calls a <em>continuation function</em>,
which was given as an argument to the callee function.
As the name implies,
the continuation function should continue the task
of the original function.
<p>
As an illustration, consider the following function:
<pre>
int original_function (lua_State *L) {
... /* code 1 */
status = lua_pcall(L, n, m, h); /* calls Lua */
... /* code 2 */
}
</pre><p>
Now we want to allow
the Lua code being run by <a href="#lua_pcall"><code>lua_pcall</code></a> to yield.
First, we can rewrite our function like here:
<pre>
int k (lua_State *L, int status, lua_KContext ctx) {
... /* code 2 */
}
int original_function (lua_State *L) {
... /* code 1 */
return k(L, lua_pcall(L, n, m, h), ctx);
}
</pre><p>
In the above code,
the new function <code>k</code> is a
<em>continuation function</em> (with type <a href="#lua_KFunction"><code>lua_KFunction</code></a>),
which should do all the work that the original function
was doing after calling <a href="#lua_pcall"><code>lua_pcall</code></a>.
Now, we must inform Lua that it must call <code>k</code> if the Lua code
being executed by <a href="#lua_pcall"><code>lua_pcall</code></a> gets interrupted in some way
(errors or yielding),
so we rewrite the code as here,
replacing <a href="#lua_pcall"><code>lua_pcall</code></a> by <a href="#lua_pcallk"><code>lua_pcallk</code></a>:
<pre>
int original_function (lua_State *L) {
... /* code 1 */
return k(L, lua_pcallk(L, n, m, h, ctx2, k), ctx1);
}
</pre><p>
Note the external, explicit call to the continuation:
Lua will call the continuation only if needed, that is,
in case of errors or resuming after a yield.
If the called function returns normally without ever yielding,
<a href="#lua_pcallk"><code>lua_pcallk</code></a> (and <a href="#lua_callk"><code>lua_callk</code></a>) will also return normally.
(Of course, instead of calling the continuation in that case,
you can do the equivalent work directly inside the original function.)
<p>
Besides the Lua state,
the continuation function has two other parameters:
the final status of the call plus the context value (<code>ctx</code>) that
was passed originally to <a href="#lua_pcallk"><code>lua_pcallk</code></a>.
(Lua does not use this context value;
it only passes this value from the original function to the
continuation function.)
For <a href="#lua_pcallk"><code>lua_pcallk</code></a>,
the status is the same value that would be returned by <a href="#lua_pcallk"><code>lua_pcallk</code></a>,
except that it is <a href="#pdf-LUA_YIELD"><code>LUA_YIELD</code></a> when being executed after a yield
(instead of <a href="#pdf-LUA_OK"><code>LUA_OK</code></a>).
For <a href="#lua_yieldk"><code>lua_yieldk</code></a> and <a href="#lua_callk"><code>lua_callk</code></a>,
the status is always <a href="#pdf-LUA_YIELD"><code>LUA_YIELD</code></a> when Lua calls the continuation.
(For these two functions,
Lua will not call the continuation in case of errors,
because they do not handle errors.)
Similarly, when using <a href="#lua_callk"><code>lua_callk</code></a>,
you should call the continuation function
with <a href="#pdf-LUA_OK"><code>LUA_OK</code></a> as the status.
(For <a href="#lua_yieldk"><code>lua_yieldk</code></a>, there is not much point in calling
directly the continuation function,
because <a href="#lua_yieldk"><code>lua_yieldk</code></a> usually does not return.)
<p>
Lua treats the continuation function as if it were the original function.
The continuation function receives the same Lua stack
from the original function,
in the same state it would be if the callee function had returned.
(For instance,
after a <a href="#lua_callk"><code>lua_callk</code></a> the function and its arguments are
removed from the stack and replaced by the results from the call.)
It also has the same upvalues.
Whatever it returns is handled by Lua as if it were the return
of the original function.
<h2>4.8 – <a name="4.8">Functions and Types</a></h2>
<p>
Here we list all functions and types from the C API in
alphabetical order.
Each function has an indicator like this:
<span class="apii">[-o, +p, <em>x</em>]</span>
<p>
The first field, <code>o</code>,
is how many elements the function pops from the stack.
The second field, <code>p</code>,
is how many elements the function pushes onto the stack.
(Any function always pushes its results after popping its arguments.)
A field in the form <code>x|y</code> means the function can push (or pop)
<code>x</code> or <code>y</code> elements,
depending on the situation;
an interrogation mark '<code>?</code>' means that
we cannot know how many elements the function pops/pushes
by looking only at its arguments
(e.g., they may depend on what is on the stack).
The third field, <code>x</code>,
tells whether the function may raise errors:
'<code>-</code>' means the function never raises any error;
'<code>m</code>' means the function may raise out-of-memory errors
and errors running a <code>__gc</code> metamethod;
'<code>e</code>' means the function may raise any errors
(it can run arbitrary Lua code,
either directly or through metamethods);
'<code>v</code>' means the function may raise an error on purpose.
<hr><h3><a name="lua_absindex"><code>lua_absindex</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_absindex (lua_State *L, int idx);</pre>
<p>
Converts the acceptable index <code>idx</code>
into an equivalent absolute index
(that is, one that does not depend on the stack top).
<hr><h3><a name="lua_Alloc"><code>lua_Alloc</code></a></h3>
<pre>typedef void * (*lua_Alloc) (void *ud,
void *ptr,
size_t osize,
size_t nsize);</pre>
<p>
The type of the memory-allocation function used by Lua states.
The allocator function must provide a
functionality similar to <code>realloc</code>,
but not exactly the same.
Its arguments are
<code>ud</code>, an opaque pointer passed to <a href="#lua_newstate"><code>lua_newstate</code></a>;
<code>ptr</code>, a pointer to the block being allocated/reallocated/freed;
<code>osize</code>, the original size of the block or some code about what
is being allocated;
and <code>nsize</code>, the new size of the block.
<p>
When <code>ptr</code> is not <code>NULL</code>,
<code>osize</code> is the size of the block pointed by <code>ptr</code>,
that is, the size given when it was allocated or reallocated.
<p>
When <code>ptr</code> is <code>NULL</code>,
<code>osize</code> encodes the kind of object that Lua is allocating.
<code>osize</code> is any of
<a href="#pdf-LUA_TSTRING"><code>LUA_TSTRING</code></a>, <a href="#pdf-LUA_TTABLE"><code>LUA_TTABLE</code></a>, <a href="#pdf-LUA_TFUNCTION"><code>LUA_TFUNCTION</code></a>,
<a href="#pdf-LUA_TUSERDATA"><code>LUA_TUSERDATA</code></a>, or <a href="#pdf-LUA_TTHREAD"><code>LUA_TTHREAD</code></a> when (and only when)
Lua is creating a new object of that type.
When <code>osize</code> is some other value,
Lua is allocating memory for something else.
<p>
Lua assumes the following behavior from the allocator function:
<p>
When <code>nsize</code> is zero,
the allocator must behave like <code>free</code>
and return <code>NULL</code>.
<p>
When <code>nsize</code> is not zero,
the allocator must behave like <code>realloc</code>.
The allocator returns <code>NULL</code>
if and only if it cannot fulfill the request.
Lua assumes that the allocator never fails when
<code>osize >= nsize</code>.
<p>
Here is a simple implementation for the allocator function.
It is used in the auxiliary library by <a href="#luaL_newstate"><code>luaL_newstate</code></a>.
<pre>
static void *l_alloc (void *ud, void *ptr, size_t osize,
size_t nsize) {
(void)ud; (void)osize; /* not used */
if (nsize == 0) {
free(ptr);
return NULL;
}
else
return realloc(ptr, nsize);
}
</pre><p>
Note that Standard C ensures
that <code>free(NULL)</code> has no effect and that
<code>realloc(NULL,size)</code> is equivalent to <code>malloc(size)</code>.
This code assumes that <code>realloc</code> does not fail when shrinking a block.
(Although Standard C does not ensure this behavior,
it seems to be a safe assumption.)
<hr><h3><a name="lua_arith"><code>lua_arith</code></a></h3><p>
<span class="apii">[-(2|1), +1, <em>e</em>]</span>
<pre>void lua_arith (lua_State *L, int op);</pre>
<p>
Performs an arithmetic or bitwise operation over the two values
(or one, in the case of negations)
at the top of the stack,
with the value at the top being the second operand,
pops these values, and pushes the result of the operation.
The function follows the semantics of the corresponding Lua operator
(that is, it may call metamethods).
<p>
The value of <code>op</code> must be one of the following constants:
<ul>
<li><b><a name="pdf-LUA_OPADD"><code>LUA_OPADD</code></a>: </b> performs addition (<code>+</code>)</li>
<li><b><a name="pdf-LUA_OPSUB"><code>LUA_OPSUB</code></a>: </b> performs subtraction (<code>-</code>)</li>
<li><b><a name="pdf-LUA_OPMUL"><code>LUA_OPMUL</code></a>: </b> performs multiplication (<code>*</code>)</li>
<li><b><a name="pdf-LUA_OPDIV"><code>LUA_OPDIV</code></a>: </b> performs float division (<code>/</code>)</li>
<li><b><a name="pdf-LUA_OPIDIV"><code>LUA_OPIDIV</code></a>: </b> performs floor division (<code>//</code>)</li>
<li><b><a name="pdf-LUA_OPMOD"><code>LUA_OPMOD</code></a>: </b> performs modulo (<code>%</code>)</li>
<li><b><a name="pdf-LUA_OPPOW"><code>LUA_OPPOW</code></a>: </b> performs exponentiation (<code>^</code>)</li>
<li><b><a name="pdf-LUA_OPUNM"><code>LUA_OPUNM</code></a>: </b> performs mathematical negation (unary <code>-</code>)</li>
<li><b><a name="pdf-LUA_OPBNOT"><code>LUA_OPBNOT</code></a>: </b> performs bitwise NOT (<code>~</code>)</li>
<li><b><a name="pdf-LUA_OPBAND"><code>LUA_OPBAND</code></a>: </b> performs bitwise AND (<code>&</code>)</li>
<li><b><a name="pdf-LUA_OPBOR"><code>LUA_OPBOR</code></a>: </b> performs bitwise OR (<code>|</code>)</li>
<li><b><a name="pdf-LUA_OPBXOR"><code>LUA_OPBXOR</code></a>: </b> performs bitwise exclusive OR (<code>~</code>)</li>
<li><b><a name="pdf-LUA_OPSHL"><code>LUA_OPSHL</code></a>: </b> performs left shift (<code><<</code>)</li>
<li><b><a name="pdf-LUA_OPSHR"><code>LUA_OPSHR</code></a>: </b> performs right shift (<code>>></code>)</li>
</ul>
<hr><h3><a name="lua_atpanic"><code>lua_atpanic</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_CFunction lua_atpanic (lua_State *L, lua_CFunction panicf);</pre>
<p>
Sets a new panic function and returns the old one (see <a href="#4.6">§4.6</a>).
<hr><h3><a name="lua_call"><code>lua_call</code></a></h3><p>
<span class="apii">[-(nargs+1), +nresults, <em>e</em>]</span>
<pre>void lua_call (lua_State *L, int nargs, int nresults);</pre>
<p>
Calls a function.
<p>
To call a function you must use the following protocol:
first, the function to be called is pushed onto the stack;
then, the arguments to the function are pushed
in direct order;
that is, the first argument is pushed first.
Finally you call <a href="#lua_call"><code>lua_call</code></a>;
<code>nargs</code> is the number of arguments that you pushed onto the stack.
All arguments and the function value are popped from the stack
when the function is called.
The function results are pushed onto the stack when the function returns.
The number of results is adjusted to <code>nresults</code>,
unless <code>nresults</code> is <a name="pdf-LUA_MULTRET"><code>LUA_MULTRET</code></a>.
In this case, all results from the function are pushed.
Lua takes care that the returned values fit into the stack space,
but it does not ensure any extra space in the stack.
The function results are pushed onto the stack in direct order
(the first result is pushed first),
so that after the call the last result is on the top of the stack.
<p>
Any error inside the called function is propagated upwards
(with a <code>longjmp</code>).
<p>
The following example shows how the host program can do the
equivalent to this Lua code:
<pre>
a = f("how", t.x, 14)
</pre><p>
Here it is in C:
<pre>
lua_getglobal(L, "f"); /* function to be called */
lua_pushliteral(L, "how"); /* 1st argument */
lua_getglobal(L, "t"); /* table to be indexed */
lua_getfield(L, -1, "x"); /* push result of t.x (2nd arg) */
lua_remove(L, -2); /* remove 't' from the stack */
lua_pushinteger(L, 14); /* 3rd argument */
lua_call(L, 3, 1); /* call 'f' with 3 arguments and 1 result */
lua_setglobal(L, "a"); /* set global 'a' */
</pre><p>
Note that the code above is <em>balanced</em>:
at its end, the stack is back to its original configuration.
This is considered good programming practice.
<hr><h3><a name="lua_callk"><code>lua_callk</code></a></h3><p>
<span class="apii">[-(nargs + 1), +nresults, <em>e</em>]</span>
<pre>void lua_callk (lua_State *L,
int nargs,
int nresults,
lua_KContext ctx,
lua_KFunction k);</pre>
<p>
This function behaves exactly like <a href="#lua_call"><code>lua_call</code></a>,
but allows the called function to yield (see <a href="#4.7">§4.7</a>).
<hr><h3><a name="lua_CFunction"><code>lua_CFunction</code></a></h3>
<pre>typedef int (*lua_CFunction) (lua_State *L);</pre>
<p>
Type for C functions.
<p>
In order to communicate properly with Lua,
a C function must use the following protocol,
which defines the way parameters and results are passed:
a C function receives its arguments from Lua in its stack
in direct order (the first argument is pushed first).
So, when the function starts,
<code>lua_gettop(L)</code> returns the number of arguments received by the function.
The first argument (if any) is at index 1
and its last argument is at index <code>lua_gettop(L)</code>.
To return values to Lua, a C function just pushes them onto the stack,
in direct order (the first result is pushed first),
and returns the number of results.
Any other value in the stack below the results will be properly
discarded by Lua.
Like a Lua function, a C function called by Lua can also return
many results.
<p>
As an example, the following function receives a variable number
of numeric arguments and returns their average and their sum:
<pre>
static int foo (lua_State *L) {
int n = lua_gettop(L); /* number of arguments */
lua_Number sum = 0.0;
int i;
for (i = 1; i <= n; i++) {
if (!lua_isnumber(L, i)) {
lua_pushliteral(L, "incorrect argument");
lua_error(L);
}
sum += lua_tonumber(L, i);
}
lua_pushnumber(L, sum/n); /* first result */
lua_pushnumber(L, sum); /* second result */
return 2; /* number of results */
}
</pre>
<hr><h3><a name="lua_checkstack"><code>lua_checkstack</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_checkstack (lua_State *L, int n);</pre>
<p>
Ensures that the stack has space for at least <code>n</code> extra slots
(that is, that you can safely push up to <code>n</code> values into it).
It returns false if it cannot fulfill the request,
either because it would cause the stack
to be larger than a fixed maximum size
(typically at least several thousand elements) or
because it cannot allocate memory for the extra space.
This function never shrinks the stack;
if the stack already has space for the extra slots,
it is left unchanged.
<hr><h3><a name="lua_close"><code>lua_close</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void lua_close (lua_State *L);</pre>
<p>
Destroys all objects in the given Lua state
(calling the corresponding garbage-collection metamethods, if any)
and frees all dynamic memory used by this state.
On several platforms, you may not need to call this function,
because all resources are naturally released when the host program ends.
On the other hand, long-running programs that create multiple states,
such as daemons or web servers,
will probably need to close states as soon as they are not needed.
<hr><h3><a name="lua_compare"><code>lua_compare</code></a></h3><p>
<span class="apii">[-0, +0, <em>e</em>]</span>
<pre>int lua_compare (lua_State *L, int index1, int index2, int op);</pre>
<p>
Compares two Lua values.
Returns 1 if the value at index <code>index1</code> satisfies <code>op</code>
when compared with the value at index <code>index2</code>,
following the semantics of the corresponding Lua operator
(that is, it may call metamethods).
Otherwise returns 0.
Also returns 0 if any of the indices is not valid.
<p>
The value of <code>op</code> must be one of the following constants:
<ul>
<li><b><a name="pdf-LUA_OPEQ"><code>LUA_OPEQ</code></a>: </b> compares for equality (<code>==</code>)</li>
<li><b><a name="pdf-LUA_OPLT"><code>LUA_OPLT</code></a>: </b> compares for less than (<code><</code>)</li>
<li><b><a name="pdf-LUA_OPLE"><code>LUA_OPLE</code></a>: </b> compares for less or equal (<code><=</code>)</li>
</ul>
<hr><h3><a name="lua_concat"><code>lua_concat</code></a></h3><p>
<span class="apii">[-n, +1, <em>e</em>]</span>
<pre>void lua_concat (lua_State *L, int n);</pre>
<p>
Concatenates the <code>n</code> values at the top of the stack,
pops them, and leaves the result at the top.
If <code>n</code> is 1, the result is the single value on the stack
(that is, the function does nothing);
if <code>n</code> is 0, the result is the empty string.
Concatenation is performed following the usual semantics of Lua
(see <a href="#3.4.6">§3.4.6</a>).
<hr><h3><a name="lua_copy"><code>lua_copy</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void lua_copy (lua_State *L, int fromidx, int toidx);</pre>
<p>
Copies the element at index <code>fromidx</code>
into the valid index <code>toidx</code>,
replacing the value at that position.
Values at other positions are not affected.
<hr><h3><a name="lua_createtable"><code>lua_createtable</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>void lua_createtable (lua_State *L, int narr, int nrec);</pre>
<p>
Creates a new empty table and pushes it onto the stack.
Parameter <code>narr</code> is a hint for how many elements the table
will have as a sequence;
parameter <code>nrec</code> is a hint for how many other elements
the table will have.
Lua may use these hints to preallocate memory for the new table.
This preallocation is useful for performance when you know in advance
how many elements the table will have.
Otherwise you can use the function <a href="#lua_newtable"><code>lua_newtable</code></a>.
<hr><h3><a name="lua_dump"><code>lua_dump</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_dump (lua_State *L,
lua_Writer writer,
void *data,
int strip);</pre>
<p>
Dumps a function as a binary chunk.
Receives a Lua function on the top of the stack
and produces a binary chunk that,
if loaded again,
results in a function equivalent to the one dumped.
As it produces parts of the chunk,
<a href="#lua_dump"><code>lua_dump</code></a> calls function <code>writer</code> (see <a href="#lua_Writer"><code>lua_Writer</code></a>)
with the given <code>data</code>
to write them.
<p>
If <code>strip</code> is true,
the binary representation may not include all debug information
about the function,
to save space.
<p>
The value returned is the error code returned by the last
call to the writer;
0 means no errors.
<p>
This function does not pop the Lua function from the stack.
<hr><h3><a name="lua_error"><code>lua_error</code></a></h3><p>
<span class="apii">[-1, +0, <em>v</em>]</span>
<pre>int lua_error (lua_State *L);</pre>
<p>
Generates a Lua error,
using the value at the top of the stack as the error object.
This function does a long jump,
and therefore never returns
(see <a href="#luaL_error"><code>luaL_error</code></a>).
<hr><h3><a name="lua_gc"><code>lua_gc</code></a></h3><p>
<span class="apii">[-0, +0, <em>m</em>]</span>
<pre>int lua_gc (lua_State *L, int what, int data);</pre>
<p>
Controls the garbage collector.
<p>
This function performs several tasks,
according to the value of the parameter <code>what</code>:
<ul>
<li><b><code>LUA_GCSTOP</code>: </b>
stops the garbage collector.
</li>
<li><b><code>LUA_GCRESTART</code>: </b>
restarts the garbage collector.
</li>
<li><b><code>LUA_GCCOLLECT</code>: </b>
performs a full garbage-collection cycle.
</li>
<li><b><code>LUA_GCCOUNT</code>: </b>
returns the current amount of memory (in Kbytes) in use by Lua.
</li>
<li><b><code>LUA_GCCOUNTB</code>: </b>
returns the remainder of dividing the current amount of bytes of
memory in use by Lua by 1024.
</li>
<li><b><code>LUA_GCSTEP</code>: </b>
performs an incremental step of garbage collection.
</li>
<li><b><code>LUA_GCSETPAUSE</code>: </b>
sets <code>data</code> as the new value
for the <em>pause</em> of the collector (see <a href="#2.5">§2.5</a>)
and returns the previous value of the pause.
</li>
<li><b><code>LUA_GCSETSTEPMUL</code>: </b>
sets <code>data</code> as the new value for the <em>step multiplier</em> of
the collector (see <a href="#2.5">§2.5</a>)
and returns the previous value of the step multiplier.
</li>
<li><b><code>LUA_GCISRUNNING</code>: </b>
returns a boolean that tells whether the collector is running
(i.e., not stopped).
</li>
</ul>
<p>
For more details about these options,
see <a href="#pdf-collectgarbage"><code>collectgarbage</code></a>.
<hr><h3><a name="lua_getallocf"><code>lua_getallocf</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_Alloc lua_getallocf (lua_State *L, void **ud);</pre>
<p>
Returns the memory-allocation function of a given state.
If <code>ud</code> is not <code>NULL</code>, Lua stores in <code>*ud</code> the
opaque pointer given when the memory-allocator function was set.
<hr><h3><a name="lua_getfield"><code>lua_getfield</code></a></h3><p>
<span class="apii">[-0, +1, <em>e</em>]</span>
<pre>int lua_getfield (lua_State *L, int index, const char *k);</pre>
<p>
Pushes onto the stack the value <code>t[k]</code>,
where <code>t</code> is the value at the given index.
As in Lua, this function may trigger a metamethod
for the "index" event (see <a href="#2.4">§2.4</a>).
<p>
Returns the type of the pushed value.
<hr><h3><a name="lua_getextraspace"><code>lua_getextraspace</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void *lua_getextraspace (lua_State *L);</pre>
<p>
Returns a pointer to a raw memory area associated with the
given Lua state.
The application can use this area for any purpose;
Lua does not use it for anything.
<p>
Each new thread has this area initialized with a copy
of the area of the main thread.
<p>
By default, this area has the size of a pointer to void,
but you can recompile Lua with a different size for this area.
(See <code>LUA_EXTRASPACE</code> in <code>luaconf.h</code>.)
<hr><h3><a name="lua_getglobal"><code>lua_getglobal</code></a></h3><p>
<span class="apii">[-0, +1, <em>e</em>]</span>
<pre>int lua_getglobal (lua_State *L, const char *name);</pre>
<p>
Pushes onto the stack the value of the global <code>name</code>.
Returns the type of that value.
<hr><h3><a name="lua_geti"><code>lua_geti</code></a></h3><p>
<span class="apii">[-0, +1, <em>e</em>]</span>
<pre>int lua_geti (lua_State *L, int index, lua_Integer i);</pre>
<p>
Pushes onto the stack the value <code>t[i]</code>,
where <code>t</code> is the value at the given index.
As in Lua, this function may trigger a metamethod
for the "index" event (see <a href="#2.4">§2.4</a>).
<p>
Returns the type of the pushed value.
<hr><h3><a name="lua_getmetatable"><code>lua_getmetatable</code></a></h3><p>
<span class="apii">[-0, +(0|1), –]</span>
<pre>int lua_getmetatable (lua_State *L, int index);</pre>
<p>
If the value at the given index has a metatable,
the function pushes that metatable onto the stack and returns 1.
Otherwise,
the function returns 0 and pushes nothing on the stack.
<hr><h3><a name="lua_gettable"><code>lua_gettable</code></a></h3><p>
<span class="apii">[-1, +1, <em>e</em>]</span>
<pre>int lua_gettable (lua_State *L, int index);</pre>
<p>
Pushes onto the stack the value <code>t[k]</code>,
where <code>t</code> is the value at the given index
and <code>k</code> is the value at the top of the stack.
<p>
This function pops the key from the stack,
pushing the resulting value in its place.
As in Lua, this function may trigger a metamethod
for the "index" event (see <a href="#2.4">§2.4</a>).
<p>
Returns the type of the pushed value.
<hr><h3><a name="lua_gettop"><code>lua_gettop</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_gettop (lua_State *L);</pre>
<p>
Returns the index of the top element in the stack.
Because indices start at 1,
this result is equal to the number of elements in the stack;
in particular, 0 means an empty stack.
<hr><h3><a name="lua_getuservalue"><code>lua_getuservalue</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>int lua_getuservalue (lua_State *L, int index);</pre>
<p>
Pushes onto the stack the Lua value associated with the userdata
at the given index.
<p>
Returns the type of the pushed value.
<hr><h3><a name="lua_insert"><code>lua_insert</code></a></h3><p>
<span class="apii">[-1, +1, –]</span>
<pre>void lua_insert (lua_State *L, int index);</pre>
<p>
Moves the top element into the given valid index,
shifting up the elements above this index to open space.
This function cannot be called with a pseudo-index,
because a pseudo-index is not an actual stack position.
<hr><h3><a name="lua_Integer"><code>lua_Integer</code></a></h3>
<pre>typedef ... lua_Integer;</pre>
<p>
The type of integers in Lua.
<p>
By default this type is <code>long long</code>,
(usually a 64-bit two-complement integer),
but that can be changed to <code>long</code> or <code>int</code>
(usually a 32-bit two-complement integer).
(See <code>LUA_INT_TYPE</code> in <code>luaconf.h</code>.)
<p>
Lua also defines the constants
<a name="pdf-LUA_MININTEGER"><code>LUA_MININTEGER</code></a> and <a name="pdf-LUA_MAXINTEGER"><code>LUA_MAXINTEGER</code></a>,
with the minimum and the maximum values that fit in this type.
<hr><h3><a name="lua_isboolean"><code>lua_isboolean</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isboolean (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a boolean,
and 0 otherwise.
<hr><h3><a name="lua_iscfunction"><code>lua_iscfunction</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_iscfunction (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a C function,
and 0 otherwise.
<hr><h3><a name="lua_isfunction"><code>lua_isfunction</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isfunction (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a function
(either C or Lua), and 0 otherwise.
<hr><h3><a name="lua_isinteger"><code>lua_isinteger</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isinteger (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is an integer
(that is, the value is a number and is represented as an integer),
and 0 otherwise.
<hr><h3><a name="lua_islightuserdata"><code>lua_islightuserdata</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_islightuserdata (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a light userdata,
and 0 otherwise.
<hr><h3><a name="lua_isnil"><code>lua_isnil</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isnil (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is <b>nil</b>,
and 0 otherwise.
<hr><h3><a name="lua_isnone"><code>lua_isnone</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isnone (lua_State *L, int index);</pre>
<p>
Returns 1 if the given index is not valid,
and 0 otherwise.
<hr><h3><a name="lua_isnoneornil"><code>lua_isnoneornil</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isnoneornil (lua_State *L, int index);</pre>
<p>
Returns 1 if the given index is not valid
or if the value at this index is <b>nil</b>,
and 0 otherwise.
<hr><h3><a name="lua_isnumber"><code>lua_isnumber</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isnumber (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a number
or a string convertible to a number,
and 0 otherwise.
<hr><h3><a name="lua_isstring"><code>lua_isstring</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isstring (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a string
or a number (which is always convertible to a string),
and 0 otherwise.
<hr><h3><a name="lua_istable"><code>lua_istable</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_istable (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a table,
and 0 otherwise.
<hr><h3><a name="lua_isthread"><code>lua_isthread</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isthread (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a thread,
and 0 otherwise.
<hr><h3><a name="lua_isuserdata"><code>lua_isuserdata</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isuserdata (lua_State *L, int index);</pre>
<p>
Returns 1 if the value at the given index is a userdata
(either full or light), and 0 otherwise.
<hr><h3><a name="lua_isyieldable"><code>lua_isyieldable</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_isyieldable (lua_State *L);</pre>
<p>
Returns 1 if the given coroutine can yield,
and 0 otherwise.
<hr><h3><a name="lua_KContext"><code>lua_KContext</code></a></h3>
<pre>typedef ... lua_KContext;</pre>
<p>
The type for continuation-function contexts.
It must be a numeric type.
This type is defined as <code>intptr_t</code>
when <code>intptr_t</code> is available,
so that it can store pointers too.
Otherwise, it is defined as <code>ptrdiff_t</code>.
<hr><h3><a name="lua_KFunction"><code>lua_KFunction</code></a></h3>
<pre>typedef int (*lua_KFunction) (lua_State *L, int status, lua_KContext ctx);</pre>
<p>
Type for continuation functions (see <a href="#4.7">§4.7</a>).
<hr><h3><a name="lua_len"><code>lua_len</code></a></h3><p>
<span class="apii">[-0, +1, <em>e</em>]</span>
<pre>void lua_len (lua_State *L, int index);</pre>
<p>
Returns the length of the value at the given index.
It is equivalent to the '<code>#</code>' operator in Lua (see <a href="#3.4.7">§3.4.7</a>) and
may trigger a metamethod for the "length" event (see <a href="#2.4">§2.4</a>).
The result is pushed on the stack.
<hr><h3><a name="lua_load"><code>lua_load</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>int lua_load (lua_State *L,
lua_Reader reader,
void *data,
const char *chunkname,
const char *mode);</pre>
<p>
Loads a Lua chunk without running it.
If there are no errors,
<code>lua_load</code> pushes the compiled chunk as a Lua
function on top of the stack.
Otherwise, it pushes an error message.
<p>
The return values of <code>lua_load</code> are:
<ul>
<li><b><a href="#pdf-LUA_OK"><code>LUA_OK</code></a>: </b> no errors;</li>
<li><b><a name="pdf-LUA_ERRSYNTAX"><code>LUA_ERRSYNTAX</code></a>: </b>
syntax error during precompilation;</li>
<li><b><a href="#pdf-LUA_ERRMEM"><code>LUA_ERRMEM</code></a>: </b>
memory allocation (out-of-memory) error;</li>
<li><b><a href="#pdf-LUA_ERRGCMM"><code>LUA_ERRGCMM</code></a>: </b>
error while running a <code>__gc</code> metamethod.
(This error has no relation with the chunk being loaded.
It is generated by the garbage collector.)
</li>
</ul>
<p>
The <code>lua_load</code> function uses a user-supplied <code>reader</code> function
to read the chunk (see <a href="#lua_Reader"><code>lua_Reader</code></a>).
The <code>data</code> argument is an opaque value passed to the reader function.
<p>
The <code>chunkname</code> argument gives a name to the chunk,
which is used for error messages and in debug information (see <a href="#4.9">§4.9</a>).
<p>
<code>lua_load</code> automatically detects whether the chunk is text or binary
and loads it accordingly (see program <code>luac</code>).
The string <code>mode</code> works as in function <a href="#pdf-load"><code>load</code></a>,
with the addition that
a <code>NULL</code> value is equivalent to the string "<code>bt</code>".
<p>
<code>lua_load</code> uses the stack internally,
so the reader function must always leave the stack
unmodified when returning.
<p>
If the resulting function has upvalues,
its first upvalue is set to the value of the global environment
stored at index <code>LUA_RIDX_GLOBALS</code> in the registry (see <a href="#4.5">§4.5</a>).
When loading main chunks,
this upvalue will be the <code>_ENV</code> variable (see <a href="#2.2">§2.2</a>).
Other upvalues are initialized with <b>nil</b>.
<hr><h3><a name="lua_newstate"><code>lua_newstate</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_State *lua_newstate (lua_Alloc f, void *ud);</pre>
<p>
Creates a new thread running in a new, independent state.
Returns <code>NULL</code> if it cannot create the thread or the state
(due to lack of memory).
The argument <code>f</code> is the allocator function;
Lua does all memory allocation for this state through this function.
The second argument, <code>ud</code>, is an opaque pointer that Lua
passes to the allocator in every call.
<hr><h3><a name="lua_newtable"><code>lua_newtable</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>void lua_newtable (lua_State *L);</pre>
<p>
Creates a new empty table and pushes it onto the stack.
It is equivalent to <code>lua_createtable(L, 0, 0)</code>.
<hr><h3><a name="lua_newthread"><code>lua_newthread</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>lua_State *lua_newthread (lua_State *L);</pre>
<p>
Creates a new thread, pushes it on the stack,
and returns a pointer to a <a href="#lua_State"><code>lua_State</code></a> that represents this new thread.
The new thread returned by this function shares with the original thread
its global environment,
but has an independent execution stack.
<p>
There is no explicit function to close or to destroy a thread.
Threads are subject to garbage collection,
like any Lua object.
<hr><h3><a name="lua_newuserdata"><code>lua_newuserdata</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>void *lua_newuserdata (lua_State *L, size_t size);</pre>
<p>
This function allocates a new block of memory with the given size,
pushes onto the stack a new full userdata with the block address,
and returns this address.
The host program can freely use this memory.
<hr><h3><a name="lua_next"><code>lua_next</code></a></h3><p>
<span class="apii">[-1, +(2|0), <em>e</em>]</span>
<pre>int lua_next (lua_State *L, int index);</pre>
<p>
Pops a key from the stack,
and pushes a key–value pair from the table at the given index
(the "next" pair after the given key).
If there are no more elements in the table,
then <a href="#lua_next"><code>lua_next</code></a> returns 0 (and pushes nothing).
<p>
A typical traversal looks like this:
<pre>
/* table is in the stack at index 't' */
lua_pushnil(L); /* first key */
while (lua_next(L, t) != 0) {
/* uses 'key' (at index -2) and 'value' (at index -1) */
printf("%s - %s\n",
lua_typename(L, lua_type(L, -2)),
lua_typename(L, lua_type(L, -1)));
/* removes 'value'; keeps 'key' for next iteration */
lua_pop(L, 1);
}
</pre>
<p>
While traversing a table,
do not call <a href="#lua_tolstring"><code>lua_tolstring</code></a> directly on a key,
unless you know that the key is actually a string.
Recall that <a href="#lua_tolstring"><code>lua_tolstring</code></a> may change
the value at the given index;
this confuses the next call to <a href="#lua_next"><code>lua_next</code></a>.
<p>
See function <a href="#pdf-next"><code>next</code></a> for the caveats of modifying
the table during its traversal.
<hr><h3><a name="lua_Number"><code>lua_Number</code></a></h3>
<pre>typedef ... lua_Number;</pre>
<p>
The type of floats in Lua.
<p>
By default this type is double,
but that can be changed to a single float or a long double.
(See <code>LUA_FLOAT_TYPE</code> in <code>luaconf.h</code>.)
<hr><h3><a name="lua_numbertointeger"><code>lua_numbertointeger</code></a></h3>
<pre>int lua_numbertointeger (lua_Number n, lua_Integer *p);</pre>
<p>
Converts a Lua float to a Lua integer.
This macro assumes that <code>n</code> has an integral value.
If that value is within the range of Lua integers,
it is converted to an integer and assigned to <code>*p</code>.
The macro results in a boolean indicating whether the
conversion was successful.
(Note that this range test can be tricky to do
correctly without this macro,
due to roundings.)
<p>
This macro may evaluate its arguments more than once.
<hr><h3><a name="lua_pcall"><code>lua_pcall</code></a></h3><p>
<span class="apii">[-(nargs + 1), +(nresults|1), –]</span>
<pre>int lua_pcall (lua_State *L, int nargs, int nresults, int msgh);</pre>
<p>
Calls a function in protected mode.
<p>
Both <code>nargs</code> and <code>nresults</code> have the same meaning as
in <a href="#lua_call"><code>lua_call</code></a>.
If there are no errors during the call,
<a href="#lua_pcall"><code>lua_pcall</code></a> behaves exactly like <a href="#lua_call"><code>lua_call</code></a>.
However, if there is any error,
<a href="#lua_pcall"><code>lua_pcall</code></a> catches it,
pushes a single value on the stack (the error object),
and returns an error code.
Like <a href="#lua_call"><code>lua_call</code></a>,
<a href="#lua_pcall"><code>lua_pcall</code></a> always removes the function
and its arguments from the stack.
<p>
If <code>msgh</code> is 0,
then the error object returned on the stack
is exactly the original error object.
Otherwise, <code>msgh</code> is the stack index of a
<em>message handler</em>.
(This index cannot be a pseudo-index.)
In case of runtime errors,
this function will be called with the error object
and its return value will be the object
returned on the stack by <a href="#lua_pcall"><code>lua_pcall</code></a>.
<p>
Typically, the message handler is used to add more debug
information to the error object, such as a stack traceback.
Such information cannot be gathered after the return of <a href="#lua_pcall"><code>lua_pcall</code></a>,
since by then the stack has unwound.
<p>
The <a href="#lua_pcall"><code>lua_pcall</code></a> function returns one of the following constants
(defined in <code>lua.h</code>):
<ul>
<li><b><a name="pdf-LUA_OK"><code>LUA_OK</code></a> (0): </b>
success.</li>
<li><b><a name="pdf-LUA_ERRRUN"><code>LUA_ERRRUN</code></a>: </b>
a runtime error.
</li>
<li><b><a name="pdf-LUA_ERRMEM"><code>LUA_ERRMEM</code></a>: </b>
memory allocation error.
For such errors, Lua does not call the message handler.
</li>
<li><b><a name="pdf-LUA_ERRERR"><code>LUA_ERRERR</code></a>: </b>
error while running the message handler.
</li>
<li><b><a name="pdf-LUA_ERRGCMM"><code>LUA_ERRGCMM</code></a>: </b>
error while running a <code>__gc</code> metamethod.
(This error typically has no relation with the function being called.)
</li>
</ul>
<hr><h3><a name="lua_pcallk"><code>lua_pcallk</code></a></h3><p>
<span class="apii">[-(nargs + 1), +(nresults|1), –]</span>
<pre>int lua_pcallk (lua_State *L,
int nargs,
int nresults,
int msgh,
lua_KContext ctx,
lua_KFunction k);</pre>
<p>
This function behaves exactly like <a href="#lua_pcall"><code>lua_pcall</code></a>,
but allows the called function to yield (see <a href="#4.7">§4.7</a>).
<hr><h3><a name="lua_pop"><code>lua_pop</code></a></h3><p>
<span class="apii">[-n, +0, –]</span>
<pre>void lua_pop (lua_State *L, int n);</pre>
<p>
Pops <code>n</code> elements from the stack.
<hr><h3><a name="lua_pushboolean"><code>lua_pushboolean</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>void lua_pushboolean (lua_State *L, int b);</pre>
<p>
Pushes a boolean value with value <code>b</code> onto the stack.
<hr><h3><a name="lua_pushcclosure"><code>lua_pushcclosure</code></a></h3><p>
<span class="apii">[-n, +1, <em>m</em>]</span>
<pre>void lua_pushcclosure (lua_State *L, lua_CFunction fn, int n);</pre>
<p>
Pushes a new C closure onto the stack.
<p>
When a C function is created,
it is possible to associate some values with it,
thus creating a C closure (see <a href="#4.4">§4.4</a>);
these values are then accessible to the function whenever it is called.
To associate values with a C function,
first these values must be pushed onto the stack
(when there are multiple values, the first value is pushed first).
Then <a href="#lua_pushcclosure"><code>lua_pushcclosure</code></a>
is called to create and push the C function onto the stack,
with the argument <code>n</code> telling how many values will be
associated with the function.
<a href="#lua_pushcclosure"><code>lua_pushcclosure</code></a> also pops these values from the stack.
<p>
The maximum value for <code>n</code> is 255.
<p>
When <code>n</code> is zero,
this function creates a <em>light C function</em>,
which is just a pointer to the C function.
In that case, it never raises a memory error.
<hr><h3><a name="lua_pushcfunction"><code>lua_pushcfunction</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>void lua_pushcfunction (lua_State *L, lua_CFunction f);</pre>
<p>
Pushes a C function onto the stack.
This function receives a pointer to a C function
and pushes onto the stack a Lua value of type <code>function</code> that,
when called, invokes the corresponding C function.
<p>
Any function to be callable by Lua must
follow the correct protocol to receive its parameters
and return its results (see <a href="#lua_CFunction"><code>lua_CFunction</code></a>).
<hr><h3><a name="lua_pushfstring"><code>lua_pushfstring</code></a></h3><p>
<span class="apii">[-0, +1, <em>e</em>]</span>
<pre>const char *lua_pushfstring (lua_State *L, const char *fmt, ...);</pre>
<p>
Pushes onto the stack a formatted string
and returns a pointer to this string.
It is similar to the ISO C function <code>sprintf</code>,
but has some important differences:
<ul>
<li>
You do not have to allocate space for the result:
the result is a Lua string and Lua takes care of memory allocation
(and deallocation, through garbage collection).
</li>
<li>
The conversion specifiers are quite restricted.
There are no flags, widths, or precisions.
The conversion specifiers can only be
'<code>%%</code>' (inserts the character '<code>%</code>'),
'<code>%s</code>' (inserts a zero-terminated string, with no size restrictions),
'<code>%f</code>' (inserts a <a href="#lua_Number"><code>lua_Number</code></a>),
'<code>%I</code>' (inserts a <a href="#lua_Integer"><code>lua_Integer</code></a>),
'<code>%p</code>' (inserts a pointer as a hexadecimal numeral),
'<code>%d</code>' (inserts an <code>int</code>),
'<code>%c</code>' (inserts an <code>int</code> as a one-byte character), and
'<code>%U</code>' (inserts a <code>long int</code> as a UTF-8 byte sequence).
</li>
</ul>
<p>
Unlike other push functions,
this function checks for the stack space it needs,
including the slot for its result.
<hr><h3><a name="lua_pushglobaltable"><code>lua_pushglobaltable</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>void lua_pushglobaltable (lua_State *L);</pre>
<p>
Pushes the global environment onto the stack.
<hr><h3><a name="lua_pushinteger"><code>lua_pushinteger</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>void lua_pushinteger (lua_State *L, lua_Integer n);</pre>
<p>
Pushes an integer with value <code>n</code> onto the stack.
<hr><h3><a name="lua_pushlightuserdata"><code>lua_pushlightuserdata</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>void lua_pushlightuserdata (lua_State *L, void *p);</pre>
<p>
Pushes a light userdata onto the stack.
<p>
Userdata represent C values in Lua.
A <em>light userdata</em> represents a pointer, a <code>void*</code>.
It is a value (like a number):
you do not create it, it has no individual metatable,
and it is not collected (as it was never created).
A light userdata is equal to "any"
light userdata with the same C address.
<hr><h3><a name="lua_pushliteral"><code>lua_pushliteral</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>const char *lua_pushliteral (lua_State *L, const char *s);</pre>
<p>
This macro is equivalent to <a href="#lua_pushstring"><code>lua_pushstring</code></a>,
but should be used only when <code>s</code> is a literal string.
<hr><h3><a name="lua_pushlstring"><code>lua_pushlstring</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>const char *lua_pushlstring (lua_State *L, const char *s, size_t len);</pre>
<p>
Pushes the string pointed to by <code>s</code> with size <code>len</code>
onto the stack.
Lua makes (or reuses) an internal copy of the given string,
so the memory at <code>s</code> can be freed or reused immediately after
the function returns.
The string can contain any binary data,
including embedded zeros.
<p>
Returns a pointer to the internal copy of the string.
<hr><h3><a name="lua_pushnil"><code>lua_pushnil</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>void lua_pushnil (lua_State *L);</pre>
<p>
Pushes a nil value onto the stack.
<hr><h3><a name="lua_pushnumber"><code>lua_pushnumber</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>void lua_pushnumber (lua_State *L, lua_Number n);</pre>
<p>
Pushes a float with value <code>n</code> onto the stack.
<hr><h3><a name="lua_pushstring"><code>lua_pushstring</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>const char *lua_pushstring (lua_State *L, const char *s);</pre>
<p>
Pushes the zero-terminated string pointed to by <code>s</code>
onto the stack.
Lua makes (or reuses) an internal copy of the given string,
so the memory at <code>s</code> can be freed or reused immediately after
the function returns.
<p>
Returns a pointer to the internal copy of the string.
<p>
If <code>s</code> is <code>NULL</code>, pushes <b>nil</b> and returns <code>NULL</code>.
<hr><h3><a name="lua_pushthread"><code>lua_pushthread</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>int lua_pushthread (lua_State *L);</pre>
<p>
Pushes the thread represented by <code>L</code> onto the stack.
Returns 1 if this thread is the main thread of its state.
<hr><h3><a name="lua_pushvalue"><code>lua_pushvalue</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>void lua_pushvalue (lua_State *L, int index);</pre>
<p>
Pushes a copy of the element at the given index
onto the stack.
<hr><h3><a name="lua_pushvfstring"><code>lua_pushvfstring</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>const char *lua_pushvfstring (lua_State *L,
const char *fmt,
va_list argp);</pre>
<p>
Equivalent to <a href="#lua_pushfstring"><code>lua_pushfstring</code></a>, except that it receives a <code>va_list</code>
instead of a variable number of arguments.
<hr><h3><a name="lua_rawequal"><code>lua_rawequal</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_rawequal (lua_State *L, int index1, int index2);</pre>
<p>
Returns 1 if the two values in indices <code>index1</code> and
<code>index2</code> are primitively equal
(that is, without calling the <code>__eq</code> metamethod).
Otherwise returns 0.
Also returns 0 if any of the indices are not valid.
<hr><h3><a name="lua_rawget"><code>lua_rawget</code></a></h3><p>
<span class="apii">[-1, +1, –]</span>
<pre>int lua_rawget (lua_State *L, int index);</pre>
<p>
Similar to <a href="#lua_gettable"><code>lua_gettable</code></a>, but does a raw access
(i.e., without metamethods).
<hr><h3><a name="lua_rawgeti"><code>lua_rawgeti</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>int lua_rawgeti (lua_State *L, int index, lua_Integer n);</pre>
<p>
Pushes onto the stack the value <code>t[n]</code>,
where <code>t</code> is the table at the given index.
The access is raw,
that is, it does not invoke the <code>__index</code> metamethod.
<p>
Returns the type of the pushed value.
<hr><h3><a name="lua_rawgetp"><code>lua_rawgetp</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>int lua_rawgetp (lua_State *L, int index, const void *p);</pre>
<p>
Pushes onto the stack the value <code>t[k]</code>,
where <code>t</code> is the table at the given index and
<code>k</code> is the pointer <code>p</code> represented as a light userdata.
The access is raw;
that is, it does not invoke the <code>__index</code> metamethod.
<p>
Returns the type of the pushed value.
<hr><h3><a name="lua_rawlen"><code>lua_rawlen</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>size_t lua_rawlen (lua_State *L, int index);</pre>
<p>
Returns the raw "length" of the value at the given index:
for strings, this is the string length;
for tables, this is the result of the length operator ('<code>#</code>')
with no metamethods;
for userdata, this is the size of the block of memory allocated
for the userdata;
for other values, it is 0.
<hr><h3><a name="lua_rawset"><code>lua_rawset</code></a></h3><p>
<span class="apii">[-2, +0, <em>m</em>]</span>
<pre>void lua_rawset (lua_State *L, int index);</pre>
<p>
Similar to <a href="#lua_settable"><code>lua_settable</code></a>, but does a raw assignment
(i.e., without metamethods).
<hr><h3><a name="lua_rawseti"><code>lua_rawseti</code></a></h3><p>
<span class="apii">[-1, +0, <em>m</em>]</span>
<pre>void lua_rawseti (lua_State *L, int index, lua_Integer i);</pre>
<p>
Does the equivalent of <code>t[i] = v</code>,
where <code>t</code> is the table at the given index
and <code>v</code> is the value at the top of the stack.
<p>
This function pops the value from the stack.
The assignment is raw,
that is, it does not invoke the <code>__newindex</code> metamethod.
<hr><h3><a name="lua_rawsetp"><code>lua_rawsetp</code></a></h3><p>
<span class="apii">[-1, +0, <em>m</em>]</span>
<pre>void lua_rawsetp (lua_State *L, int index, const void *p);</pre>
<p>
Does the equivalent of <code>t[p] = v</code>,
where <code>t</code> is the table at the given index,
<code>p</code> is encoded as a light userdata,
and <code>v</code> is the value at the top of the stack.
<p>
This function pops the value from the stack.
The assignment is raw,
that is, it does not invoke <code>__newindex</code> metamethod.
<hr><h3><a name="lua_Reader"><code>lua_Reader</code></a></h3>
<pre>typedef const char * (*lua_Reader) (lua_State *L,
void *data,
size_t *size);</pre>
<p>
The reader function used by <a href="#lua_load"><code>lua_load</code></a>.
Every time it needs another piece of the chunk,
<a href="#lua_load"><code>lua_load</code></a> calls the reader,
passing along its <code>data</code> parameter.
The reader must return a pointer to a block of memory
with a new piece of the chunk
and set <code>size</code> to the block size.
The block must exist until the reader function is called again.
To signal the end of the chunk,
the reader must return <code>NULL</code> or set <code>size</code> to zero.
The reader function may return pieces of any size greater than zero.
<hr><h3><a name="lua_register"><code>lua_register</code></a></h3><p>
<span class="apii">[-0, +0, <em>e</em>]</span>
<pre>void lua_register (lua_State *L, const char *name, lua_CFunction f);</pre>
<p>
Sets the C function <code>f</code> as the new value of global <code>name</code>.
It is defined as a macro:
<pre>
#define lua_register(L,n,f) \
(lua_pushcfunction(L, f), lua_setglobal(L, n))
</pre>
<hr><h3><a name="lua_remove"><code>lua_remove</code></a></h3><p>
<span class="apii">[-1, +0, –]</span>
<pre>void lua_remove (lua_State *L, int index);</pre>
<p>
Removes the element at the given valid index,
shifting down the elements above this index to fill the gap.
This function cannot be called with a pseudo-index,
because a pseudo-index is not an actual stack position.
<hr><h3><a name="lua_replace"><code>lua_replace</code></a></h3><p>
<span class="apii">[-1, +0, –]</span>
<pre>void lua_replace (lua_State *L, int index);</pre>
<p>
Moves the top element into the given valid index
without shifting any element
(therefore replacing the value at that given index),
and then pops the top element.
<hr><h3><a name="lua_resume"><code>lua_resume</code></a></h3><p>
<span class="apii">[-?, +?, –]</span>
<pre>int lua_resume (lua_State *L, lua_State *from, int nargs);</pre>
<p>
Starts and resumes a coroutine in the given thread <code>L</code>.
<p>
To start a coroutine,
you push onto the thread stack the main function plus any arguments;
then you call <a href="#lua_resume"><code>lua_resume</code></a>,
with <code>nargs</code> being the number of arguments.
This call returns when the coroutine suspends or finishes its execution.
When it returns, the stack contains all values passed to <a href="#lua_yield"><code>lua_yield</code></a>,
or all values returned by the body function.
<a href="#lua_resume"><code>lua_resume</code></a> returns
<a href="#pdf-LUA_YIELD"><code>LUA_YIELD</code></a> if the coroutine yields,
<a href="#pdf-LUA_OK"><code>LUA_OK</code></a> if the coroutine finishes its execution
without errors,
or an error code in case of errors (see <a href="#lua_pcall"><code>lua_pcall</code></a>).
<p>
In case of errors,
the stack is not unwound,
so you can use the debug API over it.
The error object is on the top of the stack.
<p>
To resume a coroutine,
you remove any results from the last <a href="#lua_yield"><code>lua_yield</code></a>,
put on its stack only the values to
be passed as results from <code>yield</code>,
and then call <a href="#lua_resume"><code>lua_resume</code></a>.
<p>
The parameter <code>from</code> represents the coroutine that is resuming <code>L</code>.
If there is no such coroutine,
this parameter can be <code>NULL</code>.
<hr><h3><a name="lua_rotate"><code>lua_rotate</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void lua_rotate (lua_State *L, int idx, int n);</pre>
<p>
Rotates the stack elements between the valid index <code>idx</code>
and the top of the stack.
The elements are rotated <code>n</code> positions in the direction of the top,
for a positive <code>n</code>,
or <code>-n</code> positions in the direction of the bottom,
for a negative <code>n</code>.
The absolute value of <code>n</code> must not be greater than the size
of the slice being rotated.
This function cannot be called with a pseudo-index,
because a pseudo-index is not an actual stack position.
<hr><h3><a name="lua_setallocf"><code>lua_setallocf</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void lua_setallocf (lua_State *L, lua_Alloc f, void *ud);</pre>
<p>
Changes the allocator function of a given state to <code>f</code>
with user data <code>ud</code>.
<hr><h3><a name="lua_setfield"><code>lua_setfield</code></a></h3><p>
<span class="apii">[-1, +0, <em>e</em>]</span>
<pre>void lua_setfield (lua_State *L, int index, const char *k);</pre>
<p>
Does the equivalent to <code>t[k] = v</code>,
where <code>t</code> is the value at the given index
and <code>v</code> is the value at the top of the stack.
<p>
This function pops the value from the stack.
As in Lua, this function may trigger a metamethod
for the "newindex" event (see <a href="#2.4">§2.4</a>).
<hr><h3><a name="lua_setglobal"><code>lua_setglobal</code></a></h3><p>
<span class="apii">[-1, +0, <em>e</em>]</span>
<pre>void lua_setglobal (lua_State *L, const char *name);</pre>
<p>
Pops a value from the stack and
sets it as the new value of global <code>name</code>.
<hr><h3><a name="lua_seti"><code>lua_seti</code></a></h3><p>
<span class="apii">[-1, +0, <em>e</em>]</span>
<pre>void lua_seti (lua_State *L, int index, lua_Integer n);</pre>
<p>
Does the equivalent to <code>t[n] = v</code>,
where <code>t</code> is the value at the given index
and <code>v</code> is the value at the top of the stack.
<p>
This function pops the value from the stack.
As in Lua, this function may trigger a metamethod
for the "newindex" event (see <a href="#2.4">§2.4</a>).
<hr><h3><a name="lua_setmetatable"><code>lua_setmetatable</code></a></h3><p>
<span class="apii">[-1, +0, –]</span>
<pre>void lua_setmetatable (lua_State *L, int index);</pre>
<p>
Pops a table from the stack and
sets it as the new metatable for the value at the given index.
<hr><h3><a name="lua_settable"><code>lua_settable</code></a></h3><p>
<span class="apii">[-2, +0, <em>e</em>]</span>
<pre>void lua_settable (lua_State *L, int index);</pre>
<p>
Does the equivalent to <code>t[k] = v</code>,
where <code>t</code> is the value at the given index,
<code>v</code> is the value at the top of the stack,
and <code>k</code> is the value just below the top.
<p>
This function pops both the key and the value from the stack.
As in Lua, this function may trigger a metamethod
for the "newindex" event (see <a href="#2.4">§2.4</a>).
<hr><h3><a name="lua_settop"><code>lua_settop</code></a></h3><p>
<span class="apii">[-?, +?, –]</span>
<pre>void lua_settop (lua_State *L, int index);</pre>
<p>
Accepts any index, or 0,
and sets the stack top to this index.
If the new top is larger than the old one,
then the new elements are filled with <b>nil</b>.
If <code>index</code> is 0, then all stack elements are removed.
<hr><h3><a name="lua_setuservalue"><code>lua_setuservalue</code></a></h3><p>
<span class="apii">[-1, +0, –]</span>
<pre>void lua_setuservalue (lua_State *L, int index);</pre>
<p>
Pops a value from the stack and sets it as
the new value associated to the userdata at the given index.
<hr><h3><a name="lua_State"><code>lua_State</code></a></h3>
<pre>typedef struct lua_State lua_State;</pre>
<p>
An opaque structure that points to a thread and indirectly
(through the thread) to the whole state of a Lua interpreter.
The Lua library is fully reentrant:
it has no global variables.
All information about a state is accessible through this structure.
<p>
A pointer to this structure must be passed as the first argument to
every function in the library, except to <a href="#lua_newstate"><code>lua_newstate</code></a>,
which creates a Lua state from scratch.
<hr><h3><a name="lua_status"><code>lua_status</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_status (lua_State *L);</pre>
<p>
Returns the status of the thread <code>L</code>.
<p>
The status can be 0 (<a href="#pdf-LUA_OK"><code>LUA_OK</code></a>) for a normal thread,
an error code if the thread finished the execution
of a <a href="#lua_resume"><code>lua_resume</code></a> with an error,
or <a name="pdf-LUA_YIELD"><code>LUA_YIELD</code></a> if the thread is suspended.
<p>
You can only call functions in threads with status <a href="#pdf-LUA_OK"><code>LUA_OK</code></a>.
You can resume threads with status <a href="#pdf-LUA_OK"><code>LUA_OK</code></a>
(to start a new coroutine) or <a href="#pdf-LUA_YIELD"><code>LUA_YIELD</code></a>
(to resume a coroutine).
<hr><h3><a name="lua_stringtonumber"><code>lua_stringtonumber</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>size_t lua_stringtonumber (lua_State *L, const char *s);</pre>
<p>
Converts the zero-terminated string <code>s</code> to a number,
pushes that number into the stack,
and returns the total size of the string,
that is, its length plus one.
The conversion can result in an integer or a float,
according to the lexical conventions of Lua (see <a href="#3.1">§3.1</a>).
The string may have leading and trailing spaces and a sign.
If the string is not a valid numeral,
returns 0 and pushes nothing.
(Note that the result can be used as a boolean,
true if the conversion succeeds.)
<hr><h3><a name="lua_toboolean"><code>lua_toboolean</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_toboolean (lua_State *L, int index);</pre>
<p>
Converts the Lua value at the given index to a C boolean
value (0 or 1).
Like all tests in Lua,
<a href="#lua_toboolean"><code>lua_toboolean</code></a> returns true for any Lua value
different from <b>false</b> and <b>nil</b>;
otherwise it returns false.
(If you want to accept only actual boolean values,
use <a href="#lua_isboolean"><code>lua_isboolean</code></a> to test the value's type.)
<hr><h3><a name="lua_tocfunction"><code>lua_tocfunction</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_CFunction lua_tocfunction (lua_State *L, int index);</pre>
<p>
Converts a value at the given index to a C function.
That value must be a C function;
otherwise, returns <code>NULL</code>.
<hr><h3><a name="lua_tointeger"><code>lua_tointeger</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_Integer lua_tointeger (lua_State *L, int index);</pre>
<p>
Equivalent to <a href="#lua_tointegerx"><code>lua_tointegerx</code></a> with <code>isnum</code> equal to <code>NULL</code>.
<hr><h3><a name="lua_tointegerx"><code>lua_tointegerx</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_Integer lua_tointegerx (lua_State *L, int index, int *isnum);</pre>
<p>
Converts the Lua value at the given index
to the signed integral type <a href="#lua_Integer"><code>lua_Integer</code></a>.
The Lua value must be an integer,
or a number or string convertible to an integer (see <a href="#3.4.3">§3.4.3</a>);
otherwise, <code>lua_tointegerx</code> returns 0.
<p>
If <code>isnum</code> is not <code>NULL</code>,
its referent is assigned a boolean value that
indicates whether the operation succeeded.
<hr><h3><a name="lua_tolstring"><code>lua_tolstring</code></a></h3><p>
<span class="apii">[-0, +0, <em>m</em>]</span>
<pre>const char *lua_tolstring (lua_State *L, int index, size_t *len);</pre>
<p>
Converts the Lua value at the given index to a C string.
If <code>len</code> is not <code>NULL</code>,
it sets <code>*len</code> with the string length.
The Lua value must be a string or a number;
otherwise, the function returns <code>NULL</code>.
If the value is a number,
then <code>lua_tolstring</code> also
<em>changes the actual value in the stack to a string</em>.
(This change confuses <a href="#lua_next"><code>lua_next</code></a>
when <code>lua_tolstring</code> is applied to keys during a table traversal.)
<p>
<code>lua_tolstring</code> returns a pointer
to a string inside the Lua state.
This string always has a zero ('<code>\0</code>')
after its last character (as in C),
but can contain other zeros in its body.
<p>
Because Lua has garbage collection,
there is no guarantee that the pointer returned by <code>lua_tolstring</code>
will be valid after the corresponding Lua value is removed from the stack.
<hr><h3><a name="lua_tonumber"><code>lua_tonumber</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_Number lua_tonumber (lua_State *L, int index);</pre>
<p>
Equivalent to <a href="#lua_tonumberx"><code>lua_tonumberx</code></a> with <code>isnum</code> equal to <code>NULL</code>.
<hr><h3><a name="lua_tonumberx"><code>lua_tonumberx</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_Number lua_tonumberx (lua_State *L, int index, int *isnum);</pre>
<p>
Converts the Lua value at the given index
to the C type <a href="#lua_Number"><code>lua_Number</code></a> (see <a href="#lua_Number"><code>lua_Number</code></a>).
The Lua value must be a number or a string convertible to a number
(see <a href="#3.4.3">§3.4.3</a>);
otherwise, <a href="#lua_tonumberx"><code>lua_tonumberx</code></a> returns 0.
<p>
If <code>isnum</code> is not <code>NULL</code>,
its referent is assigned a boolean value that
indicates whether the operation succeeded.
<hr><h3><a name="lua_topointer"><code>lua_topointer</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>const void *lua_topointer (lua_State *L, int index);</pre>
<p>
Converts the value at the given index to a generic
C pointer (<code>void*</code>).
The value can be a userdata, a table, a thread, or a function;
otherwise, <code>lua_topointer</code> returns <code>NULL</code>.
Different objects will give different pointers.
There is no way to convert the pointer back to its original value.
<p>
Typically this function is used only for hashing and debug information.
<hr><h3><a name="lua_tostring"><code>lua_tostring</code></a></h3><p>
<span class="apii">[-0, +0, <em>m</em>]</span>
<pre>const char *lua_tostring (lua_State *L, int index);</pre>
<p>
Equivalent to <a href="#lua_tolstring"><code>lua_tolstring</code></a> with <code>len</code> equal to <code>NULL</code>.
<hr><h3><a name="lua_tothread"><code>lua_tothread</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_State *lua_tothread (lua_State *L, int index);</pre>
<p>
Converts the value at the given index to a Lua thread
(represented as <code>lua_State*</code>).
This value must be a thread;
otherwise, the function returns <code>NULL</code>.
<hr><h3><a name="lua_touserdata"><code>lua_touserdata</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void *lua_touserdata (lua_State *L, int index);</pre>
<p>
If the value at the given index is a full userdata,
returns its block address.
If the value is a light userdata,
returns its pointer.
Otherwise, returns <code>NULL</code>.
<hr><h3><a name="lua_type"><code>lua_type</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_type (lua_State *L, int index);</pre>
<p>
Returns the type of the value in the given valid index,
or <code>LUA_TNONE</code> for a non-valid (but acceptable) index.
The types returned by <a href="#lua_type"><code>lua_type</code></a> are coded by the following constants
defined in <code>lua.h</code>:
<a name="pdf-LUA_TNIL"><code>LUA_TNIL</code></a> (0),
<a name="pdf-LUA_TNUMBER"><code>LUA_TNUMBER</code></a>,
<a name="pdf-LUA_TBOOLEAN"><code>LUA_TBOOLEAN</code></a>,
<a name="pdf-LUA_TSTRING"><code>LUA_TSTRING</code></a>,
<a name="pdf-LUA_TTABLE"><code>LUA_TTABLE</code></a>,
<a name="pdf-LUA_TFUNCTION"><code>LUA_TFUNCTION</code></a>,
<a name="pdf-LUA_TUSERDATA"><code>LUA_TUSERDATA</code></a>,
<a name="pdf-LUA_TTHREAD"><code>LUA_TTHREAD</code></a>,
and
<a name="pdf-LUA_TLIGHTUSERDATA"><code>LUA_TLIGHTUSERDATA</code></a>.
<hr><h3><a name="lua_typename"><code>lua_typename</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>const char *lua_typename (lua_State *L, int tp);</pre>
<p>
Returns the name of the type encoded by the value <code>tp</code>,
which must be one the values returned by <a href="#lua_type"><code>lua_type</code></a>.
<hr><h3><a name="lua_Unsigned"><code>lua_Unsigned</code></a></h3>
<pre>typedef ... lua_Unsigned;</pre>
<p>
The unsigned version of <a href="#lua_Integer"><code>lua_Integer</code></a>.
<hr><h3><a name="lua_upvalueindex"><code>lua_upvalueindex</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_upvalueindex (int i);</pre>
<p>
Returns the pseudo-index that represents the <code>i</code>-th upvalue of
the running function (see <a href="#4.4">§4.4</a>).
<hr><h3><a name="lua_version"><code>lua_version</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>const lua_Number *lua_version (lua_State *L);</pre>
<p>
Returns the address of the version number
(a C static variable)
stored in the Lua core.
When called with a valid <a href="#lua_State"><code>lua_State</code></a>,
returns the address of the version used to create that state.
When called with <code>NULL</code>,
returns the address of the version running the call.
<hr><h3><a name="lua_Writer"><code>lua_Writer</code></a></h3>
<pre>typedef int (*lua_Writer) (lua_State *L,
const void* p,
size_t sz,
void* ud);</pre>
<p>
The type of the writer function used by <a href="#lua_dump"><code>lua_dump</code></a>.
Every time it produces another piece of chunk,
<a href="#lua_dump"><code>lua_dump</code></a> calls the writer,
passing along the buffer to be written (<code>p</code>),
its size (<code>sz</code>),
and the <code>data</code> parameter supplied to <a href="#lua_dump"><code>lua_dump</code></a>.
<p>
The writer returns an error code:
0 means no errors;
any other value means an error and stops <a href="#lua_dump"><code>lua_dump</code></a> from
calling the writer again.
<hr><h3><a name="lua_xmove"><code>lua_xmove</code></a></h3><p>
<span class="apii">[-?, +?, –]</span>
<pre>void lua_xmove (lua_State *from, lua_State *to, int n);</pre>
<p>
Exchange values between different threads of the same state.
<p>
This function pops <code>n</code> values from the stack <code>from</code>,
and pushes them onto the stack <code>to</code>.
<hr><h3><a name="lua_yield"><code>lua_yield</code></a></h3><p>
<span class="apii">[-?, +?, <em>e</em>]</span>
<pre>int lua_yield (lua_State *L, int nresults);</pre>
<p>
This function is equivalent to <a href="#lua_yieldk"><code>lua_yieldk</code></a>,
but it has no continuation (see <a href="#4.7">§4.7</a>).
Therefore, when the thread resumes,
it continues the function that called
the function calling <code>lua_yield</code>.
<hr><h3><a name="lua_yieldk"><code>lua_yieldk</code></a></h3><p>
<span class="apii">[-?, +?, <em>e</em>]</span>
<pre>int lua_yieldk (lua_State *L,
int nresults,
lua_KContext ctx,
lua_KFunction k);</pre>
<p>
Yields a coroutine (thread).
<p>
When a C function calls <a href="#lua_yieldk"><code>lua_yieldk</code></a>,
the running coroutine suspends its execution,
and the call to <a href="#lua_resume"><code>lua_resume</code></a> that started this coroutine returns.
The parameter <code>nresults</code> is the number of values from the stack
that will be passed as results to <a href="#lua_resume"><code>lua_resume</code></a>.
<p>
When the coroutine is resumed again,
Lua calls the given continuation function <code>k</code> to continue
the execution of the C function that yielded (see <a href="#4.7">§4.7</a>).
This continuation function receives the same stack
from the previous function,
with the <code>n</code> results removed and
replaced by the arguments passed to <a href="#lua_resume"><code>lua_resume</code></a>.
Moreover,
the continuation function receives the value <code>ctx</code>
that was passed to <a href="#lua_yieldk"><code>lua_yieldk</code></a>.
<p>
Usually, this function does not return;
when the coroutine eventually resumes,
it continues executing the continuation function.
However, there is one special case,
which is when this function is called
from inside a line or a count hook (see <a href="#4.9">§4.9</a>).
In that case, <code>lua_yieldk</code> should be called with no continuation
(probably in the form of <a href="#lua_yield"><code>lua_yield</code></a>) and no results,
and the hook should return immediately after the call.
Lua will yield and,
when the coroutine resumes again,
it will continue the normal execution
of the (Lua) function that triggered the hook.
<p>
This function can raise an error if it is called from a thread
with a pending C call with no continuation function,
or it is called from a thread that is not running inside a resume
(e.g., the main thread).
<h2>4.9 – <a name="4.9">The Debug Interface</a></h2>
<p>
Lua has no built-in debugging facilities.
Instead, it offers a special interface
by means of functions and <em>hooks</em>.
This interface allows the construction of different
kinds of debuggers, profilers, and other tools
that need "inside information" from the interpreter.
<hr><h3><a name="lua_Debug"><code>lua_Debug</code></a></h3>
<pre>typedef struct lua_Debug {
int event;
const char *name; /* (n) */
const char *namewhat; /* (n) */
const char *what; /* (S) */
const char *source; /* (S) */
int currentline; /* (l) */
int linedefined; /* (S) */
int lastlinedefined; /* (S) */
unsigned char nups; /* (u) number of upvalues */
unsigned char nparams; /* (u) number of parameters */
char isvararg; /* (u) */
char istailcall; /* (t) */
char short_src[LUA_IDSIZE]; /* (S) */
/* private part */
<em>other fields</em>
} lua_Debug;</pre>
<p>
A structure used to carry different pieces of
information about a function or an activation record.
<a href="#lua_getstack"><code>lua_getstack</code></a> fills only the private part
of this structure, for later use.
To fill the other fields of <a href="#lua_Debug"><code>lua_Debug</code></a> with useful information,
call <a href="#lua_getinfo"><code>lua_getinfo</code></a>.
<p>
The fields of <a href="#lua_Debug"><code>lua_Debug</code></a> have the following meaning:
<ul>
<li><b><code>source</code>: </b>
the name of the chunk that created the function.
If <code>source</code> starts with a '<code>@</code>',
it means that the function was defined in a file where
the file name follows the '<code>@</code>'.
If <code>source</code> starts with a '<code>=</code>',
the remainder of its contents describe the source in a user-dependent manner.
Otherwise,
the function was defined in a string where
<code>source</code> is that string.
</li>
<li><b><code>short_src</code>: </b>
a "printable" version of <code>source</code>, to be used in error messages.
</li>
<li><b><code>linedefined</code>: </b>
the line number where the definition of the function starts.
</li>
<li><b><code>lastlinedefined</code>: </b>
the line number where the definition of the function ends.
</li>
<li><b><code>what</code>: </b>
the string <code>"Lua"</code> if the function is a Lua function,
<code>"C"</code> if it is a C function,
<code>"main"</code> if it is the main part of a chunk.
</li>
<li><b><code>currentline</code>: </b>
the current line where the given function is executing.
When no line information is available,
<code>currentline</code> is set to -1.
</li>
<li><b><code>name</code>: </b>
a reasonable name for the given function.
Because functions in Lua are first-class values,
they do not have a fixed name:
some functions can be the value of multiple global variables,
while others can be stored only in a table field.
The <code>lua_getinfo</code> function checks how the function was
called to find a suitable name.
If it cannot find a name,
then <code>name</code> is set to <code>NULL</code>.
</li>
<li><b><code>namewhat</code>: </b>
explains the <code>name</code> field.
The value of <code>namewhat</code> can be
<code>"global"</code>, <code>"local"</code>, <code>"method"</code>,
<code>"field"</code>, <code>"upvalue"</code>, or <code>""</code> (the empty string),
according to how the function was called.
(Lua uses the empty string when no other option seems to apply.)
</li>
<li><b><code>istailcall</code>: </b>
true if this function invocation was called by a tail call.
In this case, the caller of this level is not in the stack.
</li>
<li><b><code>nups</code>: </b>
the number of upvalues of the function.
</li>
<li><b><code>nparams</code>: </b>
the number of fixed parameters of the function
(always 0 for C functions).
</li>
<li><b><code>isvararg</code>: </b>
true if the function is a vararg function
(always true for C functions).
</li>
</ul>
<hr><h3><a name="lua_gethook"><code>lua_gethook</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_Hook lua_gethook (lua_State *L);</pre>
<p>
Returns the current hook function.
<hr><h3><a name="lua_gethookcount"><code>lua_gethookcount</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_gethookcount (lua_State *L);</pre>
<p>
Returns the current hook count.
<hr><h3><a name="lua_gethookmask"><code>lua_gethookmask</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_gethookmask (lua_State *L);</pre>
<p>
Returns the current hook mask.
<hr><h3><a name="lua_getinfo"><code>lua_getinfo</code></a></h3><p>
<span class="apii">[-(0|1), +(0|1|2), <em>e</em>]</span>
<pre>int lua_getinfo (lua_State *L, const char *what, lua_Debug *ar);</pre>
<p>
Gets information about a specific function or function invocation.
<p>
To get information about a function invocation,
the parameter <code>ar</code> must be a valid activation record that was
filled by a previous call to <a href="#lua_getstack"><code>lua_getstack</code></a> or
given as argument to a hook (see <a href="#lua_Hook"><code>lua_Hook</code></a>).
<p>
To get information about a function you push it onto the stack
and start the <code>what</code> string with the character '<code>></code>'.
(In that case,
<code>lua_getinfo</code> pops the function from the top of the stack.)
For instance, to know in which line a function <code>f</code> was defined,
you can write the following code:
<pre>
lua_Debug ar;
lua_getglobal(L, "f"); /* get global 'f' */
lua_getinfo(L, ">S", &ar);
printf("%d\n", ar.linedefined);
</pre>
<p>
Each character in the string <code>what</code>
selects some fields of the structure <code>ar</code> to be filled or
a value to be pushed on the stack:
<ul>
<li><b>'<code>n</code>': </b> fills in the field <code>name</code> and <code>namewhat</code>;
</li>
<li><b>'<code>S</code>': </b>
fills in the fields <code>source</code>, <code>short_src</code>,
<code>linedefined</code>, <code>lastlinedefined</code>, and <code>what</code>;
</li>
<li><b>'<code>l</code>': </b> fills in the field <code>currentline</code>;
</li>
<li><b>'<code>t</code>': </b> fills in the field <code>istailcall</code>;
</li>
<li><b>'<code>u</code>': </b> fills in the fields
<code>nups</code>, <code>nparams</code>, and <code>isvararg</code>;
</li>
<li><b>'<code>f</code>': </b>
pushes onto the stack the function that is
running at the given level;
</li>
<li><b>'<code>L</code>': </b>
pushes onto the stack a table whose indices are the
numbers of the lines that are valid on the function.
(A <em>valid line</em> is a line with some associated code,
that is, a line where you can put a break point.
Non-valid lines include empty lines and comments.)
<p>
If this option is given together with option '<code>f</code>',
its table is pushed after the function.
</li>
</ul>
<p>
This function returns 0 on error
(for instance, an invalid option in <code>what</code>).
<hr><h3><a name="lua_getlocal"><code>lua_getlocal</code></a></h3><p>
<span class="apii">[-0, +(0|1), –]</span>
<pre>const char *lua_getlocal (lua_State *L, const lua_Debug *ar, int n);</pre>
<p>
Gets information about a local variable of
a given activation record or a given function.
<p>
In the first case,
the parameter <code>ar</code> must be a valid activation record that was
filled by a previous call to <a href="#lua_getstack"><code>lua_getstack</code></a> or
given as argument to a hook (see <a href="#lua_Hook"><code>lua_Hook</code></a>).
The index <code>n</code> selects which local variable to inspect;
see <a href="#pdf-debug.getlocal"><code>debug.getlocal</code></a> for details about variable indices
and names.
<p>
<a href="#lua_getlocal"><code>lua_getlocal</code></a> pushes the variable's value onto the stack
and returns its name.
<p>
In the second case, <code>ar</code> must be <code>NULL</code> and the function
to be inspected must be at the top of the stack.
In this case, only parameters of Lua functions are visible
(as there is no information about what variables are active)
and no values are pushed onto the stack.
<p>
Returns <code>NULL</code> (and pushes nothing)
when the index is greater than
the number of active local variables.
<hr><h3><a name="lua_getstack"><code>lua_getstack</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>int lua_getstack (lua_State *L, int level, lua_Debug *ar);</pre>
<p>
Gets information about the interpreter runtime stack.
<p>
This function fills parts of a <a href="#lua_Debug"><code>lua_Debug</code></a> structure with
an identification of the <em>activation record</em>
of the function executing at a given level.
Level 0 is the current running function,
whereas level <em>n+1</em> is the function that has called level <em>n</em>
(except for tail calls, which do not count on the stack).
When there are no errors, <a href="#lua_getstack"><code>lua_getstack</code></a> returns 1;
when called with a level greater than the stack depth,
it returns 0.
<hr><h3><a name="lua_getupvalue"><code>lua_getupvalue</code></a></h3><p>
<span class="apii">[-0, +(0|1), –]</span>
<pre>const char *lua_getupvalue (lua_State *L, int funcindex, int n);</pre>
<p>
Gets information about the <code>n</code>-th upvalue
of the closure at index <code>funcindex</code>.
It pushes the upvalue's value onto the stack
and returns its name.
Returns <code>NULL</code> (and pushes nothing)
when the index <code>n</code> is greater than the number of upvalues.
<p>
For C functions, this function uses the empty string <code>""</code>
as a name for all upvalues.
(For Lua functions,
upvalues are the external local variables that the function uses,
and that are consequently included in its closure.)
<p>
Upvalues have no particular order,
as they are active through the whole function.
They are numbered in an arbitrary order.
<hr><h3><a name="lua_Hook"><code>lua_Hook</code></a></h3>
<pre>typedef void (*lua_Hook) (lua_State *L, lua_Debug *ar);</pre>
<p>
Type for debugging hook functions.
<p>
Whenever a hook is called, its <code>ar</code> argument has its field
<code>event</code> set to the specific event that triggered the hook.
Lua identifies these events with the following constants:
<a name="pdf-LUA_HOOKCALL"><code>LUA_HOOKCALL</code></a>, <a name="pdf-LUA_HOOKRET"><code>LUA_HOOKRET</code></a>,
<a name="pdf-LUA_HOOKTAILCALL"><code>LUA_HOOKTAILCALL</code></a>, <a name="pdf-LUA_HOOKLINE"><code>LUA_HOOKLINE</code></a>,
and <a name="pdf-LUA_HOOKCOUNT"><code>LUA_HOOKCOUNT</code></a>.
Moreover, for line events, the field <code>currentline</code> is also set.
To get the value of any other field in <code>ar</code>,
the hook must call <a href="#lua_getinfo"><code>lua_getinfo</code></a>.
<p>
For call events, <code>event</code> can be <code>LUA_HOOKCALL</code>,
the normal value, or <code>LUA_HOOKTAILCALL</code>, for a tail call;
in this case, there will be no corresponding return event.
<p>
While Lua is running a hook, it disables other calls to hooks.
Therefore, if a hook calls back Lua to execute a function or a chunk,
this execution occurs without any calls to hooks.
<p>
Hook functions cannot have continuations,
that is, they cannot call <a href="#lua_yieldk"><code>lua_yieldk</code></a>,
<a href="#lua_pcallk"><code>lua_pcallk</code></a>, or <a href="#lua_callk"><code>lua_callk</code></a> with a non-null <code>k</code>.
<p>
Hook functions can yield under the following conditions:
Only count and line events can yield;
to yield, a hook function must finish its execution
calling <a href="#lua_yield"><code>lua_yield</code></a> with <code>nresults</code> equal to zero
(that is, with no values).
<hr><h3><a name="lua_sethook"><code>lua_sethook</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void lua_sethook (lua_State *L, lua_Hook f, int mask, int count);</pre>
<p>
Sets the debugging hook function.
<p>
Argument <code>f</code> is the hook function.
<code>mask</code> specifies on which events the hook will be called:
it is formed by a bitwise OR of the constants
<a name="pdf-LUA_MASKCALL"><code>LUA_MASKCALL</code></a>,
<a name="pdf-LUA_MASKRET"><code>LUA_MASKRET</code></a>,
<a name="pdf-LUA_MASKLINE"><code>LUA_MASKLINE</code></a>,
and <a name="pdf-LUA_MASKCOUNT"><code>LUA_MASKCOUNT</code></a>.
The <code>count</code> argument is only meaningful when the mask
includes <code>LUA_MASKCOUNT</code>.
For each event, the hook is called as explained below:
<ul>
<li><b>The call hook: </b> is called when the interpreter calls a function.
The hook is called just after Lua enters the new function,
before the function gets its arguments.
</li>
<li><b>The return hook: </b> is called when the interpreter returns from a function.
The hook is called just before Lua leaves the function.
There is no standard way to access the values
to be returned by the function.
</li>
<li><b>The line hook: </b> is called when the interpreter is about to
start the execution of a new line of code,
or when it jumps back in the code (even to the same line).
(This event only happens while Lua is executing a Lua function.)
</li>
<li><b>The count hook: </b> is called after the interpreter executes every
<code>count</code> instructions.
(This event only happens while Lua is executing a Lua function.)
</li>
</ul>
<p>
A hook is disabled by setting <code>mask</code> to zero.
<hr><h3><a name="lua_setlocal"><code>lua_setlocal</code></a></h3><p>
<span class="apii">[-(0|1), +0, –]</span>
<pre>const char *lua_setlocal (lua_State *L, const lua_Debug *ar, int n);</pre>
<p>
Sets the value of a local variable of a given activation record.
It assigns the value at the top of the stack
to the variable and returns its name.
It also pops the value from the stack.
<p>
Returns <code>NULL</code> (and pops nothing)
when the index is greater than
the number of active local variables.
<p>
Parameters <code>ar</code> and <code>n</code> are as in function <a href="#lua_getlocal"><code>lua_getlocal</code></a>.
<hr><h3><a name="lua_setupvalue"><code>lua_setupvalue</code></a></h3><p>
<span class="apii">[-(0|1), +0, –]</span>
<pre>const char *lua_setupvalue (lua_State *L, int funcindex, int n);</pre>
<p>
Sets the value of a closure's upvalue.
It assigns the value at the top of the stack
to the upvalue and returns its name.
It also pops the value from the stack.
<p>
Returns <code>NULL</code> (and pops nothing)
when the index <code>n</code> is greater than the number of upvalues.
<p>
Parameters <code>funcindex</code> and <code>n</code> are as in function <a href="#lua_getupvalue"><code>lua_getupvalue</code></a>.
<hr><h3><a name="lua_upvalueid"><code>lua_upvalueid</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void *lua_upvalueid (lua_State *L, int funcindex, int n);</pre>
<p>
Returns a unique identifier for the upvalue numbered <code>n</code>
from the closure at index <code>funcindex</code>.
<p>
These unique identifiers allow a program to check whether different
closures share upvalues.
Lua closures that share an upvalue
(that is, that access a same external local variable)
will return identical ids for those upvalue indices.
<p>
Parameters <code>funcindex</code> and <code>n</code> are as in function <a href="#lua_getupvalue"><code>lua_getupvalue</code></a>,
but <code>n</code> cannot be greater than the number of upvalues.
<hr><h3><a name="lua_upvaluejoin"><code>lua_upvaluejoin</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void lua_upvaluejoin (lua_State *L, int funcindex1, int n1,
int funcindex2, int n2);</pre>
<p>
Make the <code>n1</code>-th upvalue of the Lua closure at index <code>funcindex1</code>
refer to the <code>n2</code>-th upvalue of the Lua closure at index <code>funcindex2</code>.
<h1>5 – <a name="5">The Auxiliary Library</a></h1>
<p>
The <em>auxiliary library</em> provides several convenient functions
to interface C with Lua.
While the basic API provides the primitive functions for all
interactions between C and Lua,
the auxiliary library provides higher-level functions for some
common tasks.
<p>
All functions and types from the auxiliary library
are defined in header file <code>lauxlib.h</code> and
have a prefix <code>luaL_</code>.
<p>
All functions in the auxiliary library are built on
top of the basic API,
and so they provide nothing that cannot be done with that API.
Nevertheless, the use of the auxiliary library ensures
more consistency to your code.
<p>
Several functions in the auxiliary library use internally some
extra stack slots.
When a function in the auxiliary library uses less than five slots,
it does not check the stack size;
it simply assumes that there are enough slots.
<p>
Several functions in the auxiliary library are used to
check C function arguments.
Because the error message is formatted for arguments
(e.g., "<code>bad argument #1</code>"),
you should not use these functions for other stack values.
<p>
Functions called <code>luaL_check*</code>
always raise an error if the check is not satisfied.
<h2>5.1 – <a name="5.1">Functions and Types</a></h2>
<p>
Here we list all functions and types from the auxiliary library
in alphabetical order.
<hr><h3><a name="luaL_addchar"><code>luaL_addchar</code></a></h3><p>
<span class="apii">[-?, +?, <em>m</em>]</span>
<pre>void luaL_addchar (luaL_Buffer *B, char c);</pre>
<p>
Adds the byte <code>c</code> to the buffer <code>B</code>
(see <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>).
<hr><h3><a name="luaL_addlstring"><code>luaL_addlstring</code></a></h3><p>
<span class="apii">[-?, +?, <em>m</em>]</span>
<pre>void luaL_addlstring (luaL_Buffer *B, const char *s, size_t l);</pre>
<p>
Adds the string pointed to by <code>s</code> with length <code>l</code> to
the buffer <code>B</code>
(see <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>).
The string can contain embedded zeros.
<hr><h3><a name="luaL_addsize"><code>luaL_addsize</code></a></h3><p>
<span class="apii">[-?, +?, –]</span>
<pre>void luaL_addsize (luaL_Buffer *B, size_t n);</pre>
<p>
Adds to the buffer <code>B</code> (see <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>)
a string of length <code>n</code> previously copied to the
buffer area (see <a href="#luaL_prepbuffer"><code>luaL_prepbuffer</code></a>).
<hr><h3><a name="luaL_addstring"><code>luaL_addstring</code></a></h3><p>
<span class="apii">[-?, +?, <em>m</em>]</span>
<pre>void luaL_addstring (luaL_Buffer *B, const char *s);</pre>
<p>
Adds the zero-terminated string pointed to by <code>s</code>
to the buffer <code>B</code>
(see <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>).
<hr><h3><a name="luaL_addvalue"><code>luaL_addvalue</code></a></h3><p>
<span class="apii">[-1, +?, <em>m</em>]</span>
<pre>void luaL_addvalue (luaL_Buffer *B);</pre>
<p>
Adds the value at the top of the stack
to the buffer <code>B</code>
(see <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>).
Pops the value.
<p>
This is the only function on string buffers that can (and must)
be called with an extra element on the stack,
which is the value to be added to the buffer.
<hr><h3><a name="luaL_argcheck"><code>luaL_argcheck</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>void luaL_argcheck (lua_State *L,
int cond,
int arg,
const char *extramsg);</pre>
<p>
Checks whether <code>cond</code> is true.
If it is not, raises an error with a standard message (see <a href="#luaL_argerror"><code>luaL_argerror</code></a>).
<hr><h3><a name="luaL_argerror"><code>luaL_argerror</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>int luaL_argerror (lua_State *L, int arg, const char *extramsg);</pre>
<p>
Raises an error reporting a problem with argument <code>arg</code>
of the C function that called it,
using a standard message
that includes <code>extramsg</code> as a comment:
<pre>
bad argument #<em>arg</em> to '<em>funcname</em>' (<em>extramsg</em>)
</pre><p>
This function never returns.
<hr><h3><a name="luaL_Buffer"><code>luaL_Buffer</code></a></h3>
<pre>typedef struct luaL_Buffer luaL_Buffer;</pre>
<p>
Type for a <em>string buffer</em>.
<p>
A string buffer allows C code to build Lua strings piecemeal.
Its pattern of use is as follows:
<ul>
<li>First declare a variable <code>b</code> of type <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>.</li>
<li>Then initialize it with a call <code>luaL_buffinit(L, &b)</code>.</li>
<li>
Then add string pieces to the buffer calling any of
the <code>luaL_add*</code> functions.
</li>
<li>
Finish by calling <code>luaL_pushresult(&b)</code>.
This call leaves the final string on the top of the stack.
</li>
</ul>
<p>
If you know beforehand the total size of the resulting string,
you can use the buffer like this:
<ul>
<li>First declare a variable <code>b</code> of type <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>.</li>
<li>Then initialize it and preallocate a space of
size <code>sz</code> with a call <code>luaL_buffinitsize(L, &b, sz)</code>.</li>
<li>Then copy the string into that space.</li>
<li>
Finish by calling <code>luaL_pushresultsize(&b, sz)</code>,
where <code>sz</code> is the total size of the resulting string
copied into that space.
</li>
</ul>
<p>
During its normal operation,
a string buffer uses a variable number of stack slots.
So, while using a buffer, you cannot assume that you know where
the top of the stack is.
You can use the stack between successive calls to buffer operations
as long as that use is balanced;
that is,
when you call a buffer operation,
the stack is at the same level
it was immediately after the previous buffer operation.
(The only exception to this rule is <a href="#luaL_addvalue"><code>luaL_addvalue</code></a>.)
After calling <a href="#luaL_pushresult"><code>luaL_pushresult</code></a> the stack is back to its
level when the buffer was initialized,
plus the final string on its top.
<hr><h3><a name="luaL_buffinit"><code>luaL_buffinit</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void luaL_buffinit (lua_State *L, luaL_Buffer *B);</pre>
<p>
Initializes a buffer <code>B</code>.
This function does not allocate any space;
the buffer must be declared as a variable
(see <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>).
<hr><h3><a name="luaL_buffinitsize"><code>luaL_buffinitsize</code></a></h3><p>
<span class="apii">[-?, +?, <em>m</em>]</span>
<pre>char *luaL_buffinitsize (lua_State *L, luaL_Buffer *B, size_t sz);</pre>
<p>
Equivalent to the sequence
<a href="#luaL_buffinit"><code>luaL_buffinit</code></a>, <a href="#luaL_prepbuffsize"><code>luaL_prepbuffsize</code></a>.
<hr><h3><a name="luaL_callmeta"><code>luaL_callmeta</code></a></h3><p>
<span class="apii">[-0, +(0|1), <em>e</em>]</span>
<pre>int luaL_callmeta (lua_State *L, int obj, const char *e);</pre>
<p>
Calls a metamethod.
<p>
If the object at index <code>obj</code> has a metatable and this
metatable has a field <code>e</code>,
this function calls this field passing the object as its only argument.
In this case this function returns true and pushes onto the
stack the value returned by the call.
If there is no metatable or no metamethod,
this function returns false (without pushing any value on the stack).
<hr><h3><a name="luaL_checkany"><code>luaL_checkany</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>void luaL_checkany (lua_State *L, int arg);</pre>
<p>
Checks whether the function has an argument
of any type (including <b>nil</b>) at position <code>arg</code>.
<hr><h3><a name="luaL_checkinteger"><code>luaL_checkinteger</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>lua_Integer luaL_checkinteger (lua_State *L, int arg);</pre>
<p>
Checks whether the function argument <code>arg</code> is an integer
(or can be converted to an integer)
and returns this integer cast to a <a href="#lua_Integer"><code>lua_Integer</code></a>.
<hr><h3><a name="luaL_checklstring"><code>luaL_checklstring</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>const char *luaL_checklstring (lua_State *L, int arg, size_t *l);</pre>
<p>
Checks whether the function argument <code>arg</code> is a string
and returns this string;
if <code>l</code> is not <code>NULL</code> fills <code>*l</code>
with the string's length.
<p>
This function uses <a href="#lua_tolstring"><code>lua_tolstring</code></a> to get its result,
so all conversions and caveats of that function apply here.
<hr><h3><a name="luaL_checknumber"><code>luaL_checknumber</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>lua_Number luaL_checknumber (lua_State *L, int arg);</pre>
<p>
Checks whether the function argument <code>arg</code> is a number
and returns this number.
<hr><h3><a name="luaL_checkoption"><code>luaL_checkoption</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>int luaL_checkoption (lua_State *L,
int arg,
const char *def,
const char *const lst[]);</pre>
<p>
Checks whether the function argument <code>arg</code> is a string and
searches for this string in the array <code>lst</code>
(which must be NULL-terminated).
Returns the index in the array where the string was found.
Raises an error if the argument is not a string or
if the string cannot be found.
<p>
If <code>def</code> is not <code>NULL</code>,
the function uses <code>def</code> as a default value when
there is no argument <code>arg</code> or when this argument is <b>nil</b>.
<p>
This is a useful function for mapping strings to C enums.
(The usual convention in Lua libraries is
to use strings instead of numbers to select options.)
<hr><h3><a name="luaL_checkstack"><code>luaL_checkstack</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>void luaL_checkstack (lua_State *L, int sz, const char *msg);</pre>
<p>
Grows the stack size to <code>top + sz</code> elements,
raising an error if the stack cannot grow to that size.
<code>msg</code> is an additional text to go into the error message
(or <code>NULL</code> for no additional text).
<hr><h3><a name="luaL_checkstring"><code>luaL_checkstring</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>const char *luaL_checkstring (lua_State *L, int arg);</pre>
<p>
Checks whether the function argument <code>arg</code> is a string
and returns this string.
<p>
This function uses <a href="#lua_tolstring"><code>lua_tolstring</code></a> to get its result,
so all conversions and caveats of that function apply here.
<hr><h3><a name="luaL_checktype"><code>luaL_checktype</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>void luaL_checktype (lua_State *L, int arg, int t);</pre>
<p>
Checks whether the function argument <code>arg</code> has type <code>t</code>.
See <a href="#lua_type"><code>lua_type</code></a> for the encoding of types for <code>t</code>.
<hr><h3><a name="luaL_checkudata"><code>luaL_checkudata</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>void *luaL_checkudata (lua_State *L, int arg, const char *tname);</pre>
<p>
Checks whether the function argument <code>arg</code> is a userdata
of the type <code>tname</code> (see <a href="#luaL_newmetatable"><code>luaL_newmetatable</code></a>) and
returns the userdata address (see <a href="#lua_touserdata"><code>lua_touserdata</code></a>).
<hr><h3><a name="luaL_checkversion"><code>luaL_checkversion</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>void luaL_checkversion (lua_State *L);</pre>
<p>
Checks whether the core running the call,
the core that created the Lua state,
and the code making the call are all using the same version of Lua.
Also checks whether the core running the call
and the core that created the Lua state
are using the same address space.
<hr><h3><a name="luaL_dofile"><code>luaL_dofile</code></a></h3><p>
<span class="apii">[-0, +?, <em>e</em>]</span>
<pre>int luaL_dofile (lua_State *L, const char *filename);</pre>
<p>
Loads and runs the given file.
It is defined as the following macro:
<pre>
(luaL_loadfile(L, filename) || lua_pcall(L, 0, LUA_MULTRET, 0))
</pre><p>
It returns false if there are no errors
or true in case of errors.
<hr><h3><a name="luaL_dostring"><code>luaL_dostring</code></a></h3><p>
<span class="apii">[-0, +?, –]</span>
<pre>int luaL_dostring (lua_State *L, const char *str);</pre>
<p>
Loads and runs the given string.
It is defined as the following macro:
<pre>
(luaL_loadstring(L, str) || lua_pcall(L, 0, LUA_MULTRET, 0))
</pre><p>
It returns false if there are no errors
or true in case of errors.
<hr><h3><a name="luaL_error"><code>luaL_error</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>int luaL_error (lua_State *L, const char *fmt, ...);</pre>
<p>
Raises an error.
The error message format is given by <code>fmt</code>
plus any extra arguments,
following the same rules of <a href="#lua_pushfstring"><code>lua_pushfstring</code></a>.
It also adds at the beginning of the message the file name and
the line number where the error occurred,
if this information is available.
<p>
This function never returns,
but it is an idiom to use it in C functions
as <code>return luaL_error(<em>args</em>)</code>.
<hr><h3><a name="luaL_execresult"><code>luaL_execresult</code></a></h3><p>
<span class="apii">[-0, +3, <em>m</em>]</span>
<pre>int luaL_execresult (lua_State *L, int stat);</pre>
<p>
This function produces the return values for
process-related functions in the standard library
(<a href="#pdf-os.execute"><code>os.execute</code></a> and <a href="#pdf-io.close"><code>io.close</code></a>).
<hr><h3><a name="luaL_fileresult"><code>luaL_fileresult</code></a></h3><p>
<span class="apii">[-0, +(1|3), <em>m</em>]</span>
<pre>int luaL_fileresult (lua_State *L, int stat, const char *fname);</pre>
<p>
This function produces the return values for
file-related functions in the standard library
(<a href="#pdf-io.open"><code>io.open</code></a>, <a href="#pdf-os.rename"><code>os.rename</code></a>, <a href="#pdf-file:seek"><code>file:seek</code></a>, etc.).
<hr><h3><a name="luaL_getmetafield"><code>luaL_getmetafield</code></a></h3><p>
<span class="apii">[-0, +(0|1), <em>m</em>]</span>
<pre>int luaL_getmetafield (lua_State *L, int obj, const char *e);</pre>
<p>
Pushes onto the stack the field <code>e</code> from the metatable
of the object at index <code>obj</code> and returns the type of pushed value.
If the object does not have a metatable,
or if the metatable does not have this field,
pushes nothing and returns <code>LUA_TNIL</code>.
<hr><h3><a name="luaL_getmetatable"><code>luaL_getmetatable</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>int luaL_getmetatable (lua_State *L, const char *tname);</pre>
<p>
Pushes onto the stack the metatable associated with name <code>tname</code>
in the registry (see <a href="#luaL_newmetatable"><code>luaL_newmetatable</code></a>)
(<b>nil</b> if there is no metatable associated with that name).
Returns the type of the pushed value.
<hr><h3><a name="luaL_getsubtable"><code>luaL_getsubtable</code></a></h3><p>
<span class="apii">[-0, +1, <em>e</em>]</span>
<pre>int luaL_getsubtable (lua_State *L, int idx, const char *fname);</pre>
<p>
Ensures that the value <code>t[fname]</code>,
where <code>t</code> is the value at index <code>idx</code>,
is a table,
and pushes that table onto the stack.
Returns true if it finds a previous table there
and false if it creates a new table.
<hr><h3><a name="luaL_gsub"><code>luaL_gsub</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>const char *luaL_gsub (lua_State *L,
const char *s,
const char *p,
const char *r);</pre>
<p>
Creates a copy of string <code>s</code> by replacing
any occurrence of the string <code>p</code>
with the string <code>r</code>.
Pushes the resulting string on the stack and returns it.
<hr><h3><a name="luaL_len"><code>luaL_len</code></a></h3><p>
<span class="apii">[-0, +0, <em>e</em>]</span>
<pre>lua_Integer luaL_len (lua_State *L, int index);</pre>
<p>
Returns the "length" of the value at the given index
as a number;
it is equivalent to the '<code>#</code>' operator in Lua (see <a href="#3.4.7">§3.4.7</a>).
Raises an error if the result of the operation is not an integer.
(This case only can happen through metamethods.)
<hr><h3><a name="luaL_loadbuffer"><code>luaL_loadbuffer</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>int luaL_loadbuffer (lua_State *L,
const char *buff,
size_t sz,
const char *name);</pre>
<p>
Equivalent to <a href="#luaL_loadbufferx"><code>luaL_loadbufferx</code></a> with <code>mode</code> equal to <code>NULL</code>.
<hr><h3><a name="luaL_loadbufferx"><code>luaL_loadbufferx</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>int luaL_loadbufferx (lua_State *L,
const char *buff,
size_t sz,
const char *name,
const char *mode);</pre>
<p>
Loads a buffer as a Lua chunk.
This function uses <a href="#lua_load"><code>lua_load</code></a> to load the chunk in the
buffer pointed to by <code>buff</code> with size <code>sz</code>.
<p>
This function returns the same results as <a href="#lua_load"><code>lua_load</code></a>.
<code>name</code> is the chunk name,
used for debug information and error messages.
The string <code>mode</code> works as in function <a href="#lua_load"><code>lua_load</code></a>.
<hr><h3><a name="luaL_loadfile"><code>luaL_loadfile</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>int luaL_loadfile (lua_State *L, const char *filename);</pre>
<p>
Equivalent to <a href="#luaL_loadfilex"><code>luaL_loadfilex</code></a> with <code>mode</code> equal to <code>NULL</code>.
<hr><h3><a name="luaL_loadfilex"><code>luaL_loadfilex</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>int luaL_loadfilex (lua_State *L, const char *filename,
const char *mode);</pre>
<p>
Loads a file as a Lua chunk.
This function uses <a href="#lua_load"><code>lua_load</code></a> to load the chunk in the file
named <code>filename</code>.
If <code>filename</code> is <code>NULL</code>,
then it loads from the standard input.
The first line in the file is ignored if it starts with a <code>#</code>.
<p>
The string <code>mode</code> works as in function <a href="#lua_load"><code>lua_load</code></a>.
<p>
This function returns the same results as <a href="#lua_load"><code>lua_load</code></a>,
but it has an extra error code <a name="pdf-LUA_ERRFILE"><code>LUA_ERRFILE</code></a>
if it cannot open/read the file or the file has a wrong mode.
<p>
As <a href="#lua_load"><code>lua_load</code></a>, this function only loads the chunk;
it does not run it.
<hr><h3><a name="luaL_loadstring"><code>luaL_loadstring</code></a></h3><p>
<span class="apii">[-0, +1, –]</span>
<pre>int luaL_loadstring (lua_State *L, const char *s);</pre>
<p>
Loads a string as a Lua chunk.
This function uses <a href="#lua_load"><code>lua_load</code></a> to load the chunk in
the zero-terminated string <code>s</code>.
<p>
This function returns the same results as <a href="#lua_load"><code>lua_load</code></a>.
<p>
Also as <a href="#lua_load"><code>lua_load</code></a>, this function only loads the chunk;
it does not run it.
<hr><h3><a name="luaL_newlib"><code>luaL_newlib</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>void luaL_newlib (lua_State *L, const luaL_Reg l[]);</pre>
<p>
Creates a new table and registers there
the functions in list <code>l</code>.
<p>
It is implemented as the following macro:
<pre>
(luaL_newlibtable(L,l), luaL_setfuncs(L,l,0))
</pre><p>
The array <code>l</code> must be the actual array,
not a pointer to it.
<hr><h3><a name="luaL_newlibtable"><code>luaL_newlibtable</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>void luaL_newlibtable (lua_State *L, const luaL_Reg l[]);</pre>
<p>
Creates a new table with a size optimized
to store all entries in the array <code>l</code>
(but does not actually store them).
It is intended to be used in conjunction with <a href="#luaL_setfuncs"><code>luaL_setfuncs</code></a>
(see <a href="#luaL_newlib"><code>luaL_newlib</code></a>).
<p>
It is implemented as a macro.
The array <code>l</code> must be the actual array,
not a pointer to it.
<hr><h3><a name="luaL_newmetatable"><code>luaL_newmetatable</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>int luaL_newmetatable (lua_State *L, const char *tname);</pre>
<p>
If the registry already has the key <code>tname</code>,
returns 0.
Otherwise,
creates a new table to be used as a metatable for userdata,
adds to this new table the pair <code>__name = tname</code>,
adds to the registry the pair <code>[tname] = new table</code>,
and returns 1.
(The entry <code>__name</code> is used by some error-reporting functions.)
<p>
In both cases pushes onto the stack the final value associated
with <code>tname</code> in the registry.
<hr><h3><a name="luaL_newstate"><code>luaL_newstate</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>lua_State *luaL_newstate (void);</pre>
<p>
Creates a new Lua state.
It calls <a href="#lua_newstate"><code>lua_newstate</code></a> with an
allocator based on the standard C <code>realloc</code> function
and then sets a panic function (see <a href="#4.6">§4.6</a>) that prints
an error message to the standard error output in case of fatal
errors.
<p>
Returns the new state,
or <code>NULL</code> if there is a memory allocation error.
<hr><h3><a name="luaL_openlibs"><code>luaL_openlibs</code></a></h3><p>
<span class="apii">[-0, +0, <em>e</em>]</span>
<pre>void luaL_openlibs (lua_State *L);</pre>
<p>
Opens all standard Lua libraries into the given state.
<hr><h3><a name="luaL_opt"><code>luaL_opt</code></a></h3><p>
<span class="apii">[-0, +0, <em>e</em>]</span>
<pre>T luaL_opt (L, func, arg, dflt);</pre>
<p>
This macro is defined as follows:
<pre>
(lua_isnoneornil(L,(arg)) ? (dflt) : func(L,(arg)))
</pre><p>
In words, if the argument <code>arg</code> is nil or absent,
the macro results in the default <code>dflt</code>.
Otherwise, it results in the result of calling <code>func</code>
with the state <code>L</code> and the argument index <code>arg</code> as
parameters.
Note that it evaluates the expression <code>dflt</code> only if needed.
<hr><h3><a name="luaL_optinteger"><code>luaL_optinteger</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>lua_Integer luaL_optinteger (lua_State *L,
int arg,
lua_Integer d);</pre>
<p>
If the function argument <code>arg</code> is an integer
(or convertible to an integer),
returns this integer.
If this argument is absent or is <b>nil</b>,
returns <code>d</code>.
Otherwise, raises an error.
<hr><h3><a name="luaL_optlstring"><code>luaL_optlstring</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>const char *luaL_optlstring (lua_State *L,
int arg,
const char *d,
size_t *l);</pre>
<p>
If the function argument <code>arg</code> is a string,
returns this string.
If this argument is absent or is <b>nil</b>,
returns <code>d</code>.
Otherwise, raises an error.
<p>
If <code>l</code> is not <code>NULL</code>,
fills the position <code>*l</code> with the result's length.
If the result is <code>NULL</code>
(only possible when returning <code>d</code> and <code>d == NULL</code>),
its length is considered zero.
<hr><h3><a name="luaL_optnumber"><code>luaL_optnumber</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>lua_Number luaL_optnumber (lua_State *L, int arg, lua_Number d);</pre>
<p>
If the function argument <code>arg</code> is a number,
returns this number.
If this argument is absent or is <b>nil</b>,
returns <code>d</code>.
Otherwise, raises an error.
<hr><h3><a name="luaL_optstring"><code>luaL_optstring</code></a></h3><p>
<span class="apii">[-0, +0, <em>v</em>]</span>
<pre>const char *luaL_optstring (lua_State *L,
int arg,
const char *d);</pre>
<p>
If the function argument <code>arg</code> is a string,
returns this string.
If this argument is absent or is <b>nil</b>,
returns <code>d</code>.
Otherwise, raises an error.
<hr><h3><a name="luaL_prepbuffer"><code>luaL_prepbuffer</code></a></h3><p>
<span class="apii">[-?, +?, <em>m</em>]</span>
<pre>char *luaL_prepbuffer (luaL_Buffer *B);</pre>
<p>
Equivalent to <a href="#luaL_prepbuffsize"><code>luaL_prepbuffsize</code></a>
with the predefined size <a name="pdf-LUAL_BUFFERSIZE"><code>LUAL_BUFFERSIZE</code></a>.
<hr><h3><a name="luaL_prepbuffsize"><code>luaL_prepbuffsize</code></a></h3><p>
<span class="apii">[-?, +?, <em>m</em>]</span>
<pre>char *luaL_prepbuffsize (luaL_Buffer *B, size_t sz);</pre>
<p>
Returns an address to a space of size <code>sz</code>
where you can copy a string to be added to buffer <code>B</code>
(see <a href="#luaL_Buffer"><code>luaL_Buffer</code></a>).
After copying the string into this space you must call
<a href="#luaL_addsize"><code>luaL_addsize</code></a> with the size of the string to actually add
it to the buffer.
<hr><h3><a name="luaL_pushresult"><code>luaL_pushresult</code></a></h3><p>
<span class="apii">[-?, +1, <em>m</em>]</span>
<pre>void luaL_pushresult (luaL_Buffer *B);</pre>
<p>
Finishes the use of buffer <code>B</code> leaving the final string on
the top of the stack.
<hr><h3><a name="luaL_pushresultsize"><code>luaL_pushresultsize</code></a></h3><p>
<span class="apii">[-?, +1, <em>m</em>]</span>
<pre>void luaL_pushresultsize (luaL_Buffer *B, size_t sz);</pre>
<p>
Equivalent to the sequence <a href="#luaL_addsize"><code>luaL_addsize</code></a>, <a href="#luaL_pushresult"><code>luaL_pushresult</code></a>.
<hr><h3><a name="luaL_ref"><code>luaL_ref</code></a></h3><p>
<span class="apii">[-1, +0, <em>m</em>]</span>
<pre>int luaL_ref (lua_State *L, int t);</pre>
<p>
Creates and returns a <em>reference</em>,
in the table at index <code>t</code>,
for the object at the top of the stack (and pops the object).
<p>
A reference is a unique integer key.
As long as you do not manually add integer keys into table <code>t</code>,
<a href="#luaL_ref"><code>luaL_ref</code></a> ensures the uniqueness of the key it returns.
You can retrieve an object referred by reference <code>r</code>
by calling <code>lua_rawgeti(L, t, r)</code>.
Function <a href="#luaL_unref"><code>luaL_unref</code></a> frees a reference and its associated object.
<p>
If the object at the top of the stack is <b>nil</b>,
<a href="#luaL_ref"><code>luaL_ref</code></a> returns the constant <a name="pdf-LUA_REFNIL"><code>LUA_REFNIL</code></a>.
The constant <a name="pdf-LUA_NOREF"><code>LUA_NOREF</code></a> is guaranteed to be different
from any reference returned by <a href="#luaL_ref"><code>luaL_ref</code></a>.
<hr><h3><a name="luaL_Reg"><code>luaL_Reg</code></a></h3>
<pre>typedef struct luaL_Reg {
const char *name;
lua_CFunction func;
} luaL_Reg;</pre>
<p>
Type for arrays of functions to be registered by
<a href="#luaL_setfuncs"><code>luaL_setfuncs</code></a>.
<code>name</code> is the function name and <code>func</code> is a pointer to
the function.
Any array of <a href="#luaL_Reg"><code>luaL_Reg</code></a> must end with a sentinel entry
in which both <code>name</code> and <code>func</code> are <code>NULL</code>.
<hr><h3><a name="luaL_requiref"><code>luaL_requiref</code></a></h3><p>
<span class="apii">[-0, +1, <em>e</em>]</span>
<pre>void luaL_requiref (lua_State *L, const char *modname,
lua_CFunction openf, int glb);</pre>
<p>
If <code>modname</code> is not already present in <a href="#pdf-package.loaded"><code>package.loaded</code></a>,
calls function <code>openf</code> with string <code>modname</code> as an argument
and sets the call result in <code>package.loaded[modname]</code>,
as if that function has been called through <a href="#pdf-require"><code>require</code></a>.
<p>
If <code>glb</code> is true,
also stores the module into global <code>modname</code>.
<p>
Leaves a copy of the module on the stack.
<hr><h3><a name="luaL_setfuncs"><code>luaL_setfuncs</code></a></h3><p>
<span class="apii">[-nup, +0, <em>m</em>]</span>
<pre>void luaL_setfuncs (lua_State *L, const luaL_Reg *l, int nup);</pre>
<p>
Registers all functions in the array <code>l</code>
(see <a href="#luaL_Reg"><code>luaL_Reg</code></a>) into the table on the top of the stack
(below optional upvalues, see next).
<p>
When <code>nup</code> is not zero,
all functions are created sharing <code>nup</code> upvalues,
which must be previously pushed on the stack
on top of the library table.
These values are popped from the stack after the registration.
<hr><h3><a name="luaL_setmetatable"><code>luaL_setmetatable</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void luaL_setmetatable (lua_State *L, const char *tname);</pre>
<p>
Sets the metatable of the object at the top of the stack
as the metatable associated with name <code>tname</code>
in the registry (see <a href="#luaL_newmetatable"><code>luaL_newmetatable</code></a>).
<hr><h3><a name="luaL_Stream"><code>luaL_Stream</code></a></h3>
<pre>typedef struct luaL_Stream {
FILE *f;
lua_CFunction closef;
} luaL_Stream;</pre>
<p>
The standard representation for file handles,
which is used by the standard I/O library.
<p>
A file handle is implemented as a full userdata,
with a metatable called <code>LUA_FILEHANDLE</code>
(where <code>LUA_FILEHANDLE</code> is a macro with the actual metatable's name).
The metatable is created by the I/O library
(see <a href="#luaL_newmetatable"><code>luaL_newmetatable</code></a>).
<p>
This userdata must start with the structure <code>luaL_Stream</code>;
it can contain other data after this initial structure.
Field <code>f</code> points to the corresponding C stream
(or it can be <code>NULL</code> to indicate an incompletely created handle).
Field <code>closef</code> points to a Lua function
that will be called to close the stream
when the handle is closed or collected;
this function receives the file handle as its sole argument and
must return either <b>true</b> (in case of success)
or <b>nil</b> plus an error message (in case of error).
Once Lua calls this field,
it changes the field value to <code>NULL</code>
to signal that the handle is closed.
<hr><h3><a name="luaL_testudata"><code>luaL_testudata</code></a></h3><p>
<span class="apii">[-0, +0, <em>m</em>]</span>
<pre>void *luaL_testudata (lua_State *L, int arg, const char *tname);</pre>
<p>
This function works like <a href="#luaL_checkudata"><code>luaL_checkudata</code></a>,
except that, when the test fails,
it returns <code>NULL</code> instead of raising an error.
<hr><h3><a name="luaL_tolstring"><code>luaL_tolstring</code></a></h3><p>
<span class="apii">[-0, +1, <em>e</em>]</span>
<pre>const char *luaL_tolstring (lua_State *L, int idx, size_t *len);</pre>
<p>
Converts any Lua value at the given index to a C string
in a reasonable format.
The resulting string is pushed onto the stack and also
returned by the function.
If <code>len</code> is not <code>NULL</code>,
the function also sets <code>*len</code> with the string length.
<p>
If the value has a metatable with a <code>__tostring</code> field,
then <code>luaL_tolstring</code> calls the corresponding metamethod
with the value as argument,
and uses the result of the call as its result.
<hr><h3><a name="luaL_traceback"><code>luaL_traceback</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>void luaL_traceback (lua_State *L, lua_State *L1, const char *msg,
int level);</pre>
<p>
Creates and pushes a traceback of the stack <code>L1</code>.
If <code>msg</code> is not <code>NULL</code> it is appended
at the beginning of the traceback.
The <code>level</code> parameter tells at which level
to start the traceback.
<hr><h3><a name="luaL_typename"><code>luaL_typename</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>const char *luaL_typename (lua_State *L, int index);</pre>
<p>
Returns the name of the type of the value at the given index.
<hr><h3><a name="luaL_unref"><code>luaL_unref</code></a></h3><p>
<span class="apii">[-0, +0, –]</span>
<pre>void luaL_unref (lua_State *L, int t, int ref);</pre>
<p>
Releases reference <code>ref</code> from the table at index <code>t</code>
(see <a href="#luaL_ref"><code>luaL_ref</code></a>).
The entry is removed from the table,
so that the referred object can be collected.
The reference <code>ref</code> is also freed to be used again.
<p>
If <code>ref</code> is <a href="#pdf-LUA_NOREF"><code>LUA_NOREF</code></a> or <a href="#pdf-LUA_REFNIL"><code>LUA_REFNIL</code></a>,
<a href="#luaL_unref"><code>luaL_unref</code></a> does nothing.
<hr><h3><a name="luaL_where"><code>luaL_where</code></a></h3><p>
<span class="apii">[-0, +1, <em>m</em>]</span>
<pre>void luaL_where (lua_State *L, int lvl);</pre>
<p>
Pushes onto the stack a string identifying the current position
of the control at level <code>lvl</code> in the call stack.
Typically this string has the following format:
<pre>
<em>chunkname</em>:<em>currentline</em>:
</pre><p>
Level 0 is the running function,
level 1 is the function that called the running function,
etc.
<p>
This function is used to build a prefix for error messages.
<h1>6 – <a name="6">Standard Libraries</a></h1>
<p>
The standard Lua libraries provide useful functions
that are implemented directly through the C API.
Some of these functions provide essential services to the language
(e.g., <a href="#pdf-type"><code>type</code></a> and <a href="#pdf-getmetatable"><code>getmetatable</code></a>);
others provide access to "outside" services (e.g., I/O);
and others could be implemented in Lua itself,
but are quite useful or have critical performance requirements that
deserve an implementation in C (e.g., <a href="#pdf-table.sort"><code>table.sort</code></a>).
<p>
All libraries are implemented through the official C API
and are provided as separate C modules.
Currently, Lua has the following standard libraries:
<ul>
<li>basic library (<a href="#6.1">§6.1</a>);</li>
<li>coroutine library (<a href="#6.2">§6.2</a>);</li>
<li>package library (<a href="#6.3">§6.3</a>);</li>
<li>string manipulation (<a href="#6.4">§6.4</a>);</li>
<li>basic UTF-8 support (<a href="#6.5">§6.5</a>);</li>
<li>table manipulation (<a href="#6.6">§6.6</a>);</li>
<li>mathematical functions (<a href="#6.7">§6.7</a>) (sin, log, etc.);</li>
<li>input and output (<a href="#6.8">§6.8</a>);</li>
<li>operating system facilities (<a href="#6.9">§6.9</a>);</li>
<li>debug facilities (<a href="#6.10">§6.10</a>).</li>
</ul><p>
Except for the basic and the package libraries,
each library provides all its functions as fields of a global table
or as methods of its objects.
<p>
To have access to these libraries,
the C host program should call the <a href="#luaL_openlibs"><code>luaL_openlibs</code></a> function,
which opens all standard libraries.
Alternatively,
the host program can open them individually by using
<a href="#luaL_requiref"><code>luaL_requiref</code></a> to call
<a name="pdf-luaopen_base"><code>luaopen_base</code></a> (for the basic library),
<a name="pdf-luaopen_package"><code>luaopen_package</code></a> (for the package library),
<a name="pdf-luaopen_coroutine"><code>luaopen_coroutine</code></a> (for the coroutine library),
<a name="pdf-luaopen_string"><code>luaopen_string</code></a> (for the string library),
<a name="pdf-luaopen_utf8"><code>luaopen_utf8</code></a> (for the UTF8 library),
<a name="pdf-luaopen_table"><code>luaopen_table</code></a> (for the table library),
<a name="pdf-luaopen_math"><code>luaopen_math</code></a> (for the mathematical library),
<a name="pdf-luaopen_io"><code>luaopen_io</code></a> (for the I/O library),
<a name="pdf-luaopen_os"><code>luaopen_os</code></a> (for the operating system library),
and <a name="pdf-luaopen_debug"><code>luaopen_debug</code></a> (for the debug library).
These functions are declared in <a name="pdf-lualib.h"><code>lualib.h</code></a>.
<h2>6.1 – <a name="6.1">Basic Functions</a></h2>
<p>
The basic library provides core functions to Lua.
If you do not include this library in your application,
you should check carefully whether you need to provide
implementations for some of its facilities.
<p>
<hr><h3><a name="pdf-assert"><code>assert (v [, message])</code></a></h3>
<p>
Calls <a href="#pdf-error"><code>error</code></a> if
the value of its argument <code>v</code> is false (i.e., <b>nil</b> or <b>false</b>);
otherwise, returns all its arguments.
In case of error,
<code>message</code> is the error object;
when absent, it defaults to "<code>assertion failed!</code>"
<p>
<hr><h3><a name="pdf-collectgarbage"><code>collectgarbage ([opt [, arg]])</code></a></h3>
<p>
This function is a generic interface to the garbage collector.
It performs different functions according to its first argument, <code>opt</code>:
<ul>
<li><b>"<code>collect</code>": </b>
performs a full garbage-collection cycle.
This is the default option.
</li>
<li><b>"<code>stop</code>": </b>
stops automatic execution of the garbage collector.
The collector will run only when explicitly invoked,
until a call to restart it.
</li>
<li><b>"<code>restart</code>": </b>
restarts automatic execution of the garbage collector.
</li>
<li><b>"<code>count</code>": </b>
returns the total memory in use by Lua in Kbytes.
The value has a fractional part,
so that it multiplied by 1024
gives the exact number of bytes in use by Lua
(except for overflows).
</li>
<li><b>"<code>step</code>": </b>
performs a garbage-collection step.
The step "size" is controlled by <code>arg</code>.
With a zero value,
the collector will perform one basic (indivisible) step.
For non-zero values,
the collector will perform as if that amount of memory
(in KBytes) had been allocated by Lua.
Returns <b>true</b> if the step finished a collection cycle.
</li>
<li><b>"<code>setpause</code>": </b>
sets <code>arg</code> as the new value for the <em>pause</em> of
the collector (see <a href="#2.5">§2.5</a>).
Returns the previous value for <em>pause</em>.
</li>
<li><b>"<code>setstepmul</code>": </b>
sets <code>arg</code> as the new value for the <em>step multiplier</em> of
the collector (see <a href="#2.5">§2.5</a>).
Returns the previous value for <em>step</em>.
</li>
<li><b>"<code>isrunning</code>": </b>
returns a boolean that tells whether the collector is running
(i.e., not stopped).
</li>
</ul>
<p>
<hr><h3><a name="pdf-dofile"><code>dofile ([filename])</code></a></h3>
Opens the named file and executes its contents as a Lua chunk.
When called without arguments,
<code>dofile</code> executes the contents of the standard input (<code>stdin</code>).
Returns all values returned by the chunk.
In case of errors, <code>dofile</code> propagates the error
to its caller (that is, <code>dofile</code> does not run in protected mode).
<p>
<hr><h3><a name="pdf-error"><code>error (message [, level])</code></a></h3>
Terminates the last protected function called
and returns <code>message</code> as the error object.
Function <code>error</code> never returns.
<p>
Usually, <code>error</code> adds some information about the error position
at the beginning of the message, if the message is a string.
The <code>level</code> argument specifies how to get the error position.
With level 1 (the default), the error position is where the
<code>error</code> function was called.
Level 2 points the error to where the function
that called <code>error</code> was called; and so on.
Passing a level 0 avoids the addition of error position information
to the message.
<p>
<hr><h3><a name="pdf-_G"><code>_G</code></a></h3>
A global variable (not a function) that
holds the global environment (see <a href="#2.2">§2.2</a>).
Lua itself does not use this variable;
changing its value does not affect any environment,
nor vice versa.
<p>
<hr><h3><a name="pdf-getmetatable"><code>getmetatable (object)</code></a></h3>
<p>
If <code>object</code> does not have a metatable, returns <b>nil</b>.
Otherwise,
if the object's metatable has a <code>__metatable</code> field,
returns the associated value.
Otherwise, returns the metatable of the given object.
<p>
<hr><h3><a name="pdf-ipairs"><code>ipairs (t)</code></a></h3>
<p>
Returns three values (an iterator function, the table <code>t</code>, and 0)
so that the construction
<pre>
for i,v in ipairs(t) do <em>body</em> end
</pre><p>
will iterate over the key–value pairs
(<code>1,t[1]</code>), (<code>2,t[2]</code>), ...,
up to the first nil value.
<p>
<hr><h3><a name="pdf-load"><code>load (chunk [, chunkname [, mode [, env]]])</code></a></h3>
<p>
Loads a chunk.
<p>
If <code>chunk</code> is a string, the chunk is this string.
If <code>chunk</code> is a function,
<code>load</code> calls it repeatedly to get the chunk pieces.
Each call to <code>chunk</code> must return a string that concatenates
with previous results.
A return of an empty string, <b>nil</b>, or no value signals the end of the chunk.
<p>
If there are no syntactic errors,
returns the compiled chunk as a function;
otherwise, returns <b>nil</b> plus the error message.
<p>
If the resulting function has upvalues,
the first upvalue is set to the value of <code>env</code>,
if that parameter is given,
or to the value of the global environment.
Other upvalues are initialized with <b>nil</b>.
(When you load a main chunk,
the resulting function will always have exactly one upvalue,
the <code>_ENV</code> variable (see <a href="#2.2">§2.2</a>).
However,
when you load a binary chunk created from a function (see <a href="#pdf-string.dump"><code>string.dump</code></a>),
the resulting function can have an arbitrary number of upvalues.)
All upvalues are fresh, that is,
they are not shared with any other function.
<p>
<code>chunkname</code> is used as the name of the chunk for error messages
and debug information (see <a href="#4.9">§4.9</a>).
When absent,
it defaults to <code>chunk</code>, if <code>chunk</code> is a string,
or to "<code>=(load)</code>" otherwise.
<p>
The string <code>mode</code> controls whether the chunk can be text or binary
(that is, a precompiled chunk).
It may be the string "<code>b</code>" (only binary chunks),
"<code>t</code>" (only text chunks),
or "<code>bt</code>" (both binary and text).
The default is "<code>bt</code>".
<p>
Lua does not check the consistency of binary chunks.
Maliciously crafted binary chunks can crash
the interpreter.
<p>
<hr><h3><a name="pdf-loadfile"><code>loadfile ([filename [, mode [, env]]])</code></a></h3>
<p>
Similar to <a href="#pdf-load"><code>load</code></a>,
but gets the chunk from file <code>filename</code>
or from the standard input,
if no file name is given.
<p>
<hr><h3><a name="pdf-next"><code>next (table [, index])</code></a></h3>
<p>
Allows a program to traverse all fields of a table.
Its first argument is a table and its second argument
is an index in this table.
<code>next</code> returns the next index of the table
and its associated value.
When called with <b>nil</b> as its second argument,
<code>next</code> returns an initial index
and its associated value.
When called with the last index,
or with <b>nil</b> in an empty table,
<code>next</code> returns <b>nil</b>.
If the second argument is absent, then it is interpreted as <b>nil</b>.
In particular,
you can use <code>next(t)</code> to check whether a table is empty.
<p>
The order in which the indices are enumerated is not specified,
<em>even for numeric indices</em>.
(To traverse a table in numerical order,
use a numerical <b>for</b>.)
<p>
The behavior of <code>next</code> is undefined if,
during the traversal,
you assign any value to a non-existent field in the table.
You may however modify existing fields.
In particular, you may clear existing fields.
<p>
<hr><h3><a name="pdf-pairs"><code>pairs (t)</code></a></h3>
<p>
If <code>t</code> has a metamethod <code>__pairs</code>,
calls it with <code>t</code> as argument and returns the first three
results from the call.
<p>
Otherwise,
returns three values: the <a href="#pdf-next"><code>next</code></a> function, the table <code>t</code>, and <b>nil</b>,
so that the construction
<pre>
for k,v in pairs(t) do <em>body</em> end
</pre><p>
will iterate over all key–value pairs of table <code>t</code>.
<p>
See function <a href="#pdf-next"><code>next</code></a> for the caveats of modifying
the table during its traversal.
<p>
<hr><h3><a name="pdf-pcall"><code>pcall (f [, arg1, ···])</code></a></h3>
<p>
Calls function <code>f</code> with
the given arguments in <em>protected mode</em>.
This means that any error inside <code>f</code> is not propagated;
instead, <code>pcall</code> catches the error
and returns a status code.
Its first result is the status code (a boolean),
which is true if the call succeeds without errors.
In such case, <code>pcall</code> also returns all results from the call,
after this first result.
In case of any error, <code>pcall</code> returns <b>false</b> plus the error message.
<p>
<hr><h3><a name="pdf-print"><code>print (···)</code></a></h3>
Receives any number of arguments
and prints their values to <code>stdout</code>,
using the <a href="#pdf-tostring"><code>tostring</code></a> function to convert each argument to a string.
<code>print</code> is not intended for formatted output,
but only as a quick way to show a value,
for instance for debugging.
For complete control over the output,
use <a href="#pdf-string.format"><code>string.format</code></a> and <a href="#pdf-io.write"><code>io.write</code></a>.
<p>
<hr><h3><a name="pdf-rawequal"><code>rawequal (v1, v2)</code></a></h3>
Checks whether <code>v1</code> is equal to <code>v2</code>,
without invoking the <code>__eq</code> metamethod.
Returns a boolean.
<p>
<hr><h3><a name="pdf-rawget"><code>rawget (table, index)</code></a></h3>
Gets the real value of <code>table[index]</code>,
without invoking the <code>__index</code> metamethod.
<code>table</code> must be a table;
<code>index</code> may be any value.
<p>
<hr><h3><a name="pdf-rawlen"><code>rawlen (v)</code></a></h3>
Returns the length of the object <code>v</code>,
which must be a table or a string,
without invoking the <code>__len</code> metamethod.
Returns an integer.
<p>
<hr><h3><a name="pdf-rawset"><code>rawset (table, index, value)</code></a></h3>
Sets the real value of <code>table[index]</code> to <code>value</code>,
without invoking the <code>__newindex</code> metamethod.
<code>table</code> must be a table,
<code>index</code> any value different from <b>nil</b> and NaN,
and <code>value</code> any Lua value.
<p>
This function returns <code>table</code>.
<p>
<hr><h3><a name="pdf-select"><code>select (index, ···)</code></a></h3>
<p>
If <code>index</code> is a number,
returns all arguments after argument number <code>index</code>;
a negative number indexes from the end (-1 is the last argument).
Otherwise, <code>index</code> must be the string <code>"#"</code>,
and <code>select</code> returns the total number of extra arguments it received.
<p>
<hr><h3><a name="pdf-setmetatable"><code>setmetatable (table, metatable)</code></a></h3>
<p>
Sets the metatable for the given table.
(To change the metatable of other types from Lua code,
you must use the debug library (<a href="#6.10">§6.10</a>).)
If <code>metatable</code> is <b>nil</b>,
removes the metatable of the given table.
If the original metatable has a <code>__metatable</code> field,
raises an error.
<p>
This function returns <code>table</code>.
<p>
<hr><h3><a name="pdf-tonumber"><code>tonumber (e [, base])</code></a></h3>
<p>
When called with no <code>base</code>,
<code>tonumber</code> tries to convert its argument to a number.
If the argument is already a number or
a string convertible to a number,
then <code>tonumber</code> returns this number;
otherwise, it returns <b>nil</b>.
<p>
The conversion of strings can result in integers or floats,
according to the lexical conventions of Lua (see <a href="#3.1">§3.1</a>).
(The string may have leading and trailing spaces and a sign.)
<p>
When called with <code>base</code>,
then <code>e</code> must be a string to be interpreted as
an integer numeral in that base.
The base may be any integer between 2 and 36, inclusive.
In bases above 10, the letter '<code>A</code>' (in either upper or lower case)
represents 10, '<code>B</code>' represents 11, and so forth,
with '<code>Z</code>' representing 35.
If the string <code>e</code> is not a valid numeral in the given base,
the function returns <b>nil</b>.
<p>
<hr><h3><a name="pdf-tostring"><code>tostring (v)</code></a></h3>
Receives a value of any type and
converts it to a string in a human-readable format.
(For complete control of how numbers are converted,
use <a href="#pdf-string.format"><code>string.format</code></a>.)
<p>
If the metatable of <code>v</code> has a <code>__tostring</code> field,
then <code>tostring</code> calls the corresponding value
with <code>v</code> as argument,
and uses the result of the call as its result.
<p>
<hr><h3><a name="pdf-type"><code>type (v)</code></a></h3>
Returns the type of its only argument, coded as a string.
The possible results of this function are
"<code>nil</code>" (a string, not the value <b>nil</b>),
"<code>number</code>",
"<code>string</code>",
"<code>boolean</code>",
"<code>table</code>",
"<code>function</code>",
"<code>thread</code>",
and "<code>userdata</code>".
<p>
<hr><h3><a name="pdf-_VERSION"><code>_VERSION</code></a></h3>
<p>
A global variable (not a function) that
holds a string containing the running Lua version.
The current value of this variable is "<code>Lua 5.3</code>".
<p>
<hr><h3><a name="pdf-xpcall"><code>xpcall (f, msgh [, arg1, ···])</code></a></h3>
<p>
This function is similar to <a href="#pdf-pcall"><code>pcall</code></a>,
except that it sets a new message handler <code>msgh</code>.
<h2>6.2 – <a name="6.2">Coroutine Manipulation</a></h2>
<p>
This library comprises the operations to manipulate coroutines,
which come inside the table <a name="pdf-coroutine"><code>coroutine</code></a>.
See <a href="#2.6">§2.6</a> for a general description of coroutines.
<p>
<hr><h3><a name="pdf-coroutine.create"><code>coroutine.create (f)</code></a></h3>
<p>
Creates a new coroutine, with body <code>f</code>.
<code>f</code> must be a function.
Returns this new coroutine,
an object with type <code>"thread"</code>.
<p>
<hr><h3><a name="pdf-coroutine.isyieldable"><code>coroutine.isyieldable ()</code></a></h3>
<p>
Returns true when the running coroutine can yield.
<p>
A running coroutine is yieldable if it is not the main thread and
it is not inside a non-yieldable C function.
<p>
<hr><h3><a name="pdf-coroutine.resume"><code>coroutine.resume (co [, val1, ···])</code></a></h3>
<p>
Starts or continues the execution of coroutine <code>co</code>.
The first time you resume a coroutine,
it starts running its body.
The values <code>val1</code>, ... are passed
as the arguments to the body function.
If the coroutine has yielded,
<code>resume</code> restarts it;
the values <code>val1</code>, ... are passed
as the results from the yield.
<p>
If the coroutine runs without any errors,
<code>resume</code> returns <b>true</b> plus any values passed to <code>yield</code>
(when the coroutine yields) or any values returned by the body function
(when the coroutine terminates).
If there is any error,
<code>resume</code> returns <b>false</b> plus the error message.
<p>
<hr><h3><a name="pdf-coroutine.running"><code>coroutine.running ()</code></a></h3>
<p>
Returns the running coroutine plus a boolean,
true when the running coroutine is the main one.
<p>
<hr><h3><a name="pdf-coroutine.status"><code>coroutine.status (co)</code></a></h3>
<p>
Returns the status of coroutine <code>co</code>, as a string:
<code>"running"</code>,
if the coroutine is running (that is, it called <code>status</code>);
<code>"suspended"</code>, if the coroutine is suspended in a call to <code>yield</code>,
or if it has not started running yet;
<code>"normal"</code> if the coroutine is active but not running
(that is, it has resumed another coroutine);
and <code>"dead"</code> if the coroutine has finished its body function,
or if it has stopped with an error.
<p>
<hr><h3><a name="pdf-coroutine.wrap"><code>coroutine.wrap (f)</code></a></h3>
<p>
Creates a new coroutine, with body <code>f</code>.
<code>f</code> must be a function.
Returns a function that resumes the coroutine each time it is called.
Any arguments passed to the function behave as the
extra arguments to <code>resume</code>.
Returns the same values returned by <code>resume</code>,
except the first boolean.
In case of error, propagates the error.
<p>
<hr><h3><a name="pdf-coroutine.yield"><code>coroutine.yield (···)</code></a></h3>
<p>
Suspends the execution of the calling coroutine.
Any arguments to <code>yield</code> are passed as extra results to <code>resume</code>.
<h2>6.3 – <a name="6.3">Modules</a></h2>
<p>
The package library provides basic
facilities for loading modules in Lua.
It exports one function directly in the global environment:
<a href="#pdf-require"><code>require</code></a>.
Everything else is exported in a table <a name="pdf-package"><code>package</code></a>.
<p>
<hr><h3><a name="pdf-require"><code>require (modname)</code></a></h3>
<p>
Loads the given module.
The function starts by looking into the <a href="#pdf-package.loaded"><code>package.loaded</code></a> table
to determine whether <code>modname</code> is already loaded.
If it is, then <code>require</code> returns the value stored
at <code>package.loaded[modname]</code>.
Otherwise, it tries to find a <em>loader</em> for the module.
<p>
To find a loader,
<code>require</code> is guided by the <a href="#pdf-package.searchers"><code>package.searchers</code></a> sequence.
By changing this sequence,
we can change how <code>require</code> looks for a module.
The following explanation is based on the default configuration
for <a href="#pdf-package.searchers"><code>package.searchers</code></a>.
<p>
First <code>require</code> queries <code>package.preload[modname]</code>.
If it has a value,
this value (which must be a function) is the loader.
Otherwise <code>require</code> searches for a Lua loader using the
path stored in <a href="#pdf-package.path"><code>package.path</code></a>.
If that also fails, it searches for a C loader using the
path stored in <a href="#pdf-package.cpath"><code>package.cpath</code></a>.
If that also fails,
it tries an <em>all-in-one</em> loader (see <a href="#pdf-package.searchers"><code>package.searchers</code></a>).
<p>
Once a loader is found,
<code>require</code> calls the loader with two arguments:
<code>modname</code> and an extra value dependent on how it got the loader.
(If the loader came from a file,
this extra value is the file name.)
If the loader returns any non-nil value,
<code>require</code> assigns the returned value to <code>package.loaded[modname]</code>.
If the loader does not return a non-nil value and
has not assigned any value to <code>package.loaded[modname]</code>,
then <code>require</code> assigns <b>true</b> to this entry.
In any case, <code>require</code> returns the
final value of <code>package.loaded[modname]</code>.
<p>
If there is any error loading or running the module,
or if it cannot find any loader for the module,
then <code>require</code> raises an error.
<p>
<hr><h3><a name="pdf-package.config"><code>package.config</code></a></h3>
<p>
A string describing some compile-time configurations for packages.
This string is a sequence of lines:
<ul>
<li>The first line is the directory separator string.
Default is '<code>\</code>' for Windows and '<code>/</code>' for all other systems.</li>
<li>The second line is the character that separates templates in a path.
Default is '<code>;</code>'.</li>
<li>The third line is the string that marks the
substitution points in a template.
Default is '<code>?</code>'.</li>
<li>The fourth line is a string that, in a path in Windows,
is replaced by the executable's directory.
Default is '<code>!</code>'.</li>
<li>The fifth line is a mark to ignore all text after it
when building the <code>luaopen_</code> function name.
Default is '<code>-</code>'.</li>
</ul>
<p>
<hr><h3><a name="pdf-package.cpath"><code>package.cpath</code></a></h3>
<p>
The path used by <a href="#pdf-require"><code>require</code></a> to search for a C loader.
<p>
Lua initializes the C path <a href="#pdf-package.cpath"><code>package.cpath</code></a> in the same way
it initializes the Lua path <a href="#pdf-package.path"><code>package.path</code></a>,
using the environment variable <a name="pdf-LUA_CPATH_5_3"><code>LUA_CPATH_5_3</code></a>
or the environment variable <a name="pdf-LUA_CPATH"><code>LUA_CPATH</code></a>
or a default path defined in <code>luaconf.h</code>.
<p>
<hr><h3><a name="pdf-package.loaded"><code>package.loaded</code></a></h3>
<p>
A table used by <a href="#pdf-require"><code>require</code></a> to control which
modules are already loaded.
When you require a module <code>modname</code> and
<code>package.loaded[modname]</code> is not false,
<a href="#pdf-require"><code>require</code></a> simply returns the value stored there.
<p>
This variable is only a reference to the real table;
assignments to this variable do not change the
table used by <a href="#pdf-require"><code>require</code></a>.
<p>
<hr><h3><a name="pdf-package.loadlib"><code>package.loadlib (libname, funcname)</code></a></h3>
<p>
Dynamically links the host program with the C library <code>libname</code>.
<p>
If <code>funcname</code> is "<code>*</code>",
then it only links with the library,
making the symbols exported by the library
available to other dynamically linked libraries.
Otherwise,
it looks for a function <code>funcname</code> inside the library
and returns this function as a C function.
So, <code>funcname</code> must follow the <a href="#lua_CFunction"><code>lua_CFunction</code></a> prototype
(see <a href="#lua_CFunction"><code>lua_CFunction</code></a>).
<p>
This is a low-level function.
It completely bypasses the package and module system.
Unlike <a href="#pdf-require"><code>require</code></a>,
it does not perform any path searching and
does not automatically adds extensions.
<code>libname</code> must be the complete file name of the C library,
including if necessary a path and an extension.
<code>funcname</code> must be the exact name exported by the C library
(which may depend on the C compiler and linker used).
<p>
This function is not supported by Standard C.
As such, it is only available on some platforms
(Windows, Linux, Mac OS X, Solaris, BSD,
plus other Unix systems that support the <code>dlfcn</code> standard).
<p>
<hr><h3><a name="pdf-package.path"><code>package.path</code></a></h3>
<p>
The path used by <a href="#pdf-require"><code>require</code></a> to search for a Lua loader.
<p>
At start-up, Lua initializes this variable with
the value of the environment variable <a name="pdf-LUA_PATH_5_3"><code>LUA_PATH_5_3</code></a> or
the environment variable <a name="pdf-LUA_PATH"><code>LUA_PATH</code></a> or
with a default path defined in <code>luaconf.h</code>,
if those environment variables are not defined.
Any "<code>;;</code>" in the value of the environment variable
is replaced by the default path.
<p>
<hr><h3><a name="pdf-package.preload"><code>package.preload</code></a></h3>
<p>
A table to store loaders for specific modules
(see <a href="#pdf-require"><code>require</code></a>).
<p>
This variable is only a reference to the real table;
assignments to this variable do not change the
table used by <a href="#pdf-require"><code>require</code></a>.
<p>
<hr><h3><a name="pdf-package.searchers"><code>package.searchers</code></a></h3>
<p>
A table used by <a href="#pdf-require"><code>require</code></a> to control how to load modules.
<p>
Each entry in this table is a <em>searcher function</em>.
When looking for a module,
<a href="#pdf-require"><code>require</code></a> calls each of these searchers in ascending order,
with the module name (the argument given to <a href="#pdf-require"><code>require</code></a>) as its
sole parameter.
The function can return another function (the module <em>loader</em>)
plus an extra value that will be passed to that loader,
or a string explaining why it did not find that module
(or <b>nil</b> if it has nothing to say).
<p>
Lua initializes this table with four searcher functions.
<p>
The first searcher simply looks for a loader in the
<a href="#pdf-package.preload"><code>package.preload</code></a> table.
<p>
The second searcher looks for a loader as a Lua library,
using the path stored at <a href="#pdf-package.path"><code>package.path</code></a>.
The search is done as described in function <a href="#pdf-package.searchpath"><code>package.searchpath</code></a>.
<p>
The third searcher looks for a loader as a C library,
using the path given by the variable <a href="#pdf-package.cpath"><code>package.cpath</code></a>.
Again,
the search is done as described in function <a href="#pdf-package.searchpath"><code>package.searchpath</code></a>.
For instance,
if the C path is the string
<pre>
"./?.so;./?.dll;/usr/local/?/init.so"
</pre><p>
the searcher for module <code>foo</code>
will try to open the files <code>./foo.so</code>, <code>./foo.dll</code>,
and <code>/usr/local/foo/init.so</code>, in that order.
Once it finds a C library,
this searcher first uses a dynamic link facility to link the
application with the library.
Then it tries to find a C function inside the library to
be used as the loader.
The name of this C function is the string "<code>luaopen_</code>"
concatenated with a copy of the module name where each dot
is replaced by an underscore.
Moreover, if the module name has a hyphen,
its suffix after (and including) the first hyphen is removed.
For instance, if the module name is <code>a.b.c-v2.1</code>,
the function name will be <code>luaopen_a_b_c</code>.
<p>
The fourth searcher tries an <em>all-in-one loader</em>.
It searches the C path for a library for
the root name of the given module.
For instance, when requiring <code>a.b.c</code>,
it will search for a C library for <code>a</code>.
If found, it looks into it for an open function for
the submodule;
in our example, that would be <code>luaopen_a_b_c</code>.
With this facility, a package can pack several C submodules
into one single library,
with each submodule keeping its original open function.
<p>
All searchers except the first one (preload) return as the extra value
the file name where the module was found,
as returned by <a href="#pdf-package.searchpath"><code>package.searchpath</code></a>.
The first searcher returns no extra value.
<p>
<hr><h3><a name="pdf-package.searchpath"><code>package.searchpath (name, path [, sep [, rep]])</code></a></h3>
<p>
Searches for the given <code>name</code> in the given <code>path</code>.
<p>
A path is a string containing a sequence of
<em>templates</em> separated by semicolons.
For each template,
the function replaces each interrogation mark (if any)
in the template with a copy of <code>name</code>
wherein all occurrences of <code>sep</code>
(a dot, by default)
were replaced by <code>rep</code>
(the system's directory separator, by default),
and then tries to open the resulting file name.
<p>
For instance, if the path is the string
<pre>
"./?.lua;./?.lc;/usr/local/?/init.lua"
</pre><p>
the search for the name <code>foo.a</code>
will try to open the files
<code>./foo/a.lua</code>, <code>./foo/a.lc</code>, and
<code>/usr/local/foo/a/init.lua</code>, in that order.
<p>
Returns the resulting name of the first file that it can
open in read mode (after closing the file),
or <b>nil</b> plus an error message if none succeeds.
(This error message lists all file names it tried to open.)
<h2>6.4 – <a name="6.4">String Manipulation</a></h2>
<p>
This library provides generic functions for string manipulation,
such as finding and extracting substrings, and pattern matching.
When indexing a string in Lua, the first character is at position 1
(not at 0, as in C).
Indices are allowed to be negative and are interpreted as indexing backwards,
from the end of the string.
Thus, the last character is at position -1, and so on.
<p>
The string library provides all its functions inside the table
<a name="pdf-string"><code>string</code></a>.
It also sets a metatable for strings
where the <code>__index</code> field points to the <code>string</code> table.
Therefore, you can use the string functions in object-oriented style.
For instance, <code>string.byte(s,i)</code>
can be written as <code>s:byte(i)</code>.
<p>
The string library assumes one-byte character encodings.
<p>
<hr><h3><a name="pdf-string.byte"><code>string.byte (s [, i [, j]])</code></a></h3>
Returns the internal numeric codes of the characters <code>s[i]</code>,
<code>s[i+1]</code>, ..., <code>s[j]</code>.
The default value for <code>i</code> is 1;
the default value for <code>j</code> is <code>i</code>.
These indices are corrected
following the same rules of function <a href="#pdf-string.sub"><code>string.sub</code></a>.
<p>
Numeric codes are not necessarily portable across platforms.
<p>
<hr><h3><a name="pdf-string.char"><code>string.char (···)</code></a></h3>
Receives zero or more integers.
Returns a string with length equal to the number of arguments,
in which each character has the internal numeric code equal
to its corresponding argument.
<p>
Numeric codes are not necessarily portable across platforms.
<p>
<hr><h3><a name="pdf-string.dump"><code>string.dump (function [, strip])</code></a></h3>
<p>
Returns a string containing a binary representation
(a <em>binary chunk</em>)
of the given function,
so that a later <a href="#pdf-load"><code>load</code></a> on this string returns
a copy of the function (but with new upvalues).
If <code>strip</code> is a true value,
the binary representation may not include all debug information
about the function,
to save space.
<p>
Functions with upvalues have only their number of upvalues saved.
When (re)loaded,
those upvalues receive fresh instances containing <b>nil</b>.
(You can use the debug library to serialize
and reload the upvalues of a function
in a way adequate to your needs.)
<p>
<hr><h3><a name="pdf-string.find"><code>string.find (s, pattern [, init [, plain]])</code></a></h3>
<p>
Looks for the first match of
<code>pattern</code> (see <a href="#6.4.1">§6.4.1</a>) in the string <code>s</code>.
If it finds a match, then <code>find</code> returns the indices of <code>s</code>
where this occurrence starts and ends;
otherwise, it returns <b>nil</b>.
A third, optional numeric argument <code>init</code> specifies
where to start the search;
its default value is 1 and can be negative.
A value of <b>true</b> as a fourth, optional argument <code>plain</code>
turns off the pattern matching facilities,
so the function does a plain "find substring" operation,
with no characters in <code>pattern</code> being considered magic.
Note that if <code>plain</code> is given, then <code>init</code> must be given as well.
<p>
If the pattern has captures,
then in a successful match
the captured values are also returned,
after the two indices.
<p>
<hr><h3><a name="pdf-string.format"><code>string.format (formatstring, ···)</code></a></h3>
<p>
Returns a formatted version of its variable number of arguments
following the description given in its first argument (which must be a string).
The format string follows the same rules as the ISO C function <code>sprintf</code>.
The only differences are that the options/modifiers
<code>*</code>, <code>h</code>, <code>L</code>, <code>l</code>, <code>n</code>,
and <code>p</code> are not supported
and that there is an extra option, <code>q</code>.
<p>
The <code>q</code> option formats a string between double quotes,
using escape sequences when necessary to ensure that
it can safely be read back by the Lua interpreter.
For instance, the call
<pre>
string.format('%q', 'a string with "quotes" and \n new line')
</pre><p>
may produce the string:
<pre>
"a string with \"quotes\" and \
new line"
</pre>
<p>
Options
<code>A</code>, <code>a</code>, <code>E</code>, <code>e</code>, <code>f</code>,
<code>G</code>, and <code>g</code> all expect a number as argument.
Options <code>c</code>, <code>d</code>,
<code>i</code>, <code>o</code>, <code>u</code>, <code>X</code>, and <code>x</code>
expect an integer.
When Lua is compiled with a C89 compiler,
options <code>A</code> and <code>a</code> (hexadecimal floats)
do not support any modifier (flags, width, length).
<p>
Option <code>s</code> expects a string;
if its argument is not a string,
it is converted to one following the same rules of <a href="#pdf-tostring"><code>tostring</code></a>.
If the option has any modifier (flags, width, length),
the string argument should not contain embedded zeros.
<p>
<hr><h3><a name="pdf-string.gmatch"><code>string.gmatch (s, pattern)</code></a></h3>
Returns an iterator function that,
each time it is called,
returns the next captures from <code>pattern</code> (see <a href="#6.4.1">§6.4.1</a>)
over the string <code>s</code>.
If <code>pattern</code> specifies no captures,
then the whole match is produced in each call.
<p>
As an example, the following loop
will iterate over all the words from string <code>s</code>,
printing one per line:
<pre>
s = "hello world from Lua"
for w in string.gmatch(s, "%a+") do
print(w)
end
</pre><p>
The next example collects all pairs <code>key=value</code> from the
given string into a table:
<pre>
t = {}
s = "from=world, to=Lua"
for k, v in string.gmatch(s, "(%w+)=(%w+)") do
t[k] = v
end
</pre>
<p>
For this function, a caret '<code>^</code>' at the start of a pattern does not
work as an anchor, as this would prevent the iteration.
<p>
<hr><h3><a name="pdf-string.gsub"><code>string.gsub (s, pattern, repl [, n])</code></a></h3>
Returns a copy of <code>s</code>
in which all (or the first <code>n</code>, if given)
occurrences of the <code>pattern</code> (see <a href="#6.4.1">§6.4.1</a>) have been
replaced by a replacement string specified by <code>repl</code>,
which can be a string, a table, or a function.
<code>gsub</code> also returns, as its second value,
the total number of matches that occurred.
The name <code>gsub</code> comes from <em>Global SUBstitution</em>.
<p>
If <code>repl</code> is a string, then its value is used for replacement.
The character <code>%</code> works as an escape character:
any sequence in <code>repl</code> of the form <code>%<em>d</em></code>,
with <em>d</em> between 1 and 9,
stands for the value of the <em>d</em>-th captured substring.
The sequence <code>%0</code> stands for the whole match.
The sequence <code>%%</code> stands for a single <code>%</code>.
<p>
If <code>repl</code> is a table, then the table is queried for every match,
using the first capture as the key.
<p>
If <code>repl</code> is a function, then this function is called every time a
match occurs, with all captured substrings passed as arguments,
in order.
<p>
In any case,
if the pattern specifies no captures,
then it behaves as if the whole pattern was inside a capture.
<p>
If the value returned by the table query or by the function call
is a string or a number,
then it is used as the replacement string;
otherwise, if it is <b>false</b> or <b>nil</b>,
then there is no replacement
(that is, the original match is kept in the string).
<p>
Here are some examples:
<pre>
x = string.gsub("hello world", "(%w+)", "%1 %1")
--> x="hello hello world world"
x = string.gsub("hello world", "%w+", "%0 %0", 1)
--> x="hello hello world"
x = string.gsub("hello world from Lua", "(%w+)%s*(%w+)", "%2 %1")
--> x="world hello Lua from"
x = string.gsub("home = $HOME, user = $USER", "%$(%w+)", os.getenv)
--> x="home = /home/roberto, user = roberto"
x = string.gsub("4+5 = $return 4+5$", "%$(.-)%$", function (s)
return load(s)()
end)
--> x="4+5 = 9"
local t = {name="lua", version="5.3"}
x = string.gsub("$name-$version.tar.gz", "%$(%w+)", t)
--> x="lua-5.3.tar.gz"
</pre>
<p>
<hr><h3><a name="pdf-string.len"><code>string.len (s)</code></a></h3>
Receives a string and returns its length.
The empty string <code>""</code> has length 0.
Embedded zeros are counted,
so <code>"a\000bc\000"</code> has length 5.
<p>
<hr><h3><a name="pdf-string.lower"><code>string.lower (s)</code></a></h3>
Receives a string and returns a copy of this string with all
uppercase letters changed to lowercase.
All other characters are left unchanged.
The definition of what an uppercase letter is depends on the current locale.
<p>
<hr><h3><a name="pdf-string.match"><code>string.match (s, pattern [, init])</code></a></h3>
Looks for the first <em>match</em> of
<code>pattern</code> (see <a href="#6.4.1">§6.4.1</a>) in the string <code>s</code>.
If it finds one, then <code>match</code> returns
the captures from the pattern;
otherwise it returns <b>nil</b>.
If <code>pattern</code> specifies no captures,
then the whole match is returned.
A third, optional numeric argument <code>init</code> specifies
where to start the search;
its default value is 1 and can be negative.
<p>
<hr><h3><a name="pdf-string.pack"><code>string.pack (fmt, v1, v2, ···)</code></a></h3>
<p>
Returns a binary string containing the values <code>v1</code>, <code>v2</code>, etc.
packed (that is, serialized in binary form)
according to the format string <code>fmt</code> (see <a href="#6.4.2">§6.4.2</a>).
<p>
<hr><h3><a name="pdf-string.packsize"><code>string.packsize (fmt)</code></a></h3>
<p>
Returns the size of a string resulting from <a href="#pdf-string.pack"><code>string.pack</code></a>
with the given format.
The format string cannot have the variable-length options
'<code>s</code>' or '<code>z</code>' (see <a href="#6.4.2">§6.4.2</a>).
<p>
<hr><h3><a name="pdf-string.rep"><code>string.rep (s, n [, sep])</code></a></h3>
Returns a string that is the concatenation of <code>n</code> copies of
the string <code>s</code> separated by the string <code>sep</code>.
The default value for <code>sep</code> is the empty string
(that is, no separator).
Returns the empty string if <code>n</code> is not positive.
<p>
(Note that it is very easy to exhaust the memory of your machine
with a single call to this function.)
<p>
<hr><h3><a name="pdf-string.reverse"><code>string.reverse (s)</code></a></h3>
Returns a string that is the string <code>s</code> reversed.
<p>
<hr><h3><a name="pdf-string.sub"><code>string.sub (s, i [, j])</code></a></h3>
Returns the substring of <code>s</code> that
starts at <code>i</code> and continues until <code>j</code>;
<code>i</code> and <code>j</code> can be negative.
If <code>j</code> is absent, then it is assumed to be equal to -1
(which is the same as the string length).
In particular,
the call <code>string.sub(s,1,j)</code> returns a prefix of <code>s</code>
with length <code>j</code>,
and <code>string.sub(s, -i)</code> returns a suffix of <code>s</code>
with length <code>i</code>.
<p>
If, after the translation of negative indices,
<code>i</code> is less than 1,
it is corrected to 1.
If <code>j</code> is greater than the string length,
it is corrected to that length.
If, after these corrections,
<code>i</code> is greater than <code>j</code>,
the function returns the empty string.
<p>
<hr><h3><a name="pdf-string.unpack"><code>string.unpack (fmt, s [, pos])</code></a></h3>
<p>
Returns the values packed in string <code>s</code> (see <a href="#pdf-string.pack"><code>string.pack</code></a>)
according to the format string <code>fmt</code> (see <a href="#6.4.2">§6.4.2</a>).
An optional <code>pos</code> marks where
to start reading in <code>s</code> (default is 1).
After the read values,
this function also returns the index of the first unread byte in <code>s</code>.
<p>
<hr><h3><a name="pdf-string.upper"><code>string.upper (s)</code></a></h3>
Receives a string and returns a copy of this string with all
lowercase letters changed to uppercase.
All other characters are left unchanged.
The definition of what a lowercase letter is depends on the current locale.
<h3>6.4.1 – <a name="6.4.1">Patterns</a></h3>
<p>
Patterns in Lua are described by regular strings,
which are interpreted as patterns by the pattern-matching functions
<a href="#pdf-string.find"><code>string.find</code></a>,
<a href="#pdf-string.gmatch"><code>string.gmatch</code></a>,
<a href="#pdf-string.gsub"><code>string.gsub</code></a>,
and <a href="#pdf-string.match"><code>string.match</code></a>.
This section describes the syntax and the meaning
(that is, what they match) of these strings.
<h4>Character Class:</h4><p>
A <em>character class</em> is used to represent a set of characters.
The following combinations are allowed in describing a character class:
<ul>
<li><b><em>x</em>: </b>
(where <em>x</em> is not one of the <em>magic characters</em>
<code>^$()%.[]*+-?</code>)
represents the character <em>x</em> itself.
</li>
<li><b><code>.</code>: </b> (a dot) represents all characters.</li>
<li><b><code>%a</code>: </b> represents all letters.</li>
<li><b><code>%c</code>: </b> represents all control characters.</li>
<li><b><code>%d</code>: </b> represents all digits.</li>
<li><b><code>%g</code>: </b> represents all printable characters except space.</li>
<li><b><code>%l</code>: </b> represents all lowercase letters.</li>
<li><b><code>%p</code>: </b> represents all punctuation characters.</li>
<li><b><code>%s</code>: </b> represents all space characters.</li>
<li><b><code>%u</code>: </b> represents all uppercase letters.</li>
<li><b><code>%w</code>: </b> represents all alphanumeric characters.</li>
<li><b><code>%x</code>: </b> represents all hexadecimal digits.</li>
<li><b><code>%<em>x</em></code>: </b> (where <em>x</em> is any non-alphanumeric character)
represents the character <em>x</em>.
This is the standard way to escape the magic characters.
Any non-alphanumeric character
(including all punctuation characters, even the non-magical)
can be preceded by a '<code>%</code>'
when used to represent itself in a pattern.
</li>
<li><b><code>[<em>set</em>]</code>: </b>
represents the class which is the union of all
characters in <em>set</em>.
A range of characters can be specified by
separating the end characters of the range,
in ascending order, with a '<code>-</code>'.
All classes <code>%</code><em>x</em> described above can also be used as
components in <em>set</em>.
All other characters in <em>set</em> represent themselves.
For example, <code>[%w_]</code> (or <code>[_%w]</code>)
represents all alphanumeric characters plus the underscore,
<code>[0-7]</code> represents the octal digits,
and <code>[0-7%l%-]</code> represents the octal digits plus
the lowercase letters plus the '<code>-</code>' character.
<p>
You can put a closing square bracket in a set
by positioning it as the first character in the set.
You can put an hyphen in a set
by positioning it as the first or the last character in the set.
(You can also use an escape for both cases.)
<p>
The interaction between ranges and classes is not defined.
Therefore, patterns like <code>[%a-z]</code> or <code>[a-%%]</code>
have no meaning.
</li>
<li><b><code>[^<em>set</em>]</code>: </b>
represents the complement of <em>set</em>,
where <em>set</em> is interpreted as above.
</li>
</ul><p>
For all classes represented by single letters (<code>%a</code>, <code>%c</code>, etc.),
the corresponding uppercase letter represents the complement of the class.
For instance, <code>%S</code> represents all non-space characters.
<p>
The definitions of letter, space, and other character groups
depend on the current locale.
In particular, the class <code>[a-z]</code> may not be equivalent to <code>%l</code>.
<h4>Pattern Item:</h4><p>
A <em>pattern item</em> can be
<ul>
<li>
a single character class,
which matches any single character in the class;
</li>
<li>
a single character class followed by '<code>*</code>',
which matches zero or more repetitions of characters in the class.
These repetition items will always match the longest possible sequence;
</li>
<li>
a single character class followed by '<code>+</code>',
which matches one or more repetitions of characters in the class.
These repetition items will always match the longest possible sequence;
</li>
<li>
a single character class followed by '<code>-</code>',
which also matches zero or more repetitions of characters in the class.
Unlike '<code>*</code>',
these repetition items will always match the shortest possible sequence;
</li>
<li>
a single character class followed by '<code>?</code>',
which matches zero or one occurrence of a character in the class.
It always matches one occurrence if possible;
</li>
<li>
<code>%<em>n</em></code>, for <em>n</em> between 1 and 9;
such item matches a substring equal to the <em>n</em>-th captured string
(see below);
</li>
<li>
<code>%b<em>xy</em></code>, where <em>x</em> and <em>y</em> are two distinct characters;
such item matches strings that start with <em>x</em>, end with <em>y</em>,
and where the <em>x</em> and <em>y</em> are <em>balanced</em>.
This means that, if one reads the string from left to right,
counting <em>+1</em> for an <em>x</em> and <em>-1</em> for a <em>y</em>,
the ending <em>y</em> is the first <em>y</em> where the count reaches 0.
For instance, the item <code>%b()</code> matches expressions with
balanced parentheses.
</li>
<li>
<code>%f[<em>set</em>]</code>, a <em>frontier pattern</em>;
such item matches an empty string at any position such that
the next character belongs to <em>set</em>
and the previous character does not belong to <em>set</em>.
The set <em>set</em> is interpreted as previously described.
The beginning and the end of the subject are handled as if
they were the character '<code>\0</code>'.
</li>
</ul>
<h4>Pattern:</h4><p>
A <em>pattern</em> is a sequence of pattern items.
A caret '<code>^</code>' at the beginning of a pattern anchors the match at the
beginning of the subject string.
A '<code>$</code>' at the end of a pattern anchors the match at the
end of the subject string.
At other positions,
'<code>^</code>' and '<code>$</code>' have no special meaning and represent themselves.
<h4>Captures:</h4><p>
A pattern can contain sub-patterns enclosed in parentheses;
they describe <em>captures</em>.
When a match succeeds, the substrings of the subject string
that match captures are stored (<em>captured</em>) for future use.
Captures are numbered according to their left parentheses.
For instance, in the pattern <code>"(a*(.)%w(%s*))"</code>,
the part of the string matching <code>"a*(.)%w(%s*)"</code> is
stored as the first capture (and therefore has number 1);
the character matching "<code>.</code>" is captured with number 2,
and the part matching "<code>%s*</code>" has number 3.
<p>
As a special case, the empty capture <code>()</code> captures
the current string position (a number).
For instance, if we apply the pattern <code>"()aa()"</code> on the
string <code>"flaaap"</code>, there will be two captures: 3 and 5.
<h3>6.4.2 – <a name="6.4.2">Format Strings for Pack and Unpack</a></h3>
<p>
The first argument to <a href="#pdf-string.pack"><code>string.pack</code></a>,
<a href="#pdf-string.packsize"><code>string.packsize</code></a>, and <a href="#pdf-string.unpack"><code>string.unpack</code></a>
is a format string,
which describes the layout of the structure being created or read.
<p>
A format string is a sequence of conversion options.
The conversion options are as follows:
<ul>
<li><b><code><</code>: </b>sets little endian</li>
<li><b><code>></code>: </b>sets big endian</li>
<li><b><code>=</code>: </b>sets native endian</li>
<li><b><code>![<em>n</em>]</code>: </b>sets maximum alignment to <code>n</code>
(default is native alignment)</li>
<li><b><code>b</code>: </b>a signed byte (<code>char</code>)</li>
<li><b><code>B</code>: </b>an unsigned byte (<code>char</code>)</li>
<li><b><code>h</code>: </b>a signed <code>short</code> (native size)</li>
<li><b><code>H</code>: </b>an unsigned <code>short</code> (native size)</li>
<li><b><code>l</code>: </b>a signed <code>long</code> (native size)</li>
<li><b><code>L</code>: </b>an unsigned <code>long</code> (native size)</li>
<li><b><code>j</code>: </b>a <code>lua_Integer</code></li>
<li><b><code>J</code>: </b>a <code>lua_Unsigned</code></li>
<li><b><code>T</code>: </b>a <code>size_t</code> (native size)</li>
<li><b><code>i[<em>n</em>]</code>: </b>a signed <code>int</code> with <code>n</code> bytes
(default is native size)</li>
<li><b><code>I[<em>n</em>]</code>: </b>an unsigned <code>int</code> with <code>n</code> bytes
(default is native size)</li>
<li><b><code>f</code>: </b>a <code>float</code> (native size)</li>
<li><b><code>d</code>: </b>a <code>double</code> (native size)</li>
<li><b><code>n</code>: </b>a <code>lua_Number</code></li>
<li><b><code>c<em>n</em></code>: </b>a fixed-sized string with <code>n</code> bytes</li>
<li><b><code>z</code>: </b>a zero-terminated string</li>
<li><b><code>s[<em>n</em>]</code>: </b>a string preceded by its length
coded as an unsigned integer with <code>n</code> bytes
(default is a <code>size_t</code>)</li>
<li><b><code>x</code>: </b>one byte of padding</li>
<li><b><code>X<em>op</em></code>: </b>an empty item that aligns
according to option <code>op</code>
(which is otherwise ignored)</li>
<li><b>'<code> </code>': </b>(empty space) ignored</li>
</ul><p>
(A "<code>[<em>n</em>]</code>" means an optional integral numeral.)
Except for padding, spaces, and configurations
(options "<code>xX <=>!</code>"),
each option corresponds to an argument (in <a href="#pdf-string.pack"><code>string.pack</code></a>)
or a result (in <a href="#pdf-string.unpack"><code>string.unpack</code></a>).
<p>
For options "<code>!<em>n</em></code>", "<code>s<em>n</em></code>", "<code>i<em>n</em></code>", and "<code>I<em>n</em></code>",
<code>n</code> can be any integer between 1 and 16.
All integral options check overflows;
<a href="#pdf-string.pack"><code>string.pack</code></a> checks whether the given value fits in the given size;
<a href="#pdf-string.unpack"><code>string.unpack</code></a> checks whether the read value fits in a Lua integer.
<p>
Any format string starts as if prefixed by "<code>!1=</code>",
that is,
with maximum alignment of 1 (no alignment)
and native endianness.
<p>
Alignment works as follows:
For each option,
the format gets extra padding until the data starts
at an offset that is a multiple of the minimum between the
option size and the maximum alignment;
this minimum must be a power of 2.
Options "<code>c</code>" and "<code>z</code>" are not aligned;
option "<code>s</code>" follows the alignment of its starting integer.
<p>
All padding is filled with zeros by <a href="#pdf-string.pack"><code>string.pack</code></a>
(and ignored by <a href="#pdf-string.unpack"><code>string.unpack</code></a>).
<h2>6.5 – <a name="6.5">UTF-8 Support</a></h2>
<p>
This library provides basic support for UTF-8 encoding.
It provides all its functions inside the table <a name="pdf-utf8"><code>utf8</code></a>.
This library does not provide any support for Unicode other
than the handling of the encoding.
Any operation that needs the meaning of a character,
such as character classification, is outside its scope.
<p>
Unless stated otherwise,
all functions that expect a byte position as a parameter
assume that the given position is either the start of a byte sequence
or one plus the length of the subject string.
As in the string library,
negative indices count from the end of the string.
<p>
<hr><h3><a name="pdf-utf8.char"><code>utf8.char (···)</code></a></h3>
Receives zero or more integers,
converts each one to its corresponding UTF-8 byte sequence
and returns a string with the concatenation of all these sequences.
<p>
<hr><h3><a name="pdf-utf8.charpattern"><code>utf8.charpattern</code></a></h3>
The pattern (a string, not a function) "<code>[\0-\x7F\xC2-\xF4][\x80-\xBF]*</code>"
(see <a href="#6.4.1">§6.4.1</a>),
which matches exactly one UTF-8 byte sequence,
assuming that the subject is a valid UTF-8 string.
<p>
<hr><h3><a name="pdf-utf8.codes"><code>utf8.codes (s)</code></a></h3>
<p>
Returns values so that the construction
<pre>
for p, c in utf8.codes(s) do <em>body</em> end
</pre><p>
will iterate over all characters in string <code>s</code>,
with <code>p</code> being the position (in bytes) and <code>c</code> the code point
of each character.
It raises an error if it meets any invalid byte sequence.
<p>
<hr><h3><a name="pdf-utf8.codepoint"><code>utf8.codepoint (s [, i [, j]])</code></a></h3>
Returns the codepoints (as integers) from all characters in <code>s</code>
that start between byte position <code>i</code> and <code>j</code> (both included).
The default for <code>i</code> is 1 and for <code>j</code> is <code>i</code>.
It raises an error if it meets any invalid byte sequence.
<p>
<hr><h3><a name="pdf-utf8.len"><code>utf8.len (s [, i [, j]])</code></a></h3>
Returns the number of UTF-8 characters in string <code>s</code>
that start between positions <code>i</code> and <code>j</code> (both inclusive).
The default for <code>i</code> is 1 and for <code>j</code> is -1.
If it finds any invalid byte sequence,
returns a false value plus the position of the first invalid byte.
<p>
<hr><h3><a name="pdf-utf8.offset"><code>utf8.offset (s, n [, i])</code></a></h3>
Returns the position (in bytes) where the encoding of the
<code>n</code>-th character of <code>s</code>
(counting from position <code>i</code>) starts.
A negative <code>n</code> gets characters before position <code>i</code>.
The default for <code>i</code> is 1 when <code>n</code> is non-negative
and <code>#s + 1</code> otherwise,
so that <code>utf8.offset(s, -n)</code> gets the offset of the
<code>n</code>-th character from the end of the string.
If the specified character is neither in the subject
nor right after its end,
the function returns <b>nil</b>.
<p>
As a special case,
when <code>n</code> is 0 the function returns the start of the encoding
of the character that contains the <code>i</code>-th byte of <code>s</code>.
<p>
This function assumes that <code>s</code> is a valid UTF-8 string.
<h2>6.6 – <a name="6.6">Table Manipulation</a></h2>
<p>
This library provides generic functions for table manipulation.
It provides all its functions inside the table <a name="pdf-table"><code>table</code></a>.
<p>
Remember that, whenever an operation needs the length of a table,
the table must be a proper sequence
or have a <code>__len</code> metamethod (see <a href="#3.4.7">§3.4.7</a>).
All functions ignore non-numeric keys
in the tables given as arguments.
<p>
<hr><h3><a name="pdf-table.concat"><code>table.concat (list [, sep [, i [, j]]])</code></a></h3>
<p>
Given a list where all elements are strings or numbers,
returns the string <code>list[i]..sep..list[i+1] ··· sep..list[j]</code>.
The default value for <code>sep</code> is the empty string,
the default for <code>i</code> is 1,
and the default for <code>j</code> is <code>#list</code>.
If <code>i</code> is greater than <code>j</code>, returns the empty string.
<p>
<hr><h3><a name="pdf-table.insert"><code>table.insert (list, [pos,] value)</code></a></h3>
<p>
Inserts element <code>value</code> at position <code>pos</code> in <code>list</code>,
shifting up the elements
<code>list[pos], list[pos+1], ···, list[#list]</code>.
The default value for <code>pos</code> is <code>#list+1</code>,
so that a call <code>table.insert(t,x)</code> inserts <code>x</code> at the end
of list <code>t</code>.
<p>
<hr><h3><a name="pdf-table.move"><code>table.move (a1, f, e, t [,a2])</code></a></h3>
<p>
Moves elements from table <code>a1</code> to table <code>a2</code>,
performing the equivalent to the following
multiple assignment:
<code>a2[t],··· = a1[f],···,a1[e]</code>.
The default for <code>a2</code> is <code>a1</code>.
The destination range can overlap with the source range.
The number of elements to be moved must fit in a Lua integer.
<p>
Returns the destination table <code>a2</code>.
<p>
<hr><h3><a name="pdf-table.pack"><code>table.pack (···)</code></a></h3>
<p>
Returns a new table with all parameters stored into keys 1, 2, etc.
and with a field "<code>n</code>" with the total number of parameters.
Note that the resulting table may not be a sequence.
<p>
<hr><h3><a name="pdf-table.remove"><code>table.remove (list [, pos])</code></a></h3>
<p>
Removes from <code>list</code> the element at position <code>pos</code>,
returning the value of the removed element.
When <code>pos</code> is an integer between 1 and <code>#list</code>,
it shifts down the elements
<code>list[pos+1], list[pos+2], ···, list[#list]</code>
and erases element <code>list[#list]</code>;
The index <code>pos</code> can also be 0 when <code>#list</code> is 0,
or <code>#list + 1</code>;
in those cases, the function erases the element <code>list[pos]</code>.
<p>
The default value for <code>pos</code> is <code>#list</code>,
so that a call <code>table.remove(l)</code> removes the last element
of list <code>l</code>.
<p>
<hr><h3><a name="pdf-table.sort"><code>table.sort (list [, comp])</code></a></h3>
<p>
Sorts list elements in a given order, <em>in-place</em>,
from <code>list[1]</code> to <code>list[#list]</code>.
If <code>comp</code> is given,
then it must be a function that receives two list elements
and returns true when the first element must come
before the second in the final order
(so that, after the sort,
<code>i < j</code> implies <code>not comp(list[j],list[i])</code>).
If <code>comp</code> is not given,
then the standard Lua operator <code><</code> is used instead.
<p>
Note that the <code>comp</code> function must define
a strict partial order over the elements in the list;
that is, it must be asymmetric and transitive.
Otherwise, no valid sort may be possible.
<p>
The sort algorithm is not stable;
that is, elements not comparable by the given order
(e.g., equal elements)
may have their relative positions changed by the sort.
<p>
<hr><h3><a name="pdf-table.unpack"><code>table.unpack (list [, i [, j]])</code></a></h3>
<p>
Returns the elements from the given list.
This function is equivalent to
<pre>
return list[i], list[i+1], ···, list[j]
</pre><p>
By default, <code>i</code> is 1 and <code>j</code> is <code>#list</code>.
<h2>6.7 – <a name="6.7">Mathematical Functions</a></h2>
<p>
This library provides basic mathematical functions.
It provides all its functions and constants inside the table <a name="pdf-math"><code>math</code></a>.
Functions with the annotation "<code>integer/float</code>" give
integer results for integer arguments
and float results for float (or mixed) arguments.
Rounding functions
(<a href="#pdf-math.ceil"><code>math.ceil</code></a>, <a href="#pdf-math.floor"><code>math.floor</code></a>, and <a href="#pdf-math.modf"><code>math.modf</code></a>)
return an integer when the result fits in the range of an integer,
or a float otherwise.
<p>
<hr><h3><a name="pdf-math.abs"><code>math.abs (x)</code></a></h3>
<p>
Returns the absolute value of <code>x</code>. (integer/float)
<p>
<hr><h3><a name="pdf-math.acos"><code>math.acos (x)</code></a></h3>
<p>
Returns the arc cosine of <code>x</code> (in radians).
<p>
<hr><h3><a name="pdf-math.asin"><code>math.asin (x)</code></a></h3>
<p>
Returns the arc sine of <code>x</code> (in radians).
<p>
<hr><h3><a name="pdf-math.atan"><code>math.atan (y [, x])</code></a></h3>
<p>
Returns the arc tangent of <code>y/x</code> (in radians),
but uses the signs of both parameters to find the
quadrant of the result.
(It also handles correctly the case of <code>x</code> being zero.)
<p>
The default value for <code>x</code> is 1,
so that the call <code>math.atan(y)</code>
returns the arc tangent of <code>y</code>.
<p>
<hr><h3><a name="pdf-math.ceil"><code>math.ceil (x)</code></a></h3>
<p>
Returns the smallest integral value larger than or equal to <code>x</code>.
<p>
<hr><h3><a name="pdf-math.cos"><code>math.cos (x)</code></a></h3>
<p>
Returns the cosine of <code>x</code> (assumed to be in radians).
<p>
<hr><h3><a name="pdf-math.deg"><code>math.deg (x)</code></a></h3>
<p>
Converts the angle <code>x</code> from radians to degrees.
<p>
<hr><h3><a name="pdf-math.exp"><code>math.exp (x)</code></a></h3>
<p>
Returns the value <em>e<sup>x</sup></em>
(where <code>e</code> is the base of natural logarithms).
<p>
<hr><h3><a name="pdf-math.floor"><code>math.floor (x)</code></a></h3>
<p>
Returns the largest integral value smaller than or equal to <code>x</code>.
<p>
<hr><h3><a name="pdf-math.fmod"><code>math.fmod (x, y)</code></a></h3>
<p>
Returns the remainder of the division of <code>x</code> by <code>y</code>
that rounds the quotient towards zero. (integer/float)
<p>
<hr><h3><a name="pdf-math.huge"><code>math.huge</code></a></h3>
<p>
The float value <code>HUGE_VAL</code>,
a value larger than any other numeric value.
<p>
<hr><h3><a name="pdf-math.log"><code>math.log (x [, base])</code></a></h3>
<p>
Returns the logarithm of <code>x</code> in the given base.
The default for <code>base</code> is <em>e</em>
(so that the function returns the natural logarithm of <code>x</code>).
<p>
<hr><h3><a name="pdf-math.max"><code>math.max (x, ···)</code></a></h3>
<p>
Returns the argument with the maximum value,
according to the Lua operator <code><</code>. (integer/float)
<p>
<hr><h3><a name="pdf-math.maxinteger"><code>math.maxinteger</code></a></h3>
An integer with the maximum value for an integer.
<p>
<hr><h3><a name="pdf-math.min"><code>math.min (x, ···)</code></a></h3>
<p>
Returns the argument with the minimum value,
according to the Lua operator <code><</code>. (integer/float)
<p>
<hr><h3><a name="pdf-math.mininteger"><code>math.mininteger</code></a></h3>
An integer with the minimum value for an integer.
<p>
<hr><h3><a name="pdf-math.modf"><code>math.modf (x)</code></a></h3>
<p>
Returns the integral part of <code>x</code> and the fractional part of <code>x</code>.
Its second result is always a float.
<p>
<hr><h3><a name="pdf-math.pi"><code>math.pi</code></a></h3>
<p>
The value of <em>π</em>.
<p>
<hr><h3><a name="pdf-math.rad"><code>math.rad (x)</code></a></h3>
<p>
Converts the angle <code>x</code> from degrees to radians.
<p>
<hr><h3><a name="pdf-math.random"><code>math.random ([m [, n]])</code></a></h3>
<p>
When called without arguments,
returns a pseudo-random float with uniform distribution
in the range <em>[0,1)</em>.
When called with two integers <code>m</code> and <code>n</code>,
<code>math.random</code> returns a pseudo-random integer
with uniform distribution in the range <em>[m, n]</em>.
(The value <em>n-m</em> cannot be negative and must fit in a Lua integer.)
The call <code>math.random(n)</code> is equivalent to <code>math.random(1,n)</code>.
<p>
This function is an interface to the underling
pseudo-random generator function provided by C.
<p>
<hr><h3><a name="pdf-math.randomseed"><code>math.randomseed (x)</code></a></h3>
<p>
Sets <code>x</code> as the "seed"
for the pseudo-random generator:
equal seeds produce equal sequences of numbers.
<p>
<hr><h3><a name="pdf-math.sin"><code>math.sin (x)</code></a></h3>
<p>
Returns the sine of <code>x</code> (assumed to be in radians).
<p>
<hr><h3><a name="pdf-math.sqrt"><code>math.sqrt (x)</code></a></h3>
<p>
Returns the square root of <code>x</code>.
(You can also use the expression <code>x^0.5</code> to compute this value.)
<p>
<hr><h3><a name="pdf-math.tan"><code>math.tan (x)</code></a></h3>
<p>
Returns the tangent of <code>x</code> (assumed to be in radians).
<p>
<hr><h3><a name="pdf-math.tointeger"><code>math.tointeger (x)</code></a></h3>
<p>
If the value <code>x</code> is convertible to an integer,
returns that integer.
Otherwise, returns <b>nil</b>.
<p>
<hr><h3><a name="pdf-math.type"><code>math.type (x)</code></a></h3>
<p>
Returns "<code>integer</code>" if <code>x</code> is an integer,
"<code>float</code>" if it is a float,
or <b>nil</b> if <code>x</code> is not a number.
<p>
<hr><h3><a name="pdf-math.ult"><code>math.ult (m, n)</code></a></h3>
<p>
Returns a boolean,
true if integer <code>m</code> is below integer <code>n</code> when
they are compared as unsigned integers.
<h2>6.8 – <a name="6.8">Input and Output Facilities</a></h2>
<p>
The I/O library provides two different styles for file manipulation.
The first one uses implicit file handles;
that is, there are operations to set a default input file and a
default output file,
and all input/output operations are over these default files.
The second style uses explicit file handles.
<p>
When using implicit file handles,
all operations are supplied by table <a name="pdf-io"><code>io</code></a>.
When using explicit file handles,
the operation <a href="#pdf-io.open"><code>io.open</code></a> returns a file handle
and then all operations are supplied as methods of the file handle.
<p>
The table <code>io</code> also provides
three predefined file handles with their usual meanings from C:
<a name="pdf-io.stdin"><code>io.stdin</code></a>, <a name="pdf-io.stdout"><code>io.stdout</code></a>, and <a name="pdf-io.stderr"><code>io.stderr</code></a>.
The I/O library never closes these files.
<p>
Unless otherwise stated,
all I/O functions return <b>nil</b> on failure
(plus an error message as a second result and
a system-dependent error code as a third result)
and some value different from <b>nil</b> on success.
On non-POSIX systems,
the computation of the error message and error code
in case of errors
may be not thread safe,
because they rely on the global C variable <code>errno</code>.
<p>
<hr><h3><a name="pdf-io.close"><code>io.close ([file])</code></a></h3>
<p>
Equivalent to <code>file:close()</code>.
Without a <code>file</code>, closes the default output file.
<p>
<hr><h3><a name="pdf-io.flush"><code>io.flush ()</code></a></h3>
<p>
Equivalent to <code>io.output():flush()</code>.
<p>
<hr><h3><a name="pdf-io.input"><code>io.input ([file])</code></a></h3>
<p>
When called with a file name, it opens the named file (in text mode),
and sets its handle as the default input file.
When called with a file handle,
it simply sets this file handle as the default input file.
When called without parameters,
it returns the current default input file.
<p>
In case of errors this function raises the error,
instead of returning an error code.
<p>
<hr><h3><a name="pdf-io.lines"><code>io.lines ([filename, ···])</code></a></h3>
<p>
Opens the given file name in read mode
and returns an iterator function that
works like <code>file:lines(···)</code> over the opened file.
When the iterator function detects the end of file,
it returns no values (to finish the loop) and automatically closes the file.
<p>
The call <code>io.lines()</code> (with no file name) is equivalent
to <code>io.input():lines("*l")</code>;
that is, it iterates over the lines of the default input file.
In this case it does not close the file when the loop ends.
<p>
In case of errors this function raises the error,
instead of returning an error code.
<p>
<hr><h3><a name="pdf-io.open"><code>io.open (filename [, mode])</code></a></h3>
<p>
This function opens a file,
in the mode specified in the string <code>mode</code>.
In case of success,
it returns a new file handle.
<p>
The <code>mode</code> string can be any of the following:
<ul>
<li><b>"<code>r</code>": </b> read mode (the default);</li>
<li><b>"<code>w</code>": </b> write mode;</li>
<li><b>"<code>a</code>": </b> append mode;</li>
<li><b>"<code>r+</code>": </b> update mode, all previous data is preserved;</li>
<li><b>"<code>w+</code>": </b> update mode, all previous data is erased;</li>
<li><b>"<code>a+</code>": </b> append update mode, previous data is preserved,
writing is only allowed at the end of file.</li>
</ul><p>
The <code>mode</code> string can also have a '<code>b</code>' at the end,
which is needed in some systems to open the file in binary mode.
<p>
<hr><h3><a name="pdf-io.output"><code>io.output ([file])</code></a></h3>
<p>
Similar to <a href="#pdf-io.input"><code>io.input</code></a>, but operates over the default output file.
<p>
<hr><h3><a name="pdf-io.popen"><code>io.popen (prog [, mode])</code></a></h3>
<p>
This function is system dependent and is not available
on all platforms.
<p>
Starts program <code>prog</code> in a separated process and returns
a file handle that you can use to read data from this program
(if <code>mode</code> is <code>"r"</code>, the default)
or to write data to this program
(if <code>mode</code> is <code>"w"</code>).
<p>
<hr><h3><a name="pdf-io.read"><code>io.read (···)</code></a></h3>
<p>
Equivalent to <code>io.input():read(···)</code>.
<p>
<hr><h3><a name="pdf-io.tmpfile"><code>io.tmpfile ()</code></a></h3>
<p>
In case of success,
returns a handle for a temporary file.
This file is opened in update mode
and it is automatically removed when the program ends.
<p>
<hr><h3><a name="pdf-io.type"><code>io.type (obj)</code></a></h3>
<p>
Checks whether <code>obj</code> is a valid file handle.
Returns the string <code>"file"</code> if <code>obj</code> is an open file handle,
<code>"closed file"</code> if <code>obj</code> is a closed file handle,
or <b>nil</b> if <code>obj</code> is not a file handle.
<p>
<hr><h3><a name="pdf-io.write"><code>io.write (···)</code></a></h3>
<p>
Equivalent to <code>io.output():write(···)</code>.
<p>
<hr><h3><a name="pdf-file:close"><code>file:close ()</code></a></h3>
<p>
Closes <code>file</code>.
Note that files are automatically closed when
their handles are garbage collected,
but that takes an unpredictable amount of time to happen.
<p>
When closing a file handle created with <a href="#pdf-io.popen"><code>io.popen</code></a>,
<a href="#pdf-file:close"><code>file:close</code></a> returns the same values
returned by <a href="#pdf-os.execute"><code>os.execute</code></a>.
<p>
<hr><h3><a name="pdf-file:flush"><code>file:flush ()</code></a></h3>
<p>
Saves any written data to <code>file</code>.
<p>
<hr><h3><a name="pdf-file:lines"><code>file:lines (···)</code></a></h3>
<p>
Returns an iterator function that,
each time it is called,
reads the file according to the given formats.
When no format is given,
uses "<code>l</code>" as a default.
As an example, the construction
<pre>
for c in file:lines(1) do <em>body</em> end
</pre><p>
will iterate over all characters of the file,
starting at the current position.
Unlike <a href="#pdf-io.lines"><code>io.lines</code></a>, this function does not close the file
when the loop ends.
<p>
In case of errors this function raises the error,
instead of returning an error code.
<p>
<hr><h3><a name="pdf-file:read"><code>file:read (···)</code></a></h3>
<p>
Reads the file <code>file</code>,
according to the given formats, which specify what to read.
For each format,
the function returns a string or a number with the characters read,
or <b>nil</b> if it cannot read data with the specified format.
(In this latter case,
the function does not read subsequent formats.)
When called without formats,
it uses a default format that reads the next line
(see below).
<p>
The available formats are
<ul>
<li><b>"<code>n</code>": </b>
reads a numeral and returns it as a float or an integer,
following the lexical conventions of Lua.
(The numeral may have leading spaces and a sign.)
This format always reads the longest input sequence that
is a valid prefix for a numeral;
if that prefix does not form a valid numeral
(e.g., an empty string, "<code>0x</code>", or "<code>3.4e-</code>"),
it is discarded and the function returns <b>nil</b>.
</li>
<li><b>"<code>a</code>": </b>
reads the whole file, starting at the current position.
On end of file, it returns the empty string.
</li>
<li><b>"<code>l</code>": </b>
reads the next line skipping the end of line,
returning <b>nil</b> on end of file.
This is the default format.
</li>
<li><b>"<code>L</code>": </b>
reads the next line keeping the end-of-line character (if present),
returning <b>nil</b> on end of file.
</li>
<li><b><em>number</em>: </b>
reads a string with up to this number of bytes,
returning <b>nil</b> on end of file.
If <code>number</code> is zero,
it reads nothing and returns an empty string,
or <b>nil</b> on end of file.
</li>
</ul><p>
The formats "<code>l</code>" and "<code>L</code>" should be used only for text files.
<p>
<hr><h3><a name="pdf-file:seek"><code>file:seek ([whence [, offset]])</code></a></h3>
<p>
Sets and gets the file position,
measured from the beginning of the file,
to the position given by <code>offset</code> plus a base
specified by the string <code>whence</code>, as follows:
<ul>
<li><b>"<code>set</code>": </b> base is position 0 (beginning of the file);</li>
<li><b>"<code>cur</code>": </b> base is current position;</li>
<li><b>"<code>end</code>": </b> base is end of file;</li>
</ul><p>
In case of success, <code>seek</code> returns the final file position,
measured in bytes from the beginning of the file.
If <code>seek</code> fails, it returns <b>nil</b>,
plus a string describing the error.
<p>
The default value for <code>whence</code> is <code>"cur"</code>,
and for <code>offset</code> is 0.
Therefore, the call <code>file:seek()</code> returns the current
file position, without changing it;
the call <code>file:seek("set")</code> sets the position to the
beginning of the file (and returns 0);
and the call <code>file:seek("end")</code> sets the position to the
end of the file, and returns its size.
<p>
<hr><h3><a name="pdf-file:setvbuf"><code>file:setvbuf (mode [, size])</code></a></h3>
<p>
Sets the buffering mode for an output file.
There are three available modes:
<ul>
<li><b>"<code>no</code>": </b>
no buffering; the result of any output operation appears immediately.
</li>
<li><b>"<code>full</code>": </b>
full buffering; output operation is performed only
when the buffer is full or when
you explicitly <code>flush</code> the file (see <a href="#pdf-io.flush"><code>io.flush</code></a>).
</li>
<li><b>"<code>line</code>": </b>
line buffering; output is buffered until a newline is output
or there is any input from some special files
(such as a terminal device).
</li>
</ul><p>
For the last two cases, <code>size</code>
specifies the size of the buffer, in bytes.
The default is an appropriate size.
<p>
<hr><h3><a name="pdf-file:write"><code>file:write (···)</code></a></h3>
<p>
Writes the value of each of its arguments to <code>file</code>.
The arguments must be strings or numbers.
<p>
In case of success, this function returns <code>file</code>.
Otherwise it returns <b>nil</b> plus a string describing the error.
<h2>6.9 – <a name="6.9">Operating System Facilities</a></h2>
<p>
This library is implemented through table <a name="pdf-os"><code>os</code></a>.
<p>
<hr><h3><a name="pdf-os.clock"><code>os.clock ()</code></a></h3>
<p>
Returns an approximation of the amount in seconds of CPU time
used by the program.
<p>
<hr><h3><a name="pdf-os.date"><code>os.date ([format [, time]])</code></a></h3>
<p>
Returns a string or a table containing date and time,
formatted according to the given string <code>format</code>.
<p>
If the <code>time</code> argument is present,
this is the time to be formatted
(see the <a href="#pdf-os.time"><code>os.time</code></a> function for a description of this value).
Otherwise, <code>date</code> formats the current time.
<p>
If <code>format</code> starts with '<code>!</code>',
then the date is formatted in Coordinated Universal Time.
After this optional character,
if <code>format</code> is the string "<code>*t</code>",
then <code>date</code> returns a table with the following fields:
<code>year</code>, <code>month</code> (1–12), <code>day</code> (1–31),
<code>hour</code> (0–23), <code>min</code> (0–59), <code>sec</code> (0–61),
<code>wday</code> (weekday, 1–7, Sunday is 1),
<code>yday</code> (day of the year, 1–366),
and <code>isdst</code> (daylight saving flag, a boolean).
This last field may be absent
if the information is not available.
<p>
If <code>format</code> is not "<code>*t</code>",
then <code>date</code> returns the date as a string,
formatted according to the same rules as the ISO C function <code>strftime</code>.
<p>
When called without arguments,
<code>date</code> returns a reasonable date and time representation that depends on
the host system and on the current locale.
(More specifically, <code>os.date()</code> is equivalent to <code>os.date("%c")</code>.)
<p>
On non-POSIX systems,
this function may be not thread safe
because of its reliance on C function <code>gmtime</code> and C function <code>localtime</code>.
<p>
<hr><h3><a name="pdf-os.difftime"><code>os.difftime (t2, t1)</code></a></h3>
<p>
Returns the difference, in seconds,
from time <code>t1</code> to time <code>t2</code>
(where the times are values returned by <a href="#pdf-os.time"><code>os.time</code></a>).
In POSIX, Windows, and some other systems,
this value is exactly <code>t2</code><em>-</em><code>t1</code>.
<p>
<hr><h3><a name="pdf-os.execute"><code>os.execute ([command])</code></a></h3>
<p>
This function is equivalent to the ISO C function <code>system</code>.
It passes <code>command</code> to be executed by an operating system shell.
Its first result is <b>true</b>
if the command terminated successfully,
or <b>nil</b> otherwise.
After this first result
the function returns a string plus a number,
as follows:
<ul>
<li><b>"<code>exit</code>": </b>
the command terminated normally;
the following number is the exit status of the command.
</li>
<li><b>"<code>signal</code>": </b>
the command was terminated by a signal;
the following number is the signal that terminated the command.
</li>
</ul>
<p>
When called without a <code>command</code>,
<code>os.execute</code> returns a boolean that is true if a shell is available.
<p>
<hr><h3><a name="pdf-os.exit"><code>os.exit ([code [, close]])</code></a></h3>
<p>
Calls the ISO C function <code>exit</code> to terminate the host program.
If <code>code</code> is <b>true</b>,
the returned status is <code>EXIT_SUCCESS</code>;
if <code>code</code> is <b>false</b>,
the returned status is <code>EXIT_FAILURE</code>;
if <code>code</code> is a number,
the returned status is this number.
The default value for <code>code</code> is <b>true</b>.
<p>
If the optional second argument <code>close</code> is true,
closes the Lua state before exiting.
<p>
<hr><h3><a name="pdf-os.getenv"><code>os.getenv (varname)</code></a></h3>
<p>
Returns the value of the process environment variable <code>varname</code>,
or <b>nil</b> if the variable is not defined.
<p>
<hr><h3><a name="pdf-os.remove"><code>os.remove (filename)</code></a></h3>
<p>
Deletes the file (or empty directory, on POSIX systems)
with the given name.
If this function fails, it returns <b>nil</b>,
plus a string describing the error and the error code.
<p>
<hr><h3><a name="pdf-os.rename"><code>os.rename (oldname, newname)</code></a></h3>
<p>
Renames file or directory named <code>oldname</code> to <code>newname</code>.
If this function fails, it returns <b>nil</b>,
plus a string describing the error and the error code.
<p>
<hr><h3><a name="pdf-os.setlocale"><code>os.setlocale (locale [, category])</code></a></h3>
<p>
Sets the current locale of the program.
<code>locale</code> is a system-dependent string specifying a locale;
<code>category</code> is an optional string describing which category to change:
<code>"all"</code>, <code>"collate"</code>, <code>"ctype"</code>,
<code>"monetary"</code>, <code>"numeric"</code>, or <code>"time"</code>;
the default category is <code>"all"</code>.
The function returns the name of the new locale,
or <b>nil</b> if the request cannot be honored.
<p>
If <code>locale</code> is the empty string,
the current locale is set to an implementation-defined native locale.
If <code>locale</code> is the string "<code>C</code>",
the current locale is set to the standard C locale.
<p>
When called with <b>nil</b> as the first argument,
this function only returns the name of the current locale
for the given category.
<p>
This function may be not thread safe
because of its reliance on C function <code>setlocale</code>.
<p>
<hr><h3><a name="pdf-os.time"><code>os.time ([table])</code></a></h3>
<p>
Returns the current time when called without arguments,
or a time representing the local date and time specified by the given table.
This table must have fields <code>year</code>, <code>month</code>, and <code>day</code>,
and may have fields
<code>hour</code> (default is 12),
<code>min</code> (default is 0),
<code>sec</code> (default is 0),
and <code>isdst</code> (default is <b>nil</b>).
Other fields are ignored.
For a description of these fields, see the <a href="#pdf-os.date"><code>os.date</code></a> function.
<p>
The values in these fields do not need to be inside their valid ranges.
For instance, if <code>sec</code> is -10,
it means -10 seconds from the time specified by the other fields;
if <code>hour</code> is 1000,
it means +1000 hours from the time specified by the other fields.
<p>
The returned value is a number, whose meaning depends on your system.
In POSIX, Windows, and some other systems,
this number counts the number
of seconds since some given start time (the "epoch").
In other systems, the meaning is not specified,
and the number returned by <code>time</code> can be used only as an argument to
<a href="#pdf-os.date"><code>os.date</code></a> and <a href="#pdf-os.difftime"><code>os.difftime</code></a>.
<p>
<hr><h3><a name="pdf-os.tmpname"><code>os.tmpname ()</code></a></h3>
<p>
Returns a string with a file name that can
be used for a temporary file.
The file must be explicitly opened before its use
and explicitly removed when no longer needed.
<p>
On POSIX systems,
this function also creates a file with that name,
to avoid security risks.
(Someone else might create the file with wrong permissions
in the time between getting the name and creating the file.)
You still have to open the file to use it
and to remove it (even if you do not use it).
<p>
When possible,
you may prefer to use <a href="#pdf-io.tmpfile"><code>io.tmpfile</code></a>,
which automatically removes the file when the program ends.
<h2>6.10 – <a name="6.10">The Debug Library</a></h2>
<p>
This library provides
the functionality of the debug interface (<a href="#4.9">§4.9</a>) to Lua programs.
You should exert care when using this library.
Several of its functions
violate basic assumptions about Lua code
(e.g., that variables local to a function
cannot be accessed from outside;
that userdata metatables cannot be changed by Lua code;
that Lua programs do not crash)
and therefore can compromise otherwise secure code.
Moreover, some functions in this library may be slow.
<p>
All functions in this library are provided
inside the <a name="pdf-debug"><code>debug</code></a> table.
All functions that operate over a thread
have an optional first argument which is the
thread to operate over.
The default is always the current thread.
<p>
<hr><h3><a name="pdf-debug.debug"><code>debug.debug ()</code></a></h3>
<p>
Enters an interactive mode with the user,
running each string that the user enters.
Using simple commands and other debug facilities,
the user can inspect global and local variables,
change their values, evaluate expressions, and so on.
A line containing only the word <code>cont</code> finishes this function,
so that the caller continues its execution.
<p>
Note that commands for <code>debug.debug</code> are not lexically nested
within any function and so have no direct access to local variables.
<p>
<hr><h3><a name="pdf-debug.gethook"><code>debug.gethook ([thread])</code></a></h3>
<p>
Returns the current hook settings of the thread, as three values:
the current hook function, the current hook mask,
and the current hook count
(as set by the <a href="#pdf-debug.sethook"><code>debug.sethook</code></a> function).
<p>
<hr><h3><a name="pdf-debug.getinfo"><code>debug.getinfo ([thread,] f [, what])</code></a></h3>
<p>
Returns a table with information about a function.
You can give the function directly
or you can give a number as the value of <code>f</code>,
which means the function running at level <code>f</code> of the call stack
of the given thread:
level 0 is the current function (<code>getinfo</code> itself);
level 1 is the function that called <code>getinfo</code>
(except for tail calls, which do not count on the stack);
and so on.
If <code>f</code> is a number larger than the number of active functions,
then <code>getinfo</code> returns <b>nil</b>.
<p>
The returned table can contain all the fields returned by <a href="#lua_getinfo"><code>lua_getinfo</code></a>,
with the string <code>what</code> describing which fields to fill in.
The default for <code>what</code> is to get all information available,
except the table of valid lines.
If present,
the option '<code>f</code>'
adds a field named <code>func</code> with the function itself.
If present,
the option '<code>L</code>'
adds a field named <code>activelines</code> with the table of
valid lines.
<p>
For instance, the expression <code>debug.getinfo(1,"n").name</code> returns
a name for the current function,
if a reasonable name can be found,
and the expression <code>debug.getinfo(print)</code>
returns a table with all available information
about the <a href="#pdf-print"><code>print</code></a> function.
<p>
<hr><h3><a name="pdf-debug.getlocal"><code>debug.getlocal ([thread,] f, local)</code></a></h3>
<p>
This function returns the name and the value of the local variable
with index <code>local</code> of the function at level <code>f</code> of the stack.
This function accesses not only explicit local variables,
but also parameters, temporaries, etc.
<p>
The first parameter or local variable has index 1, and so on,
following the order that they are declared in the code,
counting only the variables that are active
in the current scope of the function.
Negative indices refer to vararg parameters;
-1 is the first vararg parameter.
The function returns <b>nil</b> if there is no variable with the given index,
and raises an error when called with a level out of range.
(You can call <a href="#pdf-debug.getinfo"><code>debug.getinfo</code></a> to check whether the level is valid.)
<p>
Variable names starting with '<code>(</code>' (open parenthesis)
represent variables with no known names
(internal variables such as loop control variables,
and variables from chunks saved without debug information).
<p>
The parameter <code>f</code> may also be a function.
In that case, <code>getlocal</code> returns only the name of function parameters.
<p>
<hr><h3><a name="pdf-debug.getmetatable"><code>debug.getmetatable (value)</code></a></h3>
<p>
Returns the metatable of the given <code>value</code>
or <b>nil</b> if it does not have a metatable.
<p>
<hr><h3><a name="pdf-debug.getregistry"><code>debug.getregistry ()</code></a></h3>
<p>
Returns the registry table (see <a href="#4.5">§4.5</a>).
<p>
<hr><h3><a name="pdf-debug.getupvalue"><code>debug.getupvalue (f, up)</code></a></h3>
<p>
This function returns the name and the value of the upvalue
with index <code>up</code> of the function <code>f</code>.
The function returns <b>nil</b> if there is no upvalue with the given index.
<p>
Variable names starting with '<code>(</code>' (open parenthesis)
represent variables with no known names
(variables from chunks saved without debug information).
<p>
<hr><h3><a name="pdf-debug.getuservalue"><code>debug.getuservalue (u)</code></a></h3>
<p>
Returns the Lua value associated to <code>u</code>.
If <code>u</code> is not a userdata,
returns <b>nil</b>.
<p>
<hr><h3><a name="pdf-debug.sethook"><code>debug.sethook ([thread,] hook, mask [, count])</code></a></h3>
<p>
Sets the given function as a hook.
The string <code>mask</code> and the number <code>count</code> describe
when the hook will be called.
The string mask may have any combination of the following characters,
with the given meaning:
<ul>
<li><b>'<code>c</code>': </b> the hook is called every time Lua calls a function;</li>
<li><b>'<code>r</code>': </b> the hook is called every time Lua returns from a function;</li>
<li><b>'<code>l</code>': </b> the hook is called every time Lua enters a new line of code.</li>
</ul><p>
Moreover,
with a <code>count</code> different from zero,
the hook is called also after every <code>count</code> instructions.
<p>
When called without arguments,
<a href="#pdf-debug.sethook"><code>debug.sethook</code></a> turns off the hook.
<p>
When the hook is called, its first parameter is a string
describing the event that has triggered its call:
<code>"call"</code> (or <code>"tail call"</code>),
<code>"return"</code>,
<code>"line"</code>, and <code>"count"</code>.
For line events,
the hook also gets the new line number as its second parameter.
Inside a hook,
you can call <code>getinfo</code> with level 2 to get more information about
the running function
(level 0 is the <code>getinfo</code> function,
and level 1 is the hook function).
<p>
<hr><h3><a name="pdf-debug.setlocal"><code>debug.setlocal ([thread,] level, local, value)</code></a></h3>
<p>
This function assigns the value <code>value</code> to the local variable
with index <code>local</code> of the function at level <code>level</code> of the stack.
The function returns <b>nil</b> if there is no local
variable with the given index,
and raises an error when called with a <code>level</code> out of range.
(You can call <code>getinfo</code> to check whether the level is valid.)
Otherwise, it returns the name of the local variable.
<p>
See <a href="#pdf-debug.getlocal"><code>debug.getlocal</code></a> for more information about
variable indices and names.
<p>
<hr><h3><a name="pdf-debug.setmetatable"><code>debug.setmetatable (value, table)</code></a></h3>
<p>
Sets the metatable for the given <code>value</code> to the given <code>table</code>
(which can be <b>nil</b>).
Returns <code>value</code>.
<p>
<hr><h3><a name="pdf-debug.setupvalue"><code>debug.setupvalue (f, up, value)</code></a></h3>
<p>
This function assigns the value <code>value</code> to the upvalue
with index <code>up</code> of the function <code>f</code>.
The function returns <b>nil</b> if there is no upvalue
with the given index.
Otherwise, it returns the name of the upvalue.
<p>
<hr><h3><a name="pdf-debug.setuservalue"><code>debug.setuservalue (udata, value)</code></a></h3>
<p>
Sets the given <code>value</code> as
the Lua value associated to the given <code>udata</code>.
<code>udata</code> must be a full userdata.
<p>
Returns <code>udata</code>.
<p>
<hr><h3><a name="pdf-debug.traceback"><code>debug.traceback ([thread,] [message [, level]])</code></a></h3>
<p>
If <code>message</code> is present but is neither a string nor <b>nil</b>,
this function returns <code>message</code> without further processing.
Otherwise,
it returns a string with a traceback of the call stack.
The optional <code>message</code> string is appended
at the beginning of the traceback.
An optional <code>level</code> number tells at which level
to start the traceback
(default is 1, the function calling <code>traceback</code>).
<p>
<hr><h3><a name="pdf-debug.upvalueid"><code>debug.upvalueid (f, n)</code></a></h3>
<p>
Returns a unique identifier (as a light userdata)
for the upvalue numbered <code>n</code>
from the given function.
<p>
These unique identifiers allow a program to check whether different
closures share upvalues.
Lua closures that share an upvalue
(that is, that access a same external local variable)
will return identical ids for those upvalue indices.
<p>
<hr><h3><a name="pdf-debug.upvaluejoin"><code>debug.upvaluejoin (f1, n1, f2, n2)</code></a></h3>
<p>
Make the <code>n1</code>-th upvalue of the Lua closure <code>f1</code>
refer to the <code>n2</code>-th upvalue of the Lua closure <code>f2</code>.
<h1>7 – <a name="7">Lua Standalone</a></h1>
<p>
Although Lua has been designed as an extension language,
to be embedded in a host C program,
it is also frequently used as a standalone language.
An interpreter for Lua as a standalone language,
called simply <code>lua</code>,
is provided with the standard distribution.
The standalone interpreter includes
all standard libraries, including the debug library.
Its usage is:
<pre>
lua [options] [script [args]]
</pre><p>
The options are:
<ul>
<li><b><code>-e <em>stat</em></code>: </b> executes string <em>stat</em>;</li>
<li><b><code>-l <em>mod</em></code>: </b> "requires" <em>mod</em>;</li>
<li><b><code>-i</code>: </b> enters interactive mode after running <em>script</em>;</li>
<li><b><code>-v</code>: </b> prints version information;</li>
<li><b><code>-E</code>: </b> ignores environment variables;</li>
<li><b><code>--</code>: </b> stops handling options;</li>
<li><b><code>-</code>: </b> executes <code>stdin</code> as a file and stops handling options.</li>
</ul><p>
After handling its options, <code>lua</code> runs the given <em>script</em>.
When called without arguments,
<code>lua</code> behaves as <code>lua -v -i</code>
when the standard input (<code>stdin</code>) is a terminal,
and as <code>lua -</code> otherwise.
<p>
When called without option <code>-E</code>,
the interpreter checks for an environment variable <a name="pdf-LUA_INIT_5_3"><code>LUA_INIT_5_3</code></a>
(or <a name="pdf-LUA_INIT"><code>LUA_INIT</code></a> if the versioned name is not defined)
before running any argument.
If the variable content has the format <code>@<em>filename</em></code>,
then <code>lua</code> executes the file.
Otherwise, <code>lua</code> executes the string itself.
<p>
When called with option <code>-E</code>,
besides ignoring <code>LUA_INIT</code>,
Lua also ignores
the values of <code>LUA_PATH</code> and <code>LUA_CPATH</code>,
setting the values of
<a href="#pdf-package.path"><code>package.path</code></a> and <a href="#pdf-package.cpath"><code>package.cpath</code></a>
with the default paths defined in <code>luaconf.h</code>.
<p>
All options are handled in order, except <code>-i</code> and <code>-E</code>.
For instance, an invocation like
<pre>
$ lua -e'a=1' -e 'print(a)' script.lua
</pre><p>
will first set <code>a</code> to 1, then print the value of <code>a</code>,
and finally run the file <code>script.lua</code> with no arguments.
(Here <code>$</code> is the shell prompt. Your prompt may be different.)
<p>
Before running any code,
<code>lua</code> collects all command-line arguments
in a global table called <code>arg</code>.
The script name goes to index 0,
the first argument after the script name goes to index 1,
and so on.
Any arguments before the script name
(that is, the interpreter name plus its options)
go to negative indices.
For instance, in the call
<pre>
$ lua -la b.lua t1 t2
</pre><p>
the table is like this:
<pre>
arg = { [-2] = "lua", [-1] = "-la",
[0] = "b.lua",
[1] = "t1", [2] = "t2" }
</pre><p>
If there is no script in the call,
the interpreter name goes to index 0,
followed by the other arguments.
For instance, the call
<pre>
$ lua -e "print(arg[1])"
</pre><p>
will print "<code>-e</code>".
If there is a script,
the script is called with parameters
<code>arg[1]</code>, ···, <code>arg[#arg]</code>.
(Like all chunks in Lua,
the script is compiled as a vararg function.)
<p>
In interactive mode,
Lua repeatedly prompts and waits for a line.
After reading a line,
Lua first try to interpret the line as an expression.
If it succeeds, it prints its value.
Otherwise, it interprets the line as a statement.
If you write an incomplete statement,
the interpreter waits for its completion
by issuing a different prompt.
<p>
If the global variable <a name="pdf-_PROMPT"><code>_PROMPT</code></a> contains a string,
then its value is used as the prompt.
Similarly, if the global variable <a name="pdf-_PROMPT2"><code>_PROMPT2</code></a> contains a string,
its value is used as the secondary prompt
(issued during incomplete statements).
<p>
In case of unprotected errors in the script,
the interpreter reports the error to the standard error stream.
If the error object is not a string but
has a metamethod <code>__tostring</code>,
the interpreter calls this metamethod to produce the final message.
Otherwise, the interpreter converts the error object to a string
and adds a stack traceback to it.
<p>
When finishing normally,
the interpreter closes its main Lua state
(see <a href="#lua_close"><code>lua_close</code></a>).
The script can avoid this step by
calling <a href="#pdf-os.exit"><code>os.exit</code></a> to terminate.
<p>
To allow the use of Lua as a
script interpreter in Unix systems,
the standalone interpreter skips
the first line of a chunk if it starts with <code>#</code>.
Therefore, Lua scripts can be made into executable programs
by using <code>chmod +x</code> and the <code>#!</code> form,
as in
<pre>
#!/usr/local/bin/lua
</pre><p>
(Of course,
the location of the Lua interpreter may be different in your machine.
If <code>lua</code> is in your <code>PATH</code>,
then
<pre>
#!/usr/bin/env lua
</pre><p>
is a more portable solution.)
<h1>8 – <a name="8">Incompatibilities with the Previous Version</a></h1>
<p>
Here we list the incompatibilities that you may find when moving a program
from Lua 5.2 to Lua 5.3.
You can avoid some incompatibilities by compiling Lua with
appropriate options (see file <code>luaconf.h</code>).
However,
all these compatibility options will be removed in the future.
<p>
Lua versions can always change the C API in ways that
do not imply source-code changes in a program,
such as the numeric values for constants
or the implementation of functions as macros.
Therefore,
you should not assume that binaries are compatible between
different Lua versions.
Always recompile clients of the Lua API when
using a new version.
<p>
Similarly, Lua versions can always change the internal representation
of precompiled chunks;
precompiled chunks are not compatible between different Lua versions.
<p>
The standard paths in the official distribution may
change between versions.
<h2>8.1 – <a name="8.1">Changes in the Language</a></h2>
<ul>
<li>
The main difference between Lua 5.2 and Lua 5.3 is the
introduction of an integer subtype for numbers.
Although this change should not affect "normal" computations,
some computations
(mainly those that involve some kind of overflow)
can give different results.
<p>
You can fix these differences by forcing a number to be a float
(in Lua 5.2 all numbers were float),
in particular writing constants with an ending <code>.0</code>
or using <code>x = x + 0.0</code> to convert a variable.
(This recommendation is only for a quick fix
for an occasional incompatibility;
it is not a general guideline for good programming.
For good programming,
use floats where you need floats
and integers where you need integers.)
</li>
<li>
The conversion of a float to a string now adds a <code>.0</code> suffix
to the result if it looks like an integer.
(For instance, the float 2.0 will be printed as <code>2.0</code>,
not as <code>2</code>.)
You should always use an explicit format
when you need a specific format for numbers.
<p>
(Formally this is not an incompatibility,
because Lua does not specify how numbers are formatted as strings,
but some programs assumed a specific format.)
</li>
<li>
The generational mode for the garbage collector was removed.
(It was an experimental feature in Lua 5.2.)
</li>
</ul>
<h2>8.2 – <a name="8.2">Changes in the Libraries</a></h2>
<ul>
<li>
The <code>bit32</code> library has been deprecated.
It is easy to require a compatible external library or,
better yet, to replace its functions with appropriate bitwise operations.
(Keep in mind that <code>bit32</code> operates on 32-bit integers,
while the bitwise operators in Lua 5.3 operate on Lua integers,
which by default have 64 bits.)
</li>
<li>
The Table library now respects metamethods
for setting and getting elements.
</li>
<li>
The <a href="#pdf-ipairs"><code>ipairs</code></a> iterator now respects metamethods and
its <code>__ipairs</code> metamethod has been deprecated.
</li>
<li>
Option names in <a href="#pdf-io.read"><code>io.read</code></a> do not have a starting '<code>*</code>' anymore.
For compatibility, Lua will continue to accept (and ignore) this character.
</li>
<li>
The following functions were deprecated in the mathematical library:
<code>atan2</code>, <code>cosh</code>, <code>sinh</code>, <code>tanh</code>, <code>pow</code>,
<code>frexp</code>, and <code>ldexp</code>.
You can replace <code>math.pow(x,y)</code> with <code>x^y</code>;
you can replace <code>math.atan2</code> with <code>math.atan</code>,
which now accepts one or two parameters;
you can replace <code>math.ldexp(x,exp)</code> with <code>x * 2.0^exp</code>.
For the other operations,
you can either use an external library or
implement them in Lua.
</li>
<li>
The searcher for C loaders used by <a href="#pdf-require"><code>require</code></a>
changed the way it handles versioned names.
Now, the version should come after the module name
(as is usual in most other tools).
For compatibility, that searcher still tries the old format
if it cannot find an open function according to the new style.
(Lua 5.2 already worked that way,
but it did not document the change.)
</li>
<li>
The call <code>collectgarbage("count")</code> now returns only one result.
(You can compute that second result from the fractional part
of the first result.)
</li>
</ul>
<h2>8.3 – <a name="8.3">Changes in the API</a></h2>
<ul>
<li>
Continuation functions now receive as parameters what they needed
to get through <code>lua_getctx</code>,
so <code>lua_getctx</code> has been removed.
Adapt your code accordingly.
</li>
<li>
Function <a href="#lua_dump"><code>lua_dump</code></a> has an extra parameter, <code>strip</code>.
Use 0 as the value of this parameter to get the old behavior.
</li>
<li>
Functions to inject/project unsigned integers
(<code>lua_pushunsigned</code>, <code>lua_tounsigned</code>, <code>lua_tounsignedx</code>,
<code>luaL_checkunsigned</code>, <code>luaL_optunsigned</code>)
were deprecated.
Use their signed equivalents with a type cast.
</li>
<li>
Macros to project non-default integer types
(<code>luaL_checkint</code>, <code>luaL_optint</code>, <code>luaL_checklong</code>, <code>luaL_optlong</code>)
were deprecated.
Use their equivalent over <a href="#lua_Integer"><code>lua_Integer</code></a> with a type cast
(or, when possible, use <a href="#lua_Integer"><code>lua_Integer</code></a> in your code).
</li>
</ul>
<h1>9 – <a name="9">The Complete Syntax of Lua</a></h1>
<p>
Here is the complete syntax of Lua in extended BNF.
As usual in extended BNF,
{A} means 0 or more As,
and [A] means an optional A.
(For operator precedences, see <a href="#3.4.8">§3.4.8</a>;
for a description of the terminals
Name, Numeral,
and LiteralString, see <a href="#3.1">§3.1</a>.)
<pre>
chunk ::= block
block ::= {stat} [retstat]
stat ::= ‘<b>;</b>’ |
varlist ‘<b>=</b>’ explist |
functioncall |
label |
<b>break</b> |
<b>goto</b> Name |
<b>do</b> block <b>end</b> |
<b>while</b> exp <b>do</b> block <b>end</b> |
<b>repeat</b> block <b>until</b> exp |
<b>if</b> exp <b>then</b> block {<b>elseif</b> exp <b>then</b> block} [<b>else</b> block] <b>end</b> |
<b>for</b> Name ‘<b>=</b>’ exp ‘<b>,</b>’ exp [‘<b>,</b>’ exp] <b>do</b> block <b>end</b> |
<b>for</b> namelist <b>in</b> explist <b>do</b> block <b>end</b> |
<b>function</b> funcname funcbody |
<b>local</b> <b>function</b> Name funcbody |
<b>local</b> namelist [‘<b>=</b>’ explist]
retstat ::= <b>return</b> [explist] [‘<b>;</b>’]
label ::= ‘<b>::</b>’ Name ‘<b>::</b>’
funcname ::= Name {‘<b>.</b>’ Name} [‘<b>:</b>’ Name]
varlist ::= var {‘<b>,</b>’ var}
var ::= Name | prefixexp ‘<b>[</b>’ exp ‘<b>]</b>’ | prefixexp ‘<b>.</b>’ Name
namelist ::= Name {‘<b>,</b>’ Name}
explist ::= exp {‘<b>,</b>’ exp}
exp ::= <b>nil</b> | <b>false</b> | <b>true</b> | Numeral | LiteralString | ‘<b>...</b>’ | functiondef |
prefixexp | tableconstructor | exp binop exp | unop exp
prefixexp ::= var | functioncall | ‘<b>(</b>’ exp ‘<b>)</b>’
functioncall ::= prefixexp args | prefixexp ‘<b>:</b>’ Name args
args ::= ‘<b>(</b>’ [explist] ‘<b>)</b>’ | tableconstructor | LiteralString
functiondef ::= <b>function</b> funcbody
funcbody ::= ‘<b>(</b>’ [parlist] ‘<b>)</b>’ block <b>end</b>
parlist ::= namelist [‘<b>,</b>’ ‘<b>...</b>’] | ‘<b>...</b>’
tableconstructor ::= ‘<b>{</b>’ [fieldlist] ‘<b>}</b>’
fieldlist ::= field {fieldsep field} [fieldsep]
field ::= ‘<b>[</b>’ exp ‘<b>]</b>’ ‘<b>=</b>’ exp | Name ‘<b>=</b>’ exp | exp
fieldsep ::= ‘<b>,</b>’ | ‘<b>;</b>’
binop ::= ‘<b>+</b>’ | ‘<b>-</b>’ | ‘<b>*</b>’ | ‘<b>/</b>’ | ‘<b>//</b>’ | ‘<b>^</b>’ | ‘<b>%</b>’ |
‘<b>&</b>’ | ‘<b>~</b>’ | ‘<b>|</b>’ | ‘<b>>></b>’ | ‘<b><<</b>’ | ‘<b>..</b>’ |
‘<b><</b>’ | ‘<b><=</b>’ | ‘<b>></b>’ | ‘<b>>=</b>’ | ‘<b>==</b>’ | ‘<b>~=</b>’ |
<b>and</b> | <b>or</b>
unop ::= ‘<b>-</b>’ | <b>not</b> | ‘<b>#</b>’ | ‘<b>~</b>’
</pre>
<p>
<P CLASS="footer">
Last update:
Mon May 30 13:11:08 BRT 2016
</P>
<!--
Last change: revised for Lua 5.3.3
-->
</body></html>
|
