SQLite

func.c at [4b286129]
Login

File src/func.c artifact c65447d6 part of check-in 4b286129


     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
/*
** 2002 February 23
**
** The author disclaims copyright to this source code.  In place of
** a legal notice, here is a blessing:
**
**    May you do good and not evil.
**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** This file contains the C-language implementations for many of the SQL
** functions of SQLite.  (Some function, and in particular the date and
** time functions, are implemented separately.)
*/
#include "sqliteInt.h"
#include <stdlib.h>
#include <assert.h>
#ifndef SQLITE_OMIT_FLOATING_POINT
#include <math.h>
#endif
#include "vdbeInt.h"

/*
** Return the collating function associated with a function.
*/
static CollSeq *sqlite3GetFuncCollSeq(sqlite3_context *context){
  VdbeOp *pOp;
  assert( context->pVdbe!=0 );
  pOp = &context->pVdbe->aOp[context->iOp-1];
  assert( pOp->opcode==OP_CollSeq );
  assert( pOp->p4type==P4_COLLSEQ );
  return pOp->p4.pColl;
}

/*
** Indicate that the accumulator load should be skipped on this
** iteration of the aggregate loop.
*/
static void sqlite3SkipAccumulatorLoad(sqlite3_context *context){
  assert( context->isError<=0 );
  context->isError = -1;
  context->skipFlag = 1;
}

/*
** Implementation of the non-aggregate min() and max() functions
*/
static void minmaxFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  int i;
  int mask;    /* 0 for min() or 0xffffffff for max() */
  int iBest;
  CollSeq *pColl;

  assert( argc>1 );
  mask = sqlite3_user_data(context)==0 ? 0 : -1;
  pColl = sqlite3GetFuncCollSeq(context);
  assert( pColl );
  assert( mask==-1 || mask==0 );
  iBest = 0;
  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;
  for(i=1; i<argc; i++){
    if( sqlite3_value_type(argv[i])==SQLITE_NULL ) return;
    if( (sqlite3MemCompare(argv[iBest], argv[i], pColl)^mask)>=0 ){
      testcase( mask==0 );
      iBest = i;
    }
  }
  sqlite3_result_value(context, argv[iBest]);
}

/*
** Return the type of the argument.
*/
static void typeofFunc(
  sqlite3_context *context,
  int NotUsed,
  sqlite3_value **argv
){
  static const char *azType[] = { "integer", "real", "text", "blob", "null" };
  int i = sqlite3_value_type(argv[0]) - 1;
  UNUSED_PARAMETER(NotUsed);
  assert( i>=0 && i<ArraySize(azType) );
  assert( SQLITE_INTEGER==1 );
  assert( SQLITE_FLOAT==2 );
  assert( SQLITE_TEXT==3 );
  assert( SQLITE_BLOB==4 );
  assert( SQLITE_NULL==5 );
  /* EVIDENCE-OF: R-01470-60482 The sqlite3_value_type(V) interface returns
  ** the datatype code for the initial datatype of the sqlite3_value object
  ** V. The returned value is one of SQLITE_INTEGER, SQLITE_FLOAT,
  ** SQLITE_TEXT, SQLITE_BLOB, or SQLITE_NULL. */
  sqlite3_result_text(context, azType[i], -1, SQLITE_STATIC);
}


/*
** Implementation of the length() function
*/
static void lengthFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  switch( sqlite3_value_type(argv[0]) ){
    case SQLITE_BLOB:
    case SQLITE_INTEGER:
    case SQLITE_FLOAT: {
      sqlite3_result_int(context, sqlite3_value_bytes(argv[0]));
      break;
    }
    case SQLITE_TEXT: {
      const unsigned char *z = sqlite3_value_text(argv[0]);
      const unsigned char *z0;
      unsigned char c;
      if( z==0 ) return;
      z0 = z;
      while( (c = *z)!=0 ){
        z++;
        if( c>=0xc0 ){
          while( (*z & 0xc0)==0x80 ){ z++; z0++; }
        }
      }
      sqlite3_result_int(context, (int)(z-z0));
      break;
    }
    default: {
      sqlite3_result_null(context);
      break;
    }
  }
}

/*
** Implementation of the abs() function.
**
** IMP: R-23979-26855 The abs(X) function returns the absolute value of
** the numeric argument X. 
*/
static void absFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  switch( sqlite3_value_type(argv[0]) ){
    case SQLITE_INTEGER: {
      i64 iVal = sqlite3_value_int64(argv[0]);
      if( iVal<0 ){
        if( iVal==SMALLEST_INT64 ){
          /* IMP: R-31676-45509 If X is the integer -9223372036854775808
          ** then abs(X) throws an integer overflow error since there is no
          ** equivalent positive 64-bit two complement value. */
          sqlite3_result_error(context, "integer overflow", -1);
          return;
        }
        iVal = -iVal;
      } 
      sqlite3_result_int64(context, iVal);
      break;
    }
    case SQLITE_NULL: {
      /* IMP: R-37434-19929 Abs(X) returns NULL if X is NULL. */
      sqlite3_result_null(context);
      break;
    }
    default: {
      /* Because sqlite3_value_double() returns 0.0 if the argument is not
      ** something that can be converted into a number, we have:
      ** IMP: R-01992-00519 Abs(X) returns 0.0 if X is a string or blob
      ** that cannot be converted to a numeric value.
      */
      double rVal = sqlite3_value_double(argv[0]);
      if( rVal<0 ) rVal = -rVal;
      sqlite3_result_double(context, rVal);
      break;
    }
  }
}

/*
** Implementation of the instr() function.
**
** instr(haystack,needle) finds the first occurrence of needle
** in haystack and returns the number of previous characters plus 1,
** or 0 if needle does not occur within haystack.
**
** If both haystack and needle are BLOBs, then the result is one more than
** the number of bytes in haystack prior to the first occurrence of needle,
** or 0 if needle never occurs in haystack.
*/
static void instrFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  const unsigned char *zHaystack;
  const unsigned char *zNeedle;
  int nHaystack;
  int nNeedle;
  int typeHaystack, typeNeedle;
  int N = 1;
  int isText;
  unsigned char firstChar;
  sqlite3_value *pC1 = 0;
  sqlite3_value *pC2 = 0;

  UNUSED_PARAMETER(argc);
  typeHaystack = sqlite3_value_type(argv[0]);
  typeNeedle = sqlite3_value_type(argv[1]);
  if( typeHaystack==SQLITE_NULL || typeNeedle==SQLITE_NULL ) return;
  nHaystack = sqlite3_value_bytes(argv[0]);
  nNeedle = sqlite3_value_bytes(argv[1]);
  if( nNeedle>0 ){
    if( typeHaystack==SQLITE_BLOB && typeNeedle==SQLITE_BLOB ){
      zHaystack = sqlite3_value_blob(argv[0]);
      zNeedle = sqlite3_value_blob(argv[1]);
      isText = 0;
    }else if( typeHaystack!=SQLITE_BLOB && typeNeedle!=SQLITE_BLOB ){
      zHaystack = sqlite3_value_text(argv[0]);
      zNeedle = sqlite3_value_text(argv[1]);
      isText = 1;
    }else{
      pC1 = sqlite3_value_dup(argv[0]);
      zHaystack = sqlite3_value_text(pC1);
      if( zHaystack==0 ) goto endInstrOOM;
      nHaystack = sqlite3_value_bytes(pC1);
      pC2 = sqlite3_value_dup(argv[1]);
      zNeedle = sqlite3_value_text(pC2);
      if( zNeedle==0 ) goto endInstrOOM;
      nNeedle = sqlite3_value_bytes(pC2);
      isText = 1;
    }
    if( zNeedle==0 || (nHaystack && zHaystack==0) ) goto endInstrOOM;
    firstChar = zNeedle[0];
    while( nNeedle<=nHaystack
       && (zHaystack[0]!=firstChar || memcmp(zHaystack, zNeedle, nNeedle)!=0)
    ){
      N++;
      do{
        nHaystack--;
        zHaystack++;
      }while( isText && (zHaystack[0]&0xc0)==0x80 );
    }
    if( nNeedle>nHaystack ) N = 0;
  }
  sqlite3_result_int(context, N);
endInstr:
  sqlite3_value_free(pC1);
  sqlite3_value_free(pC2);
  return;
endInstrOOM:
  sqlite3_result_error_nomem(context);
  goto endInstr;
}

/*
** Implementation of the printf() function.
*/
static void printfFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  PrintfArguments x;
  StrAccum str;
  const char *zFormat;
  int n;
  sqlite3 *db = sqlite3_context_db_handle(context);

  if( argc>=1 && (zFormat = (const char*)sqlite3_value_text(argv[0]))!=0 ){
    x.nArg = argc-1;
    x.nUsed = 0;
    x.apArg = argv+1;
    sqlite3StrAccumInit(&str, db, 0, 0, db->aLimit[SQLITE_LIMIT_LENGTH]);
    str.printfFlags = SQLITE_PRINTF_SQLFUNC;
    sqlite3_str_appendf(&str, zFormat, &x);
    n = str.nChar;
    sqlite3_result_text(context, sqlite3StrAccumFinish(&str), n,
                        SQLITE_DYNAMIC);
  }
}

/*
** Implementation of the substr() function.
**
** substr(x,p1,p2)  returns p2 characters of x[] beginning with p1.
** p1 is 1-indexed.  So substr(x,1,1) returns the first character
** of x.  If x is text, then we actually count UTF-8 characters.
** If x is a blob, then we count bytes.
**
** If p1 is negative, then we begin abs(p1) from the end of x[].
**
** If p2 is negative, return the p2 characters preceding p1.
*/
static void substrFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  const unsigned char *z;
  const unsigned char *z2;
  int len;
  int p0type;
  i64 p1, p2;
  int negP2 = 0;

  assert( argc==3 || argc==2 );
  if( sqlite3_value_type(argv[1])==SQLITE_NULL
   || (argc==3 && sqlite3_value_type(argv[2])==SQLITE_NULL)
  ){
    return;
  }
  p0type = sqlite3_value_type(argv[0]);
  p1 = sqlite3_value_int(argv[1]);
  if( p0type==SQLITE_BLOB ){
    len = sqlite3_value_bytes(argv[0]);
    z = sqlite3_value_blob(argv[0]);
    if( z==0 ) return;
    assert( len==sqlite3_value_bytes(argv[0]) );
  }else{
    z = sqlite3_value_text(argv[0]);
    if( z==0 ) return;
    len = 0;
    if( p1<0 ){
      for(z2=z; *z2; len++){
        SQLITE_SKIP_UTF8(z2);
      }
    }
  }
#ifdef SQLITE_SUBSTR_COMPATIBILITY
  /* If SUBSTR_COMPATIBILITY is defined then substr(X,0,N) work the same as
  ** as substr(X,1,N) - it returns the first N characters of X.  This
  ** is essentially a back-out of the bug-fix in check-in [5fc125d362df4b8]
  ** from 2009-02-02 for compatibility of applications that exploited the
  ** old buggy behavior. */
  if( p1==0 ) p1 = 1; /* <rdar://problem/6778339> */
#endif
  if( argc==3 ){
    p2 = sqlite3_value_int(argv[2]);
    if( p2<0 ){
      p2 = -p2;
      negP2 = 1;
    }
  }else{
    p2 = sqlite3_context_db_handle(context)->aLimit[SQLITE_LIMIT_LENGTH];
  }
  if( p1<0 ){
    p1 += len;
    if( p1<0 ){
      p2 += p1;
      if( p2<0 ) p2 = 0;
      p1 = 0;
    }
  }else if( p1>0 ){
    p1--;
  }else if( p2>0 ){
    p2--;
  }
  if( negP2 ){
    p1 -= p2;
    if( p1<0 ){
      p2 += p1;
      p1 = 0;
    }
  }
  assert( p1>=0 && p2>=0 );
  if( p0type!=SQLITE_BLOB ){
    while( *z && p1 ){
      SQLITE_SKIP_UTF8(z);
      p1--;
    }
    for(z2=z; *z2 && p2; p2--){
      SQLITE_SKIP_UTF8(z2);
    }
    sqlite3_result_text64(context, (char*)z, z2-z, SQLITE_TRANSIENT,
                          SQLITE_UTF8);
  }else{
    if( p1+p2>len ){
      p2 = len-p1;
      if( p2<0 ) p2 = 0;
    }
    sqlite3_result_blob64(context, (char*)&z[p1], (u64)p2, SQLITE_TRANSIENT);
  }
}

/*
** Implementation of the round() function
*/
#ifndef SQLITE_OMIT_FLOATING_POINT
static void roundFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  int n = 0;
  double r;
  char *zBuf;
  assert( argc==1 || argc==2 );
  if( argc==2 ){
    if( SQLITE_NULL==sqlite3_value_type(argv[1]) ) return;
    n = sqlite3_value_int(argv[1]);
    if( n>30 ) n = 30;
    if( n<0 ) n = 0;
  }
  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;
  r = sqlite3_value_double(argv[0]);
  /* If Y==0 and X will fit in a 64-bit int,
  ** handle the rounding directly,
  ** otherwise use printf.
  */
  if( r<-4503599627370496.0 || r>+4503599627370496.0 ){
    /* The value has no fractional part so there is nothing to round */
  }else if( n==0 ){  
    r = (double)((sqlite_int64)(r+(r<0?-0.5:+0.5)));
  }else{
    zBuf = sqlite3_mprintf("%.*f",n,r);
    if( zBuf==0 ){
      sqlite3_result_error_nomem(context);
      return;
    }
    sqlite3AtoF(zBuf, &r, sqlite3Strlen30(zBuf), SQLITE_UTF8);
    sqlite3_free(zBuf);
  }
  sqlite3_result_double(context, r);
}
#endif

/*
** Allocate nByte bytes of space using sqlite3Malloc(). If the
** allocation fails, call sqlite3_result_error_nomem() to notify
** the database handle that malloc() has failed and return NULL.
** If nByte is larger than the maximum string or blob length, then
** raise an SQLITE_TOOBIG exception and return NULL.
*/
static void *contextMalloc(sqlite3_context *context, i64 nByte){
  char *z;
  sqlite3 *db = sqlite3_context_db_handle(context);
  assert( nByte>0 );
  testcase( nByte==db->aLimit[SQLITE_LIMIT_LENGTH] );
  testcase( nByte==db->aLimit[SQLITE_LIMIT_LENGTH]+1 );
  if( nByte>db->aLimit[SQLITE_LIMIT_LENGTH] ){
    sqlite3_result_error_toobig(context);
    z = 0;
  }else{
    z = sqlite3Malloc(nByte);
    if( !z ){
      sqlite3_result_error_nomem(context);
    }
  }
  return z;
}

/*
** Implementation of the upper() and lower() SQL functions.
*/
static void upperFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  char *z1;
  const char *z2;
  int i, n;
  UNUSED_PARAMETER(argc);
  z2 = (char*)sqlite3_value_text(argv[0]);
  n = sqlite3_value_bytes(argv[0]);
  /* Verify that the call to _bytes() does not invalidate the _text() pointer */
  assert( z2==(char*)sqlite3_value_text(argv[0]) );
  if( z2 ){
    z1 = contextMalloc(context, ((i64)n)+1);
    if( z1 ){
      for(i=0; i<n; i++){
        z1[i] = (char)sqlite3Toupper(z2[i]);
      }
      sqlite3_result_text(context, z1, n, sqlite3_free);
    }
  }
}
static void lowerFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  char *z1;
  const char *z2;
  int i, n;
  UNUSED_PARAMETER(argc);
  z2 = (char*)sqlite3_value_text(argv[0]);
  n = sqlite3_value_bytes(argv[0]);
  /* Verify that the call to _bytes() does not invalidate the _text() pointer */
  assert( z2==(char*)sqlite3_value_text(argv[0]) );
  if( z2 ){
    z1 = contextMalloc(context, ((i64)n)+1);
    if( z1 ){
      for(i=0; i<n; i++){
        z1[i] = sqlite3Tolower(z2[i]);
      }
      sqlite3_result_text(context, z1, n, sqlite3_free);
    }
  }
}

/*
** Some functions like COALESCE() and IFNULL() and UNLIKELY() are implemented
** as VDBE code so that unused argument values do not have to be computed.
** However, we still need some kind of function implementation for this
** routines in the function table.  The noopFunc macro provides this.
** noopFunc will never be called so it doesn't matter what the implementation
** is.  We might as well use the "version()" function as a substitute.
*/
#define noopFunc versionFunc   /* Substitute function - never called */

/*
** Implementation of random().  Return a random integer.  
*/
static void randomFunc(
  sqlite3_context *context,
  int NotUsed,
  sqlite3_value **NotUsed2
){
  sqlite_int64 r;
  UNUSED_PARAMETER2(NotUsed, NotUsed2);
  sqlite3_randomness(sizeof(r), &r);
  if( r<0 ){
    /* We need to prevent a random number of 0x8000000000000000 
    ** (or -9223372036854775808) since when you do abs() of that
    ** number of you get the same value back again.  To do this
    ** in a way that is testable, mask the sign bit off of negative
    ** values, resulting in a positive value.  Then take the 
    ** 2s complement of that positive value.  The end result can
    ** therefore be no less than -9223372036854775807.
    */
    r = -(r & LARGEST_INT64);
  }
  sqlite3_result_int64(context, r);
}

/*
** Implementation of randomblob(N).  Return a random blob
** that is N bytes long.
*/
static void randomBlob(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  sqlite3_int64 n;
  unsigned char *p;
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  n = sqlite3_value_int64(argv[0]);
  if( n<1 ){
    n = 1;
  }
  p = contextMalloc(context, n);
  if( p ){
    sqlite3_randomness(n, p);
    sqlite3_result_blob(context, (char*)p, n, sqlite3_free);
  }
}

/*
** Implementation of the last_insert_rowid() SQL function.  The return
** value is the same as the sqlite3_last_insert_rowid() API function.
*/
static void last_insert_rowid(
  sqlite3_context *context, 
  int NotUsed, 
  sqlite3_value **NotUsed2
){
  sqlite3 *db = sqlite3_context_db_handle(context);
  UNUSED_PARAMETER2(NotUsed, NotUsed2);
  /* IMP: R-51513-12026 The last_insert_rowid() SQL function is a
  ** wrapper around the sqlite3_last_insert_rowid() C/C++ interface
  ** function. */
  sqlite3_result_int64(context, sqlite3_last_insert_rowid(db));
}

/*
** Implementation of the changes() SQL function.
**
** IMP: R-62073-11209 The changes() SQL function is a wrapper
** around the sqlite3_changes() C/C++ function and hence follows the same
** rules for counting changes.
*/
static void changes(
  sqlite3_context *context,
  int NotUsed,
  sqlite3_value **NotUsed2
){
  sqlite3 *db = sqlite3_context_db_handle(context);
  UNUSED_PARAMETER2(NotUsed, NotUsed2);
  sqlite3_result_int(context, sqlite3_changes(db));
}

/*
** Implementation of the total_changes() SQL function.  The return value is
** the same as the sqlite3_total_changes() API function.
*/
static void total_changes(
  sqlite3_context *context,
  int NotUsed,
  sqlite3_value **NotUsed2
){
  sqlite3 *db = sqlite3_context_db_handle(context);
  UNUSED_PARAMETER2(NotUsed, NotUsed2);
  /* IMP: R-52756-41993 This function is a wrapper around the
  ** sqlite3_total_changes() C/C++ interface. */
  sqlite3_result_int(context, sqlite3_total_changes(db));
}

/*
** A structure defining how to do GLOB-style comparisons.
*/
struct compareInfo {
  u8 matchAll;          /* "*" or "%" */
  u8 matchOne;          /* "?" or "_" */
  u8 matchSet;          /* "[" or 0 */
  u8 noCase;            /* true to ignore case differences */
};

/*
** For LIKE and GLOB matching on EBCDIC machines, assume that every
** character is exactly one byte in size.  Also, provde the Utf8Read()
** macro for fast reading of the next character in the common case where
** the next character is ASCII.
*/
#if defined(SQLITE_EBCDIC)
# define sqlite3Utf8Read(A)        (*((*A)++))
# define Utf8Read(A)               (*(A++))
#else
# define Utf8Read(A)               (A[0]<0x80?*(A++):sqlite3Utf8Read(&A))
#endif

static const struct compareInfo globInfo = { '*', '?', '[', 0 };
/* The correct SQL-92 behavior is for the LIKE operator to ignore
** case.  Thus  'a' LIKE 'A' would be true. */
static const struct compareInfo likeInfoNorm = { '%', '_',   0, 1 };
/* If SQLITE_CASE_SENSITIVE_LIKE is defined, then the LIKE operator
** is case sensitive causing 'a' LIKE 'A' to be false */
static const struct compareInfo likeInfoAlt = { '%', '_',   0, 0 };

/*
** Possible error returns from patternMatch()
*/
#define SQLITE_MATCH             0
#define SQLITE_NOMATCH           1
#define SQLITE_NOWILDCARDMATCH   2

/*
** Compare two UTF-8 strings for equality where the first string is
** a GLOB or LIKE expression.  Return values:
**
**    SQLITE_MATCH:            Match
**    SQLITE_NOMATCH:          No match
**    SQLITE_NOWILDCARDMATCH:  No match in spite of having * or % wildcards.
**
** Globbing rules:
**
**      '*'       Matches any sequence of zero or more characters.
**
**      '?'       Matches exactly one character.
**
**     [...]      Matches one character from the enclosed list of
**                characters.
**
**     [^...]     Matches one character not in the enclosed list.
**
** With the [...] and [^...] matching, a ']' character can be included
** in the list by making it the first character after '[' or '^'.  A
** range of characters can be specified using '-'.  Example:
** "[a-z]" matches any single lower-case letter.  To match a '-', make
** it the last character in the list.
**
** Like matching rules:
** 
**      '%'       Matches any sequence of zero or more characters
**
***     '_'       Matches any one character
**
**      Ec        Where E is the "esc" character and c is any other
**                character, including '%', '_', and esc, match exactly c.
**
** The comments within this routine usually assume glob matching.
**
** This routine is usually quick, but can be N**2 in the worst case.
*/
static int patternCompare(
  const u8 *zPattern,              /* The glob pattern */
  const u8 *zString,               /* The string to compare against the glob */
  const struct compareInfo *pInfo, /* Information about how to do the compare */
  u32 matchOther                   /* The escape char (LIKE) or '[' (GLOB) */
){
  u32 c, c2;                       /* Next pattern and input string chars */
  u32 matchOne = pInfo->matchOne;  /* "?" or "_" */
  u32 matchAll = pInfo->matchAll;  /* "*" or "%" */
  u8 noCase = pInfo->noCase;       /* True if uppercase==lowercase */
  const u8 *zEscaped = 0;          /* One past the last escaped input char */
  
  while( (c = Utf8Read(zPattern))!=0 ){
    if( c==matchAll ){  /* Match "*" */
      /* Skip over multiple "*" characters in the pattern.  If there
      ** are also "?" characters, skip those as well, but consume a
      ** single character of the input string for each "?" skipped */
      while( (c=Utf8Read(zPattern)) == matchAll || c == matchOne ){
        if( c==matchOne && sqlite3Utf8Read(&zString)==0 ){
          return SQLITE_NOWILDCARDMATCH;
        }
      }
      if( c==0 ){
        return SQLITE_MATCH;   /* "*" at the end of the pattern matches */
      }else if( c==matchOther ){
        if( pInfo->matchSet==0 ){
          c = sqlite3Utf8Read(&zPattern);
          if( c==0 ) return SQLITE_NOWILDCARDMATCH;
        }else{
          /* "[...]" immediately follows the "*".  We have to do a slow
          ** recursive search in this case, but it is an unusual case. */
          assert( matchOther<0x80 );  /* '[' is a single-byte character */
          while( *zString ){
            int bMatch = patternCompare(&zPattern[-1],zString,pInfo,matchOther);
            if( bMatch!=SQLITE_NOMATCH ) return bMatch;
            SQLITE_SKIP_UTF8(zString);
          }
          return SQLITE_NOWILDCARDMATCH;
        }
      }

      /* At this point variable c contains the first character of the
      ** pattern string past the "*".  Search in the input string for the
      ** first matching character and recursively continue the match from
      ** that point.
      **
      ** For a case-insensitive search, set variable cx to be the same as
      ** c but in the other case and search the input string for either
      ** c or cx.
      */
      if( c<=0x80 ){
        char zStop[3];
        int bMatch;
        if( noCase ){
          zStop[0] = sqlite3Toupper(c);
          zStop[1] = sqlite3Tolower(c);
          zStop[2] = 0;
        }else{
          zStop[0] = c;
          zStop[1] = 0;
        }
        while(1){
          zString += strcspn((const char*)zString, zStop);
          if( zString[0]==0 ) break;
          zString++;
          bMatch = patternCompare(zPattern,zString,pInfo,matchOther);
          if( bMatch!=SQLITE_NOMATCH ) return bMatch;
        }
      }else{
        int bMatch;
        while( (c2 = Utf8Read(zString))!=0 ){
          if( c2!=c ) continue;
          bMatch = patternCompare(zPattern,zString,pInfo,matchOther);
          if( bMatch!=SQLITE_NOMATCH ) return bMatch;
        }
      }
      return SQLITE_NOWILDCARDMATCH;
    }
    if( c==matchOther ){
      if( pInfo->matchSet==0 ){
        c = sqlite3Utf8Read(&zPattern);
        if( c==0 ) return SQLITE_NOMATCH;
        zEscaped = zPattern;
      }else{
        u32 prior_c = 0;
        int seen = 0;
        int invert = 0;
        c = sqlite3Utf8Read(&zString);
        if( c==0 ) return SQLITE_NOMATCH;
        c2 = sqlite3Utf8Read(&zPattern);
        if( c2=='^' ){
          invert = 1;
          c2 = sqlite3Utf8Read(&zPattern);
        }
        if( c2==']' ){
          if( c==']' ) seen = 1;
          c2 = sqlite3Utf8Read(&zPattern);
        }
        while( c2 && c2!=']' ){
          if( c2=='-' && zPattern[0]!=']' && zPattern[0]!=0 && prior_c>0 ){
            c2 = sqlite3Utf8Read(&zPattern);
            if( c>=prior_c && c<=c2 ) seen = 1;
            prior_c = 0;
          }else{
            if( c==c2 ){
              seen = 1;
            }
            prior_c = c2;
          }
          c2 = sqlite3Utf8Read(&zPattern);
        }
        if( c2==0 || (seen ^ invert)==0 ){
          return SQLITE_NOMATCH;
        }
        continue;
      }
    }
    c2 = Utf8Read(zString);
    if( c==c2 ) continue;
    if( noCase  && sqlite3Tolower(c)==sqlite3Tolower(c2) && c<0x80 && c2<0x80 ){
      continue;
    }
    if( c==matchOne && zPattern!=zEscaped && c2!=0 ) continue;
    return SQLITE_NOMATCH;
  }
  return *zString==0 ? SQLITE_MATCH : SQLITE_NOMATCH;
}

/*
** The sqlite3_strglob() interface.  Return 0 on a match (like strcmp()) and
** non-zero if there is no match.
*/
int sqlite3_strglob(const char *zGlobPattern, const char *zString){
  return patternCompare((u8*)zGlobPattern, (u8*)zString, &globInfo, '[');
}

/*
** The sqlite3_strlike() interface.  Return 0 on a match and non-zero for
** a miss - like strcmp().
*/
int sqlite3_strlike(const char *zPattern, const char *zStr, unsigned int esc){
  return patternCompare((u8*)zPattern, (u8*)zStr, &likeInfoNorm, esc);
}

/*
** Count the number of times that the LIKE operator (or GLOB which is
** just a variation of LIKE) gets called.  This is used for testing
** only.
*/
#ifdef SQLITE_TEST
int sqlite3_like_count = 0;
#endif


/*
** Implementation of the like() SQL function.  This function implements
** the build-in LIKE operator.  The first argument to the function is the
** pattern and the second argument is the string.  So, the SQL statements:
**
**       A LIKE B
**
** is implemented as like(B,A).
**
** This same function (with a different compareInfo structure) computes
** the GLOB operator.
*/
static void likeFunc(
  sqlite3_context *context, 
  int argc, 
  sqlite3_value **argv
){
  const unsigned char *zA, *zB;
  u32 escape;
  int nPat;
  sqlite3 *db = sqlite3_context_db_handle(context);
  struct compareInfo *pInfo = sqlite3_user_data(context);
  struct compareInfo backupInfo;

#ifdef SQLITE_LIKE_DOESNT_MATCH_BLOBS
  if( sqlite3_value_type(argv[0])==SQLITE_BLOB
   || sqlite3_value_type(argv[1])==SQLITE_BLOB
  ){
#ifdef SQLITE_TEST
    sqlite3_like_count++;
#endif
    sqlite3_result_int(context, 0);
    return;
  }
#endif

  /* Limit the length of the LIKE or GLOB pattern to avoid problems
  ** of deep recursion and N*N behavior in patternCompare().
  */
  nPat = sqlite3_value_bytes(argv[0]);
  testcase( nPat==db->aLimit[SQLITE_LIMIT_LIKE_PATTERN_LENGTH] );
  testcase( nPat==db->aLimit[SQLITE_LIMIT_LIKE_PATTERN_LENGTH]+1 );
  if( nPat > db->aLimit[SQLITE_LIMIT_LIKE_PATTERN_LENGTH] ){
    sqlite3_result_error(context, "LIKE or GLOB pattern too complex", -1);
    return;
  }
  if( argc==3 ){
    /* The escape character string must consist of a single UTF-8 character.
    ** Otherwise, return an error.
    */
    const unsigned char *zEsc = sqlite3_value_text(argv[2]);
    if( zEsc==0 ) return;
    if( sqlite3Utf8CharLen((char*)zEsc, -1)!=1 ){
      sqlite3_result_error(context, 
          "ESCAPE expression must be a single character", -1);
      return;
    }
    escape = sqlite3Utf8Read(&zEsc);
    if( escape==pInfo->matchAll || escape==pInfo->matchOne ){
      memcpy(&backupInfo, pInfo, sizeof(backupInfo));
      pInfo = &backupInfo;
      if( escape==pInfo->matchAll ) pInfo->matchAll = 0;
      if( escape==pInfo->matchOne ) pInfo->matchOne = 0;
    }
  }else{
    escape = pInfo->matchSet;
  }
  zB = sqlite3_value_text(argv[0]);
  zA = sqlite3_value_text(argv[1]);
  if( zA && zB ){
#ifdef SQLITE_TEST
    sqlite3_like_count++;
#endif
    sqlite3_result_int(context,
                      patternCompare(zB, zA, pInfo, escape)==SQLITE_MATCH);
  }
}

/*
** Implementation of the NULLIF(x,y) function.  The result is the first
** argument if the arguments are different.  The result is NULL if the
** arguments are equal to each other.
*/
static void nullifFunc(
  sqlite3_context *context,
  int NotUsed,
  sqlite3_value **argv
){
  CollSeq *pColl = sqlite3GetFuncCollSeq(context);
  UNUSED_PARAMETER(NotUsed);
  if( sqlite3MemCompare(argv[0], argv[1], pColl)!=0 ){
    sqlite3_result_value(context, argv[0]);
  }
}

/*
** Implementation of the sqlite_version() function.  The result is the version
** of the SQLite library that is running.
*/
static void versionFunc(
  sqlite3_context *context,
  int NotUsed,
  sqlite3_value **NotUsed2
){
  UNUSED_PARAMETER2(NotUsed, NotUsed2);
  /* IMP: R-48699-48617 This function is an SQL wrapper around the
  ** sqlite3_libversion() C-interface. */
  sqlite3_result_text(context, sqlite3_libversion(), -1, SQLITE_STATIC);
}

/*
** Implementation of the sqlite_source_id() function. The result is a string
** that identifies the particular version of the source code used to build
** SQLite.
*/
static void sourceidFunc(
  sqlite3_context *context,
  int NotUsed,
  sqlite3_value **NotUsed2
){
  UNUSED_PARAMETER2(NotUsed, NotUsed2);
  /* IMP: R-24470-31136 This function is an SQL wrapper around the
  ** sqlite3_sourceid() C interface. */
  sqlite3_result_text(context, sqlite3_sourceid(), -1, SQLITE_STATIC);
}

/*
** Implementation of the sqlite_log() function.  This is a wrapper around
** sqlite3_log().  The return value is NULL.  The function exists purely for
** its side-effects.
*/
static void errlogFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  UNUSED_PARAMETER(argc);
  UNUSED_PARAMETER(context);
  sqlite3_log(sqlite3_value_int(argv[0]), "%s", sqlite3_value_text(argv[1]));
}

/*
** Implementation of the sqlite_compileoption_used() function.
** The result is an integer that identifies if the compiler option
** was used to build SQLite.
*/
#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS
static void compileoptionusedFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  const char *zOptName;
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  /* IMP: R-39564-36305 The sqlite_compileoption_used() SQL
  ** function is a wrapper around the sqlite3_compileoption_used() C/C++
  ** function.
  */
  if( (zOptName = (const char*)sqlite3_value_text(argv[0]))!=0 ){
    sqlite3_result_int(context, sqlite3_compileoption_used(zOptName));
  }
}
#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */

/*
** Implementation of the sqlite_compileoption_get() function. 
** The result is a string that identifies the compiler options 
** used to build SQLite.
*/
#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS
static void compileoptiongetFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  int n;
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  /* IMP: R-04922-24076 The sqlite_compileoption_get() SQL function
  ** is a wrapper around the sqlite3_compileoption_get() C/C++ function.
  */
  n = sqlite3_value_int(argv[0]);
  sqlite3_result_text(context, sqlite3_compileoption_get(n), -1, SQLITE_STATIC);
}
#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */

/* Array for converting from half-bytes (nybbles) into ASCII hex
** digits. */
static const char hexdigits[] = {
  '0', '1', '2', '3', '4', '5', '6', '7',
  '8', '9', 'A', 'B', 'C', 'D', 'E', 'F' 
};

/*
** Implementation of the QUOTE() function.  This function takes a single
** argument.  If the argument is numeric, the return value is the same as
** the argument.  If the argument is NULL, the return value is the string
** "NULL".  Otherwise, the argument is enclosed in single quotes with
** single-quote escapes.
*/
static void quoteFunc(sqlite3_context *context, int argc, sqlite3_value **argv){
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  switch( sqlite3_value_type(argv[0]) ){
    case SQLITE_FLOAT: {
      double r1, r2;
      char zBuf[50];
      r1 = sqlite3_value_double(argv[0]);
      sqlite3_snprintf(sizeof(zBuf), zBuf, "%!.15g", r1);
      sqlite3AtoF(zBuf, &r2, 20, SQLITE_UTF8);
      if( r1!=r2 ){
        sqlite3_snprintf(sizeof(zBuf), zBuf, "%!.20e", r1);
      }
      sqlite3_result_text(context, zBuf, -1, SQLITE_TRANSIENT);
      break;
    }
    case SQLITE_INTEGER: {
      sqlite3_result_value(context, argv[0]);
      break;
    }
    case SQLITE_BLOB: {
      char *zText = 0;
      char const *zBlob = sqlite3_value_blob(argv[0]);
      int nBlob = sqlite3_value_bytes(argv[0]);
      assert( zBlob==sqlite3_value_blob(argv[0]) ); /* No encoding change */
      zText = (char *)contextMalloc(context, (2*(i64)nBlob)+4); 
      if( zText ){
        int i;
        for(i=0; i<nBlob; i++){
          zText[(i*2)+2] = hexdigits[(zBlob[i]>>4)&0x0F];
          zText[(i*2)+3] = hexdigits[(zBlob[i])&0x0F];
        }
        zText[(nBlob*2)+2] = '\'';
        zText[(nBlob*2)+3] = '\0';
        zText[0] = 'X';
        zText[1] = '\'';
        sqlite3_result_text(context, zText, -1, SQLITE_TRANSIENT);
        sqlite3_free(zText);
      }
      break;
    }
    case SQLITE_TEXT: {
      int i,j;
      u64 n;
      const unsigned char *zArg = sqlite3_value_text(argv[0]);
      char *z;

      if( zArg==0 ) return;
      for(i=0, n=0; zArg[i]; i++){ if( zArg[i]=='\'' ) n++; }
      z = contextMalloc(context, ((i64)i)+((i64)n)+3);
      if( z ){
        z[0] = '\'';
        for(i=0, j=1; zArg[i]; i++){
          z[j++] = zArg[i];
          if( zArg[i]=='\'' ){
            z[j++] = '\'';
          }
        }
        z[j++] = '\'';
        z[j] = 0;
        sqlite3_result_text(context, z, j, sqlite3_free);
      }
      break;
    }
    default: {
      assert( sqlite3_value_type(argv[0])==SQLITE_NULL );
      sqlite3_result_text(context, "NULL", 4, SQLITE_STATIC);
      break;
    }
  }
}

/*
** The unicode() function.  Return the integer unicode code-point value
** for the first character of the input string. 
*/
static void unicodeFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  const unsigned char *z = sqlite3_value_text(argv[0]);
  (void)argc;
  if( z && z[0] ) sqlite3_result_int(context, sqlite3Utf8Read(&z));
}

/*
** The char() function takes zero or more arguments, each of which is
** an integer.  It constructs a string where each character of the string
** is the unicode character for the corresponding integer argument.
*/
static void charFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  unsigned char *z, *zOut;
  int i;
  zOut = z = sqlite3_malloc64( argc*4+1 );
  if( z==0 ){
    sqlite3_result_error_nomem(context);
    return;
  }
  for(i=0; i<argc; i++){
    sqlite3_int64 x;
    unsigned c;
    x = sqlite3_value_int64(argv[i]);
    if( x<0 || x>0x10ffff ) x = 0xfffd;
    c = (unsigned)(x & 0x1fffff);
    if( c<0x00080 ){
      *zOut++ = (u8)(c&0xFF);
    }else if( c<0x00800 ){
      *zOut++ = 0xC0 + (u8)((c>>6)&0x1F);
      *zOut++ = 0x80 + (u8)(c & 0x3F);
    }else if( c<0x10000 ){
      *zOut++ = 0xE0 + (u8)((c>>12)&0x0F);
      *zOut++ = 0x80 + (u8)((c>>6) & 0x3F);
      *zOut++ = 0x80 + (u8)(c & 0x3F);
    }else{
      *zOut++ = 0xF0 + (u8)((c>>18) & 0x07);
      *zOut++ = 0x80 + (u8)((c>>12) & 0x3F);
      *zOut++ = 0x80 + (u8)((c>>6) & 0x3F);
      *zOut++ = 0x80 + (u8)(c & 0x3F);
    }                                                    \
  }
  sqlite3_result_text64(context, (char*)z, zOut-z, sqlite3_free, SQLITE_UTF8);
}

/*
** The hex() function.  Interpret the argument as a blob.  Return
** a hexadecimal rendering as text.
*/
static void hexFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  int i, n;
  const unsigned char *pBlob;
  char *zHex, *z;
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  pBlob = sqlite3_value_blob(argv[0]);
  n = sqlite3_value_bytes(argv[0]);
  assert( pBlob==sqlite3_value_blob(argv[0]) );  /* No encoding change */
  z = zHex = contextMalloc(context, ((i64)n)*2 + 1);
  if( zHex ){
    for(i=0; i<n; i++, pBlob++){
      unsigned char c = *pBlob;
      *(z++) = hexdigits[(c>>4)&0xf];
      *(z++) = hexdigits[c&0xf];
    }
    *z = 0;
    sqlite3_result_text(context, zHex, n*2, sqlite3_free);
  }
}

/*
** The zeroblob(N) function returns a zero-filled blob of size N bytes.
*/
static void zeroblobFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  i64 n;
  int rc;
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  n = sqlite3_value_int64(argv[0]);
  if( n<0 ) n = 0;
  rc = sqlite3_result_zeroblob64(context, n); /* IMP: R-00293-64994 */
  if( rc ){
    sqlite3_result_error_code(context, rc);
  }
}

/*
** The replace() function.  Three arguments are all strings: call
** them A, B, and C. The result is also a string which is derived
** from A by replacing every occurrence of B with C.  The match
** must be exact.  Collating sequences are not used.
*/
static void replaceFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  const unsigned char *zStr;        /* The input string A */
  const unsigned char *zPattern;    /* The pattern string B */
  const unsigned char *zRep;        /* The replacement string C */
  unsigned char *zOut;              /* The output */
  int nStr;                /* Size of zStr */
  int nPattern;            /* Size of zPattern */
  int nRep;                /* Size of zRep */
  i64 nOut;                /* Maximum size of zOut */
  int loopLimit;           /* Last zStr[] that might match zPattern[] */
  int i, j;                /* Loop counters */
  unsigned cntExpand;      /* Number zOut expansions */
  sqlite3 *db = sqlite3_context_db_handle(context);

  assert( argc==3 );
  UNUSED_PARAMETER(argc);
  zStr = sqlite3_value_text(argv[0]);
  if( zStr==0 ) return;
  nStr = sqlite3_value_bytes(argv[0]);
  assert( zStr==sqlite3_value_text(argv[0]) );  /* No encoding change */
  zPattern = sqlite3_value_text(argv[1]);
  if( zPattern==0 ){
    assert( sqlite3_value_type(argv[1])==SQLITE_NULL
            || sqlite3_context_db_handle(context)->mallocFailed );
    return;
  }
  if( zPattern[0]==0 ){
    assert( sqlite3_value_type(argv[1])!=SQLITE_NULL );
    sqlite3_result_value(context, argv[0]);
    return;
  }
  nPattern = sqlite3_value_bytes(argv[1]);
  assert( zPattern==sqlite3_value_text(argv[1]) );  /* No encoding change */
  zRep = sqlite3_value_text(argv[2]);
  if( zRep==0 ) return;
  nRep = sqlite3_value_bytes(argv[2]);
  assert( zRep==sqlite3_value_text(argv[2]) );
  nOut = nStr + 1;
  assert( nOut<SQLITE_MAX_LENGTH );
  zOut = contextMalloc(context, (i64)nOut);
  if( zOut==0 ){
    return;
  }
  loopLimit = nStr - nPattern;  
  cntExpand = 0;
  for(i=j=0; i<=loopLimit; i++){
    if( zStr[i]!=zPattern[0] || memcmp(&zStr[i], zPattern, nPattern) ){
      zOut[j++] = zStr[i];
    }else{
      if( nRep>nPattern ){
        nOut += nRep - nPattern;
        testcase( nOut-1==db->aLimit[SQLITE_LIMIT_LENGTH] );
        testcase( nOut-2==db->aLimit[SQLITE_LIMIT_LENGTH] );
        if( nOut-1>db->aLimit[SQLITE_LIMIT_LENGTH] ){
          sqlite3_result_error_toobig(context);
          sqlite3_free(zOut);
          return;
        }
        cntExpand++;
        if( (cntExpand&(cntExpand-1))==0 ){
          /* Grow the size of the output buffer only on substitutions
          ** whose index is a power of two: 1, 2, 4, 8, 16, 32, ... */
          u8 *zOld;
          zOld = zOut;
          zOut = sqlite3Realloc(zOut, (int)nOut + (nOut - nStr - 1));
          if( zOut==0 ){
            sqlite3_result_error_nomem(context);
            sqlite3_free(zOld);
            return;
          }
        }
      }
      memcpy(&zOut[j], zRep, nRep);
      j += nRep;
      i += nPattern-1;
    }
  }
  assert( j+nStr-i+1<=nOut );
  memcpy(&zOut[j], &zStr[i], nStr-i);
  j += nStr - i;
  assert( j<=nOut );
  zOut[j] = 0;
  sqlite3_result_text(context, (char*)zOut, j, sqlite3_free);
}

/*
** Implementation of the TRIM(), LTRIM(), and RTRIM() functions.
** The userdata is 0x1 for left trim, 0x2 for right trim, 0x3 for both.
*/
static void trimFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  const unsigned char *zIn;         /* Input string */
  const unsigned char *zCharSet;    /* Set of characters to trim */
  int nIn;                          /* Number of bytes in input */
  int flags;                        /* 1: trimleft  2: trimright  3: trim */
  int i;                            /* Loop counter */
  unsigned char *aLen = 0;          /* Length of each character in zCharSet */
  unsigned char **azChar = 0;       /* Individual characters in zCharSet */
  int nChar;                        /* Number of characters in zCharSet */

  if( sqlite3_value_type(argv[0])==SQLITE_NULL ){
    return;
  }
  zIn = sqlite3_value_text(argv[0]);
  if( zIn==0 ) return;
  nIn = sqlite3_value_bytes(argv[0]);
  assert( zIn==sqlite3_value_text(argv[0]) );
  if( argc==1 ){
    static const unsigned char lenOne[] = { 1 };
    static unsigned char * const azOne[] = { (u8*)" " };
    nChar = 1;
    aLen = (u8*)lenOne;
    azChar = (unsigned char **)azOne;
    zCharSet = 0;
  }else if( (zCharSet = sqlite3_value_text(argv[1]))==0 ){
    return;
  }else{
    const unsigned char *z;
    for(z=zCharSet, nChar=0; *z; nChar++){
      SQLITE_SKIP_UTF8(z);
    }
    if( nChar>0 ){
      azChar = contextMalloc(context, ((i64)nChar)*(sizeof(char*)+1));
      if( azChar==0 ){
        return;
      }
      aLen = (unsigned char*)&azChar[nChar];
      for(z=zCharSet, nChar=0; *z; nChar++){
        azChar[nChar] = (unsigned char *)z;
        SQLITE_SKIP_UTF8(z);
        aLen[nChar] = (u8)(z - azChar[nChar]);
      }
    }
  }
  if( nChar>0 ){
    flags = SQLITE_PTR_TO_INT(sqlite3_user_data(context));
    if( flags & 1 ){
      while( nIn>0 ){
        int len = 0;
        for(i=0; i<nChar; i++){
          len = aLen[i];
          if( len<=nIn && memcmp(zIn, azChar[i], len)==0 ) break;
        }
        if( i>=nChar ) break;
        zIn += len;
        nIn -= len;
      }
    }
    if( flags & 2 ){
      while( nIn>0 ){
        int len = 0;
        for(i=0; i<nChar; i++){
          len = aLen[i];
          if( len<=nIn && memcmp(&zIn[nIn-len],azChar[i],len)==0 ) break;
        }
        if( i>=nChar ) break;
        nIn -= len;
      }
    }
    if( zCharSet ){
      sqlite3_free(azChar);
    }
  }
  sqlite3_result_text(context, (char*)zIn, nIn, SQLITE_TRANSIENT);
}


#ifdef SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION
/*
** The "unknown" function is automatically substituted in place of
** any unrecognized function name when doing an EXPLAIN or EXPLAIN QUERY PLAN
** when the SQLITE_ENABLE_UNKNOWN_FUNCTION compile-time option is used.
** When the "sqlite3" command-line shell is built using this functionality,
** that allows an EXPLAIN or EXPLAIN QUERY PLAN for complex queries
** involving application-defined functions to be examined in a generic
** sqlite3 shell.
*/
static void unknownFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  /* no-op */
}
#endif /*SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION*/


/* IMP: R-25361-16150 This function is omitted from SQLite by default. It
** is only available if the SQLITE_SOUNDEX compile-time option is used
** when SQLite is built.
*/
#ifdef SQLITE_SOUNDEX
/*
** Compute the soundex encoding of a word.
**
** IMP: R-59782-00072 The soundex(X) function returns a string that is the
** soundex encoding of the string X. 
*/
static void soundexFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  char zResult[8];
  const u8 *zIn;
  int i, j;
  static const unsigned char iCode[] = {
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
    0, 0, 1, 2, 3, 0, 1, 2, 0, 0, 2, 2, 4, 5, 5, 0,
    1, 2, 6, 2, 3, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0,
    0, 0, 1, 2, 3, 0, 1, 2, 0, 0, 2, 2, 4, 5, 5, 0,
    1, 2, 6, 2, 3, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 0,
  };
  assert( argc==1 );
  zIn = (u8*)sqlite3_value_text(argv[0]);
  if( zIn==0 ) zIn = (u8*)"";
  for(i=0; zIn[i] && !sqlite3Isalpha(zIn[i]); i++){}
  if( zIn[i] ){
    u8 prevcode = iCode[zIn[i]&0x7f];
    zResult[0] = sqlite3Toupper(zIn[i]);
    for(j=1; j<4 && zIn[i]; i++){
      int code = iCode[zIn[i]&0x7f];
      if( code>0 ){
        if( code!=prevcode ){
          prevcode = code;
          zResult[j++] = code + '0';
        }
      }else{
        prevcode = 0;
      }
    }
    while( j<4 ){
      zResult[j++] = '0';
    }
    zResult[j] = 0;
    sqlite3_result_text(context, zResult, 4, SQLITE_TRANSIENT);
  }else{
    /* IMP: R-64894-50321 The string "?000" is returned if the argument
    ** is NULL or contains no ASCII alphabetic characters. */
    sqlite3_result_text(context, "?000", 4, SQLITE_STATIC);
  }
}
#endif /* SQLITE_SOUNDEX */

#ifndef SQLITE_OMIT_LOAD_EXTENSION
/*
** A function that loads a shared-library extension then returns NULL.
*/
static void loadExt(sqlite3_context *context, int argc, sqlite3_value **argv){
  const char *zFile = (const char *)sqlite3_value_text(argv[0]);
  const char *zProc;
  sqlite3 *db = sqlite3_context_db_handle(context);
  char *zErrMsg = 0;

  /* Disallow the load_extension() SQL function unless the SQLITE_LoadExtFunc
  ** flag is set.  See the sqlite3_enable_load_extension() API.
  */
  if( (db->flags & SQLITE_LoadExtFunc)==0 ){
    sqlite3_result_error(context, "not authorized", -1);
    return;
  }

  if( argc==2 ){
    zProc = (const char *)sqlite3_value_text(argv[1]);
  }else{
    zProc = 0;
  }
  if( zFile && sqlite3_load_extension(db, zFile, zProc, &zErrMsg) ){
    sqlite3_result_error(context, zErrMsg, -1);
    sqlite3_free(zErrMsg);
  }
}
#endif


/*
** An instance of the following structure holds the context of a
** sum() or avg() aggregate computation.
*/
typedef struct SumCtx SumCtx;
struct SumCtx {
  double rSum;      /* Floating point sum */
  i64 iSum;         /* Integer sum */   
  i64 cnt;          /* Number of elements summed */
  u8 overflow;      /* True if integer overflow seen */
  u8 approx;        /* True if non-integer value was input to the sum */
};

/*
** Routines used to compute the sum, average, and total.
**
** The SUM() function follows the (broken) SQL standard which means
** that it returns NULL if it sums over no inputs.  TOTAL returns
** 0.0 in that case.  In addition, TOTAL always returns a float where
** SUM might return an integer if it never encounters a floating point
** value.  TOTAL never fails, but SUM might through an exception if
** it overflows an integer.
*/
static void sumStep(sqlite3_context *context, int argc, sqlite3_value **argv){
  SumCtx *p;
  int type;
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  p = sqlite3_aggregate_context(context, sizeof(*p));
  type = sqlite3_value_numeric_type(argv[0]);
  if( p && type!=SQLITE_NULL ){
    p->cnt++;
    if( type==SQLITE_INTEGER ){
      i64 v = sqlite3_value_int64(argv[0]);
      p->rSum += v;
      if( (p->approx|p->overflow)==0 && sqlite3AddInt64(&p->iSum, v) ){
        p->approx = p->overflow = 1;
      }
    }else{
      p->rSum += sqlite3_value_double(argv[0]);
      p->approx = 1;
    }
  }
}
#ifndef SQLITE_OMIT_WINDOWFUNC
static void sumInverse(sqlite3_context *context, int argc, sqlite3_value**argv){
  SumCtx *p;
  int type;
  assert( argc==1 );
  UNUSED_PARAMETER(argc);
  p = sqlite3_aggregate_context(context, sizeof(*p));
  type = sqlite3_value_numeric_type(argv[0]);
  /* p is always non-NULL because sumStep() will have been called first
  ** to initialize it */
  if( ALWAYS(p) && type!=SQLITE_NULL ){
    assert( p->cnt>0 );
    p->cnt--;
    assert( type==SQLITE_INTEGER || p->approx );
    if( type==SQLITE_INTEGER && p->approx==0 ){
      i64 v = sqlite3_value_int64(argv[0]);
      p->rSum -= v;
      p->iSum -= v;
    }else{
      p->rSum -= sqlite3_value_double(argv[0]);
    }
  }
}
#else
# define sumInverse 0
#endif /* SQLITE_OMIT_WINDOWFUNC */
static void sumFinalize(sqlite3_context *context){
  SumCtx *p;
  p = sqlite3_aggregate_context(context, 0);
  if( p && p->cnt>0 ){
    if( p->overflow ){
      sqlite3_result_error(context,"integer overflow",-1);
    }else if( p->approx ){
      sqlite3_result_double(context, p->rSum);
    }else{
      sqlite3_result_int64(context, p->iSum);
    }
  }
}
static void avgFinalize(sqlite3_context *context){
  SumCtx *p;
  p = sqlite3_aggregate_context(context, 0);
  if( p && p->cnt>0 ){
    sqlite3_result_double(context, p->rSum/(double)p->cnt);
  }
}
static void totalFinalize(sqlite3_context *context){
  SumCtx *p;
  p = sqlite3_aggregate_context(context, 0);
  /* (double)0 In case of SQLITE_OMIT_FLOATING_POINT... */
  sqlite3_result_double(context, p ? p->rSum : (double)0);
}

/*
** The following structure keeps track of state information for the
** count() aggregate function.
*/
typedef struct CountCtx CountCtx;
struct CountCtx {
  i64 n;
#ifdef SQLITE_DEBUG
  int bInverse;                   /* True if xInverse() ever called */
#endif
};

/*
** Routines to implement the count() aggregate function.
*/
static void countStep(sqlite3_context *context, int argc, sqlite3_value **argv){
  CountCtx *p;
  p = sqlite3_aggregate_context(context, sizeof(*p));
  if( (argc==0 || SQLITE_NULL!=sqlite3_value_type(argv[0])) && p ){
    p->n++;
  }

#ifndef SQLITE_OMIT_DEPRECATED
  /* The sqlite3_aggregate_count() function is deprecated.  But just to make
  ** sure it still operates correctly, verify that its count agrees with our 
  ** internal count when using count(*) and when the total count can be
  ** expressed as a 32-bit integer. */
  assert( argc==1 || p==0 || p->n>0x7fffffff || p->bInverse
          || p->n==sqlite3_aggregate_count(context) );
#endif
}   
static void countFinalize(sqlite3_context *context){
  CountCtx *p;
  p = sqlite3_aggregate_context(context, 0);
  sqlite3_result_int64(context, p ? p->n : 0);
}
#ifndef SQLITE_OMIT_WINDOWFUNC
static void countInverse(sqlite3_context *ctx, int argc, sqlite3_value **argv){
  CountCtx *p;
  p = sqlite3_aggregate_context(ctx, sizeof(*p));
  /* p is always non-NULL since countStep() will have been called first */
  if( (argc==0 || SQLITE_NULL!=sqlite3_value_type(argv[0])) && ALWAYS(p) ){
    p->n--;
#ifdef SQLITE_DEBUG
    p->bInverse = 1;
#endif
  }
}   
#else
# define countInverse 0
#endif /* SQLITE_OMIT_WINDOWFUNC */

/*
** Routines to implement min() and max() aggregate functions.
*/
static void minmaxStep(
  sqlite3_context *context, 
  int NotUsed, 
  sqlite3_value **argv
){
  Mem *pArg  = (Mem *)argv[0];
  Mem *pBest;
  UNUSED_PARAMETER(NotUsed);

  pBest = (Mem *)sqlite3_aggregate_context(context, sizeof(*pBest));
  if( !pBest ) return;

  if( sqlite3_value_type(pArg)==SQLITE_NULL ){
    if( pBest->flags ) sqlite3SkipAccumulatorLoad(context);
  }else if( pBest->flags ){
    int max;
    int cmp;
    CollSeq *pColl = sqlite3GetFuncCollSeq(context);
    /* This step function is used for both the min() and max() aggregates,
    ** the only difference between the two being that the sense of the
    ** comparison is inverted. For the max() aggregate, the
    ** sqlite3_user_data() function returns (void *)-1. For min() it
    ** returns (void *)db, where db is the sqlite3* database pointer.
    ** Therefore the next statement sets variable 'max' to 1 for the max()
    ** aggregate, or 0 for min().
    */
    max = sqlite3_user_data(context)!=0;
    cmp = sqlite3MemCompare(pBest, pArg, pColl);
    if( (max && cmp<0) || (!max && cmp>0) ){
      sqlite3VdbeMemCopy(pBest, pArg);
    }else{
      sqlite3SkipAccumulatorLoad(context);
    }
  }else{
    pBest->db = sqlite3_context_db_handle(context);
    sqlite3VdbeMemCopy(pBest, pArg);
  }
}
static void minMaxValueFinalize(sqlite3_context *context, int bValue){
  sqlite3_value *pRes;
  pRes = (sqlite3_value *)sqlite3_aggregate_context(context, 0);
  if( pRes ){
    if( pRes->flags ){
      sqlite3_result_value(context, pRes);
    }
    if( bValue==0 ) sqlite3VdbeMemRelease(pRes);
  }
}
#ifndef SQLITE_OMIT_WINDOWFUNC
static void minMaxValue(sqlite3_context *context){
  minMaxValueFinalize(context, 1);
}
#else
# define minMaxValue 0
#endif /* SQLITE_OMIT_WINDOWFUNC */
static void minMaxFinalize(sqlite3_context *context){
  minMaxValueFinalize(context, 0);
}

/*
** group_concat(EXPR, ?SEPARATOR?)
*/
static void groupConcatStep(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  const char *zVal;
  StrAccum *pAccum;
  const char *zSep;
  int nVal, nSep;
  assert( argc==1 || argc==2 );
  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;
  pAccum = (StrAccum*)sqlite3_aggregate_context(context, sizeof(*pAccum));

  if( pAccum ){
    sqlite3 *db = sqlite3_context_db_handle(context);
    int firstTerm = pAccum->mxAlloc==0;
    pAccum->mxAlloc = db->aLimit[SQLITE_LIMIT_LENGTH];
    if( !firstTerm ){
      if( argc==2 ){
        zSep = (char*)sqlite3_value_text(argv[1]);
        nSep = sqlite3_value_bytes(argv[1]);
      }else{
        zSep = ",";
        nSep = 1;
      }
      if( zSep ) sqlite3_str_append(pAccum, zSep, nSep);
    }
    zVal = (char*)sqlite3_value_text(argv[0]);
    nVal = sqlite3_value_bytes(argv[0]);
    if( zVal ) sqlite3_str_append(pAccum, zVal, nVal);
  }
}
#ifndef SQLITE_OMIT_WINDOWFUNC
static void groupConcatInverse(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  int n;
  StrAccum *pAccum;
  assert( argc==1 || argc==2 );
  if( sqlite3_value_type(argv[0])==SQLITE_NULL ) return;
  pAccum = (StrAccum*)sqlite3_aggregate_context(context, sizeof(*pAccum));
  /* pAccum is always non-NULL since groupConcatStep() will have always
  ** run frist to initialize it */
  if( ALWAYS(pAccum) ){
    n = sqlite3_value_bytes(argv[0]);
    if( argc==2 ){
      n += sqlite3_value_bytes(argv[1]);
    }else{
      n++;
    }
    if( n>=(int)pAccum->nChar ){
      pAccum->nChar = 0;
    }else{
      pAccum->nChar -= n;
      memmove(pAccum->zText, &pAccum->zText[n], pAccum->nChar);
    }
    if( pAccum->nChar==0 ) pAccum->mxAlloc = 0;
  }
}
#else
# define groupConcatInverse 0
#endif /* SQLITE_OMIT_WINDOWFUNC */
static void groupConcatFinalize(sqlite3_context *context){
  StrAccum *pAccum;
  pAccum = sqlite3_aggregate_context(context, 0);
  if( pAccum ){
    if( pAccum->accError==SQLITE_TOOBIG ){
      sqlite3_result_error_toobig(context);
    }else if( pAccum->accError==SQLITE_NOMEM ){
      sqlite3_result_error_nomem(context);
    }else{    
      sqlite3_result_text(context, sqlite3StrAccumFinish(pAccum), -1, 
                          sqlite3_free);
    }
  }
}
#ifndef SQLITE_OMIT_WINDOWFUNC
static void groupConcatValue(sqlite3_context *context){
  sqlite3_str *pAccum;
  pAccum = (sqlite3_str*)sqlite3_aggregate_context(context, 0);
  if( pAccum ){
    if( pAccum->accError==SQLITE_TOOBIG ){
      sqlite3_result_error_toobig(context);
    }else if( pAccum->accError==SQLITE_NOMEM ){
      sqlite3_result_error_nomem(context);
    }else{    
      const char *zText = sqlite3_str_value(pAccum);
      sqlite3_result_text(context, zText, -1, SQLITE_TRANSIENT);
    }
  }
}
#else
# define groupConcatValue 0
#endif /* SQLITE_OMIT_WINDOWFUNC */

/*
** This routine does per-connection function registration.  Most
** of the built-in functions above are part of the global function set.
** This routine only deals with those that are not global.
*/
void sqlite3RegisterPerConnectionBuiltinFunctions(sqlite3 *db){
  int rc = sqlite3_overload_function(db, "MATCH", 2);
  assert( rc==SQLITE_NOMEM || rc==SQLITE_OK );
  if( rc==SQLITE_NOMEM ){
    sqlite3OomFault(db);
  }
}

/*
** Re-register the built-in LIKE functions.  The caseSensitive
** parameter determines whether or not the LIKE operator is case
** sensitive.
*/
void sqlite3RegisterLikeFunctions(sqlite3 *db, int caseSensitive){
  struct compareInfo *pInfo;
  int flags;
  if( caseSensitive ){
    pInfo = (struct compareInfo*)&likeInfoAlt;
    flags = SQLITE_FUNC_LIKE | SQLITE_FUNC_CASE;
  }else{
    pInfo = (struct compareInfo*)&likeInfoNorm;
    flags = SQLITE_FUNC_LIKE;
  }
  sqlite3CreateFunc(db, "like", 2, SQLITE_UTF8, pInfo, likeFunc, 0, 0, 0, 0, 0);
  sqlite3CreateFunc(db, "like", 3, SQLITE_UTF8, pInfo, likeFunc, 0, 0, 0, 0, 0);
  sqlite3FindFunction(db, "like", 2, SQLITE_UTF8, 0)->funcFlags |= flags;
  sqlite3FindFunction(db, "like", 3, SQLITE_UTF8, 0)->funcFlags |= flags;
}

/*
** pExpr points to an expression which implements a function.  If
** it is appropriate to apply the LIKE optimization to that function
** then set aWc[0] through aWc[2] to the wildcard characters and the
** escape character and then return TRUE.  If the function is not a 
** LIKE-style function then return FALSE.
**
** The expression "a LIKE b ESCAPE c" is only considered a valid LIKE
** operator if c is a string literal that is exactly one byte in length.
** That one byte is stored in aWc[3].  aWc[3] is set to zero if there is
** no ESCAPE clause.
**
** *pIsNocase is set to true if uppercase and lowercase are equivalent for
** the function (default for LIKE).  If the function makes the distinction
** between uppercase and lowercase (as does GLOB) then *pIsNocase is set to
** false.
*/
int sqlite3IsLikeFunction(sqlite3 *db, Expr *pExpr, int *pIsNocase, char *aWc){
  FuncDef *pDef;
  int nExpr;
  if( pExpr->op!=TK_FUNCTION || !pExpr->x.pList ){
    return 0;
  }
  assert( !ExprHasProperty(pExpr, EP_xIsSelect) );
  nExpr = pExpr->x.pList->nExpr;
  pDef = sqlite3FindFunction(db, pExpr->u.zToken, nExpr, SQLITE_UTF8, 0);
#ifdef SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION
  if( pDef==0 ) return 0;
#endif
  if( NEVER(pDef==0) || (pDef->funcFlags & SQLITE_FUNC_LIKE)==0 ){
    return 0;
  }

  /* The memcpy() statement assumes that the wildcard characters are
  ** the first three statements in the compareInfo structure.  The
  ** asserts() that follow verify that assumption
  */
  memcpy(aWc, pDef->pUserData, 3);
  assert( (char*)&likeInfoAlt == (char*)&likeInfoAlt.matchAll );
  assert( &((char*)&likeInfoAlt)[1] == (char*)&likeInfoAlt.matchOne );
  assert( &((char*)&likeInfoAlt)[2] == (char*)&likeInfoAlt.matchSet );

  if( nExpr<3 ){
    aWc[3] = 0;
  }else{
    Expr *pEscape = pExpr->x.pList->a[2].pExpr;
    char *zEscape;
    if( pEscape->op!=TK_STRING ) return 0;
    zEscape = pEscape->u.zToken;
    if( zEscape[0]==0 || zEscape[1]!=0 ) return 0;
    if( zEscape[0]==aWc[0] ) return 0;
    if( zEscape[0]==aWc[1] ) return 0;
    aWc[3] = zEscape[0];
  }

  *pIsNocase = (pDef->funcFlags & SQLITE_FUNC_CASE)==0;
  return 1;
}

/* Mathematical Constants */
#ifndef M_PI
# define M_PI   3.141592653589793238462643383279502884
#endif
#ifndef M_LN10
# define M_LN10 2.302585092994045684017991454684364208
#endif
#ifndef M_LN2
# define M_LN2  0.693147180559945309417232121458176568
#endif


/* Extra math functions that require linking with -lm
*/
#ifdef SQLITE_ENABLE_MATH_FUNCTIONS
/*
** Implementation SQL functions:
**
**   ceil(X)
**   ceiling(X)
**   floor(X)
**
** The sqlite3_user_data() pointer is a pointer to the libm implementation
** of the underlying C function.
*/
static void ceilingFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  assert( argc==1 );
  switch( sqlite3_value_numeric_type(argv[0]) ){
    case SQLITE_INTEGER: {
       sqlite3_result_int64(context, sqlite3_value_int64(argv[0]));
       break;
    }
    case SQLITE_FLOAT: {
       double (*x)(double) = (double(*)(double))sqlite3_user_data(context);
       sqlite3_result_double(context, x(sqlite3_value_double(argv[0])));
       break;
    }
    default: {
       break;
    }
  }
}

/*
** Implementation of SQL functions:
**
**   ln(X)       - natural logarithm
**   log(X)      - log X base 10
**   log10(X)    - log X base 10
**   log(B,X)    - log X base B
*/
static void logFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  double x, b, ans;
  assert( argc==1 || argc==2 );
  switch( sqlite3_value_numeric_type(argv[0]) ){
    case SQLITE_INTEGER:
    case SQLITE_FLOAT:
      x = sqlite3_value_double(argv[0]);
      if( x<0.0 ) return;
      break;
    default:
      return;
  }
  if( argc==2 ){
    switch( sqlite3_value_numeric_type(argv[0]) ){
      case SQLITE_INTEGER:
      case SQLITE_FLOAT:
        b = x;
        x = sqlite3_value_double(argv[1]);
        if( x<0.0 ) return;
        break;
     default:
        return;
    }
    ans = log(x)/log(b);
  }else{
    ans = log(x);
    switch( SQLITE_PTR_TO_INT(sqlite3_user_data(context)) ){
      case 1:
        /* Convert from natural logarithm to log base 10 */
        ans *= 1.0/M_LN10;
        break;
      case 2:
        /* Convert from natural logarithm to log base 2 */
        ans *= 1.0/M_LN2;
        break;
      default:
        break;
    }
  }
  sqlite3_result_double(context, ans);
}

/*
** Functions to converts degrees to radians and radians to degrees.
*/
static double degToRad(double x){ return x*(M_PI/180.0); }
static double radToDeg(double x){ return x*(180.0/M_PI); }

/*
** Implementation of 1-argument SQL math functions:
**
**   exp(X)  - Compute e to the X-th power
*/
static void math1Func(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  assert( argc==1 );
  int type0;
  double v0, ans;
  double (*x)(double);
  type0 = sqlite3_value_numeric_type(argv[0]);
  if( type0!=SQLITE_INTEGER && type0!=SQLITE_FLOAT ) return;
  v0 = sqlite3_value_double(argv[0]);
  x = (double(*)(double))sqlite3_user_data(context);
  ans = x(v0);
  sqlite3_result_double(context, ans);
}

/*
** Implementation of 2-argument SQL math functions:
**
**   power(X,Y)  - Compute X to the Y-th power
*/
static void math2Func(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  assert( argc==2 );
  int type0, type1;
  double v0, v1, ans;
  double (*x)(double,double);
  type0 = sqlite3_value_numeric_type(argv[0]);
  if( type0!=SQLITE_INTEGER && type0!=SQLITE_FLOAT ) return;
  type1 = sqlite3_value_numeric_type(argv[1]);
  if( type1!=SQLITE_INTEGER && type1!=SQLITE_FLOAT ) return;
  v0 = sqlite3_value_double(argv[0]);
  v1 = sqlite3_value_double(argv[1]);
  x = (double(*)(double,double))sqlite3_user_data(context);
  ans = x(v0, v1);
  sqlite3_result_double(context, ans);
}

/*
** Implementation of 2-argument SQL math functions:
**
**   power(X,Y)  - Compute X to the Y-th power
*/
static void piFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  assert( argc==0 );
  sqlite3_result_double(context, M_PI);
}

#endif /* SQLITE_ENABLE_MATH_FUNCTIONS */

/*
** Implementation of sign(X) function.
*/
static void signFunc(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  assert( argc==1 );
  int type0;
  double x;
  type0 = sqlite3_value_numeric_type(argv[0]);
  if( type0!=SQLITE_INTEGER && type0!=SQLITE_FLOAT ) return;
  x = sqlite3_value_double(argv[0]);
  sqlite3_result_int(context, x<0.0 ? -1 : x>0.0 ? +1 : 0);
}

/*
** All of the FuncDef structures in the aBuiltinFunc[] array above
** to the global function hash table.  This occurs at start-time (as
** a consequence of calling sqlite3_initialize()).
**
** After this routine runs
*/
void sqlite3RegisterBuiltinFunctions(void){
  /*
  ** The following array holds FuncDef structures for all of the functions
  ** defined in this file.
  **
  ** The array cannot be constant since changes are made to the
  ** FuncDef.pHash elements at start-time.  The elements of this array
  ** are read-only after initialization is complete.
  **
  ** For peak efficiency, put the most frequently used function last.
  */
  static FuncDef aBuiltinFunc[] = {
/***** Functions only available with SQLITE_TESTCTRL_INTERNAL_FUNCTIONS *****/
    TEST_FUNC(implies_nonnull_row, 2, INLINEFUNC_implies_nonnull_row, 0),
    TEST_FUNC(expr_compare,        2, INLINEFUNC_expr_compare,        0),
    TEST_FUNC(expr_implies_expr,   2, INLINEFUNC_expr_implies_expr,   0),
#ifdef SQLITE_DEBUG
    TEST_FUNC(affinity,          1, INLINEFUNC_affinity, 0),
#endif
/***** Regular functions *****/
#ifdef SQLITE_SOUNDEX
    FUNCTION(soundex,            1, 0, 0, soundexFunc      ),
#endif
#ifndef SQLITE_OMIT_LOAD_EXTENSION
    SFUNCTION(load_extension,    1, 0, 0, loadExt          ),
    SFUNCTION(load_extension,    2, 0, 0, loadExt          ),
#endif
#if SQLITE_USER_AUTHENTICATION
    FUNCTION(sqlite_crypt,       2, 0, 0, sqlite3CryptFunc ),
#endif
#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS
    DFUNCTION(sqlite_compileoption_used,1, 0, 0, compileoptionusedFunc  ),
    DFUNCTION(sqlite_compileoption_get, 1, 0, 0, compileoptiongetFunc  ),
#endif /* SQLITE_OMIT_COMPILEOPTION_DIAGS */
    INLINE_FUNC(unlikely,        1, INLINEFUNC_unlikely, SQLITE_FUNC_UNLIKELY),
    INLINE_FUNC(likelihood,      2, INLINEFUNC_unlikely, SQLITE_FUNC_UNLIKELY),
    INLINE_FUNC(likely,          1, INLINEFUNC_unlikely, SQLITE_FUNC_UNLIKELY),
#ifdef SQLITE_ENABLE_OFFSET_SQL_FUNC
    FUNCTION2(sqlite_offset,     1, 0, 0, noopFunc,  SQLITE_FUNC_OFFSET|
                                                     SQLITE_FUNC_TYPEOF),
#endif
    FUNCTION(ltrim,              1, 1, 0, trimFunc         ),
    FUNCTION(ltrim,              2, 1, 0, trimFunc         ),
    FUNCTION(rtrim,              1, 2, 0, trimFunc         ),
    FUNCTION(rtrim,              2, 2, 0, trimFunc         ),
    FUNCTION(trim,               1, 3, 0, trimFunc         ),
    FUNCTION(trim,               2, 3, 0, trimFunc         ),
    FUNCTION(min,               -1, 0, 1, minmaxFunc       ),
    FUNCTION(min,                0, 0, 1, 0                ),
    WAGGREGATE(min, 1, 0, 1, minmaxStep, minMaxFinalize, minMaxValue, 0,
                                          SQLITE_FUNC_MINMAX ),
    FUNCTION(max,               -1, 1, 1, minmaxFunc       ),
    FUNCTION(max,                0, 1, 1, 0                ),
    WAGGREGATE(max, 1, 1, 1, minmaxStep, minMaxFinalize, minMaxValue, 0,
                                          SQLITE_FUNC_MINMAX ),
    FUNCTION2(typeof,            1, 0, 0, typeofFunc,  SQLITE_FUNC_TYPEOF),
    FUNCTION2(length,            1, 0, 0, lengthFunc,  SQLITE_FUNC_LENGTH),
    FUNCTION(instr,              2, 0, 0, instrFunc        ),
    FUNCTION(printf,            -1, 0, 0, printfFunc       ),
    FUNCTION(unicode,            1, 0, 0, unicodeFunc      ),
    FUNCTION(char,              -1, 0, 0, charFunc         ),
    FUNCTION(abs,                1, 0, 0, absFunc          ),
#ifndef SQLITE_OMIT_FLOATING_POINT
    FUNCTION(round,              1, 0, 0, roundFunc        ),
    FUNCTION(round,              2, 0, 0, roundFunc        ),
#endif
    FUNCTION(upper,              1, 0, 0, upperFunc        ),
    FUNCTION(lower,              1, 0, 0, lowerFunc        ),
    FUNCTION(hex,                1, 0, 0, hexFunc          ),
    INLINE_FUNC(ifnull,          2, INLINEFUNC_coalesce, 0 ),
    VFUNCTION(random,            0, 0, 0, randomFunc       ),
    VFUNCTION(randomblob,        1, 0, 0, randomBlob       ),
    FUNCTION(nullif,             2, 0, 1, nullifFunc       ),
    DFUNCTION(sqlite_version,    0, 0, 0, versionFunc      ),
    DFUNCTION(sqlite_source_id,  0, 0, 0, sourceidFunc     ),
    FUNCTION(sqlite_log,         2, 0, 0, errlogFunc       ),
    FUNCTION(quote,              1, 0, 0, quoteFunc        ),
    VFUNCTION(last_insert_rowid, 0, 0, 0, last_insert_rowid),
    VFUNCTION(changes,           0, 0, 0, changes          ),
    VFUNCTION(total_changes,     0, 0, 0, total_changes    ),
    FUNCTION(replace,            3, 0, 0, replaceFunc      ),
    FUNCTION(zeroblob,           1, 0, 0, zeroblobFunc     ),
    FUNCTION(substr,             2, 0, 0, substrFunc       ),
    FUNCTION(substr,             3, 0, 0, substrFunc       ),
    FUNCTION(substring,          2, 0, 0, substrFunc       ),
    FUNCTION(substring,          3, 0, 0, substrFunc       ),
    WAGGREGATE(sum,   1,0,0, sumStep, sumFinalize, sumFinalize, sumInverse, 0),
    WAGGREGATE(total, 1,0,0, sumStep,totalFinalize,totalFinalize,sumInverse, 0),
    WAGGREGATE(avg,   1,0,0, sumStep, avgFinalize, avgFinalize, sumInverse, 0),
    WAGGREGATE(count, 0,0,0, countStep, 
        countFinalize, countFinalize, countInverse, SQLITE_FUNC_COUNT  ),
    WAGGREGATE(count, 1,0,0, countStep, 
        countFinalize, countFinalize, countInverse, 0  ),
    WAGGREGATE(group_concat, 1, 0, 0, groupConcatStep, 
        groupConcatFinalize, groupConcatValue, groupConcatInverse, 0),
    WAGGREGATE(group_concat, 2, 0, 0, groupConcatStep, 
        groupConcatFinalize, groupConcatValue, groupConcatInverse, 0),
  
    LIKEFUNC(glob, 2, &globInfo, SQLITE_FUNC_LIKE|SQLITE_FUNC_CASE),
#ifdef SQLITE_CASE_SENSITIVE_LIKE
    LIKEFUNC(like, 2, &likeInfoAlt, SQLITE_FUNC_LIKE|SQLITE_FUNC_CASE),
    LIKEFUNC(like, 3, &likeInfoAlt, SQLITE_FUNC_LIKE|SQLITE_FUNC_CASE),
#else
    LIKEFUNC(like, 2, &likeInfoNorm, SQLITE_FUNC_LIKE),
    LIKEFUNC(like, 3, &likeInfoNorm, SQLITE_FUNC_LIKE),
#endif
#ifdef SQLITE_ENABLE_UNKNOWN_SQL_FUNCTION
    FUNCTION(unknown,           -1, 0, 0, unknownFunc      ),
#endif
    FUNCTION(coalesce,           1, 0, 0, 0                ),
    FUNCTION(coalesce,           0, 0, 0, 0                ),
#ifdef SQLITE_ENABLE_MATH_FUNCTIONS
    MFUNCTION(ceil,              1, ceil,      ceilingFunc ),
    MFUNCTION(ceiling,           1, ceil,      ceilingFunc ),
    MFUNCTION(floor,             1, floor,     ceilingFunc ),
    MFUNCTION(trunc,             1, trunc,     ceilingFunc ),
    FUNCTION(ln,                 1, 0, 0,      logFunc     ),
    FUNCTION(log,                1, 1, 0,      logFunc     ),
    FUNCTION(log10,              1, 1, 0,      logFunc     ),
    FUNCTION(log2,               1, 2, 0,      logFunc     ),
    FUNCTION(log,                2, 0, 0,      logFunc     ),
    MFUNCTION(exp,               1, exp,       math1Func   ),
    MFUNCTION(pow,               2, pow,       math2Func   ),
    MFUNCTION(power,             2, pow,       math2Func   ),
    MFUNCTION(mod,               2, fmod,      math2Func   ),
    MFUNCTION(acos,              1, acos,      math1Func   ),
    MFUNCTION(asin,              1, asin,      math1Func   ),
    MFUNCTION(atan,              1, atan,      math1Func   ),
    MFUNCTION(atan2,             2, atan2,     math2Func   ),
    MFUNCTION(cos,               1, cos,       math1Func   ),
    MFUNCTION(sin,               1, sin,       math1Func   ),
    MFUNCTION(tan,               1, tan,       math1Func   ),
    MFUNCTION(cosh,              1, cosh,      math1Func   ),
    MFUNCTION(sinh,              1, sinh,      math1Func   ),
    MFUNCTION(tanh,              1, tanh,      math1Func   ),
    MFUNCTION(acosh,             1, acosh,     math1Func   ),
    MFUNCTION(asinh,             1, asinh,     math1Func   ),
    MFUNCTION(atanh,             1, atanh,     math1Func   ),
    MFUNCTION(sqrt,              1, sqrt,      math1Func   ),
    MFUNCTION(radians,           1, degToRad,  math1Func   ),
    MFUNCTION(degrees,           1, radToDeg,  math1Func   ),
    FUNCTION(pi,                 0, 0, 0,      piFunc      ),
#endif /* SQLITE_ENABLE_MATH_FUNCTIONS */
    FUNCTION(sign,               1, 0, 0,      signFunc    ),
    INLINE_FUNC(coalesce,       -1, INLINEFUNC_coalesce, 0 ),
    INLINE_FUNC(iif,             3, INLINEFUNC_iif,      0 ),
  };
#ifndef SQLITE_OMIT_ALTERTABLE
  sqlite3AlterFunctions();
#endif
  sqlite3WindowFunctions();
  sqlite3RegisterDateTimeFunctions();
  sqlite3InsertBuiltinFuncs(aBuiltinFunc, ArraySize(aBuiltinFunc));

#if 0  /* Enable to print out how the built-in functions are hashed */
  {
    int i;
    FuncDef *p;
    for(i=0; i<SQLITE_FUNC_HASH_SZ; i++){
      printf("FUNC-HASH %02d:", i);
      for(p=sqlite3BuiltinFunctions.a[i]; p; p=p->u.pHash){
        int n = sqlite3Strlen30(p->zName);
        int h = p->zName[0] + n;
        printf(" %s(%d)", p->zName, h);
      }
      printf("\n");
    }
  }
#endif
}