Adding upstream version 3.45.1.upstream/3.45.1

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 2004 insertions, 0 deletions

diff --git a/src/analyze.c b/src/analyze.c
new file mode 100644
index 0000000..59e3d98
--- /dev/null
+++ b/src/analyze.c
@@ -0,0 +1,2004 @@
+/*
+** 2005-07-08
+**
+** 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 code associated with the ANALYZE command.
+**
+** The ANALYZE command gather statistics about the content of tables
+** and indices.  These statistics are made available to the query planner
+** to help it make better decisions about how to perform queries.
+**
+** The following system tables are or have been supported:
+**
+**    CREATE TABLE sqlite_stat1(tbl, idx, stat);
+**    CREATE TABLE sqlite_stat2(tbl, idx, sampleno, sample);
+**    CREATE TABLE sqlite_stat3(tbl, idx, nEq, nLt, nDLt, sample);
+**    CREATE TABLE sqlite_stat4(tbl, idx, nEq, nLt, nDLt, sample);
+**
+** Additional tables might be added in future releases of SQLite.
+** The sqlite_stat2 table is not created or used unless the SQLite version
+** is between 3.6.18 and 3.7.8, inclusive, and unless SQLite is compiled
+** with SQLITE_ENABLE_STAT2.  The sqlite_stat2 table is deprecated.
+** The sqlite_stat2 table is superseded by sqlite_stat3, which is only
+** created and used by SQLite versions 3.7.9 through 3.29.0 when
+** SQLITE_ENABLE_STAT3 defined.  The functionality of sqlite_stat3
+** is a superset of sqlite_stat2 and is also now deprecated.  The
+** sqlite_stat4 is an enhanced version of sqlite_stat3 and is only 
+** available when compiled with SQLITE_ENABLE_STAT4 and in SQLite
+** versions 3.8.1 and later.  STAT4 is the only variant that is still
+** supported.
+**
+** For most applications, sqlite_stat1 provides all the statistics required
+** for the query planner to make good choices.
+**
+** Format of sqlite_stat1:
+**
+** There is normally one row per index, with the index identified by the
+** name in the idx column.  The tbl column is the name of the table to
+** which the index belongs.  In each such row, the stat column will be
+** a string consisting of a list of integers.  The first integer in this
+** list is the number of rows in the index.  (This is the same as the
+** number of rows in the table, except for partial indices.)  The second
+** integer is the average number of rows in the index that have the same
+** value in the first column of the index.  The third integer is the average
+** number of rows in the index that have the same value for the first two
+** columns.  The N-th integer (for N>1) is the average number of rows in 
+** the index which have the same value for the first N-1 columns.  For
+** a K-column index, there will be K+1 integers in the stat column.  If
+** the index is unique, then the last integer will be 1.
+**
+** The list of integers in the stat column can optionally be followed
+** by the keyword "unordered".  The "unordered" keyword, if it is present,
+** must be separated from the last integer by a single space.  If the
+** "unordered" keyword is present, then the query planner assumes that
+** the index is unordered and will not use the index for a range query.
+** 
+** If the sqlite_stat1.idx column is NULL, then the sqlite_stat1.stat
+** column contains a single integer which is the (estimated) number of
+** rows in the table identified by sqlite_stat1.tbl.
+**
+** Format of sqlite_stat2:
+**
+** The sqlite_stat2 is only created and is only used if SQLite is compiled
+** with SQLITE_ENABLE_STAT2 and if the SQLite version number is between
+** 3.6.18 and 3.7.8.  The "stat2" table contains additional information
+** about the distribution of keys within an index.  The index is identified by
+** the "idx" column and the "tbl" column is the name of the table to which
+** the index belongs.  There are usually 10 rows in the sqlite_stat2
+** table for each index.
+**
+** The sqlite_stat2 entries for an index that have sampleno between 0 and 9
+** inclusive are samples of the left-most key value in the index taken at
+** evenly spaced points along the index.  Let the number of samples be S
+** (10 in the standard build) and let C be the number of rows in the index.
+** Then the sampled rows are given by:
+**
+**     rownumber = (i*C*2 + C)/(S*2)
+**
+** For i between 0 and S-1.  Conceptually, the index space is divided into
+** S uniform buckets and the samples are the middle row from each bucket.
+**
+** The format for sqlite_stat2 is recorded here for legacy reference.  This
+** version of SQLite does not support sqlite_stat2.  It neither reads nor
+** writes the sqlite_stat2 table.  This version of SQLite only supports
+** sqlite_stat3.
+**
+** Format for sqlite_stat3:
+**
+** The sqlite_stat3 format is a subset of sqlite_stat4.  Hence, the
+** sqlite_stat4 format will be described first.  Further information
+** about sqlite_stat3 follows the sqlite_stat4 description.
+**
+** Format for sqlite_stat4:
+**
+** As with sqlite_stat2, the sqlite_stat4 table contains histogram data
+** to aid the query planner in choosing good indices based on the values
+** that indexed columns are compared against in the WHERE clauses of
+** queries.
+**
+** The sqlite_stat4 table contains multiple entries for each index.
+** The idx column names the index and the tbl column is the table of the
+** index.  If the idx and tbl columns are the same, then the sample is
+** of the INTEGER PRIMARY KEY.  The sample column is a blob which is the
+** binary encoding of a key from the index.  The nEq column is a
+** list of integers.  The first integer is the approximate number
+** of entries in the index whose left-most column exactly matches
+** the left-most column of the sample.  The second integer in nEq
+** is the approximate number of entries in the index where the
+** first two columns match the first two columns of the sample.
+** And so forth.  nLt is another list of integers that show the approximate
+** number of entries that are strictly less than the sample.  The first
+** integer in nLt contains the number of entries in the index where the
+** left-most column is less than the left-most column of the sample.
+** The K-th integer in the nLt entry is the number of index entries 
+** where the first K columns are less than the first K columns of the
+** sample.  The nDLt column is like nLt except that it contains the 
+** number of distinct entries in the index that are less than the
+** sample.
+**
+** There can be an arbitrary number of sqlite_stat4 entries per index.
+** The ANALYZE command will typically generate sqlite_stat4 tables
+** that contain between 10 and 40 samples which are distributed across
+** the key space, though not uniformly, and which include samples with
+** large nEq values.
+**
+** Format for sqlite_stat3 redux:
+**
+** The sqlite_stat3 table is like sqlite_stat4 except that it only
+** looks at the left-most column of the index.  The sqlite_stat3.sample
+** column contains the actual value of the left-most column instead
+** of a blob encoding of the complete index key as is found in
+** sqlite_stat4.sample.  The nEq, nLt, and nDLt entries of sqlite_stat3
+** all contain just a single integer which is the same as the first
+** integer in the equivalent columns in sqlite_stat4.
+*/
+#ifndef SQLITE_OMIT_ANALYZE
+#include "sqliteInt.h"
+
+#if defined(SQLITE_ENABLE_STAT4)
+# define IsStat4     1
+#else
+# define IsStat4     0
+# undef SQLITE_STAT4_SAMPLES
+# define SQLITE_STAT4_SAMPLES 1
+#endif
+
+/*
+** This routine generates code that opens the sqlite_statN tables.
+** The sqlite_stat1 table is always relevant.  sqlite_stat2 is now
+** obsolete.  sqlite_stat3 and sqlite_stat4 are only opened when
+** appropriate compile-time options are provided.
+**
+** If the sqlite_statN tables do not previously exist, it is created.
+**
+** Argument zWhere may be a pointer to a buffer containing a table name,
+** or it may be a NULL pointer. If it is not NULL, then all entries in
+** the sqlite_statN tables associated with the named table are deleted.
+** If zWhere==0, then code is generated to delete all stat table entries.
+*/
+static void openStatTable(
+  Parse *pParse,          /* Parsing context */
+  int iDb,                /* The database we are looking in */
+  int iStatCur,           /* Open the sqlite_stat1 table on this cursor */
+  const char *zWhere,     /* Delete entries for this table or index */
+  const char *zWhereType  /* Either "tbl" or "idx" */
+){
+  static const struct {
+    const char *zName;
+    const char *zCols;
+  } aTable[] = {
+    { "sqlite_stat1", "tbl,idx,stat" },
+#if defined(SQLITE_ENABLE_STAT4)
+    { "sqlite_stat4", "tbl,idx,neq,nlt,ndlt,sample" },
+#else
+    { "sqlite_stat4", 0 },
+#endif
+    { "sqlite_stat3", 0 },
+  };
+  int i;
+  sqlite3 *db = pParse->db;
+  Db *pDb;
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  u32 aRoot[ArraySize(aTable)];
+  u8 aCreateTbl[ArraySize(aTable)];
+#ifdef SQLITE_ENABLE_STAT4
+  const int nToOpen = OptimizationEnabled(db,SQLITE_Stat4) ? 2 : 1;
+#else
+  const int nToOpen = 1;
+#endif
+
+  if( v==0 ) return;
+  assert( sqlite3BtreeHoldsAllMutexes(db) );
+  assert( sqlite3VdbeDb(v)==db );
+  pDb = &db->aDb[iDb];
+
+  /* Create new statistic tables if they do not exist, or clear them
+  ** if they do already exist.
+  */
+  for(i=0; i<ArraySize(aTable); i++){
+    const char *zTab = aTable[i].zName;
+    Table *pStat;
+    aCreateTbl[i] = 0;
+    if( (pStat = sqlite3FindTable(db, zTab, pDb->zDbSName))==0 ){
+      if( i<nToOpen ){
+        /* The sqlite_statN table does not exist. Create it. Note that a 
+        ** side-effect of the CREATE TABLE statement is to leave the rootpage 
+        ** of the new table in register pParse->regRoot. This is important 
+        ** because the OpenWrite opcode below will be needing it. */
+        sqlite3NestedParse(pParse,
+            "CREATE TABLE %Q.%s(%s)", pDb->zDbSName, zTab, aTable[i].zCols
+        );
+        aRoot[i] = (u32)pParse->regRoot;
+        aCreateTbl[i] = OPFLAG_P2ISREG;
+      }
+    }else{
+      /* The table already exists. If zWhere is not NULL, delete all entries 
+      ** associated with the table zWhere. If zWhere is NULL, delete the
+      ** entire contents of the table. */
+      aRoot[i] = pStat->tnum;
+      sqlite3TableLock(pParse, iDb, aRoot[i], 1, zTab);
+      if( zWhere ){
+        sqlite3NestedParse(pParse,
+           "DELETE FROM %Q.%s WHERE %s=%Q",
+           pDb->zDbSName, zTab, zWhereType, zWhere
+        );
+#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
+      }else if( db->xPreUpdateCallback ){
+        sqlite3NestedParse(pParse, "DELETE FROM %Q.%s", pDb->zDbSName, zTab);
+#endif
+      }else{
+        /* The sqlite_stat[134] table already exists.  Delete all rows. */
+        sqlite3VdbeAddOp2(v, OP_Clear, (int)aRoot[i], iDb);
+      }
+    }
+  }
+
+  /* Open the sqlite_stat[134] tables for writing. */
+  for(i=0; i<nToOpen; i++){
+    assert( i<ArraySize(aTable) );
+    sqlite3VdbeAddOp4Int(v, OP_OpenWrite, iStatCur+i, (int)aRoot[i], iDb, 3);
+    sqlite3VdbeChangeP5(v, aCreateTbl[i]);
+    VdbeComment((v, aTable[i].zName));
+  }
+}
+
+/*
+** Recommended number of samples for sqlite_stat4
+*/
+#ifndef SQLITE_STAT4_SAMPLES
+# define SQLITE_STAT4_SAMPLES 24
+#endif
+
+/*
+** Three SQL functions - stat_init(), stat_push(), and stat_get() -
+** share an instance of the following structure to hold their state
+** information.
+*/
+typedef struct StatAccum StatAccum;
+typedef struct StatSample StatSample;
+struct StatSample {
+  tRowcnt *anDLt;                 /* sqlite_stat4.nDLt */
+#ifdef SQLITE_ENABLE_STAT4
+  tRowcnt *anEq;                  /* sqlite_stat4.nEq */
+  tRowcnt *anLt;                  /* sqlite_stat4.nLt */
+  union {
+    i64 iRowid;                     /* Rowid in main table of the key */
+    u8 *aRowid;                     /* Key for WITHOUT ROWID tables */
+  } u;
+  u32 nRowid;                     /* Sizeof aRowid[] */
+  u8 isPSample;                   /* True if a periodic sample */
+  int iCol;                       /* If !isPSample, the reason for inclusion */
+  u32 iHash;                      /* Tiebreaker hash */
+#endif
+};                                                    
+struct StatAccum {
+  sqlite3 *db;              /* Database connection, for malloc() */
+  tRowcnt nEst;             /* Estimated number of rows */
+  tRowcnt nRow;             /* Number of rows visited so far */
+  int nLimit;               /* Analysis row-scan limit */
+  int nCol;                 /* Number of columns in index + pk/rowid */
+  int nKeyCol;              /* Number of index columns w/o the pk/rowid */
+  u8 nSkipAhead;            /* Number of times of skip-ahead */
+  StatSample current;       /* Current row as a StatSample */
+#ifdef SQLITE_ENABLE_STAT4
+  tRowcnt nPSample;         /* How often to do a periodic sample */
+  int mxSample;             /* Maximum number of samples to accumulate */
+  u32 iPrn;                 /* Pseudo-random number used for sampling */
+  StatSample *aBest;        /* Array of nCol best samples */
+  int iMin;                 /* Index in a[] of entry with minimum score */
+  int nSample;              /* Current number of samples */
+  int nMaxEqZero;           /* Max leading 0 in anEq[] for any a[] entry */
+  int iGet;                 /* Index of current sample accessed by stat_get() */
+  StatSample *a;            /* Array of mxSample StatSample objects */
+#endif
+};
+
+/* Reclaim memory used by a StatSample
+*/
+#ifdef SQLITE_ENABLE_STAT4
+static void sampleClear(sqlite3 *db, StatSample *p){
+  assert( db!=0 );
+  if( p->nRowid ){
+    sqlite3DbFree(db, p->u.aRowid);
+    p->nRowid = 0;
+  }
+}
+#endif
+
+/* Initialize the BLOB value of a ROWID
+*/
+#ifdef SQLITE_ENABLE_STAT4
+static void sampleSetRowid(sqlite3 *db, StatSample *p, int n, const u8 *pData){
+  assert( db!=0 );
+  if( p->nRowid ) sqlite3DbFree(db, p->u.aRowid);
+  p->u.aRowid = sqlite3DbMallocRawNN(db, n);
+  if( p->u.aRowid ){
+    p->nRowid = n;
+    memcpy(p->u.aRowid, pData, n);
+  }else{
+    p->nRowid = 0;
+  }
+}
+#endif
+
+/* Initialize the INTEGER value of a ROWID.
+*/
+#ifdef SQLITE_ENABLE_STAT4
+static void sampleSetRowidInt64(sqlite3 *db, StatSample *p, i64 iRowid){
+  assert( db!=0 );
+  if( p->nRowid ) sqlite3DbFree(db, p->u.aRowid);
+  p->nRowid = 0;
+  p->u.iRowid = iRowid;
+}
+#endif
+
+
+/*
+** Copy the contents of object (*pFrom) into (*pTo).
+*/
+#ifdef SQLITE_ENABLE_STAT4
+static void sampleCopy(StatAccum *p, StatSample *pTo, StatSample *pFrom){
+  pTo->isPSample = pFrom->isPSample;
+  pTo->iCol = pFrom->iCol;
+  pTo->iHash = pFrom->iHash;
+  memcpy(pTo->anEq, pFrom->anEq, sizeof(tRowcnt)*p->nCol);
+  memcpy(pTo->anLt, pFrom->anLt, sizeof(tRowcnt)*p->nCol);
+  memcpy(pTo->anDLt, pFrom->anDLt, sizeof(tRowcnt)*p->nCol);
+  if( pFrom->nRowid ){
+    sampleSetRowid(p->db, pTo, pFrom->nRowid, pFrom->u.aRowid);
+  }else{
+    sampleSetRowidInt64(p->db, pTo, pFrom->u.iRowid);
+  }
+}
+#endif
+
+/*
+** Reclaim all memory of a StatAccum structure.
+*/
+static void statAccumDestructor(void *pOld){
+  StatAccum *p = (StatAccum*)pOld;
+#ifdef SQLITE_ENABLE_STAT4
+  if( p->mxSample ){
+    int i;
+    for(i=0; i<p->nCol; i++) sampleClear(p->db, p->aBest+i);
+    for(i=0; i<p->mxSample; i++) sampleClear(p->db, p->a+i);
+    sampleClear(p->db, &p->current);
+  }
+#endif
+  sqlite3DbFree(p->db, p);
+}
+
+/*
+** Implementation of the stat_init(N,K,C,L) SQL function. The four parameters
+** are:
+**     N:    The number of columns in the index including the rowid/pk (note 1)
+**     K:    The number of columns in the index excluding the rowid/pk.
+**     C:    Estimated number of rows in the index
+**     L:    A limit on the number of rows to scan, or 0 for no-limit 
+**
+** Note 1:  In the special case of the covering index that implements a
+** WITHOUT ROWID table, N is the number of PRIMARY KEY columns, not the
+** total number of columns in the table.
+**
+** For indexes on ordinary rowid tables, N==K+1.  But for indexes on
+** WITHOUT ROWID tables, N=K+P where P is the number of columns in the
+** PRIMARY KEY of the table.  The covering index that implements the
+** original WITHOUT ROWID table as N==K as a special case.
+**
+** This routine allocates the StatAccum object in heap memory. The return 
+** value is a pointer to the StatAccum object.  The datatype of the
+** return value is BLOB, but it is really just a pointer to the StatAccum
+** object.
+*/
+static void statInit(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  StatAccum *p;
+  int nCol;                       /* Number of columns in index being sampled */
+  int nKeyCol;                    /* Number of key columns */
+  int nColUp;                     /* nCol rounded up for alignment */
+  int n;                          /* Bytes of space to allocate */
+  sqlite3 *db = sqlite3_context_db_handle(context);   /* Database connection */
+#ifdef SQLITE_ENABLE_STAT4
+  /* Maximum number of samples.  0 if STAT4 data is not collected */
+  int mxSample = OptimizationEnabled(db,SQLITE_Stat4) ?SQLITE_STAT4_SAMPLES :0;
+#endif
+
+  /* Decode the three function arguments */
+  UNUSED_PARAMETER(argc);
+  nCol = sqlite3_value_int(argv[0]);
+  assert( nCol>0 );
+  nColUp = sizeof(tRowcnt)<8 ? (nCol+1)&~1 : nCol;
+  nKeyCol = sqlite3_value_int(argv[1]);
+  assert( nKeyCol<=nCol );
+  assert( nKeyCol>0 );
+
+  /* Allocate the space required for the StatAccum object */
+  n = sizeof(*p) 
+    + sizeof(tRowcnt)*nColUp;                    /* StatAccum.anDLt */
+#ifdef SQLITE_ENABLE_STAT4
+  n += sizeof(tRowcnt)*nColUp;                   /* StatAccum.anEq */
+  if( mxSample ){
+    n += sizeof(tRowcnt)*nColUp                  /* StatAccum.anLt */
+      + sizeof(StatSample)*(nCol+mxSample)       /* StatAccum.aBest[], a[] */
+      + sizeof(tRowcnt)*3*nColUp*(nCol+mxSample);
+  }
+#endif
+  p = sqlite3DbMallocZero(db, n);
+  if( p==0 ){
+    sqlite3_result_error_nomem(context);
+    return;
+  }
+
+  p->db = db;
+  p->nEst = sqlite3_value_int64(argv[2]);
+  p->nRow = 0;
+  p->nLimit = sqlite3_value_int64(argv[3]);
+  p->nCol = nCol;
+  p->nKeyCol = nKeyCol;
+  p->nSkipAhead = 0;
+  p->current.anDLt = (tRowcnt*)&p[1];
+
+#ifdef SQLITE_ENABLE_STAT4
+  p->current.anEq = &p->current.anDLt[nColUp];
+  p->mxSample = p->nLimit==0 ? mxSample : 0;
+  if( mxSample ){
+    u8 *pSpace;                     /* Allocated space not yet assigned */
+    int i;                          /* Used to iterate through p->aSample[] */
+
+    p->iGet = -1;
+    p->nPSample = (tRowcnt)(p->nEst/(mxSample/3+1) + 1);
+    p->current.anLt = &p->current.anEq[nColUp];
+    p->iPrn = 0x689e962d*(u32)nCol ^ 0xd0944565*(u32)sqlite3_value_int(argv[2]);
+  
+    /* Set up the StatAccum.a[] and aBest[] arrays */
+    p->a = (struct StatSample*)&p->current.anLt[nColUp];
+    p->aBest = &p->a[mxSample];
+    pSpace = (u8*)(&p->a[mxSample+nCol]);
+    for(i=0; i<(mxSample+nCol); i++){
+      p->a[i].anEq = (tRowcnt *)pSpace; pSpace += (sizeof(tRowcnt) * nColUp);
+      p->a[i].anLt = (tRowcnt *)pSpace; pSpace += (sizeof(tRowcnt) * nColUp);
+      p->a[i].anDLt = (tRowcnt *)pSpace; pSpace += (sizeof(tRowcnt) * nColUp);
+    }
+    assert( (pSpace - (u8*)p)==n );
+  
+    for(i=0; i<nCol; i++){
+      p->aBest[i].iCol = i;
+    }
+  }
+#endif
+
+  /* Return a pointer to the allocated object to the caller.  Note that
+  ** only the pointer (the 2nd parameter) matters.  The size of the object
+  ** (given by the 3rd parameter) is never used and can be any positive
+  ** value. */
+  sqlite3_result_blob(context, p, sizeof(*p), statAccumDestructor);
+}
+static const FuncDef statInitFuncdef = {
+  4,               /* nArg */
+  SQLITE_UTF8,     /* funcFlags */
+  0,               /* pUserData */
+  0,               /* pNext */
+  statInit,        /* xSFunc */
+  0,               /* xFinalize */
+  0, 0,            /* xValue, xInverse */
+  "stat_init",     /* zName */
+  {0}
+};
+
+#ifdef SQLITE_ENABLE_STAT4
+/*
+** pNew and pOld are both candidate non-periodic samples selected for 
+** the same column (pNew->iCol==pOld->iCol). Ignoring this column and 
+** considering only any trailing columns and the sample hash value, this
+** function returns true if sample pNew is to be preferred over pOld.
+** In other words, if we assume that the cardinalities of the selected
+** column for pNew and pOld are equal, is pNew to be preferred over pOld.
+**
+** This function assumes that for each argument sample, the contents of
+** the anEq[] array from pSample->anEq[pSample->iCol+1] onwards are valid. 
+*/
+static int sampleIsBetterPost(
+  StatAccum *pAccum, 
+  StatSample *pNew, 
+  StatSample *pOld
+){
+  int nCol = pAccum->nCol;
+  int i;
+  assert( pNew->iCol==pOld->iCol );
+  for(i=pNew->iCol+1; i<nCol; i++){
+    if( pNew->anEq[i]>pOld->anEq[i] ) return 1;
+    if( pNew->anEq[i]<pOld->anEq[i] ) return 0;
+  }
+  if( pNew->iHash>pOld->iHash ) return 1;
+  return 0;
+}
+#endif
+
+#ifdef SQLITE_ENABLE_STAT4
+/*
+** Return true if pNew is to be preferred over pOld.
+**
+** This function assumes that for each argument sample, the contents of
+** the anEq[] array from pSample->anEq[pSample->iCol] onwards are valid. 
+*/
+static int sampleIsBetter(
+  StatAccum *pAccum, 
+  StatSample *pNew, 
+  StatSample *pOld
+){
+  tRowcnt nEqNew = pNew->anEq[pNew->iCol];
+  tRowcnt nEqOld = pOld->anEq[pOld->iCol];
+
+  assert( pOld->isPSample==0 && pNew->isPSample==0 );
+  assert( IsStat4 || (pNew->iCol==0 && pOld->iCol==0) );
+
+  if( (nEqNew>nEqOld) ) return 1;
+  if( nEqNew==nEqOld ){
+    if( pNew->iCol<pOld->iCol ) return 1;
+    return (pNew->iCol==pOld->iCol && sampleIsBetterPost(pAccum, pNew, pOld));
+  }
+  return 0;
+}
+
+/*
+** Copy the contents of sample *pNew into the p->a[] array. If necessary,
+** remove the least desirable sample from p->a[] to make room.
+*/
+static void sampleInsert(StatAccum *p, StatSample *pNew, int nEqZero){
+  StatSample *pSample = 0;
+  int i;
+
+  assert( IsStat4 || nEqZero==0 );
+
+  /* StatAccum.nMaxEqZero is set to the maximum number of leading 0
+  ** values in the anEq[] array of any sample in StatAccum.a[]. In
+  ** other words, if nMaxEqZero is n, then it is guaranteed that there
+  ** are no samples with StatSample.anEq[m]==0 for (m>=n). */
+  if( nEqZero>p->nMaxEqZero ){
+    p->nMaxEqZero = nEqZero;
+  }
+  if( pNew->isPSample==0 ){
+    StatSample *pUpgrade = 0;
+    assert( pNew->anEq[pNew->iCol]>0 );
+
+    /* This sample is being added because the prefix that ends in column 
+    ** iCol occurs many times in the table. However, if we have already
+    ** added a sample that shares this prefix, there is no need to add
+    ** this one. Instead, upgrade the priority of the highest priority
+    ** existing sample that shares this prefix.  */
+    for(i=p->nSample-1; i>=0; i--){
+      StatSample *pOld = &p->a[i];
+      if( pOld->anEq[pNew->iCol]==0 ){
+        if( pOld->isPSample ) return;
+        assert( pOld->iCol>pNew->iCol );
+        assert( sampleIsBetter(p, pNew, pOld) );
+        if( pUpgrade==0 || sampleIsBetter(p, pOld, pUpgrade) ){
+          pUpgrade = pOld;
+        }
+      }
+    }
+    if( pUpgrade ){
+      pUpgrade->iCol = pNew->iCol;
+      pUpgrade->anEq[pUpgrade->iCol] = pNew->anEq[pUpgrade->iCol];
+      goto find_new_min;
+    }
+  }
+
+  /* If necessary, remove sample iMin to make room for the new sample. */
+  if( p->nSample>=p->mxSample ){
+    StatSample *pMin = &p->a[p->iMin];
+    tRowcnt *anEq = pMin->anEq;
+    tRowcnt *anLt = pMin->anLt;
+    tRowcnt *anDLt = pMin->anDLt;
+    sampleClear(p->db, pMin);
+    memmove(pMin, &pMin[1], sizeof(p->a[0])*(p->nSample-p->iMin-1));
+    pSample = &p->a[p->nSample-1];
+    pSample->nRowid = 0;
+    pSample->anEq = anEq;
+    pSample->anDLt = anDLt;
+    pSample->anLt = anLt;
+    p->nSample = p->mxSample-1;
+  }
+
+  /* The "rows less-than" for the rowid column must be greater than that
+  ** for the last sample in the p->a[] array. Otherwise, the samples would
+  ** be out of order. */
+  assert( p->nSample==0 
+       || pNew->anLt[p->nCol-1] > p->a[p->nSample-1].anLt[p->nCol-1] );
+
+  /* Insert the new sample */
+  pSample = &p->a[p->nSample];
+  sampleCopy(p, pSample, pNew);
+  p->nSample++;
+
+  /* Zero the first nEqZero entries in the anEq[] array. */
+  memset(pSample->anEq, 0, sizeof(tRowcnt)*nEqZero);
+
+find_new_min:
+  if( p->nSample>=p->mxSample ){
+    int iMin = -1;
+    for(i=0; i<p->mxSample; i++){
+      if( p->a[i].isPSample ) continue;
+      if( iMin<0 || sampleIsBetter(p, &p->a[iMin], &p->a[i]) ){
+        iMin = i;
+      }
+    }
+    assert( iMin>=0 );
+    p->iMin = iMin;
+  }
+}
+#endif /* SQLITE_ENABLE_STAT4 */
+
+#ifdef SQLITE_ENABLE_STAT4
+/*
+** Field iChng of the index being scanned has changed. So at this point
+** p->current contains a sample that reflects the previous row of the
+** index. The value of anEq[iChng] and subsequent anEq[] elements are
+** correct at this point.
+*/
+static void samplePushPrevious(StatAccum *p, int iChng){
+  int i;
+
+  /* Check if any samples from the aBest[] array should be pushed
+  ** into IndexSample.a[] at this point.  */
+  for(i=(p->nCol-2); i>=iChng; i--){
+    StatSample *pBest = &p->aBest[i];
+    pBest->anEq[i] = p->current.anEq[i];
+    if( p->nSample<p->mxSample || sampleIsBetter(p, pBest, &p->a[p->iMin]) ){
+      sampleInsert(p, pBest, i);
+    }
+  }
+
+  /* Check that no sample contains an anEq[] entry with an index of
+  ** p->nMaxEqZero or greater set to zero. */
+  for(i=p->nSample-1; i>=0; i--){
+    int j;
+    for(j=p->nMaxEqZero; j<p->nCol; j++) assert( p->a[i].anEq[j]>0 );
+  }
+
+  /* Update the anEq[] fields of any samples already collected. */
+  if( iChng<p->nMaxEqZero ){
+    for(i=p->nSample-1; i>=0; i--){
+      int j;
+      for(j=iChng; j<p->nCol; j++){
+        if( p->a[i].anEq[j]==0 ) p->a[i].anEq[j] = p->current.anEq[j];
+      }
+    }
+    p->nMaxEqZero = iChng;
+  }
+}
+#endif /* SQLITE_ENABLE_STAT4 */
+
+/*
+** Implementation of the stat_push SQL function:  stat_push(P,C,R)
+** Arguments:
+**
+**    P     Pointer to the StatAccum object created by stat_init()
+**    C     Index of left-most column to differ from previous row
+**    R     Rowid for the current row.  Might be a key record for
+**          WITHOUT ROWID tables.
+**
+** The purpose of this routine is to collect statistical data and/or
+** samples from the index being analyzed into the StatAccum object.
+** The stat_get() SQL function will be used afterwards to
+** retrieve the information gathered.
+**
+** This SQL function usually returns NULL, but might return an integer
+** if it wants the byte-code to do special processing.
+**
+** The R parameter is only used for STAT4
+*/
+static void statPush(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  int i;
+
+  /* The three function arguments */
+  StatAccum *p = (StatAccum*)sqlite3_value_blob(argv[0]);
+  int iChng = sqlite3_value_int(argv[1]);
+
+  UNUSED_PARAMETER( argc );
+  UNUSED_PARAMETER( context );
+  assert( p->nCol>0 );
+  assert( iChng<p->nCol );
+
+  if( p->nRow==0 ){
+    /* This is the first call to this function. Do initialization. */
+#ifdef SQLITE_ENABLE_STAT4
+    for(i=0; i<p->nCol; i++) p->current.anEq[i] = 1;
+#endif
+  }else{
+    /* Second and subsequent calls get processed here */
+#ifdef SQLITE_ENABLE_STAT4
+    if( p->mxSample ) samplePushPrevious(p, iChng);
+#endif
+
+    /* Update anDLt[], anLt[] and anEq[] to reflect the values that apply
+    ** to the current row of the index. */
+#ifdef SQLITE_ENABLE_STAT4
+    for(i=0; i<iChng; i++){
+      p->current.anEq[i]++;
+    }
+#endif
+    for(i=iChng; i<p->nCol; i++){
+      p->current.anDLt[i]++;
+#ifdef SQLITE_ENABLE_STAT4
+      if( p->mxSample ) p->current.anLt[i] += p->current.anEq[i];
+      p->current.anEq[i] = 1;
+#endif
+    }
+  }
+
+  p->nRow++;
+#ifdef SQLITE_ENABLE_STAT4
+  if( p->mxSample ){
+    tRowcnt nLt;
+    if( sqlite3_value_type(argv[2])==SQLITE_INTEGER ){
+      sampleSetRowidInt64(p->db, &p->current, sqlite3_value_int64(argv[2]));
+    }else{
+      sampleSetRowid(p->db, &p->current, sqlite3_value_bytes(argv[2]),
+                                         sqlite3_value_blob(argv[2]));
+    }
+    p->current.iHash = p->iPrn = p->iPrn*1103515245 + 12345;
+
+    nLt = p->current.anLt[p->nCol-1];
+    /* Check if this is to be a periodic sample. If so, add it. */
+    if( (nLt/p->nPSample)!=(nLt+1)/p->nPSample ){
+      p->current.isPSample = 1;
+      p->current.iCol = 0;
+      sampleInsert(p, &p->current, p->nCol-1);
+      p->current.isPSample = 0;
+    }
+
+    /* Update the aBest[] array. */
+    for(i=0; i<(p->nCol-1); i++){
+      p->current.iCol = i;
+      if( i>=iChng || sampleIsBetterPost(p, &p->current, &p->aBest[i]) ){
+        sampleCopy(p, &p->aBest[i], &p->current);
+      }
+    }
+  }else
+#endif
+  if( p->nLimit && p->nRow>(tRowcnt)p->nLimit*(p->nSkipAhead+1) ){
+    p->nSkipAhead++;
+    sqlite3_result_int(context, p->current.anDLt[0]>0);
+  }
+}
+
+static const FuncDef statPushFuncdef = {
+  2+IsStat4,       /* nArg */
+  SQLITE_UTF8,     /* funcFlags */
+  0,               /* pUserData */
+  0,               /* pNext */
+  statPush,        /* xSFunc */
+  0,               /* xFinalize */
+  0, 0,            /* xValue, xInverse */
+  "stat_push",     /* zName */
+  {0}
+};
+
+#define STAT_GET_STAT1 0          /* "stat" column of stat1 table */
+#define STAT_GET_ROWID 1          /* "rowid" column of stat[34] entry */
+#define STAT_GET_NEQ   2          /* "neq" column of stat[34] entry */
+#define STAT_GET_NLT   3          /* "nlt" column of stat[34] entry */
+#define STAT_GET_NDLT  4          /* "ndlt" column of stat[34] entry */
+
+/*
+** Implementation of the stat_get(P,J) SQL function.  This routine is
+** used to query statistical information that has been gathered into
+** the StatAccum object by prior calls to stat_push().  The P parameter
+** has type BLOB but it is really just a pointer to the StatAccum object.
+** The content to returned is determined by the parameter J
+** which is one of the STAT_GET_xxxx values defined above.
+**
+** The stat_get(P,J) function is not available to generic SQL.  It is
+** inserted as part of a manually constructed bytecode program.  (See
+** the callStatGet() routine below.)  It is guaranteed that the P
+** parameter will always be a pointer to a StatAccum object, never a
+** NULL.
+**
+** If STAT4 is not enabled, then J is always
+** STAT_GET_STAT1 and is hence omitted and this routine becomes
+** a one-parameter function, stat_get(P), that always returns the
+** stat1 table entry information.
+*/
+static void statGet(
+  sqlite3_context *context,
+  int argc,
+  sqlite3_value **argv
+){
+  StatAccum *p = (StatAccum*)sqlite3_value_blob(argv[0]);
+#ifdef SQLITE_ENABLE_STAT4
+  /* STAT4 has a parameter on this routine. */
+  int eCall = sqlite3_value_int(argv[1]);
+  assert( argc==2 );
+  assert( eCall==STAT_GET_STAT1 || eCall==STAT_GET_NEQ 
+       || eCall==STAT_GET_ROWID || eCall==STAT_GET_NLT
+       || eCall==STAT_GET_NDLT 
+  );
+  assert( eCall==STAT_GET_STAT1 || p->mxSample );
+  if( eCall==STAT_GET_STAT1 )
+#else
+  assert( argc==1 );
+#endif
+  {
+    /* Return the value to store in the "stat" column of the sqlite_stat1
+    ** table for this index.
+    **
+    ** The value is a string composed of a list of integers describing 
+    ** the index. The first integer in the list is the total number of 
+    ** entries in the index. There is one additional integer in the list 
+    ** for each indexed column. This additional integer is an estimate of
+    ** the number of rows matched by a equality query on the index using
+    ** a key with the corresponding number of fields. In other words,
+    ** if the index is on columns (a,b) and the sqlite_stat1 value is 
+    ** "100 10 2", then SQLite estimates that:
+    **
+    **   * the index contains 100 rows,
+    **   * "WHERE a=?" matches 10 rows, and
+    **   * "WHERE a=? AND b=?" matches 2 rows.
+    **
+    ** If D is the count of distinct values and K is the total number of 
+    ** rows, then each estimate is usually computed as:
+    **
+    **        I = (K+D-1)/D
+    **
+    ** In other words, I is K/D rounded up to the next whole integer.
+    ** However, if I is between 1.0 and 1.1 (in other words if I is
+    ** close to 1.0 but just a little larger) then do not round up but
+    ** instead keep the I value at 1.0.
+    */
+    sqlite3_str sStat;   /* Text of the constructed "stat" line */
+    int i;               /* Loop counter */
+
+    sqlite3StrAccumInit(&sStat, 0, 0, 0, (p->nKeyCol+1)*100);
+    sqlite3_str_appendf(&sStat, "%llu", 
+        p->nSkipAhead ? (u64)p->nEst : (u64)p->nRow);
+    for(i=0; i<p->nKeyCol; i++){
+      u64 nDistinct = p->current.anDLt[i] + 1;
+      u64 iVal = (p->nRow + nDistinct - 1) / nDistinct;
+      if( iVal==2 && p->nRow*10 <= nDistinct*11 ) iVal = 1;
+      sqlite3_str_appendf(&sStat, " %llu", iVal);
+#ifdef SQLITE_ENABLE_STAT4
+      assert( p->current.anEq[i] );
+#endif
+    }
+    sqlite3ResultStrAccum(context, &sStat);
+  }
+#ifdef SQLITE_ENABLE_STAT4
+  else if( eCall==STAT_GET_ROWID ){
+    if( p->iGet<0 ){
+      samplePushPrevious(p, 0);
+      p->iGet = 0;
+    }
+    if( p->iGet<p->nSample ){
+      StatSample *pS = p->a + p->iGet;
+      if( pS->nRowid==0 ){
+        sqlite3_result_int64(context, pS->u.iRowid);
+      }else{
+        sqlite3_result_blob(context, pS->u.aRowid, pS->nRowid,
+                            SQLITE_TRANSIENT);
+      }
+    }
+  }else{
+    tRowcnt *aCnt = 0;
+    sqlite3_str sStat;
+    int i;
+
+    assert( p->iGet<p->nSample );
+    switch( eCall ){
+      case STAT_GET_NEQ:  aCnt = p->a[p->iGet].anEq; break;
+      case STAT_GET_NLT:  aCnt = p->a[p->iGet].anLt; break;
+      default: {
+        aCnt = p->a[p->iGet].anDLt; 
+        p->iGet++;
+        break;
+      }
+    }
+    sqlite3StrAccumInit(&sStat, 0, 0, 0, p->nCol*100);
+    for(i=0; i<p->nCol; i++){
+      sqlite3_str_appendf(&sStat, "%llu ", (u64)aCnt[i]);
+    }
+    if( sStat.nChar ) sStat.nChar--;
+    sqlite3ResultStrAccum(context, &sStat);
+  }
+#endif /* SQLITE_ENABLE_STAT4 */
+#ifndef SQLITE_DEBUG
+  UNUSED_PARAMETER( argc );
+#endif
+}
+static const FuncDef statGetFuncdef = {
+  1+IsStat4,       /* nArg */
+  SQLITE_UTF8,     /* funcFlags */
+  0,               /* pUserData */
+  0,               /* pNext */
+  statGet,         /* xSFunc */
+  0,               /* xFinalize */
+  0, 0,            /* xValue, xInverse */
+  "stat_get",      /* zName */
+  {0}
+};
+
+static void callStatGet(Parse *pParse, int regStat, int iParam, int regOut){
+#ifdef SQLITE_ENABLE_STAT4
+  sqlite3VdbeAddOp2(pParse->pVdbe, OP_Integer, iParam, regStat+1);
+#elif SQLITE_DEBUG
+  assert( iParam==STAT_GET_STAT1 );
+#else
+  UNUSED_PARAMETER( iParam );
+#endif
+  assert( regOut!=regStat && regOut!=regStat+1 );
+  sqlite3VdbeAddFunctionCall(pParse, 0, regStat, regOut, 1+IsStat4,
+                             &statGetFuncdef, 0);
+}
+
+#ifdef SQLITE_ENABLE_EXPLAIN_COMMENTS
+/* Add a comment to the most recent VDBE opcode that is the name
+** of the k-th column of the pIdx index.
+*/
+static void analyzeVdbeCommentIndexWithColumnName(
+  Vdbe *v,         /* Prepared statement under construction */
+  Index *pIdx,     /* Index whose column is being loaded */
+  int k            /* Which column index */
+){
+  int i;           /* Index of column in the table */
+  assert( k>=0 && k<pIdx->nColumn );
+  i = pIdx->aiColumn[k];
+  if( NEVER(i==XN_ROWID) ){
+    VdbeComment((v,"%s.rowid",pIdx->zName));
+  }else if( i==XN_EXPR ){
+    assert( pIdx->bHasExpr );
+    VdbeComment((v,"%s.expr(%d)",pIdx->zName, k));
+  }else{
+    VdbeComment((v,"%s.%s", pIdx->zName, pIdx->pTable->aCol[i].zCnName));
+  }
+}
+#else
+# define analyzeVdbeCommentIndexWithColumnName(a,b,c)
+#endif /* SQLITE_DEBUG */
+
+/*
+** Generate code to do an analysis of all indices associated with
+** a single table.
+*/
+static void analyzeOneTable(
+  Parse *pParse,   /* Parser context */
+  Table *pTab,     /* Table whose indices are to be analyzed */
+  Index *pOnlyIdx, /* If not NULL, only analyze this one index */
+  int iStatCur,    /* Index of VdbeCursor that writes the sqlite_stat1 table */
+  int iMem,        /* Available memory locations begin here */
+  int iTab         /* Next available cursor */
+){
+  sqlite3 *db = pParse->db;    /* Database handle */
+  Index *pIdx;                 /* An index to being analyzed */
+  int iIdxCur;                 /* Cursor open on index being analyzed */
+  int iTabCur;                 /* Table cursor */
+  Vdbe *v;                     /* The virtual machine being built up */
+  int i;                       /* Loop counter */
+  int jZeroRows = -1;          /* Jump from here if number of rows is zero */
+  int iDb;                     /* Index of database containing pTab */
+  u8 needTableCnt = 1;         /* True to count the table */
+  int regNewRowid = iMem++;    /* Rowid for the inserted record */
+  int regStat = iMem++;        /* Register to hold StatAccum object */
+  int regChng = iMem++;        /* Index of changed index field */
+  int regRowid = iMem++;       /* Rowid argument passed to stat_push() */
+  int regTemp = iMem++;        /* Temporary use register */
+  int regTemp2 = iMem++;       /* Second temporary use register */
+  int regTabname = iMem++;     /* Register containing table name */
+  int regIdxname = iMem++;     /* Register containing index name */
+  int regStat1 = iMem++;       /* Value for the stat column of sqlite_stat1 */
+  int regPrev = iMem;          /* MUST BE LAST (see below) */
+#ifdef SQLITE_ENABLE_STAT4
+  int doOnce = 1;              /* Flag for a one-time computation */
+#endif
+#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
+  Table *pStat1 = 0;
+#endif
+
+  sqlite3TouchRegister(pParse, iMem);
+  assert( sqlite3NoTempsInRange(pParse, regNewRowid, iMem) );
+  v = sqlite3GetVdbe(pParse);
+  if( v==0 || NEVER(pTab==0) ){
+    return;
+  }
+  if( !IsOrdinaryTable(pTab) ){
+    /* Do not gather statistics on views or virtual tables */
+    return;
+  }
+  if( sqlite3_strlike("sqlite\\_%", pTab->zName, '\\')==0 ){
+    /* Do not gather statistics on system tables */
+    return;
+  }
+  assert( sqlite3BtreeHoldsAllMutexes(db) );
+  iDb = sqlite3SchemaToIndex(db, pTab->pSchema);
+  assert( iDb>=0 );
+  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );
+#ifndef SQLITE_OMIT_AUTHORIZATION
+  if( sqlite3AuthCheck(pParse, SQLITE_ANALYZE, pTab->zName, 0,
+      db->aDb[iDb].zDbSName ) ){
+    return;
+  }
+#endif
+
+#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
+  if( db->xPreUpdateCallback ){
+    pStat1 = (Table*)sqlite3DbMallocZero(db, sizeof(Table) + 13);
+    if( pStat1==0 ) return;
+    pStat1->zName = (char*)&pStat1[1];
+    memcpy(pStat1->zName, "sqlite_stat1", 13);
+    pStat1->nCol = 3;
+    pStat1->iPKey = -1;
+    sqlite3VdbeAddOp4(pParse->pVdbe, OP_Noop, 0, 0, 0,(char*)pStat1,P4_DYNAMIC);
+  }
+#endif
+
+  /* Establish a read-lock on the table at the shared-cache level. 
+  ** Open a read-only cursor on the table. Also allocate a cursor number
+  ** to use for scanning indexes (iIdxCur). No index cursor is opened at
+  ** this time though.  */
+  sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);
+  iTabCur = iTab++;
+  iIdxCur = iTab++;
+  pParse->nTab = MAX(pParse->nTab, iTab);
+  sqlite3OpenTable(pParse, iTabCur, iDb, pTab, OP_OpenRead);
+  sqlite3VdbeLoadString(v, regTabname, pTab->zName);
+
+  for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
+    int nCol;                     /* Number of columns in pIdx. "N" */
+    int addrRewind;               /* Address of "OP_Rewind iIdxCur" */
+    int addrNextRow;              /* Address of "next_row:" */
+    const char *zIdxName;         /* Name of the index */
+    int nColTest;                 /* Number of columns to test for changes */
+
+    if( pOnlyIdx && pOnlyIdx!=pIdx ) continue;
+    if( pIdx->pPartIdxWhere==0 ) needTableCnt = 0;
+    if( !HasRowid(pTab) && IsPrimaryKeyIndex(pIdx) ){
+      nCol = pIdx->nKeyCol;
+      zIdxName = pTab->zName;
+      nColTest = nCol - 1;
+    }else{
+      nCol = pIdx->nColumn;
+      zIdxName = pIdx->zName;
+      nColTest = pIdx->uniqNotNull ? pIdx->nKeyCol-1 : nCol-1;
+    }
+
+    /* Populate the register containing the index name. */
+    sqlite3VdbeLoadString(v, regIdxname, zIdxName);
+    VdbeComment((v, "Analysis for %s.%s", pTab->zName, zIdxName));
+
+    /*
+    ** Pseudo-code for loop that calls stat_push():
+    **
+    **   Rewind csr
+    **   if eof(csr) goto end_of_scan;
+    **   regChng = 0
+    **   goto chng_addr_0;
+    **
+    **  next_row:
+    **   regChng = 0
+    **   if( idx(0) != regPrev(0) ) goto chng_addr_0
+    **   regChng = 1
+    **   if( idx(1) != regPrev(1) ) goto chng_addr_1
+    **   ...
+    **   regChng = N
+    **   goto chng_addr_N
+    **
+    **  chng_addr_0:
+    **   regPrev(0) = idx(0)
+    **  chng_addr_1:
+    **   regPrev(1) = idx(1)
+    **  ...
+    **
+    **  endDistinctTest:
+    **   regRowid = idx(rowid)
+    **   stat_push(P, regChng, regRowid)
+    **   Next csr
+    **   if !eof(csr) goto next_row;
+    **
+    **  end_of_scan:
+    */
+
+    /* Make sure there are enough memory cells allocated to accommodate 
+    ** the regPrev array and a trailing rowid (the rowid slot is required
+    ** when building a record to insert into the sample column of 
+    ** the sqlite_stat4 table.  */
+    sqlite3TouchRegister(pParse, regPrev+nColTest);
+
+    /* Open a read-only cursor on the index being analyzed. */
+    assert( iDb==sqlite3SchemaToIndex(db, pIdx->pSchema) );
+    sqlite3VdbeAddOp3(v, OP_OpenRead, iIdxCur, pIdx->tnum, iDb);
+    sqlite3VdbeSetP4KeyInfo(pParse, pIdx);
+    VdbeComment((v, "%s", pIdx->zName));
+
+    /* Invoke the stat_init() function. The arguments are:
+    ** 
+    **    (1) the number of columns in the index including the rowid
+    **        (or for a WITHOUT ROWID table, the number of PK columns),
+    **    (2) the number of columns in the key without the rowid/pk
+    **    (3) estimated number of rows in the index,
+    */
+    sqlite3VdbeAddOp2(v, OP_Integer, nCol, regStat+1);
+    assert( regRowid==regStat+2 );
+    sqlite3VdbeAddOp2(v, OP_Integer, pIdx->nKeyCol, regRowid);
+#ifdef SQLITE_ENABLE_STAT4
+    if( OptimizationEnabled(db, SQLITE_Stat4) ){
+      sqlite3VdbeAddOp2(v, OP_Count, iIdxCur, regTemp);
+      addrRewind = sqlite3VdbeAddOp1(v, OP_Rewind, iIdxCur);
+      VdbeCoverage(v);
+    }else
+#endif
+    {
+      addrRewind = sqlite3VdbeAddOp1(v, OP_Rewind, iIdxCur);
+      VdbeCoverage(v);
+      sqlite3VdbeAddOp3(v, OP_Count, iIdxCur, regTemp, 1);
+    }
+    assert( regTemp2==regStat+4 );
+    sqlite3VdbeAddOp2(v, OP_Integer, db->nAnalysisLimit, regTemp2);
+    sqlite3VdbeAddFunctionCall(pParse, 0, regStat+1, regStat, 4,
+                               &statInitFuncdef, 0);
+
+    /* Implementation of the following:
+    **
+    **   Rewind csr
+    **   if eof(csr) goto end_of_scan;
+    **   regChng = 0
+    **   goto next_push_0;
+    **
+    */
+    sqlite3VdbeAddOp2(v, OP_Integer, 0, regChng);
+    addrNextRow = sqlite3VdbeCurrentAddr(v);
+
+    if( nColTest>0 ){
+      int endDistinctTest = sqlite3VdbeMakeLabel(pParse);
+      int *aGotoChng;               /* Array of jump instruction addresses */
+      aGotoChng = sqlite3DbMallocRawNN(db, sizeof(int)*nColTest);
+      if( aGotoChng==0 ) continue;
+
+      /*
+      **  next_row:
+      **   regChng = 0
+      **   if( idx(0) != regPrev(0) ) goto chng_addr_0
+      **   regChng = 1
+      **   if( idx(1) != regPrev(1) ) goto chng_addr_1
+      **   ...
+      **   regChng = N
+      **   goto endDistinctTest
+      */
+      sqlite3VdbeAddOp0(v, OP_Goto);
+      addrNextRow = sqlite3VdbeCurrentAddr(v);
+      if( nColTest==1 && pIdx->nKeyCol==1 && IsUniqueIndex(pIdx) ){
+        /* For a single-column UNIQUE index, once we have found a non-NULL
+        ** row, we know that all the rest will be distinct, so skip 
+        ** subsequent distinctness tests. */
+        sqlite3VdbeAddOp2(v, OP_NotNull, regPrev, endDistinctTest);
+        VdbeCoverage(v);
+      }
+      for(i=0; i<nColTest; i++){
+        char *pColl = (char*)sqlite3LocateCollSeq(pParse, pIdx->azColl[i]);
+        sqlite3VdbeAddOp2(v, OP_Integer, i, regChng);
+        sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, i, regTemp);
+        analyzeVdbeCommentIndexWithColumnName(v,pIdx,i);
+        aGotoChng[i] = 
+        sqlite3VdbeAddOp4(v, OP_Ne, regTemp, 0, regPrev+i, pColl, P4_COLLSEQ);
+        sqlite3VdbeChangeP5(v, SQLITE_NULLEQ);
+        VdbeCoverage(v);
+      }
+      sqlite3VdbeAddOp2(v, OP_Integer, nColTest, regChng);
+      sqlite3VdbeGoto(v, endDistinctTest);
+  
+  
+      /*
+      **  chng_addr_0:
+      **   regPrev(0) = idx(0)
+      **  chng_addr_1:
+      **   regPrev(1) = idx(1)
+      **  ...
+      */
+      sqlite3VdbeJumpHere(v, addrNextRow-1);
+      for(i=0; i<nColTest; i++){
+        sqlite3VdbeJumpHere(v, aGotoChng[i]);
+        sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, i, regPrev+i);
+        analyzeVdbeCommentIndexWithColumnName(v,pIdx,i);
+      }
+      sqlite3VdbeResolveLabel(v, endDistinctTest);
+      sqlite3DbFree(db, aGotoChng);
+    }
+  
+    /*
+    **  chng_addr_N:
+    **   regRowid = idx(rowid)            // STAT4 only
+    **   stat_push(P, regChng, regRowid)  // 3rd parameter STAT4 only
+    **   Next csr
+    **   if !eof(csr) goto next_row;
+    */
+#ifdef SQLITE_ENABLE_STAT4
+    if( OptimizationEnabled(db, SQLITE_Stat4) ){
+      assert( regRowid==(regStat+2) );
+      if( HasRowid(pTab) ){
+        sqlite3VdbeAddOp2(v, OP_IdxRowid, iIdxCur, regRowid);
+      }else{
+        Index *pPk = sqlite3PrimaryKeyIndex(pIdx->pTable);
+        int j, k, regKey;
+        regKey = sqlite3GetTempRange(pParse, pPk->nKeyCol);
+        for(j=0; j<pPk->nKeyCol; j++){
+          k = sqlite3TableColumnToIndex(pIdx, pPk->aiColumn[j]);
+          assert( k>=0 && k<pIdx->nColumn );
+          sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, k, regKey+j);
+          analyzeVdbeCommentIndexWithColumnName(v,pIdx,k);
+        }
+        sqlite3VdbeAddOp3(v, OP_MakeRecord, regKey, pPk->nKeyCol, regRowid);
+        sqlite3ReleaseTempRange(pParse, regKey, pPk->nKeyCol);
+      }
+    }
+#endif
+    assert( regChng==(regStat+1) );
+    {
+      sqlite3VdbeAddFunctionCall(pParse, 1, regStat, regTemp, 2+IsStat4,
+                                 &statPushFuncdef, 0);
+      if( db->nAnalysisLimit ){
+        int j1, j2, j3;
+        j1 = sqlite3VdbeAddOp1(v, OP_IsNull, regTemp); VdbeCoverage(v);
+        j2 = sqlite3VdbeAddOp1(v, OP_If, regTemp); VdbeCoverage(v);
+        j3 = sqlite3VdbeAddOp4Int(v, OP_SeekGT, iIdxCur, 0, regPrev, 1);
+        VdbeCoverage(v);
+        sqlite3VdbeJumpHere(v, j1);
+        sqlite3VdbeAddOp2(v, OP_Next, iIdxCur, addrNextRow); VdbeCoverage(v);
+        sqlite3VdbeJumpHere(v, j2);
+        sqlite3VdbeJumpHere(v, j3);
+      }else{
+        sqlite3VdbeAddOp2(v, OP_Next, iIdxCur, addrNextRow); VdbeCoverage(v);
+      }
+    }
+
+    /* Add the entry to the stat1 table. */
+    callStatGet(pParse, regStat, STAT_GET_STAT1, regStat1);
+    assert( "BBB"[0]==SQLITE_AFF_TEXT );
+    sqlite3VdbeAddOp4(v, OP_MakeRecord, regTabname, 3, regTemp, "BBB", 0);
+    sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur, regNewRowid);
+    sqlite3VdbeAddOp3(v, OP_Insert, iStatCur, regTemp, regNewRowid);
+#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
+    sqlite3VdbeChangeP4(v, -1, (char*)pStat1, P4_TABLE);
+#endif
+    sqlite3VdbeChangeP5(v, OPFLAG_APPEND);
+
+    /* Add the entries to the stat4 table. */
+#ifdef SQLITE_ENABLE_STAT4
+    if( OptimizationEnabled(db, SQLITE_Stat4) && db->nAnalysisLimit==0 ){
+      int regEq = regStat1;
+      int regLt = regStat1+1;
+      int regDLt = regStat1+2;
+      int regSample = regStat1+3;
+      int regCol = regStat1+4;
+      int regSampleRowid = regCol + nCol;
+      int addrNext;
+      int addrIsNull;
+      u8 seekOp = HasRowid(pTab) ? OP_NotExists : OP_NotFound;
+
+      if( doOnce ){
+        int mxCol = nCol;
+        Index *pX;
+
+        /* Compute the maximum number of columns in any index */
+        for(pX=pTab->pIndex; pX; pX=pX->pNext){
+          int nColX;                     /* Number of columns in pX */
+          if( !HasRowid(pTab) && IsPrimaryKeyIndex(pX) ){
+            nColX = pX->nKeyCol;
+          }else{
+            nColX = pX->nColumn;
+          }
+          if( nColX>mxCol ) mxCol = nColX;
+        }
+
+        /* Allocate space to compute results for the largest index */
+        sqlite3TouchRegister(pParse, regCol+mxCol);
+        doOnce = 0;
+#ifdef SQLITE_DEBUG
+        /* Verify that the call to sqlite3ClearTempRegCache() below
+        ** really is needed.
+        ** https://sqlite.org/forum/forumpost/83cb4a95a0 (2023-03-25)
+        */
+        testcase( !sqlite3NoTempsInRange(pParse, regEq, regCol+mxCol) );
+#endif
+        sqlite3ClearTempRegCache(pParse);  /* tag-20230325-1 */
+        assert( sqlite3NoTempsInRange(pParse, regEq, regCol+mxCol) );
+      }
+      assert( sqlite3NoTempsInRange(pParse, regEq, regCol+nCol) );
+
+      addrNext = sqlite3VdbeCurrentAddr(v);
+      callStatGet(pParse, regStat, STAT_GET_ROWID, regSampleRowid);
+      addrIsNull = sqlite3VdbeAddOp1(v, OP_IsNull, regSampleRowid);
+      VdbeCoverage(v);
+      callStatGet(pParse, regStat, STAT_GET_NEQ, regEq);
+      callStatGet(pParse, regStat, STAT_GET_NLT, regLt);
+      callStatGet(pParse, regStat, STAT_GET_NDLT, regDLt);
+      sqlite3VdbeAddOp4Int(v, seekOp, iTabCur, addrNext, regSampleRowid, 0);
+      VdbeCoverage(v);
+      for(i=0; i<nCol; i++){
+        sqlite3ExprCodeLoadIndexColumn(pParse, pIdx, iTabCur, i, regCol+i);
+      }
+      sqlite3VdbeAddOp3(v, OP_MakeRecord, regCol, nCol, regSample);
+      sqlite3VdbeAddOp3(v, OP_MakeRecord, regTabname, 6, regTemp);
+      sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur+1, regNewRowid);
+      sqlite3VdbeAddOp3(v, OP_Insert, iStatCur+1, regTemp, regNewRowid);
+      sqlite3VdbeAddOp2(v, OP_Goto, 1, addrNext); /* P1==1 for end-of-loop */
+      sqlite3VdbeJumpHere(v, addrIsNull);
+    }
+#endif /* SQLITE_ENABLE_STAT4 */
+
+    /* End of analysis */
+    sqlite3VdbeJumpHere(v, addrRewind);
+  }
+
+
+  /* Create a single sqlite_stat1 entry containing NULL as the index
+  ** name and the row count as the content.
+  */
+  if( pOnlyIdx==0 && needTableCnt ){
+    VdbeComment((v, "%s", pTab->zName));
+    sqlite3VdbeAddOp2(v, OP_Count, iTabCur, regStat1);
+    jZeroRows = sqlite3VdbeAddOp1(v, OP_IfNot, regStat1); VdbeCoverage(v);
+    sqlite3VdbeAddOp2(v, OP_Null, 0, regIdxname);
+    assert( "BBB"[0]==SQLITE_AFF_TEXT );
+    sqlite3VdbeAddOp4(v, OP_MakeRecord, regTabname, 3, regTemp, "BBB", 0);
+    sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur, regNewRowid);
+    sqlite3VdbeAddOp3(v, OP_Insert, iStatCur, regTemp, regNewRowid);
+    sqlite3VdbeChangeP5(v, OPFLAG_APPEND);
+#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
+    sqlite3VdbeChangeP4(v, -1, (char*)pStat1, P4_TABLE);
+#endif
+    sqlite3VdbeJumpHere(v, jZeroRows);
+  }
+}
+
+
+/*
+** Generate code that will cause the most recent index analysis to
+** be loaded into internal hash tables where is can be used.
+*/
+static void loadAnalysis(Parse *pParse, int iDb){
+  Vdbe *v = sqlite3GetVdbe(pParse);
+  if( v ){
+    sqlite3VdbeAddOp1(v, OP_LoadAnalysis, iDb);
+  }
+}
+
+/*
+** Generate code that will do an analysis of an entire database
+*/
+static void analyzeDatabase(Parse *pParse, int iDb){
+  sqlite3 *db = pParse->db;
+  Schema *pSchema = db->aDb[iDb].pSchema;    /* Schema of database iDb */
+  HashElem *k;
+  int iStatCur;
+  int iMem;
+  int iTab;
+
+  sqlite3BeginWriteOperation(pParse, 0, iDb);
+  iStatCur = pParse->nTab;
+  pParse->nTab += 3;
+  openStatTable(pParse, iDb, iStatCur, 0, 0);
+  iMem = pParse->nMem+1;
+  iTab = pParse->nTab;
+  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );
+  for(k=sqliteHashFirst(&pSchema->tblHash); k; k=sqliteHashNext(k)){
+    Table *pTab = (Table*)sqliteHashData(k);
+    analyzeOneTable(pParse, pTab, 0, iStatCur, iMem, iTab);
+#ifdef SQLITE_ENABLE_STAT4
+    iMem = sqlite3FirstAvailableRegister(pParse, iMem);
+#else
+    assert( iMem==sqlite3FirstAvailableRegister(pParse,iMem) );
+#endif
+  }
+  loadAnalysis(pParse, iDb);
+}
+
+/*
+** Generate code that will do an analysis of a single table in
+** a database.  If pOnlyIdx is not NULL then it is a single index
+** in pTab that should be analyzed.
+*/
+static void analyzeTable(Parse *pParse, Table *pTab, Index *pOnlyIdx){
+  int iDb;
+  int iStatCur;
+
+  assert( pTab!=0 );
+  assert( sqlite3BtreeHoldsAllMutexes(pParse->db) );
+  iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);
+  sqlite3BeginWriteOperation(pParse, 0, iDb);
+  iStatCur = pParse->nTab;
+  pParse->nTab += 3;
+  if( pOnlyIdx ){
+    openStatTable(pParse, iDb, iStatCur, pOnlyIdx->zName, "idx");
+  }else{
+    openStatTable(pParse, iDb, iStatCur, pTab->zName, "tbl");
+  }
+  analyzeOneTable(pParse, pTab, pOnlyIdx, iStatCur,pParse->nMem+1,pParse->nTab);
+  loadAnalysis(pParse, iDb);
+}
+
+/*
+** Generate code for the ANALYZE command.  The parser calls this routine
+** when it recognizes an ANALYZE command.
+**
+**        ANALYZE                            -- 1
+**        ANALYZE  <database>                -- 2
+**        ANALYZE  ?<database>.?<tablename>  -- 3
+**
+** Form 1 causes all indices in all attached databases to be analyzed.
+** Form 2 analyzes all indices the single database named.
+** Form 3 analyzes all indices associated with the named table.
+*/
+void sqlite3Analyze(Parse *pParse, Token *pName1, Token *pName2){
+  sqlite3 *db = pParse->db;
+  int iDb;
+  int i;
+  char *z, *zDb;
+  Table *pTab;
+  Index *pIdx;
+  Token *pTableName;
+  Vdbe *v;
+
+  /* Read the database schema. If an error occurs, leave an error message
+  ** and code in pParse and return NULL. */
+  assert( sqlite3BtreeHoldsAllMutexes(pParse->db) );
+  if( SQLITE_OK!=sqlite3ReadSchema(pParse) ){
+    return;
+  }
+
+  assert( pName2!=0 || pName1==0 );
+  if( pName1==0 ){
+    /* Form 1:  Analyze everything */
+    for(i=0; i<db->nDb; i++){
+      if( i==1 ) continue;  /* Do not analyze the TEMP database */
+      analyzeDatabase(pParse, i);
+    }
+  }else if( pName2->n==0 && (iDb = sqlite3FindDb(db, pName1))>=0 ){
+    /* Analyze the schema named as the argument */
+    analyzeDatabase(pParse, iDb);
+  }else{
+    /* Form 3: Analyze the table or index named as an argument */
+    iDb = sqlite3TwoPartName(pParse, pName1, pName2, &pTableName);
+    if( iDb>=0 ){
+      zDb = pName2->n ? db->aDb[iDb].zDbSName : 0;
+      z = sqlite3NameFromToken(db, pTableName);
+      if( z ){
+        if( (pIdx = sqlite3FindIndex(db, z, zDb))!=0 ){
+          analyzeTable(pParse, pIdx->pTable, pIdx);
+        }else if( (pTab = sqlite3LocateTable(pParse, 0, z, zDb))!=0 ){
+          analyzeTable(pParse, pTab, 0);
+        }
+        sqlite3DbFree(db, z);
+      }
+    }
+  }
+  if( db->nSqlExec==0 && (v = sqlite3GetVdbe(pParse))!=0 ){
+    sqlite3VdbeAddOp0(v, OP_Expire);
+  }
+}
+
+/*
+** Used to pass information from the analyzer reader through to the
+** callback routine.
+*/
+typedef struct analysisInfo analysisInfo;
+struct analysisInfo {
+  sqlite3 *db;
+  const char *zDatabase;
+};
+
+/*
+** The first argument points to a nul-terminated string containing a
+** list of space separated integers. Read the first nOut of these into
+** the array aOut[].
+*/
+static void decodeIntArray(
+  char *zIntArray,       /* String containing int array to decode */
+  int nOut,              /* Number of slots in aOut[] */
+  tRowcnt *aOut,         /* Store integers here */
+  LogEst *aLog,          /* Or, if aOut==0, here */
+  Index *pIndex          /* Handle extra flags for this index, if not NULL */
+){
+  char *z = zIntArray;
+  int c;
+  int i;
+  tRowcnt v;
+
+#ifdef SQLITE_ENABLE_STAT4
+  if( z==0 ) z = "";
+#else
+  assert( z!=0 );
+#endif
+  for(i=0; *z && i<nOut; i++){
+    v = 0;
+    while( (c=z[0])>='0' && c<='9' ){
+      v = v*10 + c - '0';
+      z++;
+    }
+#ifdef SQLITE_ENABLE_STAT4
+    if( aOut ) aOut[i] = v;
+    if( aLog ) aLog[i] = sqlite3LogEst(v);
+#else
+    assert( aOut==0 );
+    UNUSED_PARAMETER(aOut);
+    assert( aLog!=0 );
+    aLog[i] = sqlite3LogEst(v);
+#endif
+    if( *z==' ' ) z++;
+  }
+#ifndef SQLITE_ENABLE_STAT4
+  assert( pIndex!=0 ); {
+#else
+  if( pIndex ){
+#endif
+    pIndex->bUnordered = 0;
+    pIndex->noSkipScan = 0;
+    while( z[0] ){
+      if( sqlite3_strglob("unordered*", z)==0 ){
+        pIndex->bUnordered = 1;
+      }else if( sqlite3_strglob("sz=[0-9]*", z)==0 ){
+        int sz = sqlite3Atoi(z+3);
+        if( sz<2 ) sz = 2;
+        pIndex->szIdxRow = sqlite3LogEst(sz);
+      }else if( sqlite3_strglob("noskipscan*", z)==0 ){
+        pIndex->noSkipScan = 1;
+      }
+#ifdef SQLITE_ENABLE_COSTMULT
+      else if( sqlite3_strglob("costmult=[0-9]*",z)==0 ){
+        pIndex->pTable->costMult = sqlite3LogEst(sqlite3Atoi(z+9));
+      }
+#endif
+      while( z[0]!=0 && z[0]!=' ' ) z++;
+      while( z[0]==' ' ) z++;
+    }
+
+    /* Set the bLowQual flag if the peak number of rows obtained
+    ** from a full equality match is so large that a full table scan
+    ** seems likely to be faster than using the index.
+    */
+    if( aLog[0] > 66              /* Index has more than 100 rows */
+     && aLog[0] <= aLog[nOut-1]   /* And only a single value seen */
+    ){
+      pIndex->bLowQual = 1;
+    }
+  }
+}
+
+/*
+** This callback is invoked once for each index when reading the
+** sqlite_stat1 table.  
+**
+**     argv[0] = name of the table
+**     argv[1] = name of the index (might be NULL)
+**     argv[2] = results of analysis - on integer for each column
+**
+** Entries for which argv[1]==NULL simply record the number of rows in
+** the table.
+*/
+static int analysisLoader(void *pData, int argc, char **argv, char **NotUsed){
+  analysisInfo *pInfo = (analysisInfo*)pData;
+  Index *pIndex;
+  Table *pTable;
+  const char *z;
+
+  assert( argc==3 );
+  UNUSED_PARAMETER2(NotUsed, argc);
+
+  if( argv==0 || argv[0]==0 || argv[2]==0 ){
+    return 0;
+  }
+  pTable = sqlite3FindTable(pInfo->db, argv[0], pInfo->zDatabase);
+  if( pTable==0 ){
+    return 0;
+  }
+  if( argv[1]==0 ){
+    pIndex = 0;
+  }else if( sqlite3_stricmp(argv[0],argv[1])==0 ){
+    pIndex = sqlite3PrimaryKeyIndex(pTable);
+  }else{
+    pIndex = sqlite3FindIndex(pInfo->db, argv[1], pInfo->zDatabase);
+  }
+  z = argv[2];
+
+  if( pIndex ){
+    tRowcnt *aiRowEst = 0;
+    int nCol = pIndex->nKeyCol+1;
+#ifdef SQLITE_ENABLE_STAT4
+    /* Index.aiRowEst may already be set here if there are duplicate 
+    ** sqlite_stat1 entries for this index. In that case just clobber
+    ** the old data with the new instead of allocating a new array.  */
+    if( pIndex->aiRowEst==0 ){
+      pIndex->aiRowEst = (tRowcnt*)sqlite3MallocZero(sizeof(tRowcnt) * nCol);
+      if( pIndex->aiRowEst==0 ) sqlite3OomFault(pInfo->db);
+    }
+    aiRowEst = pIndex->aiRowEst;
+#endif
+    pIndex->bUnordered = 0;
+    decodeIntArray((char*)z, nCol, aiRowEst, pIndex->aiRowLogEst, pIndex);
+    pIndex->hasStat1 = 1;
+    if( pIndex->pPartIdxWhere==0 ){
+      pTable->nRowLogEst = pIndex->aiRowLogEst[0];
+      pTable->tabFlags |= TF_HasStat1;
+    }
+  }else{
+    Index fakeIdx;
+    fakeIdx.szIdxRow = pTable->szTabRow;
+#ifdef SQLITE_ENABLE_COSTMULT
+    fakeIdx.pTable = pTable;
+#endif
+    decodeIntArray((char*)z, 1, 0, &pTable->nRowLogEst, &fakeIdx);
+    pTable->szTabRow = fakeIdx.szIdxRow;
+    pTable->tabFlags |= TF_HasStat1;
+  }
+
+  return 0;
+}
+
+/*
+** If the Index.aSample variable is not NULL, delete the aSample[] array
+** and its contents.
+*/
+void sqlite3DeleteIndexSamples(sqlite3 *db, Index *pIdx){
+  assert( db!=0 );
+  assert( pIdx!=0 );
+#ifdef SQLITE_ENABLE_STAT4
+  if( pIdx->aSample ){
+    int j;
+    for(j=0; j<pIdx->nSample; j++){
+      IndexSample *p = &pIdx->aSample[j];
+      sqlite3DbFree(db, p->p);
+    }
+    sqlite3DbFree(db, pIdx->aSample);
+  }
+  if( db->pnBytesFreed==0 ){
+    pIdx->nSample = 0;
+    pIdx->aSample = 0;
+  }
+#else
+  UNUSED_PARAMETER(db);
+  UNUSED_PARAMETER(pIdx);
+#endif /* SQLITE_ENABLE_STAT4 */
+}
+
+#ifdef SQLITE_ENABLE_STAT4
+/*
+** Populate the pIdx->aAvgEq[] array based on the samples currently
+** stored in pIdx->aSample[]. 
+*/
+static void initAvgEq(Index *pIdx){
+  if( pIdx ){
+    IndexSample *aSample = pIdx->aSample;
+    IndexSample *pFinal = &aSample[pIdx->nSample-1];
+    int iCol;
+    int nCol = 1;
+    if( pIdx->nSampleCol>1 ){
+      /* If this is stat4 data, then calculate aAvgEq[] values for all
+      ** sample columns except the last. The last is always set to 1, as
+      ** once the trailing PK fields are considered all index keys are
+      ** unique.  */
+      nCol = pIdx->nSampleCol-1;
+      pIdx->aAvgEq[nCol] = 1;
+    }
+    for(iCol=0; iCol<nCol; iCol++){
+      int nSample = pIdx->nSample;
+      int i;                    /* Used to iterate through samples */
+      tRowcnt sumEq = 0;        /* Sum of the nEq values */
+      tRowcnt avgEq = 0;
+      tRowcnt nRow;             /* Number of rows in index */
+      i64 nSum100 = 0;          /* Number of terms contributing to sumEq */
+      i64 nDist100;             /* Number of distinct values in index */
+
+      if( !pIdx->aiRowEst || iCol>=pIdx->nKeyCol || pIdx->aiRowEst[iCol+1]==0 ){
+        nRow = pFinal->anLt[iCol];
+        nDist100 = (i64)100 * pFinal->anDLt[iCol];
+        nSample--;
+      }else{
+        nRow = pIdx->aiRowEst[0];
+        nDist100 = ((i64)100 * pIdx->aiRowEst[0]) / pIdx->aiRowEst[iCol+1];
+      }
+      pIdx->nRowEst0 = nRow;
+
+      /* Set nSum to the number of distinct (iCol+1) field prefixes that
+      ** occur in the stat4 table for this index. Set sumEq to the sum of 
+      ** the nEq values for column iCol for the same set (adding the value 
+      ** only once where there exist duplicate prefixes).  */
+      for(i=0; i<nSample; i++){
+        if( i==(pIdx->nSample-1)
+         || aSample[i].anDLt[iCol]!=aSample[i+1].anDLt[iCol] 
+        ){
+          sumEq += aSample[i].anEq[iCol];
+          nSum100 += 100;
+        }
+      }
+
+      if( nDist100>nSum100 && sumEq<nRow ){
+        avgEq = ((i64)100 * (nRow - sumEq))/(nDist100 - nSum100);
+      }
+      if( avgEq==0 ) avgEq = 1;
+      pIdx->aAvgEq[iCol] = avgEq;
+    }
+  }
+}
+
+/*
+** Look up an index by name.  Or, if the name of a WITHOUT ROWID table
+** is supplied instead, find the PRIMARY KEY index for that table.
+*/
+static Index *findIndexOrPrimaryKey(
+  sqlite3 *db,
+  const char *zName,
+  const char *zDb
+){
+  Index *pIdx = sqlite3FindIndex(db, zName, zDb);
+  if( pIdx==0 ){
+    Table *pTab = sqlite3FindTable(db, zName, zDb);
+    if( pTab && !HasRowid(pTab) ) pIdx = sqlite3PrimaryKeyIndex(pTab);
+  }
+  return pIdx;
+}
+
+/*
+** Load the content from either the sqlite_stat4
+** into the relevant Index.aSample[] arrays.
+**
+** Arguments zSql1 and zSql2 must point to SQL statements that return
+** data equivalent to the following:
+**
+**    zSql1: SELECT idx,count(*) FROM %Q.sqlite_stat4 GROUP BY idx
+**    zSql2: SELECT idx,neq,nlt,ndlt,sample FROM %Q.sqlite_stat4
+**
+** where %Q is replaced with the database name before the SQL is executed.
+*/
+static int loadStatTbl(
+  sqlite3 *db,                  /* Database handle */
+  const char *zSql1,            /* SQL statement 1 (see above) */
+  const char *zSql2,            /* SQL statement 2 (see above) */
+  const char *zDb               /* Database name (e.g. "main") */
+){
+  int rc;                       /* Result codes from subroutines */
+  sqlite3_stmt *pStmt = 0;      /* An SQL statement being run */
+  char *zSql;                   /* Text of the SQL statement */
+  Index *pPrevIdx = 0;          /* Previous index in the loop */
+  IndexSample *pSample;         /* A slot in pIdx->aSample[] */
+
+  assert( db->lookaside.bDisable );
+  zSql = sqlite3MPrintf(db, zSql1, zDb);
+  if( !zSql ){
+    return SQLITE_NOMEM_BKPT;
+  }
+  rc = sqlite3_prepare(db, zSql, -1, &pStmt, 0);
+  sqlite3DbFree(db, zSql);
+  if( rc ) return rc;
+
+  while( sqlite3_step(pStmt)==SQLITE_ROW ){
+    int nIdxCol = 1;              /* Number of columns in stat4 records */
+
+    char *zIndex;   /* Index name */
+    Index *pIdx;    /* Pointer to the index object */
+    int nSample;    /* Number of samples */
+    int nByte;      /* Bytes of space required */
+    int i;          /* Bytes of space required */
+    tRowcnt *pSpace;
+
+    zIndex = (char *)sqlite3_column_text(pStmt, 0);
+    if( zIndex==0 ) continue;
+    nSample = sqlite3_column_int(pStmt, 1);
+    pIdx = findIndexOrPrimaryKey(db, zIndex, zDb);
+    assert( pIdx==0 || pIdx->nSample==0 );
+    if( pIdx==0 ) continue;
+    if( pIdx->aSample!=0 ){
+      /* The same index appears in sqlite_stat4 under multiple names */
+      continue;
+    }
+    assert( !HasRowid(pIdx->pTable) || pIdx->nColumn==pIdx->nKeyCol+1 );
+    if( !HasRowid(pIdx->pTable) && IsPrimaryKeyIndex(pIdx) ){
+      nIdxCol = pIdx->nKeyCol;
+    }else{
+      nIdxCol = pIdx->nColumn;
+    }
+    pIdx->nSampleCol = nIdxCol;
+    pIdx->mxSample = nSample;
+    nByte = sizeof(IndexSample) * nSample;
+    nByte += sizeof(tRowcnt) * nIdxCol * 3 * nSample;
+    nByte += nIdxCol * sizeof(tRowcnt);     /* Space for Index.aAvgEq[] */
+
+    pIdx->aSample = sqlite3DbMallocZero(db, nByte);
+    if( pIdx->aSample==0 ){
+      sqlite3_finalize(pStmt);
+      return SQLITE_NOMEM_BKPT;
+    }
+    pSpace = (tRowcnt*)&pIdx->aSample[nSample];
+    pIdx->aAvgEq = pSpace; pSpace += nIdxCol;
+    pIdx->pTable->tabFlags |= TF_HasStat4;
+    for(i=0; i<nSample; i++){
+      pIdx->aSample[i].anEq = pSpace; pSpace += nIdxCol;
+      pIdx->aSample[i].anLt = pSpace; pSpace += nIdxCol;
+      pIdx->aSample[i].anDLt = pSpace; pSpace += nIdxCol;
+    }
+    assert( ((u8*)pSpace)-nByte==(u8*)(pIdx->aSample) );
+  }
+  rc = sqlite3_finalize(pStmt);
+  if( rc ) return rc;
+
+  zSql = sqlite3MPrintf(db, zSql2, zDb);
+  if( !zSql ){
+    return SQLITE_NOMEM_BKPT;
+  }
+  rc = sqlite3_prepare(db, zSql, -1, &pStmt, 0);
+  sqlite3DbFree(db, zSql);
+  if( rc ) return rc;
+
+  while( sqlite3_step(pStmt)==SQLITE_ROW ){
+    char *zIndex;                 /* Index name */
+    Index *pIdx;                  /* Pointer to the index object */
+    int nCol = 1;                 /* Number of columns in index */
+
+    zIndex = (char *)sqlite3_column_text(pStmt, 0);
+    if( zIndex==0 ) continue;
+    pIdx = findIndexOrPrimaryKey(db, zIndex, zDb);
+    if( pIdx==0 ) continue;
+    if( pIdx->nSample>=pIdx->mxSample ){
+      /* Too many slots used because the same index appears in
+      ** sqlite_stat4 using multiple names */
+      continue;
+    }
+    /* This next condition is true if data has already been loaded from 
+    ** the sqlite_stat4 table. */
+    nCol = pIdx->nSampleCol;
+    if( pIdx!=pPrevIdx ){
+      initAvgEq(pPrevIdx);
+      pPrevIdx = pIdx;
+    }
+    pSample = &pIdx->aSample[pIdx->nSample];
+    decodeIntArray((char*)sqlite3_column_text(pStmt,1),nCol,pSample->anEq,0,0);
+    decodeIntArray((char*)sqlite3_column_text(pStmt,2),nCol,pSample->anLt,0,0);
+    decodeIntArray((char*)sqlite3_column_text(pStmt,3),nCol,pSample->anDLt,0,0);
+
+    /* Take a copy of the sample. Add 8 extra 0x00 bytes the end of the buffer.
+    ** This is in case the sample record is corrupted. In that case, the
+    ** sqlite3VdbeRecordCompare() may read up to two varints past the
+    ** end of the allocated buffer before it realizes it is dealing with
+    ** a corrupt record.  Or it might try to read a large integer from the
+    ** buffer.  In any case, eight 0x00 bytes prevents this from causing
+    ** a buffer overread.  */
+    pSample->n = sqlite3_column_bytes(pStmt, 4);
+    pSample->p = sqlite3DbMallocZero(db, pSample->n + 8);
+    if( pSample->p==0 ){
+      sqlite3_finalize(pStmt);
+      return SQLITE_NOMEM_BKPT;
+    }
+    if( pSample->n ){
+      memcpy(pSample->p, sqlite3_column_blob(pStmt, 4), pSample->n);
+    }
+    pIdx->nSample++;
+  }
+  rc = sqlite3_finalize(pStmt);
+  if( rc==SQLITE_OK ) initAvgEq(pPrevIdx);
+  return rc;
+}
+
+/*
+** Load content from the sqlite_stat4 table into 
+** the Index.aSample[] arrays of all indices.
+*/
+static int loadStat4(sqlite3 *db, const char *zDb){
+  int rc = SQLITE_OK;             /* Result codes from subroutines */
+  const Table *pStat4;
+
+  assert( db->lookaside.bDisable );
+  if( OptimizationEnabled(db, SQLITE_Stat4)
+   && (pStat4 = sqlite3FindTable(db, "sqlite_stat4", zDb))!=0
+   && IsOrdinaryTable(pStat4)
+  ){
+    rc = loadStatTbl(db,
+      "SELECT idx,count(*) FROM %Q.sqlite_stat4 GROUP BY idx COLLATE nocase", 
+      "SELECT idx,neq,nlt,ndlt,sample FROM %Q.sqlite_stat4",
+      zDb
+    );
+  }
+  return rc;
+}
+#endif /* SQLITE_ENABLE_STAT4 */
+
+/*
+** Load the content of the sqlite_stat1 and sqlite_stat4 tables. The
+** contents of sqlite_stat1 are used to populate the Index.aiRowEst[]
+** arrays. The contents of sqlite_stat4 are used to populate the
+** Index.aSample[] arrays.
+**
+** If the sqlite_stat1 table is not present in the database, SQLITE_ERROR
+** is returned. In this case, even if SQLITE_ENABLE_STAT4 was defined 
+** during compilation and the sqlite_stat4 table is present, no data is 
+** read from it.
+**
+** If SQLITE_ENABLE_STAT4 was defined during compilation and the 
+** sqlite_stat4 table is not present in the database, SQLITE_ERROR is
+** returned. However, in this case, data is read from the sqlite_stat1
+** table (if it is present) before returning.
+**
+** If an OOM error occurs, this function always sets db->mallocFailed.
+** This means if the caller does not care about other errors, the return
+** code may be ignored.
+*/
+int sqlite3AnalysisLoad(sqlite3 *db, int iDb){
+  analysisInfo sInfo;
+  HashElem *i;
+  char *zSql;
+  int rc = SQLITE_OK;
+  Schema *pSchema = db->aDb[iDb].pSchema;
+  const Table *pStat1;
+
+  assert( iDb>=0 && iDb<db->nDb );
+  assert( db->aDb[iDb].pBt!=0 );
+
+  /* Clear any prior statistics */
+  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );
+  for(i=sqliteHashFirst(&pSchema->tblHash); i; i=sqliteHashNext(i)){
+    Table *pTab = sqliteHashData(i);
+    pTab->tabFlags &= ~TF_HasStat1;
+  }
+  for(i=sqliteHashFirst(&pSchema->idxHash); i; i=sqliteHashNext(i)){
+    Index *pIdx = sqliteHashData(i);
+    pIdx->hasStat1 = 0;
+#ifdef SQLITE_ENABLE_STAT4
+    sqlite3DeleteIndexSamples(db, pIdx);
+    pIdx->aSample = 0;
+#endif
+  }
+
+  /* Load new statistics out of the sqlite_stat1 table */
+  sInfo.db = db;
+  sInfo.zDatabase = db->aDb[iDb].zDbSName;
+  if( (pStat1 = sqlite3FindTable(db, "sqlite_stat1", sInfo.zDatabase))
+   && IsOrdinaryTable(pStat1)
+  ){
+    zSql = sqlite3MPrintf(db, 
+        "SELECT tbl,idx,stat FROM %Q.sqlite_stat1", sInfo.zDatabase);
+    if( zSql==0 ){
+      rc = SQLITE_NOMEM_BKPT;
+    }else{
+      rc = sqlite3_exec(db, zSql, analysisLoader, &sInfo, 0);
+      sqlite3DbFree(db, zSql);
+    }
+  }
+
+  /* Set appropriate defaults on all indexes not in the sqlite_stat1 table */
+  assert( sqlite3SchemaMutexHeld(db, iDb, 0) );
+  for(i=sqliteHashFirst(&pSchema->idxHash); i; i=sqliteHashNext(i)){
+    Index *pIdx = sqliteHashData(i);
+    if( !pIdx->hasStat1 ) sqlite3DefaultRowEst(pIdx);
+  }
+
+  /* Load the statistics from the sqlite_stat4 table. */
+#ifdef SQLITE_ENABLE_STAT4
+  if( rc==SQLITE_OK ){
+    DisableLookaside;
+    rc = loadStat4(db, sInfo.zDatabase);
+    EnableLookaside;
+  }
+  for(i=sqliteHashFirst(&pSchema->idxHash); i; i=sqliteHashNext(i)){
+    Index *pIdx = sqliteHashData(i);
+    sqlite3_free(pIdx->aiRowEst);
+    pIdx->aiRowEst = 0;
+  }
+#endif
+
+  if( rc==SQLITE_NOMEM ){
+    sqlite3OomFault(db);
+  }
+  return rc;
+}
+
+
+#endif /* SQLITE_OMIT_ANALYZE */