SQLite

/*
** 2005 July 8
**
** 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);
**
** 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 3.7.7, inclusive, and unless SQLite is compiled
** with SQLITE_ENABLE_STAT2.  The sqlite_stat2 table is deprecated.
** The sqlite_stat2 table is superceded by sqlite_stat3, which is only
** created and used by SQLite versions after 2011-08-09 with
** SQLITE_ENABLE_STAT3 defined.  The fucntionality of sqlite_stat3
** is a superset of sqlite_stat2.  
**
** 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 and in the table.  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 3.7.7.  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 is an enhancement to sqlite_stat2.  A new name is
** used to avoid compatibility problems.  
**
** The format of the sqlite_stat3 table is similar to the format for
** the sqlite_stat2 table, with the following changes:  (1)
** The sampleno column is removed.  (2) Every sample has nEq, nLt, and nDLt
** columns which hold the approximate number of rows in the table that
** exactly match the sample, the approximate number of rows with values
** less than the sample, and the approximate number of distinct key values
** less than the sample, respectively.  (3) The number of samples can vary 
** from one table to the next; the sample count does not have to be 
** exactly 10 as it is with sqlite_stat2.
**
** The ANALYZE command will typically generate sqlite_stat3 tables
** that contain between 10 and 40 samples which are distributed across
** the key space, though not uniformly, and which include samples with
** largest possible nEq values.
*/
#ifndef SQLITE_OMIT_ANALYZE
#include "sqliteInt.h"

/*
** This routine generates code that opens the sqlite_stat1 table for
** writing with cursor iStatCur. If the library was built with the

** 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 *zWhere      /* Delete entries associated with this table */
  const char *zWhereType  /* Either "tbl" or "idx" */
){
  static const struct {
    const char *zName;
    const char *zCols;
  } aTable[] = {
    { "sqlite_stat1", "tbl,idx,stat" },
#ifdef SQLITE_ENABLE_STAT2
    { "sqlite_stat2", "tbl,idx,sampleno,sample" },
#ifdef SQLITE_ENABLE_STAT3
    { "sqlite_stat3", "tbl,idx,neq,nlt,ndlt,sample" },
#endif
  };
  static const char *azToDrop[] = { 
    "sqlite_stat2",
#ifndef SQLITE_ENABLE_STAT3
    "sqlite_stat3",
#endif
  };

  int aRoot[] = {0, 0};
  u8 aCreateTbl[] = {0, 0};

  int i;
  sqlite3 *db = pParse->db;
  Db *pDb;
  Vdbe *v = sqlite3GetVdbe(pParse);
  if( v==0 ) return;
  assert( sqlite3BtreeHoldsAllMutexes(db) );
  assert( sqlite3VdbeDb(v)==db );
  pDb = &db->aDb[iDb];

  /* Drop all statistics tables that this version of SQLite does not
  ** understand.
  */
  for(i=0; i<ArraySize(azToDrop); i++){
    Table *pTab = sqlite3FindTable(db, azToDrop[i], pDb->zName);
    if( pTab ) sqlite3CodeDropTable(pParse, pTab, iDb, 0);
  }

  /* 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;
    if( (pStat = sqlite3FindTable(db, zTab, pDb->zName))==0 ){
      /* The sqlite_stat[12] 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 

      /* 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 tbl=%Q", pDb->zName, zTab, zWhere
           "DELETE FROM %Q.%s WHERE %s=%Q", pDb->zName, zTab, zWhereType, zWhere
        );
      }else{
        /* The sqlite_stat[12] table already exists.  Delete all rows. */
        sqlite3VdbeAddOp2(v, OP_Clear, aRoot[i], iDb);
      }
    }
  }

  /* Open the sqlite_stat[12] tables for writing. */
  /* Open the sqlite_stat[13] tables for writing. */
  for(i=0; i<ArraySize(aTable); i++){
    sqlite3VdbeAddOp3(v, OP_OpenWrite, iStatCur+i, aRoot[i], iDb);
    sqlite3VdbeChangeP4(v, -1, (char *)3, P4_INT32);
    sqlite3VdbeChangeP5(v, aCreateTbl[i]);
  }
}

/*
** Recommended number of samples for sqlite_stat3
*/
#ifndef SQLITE_STAT3_SAMPLES
# define SQLITE_STAT3_SAMPLES 24
#endif

/*
** Three SQL functions - stat3_init(), stat3_push(), and stat3_pop() -
** share an instance of the following structure to hold their state
** information.
*/
typedef struct Stat3Accum Stat3Accum;
struct Stat3Accum {
  tRowcnt nRow;             /* Number of rows in the entire table */
  tRowcnt nPSample;         /* How often to do a periodic sample */
  int iMin;                 /* Index of entry with minimum nEq and hash */
  int mxSample;             /* Maximum number of samples to accumulate */
  int nSample;              /* Current number of samples */
  u32 iPrn;                 /* Pseudo-random number used for sampling */
  struct Stat3Sample {
    i64 iRowid;                /* Rowid in main table of the key */
    tRowcnt nEq;               /* sqlite_stat3.nEq */
    tRowcnt nLt;               /* sqlite_stat3.nLt */
    tRowcnt nDLt;              /* sqlite_stat3.nDLt */
    u8 isPSample;              /* True if a periodic sample */
    u32 iHash;                 /* Tiebreaker hash */
  } *a;                     /* An array of samples */
};

#ifdef SQLITE_ENABLE_STAT3
/*
** Implementation of the stat3_init(C,S) SQL function.  The two parameters
** are the number of rows in the table or index (C) and the number of samples
** to accumulate (S).
**
** This routine allocates the Stat3Accum object.
**
** The return value is the Stat3Accum object (P).
*/
static void stat3Init(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  Stat3Accum *p;
  tRowcnt nRow;
  int mxSample;
  int n;

  UNUSED_PARAMETER(argc);
  nRow = (tRowcnt)sqlite3_value_int64(argv[0]);
  mxSample = sqlite3_value_int(argv[1]);
  n = sizeof(*p) + sizeof(p->a[0])*mxSample;
  p = sqlite3_malloc( n );
  if( p==0 ){
    sqlite3_result_error_nomem(context);
    return;
  }
  memset(p, 0, n);
  p->a = (struct Stat3Sample*)&p[1];
  p->nRow = nRow;
  p->mxSample = mxSample;
  p->nPSample = p->nRow/(mxSample/3+1) + 1;
  sqlite3_randomness(sizeof(p->iPrn), &p->iPrn);
  sqlite3_result_blob(context, p, sizeof(p), sqlite3_free);
}
static const FuncDef stat3InitFuncdef = {
  2,                /* nArg */
  SQLITE_UTF8,      /* iPrefEnc */
  0,                /* flags */
  0,                /* pUserData */
  0,                /* pNext */
  stat3Init,        /* xFunc */
  0,                /* xStep */
  0,                /* xFinalize */
  "stat3_init",     /* zName */
  0,                /* pHash */
  0                 /* pDestructor */
};


/*
** Implementation of the stat3_push(nEq,nLt,nDLt,rowid,P) SQL function.  The
** arguments describe a single key instance.  This routine makes the 
** decision about whether or not to retain this key for the sqlite_stat3
** table.
**
** The return value is NULL.
*/
static void stat3Push(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  Stat3Accum *p = (Stat3Accum*)sqlite3_value_blob(argv[4]);
  tRowcnt nEq = sqlite3_value_int64(argv[0]);
  tRowcnt nLt = sqlite3_value_int64(argv[1]);
  tRowcnt nDLt = sqlite3_value_int64(argv[2]);
  i64 rowid = sqlite3_value_int64(argv[3]);
  u8 isPSample = 0;
  u8 doInsert = 0;
  int iMin = p->iMin;
  struct Stat3Sample *pSample;
  int i;
  u32 h;

  UNUSED_PARAMETER(context);
  UNUSED_PARAMETER(argc);
  if( nEq==0 ) return;
  h = p->iPrn = p->iPrn*1103515245 + 12345;
  if( (nLt/p->nPSample)!=((nEq+nLt)/p->nPSample) ){
    doInsert = isPSample = 1;
  }else if( p->nSample<p->mxSample ){
    doInsert = 1;
  }else{
    if( nEq>p->a[iMin].nEq || (nEq==p->a[iMin].nEq && h>p->a[iMin].iHash) ){
      doInsert = 1;
    }
  }
  if( !doInsert ) return;
  if( p->nSample==p->mxSample ){
    if( iMin<p->nSample ){
      memcpy(&p->a[iMin], &p->a[iMin+1], sizeof(p->a[0])*(p->nSample-iMin));
    }
    pSample = &p->a[p->nSample-1];
  }else{
    pSample = &p->a[p->nSample++];
  }
  pSample->iRowid = rowid;
  pSample->nEq = nEq;
  pSample->nLt = nLt;
  pSample->nDLt = nDLt;
  pSample->iHash = h;
  pSample->isPSample = isPSample;

  /* Find the new minimum */
  if( p->nSample==p->mxSample ){
    pSample = p->a;
    i = 0;
    while( pSample->isPSample ){
      i++;
      pSample++;
      assert( i<p->nSample );
    }
    nEq = pSample->nEq;
    h = pSample->iHash;
    iMin = i;
    for(i++, pSample++; i<p->nSample; i++, pSample++){
      if( pSample->isPSample ) continue;
      if( pSample->nEq<nEq
       || (pSample->nEq==nEq && pSample->iHash<h)
      ){
        iMin = i;
        nEq = pSample->nEq;
        h = pSample->iHash;
      }
    }
    p->iMin = iMin;
  }
}
static const FuncDef stat3PushFuncdef = {
  5,                /* nArg */
  SQLITE_UTF8,      /* iPrefEnc */
  0,                /* flags */
  0,                /* pUserData */
  0,                /* pNext */
  stat3Push,        /* xFunc */
  0,                /* xStep */
  0,                /* xFinalize */
  "stat3_push",     /* zName */
  0,                /* pHash */
  0                 /* pDestructor */
};

/*
** Implementation of the stat3_get(P,N,...) SQL function.  This routine is
** used to query the results.  Content is returned for the Nth sqlite_stat3
** row where N is between 0 and S-1 and S is the number of samples.  The
** value returned depends on the number of arguments.
**
**   argc==2    result:  rowid
**   argc==3    result:  nEq
**   argc==4    result:  nLt
**   argc==5    result:  nDLt
*/
static void stat3Get(
  sqlite3_context *context,
  int argc,
  sqlite3_value **argv
){
  int n = sqlite3_value_int(argv[1]);
  Stat3Accum *p = (Stat3Accum*)sqlite3_value_blob(argv[0]);

  assert( p!=0 );
  if( p->nSample<=n ) return;
  switch( argc ){
    case 2: sqlite3_result_int64(context, p->a[n].iRowid); break;
    case 3: sqlite3_result_int64(context, p->a[n].nEq);    break;
    case 4: sqlite3_result_int64(context, p->a[n].nLt);    break;
    case 5: sqlite3_result_int64(context, p->a[n].nDLt);   break;
  }
}
static const FuncDef stat3GetFuncdef = {
  -1,               /* nArg */
  SQLITE_UTF8,      /* iPrefEnc */
  0,                /* flags */
  0,                /* pUserData */
  0,                /* pNext */
  stat3Get,         /* xFunc */
  0,                /* xStep */
  0,                /* xFinalize */
  "stat3_get",     /* zName */
  0,                /* pHash */
  0                 /* pDestructor */
};
#endif /* SQLITE_ENABLE_STAT3 */




/*
** 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 */
){
  sqlite3 *db = pParse->db;    /* Database handle */
  Index *pIdx;                 /* An index to being analyzed */
  int iIdxCur;                 /* Cursor open on index being analyzed */
  Vdbe *v;                     /* The virtual machine being built up */
  int i;                       /* Loop counter */
  int topOfLoop;               /* The top of the loop */
  int endOfLoop;               /* The end of the loop */
  int addr = 0;                /* The address of an instruction */
  int jZeroRows = 0;           /* Jump from here if number of rows is zero */
  int jZeroRows = -1;          /* Jump from here if number of rows is zero */
  int iDb;                     /* Index of database containing pTab */
  int regTabname = iMem++;     /* Register containing table name */
  int regIdxname = iMem++;     /* Register containing index name */
  int regStat1 = iMem++;       /* The stat column of sqlite_stat1 */
#ifdef SQLITE_ENABLE_STAT3
  int regNumEq = regStat1;     /* Number of instances.  Same as regStat1 */
  int regNumLt = iMem++;       /* Number of keys less than regSample */
  int regNumDLt = iMem++;      /* Number of distinct keys less than regSample */
  int regSample = iMem++;      /* The next sample value */
  int regRowid = regSample;    /* Rowid of a sample */
  int regAccum = iMem++;       /* Register to hold Stat3Accum object */
  int regSampleno = iMem++;    /* Register containing next sample number */
  int regCol = iMem++;         /* Content of a column analyzed table */
  int regLoop = iMem++;        /* Loop counter */
  int regCount = iMem++;       /* Number of rows in the table or index */
  int regTemp1 = iMem++;       /* Intermediate register */
  int regTemp2 = iMem++;       /* Intermediate register */
  int once = 1;                /* One-time initialization */
  int shortJump = 0;           /* Instruction address */
  int iTabCur = pParse->nTab++; /* Table cursor */
#endif
  int regCol = iMem++;         /* Content of a column in analyzed table */
  int regRec = iMem++;         /* Register holding completed record */
  int regTemp = iMem++;        /* Temporary use register */
  int regRowid = iMem++;       /* Rowid for the inserted record */
  int regNewRowid = iMem++;    /* Rowid for the inserted record */

#ifdef SQLITE_ENABLE_STAT2
  int regTemp2 = iMem++;       /* Temporary use register */
  int regSamplerecno = iMem++; /* Index of next sample to record */
  int regRecno = iMem++;       /* Current sample index */
  int regLast = iMem++;        /* Index of last sample to record */
  int regFirst = iMem++;       /* Index of first sample to record */
#endif

  v = sqlite3GetVdbe(pParse);
  if( v==0 || NEVER(pTab==0) ){
    return;
  }
  if( pTab->tnum==0 ){
    /* Do not gather statistics on views or virtual tables */

  /* Establish a read-lock on the table at the shared-cache level. */
  sqlite3TableLock(pParse, iDb, pTab->tnum, 0, pTab->zName);

  iIdxCur = pParse->nTab++;
  sqlite3VdbeAddOp4(v, OP_String8, 0, regTabname, 0, pTab->zName, 0);
  for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
    int nCol = pIdx->nColumn;
    KeyInfo *pKey = sqlite3IndexKeyinfo(pParse, pIdx);
    int nCol;
    KeyInfo *pKey;
    int addrIfNot = 0;           /* address of OP_IfNot */
    int *aChngAddr;              /* Array of jump instruction addresses */

    if( pOnlyIdx && pOnlyIdx!=pIdx ) continue;
    VdbeNoopComment((v, "Begin analysis of %s", pIdx->zName));
    nCol = pIdx->nColumn;
    aChngAddr = sqlite3DbMallocRaw(db, sizeof(int)*nCol);
    if( aChngAddr==0 ) continue;
    pKey = sqlite3IndexKeyinfo(pParse, pIdx);
    if( iMem+1+(nCol*2)>pParse->nMem ){
      pParse->nMem = iMem+1+(nCol*2);
    }

    /* Open a cursor to the index to be analyzed. */
    assert( iDb==sqlite3SchemaToIndex(db, pIdx->pSchema) );
    sqlite3VdbeAddOp4(v, OP_OpenRead, iIdxCur, pIdx->tnum, iDb,
        (char *)pKey, P4_KEYINFO_HANDOFF);
    VdbeComment((v, "%s", pIdx->zName));

    /* Populate the register containing the index name. */
    sqlite3VdbeAddOp4(v, OP_String8, 0, regIdxname, 0, pIdx->zName, 0);

#ifdef SQLITE_ENABLE_STAT2

    /* If this iteration of the loop is generating code to analyze the
#ifdef SQLITE_ENABLE_STAT3
    if( once ){
      once = 0;
    ** first index in the pTab->pIndex list, then register regLast has
    ** not been populated. In this case populate it now.  */
    if( pTab->pIndex==pIdx ){
      sqlite3OpenTable(pParse, iTabCur, iDb, pTab, OP_OpenRead);
      sqlite3VdbeAddOp2(v, OP_Integer, SQLITE_INDEX_SAMPLES, regSamplerecno);
      sqlite3VdbeAddOp2(v, OP_Integer, SQLITE_INDEX_SAMPLES*2-1, regTemp);
      sqlite3VdbeAddOp2(v, OP_Integer, SQLITE_INDEX_SAMPLES*2, regTemp2);

      sqlite3VdbeAddOp2(v, OP_Count, iIdxCur, regLast);
      sqlite3VdbeAddOp2(v, OP_Null, 0, regFirst);
    }
    sqlite3VdbeAddOp2(v, OP_Count, iIdxCur, regCount);
    sqlite3VdbeAddOp2(v, OP_Integer, SQLITE_STAT3_SAMPLES, regTemp1);
      addr = sqlite3VdbeAddOp3(v, OP_Lt, regSamplerecno, 0, regLast);
      sqlite3VdbeAddOp3(v, OP_Divide, regTemp2, regLast, regFirst);
      sqlite3VdbeAddOp3(v, OP_Multiply, regLast, regTemp, regLast);
      sqlite3VdbeAddOp2(v, OP_AddImm, regLast, SQLITE_INDEX_SAMPLES*2-2);
    sqlite3VdbeAddOp2(v, OP_Integer, 0, regNumEq);
      sqlite3VdbeAddOp3(v, OP_Divide,  regTemp2, regLast, regLast);
      sqlite3VdbeJumpHere(v, addr);
    }

    /* Zero the regSampleno and regRecno registers. */
    sqlite3VdbeAddOp2(v, OP_Integer, 0, regSampleno);
    sqlite3VdbeAddOp2(v, OP_Integer, 0, regRecno);
    sqlite3VdbeAddOp2(v, OP_Copy, regFirst, regSamplerecno);
#endif
    sqlite3VdbeAddOp2(v, OP_Integer, 0, regNumLt);
    sqlite3VdbeAddOp2(v, OP_Integer, -1, regNumDLt);
    sqlite3VdbeAddOp4(v, OP_Function, 1, regCount, regAccum,
                      (char*)&stat3InitFuncdef, P4_FUNCDEF);
    sqlite3VdbeChangeP5(v, 2);
#endif /* SQLITE_ENABLE_STAT3 */

    /* The block of memory cells initialized here is used as follows.
    **
    **    iMem:                
    **        The total number of rows in the table.
    **
    **    iMem+1 .. iMem+nCol: 

    }

    /* Start the analysis loop. This loop runs through all the entries in
    ** the index b-tree.  */
    endOfLoop = sqlite3VdbeMakeLabel(v);
    sqlite3VdbeAddOp2(v, OP_Rewind, iIdxCur, endOfLoop);
    topOfLoop = sqlite3VdbeCurrentAddr(v);
    sqlite3VdbeAddOp2(v, OP_AddImm, iMem, 1);
    sqlite3VdbeAddOp2(v, OP_AddImm, iMem, 1);  /* Increment row counter */

    for(i=0; i<nCol; i++){
      CollSeq *pColl;
      sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, i, regCol);
      if( i==0 ){
#ifdef SQLITE_ENABLE_STAT2
        /* Check if the record that cursor iIdxCur points to contains a
        ** value that should be stored in the sqlite_stat2 table. If so,
        ** store it.  */
        int ne = sqlite3VdbeAddOp3(v, OP_Ne, regRecno, 0, regSamplerecno);
        assert( regTabname+1==regIdxname 
             && regTabname+2==regSampleno
             && regTabname+3==regCol
        );
        sqlite3VdbeChangeP5(v, SQLITE_JUMPIFNULL);
        sqlite3VdbeAddOp4(v, OP_MakeRecord, regTabname, 4, regRec, "aaab", 0);
        sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur+1, regRowid);
        sqlite3VdbeAddOp3(v, OP_Insert, iStatCur+1, regRec, regRowid);

        /* Calculate new values for regSamplerecno and regSampleno.
        **
        **   sampleno = sampleno + 1
        **   samplerecno = samplerecno+(remaining records)/(remaining samples)
        */
        sqlite3VdbeAddOp2(v, OP_AddImm, regSampleno, 1);
        sqlite3VdbeAddOp3(v, OP_Subtract, regRecno, regLast, regTemp);
        sqlite3VdbeAddOp2(v, OP_AddImm, regTemp, -1);
        sqlite3VdbeAddOp2(v, OP_Integer, SQLITE_INDEX_SAMPLES, regTemp2);
        sqlite3VdbeAddOp3(v, OP_Subtract, regSampleno, regTemp2, regTemp2);
        sqlite3VdbeAddOp3(v, OP_Divide, regTemp2, regTemp, regTemp);
        sqlite3VdbeAddOp3(v, OP_Add, regSamplerecno, regTemp, regSamplerecno);

        sqlite3VdbeJumpHere(v, ne);
        sqlite3VdbeAddOp2(v, OP_AddImm, regRecno, 1);
#endif

        /* Always record the very first row */
        sqlite3VdbeAddOp1(v, OP_IfNot, iMem+1);
        addrIfNot = sqlite3VdbeAddOp1(v, OP_IfNot, iMem+1);
      }
      assert( pIdx->azColl!=0 );
      assert( pIdx->azColl[i]!=0 );
      pColl = sqlite3LocateCollSeq(pParse, pIdx->azColl[i]);
      sqlite3VdbeAddOp4(v, OP_Ne, regCol, 0, iMem+nCol+i+1,
                       (char*)pColl, P4_COLLSEQ);
      aChngAddr[i] = sqlite3VdbeAddOp4(v, OP_Ne, regCol, 0, iMem+nCol+i+1,
                                      (char*)pColl, P4_COLLSEQ);
      sqlite3VdbeChangeP5(v, SQLITE_NULLEQ);
      VdbeComment((v, "jump if column %d changed", i));
#ifdef SQLITE_ENABLE_STAT3
      if( i==0 ){
        sqlite3VdbeAddOp2(v, OP_AddImm, regNumEq, 1);
        VdbeComment((v, "incr repeat count"));
    }
      }
    if( db->mallocFailed ){
      /* If a malloc failure has occurred, then the result of the expression 
      ** passed as the second argument to the call to sqlite3VdbeJumpHere() 
      ** below may be negative. Which causes an assert() to fail (or an
      ** out-of-bounds write if SQLITE_DEBUG is not defined).  */
      return;
#endif
    }
    sqlite3VdbeAddOp2(v, OP_Goto, 0, endOfLoop);
    for(i=0; i<nCol; i++){
      int addr2 = sqlite3VdbeCurrentAddr(v) - (nCol*2);
      sqlite3VdbeJumpHere(v, aChngAddr[i]);  /* Set jump dest for the OP_Ne */
      if( i==0 ){
        sqlite3VdbeJumpHere(v, addr2-1);  /* Set jump dest for the OP_IfNot */
        sqlite3VdbeJumpHere(v, addrIfNot);   /* Jump dest for OP_IfNot */
#ifdef SQLITE_ENABLE_STAT3
        sqlite3VdbeAddOp4(v, OP_Function, 1, regNumEq, regTemp2,
                          (char*)&stat3PushFuncdef, P4_FUNCDEF);
        sqlite3VdbeChangeP5(v, 5);
        sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, pIdx->nColumn, regRowid);
        sqlite3VdbeAddOp3(v, OP_Add, regNumEq, regNumLt, regNumLt);
        sqlite3VdbeAddOp2(v, OP_AddImm, regNumDLt, 1);
        sqlite3VdbeAddOp2(v, OP_Integer, 1, regNumEq);
#endif        
      }
      sqlite3VdbeJumpHere(v, addr2);      /* Set jump dest for the OP_Ne */
      sqlite3VdbeAddOp2(v, OP_AddImm, iMem+i+1, 1);
      sqlite3VdbeAddOp3(v, OP_Column, iIdxCur, i, iMem+nCol+i+1);
    }
    sqlite3DbFree(db, aChngAddr);

    /* End of the analysis loop. */
    /* Always jump here after updating the iMem+1...iMem+1+nCol counters */
    sqlite3VdbeResolveLabel(v, endOfLoop);

    sqlite3VdbeAddOp2(v, OP_Next, iIdxCur, topOfLoop);
    sqlite3VdbeAddOp1(v, OP_Close, iIdxCur);
#ifdef SQLITE_ENABLE_STAT3
    sqlite3VdbeAddOp4(v, OP_Function, 1, regNumEq, regTemp2,
                      (char*)&stat3PushFuncdef, P4_FUNCDEF);
    sqlite3VdbeChangeP5(v, 5);
    sqlite3VdbeAddOp2(v, OP_Integer, -1, regLoop);
    shortJump = 
    sqlite3VdbeAddOp2(v, OP_AddImm, regLoop, 1);
    sqlite3VdbeAddOp4(v, OP_Function, 1, regAccum, regTemp1,
                      (char*)&stat3GetFuncdef, P4_FUNCDEF);
    sqlite3VdbeChangeP5(v, 2);
    sqlite3VdbeAddOp1(v, OP_IsNull, regTemp1);
    sqlite3VdbeAddOp3(v, OP_NotExists, iTabCur, shortJump, regTemp1);
    sqlite3VdbeAddOp3(v, OP_Column, iTabCur, pIdx->aiColumn[0], regSample);
    sqlite3ColumnDefault(v, pTab, pIdx->aiColumn[0], regSample);
    sqlite3VdbeAddOp4(v, OP_Function, 1, regAccum, regNumEq,
                      (char*)&stat3GetFuncdef, P4_FUNCDEF);
    sqlite3VdbeChangeP5(v, 3);
    sqlite3VdbeAddOp4(v, OP_Function, 1, regAccum, regNumLt,
                      (char*)&stat3GetFuncdef, P4_FUNCDEF);
    sqlite3VdbeChangeP5(v, 4);
    sqlite3VdbeAddOp4(v, OP_Function, 1, regAccum, regNumDLt,
                      (char*)&stat3GetFuncdef, P4_FUNCDEF);
    sqlite3VdbeChangeP5(v, 5);
    sqlite3VdbeAddOp4(v, OP_MakeRecord, regTabname, 6, regRec, "bbbbbb", 0);
    sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur+1, regNewRowid);
    sqlite3VdbeAddOp3(v, OP_Insert, iStatCur+1, regRec, regNewRowid);
    sqlite3VdbeAddOp2(v, OP_Goto, 0, shortJump);
    sqlite3VdbeJumpHere(v, shortJump+2);
#endif        

    /* Store the results in sqlite_stat1.
    **
    ** The result is a single row of the sqlite_stat1 table.  The first
    ** two columns are the names of the table and index.  The third column
    ** is a string composed of a list of integer statistics about 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
    ** column of the table.  This additional integer is a guess of how many
    ** rows of the table the index will select.  If D is the count of distinct
    ** values and K is the total number of rows, then the integer is computed
    ** as:
    **
    **        I = (K+D-1)/D
    **
    ** If K==0 then no entry is made into the sqlite_stat1 table.  
    ** If K>0 then it is always the case the D>0 so division by zero
    ** is never possible.
    */
    sqlite3VdbeAddOp2(v, OP_SCopy, iMem, regSampleno);
    if( jZeroRows==0 ){
    sqlite3VdbeAddOp2(v, OP_SCopy, iMem, regStat1);
    if( jZeroRows<0 ){
      jZeroRows = sqlite3VdbeAddOp1(v, OP_IfNot, iMem);
    }
    for(i=0; i<nCol; i++){
      sqlite3VdbeAddOp4(v, OP_String8, 0, regTemp, 0, " ", 0);
      sqlite3VdbeAddOp3(v, OP_Concat, regTemp, regSampleno, regSampleno);
      sqlite3VdbeAddOp3(v, OP_Concat, regTemp, regStat1, regStat1);
      sqlite3VdbeAddOp3(v, OP_Add, iMem, iMem+i+1, regTemp);
      sqlite3VdbeAddOp2(v, OP_AddImm, regTemp, -1);
      sqlite3VdbeAddOp3(v, OP_Divide, iMem+i+1, regTemp, regTemp);
      sqlite3VdbeAddOp1(v, OP_ToInt, regTemp);
      sqlite3VdbeAddOp3(v, OP_Concat, regTemp, regSampleno, regSampleno);
      sqlite3VdbeAddOp3(v, OP_Concat, regTemp, regStat1, regStat1);
    }
    sqlite3VdbeAddOp4(v, OP_MakeRecord, regTabname, 3, regRec, "aaa", 0);
    sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur, regRowid);
    sqlite3VdbeAddOp3(v, OP_Insert, iStatCur, regRec, regRowid);
    sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur, regNewRowid);
    sqlite3VdbeAddOp3(v, OP_Insert, iStatCur, regRec, regNewRowid);
    sqlite3VdbeChangeP5(v, OPFLAG_APPEND);
  }

  /* If the table has no indices, create a single sqlite_stat1 entry
  ** containing NULL as the index name and the row count as the content.
  */
  if( pTab->pIndex==0 ){
    sqlite3VdbeAddOp3(v, OP_OpenRead, iIdxCur, pTab->tnum, iDb);
    VdbeComment((v, "%s", pTab->zName));
    sqlite3VdbeAddOp2(v, OP_Count, iIdxCur, regSampleno);
    sqlite3VdbeAddOp2(v, OP_Count, iIdxCur, regStat1);
    sqlite3VdbeAddOp1(v, OP_Close, iIdxCur);
    jZeroRows = sqlite3VdbeAddOp1(v, OP_IfNot, regStat1);
  }else{
    assert( jZeroRows>0 );
    addr = sqlite3VdbeAddOp0(v, OP_Goto);
    sqlite3VdbeJumpHere(v, jZeroRows);
    jZeroRows = sqlite3VdbeAddOp0(v, OP_Goto);
    sqlite3VdbeJumpHere(v, jZeroRows);
  }
  sqlite3VdbeAddOp2(v, OP_Null, 0, regIdxname);
  sqlite3VdbeAddOp4(v, OP_MakeRecord, regTabname, 3, regRec, "aaa", 0);
  sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur, regRowid);
  sqlite3VdbeAddOp3(v, OP_Insert, iStatCur, regRec, regRowid);
  sqlite3VdbeAddOp2(v, OP_NewRowid, iStatCur, regNewRowid);
  sqlite3VdbeAddOp3(v, OP_Insert, iStatCur, regRec, regNewRowid);
  sqlite3VdbeChangeP5(v, OPFLAG_APPEND);
  if( pParse->nMem<regRec ) pParse->nMem = regRec;
  if( jZeroRows ){
    sqlite3VdbeJumpHere(v, addr);
  }
}
  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);

  Schema *pSchema = db->aDb[iDb].pSchema;    /* Schema of database iDb */
  HashElem *k;
  int iStatCur;
  int iMem;

  sqlite3BeginWriteOperation(pParse, 0, iDb);
  iStatCur = pParse->nTab;
  pParse->nTab += 2;
  openStatTable(pParse, iDb, iStatCur, 0);
  pParse->nTab += 3;
  openStatTable(pParse, iDb, iStatCur, 0, 0);
  iMem = pParse->nMem+1;
  for(k=sqliteHashFirst(&pSchema->tblHash); k; k=sqliteHashNext(k)){
    Table *pTab = (Table*)sqliteHashData(k);
    analyzeOneTable(pParse, pTab, iStatCur, iMem);
    analyzeOneTable(pParse, pTab, 0, iStatCur, iMem);
  }
  loadAnalysis(pParse, iDb);
}

/*
** Generate code that will do an analysis of a single table in
** a database.
** 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){
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 += 2;
  openStatTable(pParse, iDb, iStatCur, pTab->zName);
  analyzeOneTable(pParse, pTab, iStatCur, pParse->nMem+1);
  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);
  loadAnalysis(pParse, iDb);
}

/*
** Generate code for the ANALYZE command.  The parser calls this routine
** when it recognizes an ANALYZE command.
**

*/
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;

  /* 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;

    /* Form 2:  Analyze the database or table named */
    iDb = sqlite3FindDb(db, pName1);
    if( iDb>=0 ){
      analyzeDatabase(pParse, iDb);
    }else{
      z = sqlite3NameFromToken(db, pName1);
      if( z ){
        if( (pIdx = sqlite3FindIndex(db, z, 0))!=0 ){
          analyzeTable(pParse, pIdx->pTable, pIdx);
        pTab = sqlite3LocateTable(pParse, 0, z, 0);
        }else if( (pTab = sqlite3LocateTable(pParse, 0, z, 0))!=0 ){
        sqlite3DbFree(db, z);
        if( pTab ){
          analyzeTable(pParse, pTab);
          analyzeTable(pParse, pTab, 0);
        }
        sqlite3DbFree(db, z);
      }
    }
  }else{
    /* Form 3: Analyze the fully qualified table name */
    iDb = sqlite3TwoPartName(pParse, pName1, pName2, &pTableName);
    if( iDb>=0 ){
      zDb = db->aDb[iDb].zName;
      z = sqlite3NameFromToken(db, pTableName);
      if( z ){
        if( (pIdx = sqlite3FindIndex(db, z, zDb))!=0 ){
          analyzeTable(pParse, pIdx->pTable, pIdx);
        pTab = sqlite3LocateTable(pParse, 0, z, zDb);
        }else if( (pTab = sqlite3LocateTable(pParse, 0, z, zDb))!=0 ){
        sqlite3DbFree(db, z);
        if( pTab ){
          analyzeTable(pParse, pTab);
          analyzeTable(pParse, pTab, 0);
        }
        sqlite3DbFree(db, z);
      }
    }   
  }
}

/*
** Used to pass information from the analyzer reader through to the

** the table.
*/
static int analysisLoader(void *pData, int argc, char **argv, char **NotUsed){
  analysisInfo *pInfo = (analysisInfo*)pData;
  Index *pIndex;
  Table *pTable;
  int i, c, n;
  unsigned int v;
  tRowcnt v;
  const char *z;

  assert( argc==3 );
  UNUSED_PARAMETER2(NotUsed, argc);

  if( argv==0 || argv[0]==0 || argv[2]==0 ){
    return 0;

}

/*
** If the Index.aSample variable is not NULL, delete the aSample[] array
** and its contents.
*/
void sqlite3DeleteIndexSamples(sqlite3 *db, Index *pIdx){
#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
  if( pIdx->aSample ){
    int j;
    for(j=0; j<SQLITE_INDEX_SAMPLES; j++){
    for(j=0; j<pIdx->nSample; j++){
      IndexSample *p = &pIdx->aSample[j];
      if( p->eType==SQLITE_TEXT || p->eType==SQLITE_BLOB ){
        sqlite3DbFree(db, p->u.z);
      }
    }
    sqlite3DbFree(db, pIdx->aSample);
  }
  if( db && db->pnBytesFreed==0 ){
    pIdx->nSample = 0;
    pIdx->aSample = 0;
  }
#else
  UNUSED_PARAMETER(db);
  UNUSED_PARAMETER(pIdx);
#endif
}

#ifdef SQLITE_ENABLE_STAT3
/*
** Load content from the sqlite_stat3 table into the Index.aSample[]
** arrays of all indices.
*/
static int loadStat3(sqlite3 *db, const char *zDb){
  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 */
  int idx = 0;                  /* slot in pIdx->aSample[] for next sample */
  int eType;                    /* Datatype of a sample */
  IndexSample *pSample;         /* A slot in pIdx->aSample[] */

  if( !sqlite3FindTable(db, "sqlite_stat3", zDb) ){
    return SQLITE_OK;
  }

  zSql = sqlite3MPrintf(db, 
      "SELECT idx,count(*) FROM %Q.sqlite_stat3"
      " GROUP BY idx", zDb);
  if( !zSql ){
    return SQLITE_NOMEM;
  }
  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 nSample;    /* Number of samples */

    zIndex = (char *)sqlite3_column_text(pStmt, 0);
    if( zIndex==0 ) continue;
    nSample = sqlite3_column_int(pStmt, 1);
    if( nSample>255 ) continue;
    pIdx = sqlite3FindIndex(db, zIndex, zDb);
    if( pIdx==0 ) continue;
    assert( pIdx->nSample==0 );
    pIdx->nSample = (u8)nSample;
    pIdx->aSample = sqlite3MallocZero( nSample*sizeof(IndexSample) );
    pIdx->avgEq = pIdx->aiRowEst[1];
    if( pIdx->aSample==0 ){
      db->mallocFailed = 1;
      sqlite3_finalize(pStmt);
      return SQLITE_NOMEM;
    }
  }
  rc = sqlite3_finalize(pStmt);
  if( rc ) return rc;

  zSql = sqlite3MPrintf(db, 
      "SELECT idx,neq,nlt,ndlt,sample FROM %Q.sqlite_stat3", zDb);
  if( !zSql ){
    return SQLITE_NOMEM;
  }
  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 i;          /* Loop counter */
    tRowcnt sumEq;  /* Sum of the nEq values */

    zIndex = (char *)sqlite3_column_text(pStmt, 0);
    if( zIndex==0 ) continue;
    pIdx = sqlite3FindIndex(db, zIndex, zDb);
    if( pIdx==0 ) continue;
    if( pIdx==pPrevIdx ){
      idx++;
    }else{
      pPrevIdx = pIdx;
      idx = 0;
    }
    assert( idx<pIdx->nSample );
    pSample = &pIdx->aSample[idx];
    pSample->nEq = (tRowcnt)sqlite3_column_int64(pStmt, 1);
    pSample->nLt = (tRowcnt)sqlite3_column_int64(pStmt, 2);
    pSample->nDLt = (tRowcnt)sqlite3_column_int64(pStmt, 3);
    if( idx==pIdx->nSample-1 ){
      if( pSample->nDLt>0 ){
        for(i=0, sumEq=0; i<=idx-1; i++) sumEq += pIdx->aSample[i].nEq;
        pIdx->avgEq = (pSample->nLt - sumEq)/pSample->nDLt;
      }
      if( pIdx->avgEq<=0 ) pIdx->avgEq = 1;
    }
    eType = sqlite3_column_type(pStmt, 4);
    pSample->eType = (u8)eType;
    switch( eType ){
      case SQLITE_INTEGER: {
        pSample->u.i = sqlite3_column_int64(pStmt, 4);
        break;
      }
      case SQLITE_FLOAT: {
        pSample->u.r = sqlite3_column_double(pStmt, 4);
        break;
      }
      case SQLITE_NULL: {
        break;
      }
      default: assert( eType==SQLITE_TEXT || eType==SQLITE_BLOB ); {
        const char *z = (const char *)(
              (eType==SQLITE_BLOB) ?
              sqlite3_column_blob(pStmt, 4):
              sqlite3_column_text(pStmt, 4)
           );
        int n = z ? sqlite3_column_bytes(pStmt, 4) : 0;
        if( n>0xffff ) n = 0xffff;
        pSample->nByte = (u16)n;
        if( n < 1){
          pSample->u.z = 0;
        }else{
          pSample->u.z = sqlite3Malloc(n);
          if( pSample->u.z==0 ){
            db->mallocFailed = 1;
            sqlite3_finalize(pStmt);
            return SQLITE_NOMEM;
          }
          memcpy(pSample->u.z, z, n);
        }
      }
    }
  }
  return sqlite3_finalize(pStmt);
}
#endif /* SQLITE_ENABLE_STAT3 */

/*
** Load the content of the sqlite_stat1 and sqlite_stat2 tables. The
** Load the content of the sqlite_stat1 and sqlite_stat3 tables. The
** contents of sqlite_stat1 are used to populate the Index.aiRowEst[]
** arrays. The contents of sqlite_stat2 are used to populate the
** arrays. The contents of sqlite_stat3 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_STAT2 was defined 
** during compilation and the sqlite_stat2 table is present, no data is 
** is returned. In this case, even if SQLITE_ENABLE_STAT3 was defined 
** during compilation and the sqlite_stat3 table is present, no data is 
** read from it.
**
** If SQLITE_ENABLE_STAT2 was defined during compilation and the 
** sqlite_stat2 table is not present in the database, SQLITE_ERROR is
** If SQLITE_ENABLE_STAT3 was defined during compilation and the 
** sqlite_stat3 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;

  assert( iDb>=0 && iDb<db->nDb );
  assert( db->aDb[iDb].pBt!=0 );
  assert( sqlite3BtreeHoldsMutex(db->aDb[iDb].pBt) );

  /* Clear any prior statistics */
  for(i=sqliteHashFirst(&db->aDb[iDb].pSchema->idxHash);i;i=sqliteHashNext(i)){
    Index *pIdx = sqliteHashData(i);
    sqlite3DefaultRowEst(pIdx);
#ifdef SQLITE_ENABLE_STAT3
    sqlite3DeleteIndexSamples(db, pIdx);
    pIdx->aSample = 0;
#endif
  }

  /* Check to make sure the sqlite_stat1 table exists */
  sInfo.db = db;
  sInfo.zDatabase = db->aDb[iDb].zName;
  if( sqlite3FindTable(db, "sqlite_stat1", sInfo.zDatabase)==0 ){
    return SQLITE_ERROR;
  }

  /* Load new statistics out of the sqlite_stat1 table */
  zSql = sqlite3MPrintf(db, 
      "SELECT tbl, idx, stat FROM %Q.sqlite_stat1", sInfo.zDatabase);
      "SELECT tbl,idx,stat FROM %Q.sqlite_stat1", sInfo.zDatabase);
  if( zSql==0 ){
    rc = SQLITE_NOMEM;
  }else{
    rc = sqlite3_exec(db, zSql, analysisLoader, &sInfo, 0);
    sqlite3DbFree(db, zSql);
  }


  /* Load the statistics from the sqlite_stat2 table. */
#ifdef SQLITE_ENABLE_STAT2
  /* Load the statistics from the sqlite_stat3 table. */
#ifdef SQLITE_ENABLE_STAT3
  if( rc==SQLITE_OK && !sqlite3FindTable(db, "sqlite_stat2", sInfo.zDatabase) ){
    rc = SQLITE_ERROR;
  }
  if( rc==SQLITE_OK ){
    sqlite3_stmt *pStmt = 0;

    zSql = sqlite3MPrintf(db, 
        "SELECT idx,sampleno,sample FROM %Q.sqlite_stat2", sInfo.zDatabase);
    rc = loadStat3(db, sInfo.zDatabase);
    if( !zSql ){
      rc = SQLITE_NOMEM;
    }else{
      rc = sqlite3_prepare(db, zSql, -1, &pStmt, 0);
      sqlite3DbFree(db, zSql);
    }

    if( rc==SQLITE_OK ){
      while( sqlite3_step(pStmt)==SQLITE_ROW ){
        char *zIndex;   /* Index name */
        Index *pIdx;    /* Pointer to the index object */

        zIndex = (char *)sqlite3_column_text(pStmt, 0);
        pIdx = zIndex ? sqlite3FindIndex(db, zIndex, sInfo.zDatabase) : 0;
        if( pIdx ){
          int iSample = sqlite3_column_int(pStmt, 1);
          if( iSample<SQLITE_INDEX_SAMPLES && iSample>=0 ){
            int eType = sqlite3_column_type(pStmt, 2);

            if( pIdx->aSample==0 ){
              static const int sz = sizeof(IndexSample)*SQLITE_INDEX_SAMPLES;
              pIdx->aSample = (IndexSample *)sqlite3DbMallocRaw(0, sz);
              if( pIdx->aSample==0 ){
                db->mallocFailed = 1;
                break;
              }
	      memset(pIdx->aSample, 0, sz);
            }

            assert( pIdx->aSample );
            {
              IndexSample *pSample = &pIdx->aSample[iSample];
              pSample->eType = (u8)eType;
              if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
                pSample->u.r = sqlite3_column_double(pStmt, 2);
              }else if( eType==SQLITE_TEXT || eType==SQLITE_BLOB ){
                const char *z = (const char *)(
                    (eType==SQLITE_BLOB) ?
                    sqlite3_column_blob(pStmt, 2):
                    sqlite3_column_text(pStmt, 2)
                );
                int n = sqlite3_column_bytes(pStmt, 2);
                if( n>24 ){
                  n = 24;
                }
                pSample->nByte = (u8)n;
                if( n < 1){
                  pSample->u.z = 0;
                }else{
                  pSample->u.z = sqlite3DbStrNDup(0, z, n);
                  if( pSample->u.z==0 ){
                    db->mallocFailed = 1;
                    break;
                  }
                }
              }
            }
          }
        }
      }
      rc = sqlite3_finalize(pStmt);
    }
  }
#endif

  if( rc==SQLITE_NOMEM ){
    db->mallocFailed = 1;
  }
  return rc;
}


#endif /* SQLITE_OMIT_ANALYZE */

      int iDb = sqlite3SchemaToIndex(pParse->db, pTab->pSchema);
      destroyRootPage(pParse, iLargest, iDb);
      iDestroyed = iLargest;
    }
  }
#endif
}

/*
** Remove entries from the sqlite_stat1 and sqlite_stat2 tables
** after a DROP INDEX or DROP TABLE command.
*/
static void sqlite3ClearStatTables(
  Parse *pParse,         /* The parsing context */
  int iDb,               /* The database number */
  const char *zType,     /* "idx" or "tbl" */
  const char *zName      /* Name of index or table */
){
  static const char *azStatTab[] = { 
    "sqlite_stat1",
    "sqlite_stat2",
    "sqlite_stat3",
  };
  int i;
  const char *zDbName = pParse->db->aDb[iDb].zName;
  for(i=0; i<ArraySize(azStatTab); i++){
    if( sqlite3FindTable(pParse->db, azStatTab[i], zDbName) ){
      sqlite3NestedParse(pParse,
        "DELETE FROM %Q.%s WHERE %s=%Q",
        zDbName, azStatTab[i], zType, zName
      );
    }
  }
}

/*
** Generate code to drop a table.
*/
void sqlite3CodeDropTable(Parse *pParse, Table *pTab, int iDb, int isView){
  Vdbe *v;
  sqlite3 *db = pParse->db;
  Trigger *pTrigger;
  Db *pDb = &db->aDb[iDb];

  v = sqlite3GetVdbe(pParse);
  assert( v!=0 );
  sqlite3BeginWriteOperation(pParse, 1, iDb);

#ifndef SQLITE_OMIT_VIRTUALTABLE
  if( IsVirtual(pTab) ){
    sqlite3VdbeAddOp0(v, OP_VBegin);
  }
#endif

  /* Drop all triggers associated with the table being dropped. Code
  ** is generated to remove entries from sqlite_master and/or
  ** sqlite_temp_master if required.
  */
  pTrigger = sqlite3TriggerList(pParse, pTab);
  while( pTrigger ){
    assert( pTrigger->pSchema==pTab->pSchema || 
        pTrigger->pSchema==db->aDb[1].pSchema );
    sqlite3DropTriggerPtr(pParse, pTrigger);
    pTrigger = pTrigger->pNext;
  }

#ifndef SQLITE_OMIT_AUTOINCREMENT
  /* Remove any entries of the sqlite_sequence table associated with
  ** the table being dropped. This is done before the table is dropped
  ** at the btree level, in case the sqlite_sequence table needs to
  ** move as a result of the drop (can happen in auto-vacuum mode).
  */
  if( pTab->tabFlags & TF_Autoincrement ){
    sqlite3NestedParse(pParse,
      "DELETE FROM %Q.sqlite_sequence WHERE name=%Q",
      pDb->zName, pTab->zName
    );
  }
#endif

  /* Drop all SQLITE_MASTER table and index entries that refer to the
  ** table. The program name loops through the master table and deletes
  ** every row that refers to a table of the same name as the one being
  ** dropped. Triggers are handled seperately because a trigger can be
  ** created in the temp database that refers to a table in another
  ** database.
  */
  sqlite3NestedParse(pParse, 
      "DELETE FROM %Q.%s WHERE tbl_name=%Q and type!='trigger'",
      pDb->zName, SCHEMA_TABLE(iDb), pTab->zName);
  if( !isView && !IsVirtual(pTab) ){
    destroyTable(pParse, pTab);
  }

  /* Remove the table entry from SQLite's internal schema and modify
  ** the schema cookie.
  */
  if( IsVirtual(pTab) ){
    sqlite3VdbeAddOp4(v, OP_VDestroy, iDb, 0, 0, pTab->zName, 0);
  }
  sqlite3VdbeAddOp4(v, OP_DropTable, iDb, 0, 0, pTab->zName, 0);
  sqlite3ChangeCookie(pParse, iDb);
  sqliteViewResetAll(db, iDb);
}

/*
** This routine is called to do the work of a DROP TABLE statement.
** pName is the name of the table to be dropped.
*/
void sqlite3DropTable(Parse *pParse, SrcList *pName, int isView, int noErr){
  Table *pTab;

      goto exit_drop_table;
    }
    if( sqlite3AuthCheck(pParse, SQLITE_DELETE, pTab->zName, 0, zDb) ){
      goto exit_drop_table;
    }
  }
#endif
  if( sqlite3StrNICmp(pTab->zName, "sqlite_", 7)==0 ){
  if( !pParse->nested && sqlite3StrNICmp(pTab->zName, "sqlite_", 7)==0 ){
    sqlite3ErrorMsg(pParse, "table %s may not be dropped", pTab->zName);
    goto exit_drop_table;
  }

#ifndef SQLITE_OMIT_VIEW
  /* Ensure DROP TABLE is not used on a view, and DROP VIEW is not used
  ** on a table.

#endif

  /* Generate code to remove the table from the master table
  ** on disk.
  */
  v = sqlite3GetVdbe(pParse);
  if( v ){
    Trigger *pTrigger;
    Db *pDb = &db->aDb[iDb];
    sqlite3BeginWriteOperation(pParse, 1, iDb);

    sqlite3ClearStatTables(pParse, iDb, "tbl", pTab->zName);
#ifndef SQLITE_OMIT_VIRTUALTABLE
    if( IsVirtual(pTab) ){
      sqlite3VdbeAddOp0(v, OP_VBegin);
    }
#endif
    sqlite3FkDropTable(pParse, pName, pTab);

    /* Drop all triggers associated with the table being dropped. Code
    ** is generated to remove entries from sqlite_master and/or
    ** sqlite_temp_master if required.
    */
    pTrigger = sqlite3TriggerList(pParse, pTab);
    while( pTrigger ){
      assert( pTrigger->pSchema==pTab->pSchema || 
          pTrigger->pSchema==db->aDb[1].pSchema );
      sqlite3DropTriggerPtr(pParse, pTrigger);
      pTrigger = pTrigger->pNext;
    }

#ifndef SQLITE_OMIT_AUTOINCREMENT
    /* Remove any entries of the sqlite_sequence table associated with
    ** the table being dropped. This is done before the table is dropped
    ** at the btree level, in case the sqlite_sequence table needs to
    ** move as a result of the drop (can happen in auto-vacuum mode).
    */
    if( pTab->tabFlags & TF_Autoincrement ){
      sqlite3NestedParse(pParse,
        "DELETE FROM %s.sqlite_sequence WHERE name=%Q",
        pDb->zName, pTab->zName
      );
    }
#endif

    /* Drop all SQLITE_MASTER table and index entries that refer to the
    ** table. The program name loops through the master table and deletes
    ** every row that refers to a table of the same name as the one being
    ** dropped. Triggers are handled seperately because a trigger can be
    ** created in the temp database that refers to a table in another
    ** database.
    */
    sqlite3NestedParse(pParse, 
        "DELETE FROM %Q.%s WHERE tbl_name=%Q and type!='trigger'",
        pDb->zName, SCHEMA_TABLE(iDb), pTab->zName);

    /* Drop any statistics from the sqlite_stat1 table, if it exists */
    if( sqlite3FindTable(db, "sqlite_stat1", db->aDb[iDb].zName) ){
      sqlite3NestedParse(pParse,
        "DELETE FROM %Q.sqlite_stat1 WHERE tbl=%Q", pDb->zName, pTab->zName
      );
    }

    if( !isView && !IsVirtual(pTab) ){
      destroyTable(pParse, pTab);
    }
    sqlite3CodeDropTable(pParse, pTab, iDb, isView);
  }

    /* Remove the table entry from SQLite's internal schema and modify
    ** the schema cookie.
    */
    if( IsVirtual(pTab) ){
      sqlite3VdbeAddOp4(v, OP_VDestroy, iDb, 0, 0, pTab->zName, 0);
    }
    sqlite3VdbeAddOp4(v, OP_DropTable, iDb, 0, 0, pTab->zName, 0);
    sqlite3ChangeCookie(pParse, iDb);
  }
  sqliteViewResetAll(db, iDb);

exit_drop_table:
  sqlite3SrcListDelete(db, pName);
}

/*
** This routine is called to create a new foreign key on the table

  /* 
  ** Allocate the index structure. 
  */
  nName = sqlite3Strlen30(zName);
  nCol = pList->nExpr;
  pIndex = sqlite3DbMallocZero(db, 
      sizeof(Index) +              /* Index structure  */
      sizeof(tRowcnt)*(nCol+1) +   /* Index.aiRowEst   */
      sizeof(int)*nCol +           /* Index.aiColumn   */
      sizeof(int)*(nCol+1) +       /* Index.aiRowEst   */
      sizeof(char *)*nCol +        /* Index.azColl     */
      sizeof(u8)*nCol +            /* Index.aSortOrder */
      nName + 1 +                  /* Index.zName      */
      nExtra                       /* Collation sequence names */
  );
  if( db->mallocFailed ){
    goto exit_create_index;
  }
  pIndex->aiRowEst = (tRowcnt*)(&pIndex[1]);
  pIndex->azColl = (char**)(&pIndex[1]);
  pIndex->azColl = (char**)(&pIndex->aiRowEst[nCol+1]);
  pIndex->aiColumn = (int *)(&pIndex->azColl[nCol]);
  pIndex->aiRowEst = (unsigned *)(&pIndex->aiColumn[nCol]);
  pIndex->aSortOrder = (u8 *)(&pIndex->aiRowEst[nCol+1]);
  pIndex->aSortOrder = (u8 *)(&pIndex->aiColumn[nCol]);
  pIndex->zName = (char *)(&pIndex->aSortOrder[nCol]);
  zExtra = (char *)(&pIndex->zName[nName+1]);
  memcpy(pIndex->zName, zName, nName+1);
  pIndex->pTable = pTab;
  pIndex->nColumn = pList->nExpr;
  pIndex->onError = (u8)onError;
  pIndex->autoIndex = (u8)(pName==0);

**           aiRowEst[N]>=1
**
** Apart from that, we have little to go on besides intuition as to
** how aiRowEst[] should be initialized.  The numbers generated here
** are based on typical values found in actual indices.
*/
void sqlite3DefaultRowEst(Index *pIdx){
  unsigned *a = pIdx->aiRowEst;
  tRowcnt *a = pIdx->aiRowEst;
  int i;
  unsigned n;
  tRowcnt n;
  assert( a!=0 );
  a[0] = pIdx->pTable->nRowEst;
  if( a[0]<10 ) a[0] = 10;
  n = 10;
  for(i=1; i<=pIdx->nColumn; i++){
    a[i] = n;
    if( n>5 ) n--;

  if( v ){
    sqlite3BeginWriteOperation(pParse, 1, iDb);
    sqlite3NestedParse(pParse,
       "DELETE FROM %Q.%s WHERE name=%Q",
       db->aDb[iDb].zName, SCHEMA_TABLE(iDb),
       pIndex->zName
    );
    if( sqlite3FindTable(db, "sqlite_stat1", db->aDb[iDb].zName) ){
      sqlite3NestedParse(pParse,
        "DELETE FROM %Q.sqlite_stat1 WHERE idx=%Q",
        db->aDb[iDb].zName, pIndex->zName
    sqlite3ClearStatTables(pParse, iDb, "idx", pIndex->zName);
      );
    }
    sqlite3ChangeCookie(pParse, iDb);
    destroyRootPage(pParse, pIndex->tnum, iDb);
    sqlite3VdbeAddOp4(v, OP_DropIndex, iDb, 0, 0, pIndex->zName, 0);
  }

exit_drop_index:
  sqlite3SrcListDelete(db, pName);

  "ENABLE_OVERSIZE_CELL_CHECK",
#endif
#ifdef SQLITE_ENABLE_RTREE
  "ENABLE_RTREE",
#endif
#ifdef SQLITE_ENABLE_STAT2
  "ENABLE_STAT2",
#endif
#ifdef SQLITE_ENABLE_STAT3
  "ENABLE_STAT3",
#endif
#ifdef SQLITE_ENABLE_UNLOCK_NOTIFY
  "ENABLE_UNLOCK_NOTIFY",
#endif
#ifdef SQLITE_ENABLE_UPDATE_DELETE_LIMIT
  "ENABLE_UPDATE_DELETE_LIMIT",
#endif

** [sqlite3_step()] would only return a generic [SQLITE_ERROR] result code
** and the application would have to make a second call to [sqlite3_reset()]
** in order to find the underlying cause of the problem. With the "v2" prepare
** interfaces, the underlying reason for the error is returned immediately.
** </li>
**
** <li>
** ^If the value of a [parameter | host parameter] in the WHERE clause might
** change the query plan for a statement, then the statement may be
** automatically recompiled (as if there had been a schema change) on the first 
** [sqlite3_step()] call following any change to the 
** [sqlite3_bind_text | bindings] of the [parameter]. 
** ^If the specific value bound to [parameter | host parameter] in the 
** WHERE clause might influence the choice of query plan for a statement,
** then the statement will be automatically recompiled, as if there had been 
** a schema change, on the first  [sqlite3_step()] call following any change
** to the [sqlite3_bind_text | bindings] of that [parameter]. 
** ^The specific value of WHERE-clause [parameter] might influence the 
** choice of query plan if the parameter is the left-hand side of a [LIKE]
** or [GLOB] operator or if the parameter is compared to an indexed column
** and the [SQLITE_ENABLE_STAT3] compile-time option is enabled.
** the 
** </li>
** </ol>
*/
int sqlite3_prepare(
  sqlite3 *db,            /* Database handle */
  const char *zSql,       /* SQL statement, UTF-8 encoded */
  int nByte,              /* Maximum length of zSql in bytes. */

** SQLITE_MAX_U32 is a u64 constant that is the maximum u64 value
** that can be stored in a u32 without loss of data.  The value
** is 0x00000000ffffffff.  But because of quirks of some compilers, we
** have to specify the value in the less intuitive manner shown:
*/
#define SQLITE_MAX_U32  ((((u64)1)<<32)-1)

/*
** The datatype used to store estimates of the number of rows in a
** table or index.  This is an unsigned integer type.  For 99.9% of
** the world, a 32-bit integer is sufficient.  But a 64-bit integer
** can be used at compile-time if desired.
*/
#ifdef SQLITE_64BIT_STATS
 typedef u64 tRowcnt;    /* 64-bit only if requested at compile-time */
#else
 typedef u32 tRowcnt;    /* 32-bit is the default */
#endif

/*
** Macros to determine whether the machine is big or little endian,
** evaluated at runtime.
*/
#ifdef SQLITE_AMALGAMATION
const int sqlite3one = 1;
#else

struct Table {
  char *zName;         /* Name of the table or view */
  int iPKey;           /* If not negative, use aCol[iPKey] as the primary key */
  int nCol;            /* Number of columns in this table */
  Column *aCol;        /* Information about each column */
  Index *pIndex;       /* List of SQL indexes on this table. */
  int tnum;            /* Root BTree node for this table (see note above) */
  unsigned nRowEst;    /* Estimated rows in table - from sqlite_stat1 table */
  tRowcnt nRowEst;     /* Estimated rows in table - from sqlite_stat1 table */
  Select *pSelect;     /* NULL for tables.  Points to definition if a view. */
  u16 nRef;            /* Number of pointers to this Table */
  u8 tabFlags;         /* Mask of TF_* values */
  u8 keyConf;          /* What to do in case of uniqueness conflict on iPKey */
  FKey *pFKey;         /* Linked list of all foreign keys in this table */
  char *zColAff;       /* String defining the affinity of each column */
#ifndef SQLITE_OMIT_CHECK

** algorithm to employ whenever an attempt is made to insert a non-unique
** element.
*/
struct Index {
  char *zName;     /* Name of this index */
  int nColumn;     /* Number of columns in the table used by this index */
  int *aiColumn;   /* Which columns are used by this index.  1st is 0 */
  unsigned *aiRowEst; /* Result of ANALYZE: Est. rows selected by each column */
  tRowcnt *aiRowEst; /* Result of ANALYZE: Est. rows selected by each column */
  Table *pTable;   /* The SQL table being indexed */
  int tnum;        /* Page containing root of this index in database file */
  u8 onError;      /* OE_Abort, OE_Ignore, OE_Replace, or OE_None */
  u8 autoIndex;    /* True if is automatically created (ex: by UNIQUE) */
  u8 bUnordered;   /* Use this index for == or IN queries only */
  u8 nSample;      /* Number of elements in aSample[] */
  char *zColAff;   /* String defining the affinity of each column */
  Index *pNext;    /* The next index associated with the same table */
  Schema *pSchema; /* Schema containing this index */
  u8 *aSortOrder;  /* Array of size Index.nColumn. True==DESC, False==ASC */
  char **azColl;   /* Array of collation sequence names for index */
#ifdef SQLITE_ENABLE_STAT3
  tRowcnt avgEq;           /* Average nEq value for key values not in aSample */
  IndexSample *aSample;    /* Array of SQLITE_INDEX_SAMPLES samples */
  IndexSample *aSample;    /* Samples of the left-most key */
#endif
};

/*
** Each sample stored in the sqlite_stat2 table is represented in memory 
** using a structure of this type.
*/
struct IndexSample {
  union {
    char *z;        /* Value if eType is SQLITE_TEXT or SQLITE_BLOB */
    double r;       /* Value if eType is SQLITE_FLOAT or SQLITE_INTEGER */
    double r;       /* Value if eType is SQLITE_FLOAT */
    i64 i;          /* Value if eType is SQLITE_INTEGER */
  } u;
  u8 eType;         /* SQLITE_NULL, SQLITE_INTEGER ... etc. */
  u8 nByte;         /* Size in byte of text or blob. */
  u16 nByte;        /* Size in byte of text or blob. */
  tRowcnt nEq;      /* Est. number of rows where the key equals this sample */
  tRowcnt nLt;      /* Est. number of rows where key is less than this sample */
  tRowcnt nDLt;     /* Est. number of distinct keys less than this sample */
};

/*
** Each token coming out of the lexer is an instance of
** this structure.  Tokens are also used as part of an expression.
**
** Note if Token.z==0 then Token.dyn and Token.n are undefined and

#if !defined(SQLITE_OMIT_VIEW) || !defined(SQLITE_OMIT_VIRTUALTABLE)
  int sqlite3ViewGetColumnNames(Parse*,Table*);
#else
# define sqlite3ViewGetColumnNames(A,B) 0
#endif

void sqlite3DropTable(Parse*, SrcList*, int, int);
void sqlite3CodeDropTable(Parse*, Table*, int, int);
void sqlite3DeleteTable(sqlite3*, Table*);
#ifndef SQLITE_OMIT_AUTOINCREMENT
  void sqlite3AutoincrementBegin(Parse *pParse);
  void sqlite3AutoincrementEnd(Parse *pParse);
#else
# define sqlite3AutoincrementBegin(X)
# define sqlite3AutoincrementEnd(X)

const void *sqlite3ValueText(sqlite3_value*, u8);
int sqlite3ValueBytes(sqlite3_value*, u8);
void sqlite3ValueSetStr(sqlite3_value*, int, const void *,u8, 
                        void(*)(void*));
void sqlite3ValueFree(sqlite3_value*);
sqlite3_value *sqlite3ValueNew(sqlite3 *);
char *sqlite3Utf16to8(sqlite3 *, const void*, int, u8);
#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
char *sqlite3Utf8to16(sqlite3 *, u8, char *, int, int *);
#endif
int sqlite3ValueFromExpr(sqlite3 *, Expr *, u8, u8, sqlite3_value **);
void sqlite3ValueApplyAffinity(sqlite3_value *, u8, u8);
#ifndef SQLITE_AMALGAMATION
extern const unsigned char sqlite3OpcodeProperty[];
extern const unsigned char sqlite3UpperToLower[];

#endif

#ifdef SQLITE_ENABLE_STAT2
  Tcl_SetVar2(interp, "sqlite_options", "stat2", "1", TCL_GLOBAL_ONLY);
#else
  Tcl_SetVar2(interp, "sqlite_options", "stat2", "0", TCL_GLOBAL_ONLY);
#endif

#ifdef SQLITE_ENABLE_STAT3
  Tcl_SetVar2(interp, "sqlite_options", "stat3", "1", TCL_GLOBAL_ONLY);
#else
  Tcl_SetVar2(interp, "sqlite_options", "stat3", "0", TCL_GLOBAL_ONLY);
#endif

#if !defined(SQLITE_ENABLE_LOCKING_STYLE)
#  if defined(__APPLE__)
#    define SQLITE_ENABLE_LOCKING_STYLE 1
#  else
#    define SQLITE_ENABLE_LOCKING_STYLE 0
#  endif

** is set to the length of the returned string in bytes. The call should
** arrange to call sqlite3DbFree() on the returned pointer when it is
** no longer required.
** 
** If a malloc failure occurs, NULL is returned and the db.mallocFailed
** flag set.
*/
#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
char *sqlite3Utf8to16(sqlite3 *db, u8 enc, char *z, int n, int *pnOut){
  Mem m;
  memset(&m, 0, sizeof(m));
  m.db = db;
  sqlite3VdbeMemSetStr(&m, z, n, SQLITE_UTF8, SQLITE_STATIC);
  if( sqlite3VdbeMemTranslate(&m, enc) ){
    assert( db->mallocFailed );

}

/*
** Change the P2 operand of instruction addr so that it points to
** the address of the next instruction to be coded.
*/
void sqlite3VdbeJumpHere(Vdbe *p, int addr){
  assert( addr>=0 || p->db->mallocFailed );
  sqlite3VdbeChangeP2(p, addr, p->nOp);
  if( addr>=0 ) sqlite3VdbeChangeP2(p, addr, p->nOp);
}


/*
** If the input FuncDef structure is ephemeral, then free it.  If
** the FuncDef is not ephermal, then do nothing.
*/

  if( !pExpr ){
    *ppVal = 0;
    return SQLITE_OK;
  }
  op = pExpr->op;

  /* op can only be TK_REGISTER if we have compiled with SQLITE_ENABLE_STAT2.
  /* op can only be TK_REGISTER if we have compiled with SQLITE_ENABLE_STAT3.
  ** The ifdef here is to enable us to achieve 100% branch test coverage even
  ** when SQLITE_ENABLE_STAT2 is omitted.
  ** when SQLITE_ENABLE_STAT3 is omitted.
  */
#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
  if( op==TK_REGISTER ) op = pExpr->op2;
#else
  if( NEVER(op==TK_REGISTER) ) op = pExpr->op2;
#endif

  if( op==TK_STRING || op==TK_FLOAT || op==TK_INTEGER ){
    pVal = sqlite3ValueNew(db);

#define TERM_DYNAMIC    0x01   /* Need to call sqlite3ExprDelete(db, pExpr) */
#define TERM_VIRTUAL    0x02   /* Added by the optimizer.  Do not code */
#define TERM_CODED      0x04   /* This term is already coded */
#define TERM_COPIED     0x08   /* Has a child */
#define TERM_ORINFO     0x10   /* Need to free the WhereTerm.u.pOrInfo object */
#define TERM_ANDINFO    0x20   /* Need to free the WhereTerm.u.pAndInfo obj */
#define TERM_OR_OK      0x40   /* Used during OR-clause processing */
#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
#  define TERM_VNULL    0x80   /* Manufactured x>NULL or x<=NULL term */
#else
#  define TERM_VNULL    0x00   /* Disabled if not using stat2 */
#endif

/*
** An instance of the following structure holds all information about a

      pTerm->nChild = 1;
      pTerm->wtFlags |= TERM_COPIED;
      pNewTerm->prereqAll = pTerm->prereqAll;
    }
  }
#endif /* SQLITE_OMIT_VIRTUALTABLE */

#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
  /* When sqlite_stat2 histogram data is available an operator of the
  ** form "x IS NOT NULL" can sometimes be evaluated more efficiently
  ** as "x>NULL" if x is not an INTEGER PRIMARY KEY.  So construct a
  ** virtual term of that form.
  **
  ** Note that the virtual term must be tagged with TERM_VNULL.  This
  ** TERM_VNULL tag will suppress the not-null check at the beginning

      pNewTerm->iParent = idxTerm;
      pTerm = &pWC->a[idxTerm];
      pTerm->nChild = 1;
      pTerm->wtFlags |= TERM_COPIED;
      pNewTerm->prereqAll = pTerm->prereqAll;
    }
  }
#endif /* SQLITE_ENABLE_STAT2 */
#endif /* SQLITE_ENABLE_STAT */

  /* Prevent ON clause terms of a LEFT JOIN from being used to drive
  ** an index for tables to the left of the join.
  */
  pTerm->prereqRight |= extraRight;
}

  /* Try to find a more efficient access pattern by using multiple indexes
  ** to optimize an OR expression within the WHERE clause. 
  */
  bestOrClauseIndex(pParse, pWC, pSrc, notReady, notValid, pOrderBy, pCost);
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

#ifdef SQLITE_ENABLE_STAT3
/*
** Argument pIdx is a pointer to an index structure that has an array of
** SQLITE_INDEX_SAMPLES evenly spaced samples of the first indexed column
** Estimate the location of a particular key among all keys in an
** stored in Index.aSample. These samples divide the domain of values stored
** the index into (SQLITE_INDEX_SAMPLES+1) regions.
** index.  Store the results in aStat as follows:
** Region 0 contains all values less than the first sample value. Region
** 1 contains values between the first and second samples.  Region 2 contains
** values between samples 2 and 3.  And so on.  Region SQLITE_INDEX_SAMPLES
** contains values larger than the last sample.
**
** If the index contains many duplicates of a single value, then it is
** possible that two or more adjacent samples can hold the same value.
** When that is the case, the smallest possible region code is returned
** when roundUp is false and the largest possible region code is returned
** when roundUp is true.
**    aStat[0]      Est. number of rows less than pVal
**    aStat[1]      Est. number of rows equal to pVal
**
** If successful, this function determines which of the regions value 
** pVal lies in, sets *piRegion to the region index (a value between 0
** and SQLITE_INDEX_SAMPLES+1, inclusive) and returns SQLITE_OK.
** Return SQLITE_OK on success.
** Or, if an OOM occurs while converting text values between encodings,
** SQLITE_NOMEM is returned and *piRegion is undefined.
*/
#ifdef SQLITE_ENABLE_STAT2
static int whereRangeRegion(
static int whereKeyStats(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  sqlite3_value *pVal,        /* Value to consider */
  int roundUp,                /* Return largest valid region if true */
  int *piRegion               /* OUT: Region of domain in which value lies */
  int roundUp,                /* Round up if true.  Round down if false */
  tRowcnt *aStat              /* OUT: stats written here */
){
  tRowcnt n;
  IndexSample *aSample;
  int i, eType;
  int isEq = 0;
  i64 v;
  double r, rS;

  assert( roundUp==0 || roundUp==1 );
  if( ALWAYS(pVal) ){
    IndexSample *aSample = pIdx->aSample;
    int i = 0;
    int eType = sqlite3_value_type(pVal);
  if( pVal==0 ) return SQLITE_ERROR;
  n = pIdx->aiRowEst[0];
  aSample = pIdx->aSample;
  i = 0;
  eType = sqlite3_value_type(pVal);

    if( eType==SQLITE_INTEGER || eType==SQLITE_FLOAT ){
      double r = sqlite3_value_double(pVal);
      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){
        if( aSample[i].eType==SQLITE_NULL ) continue;
        if( aSample[i].eType>=SQLITE_TEXT ) break;
        if( roundUp ){
          if( aSample[i].u.r>r ) break;
        }else{
          if( aSample[i].u.r>=r ) break;
  if( eType==SQLITE_INTEGER ){
    v = sqlite3_value_int64(pVal);
    r = (i64)v;
    for(i=0; i<pIdx->nSample; i++){
      if( aSample[i].eType==SQLITE_NULL ) continue;
      if( aSample[i].eType>=SQLITE_TEXT ) break;
      if( aSample[i].eType==SQLITE_INTEGER ){
        if( aSample[i].u.i>=v ){
          isEq = aSample[i].u.i==v;
          break;
        }
      }else{
        assert( aSample[i].eType==SQLITE_FLOAT );
        if( aSample[i].u.r>=r ){
          isEq = aSample[i].u.r==r;
          break;
        }
      }
    }
    }else if( eType==SQLITE_NULL ){
      i = 0;
      if( roundUp ){
        while( i<SQLITE_INDEX_SAMPLES && aSample[i].eType==SQLITE_NULL ) i++;
  }else if( eType==SQLITE_FLOAT ){
    r = sqlite3_value_double(pVal);
    for(i=0; i<pIdx->nSample; i++){
      if( aSample[i].eType==SQLITE_NULL ) continue;
      if( aSample[i].eType>=SQLITE_TEXT ) break;
      if( aSample[i].eType==SQLITE_FLOAT ){
        rS = aSample[i].u.r;
      }else{
        rS = aSample[i].u.i;
      }
      if( rS>=r ){
        isEq = rS==r;
        break;
      }
    }
  }else if( eType==SQLITE_NULL ){
    i = 0;
    if( pIdx->nSample>=1 && aSample[0].eType==SQLITE_NULL ) isEq = 1;
    }else{ 
  }else{
    assert( eType==SQLITE_TEXT || eType==SQLITE_BLOB );
    for(i=0; i<pIdx->nSample; i++){
      if( aSample[i].eType==SQLITE_TEXT || aSample[i].eType==SQLITE_BLOB ){
        break;
      }
    }
    if( i<pIdx->nSample ){      
      sqlite3 *db = pParse->db;
      CollSeq *pColl;
      const u8 *z;
      int n;

      /* pVal comes from sqlite3ValueFromExpr() so the type cannot be NULL */
      assert( eType==SQLITE_TEXT || eType==SQLITE_BLOB );

      if( eType==SQLITE_BLOB ){
        z = (const u8 *)sqlite3_value_blob(pVal);
        pColl = db->pDfltColl;
        assert( pColl->enc==SQLITE_UTF8 );
      }else{
        pColl = sqlite3GetCollSeq(db, SQLITE_UTF8, 0, *pIdx->azColl);
        if( pColl==0 ){
          sqlite3ErrorMsg(pParse, "no such collation sequence: %s",
                          *pIdx->azColl);
          return SQLITE_ERROR;
        }
        z = (const u8 *)sqlite3ValueText(pVal, pColl->enc);
        if( !z ){
          return SQLITE_NOMEM;
        }
        assert( z && pColl && pColl->xCmp );
      }
      n = sqlite3ValueBytes(pVal, pColl->enc);

      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){
  
      for(; i<pIdx->nSample; i++){
        int c;
        int eSampletype = aSample[i].eType;
        if( eSampletype==SQLITE_NULL || eSampletype<eType ) continue;
        if( (eSampletype!=eType) ) break;
        if( eSampletype<eType ) continue;
        if( eSampletype!=eType ) break;
#ifndef SQLITE_OMIT_UTF16
        if( pColl->enc!=SQLITE_UTF8 ){
          int nSample;
          char *zSample = sqlite3Utf8to16(
              db, pColl->enc, aSample[i].u.z, aSample[i].nByte, &nSample
          );
          if( !zSample ){
            assert( db->mallocFailed );
            return SQLITE_NOMEM;
          }
          c = pColl->xCmp(pColl->pUser, nSample, zSample, n, z);
          sqlite3DbFree(db, zSample);
        }else
#endif
        {
          c = pColl->xCmp(pColl->pUser, aSample[i].nByte, aSample[i].u.z, n, z);
        }
        if( c>=0 ){
          if( c==0 ) isEq = 1;
        if( c-roundUp>=0 ) break;
      }
    }

    assert( i>=0 && i<=SQLITE_INDEX_SAMPLES );
    *piRegion = i;
  }
          break;
        }
      }
    }
  }

  /* At this point, aSample[i] is the first sample that is greater than
  ** or equal to pVal.  Or if i==pIdx->nSample, then all samples are less
  ** than pVal.  If aSample[i]==pVal, then isEq==1.
  */
  if( isEq ){
    assert( i<pIdx->nSample );
    aStat[0] = aSample[i].nLt;
    aStat[1] = aSample[i].nEq;
  }else{
    tRowcnt iLower, iUpper, iGap;
    if( i==0 ){
      iLower = 0;
      iUpper = aSample[0].nLt;
    }else{
      iUpper = i>=pIdx->nSample ? n : aSample[i].nLt;
      iLower = aSample[i-1].nEq + aSample[i-1].nLt;
    }
    aStat[1] = pIdx->avgEq;
    if( iLower>=iUpper ){
      iGap = 0;
    }else{
      iGap = iUpper - iLower;
      if( iGap>=aStat[1]/2 ) iGap -= aStat[1]/2;
    }
    if( roundUp ){
      iGap = (iGap*2)/3;
    }else{
      iGap = iGap/3;
    }
    aStat[0] = iLower + iGap;
  }
  return SQLITE_OK;
}
#endif   /* #ifdef SQLITE_ENABLE_STAT2 */
#endif /* SQLITE_ENABLE_STAT3 */

/*
** If expression pExpr represents a literal value, set *pp to point to
** an sqlite3_value structure containing the same value, with affinity
** aff applied to it, before returning. It is the responsibility of the 
** caller to eventually release this structure by passing it to 
** sqlite3ValueFree().
**
** If the current parse is a recompile (sqlite3Reprepare()) and pExpr
** is an SQL variable that currently has a non-NULL value bound to it,
** create an sqlite3_value structure containing this value, again with
** affinity aff applied to it, instead.
**
** If neither of the above apply, set *pp to NULL.
**
** If an error occurs, return an error code. Otherwise, SQLITE_OK.
*/
#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
static int valueFromExpr(
  Parse *pParse, 
  Expr *pExpr, 
  u8 aff, 
  sqlite3_value **pp
){
  if( pExpr->op==TK_VARIABLE

** then nEq should be passed the value 1 (as the range restricted column,
** b, is the second left-most column of the index). Or, if the query is:
**
**   ... FROM t1 WHERE a > ? AND a < ? ...
**
** then nEq should be passed 0.
**
** The returned value is an integer between 1 and 100, inclusive. A return
** The returned value is an integer divisor to reduce the estimated
** value of 1 indicates that the proposed range scan is expected to visit
** approximately 1/100th (1%) of the rows selected by the nEq equality
** constraints (if any). A return value of 100 indicates that it is expected
** search space.  A return value of 1 means that range constraints are
** that the range scan will visit every row (100%) selected by the equality
** constraints.
** no help at all.  A return value of 2 means range constraints are
** expected to reduce the search space by half.  And so forth...
**
** In the absence of sqlite_stat2 ANALYZE data, each range inequality
** reduces the search space by 3/4ths.  Hence a single constraint (x>?)
** results in a return of 25 and a range constraint (x>? AND x<?) results
** in a return of 6.
** In the absence of sqlite_stat3 ANALYZE data, each range inequality
** reduces the search space by a factor of 4.  Hence a single constraint (x>?)
** results in a return of 4 and a range constraint (x>? AND x<?) results
** in a return of 16.
*/
static int whereRangeScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index containing the range-compared column; "x" */
  int nEq,             /* index into p->aCol[] of the range-compared column */
  WhereTerm *pLower,   /* Lower bound on the range. ex: "x>123" Might be NULL */
  WhereTerm *pUpper,   /* Upper bound on the range. ex: "x<455" Might be NULL */
  int *piEst           /* OUT: Return value */
  double *pRangeDiv   /* OUT: Reduce search space by this divisor */
){
  int rc = SQLITE_OK;

#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3

  if( nEq==0 && p->aSample ){
    sqlite3_value *pLowerVal = 0;
  if( nEq==0 && p->nSample ){
    sqlite3_value *pRangeVal;
    sqlite3_value *pUpperVal = 0;
    int iEst;
    int iLower = 0;
    int iUpper = SQLITE_INDEX_SAMPLES;
    int roundUpUpper;
    tRowcnt iLower = 0;
    tRowcnt iUpper = p->aiRowEst[0];
    tRowcnt a[2];
    int roundUpLower;
    u8 aff = p->pTable->aCol[p->aiColumn[0]].affinity;

    if( pLower ){
      Expr *pExpr = pLower->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pLowerVal);
      rc = valueFromExpr(pParse, pExpr, aff, &pRangeVal);
      assert( pLower->eOperator==WO_GT || pLower->eOperator==WO_GE );
      if( rc==SQLITE_OK
       && whereKeyStats(pParse, p, pRangeVal, 0, a)==SQLITE_OK
      ){
        iLower = a[0];
      roundUpLower = (pLower->eOperator==WO_GT) ?1:0;
        if( pLower->eOperator==WO_GT ) iLower += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK && pUpper ){
      Expr *pExpr = pUpper->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pUpperVal);
      rc = valueFromExpr(pParse, pExpr, aff, &pRangeVal);
      assert( pUpper->eOperator==WO_LT || pUpper->eOperator==WO_LE );
      if( rc==SQLITE_OK
       && whereKeyStats(pParse, p, pRangeVal, 1, a)==SQLITE_OK
      ){
        iUpper = a[0];
      roundUpUpper = (pUpper->eOperator==WO_LE) ?1:0;
    }

    if( rc!=SQLITE_OK || (pLowerVal==0 && pUpperVal==0) ){
        if( pUpper->eOperator==WO_LE ) iUpper += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK ){
      sqlite3ValueFree(pLowerVal);
      sqlite3ValueFree(pUpperVal);
      goto range_est_fallback;
    }else if( pLowerVal==0 ){
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( pLower ) iLower = iUpper/2;
      if( iUpper<=iLower ){
    }else if( pUpperVal==0 ){
      rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
        *pRangeDiv = (double)p->aiRowEst[0];
      if( pUpper ) iUpper = (iLower + SQLITE_INDEX_SAMPLES + 1)/2;
    }else{
      }else{
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( rc==SQLITE_OK ){
        rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
        *pRangeDiv = (double)p->aiRowEst[0]/(double)(iUpper - iLower);
      }
    }
    WHERETRACE(("range scan regions: %d..%d\n", iLower, iUpper));

      WHERETRACE(("range scan regions: %u..%u  div=%g\n",
                  (u32)iLower, (u32)iUpper, *pRangeDiv));
    iEst = iUpper - iLower;
    testcase( iEst==SQLITE_INDEX_SAMPLES );
    assert( iEst<=SQLITE_INDEX_SAMPLES );
    if( iEst<1 ){
      *piEst = 50/SQLITE_INDEX_SAMPLES;
      return SQLITE_OK;
    }else{
      *piEst = (iEst*100)/SQLITE_INDEX_SAMPLES;
    }
    sqlite3ValueFree(pLowerVal);
    sqlite3ValueFree(pUpperVal);
    return rc;
  }
range_est_fallback:
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *piEst = 100;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ) *piEst /= 4;
  if( pUpper ) *piEst /= 4;
  *pRangeDiv = (double)1;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ) *pRangeDiv *= (double)4;
  if( pUpper ) *pRangeDiv *= (double)4;
  return rc;
}

#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the number of rows that will be returned based on
** an equality constraint x=VALUE and where that VALUE occurs in
** the histogram data.  This only works when x is the left-most
** column of an index and sqlite_stat2 histogram data is available
** column of an index and sqlite_stat3 histogram data is available
** for that index.
**
** Write the estimated row count into *pnRow and return SQLITE_OK. 
** If unable to make an estimate, leave *pnRow unchanged and return
** non-zero.
**
** This routine can fail if it is unable to load a collating sequence
** required for string comparison, or if unable to allocate memory
** for a UTF conversion required for comparison.  The error is stored
** in the pParse structure.
*/
int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  double *pnRow        /* Write the revised row estimate here */
){
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */
  int iLower, iUpper;       /* Range of histogram regions containing pRhs */
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  double nRowEst;           /* New estimate of the number of rows */
  tRowcnt a[2];             /* Statistics */

  assert( p->aSample!=0 );
  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  if( pExpr ){
    rc = valueFromExpr(pParse, pExpr, aff, &pRhs);
    if( rc ) goto whereEqualScanEst_cancel;
  }else{
    pRhs = sqlite3ValueNew(pParse->db);
  }
  if( pRhs==0 ) return SQLITE_NOTFOUND;
  rc = whereRangeRegion(pParse, p, pRhs, 0, &iLower);
  if( rc ) goto whereEqualScanEst_cancel;
  rc = whereKeyStats(pParse, p, pRhs, 0, a);
  if( rc==SQLITE_OK ){
  rc = whereRangeRegion(pParse, p, pRhs, 1, &iUpper);
  if( rc ) goto whereEqualScanEst_cancel;
  WHERETRACE(("equality scan regions: %d..%d\n", iLower, iUpper));
    WHERETRACE(("equality scan regions: %d\n", (int)a[1]));
  if( iLower>=iUpper ){
    nRowEst = p->aiRowEst[0]/(SQLITE_INDEX_SAMPLES*2);
    if( nRowEst<*pnRow ) *pnRow = nRowEst;
  }else{
    nRowEst = (iUpper-iLower)*p->aiRowEst[0]/SQLITE_INDEX_SAMPLES;
    *pnRow = nRowEst;
    *pnRow = a[1];
  }

whereEqualScanEst_cancel:
  sqlite3ValueFree(pRhs);
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT2) */
#endif /* defined(SQLITE_ENABLE_STAT3) */

#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
/*
** Estimate the number of rows that will be returned based on
** an IN constraint where the right-hand side of the IN operator
** is a list of values.  Example:
**
**        WHERE x IN (1,2,3,4)
**

*/
int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  Index *p,            /* The index whose left-most column is pTerm */
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  double *pnRow        /* Write the revised row estimate here */
){
  sqlite3_value *pVal = 0;  /* One value from list */
  int iLower, iUpper;       /* Range of histogram regions containing pRhs */
  u8 aff;                   /* Column affinity */
  int rc = SQLITE_OK;       /* Subfunction return code */
  double nRowEst;           /* New estimate of the number of rows */
  int rc = SQLITE_OK;         /* Subfunction return code */
  double nEst;                /* Number of rows for a single term */
  double nRowEst = (double)0; /* New estimate of the number of rows */
  int nSpan = 0;            /* Number of histogram regions spanned */
  int nSingle = 0;          /* Histogram regions hit by a single value */
  int nNotFound = 0;        /* Count of values that are not constants */
  int i;                               /* Loop counter */
  int i;                      /* Loop counter */
  u8 aSpan[SQLITE_INDEX_SAMPLES+1];    /* Histogram regions that are spanned */
  u8 aSingle[SQLITE_INDEX_SAMPLES+1];  /* Histogram regions hit once */

  assert( p->aSample!=0 );
  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  memset(aSpan, 0, sizeof(aSpan));
  memset(aSingle, 0, sizeof(aSingle));
  for(i=0; i<pList->nExpr; i++){
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    sqlite3ValueFree(pVal);
    rc = valueFromExpr(pParse, pList->a[i].pExpr, aff, &pVal);
    nEst = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, p, pList->a[i].pExpr, &nEst);
    if( rc ) break;
    if( pVal==0 || sqlite3_value_type(pVal)==SQLITE_NULL ){
      nNotFound++;
      continue;
    }
    rc = whereRangeRegion(pParse, p, pVal, 0, &iLower);
    if( rc ) break;
    rc = whereRangeRegion(pParse, p, pVal, 1, &iUpper);
    if( rc ) break;
    if( iLower>=iUpper ){
    nRowEst += nEst;
      aSingle[iLower] = 1;
    }else{
      assert( iLower>=0 && iUpper<=SQLITE_INDEX_SAMPLES );
      while( iLower<iUpper ) aSpan[iLower++] = 1;
    }
  }
  }
  if( rc==SQLITE_OK ){
    for(i=nSpan=0; i<=SQLITE_INDEX_SAMPLES; i++){
      if( aSpan[i] ){
        nSpan++;
      }else if( aSingle[i] ){
        nSingle++;
      }
    }
    nRowEst = (nSpan*2+nSingle)*p->aiRowEst[0]/(2*SQLITE_INDEX_SAMPLES)
               + nNotFound*p->aiRowEst[1];
    if( nRowEst > p->aiRowEst[0] ) nRowEst = p->aiRowEst[0];
    *pnRow = nRowEst;
    WHERETRACE(("IN row estimate: nSpan=%d, nSingle=%d, nNotFound=%d, est=%g\n",
    WHERETRACE(("IN row estimate: est=%g\n", nRowEst));
                 nSpan, nSingle, nNotFound, nRowEst));
  }
  sqlite3ValueFree(pVal);
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT2) */
#endif /* defined(SQLITE_ENABLE_STAT3) */


/*
** Find the best query plan for accessing a particular table.  Write the
** best query plan and its cost into the WhereCost object supplied as the
** last parameter.
**

){
  int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  Index *pProbe;              /* An index we are evaluating */
  Index *pIdx;                /* Copy of pProbe, or zero for IPK index */
  int eqTermMask;             /* Current mask of valid equality operators */
  int idxEqTermMask;          /* Index mask of valid equality operators */
  Index sPk;                  /* A fake index object for the primary key */
  unsigned int aiRowEstPk[2]; /* The aiRowEst[] value for the sPk index */
  tRowcnt aiRowEstPk[2];      /* The aiRowEst[] value for the sPk index */
  int aiColumnPk = -1;        /* The aColumn[] value for the sPk index */
  int wsFlagMask;             /* Allowed flags in pCost->plan.wsFlag */

  /* Initialize the cost to a worst-case value */
  memset(pCost, 0, sizeof(*pCost));
  pCost->rCost = SQLITE_BIG_DBL;

    eqTermMask = WO_EQ|WO_IN;
    pIdx = 0;
  }

  /* Loop over all indices looking for the best one to use
  */
  for(; pProbe; pIdx=pProbe=pProbe->pNext){
    const unsigned int * const aiRowEst = pProbe->aiRowEst;
    const tRowcnt * const aiRowEst = pProbe->aiRowEst;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    double log10N;              /* base-10 logarithm of nRow (inexact) */
    int rev;                    /* True to scan in reverse order */
    int wsFlags = 0;
    Bitmask used = 0;

    **
    **  bInEst:  
    **    Set to true if there was at least one "x IN (SELECT ...)" term used 
    **    in determining the value of nInMul.  Note that the RHS of the
    **    IN operator must be a SELECT, not a value list, for this variable
    **    to be true.
    **
    **  estBound:
    **    An estimate on the amount of the table that must be searched.  A
    **  rangeDiv:
    **    An estimate of a divisor by which to reduce the search space due
    **    value of 100 means the entire table is searched.  Range constraints
    **    might reduce this to a value less than 100 to indicate that only
    **    a fraction of the table needs searching.  In the absence of
    **    sqlite_stat2 ANALYZE data, a single inequality reduces the search
    **    space to 1/4rd its original size.  So an x>? constraint reduces
    **    to inequality constraints.  In the absence of sqlite_stat3 ANALYZE
    **    data, a single inequality reduces the search space to 1/4rd its
    **    original size (rangeDiv==4).  Two inequalities reduce the search
    **    space to 1/16th of its original size (rangeDiv==16).
    **    estBound to 25.  Two constraints (x>? AND x<?) reduce estBound to 6.
    **
    **  bSort:   
    **    Boolean. True if there is an ORDER BY clause that will require an 
    **    external sort (i.e. scanning the index being evaluated will not 
    **    correctly order records).
    **
    **  bLookup: 

    **
    **             SELECT a, b    FROM tbl WHERE a = 1;
    **             SELECT a, b, c FROM tbl WHERE a = 1;
    */
    int nEq;                      /* Number of == or IN terms matching index */
    int bInEst = 0;               /* True if "x IN (SELECT...)" seen */
    int nInMul = 1;               /* Number of distinct equalities to lookup */
    int estBound = 100;           /* Estimated reduction in search space */
    double rangeDiv = (double)1;  /* Estimated reduction in search space */
    int nBound = 0;               /* Number of range constraints seen */
    int bSort = !!pOrderBy;       /* True if external sort required */
    int bDist = !!pDistinct;      /* True if index cannot help with DISTINCT */
    int bLookup = 0;              /* True if not a covering index */
    WhereTerm *pTerm;             /* A single term of the WHERE clause */
#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
    WhereTerm *pFirstTerm = 0;    /* First term matching the index */
#endif

    /* Determine the values of nEq and nInMul */
    for(nEq=0; nEq<pProbe->nColumn; nEq++){
      int j = pProbe->aiColumn[nEq];
      pTerm = findTerm(pWC, iCur, j, notReady, eqTermMask, pIdx);

        }else if( ALWAYS(pExpr->x.pList && pExpr->x.pList->nExpr) ){
          /* "x IN (value, value, ...)" */
          nInMul *= pExpr->x.pList->nExpr;
        }
      }else if( pTerm->eOperator & WO_ISNULL ){
        wsFlags |= WHERE_COLUMN_NULL;
      }
#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
      if( nEq==0 && pProbe->aSample ) pFirstTerm = pTerm;
#endif
      used |= pTerm->prereqRight;
    }

    /* Determine the value of estBound. */
    /* Determine the value of rangeDiv */
    if( nEq<pProbe->nColumn && pProbe->bUnordered==0 ){
      int j = pProbe->aiColumn[nEq];
      if( findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE|WO_GT|WO_GE, pIdx) ){
        WhereTerm *pTop = findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE, pIdx);
        WhereTerm *pBtm = findTerm(pWC, iCur, j, notReady, WO_GT|WO_GE, pIdx);
        whereRangeScanEst(pParse, pProbe, nEq, pBtm, pTop, &estBound);
        whereRangeScanEst(pParse, pProbe, nEq, pBtm, pTop, &rangeDiv);
        if( pTop ){
          nBound = 1;
          wsFlags |= WHERE_TOP_LIMIT;
          used |= pTop->prereqRight;
        }
        if( pBtm ){
          nBound++;

    */
    nRow = (double)(aiRowEst[nEq] * nInMul);
    if( bInEst && nRow*2>aiRowEst[0] ){
      nRow = aiRowEst[0]/2;
      nInMul = (int)(nRow / aiRowEst[nEq]);
    }

#ifdef SQLITE_ENABLE_STAT2
#ifdef SQLITE_ENABLE_STAT3
    /* If the constraint is of the form x=VALUE or x IN (E1,E2,...)
    ** and we do not think that values of x are unique and if histogram
    ** data is available for column x, then it might be possible
    ** to get a better estimate on the number of rows based on
    ** VALUE and how common that value is according to the histogram.
    */
    if( nRow>(double)1 && nEq==1 && pFirstTerm!=0 && aiRowEst[1]>1 ){
      if( pFirstTerm->eOperator & (WO_EQ|WO_ISNULL) ){
        testcase( pFirstTerm->eOperator==WO_EQ );
        testcase( pFirstTerm->pOperator==WO_ISNULL );
        whereEqualScanEst(pParse, pProbe, pFirstTerm->pExpr->pRight, &nRow);
      }else if( pFirstTerm->eOperator==WO_IN && bInEst==0 ){
        whereInScanEst(pParse, pProbe, pFirstTerm->pExpr->x.pList, &nRow);
      }
    }
#endif /* SQLITE_ENABLE_STAT2 */
#endif /* SQLITE_ENABLE_STAT3 */

    /* Adjust the number of output rows and downward to reflect rows
    ** that are excluded by range constraints.
    */
    nRow = (nRow * (double)estBound) / (double)100;
    nRow = nRow/rangeDiv;
    if( nRow<1 ) nRow = 1;

    /* Experiments run on real SQLite databases show that the time needed
    ** to do a binary search to locate a row in a table or index is roughly
    ** log10(N) times the time to move from one row to the next row within
    ** a table or index.  The actual times can vary, with the size of
    ** records being an important factor.  Both moves and searches are

        }
      }
      if( nRow<2 ) nRow = 2;
    }


    WHERETRACE((
      "%s(%s): nEq=%d nInMul=%d estBound=%d bSort=%d bLookup=%d wsFlags=0x%x\n"
      "%s(%s): nEq=%d nInMul=%d rangeDiv=%d bSort=%d bLookup=%d wsFlags=0x%x\n"
      "         notReady=0x%llx log10N=%.1f nRow=%.1f cost=%.1f used=0x%llx\n",
      pSrc->pTab->zName, (pIdx ? pIdx->zName : "ipk"), 
      nEq, nInMul, estBound, bSort, bLookup, wsFlags,
      nEq, nInMul, (int)rangeDiv, bSort, bLookup, wsFlags,
      notReady, log10N, nRow, cost, used
    ));

    /* If this index is the best we have seen so far, then record this
    ** index and its cost in the pCost structure.
    */
    if( (!pIdx || wsFlags)

do_test analyze-1.6.3 {
  catchsql {
    CREATE INDEX main.stat1idx ON SQLite_stat1(idx);
  }
} {1 {table sqlite_stat1 may not be indexed}}
do_test analyze-1.7 {
  execsql {
    SELECT * FROM sqlite_stat1
    SELECT * FROM sqlite_stat1 WHERE idx NOT NULL
  }
} {}
do_test analyze-1.8 {
  catchsql {
    ANALYZE main
  }
} {0 {}}
do_test analyze-1.9 {
  execsql {
    SELECT * FROM sqlite_stat1
    SELECT * FROM sqlite_stat1 WHERE idx NOT NULL
  }
} {}
do_test analyze-1.10 {
  catchsql {
    CREATE TABLE t1(a,b);
    ANALYZE main.t1;
  }
} {0 {}}
do_test analyze-1.11 {
  execsql {
    SELECT * FROM sqlite_stat1
  }
} {t1 {} 0}
} {}
do_test analyze-1.12 {
  catchsql {
    ANALYZE t1;
  }
} {0 {}}
do_test analyze-1.13 {
  execsql {
    SELECT * FROM sqlite_stat1
  }
} {t1 {} 0}
} {}

# Create some indices that can be analyzed.  But do not yet add
# data.  Without data in the tables, no analysis is done.
#
do_test analyze-2.1 {
  execsql {
    CREATE INDEX t1i1 ON t1(a);
    ANALYZE main.t1;
    SELECT * FROM sqlite_stat1 ORDER BY idx;
  }
} {t1 {} 0}
} {}
do_test analyze-2.2 {
  execsql {
    CREATE INDEX t1i2 ON t1(b);
    ANALYZE t1;
    SELECT * FROM sqlite_stat1 ORDER BY idx;
  }
} {t1 {} 0}
} {}
do_test analyze-2.3 {
  execsql {
    CREATE INDEX t1i3 ON t1(a,b);
    ANALYZE main;
    SELECT * FROM sqlite_stat1 ORDER BY idx;
  }
} {t1 {} 0}
} {}

# Start adding data to the table.  Verify that the analysis
# is done correctly.
#
do_test analyze-3.1 {
  execsql {
    INSERT INTO t1 VALUES(1,2);

  }
  db close
  sqlite3 db test.db
  execsql {
    SELECT * FROM t4 WHERE x=1234;
  }
} {}

# Verify that DROP TABLE and DROP INDEX remove entries from the 
# sqlite_stat1 and sqlite_stat3 tables.
#
do_test analyze-5.0 {
  execsql {
    DELETE FROM t3;
    DELETE FROM t4;
    INSERT INTO t3 VALUES(1,2,3,4);
    INSERT INTO t3 VALUES(5,6,7,8);
    INSERT INTO t3 SELECT a+8, b+8, c+8, d+8 FROM t3;
    INSERT INTO t3 SELECT a+16, b+16, c+16, d+16 FROM t3;
    INSERT INTO t3 SELECT a+32, b+32, c+32, d+32 FROM t3;
    INSERT INTO t3 SELECT a+64, b+64, c+64, d+64 FROM t3;
    INSERT INTO t4 SELECT a, b, c FROM t3;
    ANALYZE;
    SELECT DISTINCT idx FROM sqlite_stat1 ORDER BY 1;
    SELECT DISTINCT tbl FROM sqlite_stat1 ORDER BY 1;
  }
} {t3i1 t3i2 t3i3 t4i1 t4i2 t3 t4}
ifcapable stat3 {
  do_test analyze-5.1 {
    execsql {
      SELECT DISTINCT idx FROM sqlite_stat3 ORDER BY 1;
      SELECT DISTINCT tbl FROM sqlite_stat3 ORDER BY 1;
    }
  } {t3i1 t3i2 t3i3 t4i1 t4i2 t3 t4}
}
do_test analyze-5.2 {
  execsql {
    DROP INDEX t3i2;
    SELECT DISTINCT idx FROM sqlite_stat1 ORDER BY 1;
    SELECT DISTINCT tbl FROM sqlite_stat1 ORDER BY 1;
  }
} {t3i1 t3i3 t4i1 t4i2 t3 t4}
ifcapable stat3 {
  do_test analyze-5.3 {
    execsql {
      SELECT DISTINCT idx FROM sqlite_stat3 ORDER BY 1;
      SELECT DISTINCT tbl FROM sqlite_stat3 ORDER BY 1;
    }
  } {t3i1 t3i3 t4i1 t4i2 t3 t4}
}
do_test analyze-5.4 {
  execsql {
    DROP TABLE t3;
    SELECT DISTINCT idx FROM sqlite_stat1 ORDER BY 1;
    SELECT DISTINCT tbl FROM sqlite_stat1 ORDER BY 1;
  }
} {t4i1 t4i2 t4}
ifcapable stat3 {
  do_test analyze-5.5 {
    execsql {
      SELECT DISTINCT idx FROM sqlite_stat3 ORDER BY 1;
      SELECT DISTINCT tbl FROM sqlite_stat3 ORDER BY 1;
    }
  } {t4i1 t4i2 t4}
}

# This test corrupts the database file so it must be the last test
# in the series.
#
do_test analyze-99.1 {
  execsql {
    PRAGMA writable_schema=on;

# implements tests for range and LIKE constraints that use bound variables
# instead of literal constant arguments.
#

set testdir [file dirname $argv0]
source $testdir/tester.tcl

ifcapable !stat2 {
ifcapable !stat3 {
  finish_test
  return
}

#----------------------------------------------------------------------
# Test Organization:
#

    COMMIT;
    ANALYZE;
  }
} {}

do_eqp_test analyze3-1.1.2 {
  SELECT sum(y) FROM t1 WHERE x>200 AND x<300
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (x>? AND x<?) (~100 rows)}}
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (x>? AND x<?) (~179 rows)}}
do_eqp_test analyze3-1.1.3 {
  SELECT sum(y) FROM t1 WHERE x>0 AND x<1100 
} {0 0 0 {SCAN TABLE t1 (~111 rows)}}
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (x>? AND x<?) (~959 rows)}}

do_test analyze3-1.1.4 {
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>200 AND x<300 }
} {199 0 14850}
do_test analyze3-1.1.5 {
  set l [string range "200" 0 end]
  set u [string range "300" 0 end]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {199 0 14850}
do_test analyze3-1.1.6 {
  set l [expr int(200)]
  set u [expr int(300)]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {199 0 14850}
do_test analyze3-1.1.7 {
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>0 AND x<1100 }
} {999 999 499500}
} {2000 0 499500}
do_test analyze3-1.1.8 {
  set l [string range "0" 0 end]
  set u [string range "1100" 0 end]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {999 999 499500}
} {2000 0 499500}
do_test analyze3-1.1.9 {
  set l [expr int(0)]
  set u [expr int(1100)]
  sf_execsql { SELECT sum(y) FROM t1 WHERE x>$l AND x<$u }
} {999 999 499500}
} {2000 0 499500}


# The following tests are similar to the block above. The difference is
# that the indexed column has TEXT affinity in this case. In the tests
# above the affinity is INTEGER.
#
do_test analyze3-1.2.1 {
  execsql {
    BEGIN;
      CREATE TABLE t2(x TEXT, y);
      INSERT INTO t2 SELECT * FROM t1;
      CREATE INDEX i2 ON t2(x);
    COMMIT;
    ANALYZE;
  }
} {}
do_eqp_test analyze3-1.2.2 {
  SELECT sum(y) FROM t2 WHERE x>1 AND x<2
} {0 0 0 {SEARCH TABLE t2 USING INDEX i2 (x>? AND x<?) (~200 rows)}}
} {0 0 0 {SEARCH TABLE t2 USING INDEX i2 (x>? AND x<?) (~196 rows)}}
do_eqp_test analyze3-1.2.3 {
  SELECT sum(y) FROM t2 WHERE x>0 AND x<99
} {0 0 0 {SCAN TABLE t2 (~111 rows)}}
} {0 0 0 {SEARCH TABLE t2 USING INDEX i2 (x>? AND x<?) (~968 rows)}}
do_test analyze3-1.2.4 {
  sf_execsql { SELECT sum(y) FROM t2 WHERE x>12 AND x<20 }
} {161 0 4760}
do_test analyze3-1.2.5 {
  set l [string range "12" 0 end]
  set u [string range "20" 0 end]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {161 0 text text 4760}
do_test analyze3-1.2.6 {
  set l [expr int(12)]
  set u [expr int(20)]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {161 0 integer integer 4760}
do_test analyze3-1.2.7 {
  sf_execsql { SELECT sum(y) FROM t2 WHERE x>0 AND x<99 }
} {999 999 490555}
} {1981 0 490555}
do_test analyze3-1.2.8 {
  set l [string range "0" 0 end]
  set u [string range "99" 0 end]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {999 999 text text 490555}
} {1981 0 text text 490555}
do_test analyze3-1.2.9 {
  set l [expr int(0)]
  set u [expr int(99)]
  sf_execsql {SELECT typeof($l), typeof($u), sum(y) FROM t2 WHERE x>$l AND x<$u}
} {999 999 integer integer 490555}
} {1981 0 integer integer 490555}

# Same tests a third time. This time, column x has INTEGER affinity and
# is not the leftmost column of the table. This triggered a bug causing
# SQLite to use sub-optimal query plans in 3.6.18 and earlier.
#
do_test analyze3-1.3.1 {
  execsql {
    BEGIN;
      CREATE TABLE t3(y TEXT, x INTEGER);
      INSERT INTO t3 SELECT y, x FROM t1;
      CREATE INDEX i3 ON t3(x);
    COMMIT;
    ANALYZE;
  }
} {}
do_eqp_test analyze3-1.3.2 {
  SELECT sum(y) FROM t3 WHERE x>200 AND x<300
} {0 0 0 {SEARCH TABLE t3 USING INDEX i3 (x>? AND x<?) (~100 rows)}}
} {0 0 0 {SEARCH TABLE t3 USING INDEX i3 (x>? AND x<?) (~156 rows)}}
do_eqp_test analyze3-1.3.3 {
  SELECT sum(y) FROM t3 WHERE x>0 AND x<1100
} {0 0 0 {SCAN TABLE t3 (~111 rows)}}
} {0 0 0 {SEARCH TABLE t3 USING INDEX i3 (x>? AND x<?) (~989 rows)}}

do_test analyze3-1.3.4 {
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>200 AND x<300 }
} {199 0 14850}
do_test analyze3-1.3.5 {
  set l [string range "200" 0 end]
  set u [string range "300" 0 end]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {199 0 14850}
do_test analyze3-1.3.6 {
  set l [expr int(200)]
  set u [expr int(300)]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {199 0 14850}
do_test analyze3-1.3.7 {
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>0 AND x<1100 }
} {999 999 499500}
} {2000 0 499500}
do_test analyze3-1.3.8 {
  set l [string range "0" 0 end]
  set u [string range "1100" 0 end]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {999 999 499500}
} {2000 0 499500}
do_test analyze3-1.3.9 {
  set l [expr int(0)]
  set u [expr int(1100)]
  sf_execsql { SELECT sum(y) FROM t3 WHERE x>$l AND x<$u }
} {999 999 499500}
} {2000 0 499500}

#-------------------------------------------------------------------------
# Test that the values of bound SQL variables may be used for the LIKE
# optimization.
#
drop_all_tables
do_test analyze3-2.1 {

    append t [lindex {a b c d e f g h i j} [expr ($i%10)]]
    execsql { INSERT INTO t1 VALUES($i, $t) }
  }
  execsql COMMIT
} {}
do_eqp_test analyze3-2.2 {
  SELECT count(a) FROM t1 WHERE b LIKE 'a%'
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (b>? AND b<?) (~30000 rows)}}
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (b>? AND b<?) (~31250 rows)}}
do_eqp_test analyze3-2.3 {
  SELECT count(a) FROM t1 WHERE b LIKE '%a'
} {0 0 0 {SCAN TABLE t1 (~500000 rows)}}

do_test analyze3-2.4 {
  sf_execsql { SELECT count(*) FROM t1 WHERE b LIKE 'a%' }
} {101 0 100}

# 2011 January 19
#
# 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 implements tests for SQLite library.  The focus of the tests
# in this file is the use of the sqlite_stat2 histogram data on tables
# in this file is the use of the sqlite_stat3 histogram data on tables
# with many repeated values and only a few distinct values.
#

set testdir [file dirname $argv0]
source $testdir/tester.tcl

ifcapable !stat2 {
ifcapable !stat3 {
  finish_test
  return
}

set testprefix analyze5

proc eqp {sql {db db}} {

    CREATE INDEX t1u ON t1(u);  -- text
    CREATE INDEX t1v ON t1(v);  -- mixed case text
    CREATE INDEX t1w ON t1(w);  -- integers 0, 1, 2 and a few NULLs
    CREATE INDEX t1x ON t1(x);  -- integers 1, 2, 3 and many NULLs
    CREATE INDEX t1y ON t1(y);  -- integers 0 and very few 1s
    CREATE INDEX t1z ON t1(z);  -- integers 0, 1, 2, and 3
    ANALYZE;
    SELECT sample FROM sqlite_stat2 WHERE idx='t1u' ORDER BY sampleno;
    SELECT sample FROM sqlite_stat3 WHERE idx='t1u' ORDER BY nlt;
  }
} {alpha alpha alpha alpha bravo bravo bravo charlie charlie delta}
do_test analyze5-1.1 {
} {alpha bravo charlie delta}

  string tolower \
   [db eval {SELECT sample from sqlite_stat2 WHERE idx='t1v' ORDER BY sampleno}]
} {alpha alpha alpha alpha bravo bravo bravo charlie charlie delta}
do_test analyze5-1.2 {
  db eval {SELECT sample from sqlite_stat2 WHERE idx='t1w' ORDER BY sampleno}
do_test analyze5-1.1 {
  db eval {SELECT DISTINCT lower(sample) FROM sqlite_stat3 WHERE idx='t1v'
} {{} 0 0 0 0 1 1 1 2 2}
do_test analyze5-1.3 {
  db eval {SELECT sample from sqlite_stat2 WHERE idx='t1x' ORDER BY sampleno}
} {{} {} {} {} 1 1 1 2 2 3}
do_test analyze5-1.4 {
  db eval {SELECT sample from sqlite_stat2 WHERE idx='t1y' ORDER BY sampleno}
             ORDER BY 1}
} {alpha bravo charlie delta}
do_test analyze5-1.2 {
  db eval {SELECT idx, count(*) FROM sqlite_stat3 GROUP BY 1 ORDER BY 1}
} {0 0 0 0 0 0 0 0 0 0}
do_test analyze5-1.5 {
  db eval {SELECT sample from sqlite_stat2 WHERE idx='t1z' ORDER BY sampleno}
} {0 0 0 0 1 1 1 2 2 3}
do_test analyze5-1.6 {
  db eval {SELECT sample from sqlite_stat2 WHERE idx='t1t' ORDER BY sampleno}
} {0.5 0.5 0.5 0.5 1.5 1.5 1.5 2.5 2.5 3.5}

} {t1t 4 t1u 4 t1v 4 t1w 4 t1x 4 t1y 2 t1z 4}

# Verify that range queries generate the correct row count estimates
#
foreach {testid where index rows} {
    1  {z>=0 AND z<=0}       t1z  400
    2  {z>=1 AND z<=1}       t1z  300
    3  {z>=2 AND z<=2}       t1z  200
    4  {z>=3 AND z<=3}       t1z  100
    5  {z>=4 AND z<=4}       t1z   50
    6  {z>=-1 AND z<=-1}     t1z   50
    7  {z>1 AND z<3}         t1z  200
    3  {z>=2 AND z<=2}       t1z  175
    4  {z>=3 AND z<=3}       t1z  125
    5  {z>=4 AND z<=4}       t1z    1
    6  {z>=-1 AND z<=-1}     t1z    1
    7  {z>1 AND z<3}         t1z  175
    8  {z>0 AND z<100}       t1z  600
    9  {z>=1 AND z<100}      t1z  600
   10  {z>1 AND z<100}       t1z  300
   11  {z>=2 AND z<100}      t1z  300
   12  {z>2 AND z<100}       t1z  100
   13  {z>=3 AND z<100}      t1z  100
   14  {z>3 AND z<100}       t1z   50
   15  {z>=4 AND z<100}      t1z   50
   16  {z>=-100 AND z<=-1}   t1z   50
   12  {z>2 AND z<100}       t1z  125
   13  {z>=3 AND z<100}      t1z  125
   14  {z>3 AND z<100}       t1z    1
   15  {z>=4 AND z<100}      t1z    1
   16  {z>=-100 AND z<=-1}   t1z    1
   17  {z>=-100 AND z<=0}    t1z  400
   18  {z>=-100 AND z<0}     t1z   50
   18  {z>=-100 AND z<0}     t1z    1
   19  {z>=-100 AND z<=1}    t1z  700
   20  {z>=-100 AND z<2}     t1z  700
   21  {z>=-100 AND z<=2}    t1z  900
   22  {z>=-100 AND z<3}     t1z  900
   21  {z>=-100 AND z<=2}    t1z  875
   22  {z>=-100 AND z<3}     t1z  875
  
   31  {z>=0.0 AND z<=0.0}   t1z  400
   32  {z>=1.0 AND z<=1.0}   t1z  300
   33  {z>=2.0 AND z<=2.0}   t1z  200
   34  {z>=3.0 AND z<=3.0}   t1z  100
   35  {z>=4.0 AND z<=4.0}   t1z   50
   36  {z>=-1.0 AND z<=-1.0} t1z   50
   37  {z>1.5 AND z<3.0}     t1z  200
   38  {z>0.5 AND z<100}     t1z  600
   33  {z>=2.0 AND z<=2.0}   t1z  175
   34  {z>=3.0 AND z<=3.0}   t1z  125
   35  {z>=4.0 AND z<=4.0}   t1z    1
   36  {z>=-1.0 AND z<=-1.0} t1z    1
   37  {z>1.5 AND z<3.0}     t1z  174
   38  {z>0.5 AND z<100}     t1z  599
   39  {z>=1.0 AND z<100}    t1z  600
   40  {z>1.5 AND z<100}     t1z  300
   40  {z>1.5 AND z<100}     t1z  299
   41  {z>=2.0 AND z<100}    t1z  300
   42  {z>2.1 AND z<100}     t1z  100
   43  {z>=3.0 AND z<100}    t1z  100
   44  {z>3.2 AND z<100}     t1z   50
   45  {z>=4.0 AND z<100}    t1z   50
   46  {z>=-100 AND z<=-1.0} t1z   50
   42  {z>2.1 AND z<100}     t1z  124
   43  {z>=3.0 AND z<100}    t1z  125
   44  {z>3.2 AND z<100}     t1z    1
   45  {z>=4.0 AND z<100}    t1z    1
   46  {z>=-100 AND z<=-1.0} t1z    1
   47  {z>=-100 AND z<=0.0}  t1z  400
   48  {z>=-100 AND z<0.0}   t1z   50
   48  {z>=-100 AND z<0.0}   t1z    1
   49  {z>=-100 AND z<=1.0}  t1z  700
   50  {z>=-100 AND z<2.0}   t1z  700
   51  {z>=-100 AND z<=2.0}  t1z  900
   52  {z>=-100 AND z<3.0}   t1z  900
   51  {z>=-100 AND z<=2.0}  t1z  875
   52  {z>=-100 AND z<3.0}   t1z  875
  
  101  {z=-1}                t1z   50
  101  {z=-1}                t1z    1
  102  {z=0}                 t1z  400
  103  {z=1}                 t1z  300
  104  {z=2}                 t1z  200
  105  {z=3}                 t1z  100
  106  {z=4}                 t1z   50
  107  {z=-10.0}             t1z   50
  104  {z=2}                 t1z  175
  105  {z=3}                 t1z  125
  106  {z=4}                 t1z    1
  107  {z=-10.0}             t1z    1
  108  {z=0.0}               t1z  400
  109  {z=1.0}               t1z  300
  110  {z=2.0}               t1z  200
  111  {z=3.0}               t1z  100
  112  {z=4.0}               t1z   50
  113  {z=1.5}               t1z   50
  114  {z=2.5}               t1z   50
  110  {z=2.0}               t1z  175
  111  {z=3.0}               t1z  125
  112  {z=4.0}               t1z    1
  113  {z=1.5}               t1z    1
  114  {z=2.5}               t1z    1
  
  201  {z IN (-1)}           t1z   50
  201  {z IN (-1)}           t1z    1
  202  {z IN (0)}            t1z  400
  203  {z IN (1)}            t1z  300
  204  {z IN (2)}            t1z  200
  205  {z IN (3)}            t1z  100
  206  {z IN (4)}            t1z   50
  207  {z IN (0.5)}          t1z   50
  204  {z IN (2)}            t1z  175
  205  {z IN (3)}            t1z  125
  206  {z IN (4)}            t1z    1
  207  {z IN (0.5)}          t1z    1
  208  {z IN (0,1)}          t1z  700
  209  {z IN (0,1,2)}        t1z  900
  209  {z IN (0,1,2)}        t1z  875
  210  {z IN (0,1,2,3)}      {}   100
  211  {z IN (0,1,2,3,4,5)}  {}   100
  212  {z IN (1,2)}          t1z  500
  212  {z IN (1,2)}          t1z  475
  213  {z IN (2,3)}          t1z  300
  214  {z=3 OR z=2}          t1z  300
  215  {z IN (-1,3)}         t1z  150
  216  {z=-1 OR z=3}         t1z  150
  215  {z IN (-1,3)}         t1z  126
  216  {z=-1 OR z=3}         t1z  126

  300  {y=0}                 {}   100
  301  {y=1}                 t1y   50
  302  {y=0.1}               t1y   50
  300  {y=0}                 t1y  974
  301  {y=1}                 t1y   26
  302  {y=0.1}               t1y    1

  400  {x IS NULL}           t1x  400

} {
  # Verify that the expected index is used with the expected row count
  do_test analyze5-1.${testid}a {
    set x [lindex [eqp "SELECT * FROM t1 WHERE $where"] 3]

    WHERE rowid IN (SELECT rowid FROM t1 ORDER BY random() LIMIT 5);
   ANALYZE;
}

# Verify that range queries generate the correct row count estimates
#
foreach {testid where index rows} {
  500  {x IS NULL AND u='charlie'}         t1u  20
  501  {x=1 AND u='charlie'}               t1x   5
  502  {x IS NULL}                          {} 100
  503  {x=1}                               t1x  50
  504  {x IS NOT NULL}                     t1x  25
  500  {x IS NULL AND u='charlie'}         t1u  17
  501  {x=1 AND u='charlie'}               t1x   1
  502  {x IS NULL}                         t1x 995
  503  {x=1}                               t1x   1
  504  {x IS NOT NULL}                     t1x   2
  505  {+x IS NOT NULL}                     {} 500
  506  {upper(x) IS NOT NULL}               {} 500

} {
  # Verify that the expected index is used with the expected row count
if {$testid==50299} {breakpoint; set sqlite_where_trace 1}
  do_test analyze5-1.${testid}a {
    set x [lindex [eqp "SELECT * FROM t1 WHERE $where"] 3]
    set idx {}
    regexp {INDEX (t1.) } $x all idx
    regexp {~([0-9]+) rows} $x all nrow
    list $idx $nrow
  } [list $index $rows]
if {$testid==50299} exit

  # Verify that the same result is achieved regardless of whether or not
  # the index is used
  do_test analyze5-1.${testid}b {
    set w2 [string map {y +y z +z} $where]
    set a1 [db eval "SELECT rowid FROM t1 NOT INDEXED WHERE $w2\
                     ORDER BY +rowid"]

# in this file a corner-case query planner optimization involving the
# join order of two tables of different sizes.
#

set testdir [file dirname $argv0]
source $testdir/tester.tcl

ifcapable !stat2 {
ifcapable !stat3 {
  finish_test
  return
}

set testprefix analyze6

proc eqp {sql {db db}} {

# 2011 August 13
#
# 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 implements tests for SQLite library.  The focus of the tests
# in this file is testing the capabilities of sqlite_stat3.
#

set testdir [file dirname $argv0]
source $testdir/tester.tcl

ifcapable !stat3 {
  finish_test
  return
}

set testprefix analyze8

proc eqp {sql {db db}} {
  uplevel execsql [list "EXPLAIN QUERY PLAN $sql"] $db
}

# Scenario:
#
#    Two indices.  One has mostly singleton entries, but for a few
#    values there are hundreds of entries.  The other has 10-20
#    entries per value.
#
# Verify that the query planner chooses the first index for the singleton
# entries and the second index for the others.
#
do_test 1.0 {
  db eval {
    CREATE TABLE t1(a,b,c,d);
    CREATE INDEX t1a ON t1(a);
    CREATE INDEX t1b ON t1(b);
    CREATE INDEX t1c ON t1(c);
  }
  for {set i 0} {$i<1000} {incr i} {
    if {$i%2==0} {set a $i} {set a [expr {($i%8)*100}]}
    set b [expr {$i/10}]
    set c [expr {$i/8}]
    set c [expr {$c*$c*$c}]
    db eval {INSERT INTO t1 VALUES($a,$b,$c,$i)}
  }
  db eval {ANALYZE}
} {}

# The a==100 comparison is expensive because there are many rows
# with a==100.  And so for those cases, choose the t1b index.
#
# Buf ro a==99 and a==101, there are far fewer rows so choose
# the t1a index.
#
do_test 1.1 {
  eqp {SELECT * FROM t1 WHERE a=100 AND b=55}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b=?) (~2 rows)}}
do_test 1.2 {
  eqp {SELECT * FROM t1 WHERE a=99 AND b=55}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1a (a=?) (~1 rows)}}
do_test 1.3 {
  eqp {SELECT * FROM t1 WHERE a=101 AND b=55}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1a (a=?) (~1 rows)}}
do_test 1.4 {
  eqp {SELECT * FROM t1 WHERE a=100 AND b=56}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b=?) (~2 rows)}}
do_test 1.5 {
  eqp {SELECT * FROM t1 WHERE a=99 AND b=56}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1a (a=?) (~1 rows)}}
do_test 1.6 {
  eqp {SELECT * FROM t1 WHERE a=101 AND b=56}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1a (a=?) (~1 rows)}}
do_test 2.1 {
  eqp {SELECT * FROM t1 WHERE a=100 AND b BETWEEN 50 AND 54}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b>? AND b<?) (~2 rows)}}

# There are many more values of c between 0 and 100000 than there are
# between 800000 and 900000.  So t1c is more selective for the latter
# range.
#
do_test 3.1 {
  eqp {SELECT * FROM t1 WHERE b BETWEEN 50 AND 54 AND c BETWEEN 0 AND 100000}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b>? AND b<?) (~6 rows)}}
do_test 3.2 {
  eqp {SELECT * FROM t1
       WHERE b BETWEEN 50 AND 54 AND c BETWEEN 800000 AND 900000}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1c (c>? AND c<?) (~4 rows)}}
do_test 3.3 {
  eqp {SELECT * FROM t1 WHERE a=100 AND c BETWEEN 0 AND 100000}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1a (a=?) (~63 rows)}}
do_test 3.4 {
  eqp {SELECT * FROM t1
       WHERE a=100 AND c BETWEEN 800000 AND 900000}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1c (c>? AND c<?) (~2 rows)}}

finish_test

        DROP TABLE v1chng;
      }
    }
  }
  ifcapable stat2 {
    set stat2 "sqlite_stat2 "
  } else {
    ifcapable stat3 {
      set stat2 "sqlite_stat3 "
    } else {
    set stat2 ""
      set stat2 ""
    }
  }
  do_test auth-5.2 {
    execsql {
      SELECT name FROM (
        SELECT * FROM sqlite_master UNION ALL SELECT * FROM sqlite_temp_master)
      WHERE type='table'
      ORDER BY name

proc lookaside {db} {
  expr { $::lookaside_buffer_size *
    [lindex [sqlite3_db_status $db SQLITE_DBSTATUS_LOOKASIDE_USED 0] 1]
  }
}

ifcapable stat3 {
  set STAT3 1
} else {
  set STAT3 0
}

#---------------------------------------------------------------------------
# Run the dbstatus-2 and dbstatus-3 tests with several of different
# lookaside buffer sizes.
#
foreach ::lookaside_buffer_size {0 64 120} {

      END;
    }
    5 {
      CREATE TABLE t1(a, b);
      CREATE TABLE t2(c, d);
      CREATE VIEW v1 AS SELECT * FROM t1 UNION SELECT * FROM t2;
    }
    6 {
    6y {
      CREATE TABLE t1(a, b);
      CREATE INDEX i1 ON t1(a);
      CREATE INDEX i2 ON t1(a,b);
      CREATE INDEX i3 ON t1(b,b);
      INSERT INTO t1 VALUES(randomblob(20), randomblob(25));
      INSERT INTO t1 SELECT randomblob(20), randomblob(25) FROM t1;
      INSERT INTO t1 SELECT randomblob(20), randomblob(25) FROM t1;

    # for any reason is not counted as "schema memory".
    #
    # Additionally, in auto-vacuum mode, dropping tables and indexes causes
    # the page-cache to shrink. So the amount of memory freed is always
    # much greater than just that reported by DBSTATUS_SCHEMA_USED in this
    # case.
    #
    # Some of the memory used for sqlite_stat3 is unaccounted for by
    # dbstatus.
    #
    if {[string match *x $tn] || $AUTOVACUUM} {
    if {[string match *x $tn] || $AUTOVACUUM
         || ([string match *y $tn] && $STAT3)} {
      do_test dbstatus-2.$tn.ax { expr {($nSchema1-$nSchema2)<=$nFree} } 1
    } else {
      do_test dbstatus-2.$tn.a { expr {$nSchema1-$nSchema2} } $nFree
    }
  
    do_test dbstatus-2.$tn.b { list $nAlloc1 $nSchema1 } "$nAlloc3 $nSchema3"
    do_test dbstatus-2.$tn.c { list $nAlloc2 $nSchema2 } "$nAlloc4 $nSchema4"

# 2011 August 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 implements regression tests for SQLite library. This file 
# implements tests for the extra functionality provided by the ANALYZE 
# command when the library is compiled with SQLITE_ENABLE_STAT3 defined.
#

set testdir [file dirname $argv0]
source $testdir/tester.tcl

set testprefix stat3


# Verify that if not compiled with SQLITE_ENABLE_STAT2 that the ANALYZE
# command will delete the sqlite_stat2 table.  Likewise, if not compiled
# with SQLITE_ENABLE_STAT3, the sqlite_stat3 table is deleted.
#
do_test 1.1 {
  db eval {
    PRAGMA writable_schema=ON;
    CREATE TABLE sqlite_stat2(tbl,idx,sampleno,sample);
    CREATE TABLE sqlite_stat3(tbl,idx,neq,nlt,ndlt,sample);
    SELECT name FROM sqlite_master ORDER BY 1;
  }
} {sqlite_stat2 sqlite_stat3}
do_test 1.2 {
  db close
  sqlite3 db test.db
  db eval {SELECT name FROM sqlite_master ORDER BY 1}
} {sqlite_stat2 sqlite_stat3}

ifcapable {stat3} {
  do_test 1.3 {
    db eval {ANALYZE; SELECT name FROM sqlite_master ORDER BY 1}
  } {sqlite_stat1 sqlite_stat3}
} else {
  do_test 1.4 {
    db eval {ANALYZE; SELECT name FROM sqlite_master ORDER BY 1}
  } {sqlite_stat1}
  finish_test
  return
}




finish_test

# This file implements tests to verify that ticket [cbd054fa6b] has been
# fixed.  
#

set testdir [file dirname $argv0]
source $testdir/tester.tcl

ifcapable !stat2 {
ifcapable !stat3 {
  finish_test
  return
}

do_test tkt-cbd05-1.1 {
  db eval {
    CREATE TABLE t1(a INTEGER PRIMARY KEY, b TEXT UNIQUE NOT NULL);

  db eval {
    ANALYZE;
  }
} {}
do_test tkt-cbd05-1.3 {
  execsql { 
    SELECT tbl,idx,group_concat(sample,' ') 
    FROM sqlite_stat2 
    FROM sqlite_stat3 
    WHERE idx = 't1_x' 
    GROUP BY tbl,idx
  }
} {t1 t1_x { A B C D E F G H I}}

do_test tkt-cbd05-2.1 {
  db eval {

  db eval {
    ANALYZE;
  }
} {}
do_test tkt-cbd05-2.3 {
  execsql { 
    SELECT tbl,idx,group_concat(sample,' ') 
    FROM sqlite_stat2 
    FROM sqlite_stat3 
    WHERE idx = 't1_x' 
    GROUP BY tbl,idx
  }
} {t1 t1_x { A B C D E F G H I}}

finish_test

set testdir [file dirname $argv0]
source $testdir/tester.tcl

# A variable with only a string representation comes in as TEXT
do_test types3-1.1 {
  set V {}
  append V {}
  append V x
  concat [tcl_variable_type V] [execsql {SELECT typeof(:V)}]
} {string text}

# A variable with an integer representation comes in as INTEGER
do_test types3-1.2 {
  set V [expr {int(1+2)}]
  concat [tcl_variable_type V] [execsql {SELECT typeof(:V)}]

  INSERT INTO t1 SELECT a+16, b FROM t1;
  INSERT INTO t1 SELECT a+32, b FROM t1;
  INSERT INTO t1 SELECT a+64, b FROM t1;
  ANALYZE;
} {}

foreach idxmode {ordered unordered} {
  catchsql { DELETE FROM sqlite_stat2 }
  catchsql { DELETE FROM sqlite_stat3 }
  if {$idxmode == "unordered"} {
    execsql { UPDATE sqlite_stat1 SET stat = stat || ' unordered' }
  }
    db close
    sqlite3 db test.db
  db close
  sqlite3 db test.db
  }
  foreach {tn sql r(ordered) r(unordered)} {
    1   "SELECT * FROM t1 ORDER BY a"
        {0 0 0 {SCAN TABLE t1 USING INDEX i1 (~128 rows)}}
        {0 0 0 {SCAN TABLE t1 (~128 rows)}}
    2   "SELECT * FROM t1 WHERE a >?"
        {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a>?) (~32 rows)}}
        {0 0 0 {SCAN TABLE t1 (~42 rows)}}

    CREATE INDEX t301c ON t301(c);
    INSERT INTO t301 VALUES(1,2,3);
    CREATE TABLE t302(x, y);
    ANALYZE;
    explain query plan
    SELECT * FROM t302, t301 WHERE t302.x=5 AND t301.a=t302.y;
  }
} {0 0 0 {SCAN TABLE t302 (~1 rows)} 0 1 1 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
} {0 0 0 {SCAN TABLE t302 (~100000 rows)} 0 1 1 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
do_test where3-3.1 {
  execsql {
    explain query plan
    SELECT * FROM t301, t302 WHERE t302.x=5 AND t301.a=t302.y;
  }
} {0 0 1 {SCAN TABLE t302 (~1 rows)} 0 1 0 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
} {0 0 1 {SCAN TABLE t302 (~100000 rows)} 0 1 0 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}

# Verify that when there are multiple tables in a join which must be
# full table scans that the query planner attempts put the table with
# the fewest number of output rows as the outer loop.
#
do_test where3-4.0 {
  execsql {