if( SQLITE_OK==sqlite3ValueFromExpr(db,pExpr->pLeft,enc,affinity,&pVal) ){
      sqlite3VdbeMemNumerify(pVal);
      pVal->u.i = -1 * pVal->u.i;
      /* (double)-1 In case of SQLITE_OMIT_FLOATING_POINT... */
      pVal->r = (double)-1 * pVal->r;
      sqlite3ValueApplyAffinity(pVal, affinity, enc);
    }
  }else if( op==TK_NULL ){
    pVal = sqlite3ValueNew(db);
  }
#ifndef SQLITE_OMIT_BLOB_LITERAL
  else if( op==TK_BLOB ){
    int nVal;
    assert( pExpr->u.zToken[0]=='x' || pExpr->u.zToken[0]=='X' );
    assert( pExpr->u.zToken[1]=='\'' );
    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 */
#define TERM_VNULL      0x80   /* Manufactured x>NULL or x<=NULL term */

/*
** An instance of the following structure holds all information about a
** WHERE clause.  Mostly this is a container for one or more WhereTerms.
*/
struct WhereClause {
  Parse *pParse;           /* The parser context */

#define WO_LE     (WO_EQ<<(TK_LE-TK_EQ))
#define WO_GT     (WO_EQ<<(TK_GT-TK_EQ))
#define WO_GE     (WO_EQ<<(TK_GE-TK_EQ))
#define WO_MATCH  0x040
#define WO_ISNULL 0x080
#define WO_OR     0x100       /* Two or more OR-connected terms */
#define WO_AND    0x200       /* Two or more AND-connected terms */
#define WO_NOOP   0x800       /* This term does not restrict search space */

#define WO_ALL    0xfff       /* Mask of all possible WO_* values */
#define WO_SINGLE 0x0ff       /* Mask of all non-compound WO_* values */

/*
** Value for wsFlags returned by bestIndex() and stored in
** WhereLevel.wsFlags.  These flags determine which search

        exprAnalyze(pSrc, pWC, idxNew);
        pTerm = &pWC->a[idxTerm];
        pWC->a[idxNew].iParent = idxTerm;
        pTerm->nChild = 1;
      }else{
        sqlite3ExprListDelete(db, pList);
      }
      pTerm->eOperator = 0;  /* case 1 trumps case 2 */
      pTerm->eOperator = WO_NOOP;  /* case 1 trumps case 2 */
    }
  }
}
#endif /* !SQLITE_OMIT_OR_OPTIMIZATION && !SQLITE_OMIT_SUBQUERY */


/*

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

#ifdef SQLITE_ENABLE_STAT2
  /* 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
  ** of the loop.  Without the TERM_VNULL flag, the not-null check at
  ** the start of the loop will prevent any results from being returned.
  */
  if( pExpr->op==TK_NOTNULL && pExpr->pLeft->iColumn>=0 ){
    Expr *pNewExpr;
    Expr *pLeft = pExpr->pLeft;
    int idxNew;
    WhereTerm *pNewTerm;

    pNewExpr = sqlite3PExpr(pParse, TK_GT,
                            sqlite3ExprDup(db, pLeft, 0),
                            sqlite3PExpr(pParse, TK_NULL, 0, 0, 0), 0);

    idxNew = whereClauseInsert(pWC, pNewExpr,
                              TERM_VIRTUAL|TERM_DYNAMIC|TERM_VNULL);
    testcase( idxNew==0 );
    pNewTerm = &pWC->a[idxNew];
    pNewTerm->leftCursor = pLeft->iTable;
    pNewTerm->u.leftColumn = pLeft->iColumn;
    pNewTerm->eOperator = WO_GT;
    pNewTerm->iParent = idxTerm;
    pTerm = &pWC->a[idxTerm];
    pTerm->nChild = 1;
    pTerm->wtFlags |= TERM_COPIED;
    pNewTerm->prereqAll = pTerm->prereqAll;
  }
#endif /* SQLITE_ENABLE_STAT2 */

  /* 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;
}

/*

  bestOrClauseIndex(pParse, pWC, pSrc, notReady, notValid, pOrderBy, pCost);
}
#endif /* SQLITE_OMIT_VIRTUALTABLE */

/*
** 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
** stored in Index.aSample. The domain of values stored in said column
** may be thought of as divided into (SQLITE_INDEX_SAMPLES+1) regions.
** Region 0 contains all values smaller than the first sample value. Region
** 1 contains values larger than or equal to the value of the first sample,
** but smaller than the value of the second. And so on.
** stored in Index.aSample. These samples divide the domain of values stored
** the index into (SQLITE_INDEX_SAMPLES+1) regions.
** 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.
**
** 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.
** 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(
  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 */
){
  assert( roundUp==0 || roundUp==1 );
  if( ALWAYS(pVal) ){
    IndexSample *aSample = pIdx->aSample;
    int i = 0;
    int 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 || aSample[i].u.r>r ) break;
        if( aSample[i].eType>=SQLITE_TEXT ) break;
        if( roundUp ){
          if( aSample[i].u.r>r ) break;
        }else{
          if( 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{ 
      sqlite3 *db = pParse->db;
      CollSeq *pColl;
      const u8 *z;
      int n;

          return SQLITE_NOMEM;
        }
        assert( z && pColl && pColl->xCmp );
      }
      n = sqlite3ValueBytes(pVal, pColl->enc);

      for(i=0; i<SQLITE_INDEX_SAMPLES; i++){
        int r;
        int c;
        int eSampletype = aSample[i].eType;
        if( eSampletype==SQLITE_NULL || 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;
          }
          r = pColl->xCmp(pColl->pUser, nSample, zSample, n, z);
          c = pColl->xCmp(pColl->pUser, nSample, zSample, n, z);
          sqlite3DbFree(db, zSample);
        }else
#endif
        {
          r = pColl->xCmp(pColl->pUser, aSample[i].nByte, aSample[i].u.z, n, z);
          c = pColl->xCmp(pColl->pUser, aSample[i].nByte, aSample[i].u.z, n, z);
        }
        if( r>0 ) break;
        if( c-roundUp>=0 ) break;
      }
    }

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

** 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
** that the range scan will visit every row (100%) selected by the equality
** constraints.
**
** In the absence of sqlite_stat2 ANALYZE data, each range inequality
** reduces the search space by 2/3rds.  Hence a single constraint (x>?)
** results in a return of 33 and a range constraint (x>? AND x<?) results
** in a return of 11.
** 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.
*/
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 */
){
  int rc = SQLITE_OK;

#ifdef SQLITE_ENABLE_STAT2

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

    if( pLower ){
      Expr *pExpr = pLower->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pLowerVal);
      assert( pLower->eOperator==WO_GT || pLower->eOperator==WO_GE );
      roundUpLower = (pLower->eOperator==WO_GT) ?1:0;
    }
    if( rc==SQLITE_OK && pUpper ){
      Expr *pExpr = pUpper->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pUpperVal);
      assert( pUpper->eOperator==WO_LT || pUpper->eOperator==WO_LE );
      roundUpUpper = (pUpper->eOperator==WO_LE) ?1:0;
    }

    if( rc!=SQLITE_OK || (pLowerVal==0 && pUpperVal==0) ){
      sqlite3ValueFree(pLowerVal);
      sqlite3ValueFree(pUpperVal);
      goto range_est_fallback;
    }else if( pLowerVal==0 ){
      rc = whereRangeRegion(pParse, p, pUpperVal, &iUpper);
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( pLower ) iLower = iUpper/2;
    }else if( pUpperVal==0 ){
      rc = whereRangeRegion(pParse, p, pLowerVal, &iLower);
      rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
      if( pUpper ) iUpper = (iLower + SQLITE_INDEX_SAMPLES + 1)/2;
    }else{
      rc = whereRangeRegion(pParse, p, pUpperVal, &iUpper);
      rc = whereRangeRegion(pParse, p, pUpperVal, roundUpUpper, &iUpper);
      if( rc==SQLITE_OK ){
        rc = whereRangeRegion(pParse, p, pLowerVal, &iLower);
        rc = whereRangeRegion(pParse, p, pLowerVal, roundUpLower, &iLower);
      }
    }
    WHERETRACE(("range scan regions: %d..%d\n", iLower, iUpper));

    iEst = iUpper - iLower;
    testcase( iEst==SQLITE_INDEX_SAMPLES );
    assert( iEst<=SQLITE_INDEX_SAMPLES );
    if( iEst<1 ){
      iEst = 1;
    }

      *piEst = 50/SQLITE_INDEX_SAMPLES;
    }else{
      *piEst = (iEst*100)/SQLITE_INDEX_SAMPLES;
    }
    sqlite3ValueFree(pLowerVal);
    sqlite3ValueFree(pUpperVal);
    *piEst = (iEst * 100)/SQLITE_INDEX_SAMPLES;
    return rc;
  }
range_est_fallback:
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *piEst = 100;
  if( pLower && pUpper ){
    *piEst = 11;
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ) *piEst /= 4;
  if( pUpper ) *piEst /= 4;
  return rc;
}

#ifdef SQLITE_ENABLE_STAT2
/*
** 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
** 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 */

  assert( p->aSample!=0 );
  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  rc = valueFromExpr(pParse, pExpr, aff, &pRhs);
  if( rc ) goto whereEqualScanEst_cancel;
  if( pRhs==0 ) return SQLITE_NOTFOUND;
  rc = whereRangeRegion(pParse, p, pRhs, 0, &iLower);
  if( rc ) goto whereEqualScanEst_cancel;
  rc = whereRangeRegion(pParse, p, pRhs, 1, &iUpper);
  if( rc ) goto whereEqualScanEst_cancel;
  WHERETRACE(("equality scan regions: %d..%d\n", iLower, iUpper));
  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;
  }
    *piEst = 33;
  }

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

#ifdef SQLITE_ENABLE_STAT2
/*
** 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)
**
** 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 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 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 */
  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++){
    sqlite3ValueFree(pVal);
    rc = valueFromExpr(pParse, pList->a[i].pExpr, aff, &pVal);
    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 ){
      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",
                 nSpan, nSingle, nNotFound, nRowEst));
  }
  sqlite3ValueFree(pVal);
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT2) */


/*
** Find the query plan for accessing a particular table.  Write the
** 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.
**
** The lowest cost plan wins.  The cost is an estimate of the amount of
** CPU and disk I/O need to process the request using the selected plan.
** CPU and disk I/O needed to process the requested result.
** Factors that influence cost include:
**
**    *  The estimated number of rows that will be retrieved.  (The
**       fewer the better.)
**
**    *  Whether or not sorting must occur.
**
**    *  Whether or not there must be separate lookups in the
**       index and in the main table.
**
** If there was an INDEXED BY clause (pSrc->pIndex) attached to the table in
** the SQL statement, then this function only considers plans using the 
** named index. If no such plan is found, then the returned cost is
** SQLITE_BIG_DBL. If a plan is found that uses the named index, 
** then the cost is calculated in the usual way.
**
** If a NOT INDEXED clause (pSrc->notIndexed!=0) was attached to the table 
** in the SELECT statement, then no indexes are considered. However, the 
** selected plan may still take advantage of the tables built-in rowid
** selected plan may still take advantage of the built-in rowid primary key
** index.
*/
static void bestBtreeIndex(
  Parse *pParse,              /* The parsing context */
  WhereClause *pWC,           /* The WHERE clause */
  struct SrcList_item *pSrc,  /* The FROM clause term to search */
  Bitmask notReady,           /* Mask of cursors not available for indexing */

  if( pSrc->pIndex ){
    /* An INDEXED BY clause specifies a particular index to use */
    pIdx = pProbe = pSrc->pIndex;
    wsFlagMask = ~(WHERE_ROWID_EQ|WHERE_ROWID_RANGE);
    eqTermMask = idxEqTermMask;
  }else{
    /* There is no INDEXED BY clause.  Create a fake Index object to
    ** represent the primary key */
    Index *pFirst;                /* Any other index on the table */
    /* There is no INDEXED BY clause.  Create a fake Index object in local
    ** variable sPk to represent the rowid primary key index.  Make this
    ** fake index the first in a chain of Index objects with all of the real
    ** indices to follow */
    Index *pFirst;                  /* First of real indices on the table */
    memset(&sPk, 0, sizeof(Index));
    sPk.nColumn = 1;
    sPk.aiColumn = &aiColumnPk;
    sPk.aiRowEst = aiRowEstPk;
    sPk.onError = OE_Replace;
    sPk.pTable = pSrc->pTab;
    aiRowEstPk[0] = pSrc->pTab->nRowEst;
    aiRowEstPk[1] = 1;
    pFirst = pSrc->pTab->pIndex;
    if( pSrc->notIndexed==0 ){
      /* The real indices of the table are only considered if the
      ** NOT INDEXED qualifier is omitted from the FROM clause */
      sPk.pNext = pFirst;
    }
    pProbe = &sPk;
    wsFlagMask = ~(
        WHERE_COLUMN_IN|WHERE_COLUMN_EQ|WHERE_COLUMN_NULL|WHERE_COLUMN_RANGE
    );
    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;
    double cost;                /* Cost of using pProbe */
    double nRow;                /* Estimated number of rows in result set */
    int rev;                    /* True to scan in reverse order */
    double nSearch;             /* Estimated number of binary searches */
    int wsFlags = 0;
    Bitmask used = 0;

    /* The following variables are populated based on the properties of
    ** scan being evaluated. They are then used to determine the expected
    ** index being evaluated. They are then used to determine the expected
    ** cost and number of rows returned.
    **
    **  nEq: 
    **    Number of equality terms that can be implemented using the index.
    **    In other words, the number of initial fields in the index that
    **    are used in == or IN or NOT NULL constraints of the WHERE clause.
    **
    **  nInMul:  
    **    The "in-multiplier". This is an estimate of how many seek operations 
    **    SQLite must perform on the index in question. For example, if the 
    **    WHERE clause is:
    **
    **      WHERE a IN (1, 2, 3) AND b IN (4, 5, 6)

    **
    **    If there exists a WHERE term of the form "x IN (SELECT ...)", then 
    **    the sub-select is assumed to return 25 rows for the purposes of 
    **    determining nInMul.
    **
    **  bInEst:  
    **    Set to true if there was at least one "x IN (SELECT ...)" term used 
    **    in determining the value of nInMul.
    **    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
    **    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 1/3rd its original size.  So an x>? constraint reduces
    **    estBound to 33.  Two constraints (x>? AND x<?) reduce estBound to 11.
    **    space to 1/4rd its original size.  So an x>? constraint reduces
    **    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: 
    **    Boolean. True if for each index entry visited a lookup on the 
    **    corresponding table b-tree is required. This is always false 
    **    for the rowid index. For other indexes, it is true unless all the 
    **    columns of the table used by the SELECT statement are present in 
    **    the index (such an index is sometimes described as a covering index).
    **    Boolean. True if a table lookup is required for each index entry
    **    visited.  In other words, true if this is not a covering index.
    **    This is always false for the rowid primary key index of a table.
    **    For other indexes, it is true unless all the columns of the table
    **    used by the SELECT statement are present in the index (such an
    **    index is sometimes described as a covering index).
    **    For example, given the index on (a, b), the second of the following 
    **    two queries requires table b-tree lookups, but the first does not.
    **    two queries requires table b-tree lookups in order to find the value
    **    of column c, but the first does not because columns a and b are
    **    both available in the index.
    **
    **             SELECT a, b    FROM tbl WHERE a = 1;
    **             SELECT a, b, c FROM tbl WHERE a = 1;
    */
    int nEq;
    int bInEst = 0;
    int nInMul = 1;
    int estBound = 100;
    int nBound = 0;             /* Number of range constraints seen */
    int bSort = 0;
    int bLookup = 0;
    WhereTerm *pTerm;           /* A single term of the WHERE clause */
    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 */
    int nBound = 0;               /* Number of range constraints seen */
    int bSort = 0;                /* True if external sort required */
    int bLookup = 0;              /* True if not a covering index */
    WhereTerm *pTerm;             /* A single term of the WHERE clause */
#ifdef SQLITE_ENABLE_STAT2
    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);
      if( pTerm==0 ) break;
      wsFlags |= (WHERE_COLUMN_EQ|WHERE_ROWID_EQ);
      if( pTerm->eOperator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
        wsFlags |= WHERE_COLUMN_IN;
        if( ExprHasProperty(pExpr, EP_xIsSelect) ){
          /* "x IN (SELECT ...)":  Assume the SELECT returns 25 rows */
          nInMul *= 25;
          bInEst = 1;
        }else if( ALWAYS(pExpr->x.pList) ){
          nInMul *= pExpr->x.pList->nExpr + 1;
        }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
      if( nEq==0 && pProbe->aSample ) pFirstTerm = pTerm;
#endif
      used |= pTerm->prereqRight;
    }

    /* Determine the value of estBound. */
    if( nEq<pProbe->nColumn ){
      int j = pProbe->aiColumn[nEq];
      if( findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE|WO_GT|WO_GE, pIdx) ){

        wsFlags |= WHERE_IDX_ONLY;
      }else{
        bLookup = 1;
      }
    }

    /*
    ** Estimate the number of rows of output.  For an IN operator,
    ** do not let the estimate exceed half the rows in the table.
    ** Estimate the number of rows of output.  For an "x IN (SELECT...)"
    ** constraint, do not let the estimate exceed half the rows in the table.
    */
    nRow = (double)(aiRowEst[nEq] * nInMul);
    if( bInEst && nRow*2>aiRowEst[0] ){
      nRow = aiRowEst[0]/2;
      nInMul = (int)(nRow / aiRowEst[nEq]);
    }

#ifdef SQLITE_ENABLE_STAT2
    /* Assume constant cost to access a row and logarithmic cost to
    ** do a binary search.  Hence, the initial cost is the number of output
    /* If the constraint is of the form x=VALUE and histogram
    ** data is available for column x, then it might be possible
    ** to get a better estimate on the number of rows based on
    ** rows plus log2(table-size) times the number of binary searches.
    ** VALUE and how common that value is according to the histogram.
    */
    cost = nRow + nInMul*estLog(aiRowEst[0]);
    if( nRow>(double)1 && nEq==1 && pFirstTerm!=0 ){
      if( pFirstTerm->eOperator==WO_EQ ){
        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 */

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

    /* Assume constant cost to advance from one row to the next and
    ** logarithmic cost to do a binary search.  Hence, the initial cost
    ** is the number of output rows plus log2(table-size) times the
    ** number of binary searches.
    **
    ** Because fan-out on tables is so much higher than the fan-out on
    ** indices (because table btrees contain only integer keys in non-leaf
    ** nodes) we weight the cost of a table binary search as 1/10th the
    /* Add in the estimated cost of sorting the result
    ** cost of an index binary search.
    */
    if( pIdx ){
    if( bSort ){
      cost += cost*estLog(cost);
    }

    /* If all information can be taken directly from the index, we avoid
    ** doing table lookups.  This reduces the cost by half.  (Not really -
      if( bLookup ){
        /* For an index lookup followed by a table lookup:
        **    nInMul index searches to find the start of each index range
        **  + nRow steps through the index
        **  + nRow table searches to lookup the table entry using the rowid
        */
        nSearch = nInMul + nRow/10;
      }else{
        /* For a covering index:
        **     nInMul binary searches to find the initial entry 
        **   + nRow steps through the index
        */
        nSearch = nInMul;
      }
    }else{
      /* For a rowid primary key lookup:
      **    nInMult binary searches to find the initial entry scaled by 1/10th
      **  + nRow steps through the table
      */
      nSearch = nInMul/10;
    }
    cost = nRow + nSearch*estLog(aiRowEst[0]);

    /* Add in the estimated cost of sorting the result.  This cost is expanded
    ** this needs to be fixed.)
    ** by a fudge factor of 3.0 to account for the fact that a sorting step 
    ** involves a write and is thus more expensive than a lookup step.
    */
    if( pIdx && bLookup==0 ){
      cost /= (double)2;
    if( bSort ){
      cost += nRow*estLog(nRow)*(double)3;
    }

    /**** Cost of using this index has now been computed ****/

    /* If there are additional constraints on this table that cannot
    ** be used with the current index, but which might lower the number
    ** of output rows, adjust the nRow value accordingly.  This only 
    ** matters if the current index is the least costly, so do not bother
    ** with this step if we already know this index will not be chosen.

          }else{
            /* Assume each additional equality match reduces the result
            ** set size by a factor of 10 */
            nRow /= 10;
          }
        }else if( pTerm->eOperator & (WO_LT|WO_LE|WO_GT|WO_GE) ){
          if( nSkipRange ){
            /* Ignore the first nBound range constraints since the index
            /* Ignore the first nSkipRange range constraints since the index
            ** has already accounted for these */
            nSkipRange--;
          }else{
            /* Assume each additional range constraint reduces the result
            ** set size by a factor of 3 */
            ** set size by a factor of 3.  Indexed range constraints reduce
            ** the search space by a larger factor: 4.  We make indexed range
            ** more selective intentionally because of the subjective 
            ** observation that indexed range constraints really are more
            ** selective in practice, on average. */
            nRow /= 3;
          }
        }else{
        }else if( pTerm->eOperator!=WO_NOOP ){
          /* Any other expression lowers the output row count by half */
          nRow /= 2;
        }
      }
      if( nRow<2 ) nRow = 2;
    }

    start_constraints = pRangeStart || nEq>0;

    /* Seek the index cursor to the start of the range. */
    nConstraint = nEq;
    if( pRangeStart ){
      Expr *pRight = pRangeStart->pExpr->pRight;
      sqlite3ExprCode(pParse, pRight, regBase+nEq);
      if( (pRangeStart->wtFlags & TERM_VNULL)==0 ){
      sqlite3ExprCodeIsNullJump(v, pRight, regBase+nEq, addrNxt);
        sqlite3ExprCodeIsNullJump(v, pRight, regBase+nEq, addrNxt);
      }
      if( zStartAff ){
        if( sqlite3CompareAffinity(pRight, zStartAff[nEq])==SQLITE_AFF_NONE){
          /* Since the comparison is to be performed with no conversions
          ** applied to the operands, set the affinity to apply to pRight to 
          ** SQLITE_AFF_NONE.  */
          zStartAff[nEq] = SQLITE_AFF_NONE;
        }

    ** range (if any).
    */
    nConstraint = nEq;
    if( pRangeEnd ){
      Expr *pRight = pRangeEnd->pExpr->pRight;
      sqlite3ExprCacheRemove(pParse, regBase+nEq, 1);
      sqlite3ExprCode(pParse, pRight, regBase+nEq);
      if( (pRangeEnd->wtFlags & TERM_VNULL)==0 ){
      sqlite3ExprCodeIsNullJump(v, pRight, regBase+nEq, addrNxt);
        sqlite3ExprCodeIsNullJump(v, pRight, regBase+nEq, addrNxt);
      }
      if( zEndAff ){
        if( sqlite3CompareAffinity(pRight, zEndAff[nEq])==SQLITE_AFF_NONE){
          /* Since the comparison is to be performed with no conversions
          ** applied to the operands, set the affinity to apply to pRight to 
          ** SQLITE_AFF_NONE.  */
          zEndAff[nEq] = SQLITE_AFF_NONE;
        }

  SELECT * FROM t1 WHERE x BETWEEN 100 AND 500 AND y BETWEEN 400 AND 700
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_y (y>? AND y<?) (~75 rows)}
}
do_eqp_test 2.7 {
  SELECT * FROM t1 WHERE x BETWEEN -400 AND -300 AND y BETWEEN 100 AND 300
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_x (x>? AND x<?) (~25 rows)}
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_x (x>? AND x<?) (~12 rows)}
}
do_eqp_test 2.8 {
  SELECT * FROM t1 WHERE x BETWEEN 100 AND 300 AND y BETWEEN -400 AND -300
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_y (y>? AND y<?) (~25 rows)}
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_y (y>? AND y<?) (~12 rows)}
}
do_eqp_test 2.9 {
  SELECT * FROM t1 WHERE x BETWEEN 500 AND 100 AND y BETWEEN 100 AND 300
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_x (x>? AND x<?) (~25 rows)}
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_x (x>? AND x<?) (~12 rows)}
}
do_eqp_test 2.10 {
  SELECT * FROM t1 WHERE x BETWEEN 100 AND 300 AND y BETWEEN 500 AND 100
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_y (y>? AND y<?) (~25 rows)}
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_y (y>? AND y<?) (~12 rows)}
}

do_test analyze2-3.1 {
  set alphabet [list a b c d e f g h i j]
  execsql BEGIN
  for {set i 0} {$i < 1000} {incr i} {
    set str    [lindex $alphabet [expr ($i/100)%10]] 

  SELECT * FROM t1 WHERE x BETWEEN 100 AND 500 AND y BETWEEN 'a' AND 'b'
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_y (y>? AND y<?) (~50 rows)}
}
do_eqp_test 3.4 {
  SELECT * FROM t1 WHERE x BETWEEN 100 AND 400 AND y BETWEEN 'a' AND 'h'
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_x (x>? AND x<?) (~50 rows)}
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_x (x>? AND x<?) (~100 rows)}
}
do_eqp_test 3.5 {
  SELECT * FROM t1 WHERE x<'a' AND y>'h'
} {
  0 0 0 {SEARCH TABLE t1 USING INDEX t1_y (y>?) (~66 rows)}
}
do_eqp_test 3.6 {

    execsql { INSERT INTO t3 VALUES($str, $str) }
  }
  execsql COMMIT
  execsql ANALYZE
} {}
do_test analyze2-4.2 {
  execsql { 
    PRAGMA automatic_index=OFF;
    SELECT tbl,idx,group_concat(sample,' ') 
    FROM sqlite_stat2 
    WHERE idx = 't3a' 
    GROUP BY tbl,idx
    GROUP BY tbl,idx;
    PRAGMA automatic_index=ON;
  }
} {t3 t3a {AfA bEj CEj dEj EEj fEj GEj hEj IEj jEj}}
do_test analyze2-4.3 {
  execsql { 
    SELECT tbl,idx,group_concat(sample,' ') 
    FROM sqlite_stat2 
    WHERE idx = 't3b' 

    DELETE FROM sqlite_stat2;
  }
  sqlite3 db test.db
  eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
        t5.a>1 AND t5.a<15 AND
        t6.a>1
  }
} {0 0 0 {SEARCH TABLE t5 USING COVERING INDEX t5i (a>? AND a<?) (~110000 rows)} 0 1 1 {SEARCH TABLE t6 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
} {0 0 0 {SEARCH TABLE t5 USING COVERING INDEX t5i (a>? AND a<?) (~60000 rows)} 0 1 1 {SEARCH TABLE t6 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
do_test analyze2-6.2.2 {
  db cache flush
  execsql ANALYZE
  eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
        t5.a>1 AND t5.a<15 AND
        t6.a>1
  }
} {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~2 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
} {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~1 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
do_test analyze2-6.2.3 {
  sqlite3 db test.db
  eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
        t5.a>1 AND t5.a<15 AND
        t6.a>1
  }
} {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~2 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
} {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~1 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
do_test analyze2-6.2.4 {
  execsql { 
    PRAGMA writable_schema = 1;
    DELETE FROM sqlite_master WHERE tbl_name = 'sqlite_stat1';
  }
  sqlite3 db test.db
  eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
        t5.a>1 AND t5.a<15 AND
        t6.a>1
  }
} {0 0 0 {SEARCH TABLE t5 USING COVERING INDEX t5i (a>? AND a<?) (~110000 rows)} 0 1 1 {SEARCH TABLE t6 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
} {0 0 0 {SEARCH TABLE t5 USING COVERING INDEX t5i (a>? AND a<?) (~60000 rows)} 0 1 1 {SEARCH TABLE t6 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
do_test analyze2-6.2.5 {
  execsql { 
    PRAGMA writable_schema = 1;
    DELETE FROM sqlite_master WHERE tbl_name = 'sqlite_stat2';
  }
  sqlite3 db test.db
  eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
        t5.a>1 AND t5.a<15 AND
        t6.a>1
  }
} {0 0 0 {SEARCH TABLE t5 USING COVERING INDEX t5i (a>? AND a<?) (~110000 rows)} 0 1 1 {SEARCH TABLE t6 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
} {0 0 0 {SEARCH TABLE t5 USING COVERING INDEX t5i (a>? AND a<?) (~60000 rows)} 0 1 1 {SEARCH TABLE t6 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
do_test analyze2-6.2.6 {
  execsql { 
    PRAGMA writable_schema = 1;
    INSERT INTO sqlite_master SELECT * FROM master;
  }
  sqlite3 db test.db
  execsql ANALYZE
  eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
        t5.a>1 AND t5.a<15 AND
        t6.a>1
  }
} {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~2 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
} {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~1 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}

#--------------------------------------------------------------------
# These tests, analyze2-7.*, test that the sqlite_stat2 functionality
# works in shared-cache mode. Note that these tests reuse the database
# created for the analyze2-6.* tests.
#
ifcapable shared_cache {

  } {20}

  do_test analyze2-7.5 {
    eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
          t5.a>1 AND t5.a<15 AND
          t6.a>1
    } db1
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~2 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~1 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  do_test analyze2-7.6 {
    incr_schema_cookie test.db
    execsql { SELECT * FROM sqlite_master } db2
    eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
          t5.a>1 AND t5.a<15 AND
          t6.a>1
    } db2
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~2 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~1 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  do_test analyze2-7.7 {
    incr_schema_cookie test.db
    execsql { SELECT * FROM sqlite_master } db1
    eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
          t5.a>1 AND t5.a<15 AND
          t6.a>1
    } db1
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~2 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~1 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}

  do_test analyze2-7.8 {
    execsql { DELETE FROM sqlite_stat2 } db2
    execsql { SELECT * FROM sqlite_master } db1
    eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
          t5.a>1 AND t5.a<15 AND
          t6.a>1
    } db1
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~2 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~1 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  do_test analyze2-7.9 {
    execsql { SELECT * FROM sqlite_master } db2
    eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
          t5.a>1 AND t5.a<15 AND
          t6.a>1
    } db2
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~2 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  } {0 0 1 {SEARCH TABLE t6 USING COVERING INDEX t6i (a>?) (~1 rows)} 0 1 0 {SEARCH TABLE t5 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}

  do_test analyze2-7.10 {
    incr_schema_cookie test.db
    execsql { SELECT * FROM sqlite_master } db1
    eqp { SELECT * FROM t5,t6 WHERE t5.rowid=t6.rowid AND 
          t5.a>1 AND t5.a<15 AND
          t6.a>1
    } db1
  } {0 0 0 {SEARCH TABLE t5 USING COVERING INDEX t5i (a>? AND a<?) (~2 rows)} 0 1 1 {SEARCH TABLE t6 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}
  } {0 0 0 {SEARCH TABLE t5 USING COVERING INDEX t5i (a>? AND a<?) (~1 rows)} 0 1 1 {SEARCH TABLE t6 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}}

  db1 close
  db2 close
  sqlite3_enable_shared_cache $::enable_shared_cache
}

finish_test

    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<?) (~55000 rows)}}
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (b>? AND b<?) (~30000 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
# with many repeated values and only a few distinct values.
#

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

ifcapable !stat2 {
  finish_test
  return
}

set testprefix analyze5

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

unset -nocomplain i t u v w x y z
do_test analyze5-1.0 {
  db eval {CREATE TABLE t1(t,u,v TEXT COLLATE nocase,w,x,y,z)}
  for {set i 0} {$i < 1000} {incr i} {
    set y [expr {$i>=25 && $i<=50}]
    set z [expr {($i>=400) + ($i>=700) + ($i>=875)}]
    set x $z
    set w $z
    set t [expr {$z+0.5}]
    switch $z {
      0 {set u "alpha"; unset x}
      1 {set u "bravo"}
      2 {set u "charlie"}
      3 {set u "delta"; unset w}
    }
    if {$i%2} {set v $u} {set v [string toupper $u]}
    db eval {INSERT INTO t1 VALUES($t,$u,$v,$w,$x,$y,$z)}
  }
  db eval { 
    CREATE INDEX t1t ON t1(t);  -- 0.5, 1.5, 2.5, and 3.5
    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;
  }
} {alpha alpha alpha alpha bravo bravo bravo charlie charlie delta}
do_test analyze5-1.1 {
  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}
} {{} 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}
} {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}


# 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
    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
   17  {z>=-100 AND z<=0}    t1z  400
   18  {z>=-100 AND z<0}     t1z   50
   19  {z>=-100 AND z<=1}    t1z  700
   20  {z>=-100 AND z<2}     t1z  700
   21  {z>=-100 AND z<=2}    {}   111
   22  {z>=-100 AND z<3}     {}   111
  
   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
   39  {z>=1.0 AND z<100}    t1z  600
   40  {z>1.5 AND z<100}     t1z  300
   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
   47  {z>=-100 AND z<=0.0}  t1z  400
   48  {z>=-100 AND z<0.0}   t1z   50
   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}  {}   111
   52  {z>=-100 AND z<3.0}   {}   111
  
  101  {z=-1}                t1z   50
  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
  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
  
  201  {z IN (-1)}           t1z   50
  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
  208  {z IN (0,1)}          t1z  700
  209  {z IN (0,1,2)}        {}   100
  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
  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

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

} {
  # 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]
    set idx {}
    regexp {INDEX (t1.) } $x all idx
    regexp {~([0-9]+) rows} $x all nrow
    list $idx $nrow
  } [list $index $rows]

  # 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"]
    set a2 [db eval "SELECT rowid FROM t1 WHERE $where ORDER BY +rowid"]
    if {$a1==$a2} {
      set res ok
    } else {
      set res "a1=\[$a1\] a2=\[$a2\]"
    }
    set res
  } {ok}
}


finish_test

  1    "EXPLAIN QUERY PLAN SELECT * FROM t1 WHERE b = 5" 
       {0 0 0 {SEARCH TABLE t1 USING INDEX sqlite_autoindex_t1_1 (b=?) (~1 rows)}}

  2    "EXPLAIN QUERY PLAN SELECT * FROM t2 ORDER BY b, c"
       {0 0 0 {SCAN TABLE t2 USING INDEX sqlite_autoindex_t2_1 (~1000000 rows)}}

  3    "EXPLAIN QUERY PLAN SELECT * FROM t2 WHERE b=10 AND c>10"
       {0 0 0 {SEARCH TABLE t2 USING INDEX sqlite_autoindex_t2_1 (b=? AND c>?) (~3 rows)}}
       {0 0 0 {SEARCH TABLE t2 USING INDEX sqlite_autoindex_t2_1 (b=? AND c>?) (~2 rows)}}
}

# EVIDENCE-OF: R-45493-35653 A CHECK constraint may be attached to a
# column definition or specified as a table constraint. In practice it
# makes no difference.
#
#   All the tests that deal with CHECK constraints below (4.11.* and 

# EVIDENCE-OF: R-22253-05302 sqlite> EXPLAIN QUERY PLAN SELECT t1.*,
# t2.* FROM t1, t2 WHERE t1.a=1 AND t1.b>2; 0|0|0|SEARCH TABLE t1
# USING COVERING INDEX i2 (a=? AND b>?) (~3 rows) 0|1|1|SCAN TABLE t2
# (~1000000 rows)
do_execsql_test 5.4.0 {CREATE TABLE t2(c, d)}
det 5.4.1 "SELECT t1.*, t2.* FROM t1, t2 WHERE t1.a=1 AND t1.b>2" {
  0 0 0 {SEARCH TABLE t1 USING COVERING INDEX i2 (a=? AND b>?) (~3 rows)}
  0 0 0 {SEARCH TABLE t1 USING COVERING INDEX i2 (a=? AND b>?) (~2 rows)}
  0 1 1 {SCAN TABLE t2 (~1000000 rows)}
}

# EVIDENCE-OF: R-21040-07025 sqlite> EXPLAIN QUERY PLAN SELECT t1.*,
# t2.* FROM t2, t1 WHERE t1.a=1 AND t1.b>2; 0|0|1|SEARCH TABLE t1
# USING COVERING INDEX i2 (a=? AND b>?) (~3 rows) 0|1|0|SCAN TABLE t2
# (~1000000 rows)
det 5.5 "SELECT t1.*, t2.* FROM t2, t1 WHERE t1.a=1 AND t1.b>2" {
  0 0 1 {SEARCH TABLE t1 USING COVERING INDEX i2 (a=? AND b>?) (~3 rows)}
  0 0 1 {SEARCH TABLE t1 USING COVERING INDEX i2 (a=? AND b>?) (~2 rows)}
  0 1 0 {SCAN TABLE t2 (~1000000 rows)}
}

# EVIDENCE-OF: R-39007-61103 sqlite> CREATE INDEX i3 ON t1(b);
# sqlite> EXPLAIN QUERY PLAN SELECT * FROM t1 WHERE a=1 OR b=2;
# 0|0|0|SEARCH TABLE t1 USING COVERING INDEX i2 (a=?) (~10 rows)
# 0|0|0|SEARCH TABLE t1 USING INDEX i3 (b=?) (~10 rows)

# Test embedding an INDEXED BY in a CREATE VIEW statement. This block
# also tests that nothing bad happens if an index refered to by
# a CREATE VIEW statement is dropped and recreated.
#
do_execsql_test indexedby-5.1 {
  CREATE VIEW v2 AS SELECT * FROM t1 INDEXED BY i1 WHERE a > 5;
  EXPLAIN QUERY PLAN SELECT * FROM v2 
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a>?) (~330000 rows)}}
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a>?) (~250000 rows)}}
do_execsql_test indexedby-5.2 {
  EXPLAIN QUERY PLAN SELECT * FROM v2 WHERE b = 10 
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a>?) (~33000 rows)}}
} {0 0 0 {SEARCH TABLE t1 USING INDEX i1 (a>?) (~25000 rows)}}
do_test indexedby-5.3 {
  execsql { DROP INDEX i1 }
  catchsql { SELECT * FROM v2 }
} {1 {no such index: i1}}
do_test indexedby-5.4 {
  # Recreate index i1 in such a way as it cannot be used by the view query.
  execsql { CREATE INDEX i1 ON t1(b) }

      INSERT INTO t10 VALUES(12,12,12,12,12,12);
      INSERT INTO t10 VALUES(123,123,123,123,123,123);
      INSERT INTO t10 VALUES(234,234,234,234,234,234);
      INSERT INTO t10 VALUES(345,345,345,345,345,345);
      INSERT INTO t10 VALUES(45,45,45,45,45,45);
    }
    count {
      SELECT a FROM t10 WHERE b LIKE '12%' ORDER BY a;
      SELECT a FROM t10 WHERE b LIKE '12%' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.2 {
    count {
      SELECT a FROM t10 WHERE c LIKE '12%' ORDER BY a;
      SELECT a FROM t10 WHERE c LIKE '12%' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.3 {
    count {
      SELECT a FROM t10 WHERE d LIKE '12%' ORDER BY a;
      SELECT a FROM t10 WHERE d LIKE '12%' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.4 {
    count {
      SELECT a FROM t10 WHERE e LIKE '12%' ORDER BY a;
      SELECT a FROM t10 WHERE e LIKE '12%' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.5 {
    count {
      SELECT a FROM t10 WHERE f LIKE '12%' ORDER BY a;
      SELECT a FROM t10 WHERE f LIKE '12%' ORDER BY +a;
    }
  } {12 123 scan 3 like 0}
  do_test like-10.6 {
    count {
      SELECT a FROM t10 WHERE a LIKE '12%' ORDER BY a;
      SELECT a FROM t10 WHERE a LIKE '12%' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.10 {
    execsql {
      CREATE TABLE t10b(
        a INTEGER PRIMARY KEY,
        b INTEGER UNIQUE,
        c NUMBER UNIQUE,
        d BLOB UNIQUE,
        e UNIQUE,
        f TEXT UNIQUE
      );
      INSERT INTO t10b SELECT * FROM t10;
    }
    count {
      SELECT a FROM t10b WHERE b GLOB '12*' ORDER BY a;
      SELECT a FROM t10b WHERE b GLOB '12*' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.11 {
    count {
      SELECT a FROM t10b WHERE c GLOB '12*' ORDER BY a;
      SELECT a FROM t10b WHERE c GLOB '12*' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.12 {
    count {
      SELECT a FROM t10b WHERE d GLOB '12*' ORDER BY a;
      SELECT a FROM t10b WHERE d GLOB '12*' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.13 {
    count {
      SELECT a FROM t10b WHERE e GLOB '12*' ORDER BY a;
      SELECT a FROM t10b WHERE e GLOB '12*' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
  do_test like-10.14 {
    count {
      SELECT a FROM t10b WHERE f GLOB '12*' ORDER BY a;
      SELECT a FROM t10b WHERE f GLOB '12*' ORDER BY +a;
    }
  } {12 123 scan 3 like 0}
  do_test like-10.15 {
    count {
      SELECT a FROM t10b WHERE a GLOB '12*' ORDER BY a;
      SELECT a FROM t10b WHERE a GLOB '12*' ORDER BY +a;
    }
  } {12 123 scan 5 like 6}
}

# LIKE and GLOB where the default collating sequence is not appropriate
# but an index with the appropriate collating sequence exists.
#

    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY a;
  }
} {abc abcd nosort t11 *}
do_test like-11.3 {
  queryplan {
    PRAGMA case_sensitive_like=OFF;
    CREATE INDEX t11b ON t11(b);
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY a;
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY +a;
  }
} {abc abcd ABC ABCD sort {} t11b}
do_test like-11.4 {
  queryplan {
    PRAGMA case_sensitive_like=ON;
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY a;
  }
} {abc abcd nosort t11 *}
do_test like-11.5 {
  queryplan {
    PRAGMA case_sensitive_like=OFF;
    DROP INDEX t11b;
    CREATE INDEX t11bnc ON t11(b COLLATE nocase);
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY a;
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY +a;
  }
} {abc abcd ABC ABCD sort {} t11bnc}
do_test like-11.6 {
  queryplan {
    CREATE INDEX t11bb ON t11(b COLLATE binary);
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY a;
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY +a;
  }
} {abc abcd ABC ABCD sort {} t11bnc}
do_test like-11.7 {
  queryplan {
    PRAGMA case_sensitive_like=ON;
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY a;
    SELECT b FROM t11 WHERE b LIKE 'abc%' ORDER BY +a;
  }
} {abc abcd sort {} t11bb}
do_test like-11.8 {
  queryplan {
    PRAGMA case_sensitive_like=OFF;
    SELECT b FROM t11 WHERE b GLOB 'abc*' ORDER BY a;
    SELECT b FROM t11 WHERE b GLOB 'abc*' ORDER BY +a;
  }
} {abc abcd sort {} t11bb}
do_test like-11.9 {
  queryplan {
    CREATE INDEX t11cnc ON t11(c COLLATE nocase);
    CREATE INDEX t11cb ON t11(c COLLATE binary);
    SELECT c FROM t11 WHERE c LIKE 'abc%' ORDER BY a;
    SELECT c FROM t11 WHERE c LIKE 'abc%' ORDER BY +a;
  }
} {abc abcd ABC ABCD sort {} t11cnc}
do_test like-11.10 {
  queryplan {
    SELECT c FROM t11 WHERE c GLOB 'abc*' ORDER BY a;
    SELECT c FROM t11 WHERE c GLOB 'abc*' ORDER BY +a;
  }
} {abc abcd sort {} t11cb}


finish_test

    INSERT INTO t1 VALUES('1', 'I',   'one');
    INSERT INTO t1 VALUES('2', 'IV',  'four');
    INSERT INTO t1 VALUES('2', NULL,  'three');
    INSERT INTO t1 VALUES('2', 'II',  'two');
    INSERT INTO t1 VALUES('2', 'V',   'five');
    INSERT INTO t1 VALUES('3', 'VI',  'six');
    COMMIT;
    PRAGMA automatic_index=OFF;
  }
} {}
do_test minmax3-1.1.1 {
  # Linear scan.
  count { SELECT max(y) FROM t1 WHERE x = '2'; }
} {V 5}
do_test minmax3-1.1.2 {

  CREATE TABLE t301(a INTEGER PRIMARY KEY,b,c);
  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 (~0 rows)} 
  0 0 0 {SCAN TABLE t302 (~1 rows)} 
  0 1 1 {SEARCH TABLE t301 USING INTEGER PRIMARY KEY (rowid=?) (~1 rows)}
}
exit
do_execsql_test where3-3.1 {
  explain query plan
  SELECT * FROM t301, t302 WHERE t302.x=5 AND t301.a=t302.y;
} {
  0 0 1 {SCAN TABLE t302 (~0 rows)} 
  0 0 1 {SCAN TABLE t302 (~1 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.
#

  # Likewise, inequalities in an AND are preferred over inequalities in
  # an OR.
  #
  do_execsql_test where9-5.3 {
    EXPLAIN QUERY PLAN SELECT a FROM t1 WHERE b>1000 AND (c>=31031 OR d IS NULL)
  } {
    0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b>?) (~165000 rows)}
    0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b>?) (~125000 rows)}
  }
}

############################################################################
# Make sure OR-clauses work correctly on UPDATE and DELETE statements.

do_test where9-6.2.1 {