}
  }

  return pParse->nErr;
}
#endif /* !defined(SQLITE_OMIT_VIRTUALTABLE) */


#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
/*
** Estimate the location of a particular key among all keys in an
** index.  Store the results in aStat as follows:
**
**    aStat[0]      Est. number of rows less than pVal
**    aStat[1]      Est. number of rows equal to pVal
**
** Return SQLITE_OK on success.

*/
static void whereKeyStats(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  UnpackedRecord *pRec,       /* Vector of values to consider */
  int roundUp,                /* Round up if true.  Round down if false */
  tRowcnt *aStat              /* OUT: stats written here */
){
  IndexSample *aSample = pIdx->aSample;
................................................................................
    if( roundUp ){
      iGap = (iGap*2)/3;
    }else{
      iGap = iGap/3;
    }
    aStat[0] = iLower + iGap;
  }

}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */

/*
** If it is not NULL, pTerm is a term that provides an upper or lower
** bound on a range scan. Without considering pTerm, it is estimated 
** that the scan will visit nNew rows. This function returns the number
................................................................................
**                    |_____|   |_____|
**                       |         |
**                     pLower    pUpper
**
** If either of the upper or lower bound is not present, then NULL is passed in
** place of the corresponding WhereTerm.
**
** The value in (pBuilder->pNew->u.btree.nEq) is the index of the index
** column subject to the range constraint. Or, equivalently, the number of
** equality constraints optimized by the proposed index scan. For example,
** assuming index p is on t1(a, b), and the SQL query is:
**
**   ... FROM t1 WHERE a = ? AND b > ? AND b < ? ...
**
** then nEq is set to 1 (as the range restricted column, b, is the second 
................................................................................
**
**   ... FROM t1 WHERE a > ? AND a < ? ...
**
** then nEq is set to 0.
**
** When this function is called, *pnOut is set to the sqlite3LogEst() of the
** number of rows that the index scan is expected to visit without 
** considering the range constraints. If nEq is 0, this is the number of 
** rows in the index. Assuming no error occurs, *pnOut is adjusted (reduced)
** to account for the range constraints pLower and pUpper.
** 
** In the absence of sqlite_stat4 ANALYZE data, or if such data cannot be
** used, a single range inequality reduces the search space by a factor of 4. 
** and a pair of constraints (x>? AND x<?) reduces the expected number of
** rows visited by a factor of 64.
................................................................................
  int nOut = pLoop->nOut;
  LogEst nNew;

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  Index *p = pLoop->u.btree.pIndex;
  int nEq = pLoop->u.btree.nEq;

  if( p->nSample>0
   && nEq<p->nSampleCol
  ){
    if( nEq==pBuilder->nRecValid ){
      UnpackedRecord *pRec = pBuilder->pRec;
      tRowcnt a[2];
      u8 aff;

      /* Variable iLower will be set to the estimate of the number of rows in 
      ** the index that are less than the lower bound of the range query. The
................................................................................
      ** key-prefix formed by the nEq values matched against the nEq left-most
      ** columns of the index, and $L is the value in pLower.
      **
      ** Or, if pLower is NULL or $L cannot be extracted from it (because it
      ** is not a simple variable or literal value), the lower bound of the
      ** range is $P. Due to a quirk in the way whereKeyStats() works, even
      ** if $L is available, whereKeyStats() is called for both ($P) and 
      ** ($P:$L) and the larger of the two returned values used.
      **
      ** Similarly, iUpper is to be set to the estimate of the number of rows
      ** less than the upper bound of the range query. Where the upper bound
      ** is either ($P) or ($P:$U). Again, even if $U is available, both values
      ** of iUpper are requested of whereKeyStats() and the smaller used.


      */
      tRowcnt iLower;
      tRowcnt iUpper;



      if( pRec ){
        testcase( pRec->nField!=pBuilder->nRecValid );
        pRec->nField = pBuilder->nRecValid;
      }
      if( nEq==p->nKeyCol ){
        aff = SQLITE_AFF_INTEGER;
................................................................................
      /* If possible, improve on the iLower estimate using ($P:$L). */
      if( pLower ){
        int bOk;                    /* True if value is extracted from pExpr */
        Expr *pExpr = pLower->pExpr->pRight;
        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
        if( rc==SQLITE_OK && bOk ){
          tRowcnt iNew;
          whereKeyStats(pParse, p, pRec, 0, a);
          iNew = a[0] + ((pLower->eOperator & (WO_GT|WO_LE)) ? a[1] : 0);
          if( iNew>iLower ) iLower = iNew;
          nOut--;
          pLower = 0;
        }
      }

................................................................................
      /* If possible, improve on the iUpper estimate using ($P:$U). */
      if( pUpper ){
        int bOk;                    /* True if value is extracted from pExpr */
        Expr *pExpr = pUpper->pExpr->pRight;
        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
        if( rc==SQLITE_OK && bOk ){
          tRowcnt iNew;
          whereKeyStats(pParse, p, pRec, 1, a);
          iNew = a[0] + ((pUpper->eOperator & (WO_GT|WO_LE)) ? a[1] : 0);
          if( iNew<iUpper ) iUpper = iNew;
          nOut--;
          pUpper = 0;
        }
      }

      pBuilder->pRec = pRec;
      if( rc==SQLITE_OK ){
        if( iUpper>iLower ){
          nNew = sqlite3LogEst(iUpper - iLower);





        }else{
          nNew = 10;        assert( 10==sqlite3LogEst(2) );
        }
        if( nNew<nOut ){
          nOut = nNew;
        }
        WHERETRACE(0x10, ("STAT4 range scan: %u..%u  est=%d\n",

    }
  }

  return pParse->nErr;
}
#endif /* !defined(SQLITE_OMIT_VIRTUALTABLE) */


#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
/*
** Estimate the location of a particular key among all keys in an
** index.  Store the results in aStat as follows:
**
**    aStat[0]      Est. number of rows less than pVal
**    aStat[1]      Est. number of rows equal to pVal
**
** Return the index of the sample that is the smallest sample that
** is greater than or equal to pRec.
*/
static int whereKeyStats(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  UnpackedRecord *pRec,       /* Vector of values to consider */
  int roundUp,                /* Round up if true.  Round down if false */
  tRowcnt *aStat              /* OUT: stats written here */
){
  IndexSample *aSample = pIdx->aSample;
................................................................................
    if( roundUp ){
      iGap = (iGap*2)/3;
    }else{
      iGap = iGap/3;
    }
    aStat[0] = iLower + iGap;
  }
  return i;
}
#endif /* SQLITE_ENABLE_STAT3_OR_STAT4 */

/*
** If it is not NULL, pTerm is a term that provides an upper or lower
** bound on a range scan. Without considering pTerm, it is estimated 
** that the scan will visit nNew rows. This function returns the number
................................................................................
**                    |_____|   |_____|
**                       |         |
**                     pLower    pUpper
**
** If either of the upper or lower bound is not present, then NULL is passed in
** place of the corresponding WhereTerm.
**
** The value in (pBuilder->pNew->u.btree.nEq) is the number of the index
** column subject to the range constraint. Or, equivalently, the number of
** equality constraints optimized by the proposed index scan. For example,
** assuming index p is on t1(a, b), and the SQL query is:
**
**   ... FROM t1 WHERE a = ? AND b > ? AND b < ? ...
**
** then nEq is set to 1 (as the range restricted column, b, is the second 
................................................................................
**
**   ... FROM t1 WHERE a > ? AND a < ? ...
**
** then nEq is set to 0.
**
** When this function is called, *pnOut is set to the sqlite3LogEst() of the
** number of rows that the index scan is expected to visit without 
** considering the range constraints. If nEq is 0, then *pnOut is the number of 
** rows in the index. Assuming no error occurs, *pnOut is adjusted (reduced)
** to account for the range constraints pLower and pUpper.
** 
** In the absence of sqlite_stat4 ANALYZE data, or if such data cannot be
** used, a single range inequality reduces the search space by a factor of 4. 
** and a pair of constraints (x>? AND x<?) reduces the expected number of
** rows visited by a factor of 64.
................................................................................
  int nOut = pLoop->nOut;
  LogEst nNew;

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  Index *p = pLoop->u.btree.pIndex;
  int nEq = pLoop->u.btree.nEq;


  if( p->nSample>0 && nEq<p->nSampleCol ){

    if( nEq==pBuilder->nRecValid ){
      UnpackedRecord *pRec = pBuilder->pRec;
      tRowcnt a[2];
      u8 aff;

      /* Variable iLower will be set to the estimate of the number of rows in 
      ** the index that are less than the lower bound of the range query. The
................................................................................
      ** key-prefix formed by the nEq values matched against the nEq left-most
      ** columns of the index, and $L is the value in pLower.
      **
      ** Or, if pLower is NULL or $L cannot be extracted from it (because it
      ** is not a simple variable or literal value), the lower bound of the
      ** range is $P. Due to a quirk in the way whereKeyStats() works, even
      ** if $L is available, whereKeyStats() is called for both ($P) and 
      ** ($P:$L) and the larger of the two returned values is used.
      **
      ** Similarly, iUpper is to be set to the estimate of the number of rows
      ** less than the upper bound of the range query. Where the upper bound
      ** is either ($P) or ($P:$U). Again, even if $U is available, both values
      ** of iUpper are requested of whereKeyStats() and the smaller used.
      **
      ** The number of rows between the two bounds is then just iUpper-iLower.
      */
      tRowcnt iLower;     /* Rows less than the lower bound */
      tRowcnt iUpper;     /* Rows less than the upper bound */
      int iLwrIdx = -2;   /* aSample[] for the lower bound */
      int iUprIdx = -1;   /* aSample[] for the upper bound */

      if( pRec ){
        testcase( pRec->nField!=pBuilder->nRecValid );
        pRec->nField = pBuilder->nRecValid;
      }
      if( nEq==p->nKeyCol ){
        aff = SQLITE_AFF_INTEGER;
................................................................................
      /* If possible, improve on the iLower estimate using ($P:$L). */
      if( pLower ){
        int bOk;                    /* True if value is extracted from pExpr */
        Expr *pExpr = pLower->pExpr->pRight;
        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
        if( rc==SQLITE_OK && bOk ){
          tRowcnt iNew;
          iLwrIdx = whereKeyStats(pParse, p, pRec, 0, a);
          iNew = a[0] + ((pLower->eOperator & (WO_GT|WO_LE)) ? a[1] : 0);
          if( iNew>iLower ) iLower = iNew;
          nOut--;
          pLower = 0;
        }
      }

................................................................................
      /* If possible, improve on the iUpper estimate using ($P:$U). */
      if( pUpper ){
        int bOk;                    /* True if value is extracted from pExpr */
        Expr *pExpr = pUpper->pExpr->pRight;
        rc = sqlite3Stat4ProbeSetValue(pParse, p, &pRec, pExpr, aff, nEq, &bOk);
        if( rc==SQLITE_OK && bOk ){
          tRowcnt iNew;
          iUprIdx = whereKeyStats(pParse, p, pRec, 1, a);
          iNew = a[0] + ((pUpper->eOperator & (WO_GT|WO_LE)) ? a[1] : 0);
          if( iNew<iUpper ) iUpper = iNew;
          nOut--;
          pUpper = 0;
        }
      }

      pBuilder->pRec = pRec;
      if( rc==SQLITE_OK ){
        if( iUpper>iLower ){
          nNew = sqlite3LogEst(iUpper - iLower);
          /* TUNING:  If both iUpper and iLower are derived from the same
          ** sample, then assume they are 4x more selective.  This brings
          ** the estimated selectivity more in line with what it would be
          ** if estimated without the use of STAT3/4 tables. */
          if( iLwrIdx==iUprIdx ) nNew -= 20;  assert( 20==sqlite3LogEst(4) );
        }else{
          nNew = 10;        assert( 10==sqlite3LogEst(2) );
        }
        if( nNew<nOut ){
          nOut = nNew;
        }
        WHERETRACE(0x10, ("STAT4 range scan: %u..%u  est=%d\n",

} {0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b>? AND b<?)}}

# 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.
# 
# Test 3.2 is a little unstable. It depends on the planner estimating
# that (b BETWEEN 50 AND 54) will match more rows than (c BETWEEN
# 800000 AND 900000). Which is a pretty close call (50 vs. 32), so
# the planner could get it wrong with an unlucky set of samples. This
# case happens to work, but others ("b BETWEEN 40 AND 44" for example) 
# will fail.
#
do_execsql_test 3.0 {
  SELECT count(*) FROM t1 WHERE b BETWEEN 50 AND 54;
  SELECT count(*) FROM t1 WHERE c BETWEEN 0 AND 100000;
  SELECT count(*) FROM t1 WHERE c BETWEEN 800000 AND 900000;
} {50 376 32}
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<?)}}
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<?)}}
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=?)}}
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<?)}}

finish_test

} {0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b>? AND b<?)}}

# 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.
# 
# Test 3.2 is a little unstable. It depends on the planner estimating
# that (b BETWEEN 30 AND 34) will match more rows than (c BETWEEN
# 800000 AND 900000). Which is a pretty close call (50 vs. 32), so
# the planner could get it wrong with an unlucky set of samples. This
# case happens to work, but others ("b BETWEEN 40 AND 44" for example) 
# will fail.
#
do_execsql_test 3.0 {
  SELECT count(*) FROM t1 WHERE b BETWEEN 30 AND 34;
  SELECT count(*) FROM t1 WHERE c BETWEEN 0 AND 100000;
  SELECT count(*) FROM t1 WHERE c BETWEEN 800000 AND 900000;
} {50 376 32}
do_test 3.1 {
  eqp {SELECT * FROM t1 WHERE b BETWEEN 30 AND 34 AND c BETWEEN 0 AND 100000}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1b (b>? AND b<?)}}
do_test 3.2 {
  eqp {SELECT * FROM t1
       WHERE b BETWEEN 30 AND 34 AND c BETWEEN 800000 AND 900000}
} {0 0 0 {SEARCH TABLE t1 USING INDEX t1c (c>? AND c<?)}}
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=?)}}
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<?)}}

finish_test