** if the index is on columns (a,b) and the sqlite_stat1 value is 
    ** "100 10 2", then SQLite estimates that:
    **
    **   * the index contains 100 rows,
    **   * "WHERE a=?" matches 10 rows, and
    **   * "WHERE a=? AND b=?" matches 2 rows.
    **
    ** Use the worst-case estimate: the maximum number of repeated entries
    ** in the index.  The worst-case estimate is best for picking indexes.
    ** But for skip-scan, we want an average case estimate.  The worst-case
    ** estimate might be too high.  To avoid undesirable skip-scans, if the
    ** worst-case estimate is above the WHERE_SKIPSCAN_ONSET but the average
    ** estimate is below, simply disable skipscans on this index by adding
    ** the "noskipscan" modifier onto the end of the stat line.


    */
    char *z;
    int i;
    int noSkipScan = 0;

    char *zRet = sqlite3MallocZero( (p->nKeyCol+2)*25 );
    if( zRet==0 ){
................................................................................
    sqlite3_snprintf(24, zRet, "%llu", (u64)p->nRow);
    z = zRet + sqlite3Strlen30(zRet);
    for(i=0; i<p->nKeyCol; i++){
      u64 iVal = p->current.amxEq[i];
      sqlite3_snprintf(24, z, " %llu", iVal);
      z += sqlite3Strlen30(z);
      assert( p->current.anEq[i] );
      if( i>0 && iVal>=WHERE_SKIPSCAN_ONSET+5 ){
        iVal = p->current.anDLt[i];
        iVal = (p->nRow + iVal)/(iVal + 1);
        if( iVal<WHERE_SKIPSCAN_ONSET-5 ) noSkipScan = 1;
      }
    }
    if( noSkipScan ) sqlite3_snprintf(14, z, " noskipscan");
    sqlite3_result_text(context, zRet, -1, sqlite3_free);
  }
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  else if( eCall==STAT_GET_ROWID ){

    ** if the index is on columns (a,b) and the sqlite_stat1 value is 
    ** "100 10 2", then SQLite estimates that:
    **
    **   * the index contains 100 rows,
    **   * "WHERE a=?" matches 10 rows, and
    **   * "WHERE a=? AND b=?" matches 2 rows.
    **
    ** A worst-case estimate is used:  the maximum number of rows that
    ** could be select for any set of query parameters.  The worst case
    ** is the estimate we want for choosing indexes.
    **
    ** For deciding whether or not to do a skip-scan, we want to know the
    ** average number of rows with the same key.  We can approximate this
    ** using the (worst case) most number of rows with the same key.  But
    ** sometimes that approximation can be badly off.  In those cases,
    ** mark the index as "noskipscan" to avoid suboptimal skip-scan plans.
    */
    char *z;
    int i;
    int noSkipScan = 0;

    char *zRet = sqlite3MallocZero( (p->nKeyCol+2)*25 );
    if( zRet==0 ){
................................................................................
    sqlite3_snprintf(24, zRet, "%llu", (u64)p->nRow);
    z = zRet + sqlite3Strlen30(zRet);
    for(i=0; i<p->nKeyCol; i++){
      u64 iVal = p->current.amxEq[i];
      sqlite3_snprintf(24, z, " %llu", iVal);
      z += sqlite3Strlen30(z);
      assert( p->current.anEq[i] );
      if( iVal>=WHERE_SKIPSCAN_ONSET
       && p->current.anDLt[i] > p->nRow/(WHERE_SKIPSCAN_ONSET*2/3)
      ){
        noSkipScan = 1;
      }
    }
    if( noSkipScan ) sqlite3_snprintf(14, z, " noskipscan");
    sqlite3_result_text(context, zRet, -1, sqlite3_free);
  }
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  else if( eCall==STAT_GET_ROWID ){

  INSERT INTO people VALUES('Nathan','student',163);
  INSERT INTO people VALUES('Olivia','student',161);
  INSERT INTO people VALUES('Patrick','teacher',180);
  INSERT INTO people VALUES('Quiana','student',182);
  INSERT INTO people VALUES('Robert','student',159);
  INSERT INTO people VALUES('Sally','student',166);
  INSERT INTO people VALUES('Tom','student',171);

  INSERT INTO people VALUES('Ursula','student',170);
  INSERT INTO people VALUES('Vance','student',179);
  INSERT INTO people VALUES('Willma','student',175);
  INSERT INTO people VALUES('Xavier','teacher',185);
  INSERT INTO people VALUES('Yvonne','student',149);
  INSERT INTO people VALUES('Zach','student',170);

}

# Without ANALYZE, a skip-scan is not used
#
do_execsql_test skipscan2-1.3 {
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-1.3eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {~/*INDEX people_idx1 */}

# Now do an ANALYZE.  A skip-scan can be used after ANALYZE.
#
do_execsql_test skipscan2-1.4 {
  ANALYZE;
  -- We do not have enough people above to actually force the use
................................................................................
  -- to make it seem like there are many more.
  UPDATE sqlite_stat1 SET stat='10000 5000 20' WHERE idx='people_idx1';
  UPDATE sqlite_stat1 SET stat='10000 1' WHERE idx='sqlite_autoindex_people_1';
  ANALYZE sqlite_master;
}
db cache flush
do_execsql_test skipscan2-1.5 {
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-1.5eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {/*INDEX people_idx1 */}

# Same answer with other formulations of the same query
#
do_execsql_test skipscan2-1.6 {
  SELECT name FROM people
   WHERE role IN (SELECT DISTINCT role FROM people)
     AND height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-1.7 {
  SELECT name FROM people WHERE role='teacher' AND height>=180
  UNION ALL
  SELECT name FROM people WHERE role='student' AND height>=180
  ORDER BY 1;
} {David Jack Patrick Quiana Xavier}

# Add 8 more people, bringing the total to 34.  Then the number of
# duplicates in the left-column of the index will be 17 and 
# skip-scan should not be used after an (unfudged) ANALYZE.
#
do_execsql_test skipscan2-1.8 {
  INSERT INTO people VALUES('Angie','student',166);
  INSERT INTO people VALUES('Brad','student',176);
  INSERT INTO people VALUES('Claire','student',168);
  INSERT INTO people VALUES('Donald','student',162);
  INSERT INTO people VALUES('Elaine','student',177);
  INSERT INTO people VALUES('Frazier','student',159);
  INSERT INTO people VALUES('Grace','student',179);
  INSERT INTO people VALUES('Horace','student',166);
  ANALYZE;
  SELECT stat FROM sqlite_stat1 WHERE idx='people_idx1';
} {{34 17 2}}

db cache flush
do_execsql_test skipscan2-1.9 {
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}

do_execsql_test skipscan2-1.9eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {~/*INDEX people_idx1 */}

# Add 2 more people, bringing the total to 36.  Then the number of
# duplicates in the left-column of the index will be 18 and 
# skip-scan will be used after an (unfudged) ANALYZE.
#
do_execsql_test skipscan2-1.10 {
  INSERT INTO people VALUES('Ingrad','student',155);
  INSERT INTO people VALUES('Jacob','student',179);
  ANALYZE;
  SELECT stat FROM sqlite_stat1 WHERE idx='people_idx1';
} {{36 18 2}}
db cache flush
do_execsql_test skipscan2-1.11 {
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-1.11eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM people WHERE height>=180 ORDER BY +name;
} {/*INDEX people_idx1 */}


# Repeat using a WITHOUT ROWID table.
#
do_execsql_test skipscan2-2.1 {
  CREATE TABLE peoplew(
    name TEXT PRIMARY KEY,
    role TEXT NOT NULL,
................................................................................
    height INT NOT NULL, -- in cm
    CHECK( role IN ('student','teacher') )
  ) WITHOUT ROWID;
  CREATE INDEX peoplew_idx1 ON peoplew(role, height);
  INSERT INTO peoplew(name,role,height)
     SELECT name, role, height FROM  people;
  ALTER TABLE people RENAME TO old_people;
  SELECT name FROM peoplew WHERE height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-2.2 {
  SELECT name FROM peoplew
   WHERE role IN (SELECT DISTINCT role FROM peoplew)
     AND height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-2.2 {
  SELECT name FROM peoplew WHERE role='teacher' AND height>=180
  UNION ALL
  SELECT name FROM peoplew WHERE role='student' AND height>=180
  ORDER BY 1;
} {David Jack Patrick Quiana Xavier}

# Now do an ANALYZE.  A skip-scan can be used after ANALYZE.
#
do_execsql_test skipscan2-2.4 {
  ANALYZE;
}
db cache flush
do_execsql_test skipscan2-2.5 {
  SELECT name FROM peoplew WHERE height>=180 ORDER BY +name;
} {David Jack Patrick Quiana Xavier}
do_execsql_test skipscan2-2.5eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM peoplew WHERE height>=180 ORDER BY +name;
} {/*INDEX peoplew_idx1 */}

# A skip-scan on a PK index of a WITHOUT ROWID table.
#
do_execsql_test skipscan2-3.1 {
  CREATE TABLE t3(a, b, c, PRIMARY KEY(a, b)) WITHOUT ROWID;
}

  INSERT INTO people VALUES('Nathan','student',163);
  INSERT INTO people VALUES('Olivia','student',161);
  INSERT INTO people VALUES('Patrick','teacher',180);
  INSERT INTO people VALUES('Quiana','student',182);
  INSERT INTO people VALUES('Robert','student',159);
  INSERT INTO people VALUES('Sally','student',166);
  INSERT INTO people VALUES('Tom','student',171);
/*
  INSERT INTO people VALUES('Ursula','student',170);
  INSERT INTO people VALUES('Vance','student',179);
  INSERT INTO people VALUES('Willma','student',175);
  INSERT INTO people VALUES('Xavier','teacher',185);
  INSERT INTO people VALUES('Yvonne','student',149);
  INSERT INTO people VALUES('Zach','student',170);
*/
}

# Without ANALYZE, a skip-scan is not used
#
do_execsql_test skipscan2-1.3 {
  SELECT name FROM people WHERE height<=161 ORDER BY +name;
} {Alice Bob Cindy Emily Megan Olivia Robert}
do_execsql_test skipscan2-1.3eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM people WHERE height<=161 ORDER BY +name;
} {~/*INDEX people_idx1 */}

# Now do an ANALYZE.  A skip-scan can be used after ANALYZE.
#
do_execsql_test skipscan2-1.4 {
  ANALYZE;
  -- We do not have enough people above to actually force the use
................................................................................
  -- to make it seem like there are many more.
  UPDATE sqlite_stat1 SET stat='10000 5000 20' WHERE idx='people_idx1';
  UPDATE sqlite_stat1 SET stat='10000 1' WHERE idx='sqlite_autoindex_people_1';
  ANALYZE sqlite_master;
}
db cache flush
do_execsql_test skipscan2-1.5 {
  SELECT name FROM people WHERE height<=161 ORDER BY +name;
} {Alice Bob Cindy Emily Megan Olivia Robert}
do_execsql_test skipscan2-1.5eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM people WHERE height<=161 ORDER BY +name;
} {/*INDEX people_idx1 */}

# Same answer with other formulations of the same query
#
do_execsql_test skipscan2-1.6 {
  SELECT name FROM people
   WHERE role IN (SELECT DISTINCT role FROM people)
     AND height<=161 ORDER BY +name;
} {Alice Bob Cindy Emily Megan Olivia Robert}
do_execsql_test skipscan2-1.7 {
  SELECT name FROM people WHERE role='teacher' AND height<=161
  UNION ALL
  SELECT name FROM people WHERE role='student' AND height<=161
  ORDER BY 1;
} {Alice Bob Cindy Emily Megan Olivia Robert}

# Add more people so that the estimated number of rows per key is
# equal to the skip-scan threshold of 18.  Then run an (unfudged)
# ANALYZE.  skip-scan should work.
#
do_execsql_test skipscan2-1.8 {
  INSERT INTO people VALUES('Ursula','student',170);







  ANALYZE;
  SELECT stat FROM sqlite_stat1 WHERE idx='people_idx1';

} {{21 18 3}}
db cache flush
do_execsql_test skipscan2-1.9 {
  SELECT name FROM people WHERE height<=161 ORDER BY +name;

} {Alice Bob Cindy Emily Megan Olivia Robert}
do_execsql_test skipscan2-1.9eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM people WHERE height<=161 ORDER BY +name;
} {~/*INDEX people_idx1 */}





















# Repeat using a WITHOUT ROWID table.
#
do_execsql_test skipscan2-2.1 {
  CREATE TABLE peoplew(
    name TEXT PRIMARY KEY,
    role TEXT NOT NULL,
................................................................................
    height INT NOT NULL, -- in cm
    CHECK( role IN ('student','teacher') )
  ) WITHOUT ROWID;
  CREATE INDEX peoplew_idx1 ON peoplew(role, height);
  INSERT INTO peoplew(name,role,height)
     SELECT name, role, height FROM  people;
  ALTER TABLE people RENAME TO old_people;
  SELECT name FROM peoplew WHERE height<=161 ORDER BY +name;
} {Alice Bob Cindy Emily Megan Olivia Robert}
do_execsql_test skipscan2-2.2 {
  SELECT name FROM peoplew
   WHERE role IN (SELECT DISTINCT role FROM peoplew)
     AND height<=161 ORDER BY +name;
} {Alice Bob Cindy Emily Megan Olivia Robert}
do_execsql_test skipscan2-2.2 {
  SELECT name FROM peoplew WHERE role='teacher' AND height<=161
  UNION ALL
  SELECT name FROM peoplew WHERE role='student' AND height<=161
  ORDER BY 1;
} {Alice Bob Cindy Emily Megan Olivia Robert}

# Now do an ANALYZE.  A skip-scan can be used after ANALYZE.
#
do_execsql_test skipscan2-2.4 {
  ANALYZE;
}
db cache flush
do_execsql_test skipscan2-2.5 {
  SELECT name FROM peoplew WHERE height<=161 ORDER BY +name;
} {Alice Bob Cindy Emily Megan Olivia Robert}
do_execsql_test skipscan2-2.5eqp {
  EXPLAIN QUERY PLAN
  SELECT name FROM peoplew WHERE height<=161 ORDER BY +name;
} {/*INDEX peoplew_idx1 */}

# A skip-scan on a PK index of a WITHOUT ROWID table.
#
do_execsql_test skipscan2-3.1 {
  CREATE TABLE t3(a, b, c, PRIMARY KEY(a, b)) WITHOUT ROWID;
}