assert( nKeyCol<=nCol );
  assert( nKeyCol>0 );

  /* Allocate the space required for the Stat4Accum object */
  n = sizeof(*p) 
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anEq */
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.amxEq */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anDLt */

    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anLt */
    + sizeof(Stat4Sample)*(nCol+mxSample)     /* Stat4Accum.aBest[], a[] */
    + sizeof(tRowcnt)*3*nColUp*(nCol+mxSample)
#endif
  ;
  db = sqlite3_context_db_handle(context);
  p = sqlite3DbMallocZero(db, n);
................................................................................

  p->db = db;
  p->nRow = 0;
  p->nCol = nCol;
  p->nKeyCol = nKeyCol;
  p->current.anEq = (tRowcnt*)&p[1];
  p->current.amxEq = &p->current.anEq[nColUp];


#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  {
    u8 *pSpace;                     /* Allocated space not yet assigned */
    int i;                          /* Loop counter */

    p->iGet = -1;
    p->mxSample = mxSample;
    p->nPSample = (tRowcnt)(sqlite3_value_int64(argv[2])/(mxSample/3+1) + 1);
    p->current.anDLt = &p->current.amxEq[nColUp];
    p->current.anLt = &p->current.anDLt[nColUp];
    p->iPrn = 0x689e962d*(u32)nCol ^ 0xd0944565*(u32)sqlite3_value_int(argv[2]);
  
    /* Set up the Stat4Accum.a[] and aBest[] arrays */
    p->a = (struct Stat4Sample*)&p->current.anLt[nColUp];
    p->aBest = &p->a[mxSample];
    pSpace = (u8*)(&p->a[mxSample+nCol]);
................................................................................
    /* Update anDLt[], anLt[] and anEq[] to reflect the values that apply
    ** to the current row of the index. */
    for(i=0; i<iChng; i++){
      if( p->current.amxEq[i]==p->current.anEq[i] ) p->current.amxEq[i]++;
      p->current.anEq[i]++;
    }
    for(i=iChng; i<p->nCol; i++){
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
      p->current.anDLt[i]++;

      p->current.anLt[i] += p->current.anEq[i];
#endif
      p->current.anEq[i] = 1;
    }
  }
  p->nRow++;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
................................................................................
    ** "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.





    */
    char *z;
    int i;


    char *zRet = sqlite3MallocZero( (p->nKeyCol+1)*25 );
    if( zRet==0 ){
      sqlite3_result_error_nomem(context);
      return;
    }

    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] );




    }
    assert( z[0]=='\0' && z>zRet );


    sqlite3_result_text(context, zRet, -1, sqlite3_free);
  }
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  else if( eCall==STAT_GET_ROWID ){
    if( p->iGet<0 ){
      samplePushPrevious(p, 0);
      p->iGet = 0;

  assert( nKeyCol<=nCol );
  assert( nKeyCol>0 );

  /* Allocate the space required for the Stat4Accum object */
  n = sizeof(*p) 
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anEq */
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.amxEq */

    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anDLt */
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    + sizeof(tRowcnt)*nColUp                  /* Stat4Accum.anLt */
    + sizeof(Stat4Sample)*(nCol+mxSample)     /* Stat4Accum.aBest[], a[] */
    + sizeof(tRowcnt)*3*nColUp*(nCol+mxSample)
#endif
  ;
  db = sqlite3_context_db_handle(context);
  p = sqlite3DbMallocZero(db, n);
................................................................................

  p->db = db;
  p->nRow = 0;
  p->nCol = nCol;
  p->nKeyCol = nKeyCol;
  p->current.anEq = (tRowcnt*)&p[1];
  p->current.amxEq = &p->current.anEq[nColUp];
  p->current.anDLt = &p->current.amxEq[nColUp];

#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
  {
    u8 *pSpace;                     /* Allocated space not yet assigned */
    int i;                          /* Loop counter */

    p->iGet = -1;
    p->mxSample = mxSample;
    p->nPSample = (tRowcnt)(sqlite3_value_int64(argv[2])/(mxSample/3+1) + 1);

    p->current.anLt = &p->current.anDLt[nColUp];
    p->iPrn = 0x689e962d*(u32)nCol ^ 0xd0944565*(u32)sqlite3_value_int(argv[2]);
  
    /* Set up the Stat4Accum.a[] and aBest[] arrays */
    p->a = (struct Stat4Sample*)&p->current.anLt[nColUp];
    p->aBest = &p->a[mxSample];
    pSpace = (u8*)(&p->a[mxSample+nCol]);
................................................................................
    /* Update anDLt[], anLt[] and anEq[] to reflect the values that apply
    ** to the current row of the index. */
    for(i=0; i<iChng; i++){
      if( p->current.amxEq[i]==p->current.anEq[i] ) p->current.amxEq[i]++;
      p->current.anEq[i]++;
    }
    for(i=iChng; i<p->nCol; i++){

      p->current.anDLt[i]++;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
      p->current.anLt[i] += p->current.anEq[i];
#endif
      p->current.anEq[i] = 1;
    }
  }
  p->nRow++;
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
................................................................................
    ** "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_result_error_nomem(context);
      return;
    }

    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( p->iGet<0 ){
      samplePushPrevious(p, 0);
      p->iGet = 0;

#define JT_CROSS     0x0002    /* Explicit use of the CROSS keyword */
#define JT_NATURAL   0x0004    /* True for a "natural" join */
#define JT_LEFT      0x0008    /* Left outer join */
#define JT_RIGHT     0x0010    /* Right outer join */
#define JT_OUTER     0x0020    /* The "OUTER" keyword is present */
#define JT_ERROR     0x0040    /* unknown or unsupported join type */











/*
** Flags appropriate for the wctrlFlags parameter of sqlite3WhereBegin()
** and the WhereInfo.wctrlFlags member.
*/
#define WHERE_ORDERBY_NORMAL   0x0000 /* No-op */
#define WHERE_ORDERBY_MIN      0x0001 /* ORDER BY processing for min() func */

#define JT_CROSS     0x0002    /* Explicit use of the CROSS keyword */
#define JT_NATURAL   0x0004    /* True for a "natural" join */
#define JT_LEFT      0x0008    /* Left outer join */
#define JT_RIGHT     0x0010    /* Right outer join */
#define JT_OUTER     0x0020    /* The "OUTER" keyword is present */
#define JT_ERROR     0x0040    /* unknown or unsupported join type */

/*
** TUNING: The skip-scan optimization is only profitable if the average 
** number of repeats of an entry in the index is greater than or equal to
** WHERE_SKIPSCAN_ONSET.  If the average numbe of repeats is less
** than WHERE_SKIPSCAN_ONSET, then it is faster to do a full table
** scan.
*/
#define WHERE_SKIPSCAN_ONSET         18
#define WHERE_SKIPSCAN_ONSET_LOG     42

/*
** Flags appropriate for the wctrlFlags parameter of sqlite3WhereBegin()
** and the WhereInfo.wctrlFlags member.
*/
#define WHERE_ORDERBY_NORMAL   0x0000 /* No-op */
#define WHERE_ORDERBY_MIN      0x0001 /* ORDER BY processing for min() func */

  **
  ** The magic number 18 is selected on the basis that scanning 17 rows
  ** is almost always quicker than an index seek (even though if the index
  ** contains fewer than 2^17 rows we assume otherwise in other parts of
  ** the code). And, even if it is not, it should not be too much slower. 
  ** On the other hand, the extra seeks could end up being significantly
  ** more expensive.  */
  assert( 42==sqlite3LogEst(18) );
  if( saved_nEq==saved_nSkip
   && saved_nEq+1<pProbe->nKeyCol
   && pProbe->noSkipScan==0
   && pProbe->aiRowLogEst[saved_nEq+1]>=42  /* TUNING: Minimum for skip-scan */
   && (rc = whereLoopResize(db, pNew, pNew->nLTerm+1))==SQLITE_OK
  ){
    LogEst nIter;
    pNew->u.btree.nEq++;
    pNew->nSkip++;
    pNew->aLTerm[pNew->nLTerm++] = 0;
    pNew->wsFlags |= WHERE_SKIPSCAN;

  **
  ** The magic number 18 is selected on the basis that scanning 17 rows
  ** is almost always quicker than an index seek (even though if the index
  ** contains fewer than 2^17 rows we assume otherwise in other parts of
  ** the code). And, even if it is not, it should not be too much slower. 
  ** On the other hand, the extra seeks could end up being significantly
  ** more expensive.  */
  assert( WHERE_SKIPSCAN_ONSET_LOG==sqlite3LogEst(WHERE_SKIPSCAN_ONSET) );
  if( saved_nEq==saved_nSkip
   && saved_nEq+1<pProbe->nKeyCol
   && pProbe->noSkipScan==0
   && pProbe->aiRowLogEst[saved_nEq+1]>=WHERE_SKIPSCAN_ONSET_LOG
   && (rc = whereLoopResize(db, pNew, pNew->nLTerm+1))==SQLITE_OK
  ){
    LogEst nIter;
    pNew->u.btree.nEq++;
    pNew->nSkip++;
    pNew->aLTerm[pNew->nLTerm++] = 0;
    pNew->wsFlags |= WHERE_SKIPSCAN;