**     (3)  Bypass the creation of the sqlite_master table entry
**          for the PRIMARY KEY as the primary key index is now
**          identified by the sqlite_master table entry of the table itself.
**     (4)  Set the Index.tnum of the PRIMARY KEY Index object in the
**          schema to the rootpage from the main table.
**     (5)  Add all table columns to the PRIMARY KEY Index object
**          so that the PRIMARY KEY is a covering index.  The surplus
**          columns are part of KeyInfo.nXField and are not used for
**          sorting or lookup or uniqueness checks.
**     (6)  Replace the rowid tail on all automatically generated UNIQUE
**          indices with the PRIMARY KEY columns.
**
** For virtual tables, only (1) is performed.
*/
static void convertToWithoutRowidTable(Parse *pParse, Table *pTab){

**     (3)  Bypass the creation of the sqlite_master table entry
**          for the PRIMARY KEY as the primary key index is now
**          identified by the sqlite_master table entry of the table itself.
**     (4)  Set the Index.tnum of the PRIMARY KEY Index object in the
**          schema to the rootpage from the main table.
**     (5)  Add all table columns to the PRIMARY KEY Index object
**          so that the PRIMARY KEY is a covering index.  The surplus
**          columns are part of KeyInfo.nAllField and are not used for
**          sorting or lookup or uniqueness checks.
**     (6)  Replace the rowid tail on all automatically generated UNIQUE
**          indices with the PRIMARY KEY columns.
**
** For virtual tables, only (1) is performed.
*/
static void convertToWithoutRowidTable(Parse *pParse, Table *pTab){

    }
    VdbeCoverage(v);
    sqlite3VdbeAddOp3(v, OP_Compare, regPrevKey, regBase, pSort->nOBSat);
    pOp = sqlite3VdbeGetOp(v, pSort->addrSortIndex);
    if( pParse->db->mallocFailed ) return;
    pOp->p2 = nKey + nData;
    pKI = pOp->p4.pKeyInfo;
    memset(pKI->aSortOrder, 0, pKI->nField); /* Makes OP_Jump below testable */
    sqlite3VdbeChangeP4(v, -1, (char*)pKI, P4_KEYINFO);
    testcase( pKI->nXField>2 );
    pOp->p4.pKeyInfo = keyInfoFromExprList(pParse, pSort->pOrderBy, nOBSat,
                                           pKI->nXField-1);
    addrJmp = sqlite3VdbeCurrentAddr(v);
    sqlite3VdbeAddOp3(v, OP_Jump, addrJmp+1, 0, addrJmp+1); VdbeCoverage(v);
    pSort->labelBkOut = sqlite3VdbeMakeLabel(v);
    pSort->regReturn = ++pParse->nMem;
    sqlite3VdbeAddOp2(v, OP_Gosub, pSort->regReturn, pSort->labelBkOut);
    sqlite3VdbeAddOp1(v, OP_ResetSorter, pSort->iECursor);
    if( iLimit ){
................................................................................
** X extra columns.
*/
KeyInfo *sqlite3KeyInfoAlloc(sqlite3 *db, int N, int X){
  int nExtra = (N+X)*(sizeof(CollSeq*)+1) - sizeof(CollSeq*);
  KeyInfo *p = sqlite3DbMallocRawNN(db, sizeof(KeyInfo) + nExtra);
  if( p ){
    p->aSortOrder = (u8*)&p->aColl[N+X];
    p->nField = (u16)N;
    p->nXField = (u16)X;
    p->enc = ENC(db);
    p->db = db;
    p->nRef = 1;
    memset(&p[1], 0, nExtra);
  }else{
    sqlite3OomFault(db);
  }

    }
    VdbeCoverage(v);
    sqlite3VdbeAddOp3(v, OP_Compare, regPrevKey, regBase, pSort->nOBSat);
    pOp = sqlite3VdbeGetOp(v, pSort->addrSortIndex);
    if( pParse->db->mallocFailed ) return;
    pOp->p2 = nKey + nData;
    pKI = pOp->p4.pKeyInfo;
    memset(pKI->aSortOrder, 0, pKI->nKeyField); /* Makes OP_Jump testable */
    sqlite3VdbeChangeP4(v, -1, (char*)pKI, P4_KEYINFO);
    testcase( pKI->nAllField > pKI->nKeyField+2 );
    pOp->p4.pKeyInfo = keyInfoFromExprList(pParse, pSort->pOrderBy, nOBSat,
                                           pKI->nAllField-pKI->nKeyField-1);
    addrJmp = sqlite3VdbeCurrentAddr(v);
    sqlite3VdbeAddOp3(v, OP_Jump, addrJmp+1, 0, addrJmp+1); VdbeCoverage(v);
    pSort->labelBkOut = sqlite3VdbeMakeLabel(v);
    pSort->regReturn = ++pParse->nMem;
    sqlite3VdbeAddOp2(v, OP_Gosub, pSort->regReturn, pSort->labelBkOut);
    sqlite3VdbeAddOp1(v, OP_ResetSorter, pSort->iECursor);
    if( iLimit ){
................................................................................
** X extra columns.
*/
KeyInfo *sqlite3KeyInfoAlloc(sqlite3 *db, int N, int X){
  int nExtra = (N+X)*(sizeof(CollSeq*)+1) - sizeof(CollSeq*);
  KeyInfo *p = sqlite3DbMallocRawNN(db, sizeof(KeyInfo) + nExtra);
  if( p ){
    p->aSortOrder = (u8*)&p->aColl[N+X];
    p->nKeyField = (u16)N;
    p->nAllField = (u16)(N+X);
    p->enc = ENC(db);
    p->db = db;
    p->nRef = 1;
    memset(&p[1], 0, nExtra);
  }else{
    sqlite3OomFault(db);
  }

** Note that aSortOrder[] and aColl[] have nField+1 slots.  There
** are nField slots for the columns of an index then one extra slot
** for the rowid at the end.
*/
struct KeyInfo {
  u32 nRef;           /* Number of references to this KeyInfo object */
  u8 enc;             /* Text encoding - one of the SQLITE_UTF* values */
  u16 nField;         /* Number of key columns in the index */
  u16 nXField;        /* Number of columns beyond the key columns */
  sqlite3 *db;        /* The database connection */
  u8 *aSortOrder;     /* Sort order for each column. */
  CollSeq *aColl[1];  /* Collating sequence for each term of the key */
};

/*
** This object holds a record which has been parsed out into individual

** Note that aSortOrder[] and aColl[] have nField+1 slots.  There
** are nField slots for the columns of an index then one extra slot
** for the rowid at the end.
*/
struct KeyInfo {
  u32 nRef;           /* Number of references to this KeyInfo object */
  u8 enc;             /* Text encoding - one of the SQLITE_UTF* values */
  u16 nKeyField;      /* Number of key columns in the index */
  u16 nAllField;      /* Total columns, including key plus others */
  sqlite3 *db;        /* The database connection */
  u8 *aSortOrder;     /* Sort order for each column. */
  CollSeq *aColl[1];  /* Collating sequence for each term of the key */
};

/*
** This object holds a record which has been parsed out into individual

#endif /* SQLITE_DEBUG */
  for(i=0; i<n; i++){
    idx = aPermute ? aPermute[i] : i;
    assert( memIsValid(&aMem[p1+idx]) );
    assert( memIsValid(&aMem[p2+idx]) );
    REGISTER_TRACE(p1+idx, &aMem[p1+idx]);
    REGISTER_TRACE(p2+idx, &aMem[p2+idx]);
    assert( i<pKeyInfo->nField );
    pColl = pKeyInfo->aColl[i];
    bRev = pKeyInfo->aSortOrder[i];
    iCompare = sqlite3MemCompare(&aMem[p1+idx], &aMem[p2+idx], pColl);
    if( iCompare ){
      if( bRev ) iCompare = -iCompare;
      break;
    }
................................................................................
    ** before reaching this instruction. */
    assert( p2>=2 );
  }
  if( pOp->p4type==P4_KEYINFO ){
    pKeyInfo = pOp->p4.pKeyInfo;
    assert( pKeyInfo->enc==ENC(db) );
    assert( pKeyInfo->db==db );
    nField = pKeyInfo->nField+pKeyInfo->nXField;
  }else if( pOp->p4type==P4_INT32 ){
    nField = pOp->p4.i;
  }
  assert( pOp->p1>=0 );
  assert( nField>=0 );
  testcase( nField==0 );  /* Table with INTEGER PRIMARY KEY and nothing else */
  pCur = allocateCursor(p, pOp->p1, nField, iDb, CURTYPE_BTREE);

#endif /* SQLITE_DEBUG */
  for(i=0; i<n; i++){
    idx = aPermute ? aPermute[i] : i;
    assert( memIsValid(&aMem[p1+idx]) );
    assert( memIsValid(&aMem[p2+idx]) );
    REGISTER_TRACE(p1+idx, &aMem[p1+idx]);
    REGISTER_TRACE(p2+idx, &aMem[p2+idx]);
    assert( i<pKeyInfo->nKeyField );
    pColl = pKeyInfo->aColl[i];
    bRev = pKeyInfo->aSortOrder[i];
    iCompare = sqlite3MemCompare(&aMem[p1+idx], &aMem[p2+idx], pColl);
    if( iCompare ){
      if( bRev ) iCompare = -iCompare;
      break;
    }
................................................................................
    ** before reaching this instruction. */
    assert( p2>=2 );
  }
  if( pOp->p4type==P4_KEYINFO ){
    pKeyInfo = pOp->p4.pKeyInfo;
    assert( pKeyInfo->enc==ENC(db) );
    assert( pKeyInfo->db==db );
    nField = pKeyInfo->nAllField;
  }else if( pOp->p4type==P4_INT32 ){
    nField = pOp->p4.i;
  }
  assert( pOp->p1>=0 );
  assert( nField>=0 );
  testcase( nField==0 );  /* Table with INTEGER PRIMARY KEY and nothing else */
  pCur = allocateCursor(p, pOp->p1, nField, iDb, CURTYPE_BTREE);

  int nKey, 
  const void *pKey
){
  UnpackedRecord *pRet;           /* Return value */

  pRet = sqlite3VdbeAllocUnpackedRecord(pKeyInfo);
  if( pRet ){
    memset(pRet->aMem, 0, sizeof(Mem)*(pKeyInfo->nField+1));
    sqlite3VdbeRecordUnpack(pKeyInfo, nKey, pKey, pRet);
  }
  return pRet;
}

/*
** This function is called from within a pre-update callback to retrieve
................................................................................
#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
/*
** This function is called from within a pre-update callback to retrieve
** the number of columns in the row being updated, deleted or inserted.
*/
int sqlite3_preupdate_count(sqlite3 *db){
  PreUpdate *p = db->pPreUpdate;
  return (p ? p->keyinfo.nField : 0);
}
#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */

#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
/*
** This function is designed to be called from within a pre-update callback
** only. It returns zero if the change that caused the callback was made

  int nKey, 
  const void *pKey
){
  UnpackedRecord *pRet;           /* Return value */

  pRet = sqlite3VdbeAllocUnpackedRecord(pKeyInfo);
  if( pRet ){
    memset(pRet->aMem, 0, sizeof(Mem)*(pKeyInfo->nKeyField+1));
    sqlite3VdbeRecordUnpack(pKeyInfo, nKey, pKey, pRet);
  }
  return pRet;
}

/*
** This function is called from within a pre-update callback to retrieve
................................................................................
#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
/*
** This function is called from within a pre-update callback to retrieve
** the number of columns in the row being updated, deleted or inserted.
*/
int sqlite3_preupdate_count(sqlite3 *db){
  PreUpdate *p = db->pPreUpdate;
  return (p ? p->keyinfo.nKeyField : 0);
}
#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */

#ifdef SQLITE_ENABLE_PREUPDATE_HOOK
/*
** This function is designed to be called from within a pre-update callback
** only. It returns zero if the change that caused the callback was made

  assert( nTemp>=20 );
  sqlite3StrAccumInit(&x, 0, zTemp, nTemp, 0);
  switch( pOp->p4type ){
    case P4_KEYINFO: {
      int j;
      KeyInfo *pKeyInfo = pOp->p4.pKeyInfo;
      assert( pKeyInfo->aSortOrder!=0 );
      sqlite3XPrintf(&x, "k(%d", pKeyInfo->nField);
      for(j=0; j<pKeyInfo->nField; j++){
        CollSeq *pColl = pKeyInfo->aColl[j];
        const char *zColl = pColl ? pColl->zName : "";
        if( strcmp(zColl, "BINARY")==0 ) zColl = "B";
        sqlite3XPrintf(&x, ",%s%s", pKeyInfo->aSortOrder[j] ? "-" : "", zColl);
      }
      sqlite3StrAccumAppend(&x, ")", 1);
      break;
................................................................................
** If an OOM error occurs, NULL is returned.
*/
UnpackedRecord *sqlite3VdbeAllocUnpackedRecord(
  KeyInfo *pKeyInfo               /* Description of the record */
){
  UnpackedRecord *p;              /* Unpacked record to return */
  int nByte;                      /* Number of bytes required for *p */
  nByte = ROUND8(sizeof(UnpackedRecord)) + sizeof(Mem)*(pKeyInfo->nField+1);
  p = (UnpackedRecord *)sqlite3DbMallocRaw(pKeyInfo->db, nByte);
  if( !p ) return 0;
  p->aMem = (Mem*)&((char*)p)[ROUND8(sizeof(UnpackedRecord))];
  assert( pKeyInfo->aSortOrder!=0 );
  p->pKeyInfo = pKeyInfo;
  p->nField = pKeyInfo->nField + 1;
  return p;
}

/*
** Given the nKey-byte encoding of a record in pKey[], populate the 
** UnpackedRecord structure indicated by the fourth argument with the
** contents of the decoded record.
................................................................................
    /* pMem->flags = 0; // sqlite3VdbeSerialGet() will set this for us */
    pMem->szMalloc = 0;
    pMem->z = 0;
    d += sqlite3VdbeSerialGet(&aKey[d], serial_type, pMem);
    pMem++;
    if( (++u)>=p->nField ) break;
  }
  assert( u<=pKeyInfo->nField + 1 );
  p->nField = u;
}

#ifdef SQLITE_DEBUG
/*
** This function compares two index or table record keys in the same way
** as the sqlite3VdbeRecordCompare() routine. Unlike VdbeRecordCompare(),
................................................................................
  ** to ignore the compiler warnings and leave this variable uninitialized.
  */
  /*  mem1.u.i = 0;  // not needed, here to silence compiler warning */
  
  idx1 = getVarint32(aKey1, szHdr1);
  if( szHdr1>98307 ) return SQLITE_CORRUPT;
  d1 = szHdr1;
  assert( pKeyInfo->nField+pKeyInfo->nXField>=pPKey2->nField || CORRUPT_DB );
  assert( pKeyInfo->aSortOrder!=0 );
  assert( pKeyInfo->nField>0 );
  assert( idx1<=szHdr1 || CORRUPT_DB );
  do{
    u32 serial_type1;

    /* Read the serial types for the next element in each key. */
    idx1 += getVarint32( aKey1+idx1, serial_type1 );

................................................................................
}
#endif

#ifdef SQLITE_DEBUG
/*
** Count the number of fields (a.k.a. columns) in the record given by
** pKey,nKey.  The verify that this count is less than or equal to the
** limit given by pKeyInfo->nField + pKeyInfo->nXField.
**
** If this constraint is not satisfied, it means that the high-speed
** vdbeRecordCompareInt() and vdbeRecordCompareString() routines will
** not work correctly.  If this assert() ever fires, it probably means
** that the KeyInfo.nField or KeyInfo.nXField values were computed
** incorrectly.
*/
static void vdbeAssertFieldCountWithinLimits(
  int nKey, const void *pKey,   /* The record to verify */ 
  const KeyInfo *pKeyInfo       /* Compare size with this KeyInfo */
){
  int nField = 0;
................................................................................
  idx = getVarint32(aKey, szHdr);
  assert( nKey>=0 );
  assert( szHdr<=(u32)nKey );
  while( idx<szHdr ){
    idx += getVarint32(aKey+idx, notUsed);
    nField++;
  }
  assert( nField <= pKeyInfo->nField+pKeyInfo->nXField );
}
#else
# define vdbeAssertFieldCountWithinLimits(A,B,C)
#endif

/*
** Both *pMem1 and *pMem2 contain string values. Compare the two values
................................................................................
      pPKey2->errCode = (u8)SQLITE_CORRUPT_BKPT;
      return 0;  /* Corruption */
    }
    i = 0;
  }

  VVA_ONLY( mem1.szMalloc = 0; ) /* Only needed by assert() statements */
  assert( pPKey2->pKeyInfo->nField+pPKey2->pKeyInfo->nXField>=pPKey2->nField 
       || CORRUPT_DB );
  assert( pPKey2->pKeyInfo->aSortOrder!=0 );
  assert( pPKey2->pKeyInfo->nField>0 );
  assert( idx1<=szHdr1 || CORRUPT_DB );
  do{
    u32 serial_type;

    /* RHS is an integer */
    if( pRhs->flags & MEM_Int ){
      serial_type = aKey1[idx1];
................................................................................
  ** buffer passed to varintRecordCompareInt() this makes it convenient to
  ** limit the size of the header to 64 bytes in cases where the first field
  ** is an integer.
  **
  ** The easiest way to enforce this limit is to consider only records with
  ** 13 fields or less. If the first field is an integer, the maximum legal
  ** header size is (12*5 + 1 + 1) bytes.  */
  if( (p->pKeyInfo->nField + p->pKeyInfo->nXField)<=13 ){
    int flags = p->aMem[0].flags;
    if( p->pKeyInfo->aSortOrder[0] ){
      p->r1 = 1;
      p->r2 = -1;
    }else{
      p->r1 = -1;
      p->r2 = 1;
................................................................................

  preupdate.v = v;
  preupdate.pCsr = pCsr;
  preupdate.op = op;
  preupdate.iNewReg = iReg;
  preupdate.keyinfo.db = db;
  preupdate.keyinfo.enc = ENC(db);
  preupdate.keyinfo.nField = pTab->nCol;
  preupdate.keyinfo.aSortOrder = (u8*)&fakeSortOrder;
  preupdate.iKey1 = iKey1;
  preupdate.iKey2 = iKey2;
  preupdate.pTab = pTab;

  db->pPreUpdate = &preupdate;
  db->xPreUpdateCallback(db->pPreUpdateArg, db, op, zDb, zTbl, iKey1, iKey2);
  db->pPreUpdate = 0;
  sqlite3DbFree(db, preupdate.aRecord);
  vdbeFreeUnpacked(db, preupdate.keyinfo.nField+1, preupdate.pUnpacked);
  vdbeFreeUnpacked(db, preupdate.keyinfo.nField+1, preupdate.pNewUnpacked);
  if( preupdate.aNew ){
    int i;
    for(i=0; i<pCsr->nField; i++){
      sqlite3VdbeMemRelease(&preupdate.aNew[i]);
    }
    sqlite3DbFreeNN(db, preupdate.aNew);
  }
}
#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */

  assert( nTemp>=20 );
  sqlite3StrAccumInit(&x, 0, zTemp, nTemp, 0);
  switch( pOp->p4type ){
    case P4_KEYINFO: {
      int j;
      KeyInfo *pKeyInfo = pOp->p4.pKeyInfo;
      assert( pKeyInfo->aSortOrder!=0 );
      sqlite3XPrintf(&x, "k(%d", pKeyInfo->nKeyField);
      for(j=0; j<pKeyInfo->nKeyField; j++){
        CollSeq *pColl = pKeyInfo->aColl[j];
        const char *zColl = pColl ? pColl->zName : "";
        if( strcmp(zColl, "BINARY")==0 ) zColl = "B";
        sqlite3XPrintf(&x, ",%s%s", pKeyInfo->aSortOrder[j] ? "-" : "", zColl);
      }
      sqlite3StrAccumAppend(&x, ")", 1);
      break;
................................................................................
** If an OOM error occurs, NULL is returned.
*/
UnpackedRecord *sqlite3VdbeAllocUnpackedRecord(
  KeyInfo *pKeyInfo               /* Description of the record */
){
  UnpackedRecord *p;              /* Unpacked record to return */
  int nByte;                      /* Number of bytes required for *p */
  nByte = ROUND8(sizeof(UnpackedRecord)) + sizeof(Mem)*(pKeyInfo->nKeyField+1);
  p = (UnpackedRecord *)sqlite3DbMallocRaw(pKeyInfo->db, nByte);
  if( !p ) return 0;
  p->aMem = (Mem*)&((char*)p)[ROUND8(sizeof(UnpackedRecord))];
  assert( pKeyInfo->aSortOrder!=0 );
  p->pKeyInfo = pKeyInfo;
  p->nField = pKeyInfo->nKeyField + 1;
  return p;
}

/*
** Given the nKey-byte encoding of a record in pKey[], populate the 
** UnpackedRecord structure indicated by the fourth argument with the
** contents of the decoded record.
................................................................................
    /* pMem->flags = 0; // sqlite3VdbeSerialGet() will set this for us */
    pMem->szMalloc = 0;
    pMem->z = 0;
    d += sqlite3VdbeSerialGet(&aKey[d], serial_type, pMem);
    pMem++;
    if( (++u)>=p->nField ) break;
  }
  assert( u<=pKeyInfo->nKeyField + 1 );
  p->nField = u;
}

#ifdef SQLITE_DEBUG
/*
** This function compares two index or table record keys in the same way
** as the sqlite3VdbeRecordCompare() routine. Unlike VdbeRecordCompare(),
................................................................................
  ** to ignore the compiler warnings and leave this variable uninitialized.
  */
  /*  mem1.u.i = 0;  // not needed, here to silence compiler warning */
  
  idx1 = getVarint32(aKey1, szHdr1);
  if( szHdr1>98307 ) return SQLITE_CORRUPT;
  d1 = szHdr1;
  assert( pKeyInfo->nAllField>=pPKey2->nField || CORRUPT_DB );
  assert( pKeyInfo->aSortOrder!=0 );
  assert( pKeyInfo->nKeyField>0 );
  assert( idx1<=szHdr1 || CORRUPT_DB );
  do{
    u32 serial_type1;

    /* Read the serial types for the next element in each key. */
    idx1 += getVarint32( aKey1+idx1, serial_type1 );

................................................................................
}
#endif

#ifdef SQLITE_DEBUG
/*
** Count the number of fields (a.k.a. columns) in the record given by
** pKey,nKey.  The verify that this count is less than or equal to the
** limit given by pKeyInfo->nAllField.
**
** If this constraint is not satisfied, it means that the high-speed
** vdbeRecordCompareInt() and vdbeRecordCompareString() routines will
** not work correctly.  If this assert() ever fires, it probably means
** that the KeyInfo.nKeyField or KeyInfo.nAllField values were computed
** incorrectly.
*/
static void vdbeAssertFieldCountWithinLimits(
  int nKey, const void *pKey,   /* The record to verify */ 
  const KeyInfo *pKeyInfo       /* Compare size with this KeyInfo */
){
  int nField = 0;
................................................................................
  idx = getVarint32(aKey, szHdr);
  assert( nKey>=0 );
  assert( szHdr<=(u32)nKey );
  while( idx<szHdr ){
    idx += getVarint32(aKey+idx, notUsed);
    nField++;
  }
  assert( nField <= pKeyInfo->nAllField );
}
#else
# define vdbeAssertFieldCountWithinLimits(A,B,C)
#endif

/*
** Both *pMem1 and *pMem2 contain string values. Compare the two values
................................................................................
      pPKey2->errCode = (u8)SQLITE_CORRUPT_BKPT;
      return 0;  /* Corruption */
    }
    i = 0;
  }

  VVA_ONLY( mem1.szMalloc = 0; ) /* Only needed by assert() statements */
  assert( pPKey2->pKeyInfo->nAllField>=pPKey2->nField 
       || CORRUPT_DB );
  assert( pPKey2->pKeyInfo->aSortOrder!=0 );
  assert( pPKey2->pKeyInfo->nKeyField>0 );
  assert( idx1<=szHdr1 || CORRUPT_DB );
  do{
    u32 serial_type;

    /* RHS is an integer */
    if( pRhs->flags & MEM_Int ){
      serial_type = aKey1[idx1];
................................................................................
  ** buffer passed to varintRecordCompareInt() this makes it convenient to
  ** limit the size of the header to 64 bytes in cases where the first field
  ** is an integer.
  **
  ** The easiest way to enforce this limit is to consider only records with
  ** 13 fields or less. If the first field is an integer, the maximum legal
  ** header size is (12*5 + 1 + 1) bytes.  */
  if( p->pKeyInfo->nAllField<=13 ){
    int flags = p->aMem[0].flags;
    if( p->pKeyInfo->aSortOrder[0] ){
      p->r1 = 1;
      p->r2 = -1;
    }else{
      p->r1 = -1;
      p->r2 = 1;
................................................................................

  preupdate.v = v;
  preupdate.pCsr = pCsr;
  preupdate.op = op;
  preupdate.iNewReg = iReg;
  preupdate.keyinfo.db = db;
  preupdate.keyinfo.enc = ENC(db);
  preupdate.keyinfo.nKeyField = pTab->nCol;
  preupdate.keyinfo.aSortOrder = (u8*)&fakeSortOrder;
  preupdate.iKey1 = iKey1;
  preupdate.iKey2 = iKey2;
  preupdate.pTab = pTab;

  db->pPreUpdate = &preupdate;
  db->xPreUpdateCallback(db->pPreUpdateArg, db, op, zDb, zTbl, iKey1, iKey2);
  db->pPreUpdate = 0;
  sqlite3DbFree(db, preupdate.aRecord);
  vdbeFreeUnpacked(db, preupdate.keyinfo.nKeyField+1, preupdate.pUnpacked);
  vdbeFreeUnpacked(db, preupdate.keyinfo.nKeyField+1, preupdate.pNewUnpacked);
  if( preupdate.aNew ){
    int i;
    for(i=0; i<pCsr->nField; i++){
      sqlite3VdbeMemRelease(&preupdate.aNew[i]);
    }
    sqlite3DbFreeNN(db, preupdate.aNew);
  }
}
#endif /* SQLITE_ENABLE_PREUPDATE_HOOK */

      int nCol = pIdx->nColumn;   /* Number of index columns including rowid */
  
      nByte = sizeof(Mem) * nCol + ROUND8(sizeof(UnpackedRecord));
      pRec = (UnpackedRecord*)sqlite3DbMallocZero(db, nByte);
      if( pRec ){
        pRec->pKeyInfo = sqlite3KeyInfoOfIndex(p->pParse, pIdx);
        if( pRec->pKeyInfo ){
          assert( pRec->pKeyInfo->nField+pRec->pKeyInfo->nXField==nCol );
          assert( pRec->pKeyInfo->enc==ENC(db) );
          pRec->aMem = (Mem *)((u8*)pRec + ROUND8(sizeof(UnpackedRecord)));
          for(i=0; i<nCol; i++){
            pRec->aMem[i].flags = MEM_Null;
            pRec->aMem[i].db = db;
          }
        }else{
................................................................................
** Unless it is NULL, the argument must be an UnpackedRecord object returned
** by an earlier call to sqlite3Stat4ProbeSetValue(). This call deletes
** the object.
*/
void sqlite3Stat4ProbeFree(UnpackedRecord *pRec){
  if( pRec ){
    int i;
    int nCol = pRec->pKeyInfo->nField+pRec->pKeyInfo->nXField;
    Mem *aMem = pRec->aMem;
    sqlite3 *db = aMem[0].db;
    for(i=0; i<nCol; i++){
      sqlite3VdbeMemRelease(&aMem[i]);
    }
    sqlite3KeyInfoUnref(pRec->pKeyInfo);
    sqlite3DbFreeNN(db, pRec);

      int nCol = pIdx->nColumn;   /* Number of index columns including rowid */
  
      nByte = sizeof(Mem) * nCol + ROUND8(sizeof(UnpackedRecord));
      pRec = (UnpackedRecord*)sqlite3DbMallocZero(db, nByte);
      if( pRec ){
        pRec->pKeyInfo = sqlite3KeyInfoOfIndex(p->pParse, pIdx);
        if( pRec->pKeyInfo ){
          assert( pRec->pKeyInfo->nAllField==nCol );
          assert( pRec->pKeyInfo->enc==ENC(db) );
          pRec->aMem = (Mem *)((u8*)pRec + ROUND8(sizeof(UnpackedRecord)));
          for(i=0; i<nCol; i++){
            pRec->aMem[i].flags = MEM_Null;
            pRec->aMem[i].db = db;
          }
        }else{
................................................................................
** Unless it is NULL, the argument must be an UnpackedRecord object returned
** by an earlier call to sqlite3Stat4ProbeSetValue(). This call deletes
** the object.
*/
void sqlite3Stat4ProbeFree(UnpackedRecord *pRec){
  if( pRec ){
    int i;
    int nCol = pRec->pKeyInfo->nAllField;
    Mem *aMem = pRec->aMem;
    sqlite3 *db = aMem[0].db;
    for(i=0; i<nCol; i++){
      sqlite3VdbeMemRelease(&aMem[i]);
    }
    sqlite3KeyInfoUnref(pRec->pKeyInfo);
    sqlite3DbFreeNN(db, pRec);

  getVarint32(&p2[1], n2);
  res = memcmp(v1, v2, (MIN(n1, n2) - 13)/2);
  if( res==0 ){
    res = n1 - n2;
  }

  if( res==0 ){
    if( pTask->pSorter->pKeyInfo->nField>1 ){
      res = vdbeSorterCompareTail(
          pTask, pbKey2Cached, pKey1, nKey1, pKey2, nKey2
      );
    }
  }else{
    if( pTask->pSorter->pKeyInfo->aSortOrder[0] ){
      res = res * -1;
................................................................................
      if( *v1 & 0x80 ) res = -1;
    }else{
      if( *v2 & 0x80 ) res = +1;
    }
  }

  if( res==0 ){
    if( pTask->pSorter->pKeyInfo->nField>1 ){
      res = vdbeSorterCompareTail(
          pTask, pbKey2Cached, pKey1, nKey1, pKey2, nKey2
      );
    }
  }else if( pTask->pSorter->pKeyInfo->aSortOrder[0] ){
    res = res * -1;
  }
................................................................................

  return res;
}

/*
** Initialize the temporary index cursor just opened as a sorter cursor.
**
** Usually, the sorter module uses the value of (pCsr->pKeyInfo->nField)
** to determine the number of fields that should be compared from the
** records being sorted. However, if the value passed as argument nField
** is non-zero and the sorter is able to guarantee a stable sort, nField
** is used instead. This is used when sorting records for a CREATE INDEX
** statement. In this case, keys are always delivered to the sorter in
** order of the primary key, which happens to be make up the final part 
** of the records being sorted. So if the sort is stable, there is never
................................................................................
  if( nWorker>=SORTER_MAX_MERGE_COUNT ){
    nWorker = SORTER_MAX_MERGE_COUNT-1;
  }
#endif

  assert( pCsr->pKeyInfo && pCsr->pBtx==0 );
  assert( pCsr->eCurType==CURTYPE_SORTER );
  szKeyInfo = sizeof(KeyInfo) + (pCsr->pKeyInfo->nField-1)*sizeof(CollSeq*);
  sz = sizeof(VdbeSorter) + nWorker * sizeof(SortSubtask);

  pSorter = (VdbeSorter*)sqlite3DbMallocZero(db, sz + szKeyInfo);
  pCsr->uc.pSorter = pSorter;
  if( pSorter==0 ){
    rc = SQLITE_NOMEM_BKPT;
  }else{
    pSorter->pKeyInfo = pKeyInfo = (KeyInfo*)((u8*)pSorter + sz);
    memcpy(pKeyInfo, pCsr->pKeyInfo, szKeyInfo);
    pKeyInfo->db = 0;
    if( nField && nWorker==0 ){
      pKeyInfo->nXField += (pKeyInfo->nField - nField);
      pKeyInfo->nField = nField;
    }
    pSorter->pgsz = pgsz = sqlite3BtreeGetPageSize(db->aDb[0].pBt);
    pSorter->nTask = nWorker + 1;
    pSorter->iPrev = (u8)(nWorker - 1);
    pSorter->bUseThreads = (pSorter->nTask>1);
    pSorter->db = db;
    for(i=0; i<pSorter->nTask; i++){
................................................................................
        assert( pSorter->iMemory==0 );
        pSorter->nMemory = pgsz;
        pSorter->list.aMemory = (u8*)sqlite3Malloc(pgsz);
        if( !pSorter->list.aMemory ) rc = SQLITE_NOMEM_BKPT;
      }
    }

    if( (pKeyInfo->nField+pKeyInfo->nXField)<13 
     && (pKeyInfo->aColl[0]==0 || pKeyInfo->aColl[0]==db->pDfltColl)
    ){
      pSorter->typeMask = SORTER_TYPE_INTEGER | SORTER_TYPE_TEXT;
    }
  }

  return rc;
................................................................................
** structure at pTask->pUnpacked. Return SQLITE_OK if successful (or 
** if no allocation was required), or SQLITE_NOMEM otherwise.
*/
static int vdbeSortAllocUnpacked(SortSubtask *pTask){
  if( pTask->pUnpacked==0 ){
    pTask->pUnpacked = sqlite3VdbeAllocUnpackedRecord(pTask->pSorter->pKeyInfo);
    if( pTask->pUnpacked==0 ) return SQLITE_NOMEM_BKPT;
    pTask->pUnpacked->nField = pTask->pSorter->pKeyInfo->nField;
    pTask->pUnpacked->errCode = 0;
  }
  return SQLITE_OK;
}


/*

  getVarint32(&p2[1], n2);
  res = memcmp(v1, v2, (MIN(n1, n2) - 13)/2);
  if( res==0 ){
    res = n1 - n2;
  }

  if( res==0 ){
    if( pTask->pSorter->pKeyInfo->nKeyField>1 ){
      res = vdbeSorterCompareTail(
          pTask, pbKey2Cached, pKey1, nKey1, pKey2, nKey2
      );
    }
  }else{
    if( pTask->pSorter->pKeyInfo->aSortOrder[0] ){
      res = res * -1;
................................................................................
      if( *v1 & 0x80 ) res = -1;
    }else{
      if( *v2 & 0x80 ) res = +1;
    }
  }

  if( res==0 ){
    if( pTask->pSorter->pKeyInfo->nKeyField>1 ){
      res = vdbeSorterCompareTail(
          pTask, pbKey2Cached, pKey1, nKey1, pKey2, nKey2
      );
    }
  }else if( pTask->pSorter->pKeyInfo->aSortOrder[0] ){
    res = res * -1;
  }
................................................................................

  return res;
}

/*
** Initialize the temporary index cursor just opened as a sorter cursor.
**
** Usually, the sorter module uses the value of (pCsr->pKeyInfo->nKeyField)
** to determine the number of fields that should be compared from the
** records being sorted. However, if the value passed as argument nField
** is non-zero and the sorter is able to guarantee a stable sort, nField
** is used instead. This is used when sorting records for a CREATE INDEX
** statement. In this case, keys are always delivered to the sorter in
** order of the primary key, which happens to be make up the final part 
** of the records being sorted. So if the sort is stable, there is never
................................................................................
  if( nWorker>=SORTER_MAX_MERGE_COUNT ){
    nWorker = SORTER_MAX_MERGE_COUNT-1;
  }
#endif

  assert( pCsr->pKeyInfo && pCsr->pBtx==0 );
  assert( pCsr->eCurType==CURTYPE_SORTER );
  szKeyInfo = sizeof(KeyInfo) + (pCsr->pKeyInfo->nKeyField-1)*sizeof(CollSeq*);
  sz = sizeof(VdbeSorter) + nWorker * sizeof(SortSubtask);

  pSorter = (VdbeSorter*)sqlite3DbMallocZero(db, sz + szKeyInfo);
  pCsr->uc.pSorter = pSorter;
  if( pSorter==0 ){
    rc = SQLITE_NOMEM_BKPT;
  }else{
    pSorter->pKeyInfo = pKeyInfo = (KeyInfo*)((u8*)pSorter + sz);
    memcpy(pKeyInfo, pCsr->pKeyInfo, szKeyInfo);
    pKeyInfo->db = 0;
    if( nField && nWorker==0 ){

      pKeyInfo->nKeyField = nField;
    }
    pSorter->pgsz = pgsz = sqlite3BtreeGetPageSize(db->aDb[0].pBt);
    pSorter->nTask = nWorker + 1;
    pSorter->iPrev = (u8)(nWorker - 1);
    pSorter->bUseThreads = (pSorter->nTask>1);
    pSorter->db = db;
    for(i=0; i<pSorter->nTask; i++){
................................................................................
        assert( pSorter->iMemory==0 );
        pSorter->nMemory = pgsz;
        pSorter->list.aMemory = (u8*)sqlite3Malloc(pgsz);
        if( !pSorter->list.aMemory ) rc = SQLITE_NOMEM_BKPT;
      }
    }

    if( pKeyInfo->nAllField<13 
     && (pKeyInfo->aColl[0]==0 || pKeyInfo->aColl[0]==db->pDfltColl)
    ){
      pSorter->typeMask = SORTER_TYPE_INTEGER | SORTER_TYPE_TEXT;
    }
  }

  return rc;
................................................................................
** structure at pTask->pUnpacked. Return SQLITE_OK if successful (or 
** if no allocation was required), or SQLITE_NOMEM otherwise.
*/
static int vdbeSortAllocUnpacked(SortSubtask *pTask){
  if( pTask->pUnpacked==0 ){
    pTask->pUnpacked = sqlite3VdbeAllocUnpackedRecord(pTask->pSorter->pKeyInfo);
    if( pTask->pUnpacked==0 ) return SQLITE_NOMEM_BKPT;
    pTask->pUnpacked->nField = pTask->pSorter->pKeyInfo->nKeyField;
    pTask->pUnpacked->errCode = 0;
  }
  return SQLITE_OK;
}


/*