return;
  }

  /* Ensure the default expression is something that sqlite3ValueFromExpr()
  ** can handle (i.e. not CURRENT_TIME etc.)
  */
  if( pDflt ){
    sqlite3_value *pVal;
    if( sqlite3ValueFromExpr(db, pDflt, SQLITE_UTF8, SQLITE_AFF_NONE, &pVal) ){
      db->mallocFailed = 1;
      return;
    }
    if( !pVal ){
      sqlite3ErrorMsg(pParse, "Cannot add a column with non-constant default");
      return;

    return;
  }

  /* Ensure the default expression is something that sqlite3ValueFromExpr()
  ** can handle (i.e. not CURRENT_TIME etc.)
  */
  if( pDflt ){
    sqlite3_value *pVal = 0;
    if( sqlite3ValueFromExpr(db, pDflt, SQLITE_UTF8, SQLITE_AFF_NONE, &pVal) ){
      db->mallocFailed = 1;
      return;
    }
    if( !pVal ){
      sqlite3ErrorMsg(pParse, "Cannot add a column with non-constant default");
      return;

char *sqlite3StrAccumFinish(StrAccum*);
void sqlite3StrAccumReset(StrAccum*);
void sqlite3SelectDestInit(SelectDest*,int,int);
Expr *sqlite3CreateColumnExpr(sqlite3 *, SrcList *, int, int);

void sqlite3BackupRestart(sqlite3_backup *);
void sqlite3BackupUpdate(sqlite3_backup *, Pgno, const u8 *);





/*
** The interface to the LEMON-generated parser
*/
void *sqlite3ParserAlloc(void*(*)(size_t));
void sqlite3ParserFree(void*, void(*)(void*));
void sqlite3Parser(void*, int, Token, Parse*);

char *sqlite3StrAccumFinish(StrAccum*);
void sqlite3StrAccumReset(StrAccum*);
void sqlite3SelectDestInit(SelectDest*,int,int);
Expr *sqlite3CreateColumnExpr(sqlite3 *, SrcList *, int, int);

void sqlite3BackupRestart(sqlite3_backup *);
void sqlite3BackupUpdate(sqlite3_backup *, Pgno, const u8 *);

int sqlite3Stat4ProbeSetValue(Parse*, UnpackedRecord*, Expr*, u8, int, int*);
void sqlite3Stat4ProbeFree(UnpackedRecord*);
int sqlite3Stat4ProbeNew(Parse*, Index*, UnpackedRecord**);

/*
** The interface to the LEMON-generated parser
*/
void *sqlite3ParserAlloc(void*(*)(size_t));
void sqlite3ParserFree(void*, void(*)(void*));
void sqlite3Parser(void*, int, Token, Parse*);

** on register iReg. This is used when an equivalent integer value is 
** stored in place of an 8-byte floating point value in order to save 
** space.
*/
void sqlite3ColumnDefault(Vdbe *v, Table *pTab, int i, int iReg){
  assert( pTab!=0 );
  if( !pTab->pSelect ){
    sqlite3_value *pValue;
    u8 enc = ENC(sqlite3VdbeDb(v));
    Column *pCol = &pTab->aCol[i];
    VdbeComment((v, "%s.%s", pTab->zName, pCol->zName));
    assert( i<pTab->nCol );
    sqlite3ValueFromExpr(sqlite3VdbeDb(v), pCol->pDflt, enc, 
                         pCol->affinity, &pValue);
    if( pValue ){

** on register iReg. This is used when an equivalent integer value is 
** stored in place of an 8-byte floating point value in order to save 
** space.
*/
void sqlite3ColumnDefault(Vdbe *v, Table *pTab, int i, int iReg){
  assert( pTab!=0 );
  if( !pTab->pSelect ){
    sqlite3_value *pValue = 0;
    u8 enc = ENC(sqlite3VdbeDb(v));
    Column *pCol = &pTab->aCol[i];
    VdbeComment((v, "%s.%s", pTab->zName, pCol->zName));
    assert( i<pTab->nCol );
    sqlite3ValueFromExpr(sqlite3VdbeDb(v), pCol->pDflt, enc, 
                         pCol->affinity, &pValue);
    if( pValue ){

  if( p ){
    p->flags = MEM_Null;
    p->type = SQLITE_NULL;
    p->db = db;
  }
  return p;
}






/*
** Create a new sqlite3_value object, containing the value of pExpr.
**
** This only works for very simple expressions that consist of one constant
** token (i.e. "5", "5.1", "'a string'"). If the expression can
** be converted directly into a value, then the value is allocated and
................................................................................
    pExpr = pExpr->pLeft;
    op = pExpr->op;
    negInt = -1;
    zNeg = "-";
  }

  if( op==TK_STRING || op==TK_FLOAT || op==TK_INTEGER ){
    pVal = sqlite3ValueNew(db);
    if( pVal==0 ) goto no_mem;
    if( ExprHasProperty(pExpr, EP_IntValue) ){
      sqlite3VdbeMemSetInt64(pVal, (i64)pExpr->u.iValue*negInt);
    }else{
      zVal = sqlite3MPrintf(db, "%s%s", zNeg, pExpr->u.zToken);
      if( zVal==0 ) goto no_mem;
      sqlite3ValueSetStr(pVal, -1, zVal, SQLITE_UTF8, SQLITE_DYNAMIC);
................................................................................
      }else{
        pVal->u.i = -pVal->u.i;
      }
      pVal->r = -pVal->r;
      sqlite3ValueApplyAffinity(pVal, affinity, enc);
    }
  }else if( op==TK_NULL ){
    pVal = sqlite3ValueNew(db);
    if( pVal==0 ) goto no_mem;
  }
#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);
    if( !pVal ) goto no_mem;
    zVal = &pExpr->u.zToken[2];
    nVal = sqlite3Strlen30(zVal)-1;
    assert( zVal[nVal]=='\'' );
    sqlite3VdbeMemSetStr(pVal, sqlite3HexToBlob(db, zVal, nVal), nVal/2,
                         0, SQLITE_DYNAMIC);
  }
................................................................................
  }
  *ppVal = pVal;
  return SQLITE_OK;

no_mem:
  db->mallocFailed = 1;
  sqlite3DbFree(db, zVal);
  sqlite3ValueFree(pVal);
  *ppVal = 0;
  return SQLITE_NOMEM;
}






























































































/*
** Change the string value of an sqlite3_value object
*/
void sqlite3ValueSetStr(
  sqlite3_value *v,     /* Value to be set */
  int n,                /* Length of string z */
  const void *z,        /* Text of the new string */

  if( p ){
    p->flags = MEM_Null;
    p->type = SQLITE_NULL;
    p->db = db;
  }
  return p;
}

static sqlite3_value *valueNew(sqlite3 *db, sqlite3_value *pOld){
  if( pOld ) return pOld;
  return sqlite3ValueNew(db);
}

/*
** Create a new sqlite3_value object, containing the value of pExpr.
**
** This only works for very simple expressions that consist of one constant
** token (i.e. "5", "5.1", "'a string'"). If the expression can
** be converted directly into a value, then the value is allocated and
................................................................................
    pExpr = pExpr->pLeft;
    op = pExpr->op;
    negInt = -1;
    zNeg = "-";
  }

  if( op==TK_STRING || op==TK_FLOAT || op==TK_INTEGER ){
    pVal = valueNew(db, *ppVal);
    if( pVal==0 ) goto no_mem;
    if( ExprHasProperty(pExpr, EP_IntValue) ){
      sqlite3VdbeMemSetInt64(pVal, (i64)pExpr->u.iValue*negInt);
    }else{
      zVal = sqlite3MPrintf(db, "%s%s", zNeg, pExpr->u.zToken);
      if( zVal==0 ) goto no_mem;
      sqlite3ValueSetStr(pVal, -1, zVal, SQLITE_UTF8, SQLITE_DYNAMIC);
................................................................................
      }else{
        pVal->u.i = -pVal->u.i;
      }
      pVal->r = -pVal->r;
      sqlite3ValueApplyAffinity(pVal, affinity, enc);
    }
  }else if( op==TK_NULL ){
    pVal = valueNew(db, *ppVal);
    if( pVal==0 ) goto no_mem;
  }
#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 = valueNew(db, *ppVal);
    if( !pVal ) goto no_mem;
    zVal = &pExpr->u.zToken[2];
    nVal = sqlite3Strlen30(zVal)-1;
    assert( zVal[nVal]=='\'' );
    sqlite3VdbeMemSetStr(pVal, sqlite3HexToBlob(db, zVal, nVal), nVal/2,
                         0, SQLITE_DYNAMIC);
  }
................................................................................
  }
  *ppVal = pVal;
  return SQLITE_OK;

no_mem:
  db->mallocFailed = 1;
  sqlite3DbFree(db, zVal);
  if( *ppVal==0 ) sqlite3ValueFree(pVal);
  *ppVal = 0;
  return SQLITE_NOMEM;
}

#ifdef SQLITE_ENABLE_STAT4
int sqlite3Stat4ProbeSetValue(
  Parse *pParse,                  /* Parse context */
  UnpackedRecord *pRec,           /* Set field in this probe */
  Expr *pExpr,                    /* The expression to extract a value from */
  u8 affinity,                    /* Affinity to use */
  int iVal,                       /* Array element to populate */
  int *pbOk                       /* OUT: True if value was extracted */
){
  int rc = SQLITE_OK;
  sqlite3_value *pVal = &pRec->aMem[iVal];

#if 0
  if( iVal>0 ){ *pbOk = 0; return SQLITE_OK; }
#endif

  if( !pExpr ){
    sqlite3VdbeMemSetNull((Mem*)pVal);
    *pbOk = 1;
  }else if( pExpr->op==TK_VARIABLE
        || (pExpr->op==TK_REGISTER && pExpr->op2==TK_VARIABLE)
  ){
    Vdbe *v;
    int iVar = pExpr->iColumn;
    sqlite3VdbeSetVarmask(pParse->pVdbe, iVar);
    if( v = pParse->pReprepare ){
      rc = sqlite3VdbeMemCopy((Mem*)pVal, &v->aVar[iVal-1]);
      if( rc==SQLITE_OK ){
        sqlite3ValueApplyAffinity(pVal, affinity, SQLITE_UTF8);
      }
      pVal->db = pParse->db;
      *pbOk = 1;
      sqlite3VdbeMemStoreType((Mem*)pVal);
    }else{
      *pbOk = 0;
    }
  }else{
    sqlite3 *db = pRec->aMem[0].db;
    rc = sqlite3ValueFromExpr(db, pExpr, ENC(db), affinity, &pVal);
    *pbOk = (pVal!=0);
  }
  assert( pVal==0 || pVal->db==pParse->db );
  return rc;
}

void sqlite3Stat4ProbeFree(UnpackedRecord *pRec){
  if( pRec ){
    int i;
    Mem *aMem = pRec->aMem;
    sqlite3 *db = aMem[0].db;
    for(i=0; i<pRec->pKeyInfo->nField; i++){
      sqlite3DbFree(db, aMem[i].zMalloc);
    }
    sqlite3DbFree(db, pRec->pKeyInfo);
    sqlite3DbFree(db, pRec);
  }
}

int sqlite3Stat4ProbeNew(
  Parse *pParse,                  /* Parse context */
  Index *pIdx,                    /* Allocate record for this index */
  UnpackedRecord **ppRec          /* OUT: Allocated record */
){
  sqlite3 *db = pParse->db;       /* Database handle */
  UnpackedRecord *pRec;           /* Return value */
  int nByte;                      /* Bytes of space to allocate */
  int i;                          /* Counter variable */

  assert( *ppRec==0 );
  if( pIdx->nSample==0 ) return SQLITE_OK;

  nByte = sizeof(Mem) * pIdx->nColumn + sizeof(UnpackedRecord);
  *ppRec = pRec = (UnpackedRecord*)sqlite3DbMallocZero(db, nByte);
  if( !pRec ) return SQLITE_NOMEM;
  pRec->pKeyInfo = sqlite3IndexKeyinfo(pParse, pIdx);
  if( !pRec->pKeyInfo ){
    sqlite3DbFree(db, pRec);
    *ppRec = 0;
    return SQLITE_NOMEM;
  }
  pRec->pKeyInfo->enc = ENC(pParse->db);
  pRec->flags = UNPACKED_PREFIX_MATCH;
  pRec->aMem = (Mem *)&pRec[1];
  for(i=0; i<pIdx->nColumn; i++){
    pRec->aMem[i].flags = MEM_Null;
    pRec->aMem[i].type = SQLITE_NULL;
    pRec->aMem[i].db = db;
  }

  return SQLITE_OK;
}
#endif /* ifdef SQLITE_ENABLE_STAT4 */

/*
** Change the string value of an sqlite3_value object
*/
void sqlite3ValueSetStr(
  sqlite3_value *v,     /* Value to be set */
  int n,                /* Length of string z */
  const void *z,        /* Text of the new string */

*/
struct WhereLoopBuilder {
  WhereInfo *pWInfo;        /* Information about this WHERE */
  WhereClause *pWC;         /* WHERE clause terms */
  ExprList *pOrderBy;       /* ORDER BY clause */
  WhereLoop *pNew;          /* Template WhereLoop */
  WhereOrSet *pOrSet;       /* Record best loops here, if not NULL */





};

/*
** The WHERE clause processing routine has two halves.  The
** first part does the start of the WHERE loop and the second
** half does the tail of the WHERE loop.  An instance of
** this structure is returned by the first half and passed
................................................................................
**    aStat[1]      Est. number of rows equal to pVal
**
** Return SQLITE_OK on success.
*/
static int whereKeyStats(
  Parse *pParse,              /* Database connection */
  Index *pIdx,                /* Index to consider domain of */
  sqlite3_value *pVal,        /* Value to consider */
  int roundUp,                /* Round up if true.  Round down if false */
  tRowcnt *aStat              /* OUT: stats written here */
){
  IndexSample *aSample = pIdx->aSample;
  UnpackedRecord rec;
  int i;
  int isEq = 0;

  if( pVal==0 ) return SQLITE_ERROR;

  memset(&rec, 0, sizeof(UnpackedRecord));
  rec.pKeyInfo = sqlite3IndexKeyinfo(pParse, pIdx);
  if( rec.pKeyInfo==0 ) return SQLITE_NOMEM;
  rec.pKeyInfo->enc = ENC(pParse->db);
  rec.nField = 1;
  rec.flags = UNPACKED_PREFIX_MATCH;
  rec.aMem = pVal;

  for(i=0; i<pIdx->nSample; i++){
    int res = sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, &rec);
    if( res>=0 ){
      isEq = (res==0);
      break;
    }
  }
  sqlite3DbFree(pParse->db, rec.pKeyInfo);

  /* At this point, aSample[i] is the first sample that is greater than
  ** or equal to pVal.  Or if i==pIdx->nSample, then all samples are less
  ** than pVal.  If aSample[i]==pVal, then isEq==1.
  */
  if( isEq ){
    assert( i<pIdx->nSample );
................................................................................
    }
    aStat[0] = iLower + iGap;
  }
  return SQLITE_OK;
}
#endif /* SQLITE_ENABLE_STAT4 */

/*
** If expression pExpr represents a literal value, set *pp to point to
** an sqlite3_value structure containing the same value, with affinity
** aff applied to it, before returning. It is the responsibility of the 
** caller to eventually release this structure by passing it to 
** sqlite3ValueFree().
**
** If the current parse is a recompile (sqlite3Reprepare()) and pExpr
** is an SQL variable that currently has a non-NULL value bound to it,
** create an sqlite3_value structure containing this value, again with
** affinity aff applied to it, instead.
**
** If neither of the above apply, set *pp to NULL.
**
** If an error occurs, return an error code. Otherwise, SQLITE_OK.
*/
#ifdef SQLITE_ENABLE_STAT4
static int valueFromExpr(
  Parse *pParse, 
  Expr *pExpr, 
  u8 aff, 
  sqlite3_value **pp
){
  if( pExpr->op==TK_VARIABLE
   || (pExpr->op==TK_REGISTER && pExpr->op2==TK_VARIABLE)
  ){
    int iVar = pExpr->iColumn;
    sqlite3VdbeSetVarmask(pParse->pVdbe, iVar);
    *pp = sqlite3VdbeGetBoundValue(pParse->pReprepare, iVar, aff);
    return SQLITE_OK;
  }
  return sqlite3ValueFromExpr(pParse->db, pExpr, ENC(pParse->db), aff, pp);
}
#endif

/*
** This function is used to estimate the number of rows that will be visited
** by scanning an index for a range of values. The range may have an upper
** bound, a lower bound, or both. The WHERE clause terms that set the upper
** and lower bounds are represented by pLower and pUpper respectively. For
** example, assuming that index p is on t1(a):
**
................................................................................
** In the absence of sqlite_stat3 ANALYZE data, each range inequality
** reduces the search space by a factor of 4.  Hence a single constraint (x>?)
** results in a return of 4 and a range constraint (x>? AND x<?) results
** in a return of 16.
*/
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 */
  WhereCost *pRangeDiv /* OUT: Reduce search space by this divisor */
){
  int rc = SQLITE_OK;

#ifdef SQLITE_ENABLE_STAT4





  if( nEq==0 && p->nSample && OptimizationEnabled(pParse->db, SQLITE_Stat3) ){
    sqlite3_value *pRangeVal;


    tRowcnt iLower = 0;
    tRowcnt iUpper = p->aiRowEst[0];
    tRowcnt a[2];
    u8 aff = p->pTable->aCol[p->aiColumn[0]].affinity;

    if( pLower ){

      Expr *pExpr = pLower->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pRangeVal);
      assert( (pLower->eOperator & (WO_GT|WO_GE))!=0 );


      if( rc==SQLITE_OK
       && whereKeyStats(pParse, p, pRangeVal, 0, a)==SQLITE_OK
      ){
        iLower = a[0];
        if( (pLower->eOperator & WO_GT)!=0 ) iLower += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK && pUpper ){

      Expr *pExpr = pUpper->pExpr->pRight;
      rc = valueFromExpr(pParse, pExpr, aff, &pRangeVal);
      assert( (pUpper->eOperator & (WO_LT|WO_LE))!=0 );


      if( rc==SQLITE_OK
       && whereKeyStats(pParse, p, pRangeVal, 1, a)==SQLITE_OK
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];
      }
      sqlite3ValueFree(pRangeVal);
    }
    if( rc==SQLITE_OK ){
      WhereCost iBase = whereCost(p->aiRowEst[0]);
      if( iUpper>iLower ){
        iBase -= whereCost(iUpper - iLower);
      }



      *pRangeDiv = iBase;

      WHERETRACE(0x100, ("range scan regions: %u..%u  div=%d\n",
                         (u32)iLower, (u32)iUpper, *pRangeDiv));
      return SQLITE_OK;
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(p);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *pRangeDiv = 0;
  /* TUNING:  Each inequality constraint reduces the search space 4-fold.
  ** A BETWEEN operator, therefore, reduces the search space 16-fold */
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ){
................................................................................
** 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.
*/
static 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 */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  sqlite3_value *pRhs = 0;  /* VALUE on right-hand side of pTerm */


  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  tRowcnt a[2];             /* Statistics */




  assert( p->aSample!=0 );
  assert( p->nSample>0 );













  aff = p->pTable->aCol[p->aiColumn[0]].affinity;
  if( pExpr ){
    rc = valueFromExpr(pParse, pExpr, aff, &pRhs);
    if( rc ) goto whereEqualScanEst_cancel;
  }else{
    pRhs = sqlite3ValueNew(pParse->db);



  }
  if( pRhs==0 ) return SQLITE_NOTFOUND;



  rc = whereKeyStats(pParse, p, pRhs, 0, a);
  if( rc==SQLITE_OK ){
    WHERETRACE(0x100,("equality scan regions: %d\n", (int)a[1]));
    *pnRow = a[1];


  }
whereEqualScanEst_cancel:
  sqlite3ValueFree(pRhs);


  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT4) */

#ifdef SQLITE_ENABLE_STAT4
/*
** Estimate the number of rows that will be returned based on
................................................................................
** 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.
*/
static 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,...)" */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){


  int rc = SQLITE_OK;     /* Subfunction return code */
  tRowcnt nEst;           /* Number of rows for a single term */
  tRowcnt nRowEst = 0;    /* New estimate of the number of rows */
  int i;                  /* Loop counter */

  assert( p->aSample!=0 );
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    nEst = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, p, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;

  }

  if( rc==SQLITE_OK ){
    if( nRowEst > p->aiRowEst[0] ) nRowEst = p->aiRowEst[0];



    *pnRow = nRowEst;

    WHERETRACE(0x100,("IN row estimate: est=%g\n", nRowEst));
  }

  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT4) */

/*
** Disable a term in the WHERE clause.  Except, do not disable the term
** if it controls a LEFT OUTER JOIN and it did not originate in the ON
................................................................................
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;
  saved_nOut = pNew->nOut;
  pNew->rSetup = 0;
  rLogSize = estLog(whereCost(pProbe->aiRowEst[0]));
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 0;
    if( pTerm->prereqRight & pNew->maskSelf ) continue;
#ifdef SQLITE_ENABLE_STAT4


    if( (pTerm->wtFlags & TERM_VNULL)!=0 && pSrc->pTab->aCol[iCol].notNull ){
      continue; /* skip IS NOT NULL constraints on a NOT NULL column */
    }
#endif


    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->nLTerm = saved_nLTerm;
    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
    pNew->aLTerm[pNew->nLTerm++] = pTerm;
    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    pNew->rRun = rLogSize; /* Baseline cost is log2(N).  Adjustments below */
................................................................................
      pTop = pTerm;
      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
      WhereCost rDiv;
      whereRangeScanEst(pParse, pProbe, pNew->u.btree.nEq,
                        pBtm, pTop, &rDiv);
      pNew->nOut = saved_nOut>rDiv+10 ? saved_nOut - rDiv : 10;
    }
#ifdef SQLITE_ENABLE_STAT4
    if( pNew->u.btree.nEq==1 && pProbe->nSample
     &&  OptimizationEnabled(db, SQLITE_Stat3) ){
      tRowcnt nOut = 0;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        testcase( pTerm->eOperator & WO_EQ );
        testcase( pTerm->eOperator & WO_ISNULL );
        rc = whereEqualScanEst(pParse, pProbe, pTerm->pExpr->pRight, &nOut);


      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pTerm->pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pProbe, pTerm->pExpr->x.pList, &nOut);
      }
      assert( nOut==0 || rc==SQLITE_OK );
      if( nOut ) pNew->nOut = whereCost(nOut);
    }
#endif
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
      /* Each row involves a step of the index, then a binary search of
................................................................................
    /* TBD: Adjust nOut for additional constraints */
    rc = whereLoopInsert(pBuilder, pNew);
    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
     && pNew->u.btree.nEq<(pProbe->nColumn + (pProbe->zName!=0))
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
    }




  }
  pNew->prereq = saved_prereq;
  pNew->u.btree.nEq = saved_nEq;
  pNew->wsFlags = saved_wsFlags;
  pNew->nOut = saved_nOut;
  pNew->nLTerm = saved_nLTerm;
  return rc;
................................................................................
          ** which we will simplify to just N*log2(N) */
          pNew->rRun = rSize + rLogSize;
        }
        rc = whereLoopInsert(pBuilder, pNew);
        if( rc ) break;
      }
    }




    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);






    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;
  }
  return rc;
}

*/
struct WhereLoopBuilder {
  WhereInfo *pWInfo;        /* Information about this WHERE */
  WhereClause *pWC;         /* WHERE clause terms */
  ExprList *pOrderBy;       /* ORDER BY clause */
  WhereLoop *pNew;          /* Template WhereLoop */
  WhereOrSet *pOrSet;       /* Record best loops here, if not NULL */
#ifdef SQLITE_ENABLE_STAT4
  UnpackedRecord *pRec;     /* Probe for stat4 (if required) */
  int nRecValid;            /* Number of valid fields currently in pRec */
  tRowcnt nMaxRowcnt;       /* If !=0, the maximum estimated row count */
#endif
};

/*
** The WHERE clause processing routine has two halves.  The
** first part does the start of the WHERE loop and the second
** half does the tail of the WHERE loop.  An instance of
** this structure is returned by the first half and passed
................................................................................
**    aStat[1]      Est. number of rows equal to pVal
**
** Return SQLITE_OK on success.
*/
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;

  int i;
  int isEq = 0;











  for(i=0; i<pIdx->nSample; i++){
    int res = sqlite3VdbeRecordCompare(aSample[i].n, aSample[i].p, pRec);
    if( res>=0 ){
      isEq = (res==0);
      break;
    }
  }


  /* At this point, aSample[i] is the first sample that is greater than
  ** or equal to pVal.  Or if i==pIdx->nSample, then all samples are less
  ** than pVal.  If aSample[i]==pVal, then isEq==1.
  */
  if( isEq ){
    assert( i<pIdx->nSample );
................................................................................
    }
    aStat[0] = iLower + iGap;
  }
  return SQLITE_OK;
}
#endif /* SQLITE_ENABLE_STAT4 */




































/*
** This function is used to estimate the number of rows that will be visited
** by scanning an index for a range of values. The range may have an upper
** bound, a lower bound, or both. The WHERE clause terms that set the upper
** and lower bounds are represented by pLower and pUpper respectively. For
** example, assuming that index p is on t1(a):
**
................................................................................
** In the absence of sqlite_stat3 ANALYZE data, each range inequality
** reduces the search space by a factor of 4.  Hence a single constraint (x>?)
** results in a return of 4 and a range constraint (x>? AND x<?) results
** in a return of 16.
*/
static int whereRangeScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,

  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 */
  WhereCost *pRangeDiv /* OUT: Reduce search space by this divisor */
){
  int rc = SQLITE_OK;

#ifdef SQLITE_ENABLE_STAT4
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nEq = pBuilder->pNew->u.btree.nEq;

  if( nEq==pBuilder->nRecValid 
   && p->nSample 
   && OptimizationEnabled(pParse->db, SQLITE_Stat3) 

  ){
    UnpackedRecord *pRec = pBuilder->pRec;
    tRowcnt iLower = 0;
    tRowcnt iUpper = p->aiRowEst[0];
    tRowcnt a[2];
    u8 aff = p->pTable->aCol[p->aiColumn[0]].affinity;

    if( pLower ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pLower->pExpr->pRight;

      assert( (pLower->eOperator & (WO_GT|WO_GE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, pRec, pExpr, aff, nEq, &bOk);
      pRec->nField = nEq+1;
      if( rc==SQLITE_OK && bOk
       && whereKeyStats(pParse, p, pRec, 0, a)==SQLITE_OK
      ){
        iLower = a[0];
        if( (pLower->eOperator & WO_GT)!=0 ) iLower += a[1];
      }

    }
    if( rc==SQLITE_OK && pUpper ){
      int bOk;                    /* True if value is extracted from pExpr */
      Expr *pExpr = pUpper->pExpr->pRight;

      assert( (pUpper->eOperator & (WO_LT|WO_LE))!=0 );
      rc = sqlite3Stat4ProbeSetValue(pParse, pRec, pExpr, aff, nEq, &bOk);
      pRec->nField = nEq+1;
      if( rc==SQLITE_OK && bOk
       && whereKeyStats(pParse, p, pRec, 1, a)==SQLITE_OK
      ){
        iUpper = a[0];
        if( (pUpper->eOperator & WO_LE)!=0 ) iUpper += a[1];
      }

    }
    if( rc==SQLITE_OK ){
      WhereCost iBase = whereCost(p->aiRowEst[0]);
      if( iUpper>iLower ){
        iBase -= whereCost(iUpper - iLower);
      }
      if( pBuilder->nMaxRowcnt && iBase<pBuilder->nMaxRowcnt ){
        *pRangeDiv = pBuilder->nMaxRowcnt;
      }else{
        *pRangeDiv = iBase;
      }
      WHERETRACE(0x100, ("range scan regions: %u..%u  div=%d\n",
                         (u32)iLower, (u32)iUpper, *pRangeDiv));
      return SQLITE_OK;
    }
  }
#else
  UNUSED_PARAMETER(pParse);
  UNUSED_PARAMETER(pBuilder);
  UNUSED_PARAMETER(nEq);
#endif
  assert( pLower || pUpper );
  *pRangeDiv = 0;
  /* TUNING:  Each inequality constraint reduces the search space 4-fold.
  ** A BETWEEN operator, therefore, reduces the search space 16-fold */
  if( pLower && (pLower->wtFlags & TERM_VNULL)==0 ){
................................................................................
** 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.
*/
static int whereEqualScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  Expr *pExpr,         /* Expression for VALUE in the x=VALUE constraint */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nEq = pBuilder->pNew->u.btree.nEq;
  UnpackedRecord *pRec = pBuilder->pRec;
  u8 aff;                   /* Column affinity */
  int rc;                   /* Subfunction return code */
  tRowcnt a[2];             /* Statistics */
  int bOk;

  assert( nEq>=1 );
  assert( nEq<=(p->nColumn+1) );
  assert( p->aSample!=0 );
  assert( p->nSample>0 );
  assert( pBuilder->nRecValid<nEq );

  /* If values are not available for all fields of the index to the left
  ** of this one, no estimate can be made. Return SQLITE_NOTFOUND. */
  if( pBuilder->nRecValid<(nEq-1) ){
    return SQLITE_NOTFOUND;
  }

  if( nEq>p->nColumn ){
    *pnRow = 1;
    return SQLITE_OK;
  }

  aff = p->pTable->aCol[p->aiColumn[0]].affinity;





  rc = sqlite3Stat4ProbeSetValue(pParse, pRec, pExpr, aff, nEq-1, &bOk);
  if( rc!=SQLITE_OK ) return rc;
  if( bOk==0 ) return SQLITE_NOTFOUND;


  pBuilder->nRecValid = nEq;
  pRec->nField = nEq;

  rc = whereKeyStats(pParse, p, pRec, 0, a);
  if( rc==SQLITE_OK ){
    WHERETRACE(0x100,("equality scan regions: %d\n", (int)a[1]));
    *pnRow = a[1];
    if( pBuilder->nMaxRowcnt && *pnRow>pBuilder->nMaxRowcnt ){
      *pnRow = pBuilder->nMaxRowcnt;
    }


  }

  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT4) */

#ifdef SQLITE_ENABLE_STAT4
/*
** Estimate the number of rows that will be returned based on
................................................................................
** 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.
*/
static int whereInScanEst(
  Parse *pParse,       /* Parsing & code generating context */
  WhereLoopBuilder *pBuilder,
  ExprList *pList,     /* The value list on the RHS of "x IN (v1,v2,v3,...)" */
  tRowcnt *pnRow       /* Write the revised row estimate here */
){
  Index *p = pBuilder->pNew->u.btree.pIndex;
  int nRecValid = pBuilder->nRecValid;
  int rc = SQLITE_OK;     /* Subfunction return code */
  tRowcnt nEst;           /* Number of rows for a single term */
  tRowcnt nRowEst = 0;    /* New estimate of the number of rows */
  int i;                  /* Loop counter */

  assert( p->aSample!=0 );
  for(i=0; rc==SQLITE_OK && i<pList->nExpr; i++){
    nEst = p->aiRowEst[0];
    rc = whereEqualScanEst(pParse, pBuilder, pList->a[i].pExpr, &nEst);
    nRowEst += nEst;
    pBuilder->nRecValid = nRecValid;
  }

  if( rc==SQLITE_OK ){
    if( nRowEst > p->aiRowEst[0] ) nRowEst = p->aiRowEst[0];
    if( pBuilder->nMaxRowcnt && nRowEst>pBuilder->nMaxRowcnt ){
      *pnRow = pBuilder->nMaxRowcnt;
    }else{
      *pnRow = nRowEst;
    }
    WHERETRACE(0x100,("IN row estimate: est=%g\n", nRowEst));
  }
  assert( pBuilder->nRecValid==nRecValid );
  return rc;
}
#endif /* defined(SQLITE_ENABLE_STAT4) */

/*
** Disable a term in the WHERE clause.  Except, do not disable the term
** if it controls a LEFT OUTER JOIN and it did not originate in the ON
................................................................................
  saved_wsFlags = pNew->wsFlags;
  saved_prereq = pNew->prereq;
  saved_nOut = pNew->nOut;
  pNew->rSetup = 0;
  rLogSize = estLog(whereCost(pProbe->aiRowEst[0]));
  for(; rc==SQLITE_OK && pTerm!=0; pTerm = whereScanNext(&scan)){
    int nIn = 0;

#ifdef SQLITE_ENABLE_STAT4
    int nRecValid = pBuilder->nRecValid;
    int nMaxRowcnt = pBuilder->nMaxRowcnt;
    if( (pTerm->wtFlags & TERM_VNULL)!=0 && pSrc->pTab->aCol[iCol].notNull ){
      continue; /* skip IS NOT NULL constraints on a NOT NULL column */
    }
#endif
    if( pTerm->prereqRight & pNew->maskSelf ) continue;

    pNew->wsFlags = saved_wsFlags;
    pNew->u.btree.nEq = saved_nEq;
    pNew->nLTerm = saved_nLTerm;
    if( whereLoopResize(db, pNew, pNew->nLTerm+1) ) break; /* OOM */
    pNew->aLTerm[pNew->nLTerm++] = pTerm;
    pNew->prereq = (saved_prereq | pTerm->prereqRight) & ~pNew->maskSelf;
    pNew->rRun = rLogSize; /* Baseline cost is log2(N).  Adjustments below */
................................................................................
      pTop = pTerm;
      pBtm = (pNew->wsFlags & WHERE_BTM_LIMIT)!=0 ?
                     pNew->aLTerm[pNew->nLTerm-2] : 0;
    }
    if( pNew->wsFlags & WHERE_COLUMN_RANGE ){
      /* Adjust nOut and rRun for STAT3 range values */
      WhereCost rDiv;

      whereRangeScanEst(pParse, pBuilder, pBtm, pTop, &rDiv);
      pNew->nOut = saved_nOut>rDiv+10 ? saved_nOut - rDiv : 10;
    }
#ifdef SQLITE_ENABLE_STAT4
    if( nInMul==0 && pProbe->nSample && OptimizationEnabled(db, SQLITE_Stat3) ){
      Expr *pExpr = pTerm->pExpr;
      tRowcnt nOut = 0;
      if( (pTerm->eOperator & (WO_EQ|WO_ISNULL))!=0 ){
        testcase( pTerm->eOperator & WO_EQ );
        testcase( pTerm->eOperator & WO_ISNULL );
        rc = whereEqualScanEst(pParse, pBuilder, pExpr->pRight, &nOut);
        assert( nOut==0||pBuilder->nMaxRowcnt==0||nOut<=pBuilder->nMaxRowcnt);
        if( nOut ) pBuilder->nMaxRowcnt = nOut;
      }else if( (pTerm->eOperator & WO_IN)
             &&  !ExprHasProperty(pExpr, EP_xIsSelect)  ){
        rc = whereInScanEst(pParse, pBuilder, pExpr->x.pList, &nOut);
      }
      assert( nOut==0 || rc==SQLITE_OK );
      if( nOut ) pNew->nOut = whereCost(nOut);
    }
#endif
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
      /* Each row involves a step of the index, then a binary search of
................................................................................
    /* TBD: Adjust nOut for additional constraints */
    rc = whereLoopInsert(pBuilder, pNew);
    if( (pNew->wsFlags & WHERE_TOP_LIMIT)==0
     && pNew->u.btree.nEq<(pProbe->nColumn + (pProbe->zName!=0))
    ){
      whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, nInMul+nIn);
    }
#ifdef SQLITE_ENABLE_STAT4
    pBuilder->nRecValid = nRecValid;
    pBuilder->nMaxRowcnt = nMaxRowcnt;
#endif
  }
  pNew->prereq = saved_prereq;
  pNew->u.btree.nEq = saved_nEq;
  pNew->wsFlags = saved_wsFlags;
  pNew->nOut = saved_nOut;
  pNew->nLTerm = saved_nLTerm;
  return rc;
................................................................................
          ** which we will simplify to just N*log2(N) */
          pNew->rRun = rSize + rLogSize;
        }
        rc = whereLoopInsert(pBuilder, pNew);
        if( rc ) break;
      }
    }

    assert( pBuilder->pRec==0 );
    rc = sqlite3Stat4ProbeNew(pWInfo->pParse, pProbe, &pBuilder->pRec);
    if( rc==SQLITE_OK ){
      rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);
      sqlite3Stat4ProbeFree(pBuilder->pRec);
      pBuilder->nRecValid = 0;
      pBuilder->pRec = 0;
    }
    assert( pBuilder->pRec==0 );

    /* If there was an INDEXED BY clause, then only that one index is
    ** considered. */
    if( pSrc->pIndex ) break;
  }
  return rc;
}