Below is the file 'sqlite/where.c' from this revision. You can also download the file.

/*
** 2001 September 15
**
** The author disclaims copyright to this source code.  In place of
** a legal notice, here is a blessing:
**
**    May you do good and not evil.
**    May you find forgiveness for yourself and forgive others.
**    May you share freely, never taking more than you give.
**
*************************************************************************
** This module contains C code that generates VDBE code used to process
** the WHERE clause of SQL statements.  This module is reponsible for
** generating the code that loops through a table looking for applicable
** rows.  Indices are selected and used to speed the search when doing
** so is applicable.  Because this module is responsible for selecting
** indices, you might also think of this module as the "query optimizer".
**
** $Id: where.c,v 1.179 2005/09/20 17:42:23 drh Exp $
*/
#include "sqliteInt.h"

/*
** The number of bits in a Bitmask.  "BMS" means "BitMask Size".
*/
#define BMS  (sizeof(Bitmask)*8)

/*
** Determine the number of elements in an array.
*/
#define ARRAYSIZE(X)  (sizeof(X)/sizeof(X[0]))

/*
** Trace output macros
*/
#if defined(SQLITE_TEST) || defined(SQLITE_DEBUG)
int sqlite3_where_trace = 0;
# define TRACE(X)  if(sqlite3_where_trace) sqlite3DebugPrintf X
#else
# define TRACE(X)
#endif

/* Forward reference
*/
typedef struct WhereClause WhereClause;

/*
** The query generator uses an array of instances of this structure to
** help it analyze the subexpressions of the WHERE clause.  Each WHERE
** clause subexpression is separated from the others by an AND operator.
**
** All WhereTerms are collected into a single WhereClause structure.
** The following identity holds:
**
**        WhereTerm.pWC->a[WhereTerm.idx] == WhereTerm
**
** When a term is of the form:
**
**              X <op> <expr>
**
** where X is a column name and <op> is one of certain operators,
** then WhereTerm.leftCursor and WhereTerm.leftColumn record the
** cursor number and column number for X.  WhereTerm.operator records
** the <op> using a bitmask encoding defined by WO_xxx below.  The
** use of a bitmask encoding for the operator allows us to search
** quickly for terms that match any of several different operators.
**
** prereqRight and prereqAll record sets of cursor numbers,
** but they do so indirectly.  A single ExprMaskSet structure translates
** cursor number into bits and the translated bit is stored in the prereq
** fields.  The translation is used in order to maximize the number of
** bits that will fit in a Bitmask.  The VDBE cursor numbers might be
** spread out over the non-negative integers.  For example, the cursor
** numbers might be 3, 8, 9, 10, 20, 23, 41, and 45.  The ExprMaskSet
** translates these sparse cursor numbers into consecutive integers
** beginning with 0 in order to make the best possible use of the available
** bits in the Bitmask.  So, in the example above, the cursor numbers
** would be mapped into integers 0 through 7.
*/
typedef struct WhereTerm WhereTerm;
struct WhereTerm {
  Expr *pExpr;            /* Pointer to the subexpression */
  i16 iParent;            /* Disable pWC->a[iParent] when this term disabled */
  i16 leftCursor;         /* Cursor number of X in "X <op> <expr>" */
  i16 leftColumn;         /* Column number of X in "X <op> <expr>" */
  u16 operator;           /* A WO_xx value describing <op> */
  u8 flags;               /* Bit flags.  See below */
  u8 nChild;              /* Number of children that must disable us */
  WhereClause *pWC;       /* The clause this term is part of */
  Bitmask prereqRight;    /* Bitmask of tables used by pRight */
  Bitmask prereqAll;      /* Bitmask of tables referenced by p */
};

/*
** Allowed values of WhereTerm.flags
*/
#define TERM_DYNAMIC    0x01   /* Need to call sqlite3ExprDelete(pExpr) */
#define TERM_VIRTUAL    0x02   /* Added by the optimizer.  Do not code */
#define TERM_CODED      0x04   /* This term is already coded */
#define TERM_COPIED     0x08   /* Has a child */
#define TERM_OR_OK      0x10   /* Used during OR-clause processing */

/*
** An instance of the following structure holds all information about a
** WHERE clause.  Mostly this is a container for one or more WhereTerms.
*/
struct WhereClause {
  Parse *pParse;           /* The parser context */
  int nTerm;               /* Number of terms */
  int nSlot;               /* Number of entries in a[] */
  WhereTerm *a;            /* Each a[] describes a term of the WHERE cluase */
  WhereTerm aStatic[10];   /* Initial static space for a[] */
};

/*
** An instance of the following structure keeps track of a mapping
** between VDBE cursor numbers and bits of the bitmasks in WhereTerm.
**
** The VDBE cursor numbers are small integers contained in
** SrcList_item.iCursor and Expr.iTable fields.  For any given WHERE
** clause, the cursor numbers might not begin with 0 and they might
** contain gaps in the numbering sequence.  But we want to make maximum
** use of the bits in our bitmasks.  This structure provides a mapping
** from the sparse cursor numbers into consecutive integers beginning
** with 0.
**
** If ExprMaskSet.ix[A]==B it means that The A-th bit of a Bitmask
** corresponds VDBE cursor number B.  The A-th bit of a bitmask is 1<<A.
**
** For example, if the WHERE clause expression used these VDBE
** cursors:  4, 5, 8, 29, 57, 73.  Then the  ExprMaskSet structure
** would map those cursor numbers into bits 0 through 5.
**
** Note that the mapping is not necessarily ordered.  In the example
** above, the mapping might go like this:  4->3, 5->1, 8->2, 29->0,
** 57->5, 73->4.  Or one of 719 other combinations might be used. It
** does not really matter.  What is important is that sparse cursor
** numbers all get mapped into bit numbers that begin with 0 and contain
** no gaps.
*/
typedef struct ExprMaskSet ExprMaskSet;
struct ExprMaskSet {
  int n;                        /* Number of assigned cursor values */
  int ix[sizeof(Bitmask)*8];    /* Cursor assigned to each bit */
};


/*
** Bitmasks for the operators that indices are able to exploit.  An
** OR-ed combination of these values can be used when searching for
** terms in the where clause.
*/
#define WO_IN     1
#define WO_EQ     2
#define WO_LT     (WO_EQ<<(TK_LT-TK_EQ))
#define WO_LE     (WO_EQ<<(TK_LE-TK_EQ))
#define WO_GT     (WO_EQ<<(TK_GT-TK_EQ))
#define WO_GE     (WO_EQ<<(TK_GE-TK_EQ))

/*
** Value for flags returned by bestIndex()
*/
#define WHERE_ROWID_EQ       0x0001   /* rowid=EXPR or rowid IN (...) */
#define WHERE_ROWID_RANGE    0x0002   /* rowid<EXPR and/or rowid>EXPR */
#define WHERE_COLUMN_EQ      0x0010   /* x=EXPR or x IN (...) */
#define WHERE_COLUMN_RANGE   0x0020   /* x<EXPR and/or x>EXPR */
#define WHERE_COLUMN_IN      0x0040   /* x IN (...) */
#define WHERE_TOP_LIMIT      0x0100   /* x<EXPR or x<=EXPR constraint */
#define WHERE_BTM_LIMIT      0x0200   /* x>EXPR or x>=EXPR constraint */
#define WHERE_IDX_ONLY       0x0800   /* Use index only - omit table */
#define WHERE_ORDERBY        0x1000   /* Output will appear in correct order */
#define WHERE_REVERSE        0x2000   /* Scan in reverse order */
#define WHERE_UNIQUE         0x4000   /* Selects no more than one row */

/*
** Initialize a preallocated WhereClause structure.
*/
static void whereClauseInit(WhereClause *pWC, Parse *pParse){
  pWC->pParse = pParse;
  pWC->nTerm = 0;
  pWC->nSlot = ARRAYSIZE(pWC->aStatic);
  pWC->a = pWC->aStatic;
}

/*
** Deallocate a WhereClause structure.  The WhereClause structure
** itself is not freed.  This routine is the inverse of whereClauseInit().
*/
static void whereClauseClear(WhereClause *pWC){
  int i;
  WhereTerm *a;
  for(i=pWC->nTerm-1, a=pWC->a; i>=0; i--, a++){
    if( a->flags & TERM_DYNAMIC ){
      sqlite3ExprDelete(a->pExpr);
    }
  }
  if( pWC->a!=pWC->aStatic ){
    sqliteFree(pWC->a);
  }
}

/*
** Add a new entries to the WhereClause structure.  Increase the allocated
** space as necessary.
**
** WARNING:  This routine might reallocate the space used to store
** WhereTerms.  All pointers to WhereTerms should be invalided after
** calling this routine.  Such pointers may be reinitialized by referencing
** the pWC->a[] array.
*/
static int whereClauseInsert(WhereClause *pWC, Expr *p, int flags){
  WhereTerm *pTerm;
  int idx;
  if( pWC->nTerm>=pWC->nSlot ){
    WhereTerm *pOld = pWC->a;
    pWC->a = sqliteMalloc( sizeof(pWC->a[0])*pWC->nSlot*2 );
    if( pWC->a==0 ) return 0;
    memcpy(pWC->a, pOld, sizeof(pWC->a[0])*pWC->nTerm);
    if( pOld!=pWC->aStatic ){
      sqliteFree(pOld);
    }
    pWC->nSlot *= 2;
  }
  pTerm = &pWC->a[idx = pWC->nTerm];
  pWC->nTerm++;
  pTerm->pExpr = p;
  pTerm->flags = flags;
  pTerm->pWC = pWC;
  pTerm->iParent = -1;
  return idx;
}

/*
** This routine identifies subexpressions in the WHERE clause where
** each subexpression is separated by the AND operator or some other
** operator specified in the op parameter.  The WhereClause structure
** is filled with pointers to subexpressions.  For example:
**
**    WHERE  a=='hello' AND coalesce(b,11)<10 AND (c+12!=d OR c==22)
**           \________/     \_______________/     \________________/
**            slot[0]            slot[1]               slot[2]
**
** The original WHERE clause in pExpr is unaltered.  All this routine
** does is make slot[] entries point to substructure within pExpr.
**
** In the previous sentence and in the diagram, "slot[]" refers to
** the WhereClause.a[] array.  This array grows as needed to contain
** all terms of the WHERE clause.
*/
static void whereSplit(WhereClause *pWC, Expr *pExpr, int op){
  if( pExpr==0 ) return;
  if( pExpr->op!=op ){
    whereClauseInsert(pWC, pExpr, 0);
  }else{
    whereSplit(pWC, pExpr->pLeft, op);
    whereSplit(pWC, pExpr->pRight, op);
  }
}

/*
** Initialize an expression mask set
*/
#define initMaskSet(P)  memset(P, 0, sizeof(*P))

/*
** Return the bitmask for the given cursor number.  Return 0 if
** iCursor is not in the set.
*/
static Bitmask getMask(ExprMaskSet *pMaskSet, int iCursor){
  int i;
  for(i=0; i<pMaskSet->n; i++){
    if( pMaskSet->ix[i]==iCursor ){
      return ((Bitmask)1)<<i;
    }
  }
  return 0;
}

/*
** Create a new mask for cursor iCursor.
**
** There is one cursor per table in the FROM clause.  The number of
** tables in the FROM clause is limited by a test early in the
** sqlite3WhereBegin() routine.  So we know that the pMaskSet->ix[]
** array will never overflow.
*/
static void createMask(ExprMaskSet *pMaskSet, int iCursor){
  assert( pMaskSet->n < ARRAYSIZE(pMaskSet->ix) );
  pMaskSet->ix[pMaskSet->n++] = iCursor;
}

/*
** This routine walks (recursively) an expression tree and generates
** a bitmask indicating which tables are used in that expression
** tree.
**
** In order for this routine to work, the calling function must have
** previously invoked sqlite3ExprResolveNames() on the expression.  See
** the header comment on that routine for additional information.
** The sqlite3ExprResolveNames() routines looks for column names and
** sets their opcodes to TK_COLUMN and their Expr.iTable fields to
** the VDBE cursor number of the table.  This routine just has to
** translate the cursor numbers into bitmask values and OR all
** the bitmasks together.
*/
static Bitmask exprListTableUsage(ExprMaskSet*, ExprList*);
static Bitmask exprSelectTableUsage(ExprMaskSet*, Select*);
static Bitmask exprTableUsage(ExprMaskSet *pMaskSet, Expr *p){
  Bitmask mask = 0;
  if( p==0 ) return 0;
  if( p->op==TK_COLUMN ){
    mask = getMask(pMaskSet, p->iTable);
    return mask;
  }
  mask = exprTableUsage(pMaskSet, p->pRight);
  mask |= exprTableUsage(pMaskSet, p->pLeft);
  mask |= exprListTableUsage(pMaskSet, p->pList);
  mask |= exprSelectTableUsage(pMaskSet, p->pSelect);
  return mask;
}
static Bitmask exprListTableUsage(ExprMaskSet *pMaskSet, ExprList *pList){
  int i;
  Bitmask mask = 0;
  if( pList ){
    for(i=0; i<pList->nExpr; i++){
      mask |= exprTableUsage(pMaskSet, pList->a[i].pExpr);
    }
  }
  return mask;
}
static Bitmask exprSelectTableUsage(ExprMaskSet *pMaskSet, Select *pS){
  Bitmask mask;
  if( pS==0 ){
    mask = 0;
  }else{
    mask = exprListTableUsage(pMaskSet, pS->pEList);
    mask |= exprListTableUsage(pMaskSet, pS->pGroupBy);
    mask |= exprListTableUsage(pMaskSet, pS->pOrderBy);
    mask |= exprTableUsage(pMaskSet, pS->pWhere);
    mask |= exprTableUsage(pMaskSet, pS->pHaving);
  }
  return mask;
}

/*
** Return TRUE if the given operator is one of the operators that is
** allowed for an indexable WHERE clause term.  The allowed operators are
** "=", "<", ">", "<=", ">=", and "IN".
*/
static int allowedOp(int op){
  assert( TK_GT>TK_EQ && TK_GT<TK_GE );
  assert( TK_LT>TK_EQ && TK_LT<TK_GE );
  assert( TK_LE>TK_EQ && TK_LE<TK_GE );
  assert( TK_GE==TK_EQ+4 );
  return op==TK_IN || (op>=TK_EQ && op<=TK_GE);
}

/*
** Swap two objects of type T.
*/
#define SWAP(TYPE,A,B) {TYPE t=A; A=B; B=t;}

/*
** Commute a comparision operator.  Expressions of the form "X op Y"
** are converted into "Y op X".
*/
static void exprCommute(Expr *pExpr){
  assert( allowedOp(pExpr->op) && pExpr->op!=TK_IN );
  SWAP(CollSeq*,pExpr->pRight->pColl,pExpr->pLeft->pColl);
  SWAP(Expr*,pExpr->pRight,pExpr->pLeft);
  if( pExpr->op>=TK_GT ){
    assert( TK_LT==TK_GT+2 );
    assert( TK_GE==TK_LE+2 );
    assert( TK_GT>TK_EQ );
    assert( TK_GT<TK_LE );
    assert( pExpr->op>=TK_GT && pExpr->op<=TK_GE );
    pExpr->op = ((pExpr->op-TK_GT)^2)+TK_GT;
  }
}

/*
** Translate from TK_xx operator to WO_xx bitmask.
*/
static int operatorMask(int op){
  int c;
  assert( allowedOp(op) );
  if( op==TK_IN ){
    c = WO_IN;
  }else{
    c = WO_EQ<<(op-TK_EQ);
  }
  assert( op!=TK_IN || c==WO_IN );
  assert( op!=TK_EQ || c==WO_EQ );
  assert( op!=TK_LT || c==WO_LT );
  assert( op!=TK_LE || c==WO_LE );
  assert( op!=TK_GT || c==WO_GT );
  assert( op!=TK_GE || c==WO_GE );
  return c;
}

/*
** Search for a term in the WHERE clause that is of the form "X <op> <expr>"
** where X is a reference to the iColumn of table iCur and <op> is one of
** the WO_xx operator codes specified by the op parameter.
** Return a pointer to the term.  Return 0 if not found.
*/
static WhereTerm *findTerm(
  WhereClause *pWC,     /* The WHERE clause to be searched */
  int iCur,             /* Cursor number of LHS */
  int iColumn,          /* Column number of LHS */
  Bitmask notReady,     /* RHS must not overlap with this mask */
  u16 op,               /* Mask of WO_xx values describing operator */
  Index *pIdx           /* Must be compatible with this index, if not NULL */
){
  WhereTerm *pTerm;
  int k;
  for(pTerm=pWC->a, k=pWC->nTerm; k; k--, pTerm++){
    if( pTerm->leftCursor==iCur
       && (pTerm->prereqRight & notReady)==0
       && pTerm->leftColumn==iColumn
       && (pTerm->operator & op)!=0
    ){
      if( iCur>=0 && pIdx ){
        Expr *pX = pTerm->pExpr;
        CollSeq *pColl;
        char idxaff;
        int k;
        Parse *pParse = pWC->pParse;

        idxaff = pIdx->pTable->aCol[iColumn].affinity;
        if( !sqlite3IndexAffinityOk(pX, idxaff) ) continue;
        pColl = sqlite3ExprCollSeq(pParse, pX->pLeft);
        if( !pColl ){
          if( pX->pRight ){
            pColl = sqlite3ExprCollSeq(pParse, pX->pRight);
          }
          if( !pColl ){
            pColl = pParse->db->pDfltColl;
          }
        }
        for(k=0; k<pIdx->nColumn && pIdx->aiColumn[k]!=iColumn; k++){}
        assert( k<pIdx->nColumn );
        if( pColl!=pIdx->keyInfo.aColl[k] ) continue;
      }
      return pTerm;
    }
  }
  return 0;
}

/* Forward reference */
static void exprAnalyze(SrcList*, ExprMaskSet*, WhereClause*, int);

/*
** Call exprAnalyze on all terms in a WHERE clause.
**
**
*/
static void exprAnalyzeAll(
  SrcList *pTabList,       /* the FROM clause */
  ExprMaskSet *pMaskSet,   /* table masks */
  WhereClause *pWC         /* the WHERE clause to be analyzed */
){
  int i;
  for(i=pWC->nTerm-1; i>=0; i--){
    exprAnalyze(pTabList, pMaskSet, pWC, i);
  }
}

#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION
/*
** Check to see if the given expression is a LIKE or GLOB operator that
** can be optimized using inequality constraints.  Return TRUE if it is
** so and false if not.
**
** In order for the operator to be optimizible, the RHS must be a string
** literal that does not begin with a wildcard.
*/
static int isLikeOrGlob(
  sqlite3 *db,      /* The database */
  Expr *pExpr,      /* Test this expression */
  int *pnPattern,   /* Number of non-wildcard prefix characters */
  int *pisComplete  /* True if the only wildcard is % in the last character */
){
  const char *z;
  Expr *pRight, *pLeft;
  ExprList *pList;
  int c, cnt;
  int noCase;
  char wc[3];
  CollSeq *pColl;

  if( !sqlite3IsLikeFunction(db, pExpr, &noCase, wc) ){
    return 0;
  }
  pList = pExpr->pList;
  pRight = pList->a[0].pExpr;
  if( pRight->op!=TK_STRING ){
    return 0;
  }
  pLeft = pList->a[1].pExpr;
  if( pLeft->op!=TK_COLUMN ){
    return 0;
  }
  pColl = pLeft->pColl;
  if( pColl==0 ){
    pColl = db->pDfltColl;
  }
  if( (pColl->type!=SQLITE_COLL_BINARY || noCase) &&
      (pColl->type!=SQLITE_COLL_NOCASE || !noCase) ){
    return 0;
  }
  sqlite3DequoteExpr(pRight);
  z = pRight->token.z;
  for(cnt=0; (c=z[cnt])!=0 && c!=wc[0] && c!=wc[1] && c!=wc[2]; cnt++){}
  if( cnt==0 || 255==(u8)z[cnt] ){
    return 0;
  }
  *pisComplete = z[cnt]==wc[0] && z[cnt+1]==0;
  *pnPattern = cnt;
  return 1;
}
#endif /* SQLITE_OMIT_LIKE_OPTIMIZATION */

/*
** The input to this routine is an WhereTerm structure with only the
** "pExpr" field filled in.  The job of this routine is to analyze the
** subexpression and populate all the other fields of the WhereTerm
** structure.
**
** If the expression is of the form "<expr> <op> X" it gets commuted
** to the standard form of "X <op> <expr>".  If the expression is of
** the form "X <op> Y" where both X and Y are columns, then the original
** expression is unchanged and a new virtual expression of the form
** "Y <op> X" is added to the WHERE clause and analyzed separately.
*/
static void exprAnalyze(
  SrcList *pSrc,            /* the FROM clause */
  ExprMaskSet *pMaskSet,    /* table masks */
  WhereClause *pWC,         /* the WHERE clause */
  int idxTerm               /* Index of the term to be analyzed */
){
  WhereTerm *pTerm = &pWC->a[idxTerm];
  Expr *pExpr = pTerm->pExpr;
  Bitmask prereqLeft;
  Bitmask prereqAll;
  int nPattern;
  int isComplete;

  if( sqlite3_malloc_failed ) return;
  prereqLeft = exprTableUsage(pMaskSet, pExpr->pLeft);
  if( pExpr->op==TK_IN ){
    assert( pExpr->pRight==0 );
    pTerm->prereqRight = exprListTableUsage(pMaskSet, pExpr->pList)
                          | exprSelectTableUsage(pMaskSet, pExpr->pSelect);
  }else{
    pTerm->prereqRight = exprTableUsage(pMaskSet, pExpr->pRight);
  }
  prereqAll = exprTableUsage(pMaskSet, pExpr);
  if( ExprHasProperty(pExpr, EP_FromJoin) ){
    prereqAll |= getMask(pMaskSet, pExpr->iRightJoinTable);
  }
  pTerm->prereqAll = prereqAll;
  pTerm->leftCursor = -1;
  pTerm->iParent = -1;
  pTerm->operator = 0;
  if( allowedOp(pExpr->op) && (pTerm->prereqRight & prereqLeft)==0 ){
    Expr *pLeft = pExpr->pLeft;
    Expr *pRight = pExpr->pRight;
    if( pLeft->op==TK_COLUMN ){
      pTerm->leftCursor = pLeft->iTable;
      pTerm->leftColumn = pLeft->iColumn;
      pTerm->operator = operatorMask(pExpr->op);
    }
    if( pRight && pRight->op==TK_COLUMN ){
      WhereTerm *pNew;
      Expr *pDup;
      if( pTerm->leftCursor>=0 ){
        int idxNew;
        pDup = sqlite3ExprDup(pExpr);
        idxNew = whereClauseInsert(pWC, pDup, TERM_VIRTUAL|TERM_DYNAMIC);
        if( idxNew==0 ) return;
        pNew = &pWC->a[idxNew];
        pNew->iParent = idxTerm;
        pTerm = &pWC->a[idxTerm];
        pTerm->nChild = 1;
        pTerm->flags |= TERM_COPIED;
      }else{
        pDup = pExpr;
        pNew = pTerm;
      }
      exprCommute(pDup);
      pLeft = pDup->pLeft;
      pNew->leftCursor = pLeft->iTable;
      pNew->leftColumn = pLeft->iColumn;
      pNew->prereqRight = prereqLeft;
      pNew->prereqAll = prereqAll;
      pNew->operator = operatorMask(pDup->op);
    }
  }

#ifndef SQLITE_OMIT_BETWEEN_OPTIMIZATION
  /* If a term is the BETWEEN operator, create two new virtual terms
  ** that define the range that the BETWEEN implements.
  */
  else if( pExpr->op==TK_BETWEEN ){
    ExprList *pList = pExpr->pList;
    int i;
    static const u8 ops[] = {TK_GE, TK_LE};
    assert( pList!=0 );
    assert( pList->nExpr==2 );
    for(i=0; i<2; i++){
      Expr *pNewExpr;
      int idxNew;
      pNewExpr = sqlite3Expr(ops[i], sqlite3ExprDup(pExpr->pLeft),
                             sqlite3ExprDup(pList->a[i].pExpr), 0);
      idxNew = whereClauseInsert(pWC, pNewExpr, TERM_VIRTUAL|TERM_DYNAMIC);
      exprAnalyze(pSrc, pMaskSet, pWC, idxNew);
      pTerm = &pWC->a[idxTerm];
      pWC->a[idxNew].iParent = idxTerm;
    }
    pTerm->nChild = 2;
  }
#endif /* SQLITE_OMIT_BETWEEN_OPTIMIZATION */

#ifndef SQLITE_OMIT_OR_OPTIMIZATION
  /* Attempt to convert OR-connected terms into an IN operator so that
  ** they can make use of indices.  Example:
  **
  **      x = expr1  OR  expr2 = x  OR  x = expr3
  **
  ** is converted into
  **
  **      x IN (expr1,expr2,expr3)
  */
  else if( pExpr->op==TK_OR ){
    int ok;
    int i, j;
    int iColumn, iCursor;
    WhereClause sOr;
    WhereTerm *pOrTerm;

    assert( (pTerm->flags & TERM_DYNAMIC)==0 );
    whereClauseInit(&sOr, pWC->pParse);
    whereSplit(&sOr, pExpr, TK_OR);
    exprAnalyzeAll(pSrc, pMaskSet, &sOr);
    assert( sOr.nTerm>0 );
    j = 0;
    do{
      iColumn = sOr.a[j].leftColumn;
      iCursor = sOr.a[j].leftCursor;
      ok = iCursor>=0;
      for(i=sOr.nTerm-1, pOrTerm=sOr.a; i>=0 && ok; i--, pOrTerm++){
        if( pOrTerm->operator!=WO_EQ ){
          goto or_not_possible;
        }
        if( pOrTerm->leftCursor==iCursor && pOrTerm->leftColumn==iColumn ){
          pOrTerm->flags |= TERM_OR_OK;
        }else if( (pOrTerm->flags & TERM_COPIED)!=0 ||
                    ((pOrTerm->flags & TERM_VIRTUAL)!=0 &&
                     (sOr.a[pOrTerm->iParent].flags & TERM_OR_OK)!=0) ){
          pOrTerm->flags &= ~TERM_OR_OK;
        }else{
          ok = 0;
        }
      }
    }while( !ok && (sOr.a[j++].flags & TERM_COPIED)!=0 && j<sOr.nTerm );
    if( ok ){
      ExprList *pList = 0;
      Expr *pNew, *pDup;
      for(i=sOr.nTerm-1, pOrTerm=sOr.a; i>=0 && ok; i--, pOrTerm++){
        if( (pOrTerm->flags & TERM_OR_OK)==0 ) continue;
        pDup = sqlite3ExprDup(pOrTerm->pExpr->pRight);
        pList = sqlite3ExprListAppend(pList, pDup, 0);
      }
      pDup = sqlite3Expr(TK_COLUMN, 0, 0, 0);
      if( pDup ){
        pDup->iTable = iCursor;
        pDup->iColumn = iColumn;
      }
      pNew = sqlite3Expr(TK_IN, pDup, 0, 0);
      if( pNew ){
        pNew->pList = pList;
      }else{
        sqlite3ExprListDelete(pList);
      }
      pTerm->pExpr = pNew;
      pTerm->flags |= TERM_DYNAMIC;
      exprAnalyze(pSrc, pMaskSet, pWC, idxTerm);
      pTerm = &pWC->a[idxTerm];
    }
or_not_possible:
    whereClauseClear(&sOr);
  }
#endif /* SQLITE_OMIT_OR_OPTIMIZATION */

#ifndef SQLITE_OMIT_LIKE_OPTIMIZATION
  /* Add constraints to reduce the search space on a LIKE or GLOB
  ** operator.
  */
  if( isLikeOrGlob(pWC->pParse->db, pExpr, &nPattern, &isComplete) ){
    Expr *pLeft, *pRight;
    Expr *pStr1, *pStr2;
    Expr *pNewExpr1, *pNewExpr2;
    int idxNew1, idxNew2;

    pLeft = pExpr->pList->a[1].pExpr;
    pRight = pExpr->pList->a[0].pExpr;
    pStr1 = sqlite3Expr(TK_STRING, 0, 0, 0);
    if( pStr1 ){
      sqlite3TokenCopy(&pStr1->token, &pRight->token);
      pStr1->token.n = nPattern;
    }
    pStr2 = sqlite3ExprDup(pStr1);
    if( pStr2 ){
      assert( pStr2->token.dyn );
      ++*(u8*)&pStr2->token.z[nPattern-1];
    }
    pNewExpr1 = sqlite3Expr(TK_GE, sqlite3ExprDup(pLeft), pStr1, 0);
    idxNew1 = whereClauseInsert(pWC, pNewExpr1, TERM_VIRTUAL|TERM_DYNAMIC);
    exprAnalyze(pSrc, pMaskSet, pWC, idxNew1);
    pNewExpr2 = sqlite3Expr(TK_LT, sqlite3ExprDup(pLeft), pStr2, 0);
    idxNew2 = whereClauseInsert(pWC, pNewExpr2, TERM_VIRTUAL|TERM_DYNAMIC);
    exprAnalyze(pSrc, pMaskSet, pWC, idxNew2);
    pTerm = &pWC->a[idxTerm];
    if( isComplete ){
      pWC->a[idxNew1].iParent = idxTerm;
      pWC->a[idxNew2].iParent = idxTerm;
      pTerm->nChild = 2;
    }
  }
#endif /* SQLITE_OMIT_LIKE_OPTIMIZATION */
}


/*
** This routine decides if pIdx can be used to satisfy the ORDER BY
** clause.  If it can, it returns 1.  If pIdx cannot satisfy the
** ORDER BY clause, this routine returns 0.
**
** pOrderBy is an ORDER BY clause from a SELECT statement.  pTab is the
** left-most table in the FROM clause of that same SELECT statement and
** the table has a cursor number of "base".  pIdx is an index on pTab.
**
** nEqCol is the number of columns of pIdx that are used as equality
** constraints.  Any of these columns may be missing from the ORDER BY
** clause and the match can still be a success.
**
** All terms of the ORDER BY that match against the index must be either
** ASC or DESC.  (Terms of the ORDER BY clause past the end of a UNIQUE
** index do not need to satisfy this constraint.)  The *pbRev value is
** set to 1 if the ORDER BY clause is all DESC and it is set to 0 if
** the ORDER BY clause is all ASC.
*/
static int isSortingIndex(
  Parse *pParse,          /* Parsing context */
  Index *pIdx,            /* The index we are testing */
  Table *pTab,            /* The table to be sorted */
  int base,               /* Cursor number for pTab */
  ExprList *pOrderBy,     /* The ORDER BY clause */
  int nEqCol,             /* Number of index columns with == constraints */
  int *pbRev              /* Set to 1 if ORDER BY is DESC */
){
  int i, j;                       /* Loop counters */
  int sortOrder = SQLITE_SO_ASC;  /* Which direction we are sorting */
  int nTerm;                      /* Number of ORDER BY terms */
  struct ExprList_item *pTerm;    /* A term of the ORDER BY clause */
  sqlite3 *db = pParse->db;

  assert( pOrderBy!=0 );
  nTerm = pOrderBy->nExpr;
  assert( nTerm>0 );

  /* Match terms of the ORDER BY clause against columns of
  ** the index.
  */
  for(i=j=0, pTerm=pOrderBy->a; j<nTerm && i<pIdx->nColumn; i++){
    Expr *pExpr;       /* The expression of the ORDER BY pTerm */
    CollSeq *pColl;    /* The collating sequence of pExpr */

    pExpr = pTerm->pExpr;
    if( pExpr->op!=TK_COLUMN || pExpr->iTable!=base ){
      /* Can not use an index sort on anything that is not a column in the
      ** left-most table of the FROM clause */
      return 0;
    }
    pColl = sqlite3ExprCollSeq(pParse, pExpr);
    if( !pColl ) pColl = db->pDfltColl;
    if( pExpr->iColumn!=pIdx->aiColumn[i] || pColl!=pIdx->keyInfo.aColl[i] ){
      /* Term j of the ORDER BY clause does not match column i of the index */
      if( i<nEqCol ){
        /* If an index column that is constrained by == fails to match an
        ** ORDER BY term, that is OK.  Just ignore that column of the index
        */
        continue;
      }else{
        /* If an index column fails to match and is not constrained by ==
        ** then the index cannot satisfy the ORDER BY constraint.
        */
        return 0;
      }
    }
    if( i>nEqCol ){
      if( pTerm->sortOrder!=sortOrder ){
        /* Indices can only be used if all ORDER BY terms past the
        ** equality constraints are all either DESC or ASC. */
        return 0;
      }
    }else{
      sortOrder = pTerm->sortOrder;
    }
    j++;
    pTerm++;
  }

  /* The index can be used for sorting if all terms of the ORDER BY clause
  ** are covered.
  */
  if( j>=nTerm ){
    *pbRev = sortOrder==SQLITE_SO_DESC;
    return 1;
  }
  return 0;
}

/*
** Check table to see if the ORDER BY clause in pOrderBy can be satisfied
** by sorting in order of ROWID.  Return true if so and set *pbRev to be
** true for reverse ROWID and false for forward ROWID order.
*/
static int sortableByRowid(
  int base,               /* Cursor number for table to be sorted */
  ExprList *pOrderBy,     /* The ORDER BY clause */
  int *pbRev              /* Set to 1 if ORDER BY is DESC */
){
  Expr *p;

  assert( pOrderBy!=0 );
  assert( pOrderBy->nExpr>0 );
  p = pOrderBy->a[0].pExpr;
  if( pOrderBy->nExpr==1 && p->op==TK_COLUMN && p->iTable==base
          && p->iColumn==-1 ){
    *pbRev = pOrderBy->a[0].sortOrder;
    return 1;
  }
  return 0;
}

/*
** Prepare a crude estimate of the logarithm of the input value.
** The results need not be exact.  This is only used for estimating
** the total cost of performing operatings with O(logN) or O(NlogN)
** complexity.  Because N is just a guess, it is no great tragedy if
** logN is a little off.
*/
static double estLog(double N){
  double logN = 1.0;
  double x = 10.0;
  while( N>x ){
    logN += 1.0;
    x *= 10;
  }
  return logN;
}

/*
** Find the best index for accessing a particular table.  Return a pointer
** to the index, flags that describe how the index should be used, the
** number of equality constraints, and the "cost" for this index.
**
** The lowest cost index wins.  The cost is an estimate of the amount of
** CPU and disk I/O need to process the request using the selected index.
** Factors that influence cost include:
**
**    *  The estimated number of rows that will be retrieved.  (The
**       fewer the better.)
**
**    *  Whether or not sorting must occur.
**
**    *  Whether or not there must be separate lookups in the
**       index and in the main table.
**
*/
static double bestIndex(
  Parse *pParse,              /* The parsing context */
  WhereClause *pWC,           /* The WHERE clause */
  struct SrcList_item *pSrc,  /* The FROM clause term to search */
  Bitmask notReady,           /* Mask of cursors that are not available */
  ExprList *pOrderBy,         /* The order by clause */
  Index **ppIndex,            /* Make *ppIndex point to the best index */
  int *pFlags,                /* Put flags describing this choice in *pFlags */
  int *pnEq                   /* Put the number of == or IN constraints here */
){
  WhereTerm *pTerm;
  Index *bestIdx = 0;         /* Index that gives the lowest cost */
  double lowestCost = 1.0e99; /* The cost of using bestIdx */
  int bestFlags = 0;          /* Flags associated with bestIdx */
  int bestNEq = 0;            /* Best value for nEq */
  int iCur = pSrc->iCursor;   /* The cursor of the table to be accessed */
  Index *pProbe;              /* An index we are evaluating */
  int rev;                    /* True to scan in reverse order */
  int flags;                  /* Flags associated with pProbe */
  int nEq;                    /* Number of == or IN constraints */
  double cost;                /* Cost of using pProbe */

  TRACE(("bestIndex: tbl=%s notReady=%x\n", pSrc->pTab->zName, notReady));

  /* Check for a rowid=EXPR or rowid IN (...) constraints
  */
  pTerm = findTerm(pWC, iCur, -1, notReady, WO_EQ|WO_IN, 0);
  if( pTerm ){
    Expr *pExpr;
    *ppIndex = 0;
    bestFlags = WHERE_ROWID_EQ;
    if( pTerm->operator & WO_EQ ){
      /* Rowid== is always the best pick.  Look no further.  Because only
      ** a single row is generated, output is always in sorted order */
      *pFlags = WHERE_ROWID_EQ | WHERE_UNIQUE;
      *pnEq = 1;
      TRACE(("... best is rowid\n"));
      return 0.0;
    }else if( (pExpr = pTerm->pExpr)->pList!=0 ){
      /* Rowid IN (LIST): cost is NlogN where N is the number of list
      ** elements.  */
      lowestCost = pExpr->pList->nExpr;
      lowestCost *= estLog(lowestCost);
    }else{
      /* Rowid IN (SELECT): cost is NlogN where N is the number of rows
      ** in the result of the inner select.  We have no way to estimate
      ** that value so make a wild guess. */
      lowestCost = 200.0;
    }
    TRACE(("... rowid IN cost: %.9g\n", lowestCost));
  }

  /* Estimate the cost of a table scan.  If we do not know how many
  ** entries are in the table, use 1 million as a guess.
  */
  pProbe = pSrc->pTab->pIndex;
  cost = pProbe ? pProbe->aiRowEst[0] : 1000000.0;
  TRACE(("... table scan base cost: %.9g\n", cost));
  flags = WHERE_ROWID_RANGE;

  /* Check for constraints on a range of rowids in a table scan.
  */
  pTerm = findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE|WO_GT|WO_GE, 0);
  if( pTerm ){
    if( findTerm(pWC, iCur, -1, notReady, WO_LT|WO_LE, 0) ){
      flags |= WHERE_TOP_LIMIT;
      cost *= 0.333;  /* Guess that rowid<EXPR eliminates two-thirds or rows */
    }
    if( findTerm(pWC, iCur, -1, notReady, WO_GT|WO_GE, 0) ){
      flags |= WHERE_BTM_LIMIT;
      cost *= 0.333;  /* Guess that rowid>EXPR eliminates two-thirds of rows */
    }
    TRACE(("... rowid range reduces cost to %.9g\n", cost));
  }else{
    flags = 0;
  }

  /* If the table scan does not satisfy the ORDER BY clause, increase
  ** the cost by NlogN to cover the expense of sorting. */
  if( pOrderBy ){
    if( sortableByRowid(iCur, pOrderBy, &rev) ){
      flags |= WHERE_ORDERBY|WHERE_ROWID_RANGE;
      if( rev ){
        flags |= WHERE_REVERSE;
      }
    }else{
      cost += cost*estLog(cost);
      TRACE(("... sorting increases cost to %.9g\n", cost));
    }
  }
  if( cost<lowestCost ){
    lowestCost = cost;
    bestFlags = flags;
  }

  /* Look at each index.
  */
  for(; pProbe; pProbe=pProbe->pNext){
    int i;                       /* Loop counter */
    double inMultiplier = 1.0;

    TRACE(("... index %s:\n", pProbe->zName));

    /* Count the number of columns in the index that are satisfied
    ** by x=EXPR constraints or x IN (...) constraints.
    */
    flags = 0;
    for(i=0; i<pProbe->nColumn; i++){
      int j = pProbe->aiColumn[i];
      pTerm = findTerm(pWC, iCur, j, notReady, WO_EQ|WO_IN, pProbe);
      if( pTerm==0 ) break;
      flags |= WHERE_COLUMN_EQ;
      if( pTerm->operator & WO_IN ){
        Expr *pExpr = pTerm->pExpr;
        flags |= WHERE_COLUMN_IN;
        if( pExpr->pSelect!=0 ){
          inMultiplier *= 100.0;
        }else if( pExpr->pList!=0 ){
          inMultiplier *= pExpr->pList->nExpr + 1.0;
        }
      }
    }
    cost = pProbe->aiRowEst[i] * inMultiplier * estLog(inMultiplier);
    nEq = i;
    if( pProbe->onError!=OE_None && (flags & WHERE_COLUMN_IN)==0
         && nEq==pProbe->nColumn ){
      flags |= WHERE_UNIQUE;
    }
    TRACE(("...... nEq=%d inMult=%.9g cost=%.9g\n", nEq, inMultiplier, cost));

    /* Look for range constraints
    */
    if( nEq<pProbe->nColumn ){
      int j = pProbe->aiColumn[nEq];
      pTerm = findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE|WO_GT|WO_GE, pProbe);
      if( pTerm ){
        flags |= WHERE_COLUMN_RANGE;
        if( findTerm(pWC, iCur, j, notReady, WO_LT|WO_LE, pProbe) ){
          flags |= WHERE_TOP_LIMIT;
          cost *= 0.333;
        }
        if( findTerm(pWC, iCur, j, notReady, WO_GT|WO_GE, pProbe) ){
          flags |= WHERE_BTM_LIMIT;
          cost *= 0.333;
        }
        TRACE(("...... range reduces cost to %.9g\n", cost));
      }
    }

    /* Add the additional cost of sorting if that is a factor.
    */
    if( pOrderBy ){
      if( (flags & WHERE_COLUMN_IN)==0 &&
           isSortingIndex(pParse,pProbe,pSrc->pTab,iCur,pOrderBy,nEq,&rev) ){
        if( flags==0 ){
          flags = WHERE_COLUMN_RANGE;
        }
        flags |= WHERE_ORDERBY;
        if( rev ){
          flags |= WHERE_REVERSE;
        }
      }else{
        cost += cost*estLog(cost);
        TRACE(("...... orderby increases cost to %.9g\n", cost));
      }
    }

    /* Check to see if we can get away with using just the index without
    ** ever reading the table.  If that is the case, then halve the
    ** cost of this index.
    */
    if( flags && pSrc->colUsed < (((Bitmask)1)<<(BMS-1)) ){
      Bitmask m = pSrc->colUsed;
      int j;
      for(j=0; j<pProbe->nColumn; j++){
        int x = pProbe->aiColumn[j];
        if( x<BMS-1 ){
          m &= ~(((Bitmask)1)<<x);
        }
      }
      if( m==0 ){
        flags |= WHERE_IDX_ONLY;
        cost *= 0.5;
        TRACE(("...... idx-only reduces cost to %.9g\n", cost));
      }
    }

    /* If this index has achieved the lowest cost so far, then use it.
    */
    if( cost < lowestCost ){
      bestIdx = pProbe;
      lowestCost = cost;
      assert( flags!=0 );
      bestFlags = flags;
      bestNEq = nEq;
    }
  }

  /* Report the best result
  */
  *ppIndex = bestIdx;
  TRACE(("best index is %s, cost=%.9g, flags=%x, nEq=%d\n",
        bestIdx ? bestIdx->zName : "(none)", lowestCost, bestFlags, bestNEq));
  *pFlags = bestFlags;
  *pnEq = bestNEq;
  return lowestCost;
}


/*
** 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
** or USING clause of that join.
**
** Consider the term t2.z='ok' in the following queries:
**
**   (1)  SELECT * FROM t1 LEFT JOIN t2 ON t1.a=t2.x WHERE t2.z='ok'
**   (2)  SELECT * FROM t1 LEFT JOIN t2 ON t1.a=t2.x AND t2.z='ok'
**   (3)  SELECT * FROM t1, t2 WHERE t1.a=t2.x AND t2.z='ok'
**
** The t2.z='ok' is disabled in the in (2) because it originates
** in the ON clause.  The term is disabled in (3) because it is not part
** of a LEFT OUTER JOIN.  In (1), the term is not disabled.
**
** Disabling a term causes that term to not be tested in the inner loop
** of the join.  Disabling is an optimization.  When terms are satisfied
** by indices, we disable them to prevent redundant tests in the inner
** loop.  We would get the correct results if nothing were ever disabled,
** but joins might run a little slower.  The trick is to disable as much
** as we can without disabling too much.  If we disabled in (1), we'd get
** the wrong answer.  See ticket #813.
*/
static void disableTerm(WhereLevel *pLevel, WhereTerm *pTerm){
  if( pTerm
      && (pTerm->flags & TERM_CODED)==0
      && (pLevel->iLeftJoin==0 || ExprHasProperty(pTerm->pExpr, EP_FromJoin))
  ){
    pTerm->flags |= TERM_CODED;
    if( pTerm->iParent>=0 ){
      WhereTerm *pOther = &pTerm->pWC->a[pTerm->iParent];
      if( (--pOther->nChild)==0 ){
        disableTerm(pLevel, pOther);
      }
    }
  }
}

/*
** Generate code that builds a probe for an index.  Details:
**
**    *  Check the top nColumn entries on the stack.  If any
**       of those entries are NULL, jump immediately to brk,
**       which is the loop exit, since no index entry will match
**       if any part of the key is NULL.
**
**    *  Construct a probe entry from the top nColumn entries in
**       the stack with affinities appropriate for index pIdx.
*/
static void buildIndexProbe(Vdbe *v, int nColumn, int brk, Index *pIdx){
  sqlite3VdbeAddOp(v, OP_NotNull, -nColumn, sqlite3VdbeCurrentAddr(v)+3);
  sqlite3VdbeAddOp(v, OP_Pop, nColumn, 0);
  sqlite3VdbeAddOp(v, OP_Goto, 0, brk);
  sqlite3VdbeAddOp(v, OP_MakeRecord, nColumn, 0);
  sqlite3IndexAffinityStr(v, pIdx);
}


/*
** Generate code for a single equality term of the WHERE clause.  An equality
** term can be either X=expr or X IN (...).   pTerm is the term to be
** coded.
**
** The current value for the constraint is left on the top of the stack.
**
** For a constraint of the form X=expr, the expression is evaluated and its
** result is left on the stack.  For constraints of the form X IN (...)
** this routine sets up a loop that will iterate over all values of X.
*/
static void codeEqualityTerm(
  Parse *pParse,      /* The parsing context */
  WhereTerm *pTerm,   /* The term of the WHERE clause to be coded */
  int brk,            /* Jump here to abandon the loop */
  WhereLevel *pLevel  /* When level of the FROM clause we are working on */
){
  Expr *pX = pTerm->pExpr;
  if( pX->op!=TK_IN ){
    assert( pX->op==TK_EQ );
    sqlite3ExprCode(pParse, pX->pRight);
#ifndef SQLITE_OMIT_SUBQUERY
  }else{
    int iTab;
    int *aIn;
    Vdbe *v = pParse->pVdbe;

    sqlite3CodeSubselect(pParse, pX);
    iTab = pX->iTable;
    sqlite3VdbeAddOp(v, OP_Rewind, iTab, brk);
    VdbeComment((v, "# %.*s", pX->span.n, pX->span.z));
    pLevel->nIn++;
    sqlite3ReallocOrFree((void**)&pLevel->aInLoop,
                                 sizeof(pLevel->aInLoop[0])*3*pLevel->nIn);
    aIn = pLevel->aInLoop;
    if( aIn ){
      aIn += pLevel->nIn*3 - 3;
      aIn[0] = OP_Next;
      aIn[1] = iTab;
      aIn[2] = sqlite3VdbeAddOp(v, OP_Column, iTab, 0);
    }else{
      pLevel->nIn = 0;
    }
#endif
  }
  disableTerm(pLevel, pTerm);
}

/*
** Generate code that will evaluate all == and IN constraints for an
** index.  The values for all constraints are left on the stack.
**
** For example, consider table t1(a,b,c,d,e,f) with index i1(a,b,c).
** Suppose the WHERE clause is this:  a==5 AND b IN (1,2,3) AND c>5 AND c<10
** The index has as many as three equality constraints, but in this
** example, the third "c" value is an inequality.  So only two
** constraints are coded.  This routine will generate code to evaluate
** a==5 and b IN (1,2,3).  The current values for a and b will be left
** on the stack - a is the deepest and b the shallowest.
**
** In the example above nEq==2.  But this subroutine works for any value
** of nEq including 0.  If nEq==0, this routine is nearly a no-op.
** The only thing it does is allocate the pLevel->iMem memory cell.
**
** This routine always allocates at least one memory cell and puts
** the address of that memory cell in pLevel->iMem.  The code that
** calls this routine will use pLevel->iMem to store the termination
** key value of the loop.  If one or more IN operators appear, then
** this routine allocates an additional nEq memory cells for internal
** use.
*/