}

/*
** Skip over any TK_COLLATE and/or TK_AS operators at the root of
** an expression.
*/
Expr *sqlite3ExprSkipCollate(Expr *pExpr){

  while( pExpr && (pExpr->op==TK_COLLATE || pExpr->op==TK_AS) ){
    pExpr = pExpr->pLeft;







  }
  return pExpr;
}

/*
** Return the collation sequence for the expression pExpr. If
** there is no defined collating sequence, return NULL.
................................................................................
          sqlite3ExprCode(pParse, pFarg->a[i].pExpr, target);
          sqlite3ExprCachePop(pParse, 1);
        }
        sqlite3VdbeResolveLabel(v, endCoalesce);
        break;
      }










      if( pFarg ){
        r1 = sqlite3GetTempRange(pParse, nFarg);

        /* For length() and typeof() functions with a column argument,
        ** set the P5 parameter to the OP_Column opcode to OPFLAG_LENGTHARG
        ** or OPFLAG_TYPEOFARG respectively, to avoid unnecessary data

}

/*
** Skip over any TK_COLLATE and/or TK_AS operators at the root of
** an expression.
*/
Expr *sqlite3ExprSkipCollate(Expr *pExpr){
  while( pExpr ){
    if( pExpr->op==TK_COLLATE || pExpr->op==TK_AS ){
      pExpr = pExpr->pLeft;
    }else if( ExprHasAnyProperty(pExpr, EP_Hint) ){
      assert( !ExprHasProperty(pExpr, EP_xIsSelect) );
      assert( pExpr->x.pList->nExpr>0 );
      pExpr = pExpr->x.pList->a[0].pExpr;
    }else{
      break;
    }
  }
  return pExpr;
}

/*
** Return the collation sequence for the expression pExpr. If
** there is no defined collating sequence, return NULL.
................................................................................
          sqlite3ExprCode(pParse, pFarg->a[i].pExpr, target);
          sqlite3ExprCachePop(pParse, 1);
        }
        sqlite3VdbeResolveLabel(v, endCoalesce);
        break;
      }

      /* The UNLIKELY() function is a no-op.  The result is the value
      ** of the first argument.
      */
      if( pDef->funcFlags & SQLITE_FUNC_UNLIKELY ){
        assert( nFarg>=1 );
        sqlite3ExprCode(pParse, pFarg->a[0].pExpr, target);
        break;
      }

      if( pFarg ){
        r1 = sqlite3GetTempRange(pParse, nFarg);

        /* For length() and typeof() functions with a column argument,
        ** set the P5 parameter to the OP_Column opcode to OPFLAG_LENGTHARG
        ** or OPFLAG_TYPEOFARG respectively, to avoid unnecessary data

      }
      sqlite3_result_text(context, z1, n, sqlite3_free);
    }
  }
}

/*
** The COALESCE() and IFNULL() functions are implemented as VDBE code so
** that unused argument values do not have to be computed.  However, we
** still need some kind of function implementation for this routines in
** the function table.  That function implementation will never be called
** so it doesn't matter what the implementation is.  We might as well use
** the "version()" function as a substitute.
*/
#define ifnullFunc versionFunc   /* Substitute function - never called */

/*
** Implementation of random().  Return a random integer.  
*/
static void randomFunc(
  sqlite3_context *context,
  int NotUsed,
................................................................................
    FUNCTION(round,              1, 0, 0, roundFunc        ),
    FUNCTION(round,              2, 0, 0, roundFunc        ),
#endif
    FUNCTION(upper,              1, 0, 0, upperFunc        ),
    FUNCTION(lower,              1, 0, 0, lowerFunc        ),
    FUNCTION(coalesce,           1, 0, 0, 0                ),
    FUNCTION(coalesce,           0, 0, 0, 0                ),
    FUNCTION2(coalesce,         -1, 0, 0, ifnullFunc,  SQLITE_FUNC_COALESCE),
    FUNCTION(hex,                1, 0, 0, hexFunc          ),
    FUNCTION2(ifnull,            2, 0, 0, ifnullFunc,  SQLITE_FUNC_COALESCE),


    FUNCTION(random,             0, 0, 0, randomFunc       ),
    FUNCTION(randomblob,         1, 0, 0, randomBlob       ),
    FUNCTION(nullif,             2, 0, 1, nullifFunc       ),
    FUNCTION(sqlite_version,     0, 0, 0, versionFunc      ),
    FUNCTION(sqlite_source_id,   0, 0, 0, sourceidFunc     ),
    FUNCTION(sqlite_log,         2, 0, 0, errlogFunc       ),
#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS

      }
      sqlite3_result_text(context, z1, n, sqlite3_free);
    }
  }
}

/*
** Some functions like COALESCE() and IFNULL() and UNLIKELY() are implemented
** as VDBE code so that unused argument values do not have to be computed.
** However, we still need some kind of function implementation for this
** routines in the function table.  The noopFunc macro provides this.
** noopFunc will never be called so it doesn't matter what the implementation
** is.  We might as well use the "version()" function as a substitute.
*/
#define noopFunc versionFunc   /* Substitute function - never called */

/*
** Implementation of random().  Return a random integer.  
*/
static void randomFunc(
  sqlite3_context *context,
  int NotUsed,
................................................................................
    FUNCTION(round,              1, 0, 0, roundFunc        ),
    FUNCTION(round,              2, 0, 0, roundFunc        ),
#endif
    FUNCTION(upper,              1, 0, 0, upperFunc        ),
    FUNCTION(lower,              1, 0, 0, lowerFunc        ),
    FUNCTION(coalesce,           1, 0, 0, 0                ),
    FUNCTION(coalesce,           0, 0, 0, 0                ),
    FUNCTION2(coalesce,         -1, 0, 0, noopFunc,  SQLITE_FUNC_COALESCE),
    FUNCTION(hex,                1, 0, 0, hexFunc          ),
    FUNCTION2(ifnull,            2, 0, 0, noopFunc,  SQLITE_FUNC_COALESCE),
    FUNCTION2(unlikely,          1, 0, 0, noopFunc,  SQLITE_FUNC_UNLIKELY),
    FUNCTION2(unlikely,          2, 0, 0, noopFunc,  SQLITE_FUNC_UNLIKELY),
    FUNCTION(random,             0, 0, 0, randomFunc       ),
    FUNCTION(randomblob,         1, 0, 0, randomBlob       ),
    FUNCTION(nullif,             2, 0, 1, nullifFunc       ),
    FUNCTION(sqlite_version,     0, 0, 0, versionFunc      ),
    FUNCTION(sqlite_source_id,   0, 0, 0, sourceidFunc     ),
    FUNCTION(sqlite_log,         2, 0, 0, errlogFunc       ),
#ifndef SQLITE_OMIT_COMPILEOPTION_DIAGS

    sqlite3ErrorMsg(pParse,"%s prohibited in CHECK constraints", zMsg);
  }
}
#else
# define notValidCheckConstraint(P,N,M)
#endif














/*
** This routine is callback for sqlite3WalkExpr().
**
** Resolve symbolic names into TK_COLUMN operators for the current
** node in the expression tree.  Return 0 to continue the search down
** the tree or 2 to abort the tree walk.
................................................................................
        if( pDef==0 ){
          no_such_func = 1;
        }else{
          wrong_num_args = 1;
        }
      }else{
        is_agg = pDef->xFunc==0;













      }
#ifndef SQLITE_OMIT_AUTHORIZATION
      if( pDef ){
        auth = sqlite3AuthCheck(pParse, SQLITE_FUNCTION, 0, pDef->zName, 0);
        if( auth!=SQLITE_OK ){
          if( auth==SQLITE_DENY ){
            sqlite3ErrorMsg(pParse, "not authorized to use function: %s",

    sqlite3ErrorMsg(pParse,"%s prohibited in CHECK constraints", zMsg);
  }
}
#else
# define notValidCheckConstraint(P,N,M)
#endif

/*
** Expression p should encode a floating point value between 1.0 and 0.0.
** Return 1024 times this value.  Or return -1 if p is not a floating point
** value between 1.0 and 0.0.
*/
static int exprProbability(Expr *p){
  double r = -1.0;
  if( p->op!=TK_FLOAT ) return -1;
  sqlite3AtoF(p->u.zToken, &r, sqlite3Strlen30(p->u.zToken), SQLITE_UTF8);
  if( r<0.0 || r>1.0 ) return -1;
  return (int)(r*1000.0);
}

/*
** This routine is callback for sqlite3WalkExpr().
**
** Resolve symbolic names into TK_COLUMN operators for the current
** node in the expression tree.  Return 0 to continue the search down
** the tree or 2 to abort the tree walk.
................................................................................
        if( pDef==0 ){
          no_such_func = 1;
        }else{
          wrong_num_args = 1;
        }
      }else{
        is_agg = pDef->xFunc==0;
        if( pDef->funcFlags & SQLITE_FUNC_UNLIKELY ){
          ExprSetProperty(pExpr, EP_Hint);
          if( n==2 ){
            pExpr->iTable = exprProbability(pList->a[1].pExpr);
            if( pExpr->iTable<0 ){
              sqlite3ErrorMsg(pParse, "second parameter to unlikely() must be "
                                      "between 0.0 and 1.0");
              pNC->nErr++;
            }
          }else{
            pExpr->iTable = 100;
          }             
        }
      }
#ifndef SQLITE_OMIT_AUTHORIZATION
      if( pDef ){
        auth = sqlite3AuthCheck(pParse, SQLITE_FUNCTION, 0, pDef->zName, 0);
        if( auth!=SQLITE_OK ){
          if( auth==SQLITE_DENY ){
            sqlite3ErrorMsg(pParse, "not authorized to use function: %s",

  *********************************************************************/

#if SQLITE_MAX_EXPR_DEPTH>0
  int nHeight;           /* Height of the tree headed by this node */
#endif
  int iTable;            /* TK_COLUMN: cursor number of table holding column
                         ** TK_REGISTER: register number
                         ** TK_TRIGGER: 1 -> new, 0 -> old */

  ynVar iColumn;         /* TK_COLUMN: column index.  -1 for rowid.
                         ** TK_VARIABLE: variable number (always >= 1). */
  i16 iAgg;              /* Which entry in pAggInfo->aCol[] or ->aFunc[] */
  i16 iRightJoinTable;   /* If EP_FromJoin, the right table of the join */
  u8 flags2;             /* Second set of flags.  EP2_... */
  u8 op2;                /* TK_REGISTER: original value of Expr.op
                         ** TK_COLUMN: the value of p5 for OP_Column
................................................................................
#define EP_VarSelect  0x0020  /* pSelect is correlated, not constant */
#define EP_DblQuoted  0x0040  /* token.z was originally in "..." */
#define EP_InfixFunc  0x0080  /* True for an infix function: LIKE, GLOB, etc */
#define EP_Collate    0x0100  /* Tree contains a TK_COLLATE opeartor */
#define EP_FixedDest  0x0200  /* Result needed in a specific register */
#define EP_IntValue   0x0400  /* Integer value contained in u.iValue */
#define EP_xIsSelect  0x0800  /* x.pSelect is valid (otherwise x.pList is) */
#define EP_Hint       0x1000  /* Not used */
#define EP_Reduced    0x2000  /* Expr struct is EXPR_REDUCEDSIZE bytes only */
#define EP_TokenOnly  0x4000  /* Expr struct is EXPR_TOKENONLYSIZE bytes only */
#define EP_Static     0x8000  /* Held in memory not obtained from malloc() */

/*
** The following are the meanings of bits in the Expr.flags2 field.
*/

  *********************************************************************/

#if SQLITE_MAX_EXPR_DEPTH>0
  int nHeight;           /* Height of the tree headed by this node */
#endif
  int iTable;            /* TK_COLUMN: cursor number of table holding column
                         ** TK_REGISTER: register number
                         ** TK_TRIGGER: 1 -> new, 0 -> old
                         ** EP_Hint:  1000 times likelihood */
  ynVar iColumn;         /* TK_COLUMN: column index.  -1 for rowid.
                         ** TK_VARIABLE: variable number (always >= 1). */
  i16 iAgg;              /* Which entry in pAggInfo->aCol[] or ->aFunc[] */
  i16 iRightJoinTable;   /* If EP_FromJoin, the right table of the join */
  u8 flags2;             /* Second set of flags.  EP2_... */
  u8 op2;                /* TK_REGISTER: original value of Expr.op
                         ** TK_COLUMN: the value of p5 for OP_Column
................................................................................
#define EP_VarSelect  0x0020  /* pSelect is correlated, not constant */
#define EP_DblQuoted  0x0040  /* token.z was originally in "..." */
#define EP_InfixFunc  0x0080  /* True for an infix function: LIKE, GLOB, etc */
#define EP_Collate    0x0100  /* Tree contains a TK_COLLATE opeartor */
#define EP_FixedDest  0x0200  /* Result needed in a specific register */
#define EP_IntValue   0x0400  /* Integer value contained in u.iValue */
#define EP_xIsSelect  0x0800  /* x.pSelect is valid (otherwise x.pList is) */
#define EP_Hint       0x1000  /* The UNLIKELY() SQL function */
#define EP_Reduced    0x2000  /* Expr struct is EXPR_REDUCEDSIZE bytes only */
#define EP_TokenOnly  0x4000  /* Expr struct is EXPR_TOKENONLYSIZE bytes only */
#define EP_Static     0x8000  /* Held in memory not obtained from malloc() */

/*
** The following are the meanings of bits in the Expr.flags2 field.
*/

typedef struct WhereOrCost WhereOrCost;
typedef struct WhereOrSet WhereOrSet;

/*
** Cost X is tracked as 10*log2(X) stored in a 16-bit integer.  The
** maximum cost for ordinary tables is 64*(2**63) which becomes 6900.
** (Virtual tables can return a larger cost, but let's assume they do not.)
** So all costs can be stored in a 16-bit unsigned integer without risk
** of overflow.
**
** Costs are estimates, so no effort is made to compute 10*log2(X) exactly.
** Instead, a close estimate is used.  Any value of X<=1 is stored as 0.
** X=2 is 10.  X=3 is 16.  X=1000 is 99. etc.

**
** The tool/wherecosttest.c source file implements a command-line program
** that will convert WhereCosts to integers, convert integers to WhereCosts
** and do addition and multiplication on WhereCost values.  The wherecosttest
** command-line program is a useful utility to have around when working with
** this module.
*/
typedef unsigned short int WhereCost;

/*
** This object contains information needed to implement a single nested
** loop in WHERE clause.
**
** Contrast this object with WhereLoop.  This object describes the
** implementation of the loop.  WhereLoop describes the algorithm.
................................................................................
  int iParent;            /* Disable pWC->a[iParent] when this term disabled */
  int leftCursor;         /* Cursor number of X in "X <op> <expr>" */
  union {
    int leftColumn;         /* Column number of X in "X <op> <expr>" */
    WhereOrInfo *pOrInfo;   /* Extra information if (eOperator & WO_OR)!=0 */
    WhereAndInfo *pAndInfo; /* Extra information if (eOperator& WO_AND)!=0 */
  } u;

  u16 eOperator;          /* A WO_xx value describing <op> */
  u8 wtFlags;             /* TERM_xxx 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 pExpr->pRight */
  Bitmask prereqAll;      /* Bitmask of tables referenced by pExpr */
};
................................................................................
    }
  }
  if( pWC->a!=pWC->aStatic ){
    sqlite3DbFree(db, pWC->a);
  }
}




/*
** Add a single new WhereTerm entry to the WhereClause object pWC.
** The new WhereTerm object is constructed from Expr p and with wtFlags.
** The index in pWC->a[] of the new WhereTerm is returned on success.
** 0 is returned if the new WhereTerm could not be added due to a memory
** allocation error.  The memory allocation failure will be recorded in
** the db->mallocFailed flag so that higher-level functions can detect it.
................................................................................
    memcpy(pWC->a, pOld, sizeof(pWC->a[0])*pWC->nTerm);
    if( pOld!=pWC->aStatic ){
      sqlite3DbFree(db, pOld);
    }
    pWC->nSlot = sqlite3DbMallocSize(db, pWC->a)/sizeof(pWC->a[0]);
  }
  pTerm = &pWC->a[idx = pWC->nTerm++];





  pTerm->pExpr = sqlite3ExprSkipCollate(p);
  pTerm->wtFlags = wtFlags;
  pTerm->pWC = pWC;
  pTerm->iParent = -1;
  return idx;
}

................................................................................
  if( sqlite3WhereTrace & 0x8 ){
    sqlite3DebugPrintf("ins-noop: ");
    whereLoopPrint(pTemplate, pWInfo->pTabList);
  }
#endif
  return SQLITE_OK;  
}



























/*
** We have so far matched pBuilder->pNew->u.btree.nEq terms of the index pIndex.
** Try to match one more.
**
** If pProbe->tnum==0, that means pIndex is a fake index used for the
** INTEGER PRIMARY KEY.
................................................................................
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
      /* Each row involves a step of the index, then a binary search of
      ** the main table */
      pNew->rRun =  whereCostAdd(pNew->rRun, rLogSize>27 ? rLogSize-17 : 10);
    }
    /* Step cost for each output row */
    pNew->rRun = whereCostAdd(pNew->rRun, pNew->nOut);
    /* 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->nOut = saved_nOut;
................................................................................
      pNew->iSortIdx = b ? iSortIdx : 0;
      /* TUNING: Cost of full table scan is 3*(N + log2(N)).
      **  +  The extra 3 factor is to encourage the use of indexed lookups
      **     over full scans.  A smaller constant 2 is used for covering
      **     index scans so that a covering index scan will be favored over
      **     a table scan. */
      pNew->rRun = whereCostAdd(rSize,rLogSize) + 16;

      rc = whereLoopInsert(pBuilder, pNew);

      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsInIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
      if( b
................................................................................
          pNew->rRun = 10 + whereCostAdd(rSize,rLogSize) - b;
        }else{
          assert( b!=0 ); 
          /* TUNING: Cost of scanning a non-covering index is (N+1)*log2(N)
          ** 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);
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    sqlite3Stat4ProbeFree(pBuilder->pRec);

typedef struct WhereOrCost WhereOrCost;
typedef struct WhereOrSet WhereOrSet;

/*
** Cost X is tracked as 10*log2(X) stored in a 16-bit integer.  The
** maximum cost for ordinary tables is 64*(2**63) which becomes 6900.
** (Virtual tables can return a larger cost, but let's assume they do not.)
** So all costs can be stored in a 16-bit integer without risk
** of overflow.
**
** Costs are estimates, so no effort is made to compute 10*log2(X) exactly.
** Instead, a close estimate is used.  Any value of X=1 is stored as 0.
** X=2 is 10.  X=3 is 16.  X=1000 is 99. etc.  Negative values are allowed.
** A WhereCost of -10 means 0.5.  WhereCost of -20 means 0.25.  And so forth.
**
** The tool/wherecosttest.c source file implements a command-line program
** that will convert WhereCosts to integers, convert integers to WhereCosts
** and do addition and multiplication on WhereCost values.  The wherecosttest
** command-line program is a useful utility to have around when working with
** this module.
*/
typedef short int WhereCost;

/*
** This object contains information needed to implement a single nested
** loop in WHERE clause.
**
** Contrast this object with WhereLoop.  This object describes the
** implementation of the loop.  WhereLoop describes the algorithm.
................................................................................
  int iParent;            /* Disable pWC->a[iParent] when this term disabled */
  int leftCursor;         /* Cursor number of X in "X <op> <expr>" */
  union {
    int leftColumn;         /* Column number of X in "X <op> <expr>" */
    WhereOrInfo *pOrInfo;   /* Extra information if (eOperator & WO_OR)!=0 */
    WhereAndInfo *pAndInfo; /* Extra information if (eOperator& WO_AND)!=0 */
  } u;
  WhereCost truthProb;    /* Probability of truth for this expression */
  u16 eOperator;          /* A WO_xx value describing <op> */
  u8 wtFlags;             /* TERM_xxx 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 pExpr->pRight */
  Bitmask prereqAll;      /* Bitmask of tables referenced by pExpr */
};
................................................................................
    }
  }
  if( pWC->a!=pWC->aStatic ){
    sqlite3DbFree(db, pWC->a);
  }
}

/* Forward declaration */
static WhereCost whereCost(tRowcnt x);

/*
** Add a single new WhereTerm entry to the WhereClause object pWC.
** The new WhereTerm object is constructed from Expr p and with wtFlags.
** The index in pWC->a[] of the new WhereTerm is returned on success.
** 0 is returned if the new WhereTerm could not be added due to a memory
** allocation error.  The memory allocation failure will be recorded in
** the db->mallocFailed flag so that higher-level functions can detect it.
................................................................................
    memcpy(pWC->a, pOld, sizeof(pWC->a[0])*pWC->nTerm);
    if( pOld!=pWC->aStatic ){
      sqlite3DbFree(db, pOld);
    }
    pWC->nSlot = sqlite3DbMallocSize(db, pWC->a)/sizeof(pWC->a[0]);
  }
  pTerm = &pWC->a[idx = pWC->nTerm++];
  if( p && ExprHasAnyProperty(p, EP_Hint) ){
    pTerm->truthProb = whereCost(p->iTable) - 99;
  }else{
    pTerm->truthProb = -1;
  }
  pTerm->pExpr = sqlite3ExprSkipCollate(p);
  pTerm->wtFlags = wtFlags;
  pTerm->pWC = pWC;
  pTerm->iParent = -1;
  return idx;
}

................................................................................
  if( sqlite3WhereTrace & 0x8 ){
    sqlite3DebugPrintf("ins-noop: ");
    whereLoopPrint(pTemplate, pWInfo->pTabList);
  }
#endif
  return SQLITE_OK;  
}

/*
** Adjust the WhereLoop.nOut value downward to account for terms of the
** WHERE clause that reference the loop but which are not used by an
** index.
**
** In the current implementation, the first extra WHERE clause term reduces
** the number of output rows by a factor of 10 and each additional term
** reduces the number of output rows by sqrt(2).
*/
static void whereLoopOutputAdjust(WhereClause *pWC, WhereLoop *pLoop, int iCur){
  WhereTerm *pTerm;
  Bitmask notAllowed = ~(pLoop->prereq|pLoop->maskSelf);
  int x = 0;
  int i;
  for(i=pWC->nTerm, pTerm=pWC->a; i>0; i--, pTerm++){
    if( (pTerm->wtFlags & TERM_VIRTUAL)!=0 ) continue;
    if( (pTerm->prereqAll & pLoop->maskSelf)==0 ) continue;
    if( (pTerm->prereqAll & notAllowed)!=0 ) continue;
    x += pTerm->truthProb;
  }
  for(i=pLoop->nLTerm-1; i>=0; i--){
    x -= pLoop->aLTerm[i]->truthProb;
  }
  if( x<0 ) pLoop->nOut += x;
}

/*
** We have so far matched pBuilder->pNew->u.btree.nEq terms of the index pIndex.
** Try to match one more.
**
** If pProbe->tnum==0, that means pIndex is a fake index used for the
** INTEGER PRIMARY KEY.
................................................................................
    if( (pNew->wsFlags & (WHERE_IDX_ONLY|WHERE_IPK))==0 ){
      /* Each row involves a step of the index, then a binary search of
      ** the main table */
      pNew->rRun =  whereCostAdd(pNew->rRun, rLogSize>27 ? rLogSize-17 : 10);
    }
    /* Step cost for each output row */
    pNew->rRun = whereCostAdd(pNew->rRun, pNew->nOut);
    whereLoopOutputAdjust(pBuilder->pWC, pNew, pSrc->iCursor);
    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->nOut = saved_nOut;
................................................................................
      pNew->iSortIdx = b ? iSortIdx : 0;
      /* TUNING: Cost of full table scan is 3*(N + log2(N)).
      **  +  The extra 3 factor is to encourage the use of indexed lookups
      **     over full scans.  A smaller constant 2 is used for covering
      **     index scans so that a covering index scan will be favored over
      **     a table scan. */
      pNew->rRun = whereCostAdd(rSize,rLogSize) + 16;
      whereLoopOutputAdjust(pWC, pNew, pSrc->iCursor);
      rc = whereLoopInsert(pBuilder, pNew);
      pNew->nOut = rSize;
      if( rc ) break;
    }else{
      Bitmask m = pSrc->colUsed & ~columnsInIndex(pProbe);
      pNew->wsFlags = (m==0) ? (WHERE_IDX_ONLY|WHERE_INDEXED) : WHERE_INDEXED;

      /* Full scan via index */
      if( b
................................................................................
          pNew->rRun = 10 + whereCostAdd(rSize,rLogSize) - b;
        }else{
          assert( b!=0 ); 
          /* TUNING: Cost of scanning a non-covering index is (N+1)*log2(N)
          ** which we will simplify to just N*log2(N) */
          pNew->rRun = rSize + rLogSize;
        }
        whereLoopOutputAdjust(pWC, pNew, pSrc->iCursor);
        rc = whereLoopInsert(pBuilder, pNew);
        pNew->nOut = rSize;
        if( rc ) break;
      }
    }

    rc = whereLoopAddBtreeIndex(pBuilder, pSrc, pProbe, 0);
#ifdef SQLITE_ENABLE_STAT3_OR_STAT4
    sqlite3Stat4ProbeFree(pBuilder->pRec);

  reset_db
  execsql {
    CREATE TABLE t1(a, UNIQUE(a));
    INSERT INTO t1 VALUES($two);
    ANALYZE;
  }
  set nByte2 [lindex [sqlite3_db_status db SCHEMA_USED 0] 1]


  expr {$nByte2 > $nByte+950 && $nByte2 < $nByte+1050}
} {1}

#-------------------------------------------------------------------------
# Test that stat4 data may be used with partial indexes.
#
................................................................................
    do_execsql_test 20.3.$i {
      SELECT count(*) FROM sqlite_stat4 
      WHERE lrange(test_decode(sample), 0, 3)=$val
    } {1}
}

finish_test

  reset_db
  execsql {
    CREATE TABLE t1(a, UNIQUE(a));
    INSERT INTO t1 VALUES($two);
    ANALYZE;
  }
  set nByte2 [lindex [sqlite3_db_status db SCHEMA_USED 0] 1]
puts "$nByte $nByte2"

  expr {$nByte2 > $nByte+950 && $nByte2 < $nByte+1050}
} {1}

#-------------------------------------------------------------------------
# Test that stat4 data may be used with partial indexes.
#
................................................................................
    do_execsql_test 20.3.$i {
      SELECT count(*) FROM sqlite_stat4 
      WHERE lrange(test_decode(sample), 0, 3)=$val
    } {1}
}

finish_test