Token s;
  assert( zC!=0 );
  sqlite3TokenInit(&s, (char*)zC);
  return sqlite3ExprAddCollateToken(pParse, pExpr, &s, 0);
}

/*
** Skip over any TK_COLLATE operators.
*/
Expr *sqlite3ExprSkipCollate(Expr *pExpr){
  while( pExpr && ExprHasProperty(pExpr, EP_Skip) ){
    assert( pExpr->op==TK_COLLATE );
    pExpr = pExpr->pLeft;
  }   
  return pExpr;
}

/*
** Skip over any TK_COLLATE operators and/or any unlikely()
** or likelihood() or likely() functions at the root of an
** expression.
*/
Expr *sqlite3ExprSkipCollateAndLikely(Expr *pExpr){
  while( pExpr && ExprHasProperty(pExpr, EP_Skip|EP_Unlikely) ){
    if( ExprHasProperty(pExpr, EP_Unlikely) ){
      assert( !ExprHasProperty(pExpr, EP_xIsSelect) );
      assert( pExpr->x.pList->nExpr>0 );
      assert( pExpr->op==TK_FUNCTION );
      pExpr = pExpr->x.pList->a[0].pExpr;
    }else{

/*
** Convert a scalar expression node to a TK_REGISTER referencing
** register iReg.  The caller must ensure that iReg already contains
** the correct value for the expression.
*/
static void exprToRegister(Expr *pExpr, int iReg){
  Expr *p = sqlite3ExprSkipCollateAndLikely(pExpr);
  p->op2 = p->op;
  p->op = TK_REGISTER;
  p->iTable = iReg;
  ExprClearProperty(p, EP_Skip);
}

/*

**
** If pExpr is a constant, then this routine might generate this
** code to fill the register in the initialization section of the
** VDBE program, in order to factor it out of the evaluation loop.
*/
int sqlite3ExprCodeTemp(Parse *pParse, Expr *pExpr, int *pReg){
  int r2;
  pExpr = sqlite3ExprSkipCollateAndLikely(pExpr);
  if( ConstFactorOk(pParse)
   && pExpr->op!=TK_REGISTER
   && sqlite3ExprIsConstantNotJoin(pExpr)
  ){
    *pReg  = 0;
    r2 = sqlite3ExprCodeAtInit(pParse, pExpr, -1);
  }else{

/*
** Like sqlite3ExprCompare() except COLLATE operators at the top-level
** are ignored.
*/
int sqlite3ExprCompareSkip(Expr *pA, Expr *pB, int iTab){
  return sqlite3ExprCompare(0,
             sqlite3ExprSkipCollateAndLikely(pA),
             sqlite3ExprSkipCollateAndLikely(pB),
             iTab);
}

/*
** Return non-zero if Expr p can only be true if pNN is not NULL.
*/
static int exprImpliesNotNull(

** an ordinary JOIN.  The p argument is the WHERE clause.  If the WHERE
** clause requires that some column of the right table of the LEFT JOIN
** be non-NULL, then the LEFT JOIN can be safely converted into an
** ordinary join.
*/
int sqlite3ExprImpliesNonNullRow(Expr *p, int iTab){
  Walker w;
  p = sqlite3ExprSkipCollateAndLikely(p);
  while( p ){
    if( p->op==TK_NOTNULL ){
      p = p->pLeft;
    }else if( p->op==TK_AND ){
      if( sqlite3ExprImpliesNonNullRow(p->pLeft, iTab) ) return 1;
      p = p->pRight;
    }else{

    }
    case TK_VARIABLE: {
      notValid(pParse, pNC, "parameters", NC_IsCheck|NC_PartIdx|NC_IdxExpr);
      break;
    }
    case TK_IS:
    case TK_ISNOT: {
      Expr *pRight = sqlite3ExprSkipCollateAndLikely(pExpr->pRight);
      assert( !ExprHasProperty(pExpr, EP_Reduced) );
      /* Handle special cases of "x IS TRUE", "x IS FALSE", "x IS NOT TRUE",
      ** and "x IS NOT FALSE". */
      if( pRight->op==TK_ID ){
        int rc = resolveExprStep(pWalker, pRight);
        if( rc==WRC_Abort ) return WRC_Abort;
        if( pRight->op==TK_TRUEFALSE ){

    moreToDo = 0;
    pEList = pSelect->pEList;
    assert( pEList!=0 );
    for(i=0, pItem=pOrderBy->a; i<pOrderBy->nExpr; i++, pItem++){
      int iCol = -1;
      Expr *pE, *pDup;
      if( pItem->done ) continue;
      pE = sqlite3ExprSkipCollateAndLikely(pItem->pExpr);
      if( sqlite3ExprIsInteger(pE, &iCol) ){
        if( iCol<=0 || iCol>pEList->nExpr ){
          resolveOutOfRangeError(pParse, "ORDER", i+1, pEList->nExpr);
          return 1;
        }
      }else{
        iCol = resolveAsName(pParse, pEList, pE);

  int nResult;                   /* Number of terms in the result set */

  if( pOrderBy==0 ) return 0;
  nResult = pSelect->pEList->nExpr;
  pParse = pNC->pParse;
  for(i=0, pItem=pOrderBy->a; i<pOrderBy->nExpr; i++, pItem++){
    Expr *pE = pItem->pExpr;
    Expr *pE2 = sqlite3ExprSkipCollateAndLikely(pE);
    if( zType[0]!='G' ){
      iCol = resolveAsName(pParse, pSelect->pEList, pE2);
      if( iCol>0 ){
        /* If an AS-name match is found, mark this ORDER BY column as being
        ** a copy of the iCol-th result-set column.  The subsequent call to
        ** sqlite3ResolveOrderGroupBy() will convert the expression to a
        ** copy of the iCol-th result-set expression. */

  for(i=0, pCol=aCol; i<nCol && !db->mallocFailed; i++, pCol++){
    /* Get an appropriate name for the column
    */
    if( (zName = pEList->a[i].zName)!=0 ){
      /* If the column contains an "AS <name>" phrase, use <name> as the name */
    }else{
      Expr *pColExpr = sqlite3ExprSkipCollateAndLikely(pEList->a[i].pExpr);
      while( pColExpr->op==TK_DOT ){
        pColExpr = pColExpr->pRight;
        assert( pColExpr!=0 );
      }
      if( pColExpr->op==TK_COLUMN ){
        /* For columns use the column name name */
        int iCol = pColExpr->iColumn;

CollSeq *sqlite3LocateCollSeq(Parse *pParse, const char*zName);
CollSeq *sqlite3ExprCollSeq(Parse *pParse, Expr *pExpr);
CollSeq *sqlite3ExprNNCollSeq(Parse *pParse, Expr *pExpr);
int sqlite3ExprCollSeqMatch(Parse*,Expr*,Expr*);
Expr *sqlite3ExprAddCollateToken(Parse *pParse, Expr*, const Token*, int);
Expr *sqlite3ExprAddCollateString(Parse*,Expr*,const char*);
Expr *sqlite3ExprSkipCollate(Expr*);
Expr *sqlite3ExprSkipCollateAndLikely(Expr*);
int sqlite3CheckCollSeq(Parse *, CollSeq *);
int sqlite3WritableSchema(sqlite3*);
int sqlite3CheckObjectName(Parse*, const char*,const char*,const char*);
void sqlite3VdbeSetChanges(sqlite3 *, int);
int sqlite3AddInt64(i64*,i64);
int sqlite3SubInt64(i64*,i64);
int sqlite3MulInt64(i64*,i64);

         && (iColumn!=XN_EXPR
             || sqlite3ExprCompareSkip(pTerm->pExpr->pLeft,
                                       pScan->pIdxExpr,iCur)==0)
         && (pScan->iEquiv<=1 || !ExprHasProperty(pTerm->pExpr, EP_FromJoin))
        ){
          if( (pTerm->eOperator & WO_EQUIV)!=0
           && pScan->nEquiv<ArraySize(pScan->aiCur)
           && (pX = sqlite3ExprSkipCollateAndLikely(pTerm->pExpr->pRight))->op
               ==TK_COLUMN
          ){
            int j;
            for(j=0; j<pScan->nEquiv; j++){
              if( pScan->aiCur[j]==pX->iTable
               && pScan->aiColumn[j]==pX->iColumn ){
                  break;
              }

  Index *pIdx,                    /* Index to match column of */
  int iCol                        /* Column of index to match */
){
  int i;
  const char *zColl = pIdx->azColl[iCol];

  for(i=0; i<pList->nExpr; i++){
    Expr *p = sqlite3ExprSkipCollateAndLikely(pList->a[i].pExpr);
    if( p->op==TK_COLUMN
     && p->iColumn==pIdx->aiColumn[iCol]
     && p->iTable==iBase
    ){
      CollSeq *pColl = sqlite3ExprNNCollSeq(pParse, pList->a[i].pExpr);
      if( 0==sqlite3StrICmp(pColl->zName, zColl) ){
        return i;

  pTab = pTabList->a[0].pTab;

  /* If any of the expressions is an IPK column on table iBase, then return 
  ** true. Note: The (p->iTable==iBase) part of this test may be false if the
  ** current SELECT is a correlated sub-query.
  */
  for(i=0; i<pDistinct->nExpr; i++){
    Expr *p = sqlite3ExprSkipCollateAndLikely(pDistinct->a[i].pExpr);
    if( p->op==TK_COLUMN && p->iTable==iBase && p->iColumn<0 ) return 1;
  }

  /* Loop through all indices on the table, checking each to see if it makes
  ** the DISTINCT qualifier redundant. It does so if:
  **
  **   1. The index is itself UNIQUE, and

  ExprList *pOB;
  ExprList *aColExpr;
  int ii, jj;

  if( pIndex->bUnordered ) return 0;
  if( (pOB = pBuilder->pWInfo->pOrderBy)==0 ) return 0;
  for(ii=0; ii<pOB->nExpr; ii++){
    Expr *pExpr = sqlite3ExprSkipCollateAndLikely(pOB->a[ii].pExpr);
    if( pExpr->op==TK_COLUMN && pExpr->iTable==iCursor ){
      if( pExpr->iColumn<0 ) return 1;
      for(jj=0; jj<pIndex->nKeyCol; jj++){
        if( pExpr->iColumn==pIndex->aiColumn[jj] ) return 1;
      }
    }else if( (aColExpr = pIndex->aColExpr)!=0 ){
      for(jj=0; jj<pIndex->nKeyCol; jj++){

    /* Mark off any ORDER BY term X that is a column in the table of
    ** the current loop for which there is term in the WHERE
    ** clause of the form X IS NULL or X=? that reference only outer
    ** loops.
    */
    for(i=0; i<nOrderBy; i++){
      if( MASKBIT(i) & obSat ) continue;
      pOBExpr = sqlite3ExprSkipCollateAndLikely(pOrderBy->a[i].pExpr);
      if( pOBExpr->op!=TK_COLUMN ) continue;
      if( pOBExpr->iTable!=iCur ) continue;
      pTerm = sqlite3WhereFindTerm(&pWInfo->sWC, iCur, pOBExpr->iColumn,
                       ~ready, eqOpMask, 0);
      if( pTerm==0 ) continue;
      if( pTerm->eOperator==WO_IN ){
        /* IN terms are only valid for sorting in the ORDER BY LIMIT 

        /* Find the ORDER BY term that corresponds to the j-th column
        ** of the index and mark that ORDER BY term off 
        */
        isMatch = 0;
        for(i=0; bOnce && i<nOrderBy; i++){
          if( MASKBIT(i) & obSat ) continue;
          pOBExpr = sqlite3ExprSkipCollateAndLikely(pOrderBy->a[i].pExpr);
          testcase( wctrlFlags & WHERE_GROUPBY );
          testcase( wctrlFlags & WHERE_DISTINCTBY );
          if( (wctrlFlags & (WHERE_GROUPBY|WHERE_DISTINCTBY))==0 ) bOnce = 0;
          if( iColumn>=XN_ROWID ){
            if( pOBExpr->op!=TK_COLUMN ) continue;
            if( pOBExpr->iTable!=iCur ) continue;
            if( pOBExpr->iColumn!=iColumn ) continue;

  }
  pTerm = &pWC->a[idx = pWC->nTerm++];
  if( p && ExprHasProperty(p, EP_Unlikely) ){
    pTerm->truthProb = sqlite3LogEst(p->iTable) - 270;
  }else{
    pTerm->truthProb = 1;
  }
  pTerm->pExpr = sqlite3ExprSkipCollateAndLikely(p);
  pTerm->wtFlags = wtFlags;
  pTerm->pWC = pWC;
  pTerm->iParent = -1;
  memset(&pTerm->eOperator, 0,
         sizeof(WhereTerm) - offsetof(WhereTerm,eOperator));
  return idx;
}

** 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.  The slot[] array grows as needed to contain
** all terms of the WHERE clause.
*/
void sqlite3WhereSplit(WhereClause *pWC, Expr *pExpr, u8 op){
  Expr *pE2 = sqlite3ExprSkipCollateAndLikely(pExpr);
  pWC->op = op;
  if( pE2==0 ) return;
  if( pE2->op!=op ){
    whereClauseInsert(pWC, pExpr, 0);
  }else{
    sqlite3WhereSplit(pWC, pE2->pLeft, op);
    sqlite3WhereSplit(pWC, pE2->pRight, op);

} {1 3 1 4 9 3 9 4}
do_execsql_test 7.2 {
  SELECT likelihood(a,0.5), x FROM t1, t2 ORDER BY 1, 2;
} {1 3 1 4 9 3 9 4}
do_execsql_test 7.3 {
  SELECT coalesce(a,a), x FROM t1, t2 ORDER BY 1, 2;
} {1 3 1 4 9 3 9 4}

# 2019-08-22
# Ticket https://www.sqlite.org/src/info/7e07a3dbf5a8cd26
#
do_execsql_test 8.1 {
  DROP TABLE IF EXISTS t0;
  CREATE TABLE t0 (c0);
  INSERT INTO t0(c0) VALUES ('a');
  SELECT LIKELY(t0.rowid) <= '0' FROM t0;
} {1}
do_execsql_test 8.2 {
  SELECT * FROM t0 WHERE LIKELY(t0.rowid) <= '0';
} {a}
do_execsql_test 8.3 {
  SELECT (t0.rowid) <= '0' FROM t0;
} {0}
do_execsql_test 8.4 {
  SELECT * FROM t0 WHERE (t0.rowid) <= '0';
} {}
do_execsql_test 8.5 {
  SELECT unlikely(t0.rowid) <= '0', likelihood(t0.rowid,0.5) <= '0' FROM t0;
} {1 1}
do_execsql_test 8.6 {
  SELECT * FROM t0 WHERE unlikely(t0.rowid) <= '0';
} {a}
do_execsql_test 8.7 {
  SELECT * FROM t0 WHERE likelihood(t0.rowid, 0.5) <= '0';
} {a}
do_execsql_test 8.8 {
  SELECT unlikely(t0.rowid <= '0'),
         likely(t0.rowid <= '0'),
         likelihood(t0.rowid <= '0',0.5)
    FROM t0;
} {0 0 0}
do_execsql_test 8.9 {
  SELECT * FROM t0 WHERE unlikely(t0.rowid <= '0');
} {}
do_execsql_test 8.10 {
  SELECT * FROM t0 WHERE likelihood(t0.rowid <= '0', 0.5);
} {}




finish_test