SQLite

    i16 x = pIdx->aiColumn[i];
    assert( x<pIdx->pTable->nCol );
    wIndex += x<0 ? 1 : aCol[pIdx->aiColumn[i]].szEst;
  }
  pIdx->szIdxRow = sqlite3LogEst(wIndex*4);
}

/* Return true if column number x is any of the first nCol entries of aiCol[].
** This is used to determine if the column number x appears in any of the
** first nCol entries of an index.
*/
static int hasColumn(const i16 *aiCol, int nCol, int x){
  while( nCol-- > 0 ){
    assert( aiCol[0]>=0 );
    if( x==*(aiCol++) ){
      return 1;
    }
  }
  return 0;
}

/*
** Return true if any of the first nKey entries of index pIdx exactly
** match the iCol-th entry of pPk.  pPk is always a WITHOUT ROWID
** PRIMARY KEY index.  pIdx is an index on the same table.  pIdx may
** or may not be the same index as pPk.
**
** The first nKey entries of pIdx are guaranteed to be ordinary columns,
** not a rowid or expression.
**
** This routine differs from hasColumn() in that both the column and the
** collating sequence must match for this routine, but for hasColumn() only
** the column name must match.
*/
static int isDupColumn(Index *pIdx, int nKey, Index *pPk, int iCol){
  int i, j;
  assert( nKey<=pIdx->nColumn );
  assert( iCol<MAX(pPk->nColumn,pPk->nKeyCol) );
  assert( pPk->idxType==SQLITE_IDXTYPE_PRIMARYKEY );
  assert( pPk->pTable->tabFlags & TF_WithoutRowid );
  assert( pPk->pTable==pIdx->pTable );
  testcase( pPk==pIdx );
  j = pPk->aiColumn[iCol];
  assert( j!=XN_ROWID && j!=XN_EXPR );
  for(i=0; i<nKey; i++){
    assert( pIdx->aiColumn[i]>=0 || j>=0 );
    if( pIdx->aiColumn[i]==j 
     && sqlite3StrICmp(pIdx->azColl[i], pPk->azColl[iCol])==0
    ){
      return 1;
    }
  }
  return 0;
}

/* Recompute the colNotIdxed field of the Index.
**
** colNotIdxed is a bitmask that has a 0 bit representing each indexed
** columns that are within the first 63 columns of the table.  The

    /*
    ** Remove all redundant columns from the PRIMARY KEY.  For example, change
    ** "PRIMARY KEY(a,b,a,b,c,b,c,d)" into just "PRIMARY KEY(a,b,c,d)".  Later
    ** code assumes the PRIMARY KEY contains no repeated columns.
    */
    for(i=j=1; i<pPk->nKeyCol; i++){
      if( isDupColumn(pPk, j, pPk, i) ){
        pPk->nColumn--;
      }else{
        testcase( hasColumn(pPk->aiColumn, j, pPk->aiColumn[i]) );
        pPk->aiColumn[j++] = pPk->aiColumn[i];
      }
    }
    pPk->nKeyCol = j;
  }
  assert( pPk!=0 );
  pPk->isCovering = 1;

  /* Update the in-memory representation of all UNIQUE indices by converting
  ** the final rowid column into one or more columns of the PRIMARY KEY.
  */
  for(pIdx=pTab->pIndex; pIdx; pIdx=pIdx->pNext){
    int n;
    if( IsPrimaryKeyIndex(pIdx) ) continue;
    for(i=n=0; i<nPk; i++){
      if( !isDupColumn(pIdx, pIdx->nKeyCol, pPk, i) ){
        testcase( hasColumn(pIdx->aiColumn, pIdx->nKeyCol, pPk->aiColumn[i]) );
        n++;
      }
    }
    if( n==0 ){
      /* This index is a superset of the primary key */
      pIdx->nColumn = pIdx->nKeyCol;
      continue;
    }
    if( resizeIndexObject(db, pIdx, pIdx->nKeyCol+n) ) return;
    for(i=0, j=pIdx->nKeyCol; i<nPk; i++){
      if( !isDupColumn(pIdx, pIdx->nKeyCol, pPk, i) ){
        testcase( hasColumn(pIdx->aiColumn, pIdx->nKeyCol, pPk->aiColumn[i]) );
        pIdx->aiColumn[j] = pPk->aiColumn[i];
        pIdx->azColl[j] = pPk->azColl[i];
        j++;
      }
    }
    assert( pIdx->nColumn>=pIdx->nKeyCol+n );
    assert( pIdx->nColumn>=j );

  ** tables (when pPk!=0) this will be the declared PRIMARY KEY.  For
  ** normal tables (when pPk==0) this will be the rowid.
  */
  if( pPk ){
    for(j=0; j<pPk->nKeyCol; j++){
      int x = pPk->aiColumn[j];
      assert( x>=0 );
      if( isDupColumn(pIndex, pIndex->nKeyCol, pPk, j) ){
        pIndex->nColumn--; 
      }else{
        testcase( hasColumn(pIndex->aiColumn,pIndex->nKeyCol,x) );
        pIndex->aiColumn[i] = x;
        pIndex->azColl[i] = pPk->azColl[j];
        pIndex->aSortOrder[i] = pPk->aSortOrder[j];
        i++;
      }
    }
    assert( i==pIndex->nColumn );

  CREATE TRIGGER t1_tr BEFORE UPDATE ON t1 BEGIN
    DELETE FROM t1 WHERE a = new.a;
  END;
  UPDATE t1 SET c = c+1 WHERE a = 'a';
  SELECT * FROM t1;
} {b a 3  b b 4}

# 2019-04-29 ticket https://www.sqlite.org/src/info/3182d3879020ef3
do_execsql_test 11.1 {
  CREATE TABLE t11(a TEXT PRIMARY KEY, b INT) WITHOUT ROWID;
  CREATE INDEX t11a ON t11(a COLLATE NOCASE);
  INSERT INTO t11(a,b) VALUES ('A',1),('a',2);
  PRAGMA integrity_check;
  SELECT a FROM t11 ORDER BY a COLLATE binary;
} {ok A a}
  
finish_test