SQLite

#define WHERE_COLUMN_NULL  0x00080000  /* x IS NULL */
#define WHERE_INDEXED      0x000f0000  /* Anything that uses an index */
#define WHERE_NOT_FULLSCAN 0x100f3000  /* Does not do a full table scan */
#define WHERE_IN_ABLE      0x000f1000  /* Able to support an IN operator */
#define WHERE_TOP_LIMIT    0x00100000  /* x<EXPR or x<=EXPR constraint */
#define WHERE_BTM_LIMIT    0x00200000  /* x>EXPR or x>=EXPR constraint */
#define WHERE_BOTH_LIMIT   0x00300000  /* Both x>EXPR and x<EXPR */
#define WHERE_IDX_ONLY     0x00400000  /* Use index only - omit table */
#define WHERE_ORDERBY      0x00800000  /* Output will appear in correct order */
#define WHERE_REVERSE      0x01000000  /* Scan in reverse order */
#define WHERE_UNIQUE       0x02000000  /* Selects no more than one row */
#define WHERE_ALL_UNIQUE   0x04000000  /* This and all prior have one row */
#define WHERE_VIRTUALTABLE 0x08000000  /* Use virtual-table processing */
#define WHERE_MULTI_OR     0x10000000  /* OR using multiple indices */
#define WHERE_TEMP_INDEX   0x20000000  /* Uses an ephemeral index */
#define WHERE_DISTINCT     0x40000000  /* Correct order for DISTINCT */
#define WHERE_COVER_SCAN   0x80000000  /* Full scan of a covering index */

/*

      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 operations 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 int isOrderedColumn(WhereBestIdx *p, int iTab, int iCol, int *pbRev){
  int i, j;
  WhereLevel *pLevel = &p->aLevel[p->i-1];
  Index *pIdx;
  u8 sortOrder;
  for(i=p->i-1; i>=0; i--, pLevel--){
    if( pLevel->iTabCur!=iTab ) continue;
    if( (pLevel->plan.wsFlags & WHERE_ALL_UNIQUE)!=0 ){
      return 1;
    }
    if( (pLevel->plan.wsFlags & WHERE_INDEXED)!=0 ){
      pIdx = pLevel->plan.u.pIdx;
      if( iCol<0 ){
        sortOrder = 0;
        testcase( (pLevel->plan.wsFlags & WHERE_REVERSE)!=0 );
      }else{
        for(j=0; j<pIdx->nColumn; j++){

** by outer loops.  Return 1 if pTerm is ordered, and 0 if not.
*/
static int isOrderedTerm(WhereBestIdx *p, WhereTerm *pTerm, int *pbRev){
  Expr *pExpr = pTerm->pExpr;
  assert( pExpr->op==TK_EQ );
  assert( pExpr->pLeft!=0 && pExpr->pLeft->op==TK_COLUMN );
  assert( pExpr->pRight!=0 );



  if( pTerm->prereqRight==0 ){
    return 1;  /* RHS of the == is a constant */
  }
  if( pExpr->pRight->op==TK_COLUMN 
   && isOrderedColumn(p, pExpr->pRight->iTable, pExpr->pRight->iColumn, pbRev)
  ){
    return 1;
  }

  /* If we cannot prove that the constraint is ordered, assume it is not */
  return 0;
}

/*
** This routine decides if pIdx can be used to satisfy the ORDER BY
** clause, either in whole or in part.  The return value is the 
** cumulative number of terms in the ORDER BY clause that are satisfied
** by the index pIdx and other indices in outer loops.
**
** The table being queried has a cursor number of "base".  pIdx is the
** index that is postulated for use to access the table.
**
** nEqCol is the number of columns of pIdx that are used as equality
** constraints and where the other side of the == is an ordered column
** or constant.  An "order column" in the previous sentence means a column
** in table from an outer loop whose values will always appear in the 
** correct order due to othre index, or because the outer loop generates
** a unique result.  Any of the first nEqCol columns of pIdx may be missing
** from the ORDER BY clause and the match can still be a success.
**
** The *pbRev value is set to 0 order 1 depending on whether or not
** pIdx should be run in the forward order or in reverse order.
*/
static int isSortingIndex(
  WhereBestIdx *p,    /* Best index search context */
  Index *pIdx,        /* The index we are testing */
  int base,           /* Cursor number for the table to be sorted */
  int nEqCol,         /* Number of index columns with ordered == constraints */
  int wsFlags,        /* Index usages flags */
  int bOuterRev,      /* True if outer loops scan in reverse order */
  int *pbRev          /* Set to 1 for reverse-order scan of pIdx */
){
  int i;                        /* Number of pIdx terms used */
  int j;                        /* Number of ORDER BY terms satisfied */
  int sortOrder = 0;            /* XOR of index and ORDER BY sort direction */
  int nTerm;                    /* Number of ORDER BY terms */
  struct ExprList_item *pTerm;  /* A term of the ORDER BY clause */
  ExprList *pOrderBy;           /* The ORDER BY clause */
  Parse *pParse = p->pParse;    /* Parser context */
  sqlite3 *db = pParse->db;     /* Database connection */
  int nPriorSat;                /* ORDER BY terms satisfied by outer loops */
  int seenRowid = 0;            /* True if an ORDER BY rowid term is seen */
  int nEqOneRow;                /* Idx columns that ref unique values */

  if( p->i==0 ){
    nPriorSat = 0;
  }else{
    nPriorSat = p->aLevel[p->i-1].plan.nOBSat;
    if( OptimizationDisabled(db, SQLITE_OrderByIdxJoin) ) return nPriorSat;
  }
  if( p->i==0 || (p->aLevel[p->i-1].plan.wsFlags & WHERE_ALL_UNIQUE)!=0 ){
    nEqOneRow = nEqCol;
  }else{
    if( nEqCol==0 ) return nPriorSat;
    sortOrder = bOuterRev;
    nEqOneRow = 0;
  }
  pOrderBy = p->pOrderBy;
  assert( pOrderBy!=0 );
  if( wsFlags & WHERE_COLUMN_IN ) return nPriorSat;
  if( pIdx->bUnordered ) return nPriorSat;
  nTerm = pOrderBy->nExpr;
  assert( nTerm>0 );

  /* Argument pIdx must either point to a 'real' named index structure, 
  ** or an index structure allocated on the stack by bestBtreeIndex() to
  ** represent the rowid index that is part of every table.  */
  assert( pIdx->zName || (pIdx->nColumn==1 && pIdx->aiColumn[0]==-1) );

  /* Match terms of the ORDER BY clause against columns of
  ** the index.
  **
  ** Note that indices have pIdx->nColumn regular columns plus
  ** one additional column containing the rowid.  The rowid column
  ** of the index is also allowed to match against the ORDER BY
  ** clause.
  */
  for(i=0,j=nPriorSat,pTerm=&pOrderBy->a[j]; j<nTerm && i<=pIdx->nColumn; i++){
    Expr *pExpr;       /* The expression of the ORDER BY pTerm */
    CollSeq *pColl;    /* The collating sequence of pExpr */
    int termSortOrder; /* Sort order for this term */
    int iColumn;       /* The i-th column of the index.  -1 for rowid */
    int iSortOrder;    /* 1 for DESC, 0 for ASC on the i-th index term */
    const char *zColl; /* Name of the collating sequence for i-th index term */

    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 */
      break;
    }
    pColl = sqlite3ExprCollSeq(pParse, pExpr);
    if( !pColl ){
      pColl = db->pDfltColl;
    }
    if( pIdx->zName && i<pIdx->nColumn ){
      iColumn = pIdx->aiColumn[i];
      if( iColumn==pIdx->pTable->iPKey ){
        iColumn = -1;
      }
      iSortOrder = pIdx->aSortOrder[i];
      zColl = pIdx->azColl[i];
    }else{
      iColumn = -1;
      iSortOrder = 0;
      zColl = pColl->zName;
    }
    if( pExpr->iColumn!=iColumn || sqlite3StrICmp(pColl->zName, zColl) ){
      /* 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( i==pIdx->nColumn ){
        /* Index column i is the rowid.  All other terms match. */
        break;
      }else{
        /* If an index column fails to match and is not constrained by ==
        ** then the index cannot satisfy the ORDER BY constraint.
        */
        return nPriorSat;
      }
    }
    assert( pIdx->aSortOrder!=0 || iColumn==-1 );
    assert( pTerm->sortOrder==0 || pTerm->sortOrder==1 );
    assert( iSortOrder==0 || iSortOrder==1 );
    termSortOrder = iSortOrder ^ pTerm->sortOrder;
    if( i>nEqOneRow ){
      if( termSortOrder!=sortOrder ){
        /* Indices can only be used if all ORDER BY terms past the
        ** equality constraints are all either DESC or ASC. */
        break;
      }
    }else{
      sortOrder = termSortOrder;
    }
    j++;
    pTerm++;
    if( iColumn<0 ){
      seenRowid = 1;
      break;
    }
  }
  *pbRev = sortOrder;

  /* If there was an "ORDER BY rowid" term that matched, or it is only
  ** possible for a single row from this table to match, then skip over
  ** any additional ORDER BY terms dealing with this table.
  */
  if( seenRowid ||
     (   (wsFlags & WHERE_COLUMN_NULL)==0
      && i>=pIdx->nColumn
      && indexIsUniqueNotNull(pIdx, nEqCol)
     )
  ){
    /* Advance j over additional ORDER BY terms associated with base */
    WhereMaskSet *pMS = p->pWC->pMaskSet;
    Bitmask m = ~getMask(pMS, base);
    while( j<nTerm && (exprTableUsage(pMS, pOrderBy->a[j].pExpr)&m)==0 ){
      j++;
    }
  }
  return j;
}

/*
** Find the best query plan for accessing a particular table.  Write the
** best query plan and its cost into the p->cost.
**
** The lowest cost plan wins.  The cost is an estimate of the amount of
** CPU and disk I/O needed to process the requested result.

    ** optimized using the index. 
    */
    if( nEq==pProbe->nColumn && pProbe->onError!=OE_None ){
      testcase( wsFlags & WHERE_COLUMN_IN );
      testcase( wsFlags & WHERE_COLUMN_NULL );
      if( (wsFlags & (WHERE_COLUMN_IN|WHERE_COLUMN_NULL))==0 ){
        wsFlags |= WHERE_UNIQUE;
        if( p->i==0 || (p->aLevel[p->i-1].plan.wsFlags & WHERE_ALL_UNIQUE)!=0 ){
          wsFlags |= WHERE_ALL_UNIQUE;
        }
      }
    }else if( pProbe->bUnordered==0 ){
      int j = (nEq==pProbe->nColumn ? -1 : pProbe->aiColumn[nEq]);
      if( findTerm(pWC, iCur, j, p->notReady, WO_LT|WO_LE|WO_GT|WO_GE, pIdx) ){
        WhereTerm *pTop, *pBtm;
        pTop = findTerm(pWC, iCur, j, p->notReady, WO_LT|WO_LE, pIdx);
        pBtm = findTerm(pWC, iCur, j, p->notReady, WO_GT|WO_GE, pIdx);

# 2012 Sept 27
#
# 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 file implements regression tests for SQLite library.  The
# focus of this file is testing that the optimizations that disable
# ORDER BY clauses when the natural order of a query is correct.
#


set testdir [file dirname $argv0]
source $testdir/tester.tcl
set ::testprefix orderby2

# Generate test data for a join.  Verify that the join gets the
# correct answer.
#
do_test 1.0 {
  db eval {
    CREATE TABLE t1(a INTEGER PRIMARY KEY, b);
    INSERT INTO t1 VALUES(1,11), (2,22);
    CREATE TABLE t2(d, e, UNIQUE(d,e));
    INSERT INTO t2 VALUES(10, 'ten'), (11,'eleven'), (12,'twelve'),
                         (11, 'oneteen');
  }
} {}

do_test 1.1a {
  db eval {
    SELECT e FROM t1, t2 WHERE a=1 AND d=b ORDER BY d, e;
  }
} {eleven oneteen}
do_test 1.1b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT e FROM t1, t2 WHERE a=1 AND d=b ORDER BY d, e;
  }
} {~/ORDER BY/}

do_test 1.2a {
  db eval {
    SELECT e FROM t1, t2 WHERE a=1 AND d=b ORDER BY e;
  }
} {eleven oneteen}
do_test 1.2b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT e FROM t1, t2 WHERE a=1 AND d=b ORDER BY e;
  }
} {~/ORDER BY/}

do_test 1.3a {
  db eval {
    SELECT e, b FROM t1, t2 WHERE a=1 ORDER BY d, e;
  }
} {ten 11 eleven 11 oneteen 11 twelve 11}
do_test 1.3b {
  db eval {
    EXPLAIN QUERY PLAN
    SELECT e, b FROM t1, t2 WHERE a=1 ORDER BY d, e;
  }
} {~/ORDER BY/}


finish_test