* planner.c
* The query optimizer external interface.
*
- * Portions Copyright (c) 1996-2008, PostgreSQL Global Development Group
+ * Portions Copyright (c) 1996-2009, PostgreSQL Global Development Group
* Portions Copyright (c) 1994, Regents of the University of California
*
*
* IDENTIFICATION
- * $PostgreSQL: pgsql/src/backend/optimizer/plan/planner.c,v 1.243 2008/09/09 18:58:08 tgl Exp $
+ * $PostgreSQL: pgsql/src/backend/optimizer/plan/planner.c,v 1.250 2009/01/01 17:23:44 momjian Exp $
*
*-------------------------------------------------------------------------
*/
List *sub_tlist,
AttrNumber *groupColIdx);
static List *postprocess_setop_tlist(List *new_tlist, List *orig_tlist);
+static List *select_active_windows(PlannerInfo *root, WindowFuncLists *wflists);
+static List *make_pathkeys_for_window(PlannerInfo *root, WindowClause *wc,
+ List *tlist, bool canonicalize);
+static void get_column_info_for_window(PlannerInfo *root, WindowClause *wc,
+ List *tlist,
+ int numSortCols, AttrNumber *sortColIdx,
+ int *partNumCols,
+ AttrNumber **partColIdx,
+ Oid **partOperators,
+ int *ordNumCols,
+ AttrNumber **ordColIdx,
+ Oid **ordOperators);
/*****************************************************************************
glob->finalrtable = NIL;
glob->relationOids = NIL;
glob->invalItems = NIL;
+ glob->lastPHId = 0;
glob->transientPlan = false;
/* Determine what fraction of the plan is likely to be scanned */
}
/* primary planning entry point (may recurse for subqueries) */
- top_plan = subquery_planner(glob, parse, 1, tuple_fraction, &root);
+ top_plan = subquery_planner(glob, parse, NULL,
+ false, tuple_fraction, &root);
/*
* If creating a plan for a scrollable cursor, make sure it can run
*
* glob is the global state for the current planner run.
* parse is the querytree produced by the parser & rewriter.
- * level is the current recursion depth (1 at the top-level Query).
+ * parent_root is the immediate parent Query's info (NULL at the top level).
+ * hasRecursion is true if this is a recursive WITH query.
* tuple_fraction is the fraction of tuples we expect will be retrieved.
* tuple_fraction is interpreted as explained for grouping_planner, below.
*
*/
Plan *
subquery_planner(PlannerGlobal *glob, Query *parse,
- Index level, double tuple_fraction,
+ PlannerInfo *parent_root,
+ bool hasRecursion, double tuple_fraction,
PlannerInfo **subroot)
{
int num_old_subplans = list_length(glob->subplans);
root = makeNode(PlannerInfo);
root->parse = parse;
root->glob = glob;
- root->query_level = level;
+ root->query_level = parent_root ? parent_root->query_level + 1 : 1;
+ root->parent_root = parent_root;
root->planner_cxt = CurrentMemoryContext;
root->init_plans = NIL;
+ root->cte_plan_ids = NIL;
root->eq_classes = NIL;
root->append_rel_list = NIL;
+ root->hasRecursion = hasRecursion;
+ if (hasRecursion)
+ root->wt_param_id = SS_assign_worktable_param(root);
+ else
+ root->wt_param_id = -1;
+ root->non_recursive_plan = NULL;
+
+ /*
+ * If there is a WITH list, process each WITH query and build an
+ * initplan SubPlan structure for it.
+ */
+ if (parse->cteList)
+ SS_process_ctes(root);
+
/*
* Look for ANY and EXISTS SubLinks in WHERE and JOIN/ON clauses, and try
* to transform them into joins. Note that this step does not descend
/*
* Simplify constant expressions.
*
+ * Note: one essential effect here is to insert the current actual values
+ * of any default arguments for functions. To ensure that happens, we
+ * *must* process all expressions here. Previous PG versions sometimes
+ * skipped const-simplification if it didn't seem worth the trouble, but
+ * we can't do that anymore.
+ *
* Note: this also flattens nested AND and OR expressions into N-argument
* form. All processing of a qual expression after this point must be
* careful to maintain AND/OR flatness --- that is, do not generate a tree
* with AND directly under AND, nor OR directly under OR.
- *
- * Because this is a relatively expensive process, we skip it when the
- * query is trivial, such as "SELECT 2+2;" or "INSERT ... VALUES()". The
- * expression will only be evaluated once anyway, so no point in
- * pre-simplifying; we can't execute it any faster than the executor can,
- * and we will waste cycles copying the tree. Notice however that we
- * still must do it for quals (to get AND/OR flatness); and if we are in a
- * subquery we should not assume it will be done only once.
- *
- * For VALUES lists we never do this at all, again on the grounds that we
- * should optimize for one-time evaluation.
*/
- if (kind != EXPRKIND_VALUES &&
- (root->parse->jointree->fromlist != NIL ||
- kind == EXPRKIND_QUAL ||
- root->query_level > 1))
- expr = eval_const_expressions(root, expr);
+ expr = eval_const_expressions(root, expr);
/*
* If it's a qual or havingQual, canonicalize it.
subroot.parse = (Query *)
adjust_appendrel_attrs((Node *) parse,
appinfo);
+ subroot.returningLists = NIL;
subroot.init_plans = NIL;
+ /* We needn't modify the child's append_rel_list */
/* There shouldn't be any OJ info to translate, as yet */
Assert(subroot.join_info_list == NIL);
+ /* and we haven't created PlaceHolderInfos, either */
+ Assert(subroot.placeholder_list == NIL);
/* Generate plan */
subplan = grouping_planner(&subroot, 0.0 /* retrieve all tuples */ );
/*
* Construct the plan for set operations. The result will not need
- * any work except perhaps a top-level sort and/or LIMIT.
+ * any work except perhaps a top-level sort and/or LIMIT. Note that
+ * any special work for recursive unions is the responsibility of
+ * plan_set_operations.
*/
result_plan = plan_set_operations(root, tuple_fraction,
&set_sortclauses);
AggClauseCounts agg_counts;
int numGroupCols;
bool use_hashed_grouping = false;
+ WindowFuncLists *wflists = NULL;
+ List *activeWindows = NIL;
MemSet(&agg_counts, 0, sizeof(AggClauseCounts));
+ /* A recursive query should always have setOperations */
+ Assert(!root->hasRecursion);
+
/* Preprocess GROUP BY clause, if any */
if (parse->groupClause)
preprocess_groupclause(root);
/* Preprocess targetlist */
tlist = preprocess_targetlist(root, tlist);
+ /*
+ * Locate any window functions in the tlist. (We don't need to look
+ * anywhere else, since expressions used in ORDER BY will be in there
+ * too.) Note that they could all have been eliminated by constant
+ * folding, in which case we don't need to do any more work.
+ */
+ if (parse->hasWindowFuncs)
+ {
+ wflists = find_window_functions((Node *) tlist,
+ list_length(parse->windowClause));
+ if (wflists->numWindowFuncs > 0)
+ activeWindows = select_active_windows(root, wflists);
+ else
+ parse->hasWindowFuncs = false;
+ }
+
/*
* Generate appropriate target list for subplan; may be different from
* tlist if grouping or aggregation is needed.
else
root->group_pathkeys = NIL;
+ /* We consider only the first (bottom) window in pathkeys logic */
+ if (activeWindows != NIL)
+ {
+ WindowClause *wc = (WindowClause *) linitial(activeWindows);
+
+ root->window_pathkeys = make_pathkeys_for_window(root,
+ wc,
+ tlist,
+ false);
+ }
+ else
+ root->window_pathkeys = NIL;
+
if (parse->distinctClause &&
grouping_is_sortable(parse->distinctClause))
root->distinct_pathkeys =
* Figure out whether we want a sorted result from query_planner.
*
* If we have a sortable GROUP BY clause, then we want a result sorted
- * properly for grouping. Otherwise, if there's a sortable DISTINCT
- * clause that's more rigorous than the ORDER BY clause, we try to
- * produce output that's sufficiently well sorted for the DISTINCT.
- * Otherwise, if there is an ORDER BY clause, we want to sort by the
- * ORDER BY clause.
+ * properly for grouping. Otherwise, if we have window functions to
+ * evaluate, we try to sort for the first window. Otherwise, if
+ * there's a sortable DISTINCT clause that's more rigorous than the
+ * ORDER BY clause, we try to produce output that's sufficiently well
+ * sorted for the DISTINCT. Otherwise, if there is an ORDER BY
+ * clause, we want to sort by the ORDER BY clause.
*
* Note: if we have both ORDER BY and GROUP BY, and ORDER BY is a
* superset of GROUP BY, it would be tempting to request sort by ORDER
*/
if (root->group_pathkeys)
root->query_pathkeys = root->group_pathkeys;
+ else if (root->window_pathkeys)
+ root->query_pathkeys = root->window_pathkeys;
else if (list_length(root->distinct_pathkeys) >
list_length(root->sort_pathkeys))
root->query_pathkeys = root->distinct_pathkeys;
*
* Below this point, any tlist eval cost for added-on nodes
* should be accounted for as we create those nodes.
- * Presently, of the node types we can add on, only Agg and
- * Group project new tlists (the rest just copy their input
- * tuples) --- so make_agg() and make_group() are responsible
- * for computing the added cost.
+ * Presently, of the node types we can add on, only Agg,
+ * WindowAgg, and Group project new tlists (the rest just copy
+ * their input tuples) --- so make_agg(), make_windowagg() and
+ * make_group() are responsible for computing the added cost.
*/
cost_qual_eval(&tlist_cost, sub_tlist, root);
result_plan->startup_cost += tlist_cost.startup;
NULL);
}
} /* end of non-minmax-aggregate case */
+
+ /*
+ * Since each window function could require a different sort order,
+ * we stack up a WindowAgg node for each window, with sort steps
+ * between them as needed.
+ */
+ if (activeWindows)
+ {
+ List *window_tlist;
+ ListCell *l;
+
+ /*
+ * If the top-level plan node is one that cannot do expression
+ * evaluation, we must insert a Result node to project the
+ * desired tlist. (In some cases this might not really be
+ * required, but it's not worth trying to avoid it.) Note that
+ * on second and subsequent passes through the following loop,
+ * the top-level node will be a WindowAgg which we know can
+ * project; so we only need to check once.
+ */
+ if (!is_projection_capable_plan(result_plan))
+ {
+ result_plan = (Plan *) make_result(root,
+ NIL,
+ NULL,
+ result_plan);
+ }
+
+ /*
+ * The "base" targetlist for all steps of the windowing process
+ * is a flat tlist of all Vars and Aggs needed in the result.
+ * (In some cases we wouldn't need to propagate all of these
+ * all the way to the top, since they might only be needed as
+ * inputs to WindowFuncs. It's probably not worth trying to
+ * optimize that though.) As we climb up the stack, we add
+ * outputs for the WindowFuncs computed at each level. Also,
+ * each input tlist has to present all the columns needed to
+ * sort the data for the next WindowAgg step. That's handled
+ * internally by make_sort_from_pathkeys, but we need the
+ * copyObject steps here to ensure that each plan node has
+ * a separately modifiable tlist.
+ */
+ window_tlist = flatten_tlist(tlist);
+ if (parse->hasAggs)
+ window_tlist = add_to_flat_tlist(window_tlist,
+ pull_agg_clause((Node *) tlist));
+ result_plan->targetlist = (List *) copyObject(window_tlist);
+
+ foreach(l, activeWindows)
+ {
+ WindowClause *wc = (WindowClause *) lfirst(l);
+ List *window_pathkeys;
+ int partNumCols;
+ AttrNumber *partColIdx;
+ Oid *partOperators;
+ int ordNumCols;
+ AttrNumber *ordColIdx;
+ Oid *ordOperators;
+
+ window_pathkeys = make_pathkeys_for_window(root,
+ wc,
+ tlist,
+ true);
+
+ /*
+ * This is a bit tricky: we build a sort node even if we don't
+ * really have to sort. Even when no explicit sort is needed,
+ * we need to have suitable resjunk items added to the input
+ * plan's tlist for any partitioning or ordering columns that
+ * aren't plain Vars. Furthermore, this way we can use
+ * existing infrastructure to identify which input columns are
+ * the interesting ones.
+ */
+ if (window_pathkeys)
+ {
+ Sort *sort_plan;
+
+ sort_plan = make_sort_from_pathkeys(root,
+ result_plan,
+ window_pathkeys,
+ -1.0);
+ if (!pathkeys_contained_in(window_pathkeys,
+ current_pathkeys))
+ {
+ /* we do indeed need to sort */
+ result_plan = (Plan *) sort_plan;
+ current_pathkeys = window_pathkeys;
+ }
+ /* In either case, extract the per-column information */
+ get_column_info_for_window(root, wc, tlist,
+ sort_plan->numCols,
+ sort_plan->sortColIdx,
+ &partNumCols,
+ &partColIdx,
+ &partOperators,
+ &ordNumCols,
+ &ordColIdx,
+ &ordOperators);
+ }
+ else
+ {
+ /* empty window specification, nothing to sort */
+ partNumCols = 0;
+ partColIdx = NULL;
+ partOperators = NULL;
+ ordNumCols = 0;
+ ordColIdx = NULL;
+ ordOperators = NULL;
+ }
+
+ if (lnext(l))
+ {
+ /* Add the current WindowFuncs to the running tlist */
+ window_tlist = add_to_flat_tlist(window_tlist,
+ wflists->windowFuncs[wc->winref]);
+ }
+ else
+ {
+ /* Install the original tlist in the topmost WindowAgg */
+ window_tlist = tlist;
+ }
+
+ /* ... and make the WindowAgg plan node */
+ result_plan = (Plan *)
+ make_windowagg(root,
+ (List *) copyObject(window_tlist),
+ list_length(wflists->windowFuncs[wc->winref]),
+ wc->winref,
+ partNumCols,
+ partColIdx,
+ partOperators,
+ ordNumCols,
+ ordColIdx,
+ ordOperators,
+ wc->frameOptions,
+ result_plan);
+ }
+ }
} /* end of if (setOperations) */
/*
* If we're not grouping or aggregating, there's nothing to do here;
* query_planner should receive the unmodified target list.
*/
- if (!parse->hasAggs && !parse->groupClause && !root->hasHavingQual)
+ if (!parse->hasAggs && !parse->groupClause && !root->hasHavingQual &&
+ !parse->hasWindowFuncs)
{
*need_tlist_eval = true;
return tlist;
/*
* Otherwise, start with a "flattened" tlist (having just the vars
* mentioned in the targetlist and HAVING qual --- but not upper-level
- * Vars; they will be replaced by Params later on).
+ * Vars; they will be replaced by Params later on). Note this includes
+ * vars used in resjunk items, so we are covering the needs of ORDER BY
+ * and window specifications.
*/
sub_tlist = flatten_tlist(tlist);
- extravars = pull_var_clause(parse->havingQual, false);
+ extravars = pull_var_clause(parse->havingQual, true);
sub_tlist = add_to_flat_tlist(sub_tlist, extravars);
list_free(extravars);
*need_tlist_eval = false; /* only eval if not flat tlist */
{
SortGroupClause *grpcl = (SortGroupClause *) lfirst(gl);
Node *groupexpr = get_sortgroupclause_expr(grpcl, tlist);
- TargetEntry *te = NULL;
+ TargetEntry *te;
/*
* Find or make a matching sub_tlist entry. If the groupexpr
* won't make multiple groupClause entries for the same TLE.)
*/
if (groupexpr && IsA(groupexpr, Var))
- {
- ListCell *sl;
-
- foreach(sl, sub_tlist)
- {
- TargetEntry *lte = (TargetEntry *) lfirst(sl);
+ te = tlist_member(groupexpr, sub_tlist);
+ else
+ te = NULL;
- if (equal(groupexpr, lte->expr))
- {
- te = lte;
- break;
- }
- }
- }
if (!te)
{
te = makeTargetEntry((Expr *) groupexpr,
*
* This is only needed if we don't use the sub_tlist chosen by
* make_subplanTargetList. We have to forget the column indexes found
- * by that routine and re-locate the grouping vars in the real sub_tlist.
+ * by that routine and re-locate the grouping exprs in the real sub_tlist.
*/
static void
locate_grouping_columns(PlannerInfo *root,
{
SortGroupClause *grpcl = (SortGroupClause *) lfirst(gl);
Node *groupexpr = get_sortgroupclause_expr(grpcl, tlist);
- TargetEntry *te = NULL;
- ListCell *sl;
+ TargetEntry *te = tlist_member(groupexpr, sub_tlist);
- foreach(sl, sub_tlist)
- {
- te = (TargetEntry *) lfirst(sl);
- if (equal(groupexpr, te->expr))
- break;
- }
- if (!sl)
+ if (!te)
elog(ERROR, "failed to locate grouping columns");
-
groupColIdx[keyno++] = te->resno;
}
}
elog(ERROR, "resjunk output columns are not implemented");
return new_tlist;
}
+
+/*
+ * select_active_windows
+ * Create a list of the "active" window clauses (ie, those referenced
+ * by non-deleted WindowFuncs) in the order they are to be executed.
+ */
+static List *
+select_active_windows(PlannerInfo *root, WindowFuncLists *wflists)
+{
+ List *result;
+ List *actives;
+ ListCell *lc;
+
+ /* First, make a list of the active windows */
+ actives = NIL;
+ foreach(lc, root->parse->windowClause)
+ {
+ WindowClause *wc = (WindowClause *) lfirst(lc);
+
+ /* It's only active if wflists shows some related WindowFuncs */
+ Assert(wc->winref <= wflists->maxWinRef);
+ if (wflists->windowFuncs[wc->winref] != NIL)
+ actives = lappend(actives, wc);
+ }
+
+ /*
+ * Now, ensure that windows with identical partitioning/ordering clauses
+ * are adjacent in the list. This is required by the SQL standard, which
+ * says that only one sort is to be used for such windows, even if they
+ * are otherwise distinct (eg, different names or framing clauses).
+ *
+ * There is room to be much smarter here, for example detecting whether
+ * one window's sort keys are a prefix of another's (so that sorting
+ * for the latter would do for the former), or putting windows first
+ * that match a sort order available for the underlying query. For the
+ * moment we are content with meeting the spec.
+ */
+ result = NIL;
+ while (actives != NIL)
+ {
+ WindowClause *wc = (WindowClause *) linitial(actives);
+ ListCell *prev;
+ ListCell *next;
+
+ /* Move wc from actives to result */
+ actives = list_delete_first(actives);
+ result = lappend(result, wc);
+
+ /* Now move any matching windows from actives to result */
+ prev = NULL;
+ for (lc = list_head(actives); lc; lc = next)
+ {
+ WindowClause *wc2 = (WindowClause *) lfirst(lc);
+
+ next = lnext(lc);
+ /* framing options are NOT to be compared here! */
+ if (equal(wc->partitionClause, wc2->partitionClause) &&
+ equal(wc->orderClause, wc2->orderClause))
+ {
+ actives = list_delete_cell(actives, lc, prev);
+ result = lappend(result, wc2);
+ }
+ else
+ prev = lc;
+ }
+ }
+
+ return result;
+}
+
+/*
+ * make_pathkeys_for_window
+ * Create a pathkeys list describing the required input ordering
+ * for the given WindowClause.
+ *
+ * The required ordering is first the PARTITION keys, then the ORDER keys.
+ * In the future we might try to implement windowing using hashing, in which
+ * case the ordering could be relaxed, but for now we always sort.
+ */
+static List *
+make_pathkeys_for_window(PlannerInfo *root, WindowClause *wc,
+ List *tlist, bool canonicalize)
+{
+ List *window_pathkeys;
+ List *window_sortclauses;
+
+ /* Throw error if can't sort */
+ if (!grouping_is_sortable(wc->partitionClause))
+ ereport(ERROR,
+ (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+ errmsg("could not implement window PARTITION BY"),
+ errdetail("Window partitioning columns must be of sortable datatypes.")));
+ if (!grouping_is_sortable(wc->orderClause))
+ ereport(ERROR,
+ (errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+ errmsg("could not implement window ORDER BY"),
+ errdetail("Window ordering columns must be of sortable datatypes.")));
+
+ /* Okay, make the combined pathkeys */
+ window_sortclauses = list_concat(list_copy(wc->partitionClause),
+ list_copy(wc->orderClause));
+ window_pathkeys = make_pathkeys_for_sortclauses(root,
+ window_sortclauses,
+ tlist,
+ canonicalize);
+ list_free(window_sortclauses);
+ return window_pathkeys;
+}
+
+/*----------
+ * get_column_info_for_window
+ * Get the partitioning/ordering column numbers and equality operators
+ * for a WindowAgg node.
+ *
+ * This depends on the behavior of make_pathkeys_for_window()!
+ *
+ * We are given the target WindowClause and an array of the input column
+ * numbers associated with the resulting pathkeys. In the easy case, there
+ * are the same number of pathkey columns as partitioning + ordering columns
+ * and we just have to copy some data around. However, it's possible that
+ * some of the original partitioning + ordering columns were eliminated as
+ * redundant during the transformation to pathkeys. (This can happen even
+ * though the parser gets rid of obvious duplicates. A typical scenario is a
+ * window specification "PARTITION BY x ORDER BY y" coupled with a clause
+ * "WHERE x = y" that causes the two sort columns to be recognized as
+ * redundant.) In that unusual case, we have to work a lot harder to
+ * determine which keys are significant.
+ *
+ * The method used here is a bit brute-force: add the sort columns to a list
+ * one at a time and note when the resulting pathkey list gets longer. But
+ * it's a sufficiently uncommon case that a faster way doesn't seem worth
+ * the amount of code refactoring that'd be needed.
+ *----------
+ */
+static void
+get_column_info_for_window(PlannerInfo *root, WindowClause *wc, List *tlist,
+ int numSortCols, AttrNumber *sortColIdx,
+ int *partNumCols,
+ AttrNumber **partColIdx,
+ Oid **partOperators,
+ int *ordNumCols,
+ AttrNumber **ordColIdx,
+ Oid **ordOperators)
+{
+ int numPart = list_length(wc->partitionClause);
+ int numOrder = list_length(wc->orderClause);
+
+ if (numSortCols == numPart + numOrder)
+ {
+ /* easy case */
+ *partNumCols = numPart;
+ *partColIdx = sortColIdx;
+ *partOperators = extract_grouping_ops(wc->partitionClause);
+ *ordNumCols = numOrder;
+ *ordColIdx = sortColIdx + numPart;
+ *ordOperators = extract_grouping_ops(wc->orderClause);
+ }
+ else
+ {
+ List *sortclauses;
+ List *pathkeys;
+ int scidx;
+ ListCell *lc;
+
+ /* first, allocate what's certainly enough space for the arrays */
+ *partNumCols = 0;
+ *partColIdx = (AttrNumber *) palloc(numPart * sizeof(AttrNumber));
+ *partOperators = (Oid *) palloc(numPart * sizeof(Oid));
+ *ordNumCols = 0;
+ *ordColIdx = (AttrNumber *) palloc(numOrder * sizeof(AttrNumber));
+ *ordOperators = (Oid *) palloc(numOrder * sizeof(Oid));
+ sortclauses = NIL;
+ pathkeys = NIL;
+ scidx = 0;
+ foreach(lc, wc->partitionClause)
+ {
+ SortGroupClause *sgc = (SortGroupClause *) lfirst(lc);
+ List *new_pathkeys;
+
+ sortclauses = lappend(sortclauses, sgc);
+ new_pathkeys = make_pathkeys_for_sortclauses(root,
+ sortclauses,
+ tlist,
+ true);
+ if (list_length(new_pathkeys) > list_length(pathkeys))
+ {
+ /* this sort clause is actually significant */
+ *partColIdx[*partNumCols] = sortColIdx[scidx++];
+ *partOperators[*partNumCols] = sgc->eqop;
+ (*partNumCols)++;
+ pathkeys = new_pathkeys;
+ }
+ }
+ foreach(lc, wc->orderClause)
+ {
+ SortGroupClause *sgc = (SortGroupClause *) lfirst(lc);
+ List *new_pathkeys;
+
+ sortclauses = lappend(sortclauses, sgc);
+ new_pathkeys = make_pathkeys_for_sortclauses(root,
+ sortclauses,
+ tlist,
+ true);
+ if (list_length(new_pathkeys) > list_length(pathkeys))
+ {
+ /* this sort clause is actually significant */
+ *ordColIdx[*ordNumCols] = sortColIdx[scidx++];
+ *ordOperators[*ordNumCols] = sgc->eqop;
+ (*ordNumCols)++;
+ pathkeys = new_pathkeys;
+ }
+ }
+ /* complain if we didn't eat exactly the right number of sort cols */
+ if (scidx != numSortCols)
+ elog(ERROR, "failed to deconstruct sort operators into partitioning/ordering operators");
+ }
+}