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+/*-------------------------------------------------------------------------
+ *
+ * extended_stats.c
+ * POSTGRES extended statistics
+ *
+ * Generic code supporting statistics objects created via CREATE STATISTICS.
+ *
+ *
+ * Portions Copyright (c) 1996-2020, PostgreSQL Global Development Group
+ * Portions Copyright (c) 1994, Regents of the University of California
+ *
+ * IDENTIFICATION
+ * src/backend/statistics/extended_stats.c
+ *
+ *-------------------------------------------------------------------------
+ */
+#include "postgres.h"
+
+#include "access/detoast.h"
+#include "access/genam.h"
+#include "access/htup_details.h"
+#include "access/table.h"
+#include "catalog/indexing.h"
+#include "catalog/pg_collation.h"
+#include "catalog/pg_statistic_ext.h"
+#include "catalog/pg_statistic_ext_data.h"
+#include "commands/progress.h"
+#include "miscadmin.h"
+#include "nodes/nodeFuncs.h"
+#include "optimizer/clauses.h"
+#include "optimizer/optimizer.h"
+#include "pgstat.h"
+#include "postmaster/autovacuum.h"
+#include "statistics/extended_stats_internal.h"
+#include "statistics/statistics.h"
+#include "utils/acl.h"
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "utils/fmgroids.h"
+#include "utils/lsyscache.h"
+#include "utils/memutils.h"
+#include "utils/rel.h"
+#include "utils/selfuncs.h"
+#include "utils/syscache.h"
+
+/*
+ * To avoid consuming too much memory during analysis and/or too much space
+ * in the resulting pg_statistic rows, we ignore varlena datums that are wider
+ * than WIDTH_THRESHOLD (after detoasting!). This is legitimate for MCV
+ * and distinct-value calculations since a wide value is unlikely to be
+ * duplicated at all, much less be a most-common value. For the same reason,
+ * ignoring wide values will not affect our estimates of histogram bin
+ * boundaries very much.
+ */
+#define WIDTH_THRESHOLD 1024
+
+/*
+ * Used internally to refer to an individual statistics object, i.e.,
+ * a pg_statistic_ext entry.
+ */
+typedef struct StatExtEntry
+{
+ Oid statOid; /* OID of pg_statistic_ext entry */
+ char *schema; /* statistics object's schema */
+ char *name; /* statistics object's name */
+ Bitmapset *columns; /* attribute numbers covered by the object */
+ List *types; /* 'char' list of enabled statistics kinds */
+ int stattarget; /* statistics target (-1 for default) */
+} StatExtEntry;
+
+
+static List *fetch_statentries_for_relation(Relation pg_statext, Oid relid);
+static VacAttrStats **lookup_var_attr_stats(Relation rel, Bitmapset *attrs,
+ int nvacatts, VacAttrStats **vacatts);
+static void statext_store(Oid relid,
+ MVNDistinct *ndistinct, MVDependencies *dependencies,
+ MCVList *mcv, VacAttrStats **stats);
+static int statext_compute_stattarget(int stattarget,
+ int natts, VacAttrStats **stats);
+
+/*
+ * Compute requested extended stats, using the rows sampled for the plain
+ * (single-column) stats.
+ *
+ * This fetches a list of stats types from pg_statistic_ext, computes the
+ * requested stats, and serializes them back into the catalog.
+ */
+void
+BuildRelationExtStatistics(Relation onerel, double totalrows,
+ int numrows, HeapTuple *rows,
+ int natts, VacAttrStats **vacattrstats)
+{
+ Relation pg_stext;
+ ListCell *lc;
+ List *stats;
+ MemoryContext cxt;
+ MemoryContext oldcxt;
+ int64 ext_cnt;
+
+ cxt = AllocSetContextCreate(CurrentMemoryContext,
+ "BuildRelationExtStatistics",
+ ALLOCSET_DEFAULT_SIZES);
+ oldcxt = MemoryContextSwitchTo(cxt);
+
+ pg_stext = table_open(StatisticExtRelationId, RowExclusiveLock);
+ stats = fetch_statentries_for_relation(pg_stext, RelationGetRelid(onerel));
+
+ /* report this phase */
+ if (stats != NIL)
+ {
+ const int index[] = {
+ PROGRESS_ANALYZE_PHASE,
+ PROGRESS_ANALYZE_EXT_STATS_TOTAL
+ };
+ const int64 val[] = {
+ PROGRESS_ANALYZE_PHASE_COMPUTE_EXT_STATS,
+ list_length(stats)
+ };
+
+ pgstat_progress_update_multi_param(2, index, val);
+ }
+
+ ext_cnt = 0;
+ foreach(lc, stats)
+ {
+ StatExtEntry *stat = (StatExtEntry *) lfirst(lc);
+ MVNDistinct *ndistinct = NULL;
+ MVDependencies *dependencies = NULL;
+ MCVList *mcv = NULL;
+ VacAttrStats **stats;
+ ListCell *lc2;
+ int stattarget;
+
+ /*
+ * Check if we can build these stats based on the column analyzed. If
+ * not, report this fact (except in autovacuum) and move on.
+ */
+ stats = lookup_var_attr_stats(onerel, stat->columns,
+ natts, vacattrstats);
+ if (!stats)
+ {
+ if (!IsAutoVacuumWorkerProcess())
+ ereport(WARNING,
+ (errcode(ERRCODE_INVALID_OBJECT_DEFINITION),
+ errmsg("statistics object \"%s.%s\" could not be computed for relation \"%s.%s\"",
+ stat->schema, stat->name,
+ get_namespace_name(onerel->rd_rel->relnamespace),
+ RelationGetRelationName(onerel)),
+ errtable(onerel)));
+ continue;
+ }
+
+ /* check allowed number of dimensions */
+ Assert(bms_num_members(stat->columns) >= 2 &&
+ bms_num_members(stat->columns) <= STATS_MAX_DIMENSIONS);
+
+ /* compute statistics target for this statistics */
+ stattarget = statext_compute_stattarget(stat->stattarget,
+ bms_num_members(stat->columns),
+ stats);
+
+ /*
+ * Don't rebuild statistics objects with statistics target set to 0
+ * (we just leave the existing values around, just like we do for
+ * regular per-column statistics).
+ */
+ if (stattarget == 0)
+ continue;
+
+ /* compute statistic of each requested type */
+ foreach(lc2, stat->types)
+ {
+ char t = (char) lfirst_int(lc2);
+
+ if (t == STATS_EXT_NDISTINCT)
+ ndistinct = statext_ndistinct_build(totalrows, numrows, rows,
+ stat->columns, stats);
+ else if (t == STATS_EXT_DEPENDENCIES)
+ dependencies = statext_dependencies_build(numrows, rows,
+ stat->columns, stats);
+ else if (t == STATS_EXT_MCV)
+ mcv = statext_mcv_build(numrows, rows, stat->columns, stats,
+ totalrows, stattarget);
+ }
+
+ /* store the statistics in the catalog */
+ statext_store(stat->statOid, ndistinct, dependencies, mcv, stats);
+
+ /* for reporting progress */
+ pgstat_progress_update_param(PROGRESS_ANALYZE_EXT_STATS_COMPUTED,
+ ++ext_cnt);
+ }
+
+ table_close(pg_stext, RowExclusiveLock);
+
+ MemoryContextSwitchTo(oldcxt);
+ MemoryContextDelete(cxt);
+}
+
+/*
+ * ComputeExtStatisticsRows
+ * Compute number of rows required by extended statistics on a table.
+ *
+ * Computes number of rows we need to sample to build extended statistics on a
+ * table. This only looks at statistics we can actually build - for example
+ * when analyzing only some of the columns, this will skip statistics objects
+ * that would require additional columns.
+ *
+ * See statext_compute_stattarget for details about how we compute statistics
+ * target for a statistics objects (from the object target, attribute targets
+ * and default statistics target).
+ */
+int
+ComputeExtStatisticsRows(Relation onerel,
+ int natts, VacAttrStats **vacattrstats)
+{
+ Relation pg_stext;
+ ListCell *lc;
+ List *lstats;
+ MemoryContext cxt;
+ MemoryContext oldcxt;
+ int result = 0;
+
+ cxt = AllocSetContextCreate(CurrentMemoryContext,
+ "ComputeExtStatisticsRows",
+ ALLOCSET_DEFAULT_SIZES);
+ oldcxt = MemoryContextSwitchTo(cxt);
+
+ pg_stext = table_open(StatisticExtRelationId, RowExclusiveLock);
+ lstats = fetch_statentries_for_relation(pg_stext, RelationGetRelid(onerel));
+
+ foreach(lc, lstats)
+ {
+ StatExtEntry *stat = (StatExtEntry *) lfirst(lc);
+ int stattarget = stat->stattarget;
+ VacAttrStats **stats;
+ int nattrs = bms_num_members(stat->columns);
+
+ /*
+ * Check if we can build this statistics object based on the columns
+ * analyzed. If not, ignore it (don't report anything, we'll do that
+ * during the actual build BuildRelationExtStatistics).
+ */
+ stats = lookup_var_attr_stats(onerel, stat->columns,
+ natts, vacattrstats);
+
+ if (!stats)
+ continue;
+
+ /*
+ * Compute statistics target, based on what's set for the statistic
+ * object itself, and for its attributes.
+ */
+ stattarget = statext_compute_stattarget(stat->stattarget,
+ nattrs, stats);
+
+ /* Use the largest value for all statistics objects. */
+ if (stattarget > result)
+ result = stattarget;
+ }
+
+ table_close(pg_stext, RowExclusiveLock);
+
+ MemoryContextSwitchTo(oldcxt);
+ MemoryContextDelete(cxt);
+
+ /* compute sample size based on the statistics target */
+ return (300 * result);
+}
+
+/*
+ * statext_compute_stattarget
+ * compute statistics target for an extended statistic
+ *
+ * When computing target for extended statistics objects, we consider three
+ * places where the target may be set - the statistics object itself,
+ * attributes the statistics is defined on, and then the default statistics
+ * target.
+ *
+ * First we look at what's set for the statistics object itself, using the
+ * ALTER STATISTICS ... SET STATISTICS command. If we find a valid value
+ * there (i.e. not -1) we're done. Otherwise we look at targets set for any
+ * of the attributes the statistic is defined on, and if there are columns
+ * with defined target, we use the maximum value. We do this mostly for
+ * backwards compatibility, because this is what we did before having
+ * statistics target for extended statistics.
+ *
+ * And finally, if we still don't have a statistics target, we use the value
+ * set in default_statistics_target.
+ */
+static int
+statext_compute_stattarget(int stattarget, int nattrs, VacAttrStats **stats)
+{
+ int i;
+
+ /*
+ * If there's statistics target set for the statistics object, use it. It
+ * may be set to 0 which disables building of that statistic.
+ */
+ if (stattarget >= 0)
+ return stattarget;
+
+ /*
+ * The target for the statistics object is set to -1, in which case we
+ * look at the maximum target set for any of the attributes the object is
+ * defined on.
+ */
+ for (i = 0; i < nattrs; i++)
+ {
+ /* keep the maximmum statistics target */
+ if (stats[i]->attr->attstattarget > stattarget)
+ stattarget = stats[i]->attr->attstattarget;
+ }
+
+ /*
+ * If the value is still negative (so neither the statistics object nor
+ * any of the columns have custom statistics target set), use the global
+ * default target.
+ */
+ if (stattarget < 0)
+ stattarget = default_statistics_target;
+
+ /* As this point we should have a valid statistics target. */
+ Assert((stattarget >= 0) && (stattarget <= 10000));
+
+ return stattarget;
+}
+
+/*
+ * statext_is_kind_built
+ * Is this stat kind built in the given pg_statistic_ext_data tuple?
+ */
+bool
+statext_is_kind_built(HeapTuple htup, char type)
+{
+ AttrNumber attnum;
+
+ switch (type)
+ {
+ case STATS_EXT_NDISTINCT:
+ attnum = Anum_pg_statistic_ext_data_stxdndistinct;
+ break;
+
+ case STATS_EXT_DEPENDENCIES:
+ attnum = Anum_pg_statistic_ext_data_stxddependencies;
+ break;
+
+ case STATS_EXT_MCV:
+ attnum = Anum_pg_statistic_ext_data_stxdmcv;
+ break;
+
+ default:
+ elog(ERROR, "unexpected statistics type requested: %d", type);
+ }
+
+ return !heap_attisnull(htup, attnum, NULL);
+}
+
+/*
+ * Return a list (of StatExtEntry) of statistics objects for the given relation.
+ */
+static List *
+fetch_statentries_for_relation(Relation pg_statext, Oid relid)
+{
+ SysScanDesc scan;
+ ScanKeyData skey;
+ HeapTuple htup;
+ List *result = NIL;
+
+ /*
+ * Prepare to scan pg_statistic_ext for entries having stxrelid = this
+ * rel.
+ */
+ ScanKeyInit(&skey,
+ Anum_pg_statistic_ext_stxrelid,
+ BTEqualStrategyNumber, F_OIDEQ,
+ ObjectIdGetDatum(relid));
+
+ scan = systable_beginscan(pg_statext, StatisticExtRelidIndexId, true,
+ NULL, 1, &skey);
+
+ while (HeapTupleIsValid(htup = systable_getnext(scan)))
+ {
+ StatExtEntry *entry;
+ Datum datum;
+ bool isnull;
+ int i;
+ ArrayType *arr;
+ char *enabled;
+ Form_pg_statistic_ext staForm;
+
+ entry = palloc0(sizeof(StatExtEntry));
+ staForm = (Form_pg_statistic_ext) GETSTRUCT(htup);
+ entry->statOid = staForm->oid;
+ entry->schema = get_namespace_name(staForm->stxnamespace);
+ entry->name = pstrdup(NameStr(staForm->stxname));
+ entry->stattarget = staForm->stxstattarget;
+ for (i = 0; i < staForm->stxkeys.dim1; i++)
+ {
+ entry->columns = bms_add_member(entry->columns,
+ staForm->stxkeys.values[i]);
+ }
+
+ /* decode the stxkind char array into a list of chars */
+ datum = SysCacheGetAttr(STATEXTOID, htup,
+ Anum_pg_statistic_ext_stxkind, &isnull);
+ Assert(!isnull);
+ arr = DatumGetArrayTypeP(datum);
+ if (ARR_NDIM(arr) != 1 ||
+ ARR_HASNULL(arr) ||
+ ARR_ELEMTYPE(arr) != CHAROID)
+ elog(ERROR, "stxkind is not a 1-D char array");
+ enabled = (char *) ARR_DATA_PTR(arr);
+ for (i = 0; i < ARR_DIMS(arr)[0]; i++)
+ {
+ Assert((enabled[i] == STATS_EXT_NDISTINCT) ||
+ (enabled[i] == STATS_EXT_DEPENDENCIES) ||
+ (enabled[i] == STATS_EXT_MCV));
+ entry->types = lappend_int(entry->types, (int) enabled[i]);
+ }
+
+ result = lappend(result, entry);
+ }
+
+ systable_endscan(scan);
+
+ return result;
+}
+
+/*
+ * Using 'vacatts' of size 'nvacatts' as input data, return a newly built
+ * VacAttrStats array which includes only the items corresponding to
+ * attributes indicated by 'stxkeys'. If we don't have all of the per column
+ * stats available to compute the extended stats, then we return NULL to indicate
+ * to the caller that the stats should not be built.
+ */
+static VacAttrStats **
+lookup_var_attr_stats(Relation rel, Bitmapset *attrs,
+ int nvacatts, VacAttrStats **vacatts)
+{
+ int i = 0;
+ int x = -1;
+ VacAttrStats **stats;
+
+ stats = (VacAttrStats **)
+ palloc(bms_num_members(attrs) * sizeof(VacAttrStats *));
+
+ /* lookup VacAttrStats info for the requested columns (same attnum) */
+ while ((x = bms_next_member(attrs, x)) >= 0)
+ {
+ int j;
+
+ stats[i] = NULL;
+ for (j = 0; j < nvacatts; j++)
+ {
+ if (x == vacatts[j]->tupattnum)
+ {
+ stats[i] = vacatts[j];
+ break;
+ }
+ }
+
+ if (!stats[i])
+ {
+ /*
+ * Looks like stats were not gathered for one of the columns
+ * required. We'll be unable to build the extended stats without
+ * this column.
+ */
+ pfree(stats);
+ return NULL;
+ }
+
+ /*
+ * Sanity check that the column is not dropped - stats should have
+ * been removed in this case.
+ */
+ Assert(!stats[i]->attr->attisdropped);
+
+ i++;
+ }
+
+ return stats;
+}
+
+/*
+ * statext_store
+ * Serializes the statistics and stores them into the pg_statistic_ext_data
+ * tuple.
+ */
+static void
+statext_store(Oid statOid,
+ MVNDistinct *ndistinct, MVDependencies *dependencies,
+ MCVList *mcv, VacAttrStats **stats)
+{
+ Relation pg_stextdata;
+ HeapTuple stup,
+ oldtup;
+ Datum values[Natts_pg_statistic_ext_data];
+ bool nulls[Natts_pg_statistic_ext_data];
+ bool replaces[Natts_pg_statistic_ext_data];
+
+ pg_stextdata = table_open(StatisticExtDataRelationId, RowExclusiveLock);
+
+ memset(nulls, true, sizeof(nulls));
+ memset(replaces, false, sizeof(replaces));
+ memset(values, 0, sizeof(values));
+
+ /*
+ * Construct a new pg_statistic_ext_data tuple, replacing the calculated
+ * stats.
+ */
+ if (ndistinct != NULL)
+ {
+ bytea *data = statext_ndistinct_serialize(ndistinct);
+
+ nulls[Anum_pg_statistic_ext_data_stxdndistinct - 1] = (data == NULL);
+ values[Anum_pg_statistic_ext_data_stxdndistinct - 1] = PointerGetDatum(data);
+ }
+
+ if (dependencies != NULL)
+ {
+ bytea *data = statext_dependencies_serialize(dependencies);
+
+ nulls[Anum_pg_statistic_ext_data_stxddependencies - 1] = (data == NULL);
+ values[Anum_pg_statistic_ext_data_stxddependencies - 1] = PointerGetDatum(data);
+ }
+ if (mcv != NULL)
+ {
+ bytea *data = statext_mcv_serialize(mcv, stats);
+
+ nulls[Anum_pg_statistic_ext_data_stxdmcv - 1] = (data == NULL);
+ values[Anum_pg_statistic_ext_data_stxdmcv - 1] = PointerGetDatum(data);
+ }
+
+ /* always replace the value (either by bytea or NULL) */
+ replaces[Anum_pg_statistic_ext_data_stxdndistinct - 1] = true;
+ replaces[Anum_pg_statistic_ext_data_stxddependencies - 1] = true;
+ replaces[Anum_pg_statistic_ext_data_stxdmcv - 1] = true;
+
+ /* there should already be a pg_statistic_ext_data tuple */
+ oldtup = SearchSysCache1(STATEXTDATASTXOID, ObjectIdGetDatum(statOid));
+ if (!HeapTupleIsValid(oldtup))
+ elog(ERROR, "cache lookup failed for statistics object %u", statOid);
+
+ /* replace it */
+ stup = heap_modify_tuple(oldtup,
+ RelationGetDescr(pg_stextdata),
+ values,
+ nulls,
+ replaces);
+ ReleaseSysCache(oldtup);
+ CatalogTupleUpdate(pg_stextdata, &stup->t_self, stup);
+
+ heap_freetuple(stup);
+
+ table_close(pg_stextdata, RowExclusiveLock);
+}
+
+/* initialize multi-dimensional sort */
+MultiSortSupport
+multi_sort_init(int ndims)
+{
+ MultiSortSupport mss;
+
+ Assert(ndims >= 2);
+
+ mss = (MultiSortSupport) palloc0(offsetof(MultiSortSupportData, ssup)
+ + sizeof(SortSupportData) * ndims);
+
+ mss->ndims = ndims;
+
+ return mss;
+}
+
+/*
+ * Prepare sort support info using the given sort operator and collation
+ * at the position 'sortdim'
+ */
+void
+multi_sort_add_dimension(MultiSortSupport mss, int sortdim,
+ Oid oper, Oid collation)
+{
+ SortSupport ssup = &mss->ssup[sortdim];
+
+ ssup->ssup_cxt = CurrentMemoryContext;
+ ssup->ssup_collation = collation;
+ ssup->ssup_nulls_first = false;
+
+ PrepareSortSupportFromOrderingOp(oper, ssup);
+}
+
+/* compare all the dimensions in the selected order */
+int
+multi_sort_compare(const void *a, const void *b, void *arg)
+{
+ MultiSortSupport mss = (MultiSortSupport) arg;
+ SortItem *ia = (SortItem *) a;
+ SortItem *ib = (SortItem *) b;
+ int i;
+
+ for (i = 0; i < mss->ndims; i++)
+ {
+ int compare;
+
+ compare = ApplySortComparator(ia->values[i], ia->isnull[i],
+ ib->values[i], ib->isnull[i],
+ &mss->ssup[i]);
+
+ if (compare != 0)
+ return compare;
+ }
+
+ /* equal by default */
+ return 0;
+}
+
+/* compare selected dimension */
+int
+multi_sort_compare_dim(int dim, const SortItem *a, const SortItem *b,
+ MultiSortSupport mss)
+{
+ return ApplySortComparator(a->values[dim], a->isnull[dim],
+ b->values[dim], b->isnull[dim],
+ &mss->ssup[dim]);
+}
+
+int
+multi_sort_compare_dims(int start, int end,
+ const SortItem *a, const SortItem *b,
+ MultiSortSupport mss)
+{
+ int dim;
+
+ for (dim = start; dim <= end; dim++)
+ {
+ int r = ApplySortComparator(a->values[dim], a->isnull[dim],
+ b->values[dim], b->isnull[dim],
+ &mss->ssup[dim]);
+
+ if (r != 0)
+ return r;
+ }
+
+ return 0;
+}
+
+int
+compare_scalars_simple(const void *a, const void *b, void *arg)
+{
+ return compare_datums_simple(*(Datum *) a,
+ *(Datum *) b,
+ (SortSupport) arg);
+}
+
+int
+compare_datums_simple(Datum a, Datum b, SortSupport ssup)
+{
+ return ApplySortComparator(a, false, b, false, ssup);
+}
+
+/* simple counterpart to qsort_arg */
+void *
+bsearch_arg(const void *key, const void *base, size_t nmemb, size_t size,
+ int (*compar) (const void *, const void *, void *),
+ void *arg)
+{
+ size_t l,
+ u,
+ idx;
+ const void *p;
+ int comparison;
+
+ l = 0;
+ u = nmemb;
+ while (l < u)
+ {
+ idx = (l + u) / 2;
+ p = (void *) (((const char *) base) + (idx * size));
+ comparison = (*compar) (key, p, arg);
+
+ if (comparison < 0)
+ u = idx;
+ else if (comparison > 0)
+ l = idx + 1;
+ else
+ return (void *) p;
+ }
+
+ return NULL;
+}
+
+/*
+ * build_attnums_array
+ * Transforms a bitmap into an array of AttrNumber values.
+ *
+ * This is used for extended statistics only, so all the attribute must be
+ * user-defined. That means offsetting by FirstLowInvalidHeapAttributeNumber
+ * is not necessary here (and when querying the bitmap).
+ */
+AttrNumber *
+build_attnums_array(Bitmapset *attrs, int *numattrs)
+{
+ int i,
+ j;
+ AttrNumber *attnums;
+ int num = bms_num_members(attrs);
+
+ if (numattrs)
+ *numattrs = num;
+
+ /* build attnums from the bitmapset */
+ attnums = (AttrNumber *) palloc(sizeof(AttrNumber) * num);
+ i = 0;
+ j = -1;
+ while ((j = bms_next_member(attrs, j)) >= 0)
+ {
+ /*
+ * Make sure the bitmap contains only user-defined attributes. As
+ * bitmaps can't contain negative values, this can be violated in two
+ * ways. Firstly, the bitmap might contain 0 as a member, and secondly
+ * the integer value might be larger than MaxAttrNumber.
+ */
+ Assert(AttrNumberIsForUserDefinedAttr(j));
+ Assert(j <= MaxAttrNumber);
+
+ attnums[i++] = (AttrNumber) j;
+
+ /* protect against overflows */
+ Assert(i <= num);
+ }
+
+ return attnums;
+}
+
+/*
+ * build_sorted_items
+ * build a sorted array of SortItem with values from rows
+ *
+ * Note: All the memory is allocated in a single chunk, so that the caller
+ * can simply pfree the return value to release all of it.
+ */
+SortItem *
+build_sorted_items(int numrows, int *nitems, HeapTuple *rows, TupleDesc tdesc,
+ MultiSortSupport mss, int numattrs, AttrNumber *attnums)
+{
+ int i,
+ j,
+ len,
+ idx;
+ int nvalues = numrows * numattrs;
+
+ SortItem *items;
+ Datum *values;
+ bool *isnull;
+ char *ptr;
+
+ /* Compute the total amount of memory we need (both items and values). */
+ len = numrows * sizeof(SortItem) + nvalues * (sizeof(Datum) + sizeof(bool));
+
+ /* Allocate the memory and split it into the pieces. */
+ ptr = palloc0(len);
+
+ /* items to sort */
+ items = (SortItem *) ptr;
+ ptr += numrows * sizeof(SortItem);
+
+ /* values and null flags */
+ values = (Datum *) ptr;
+ ptr += nvalues * sizeof(Datum);
+
+ isnull = (bool *) ptr;
+ ptr += nvalues * sizeof(bool);
+
+ /* make sure we consumed the whole buffer exactly */
+ Assert((ptr - (char *) items) == len);
+
+ /* fix the pointers to Datum and bool arrays */
+ idx = 0;
+ for (i = 0; i < numrows; i++)
+ {
+ bool toowide = false;
+
+ items[idx].values = &values[idx * numattrs];
+ items[idx].isnull = &isnull[idx * numattrs];
+
+ /* load the values/null flags from sample rows */
+ for (j = 0; j < numattrs; j++)
+ {
+ Datum value;
+ bool isnull;
+
+ value = heap_getattr(rows[i], attnums[j], tdesc, &isnull);
+
+ /*
+ * If this is a varlena value, check if it's too wide and if yes
+ * then skip the whole item. Otherwise detoast the value.
+ *
+ * XXX It may happen that we've already detoasted some preceding
+ * values for the current item. We don't bother to cleanup those
+ * on the assumption that those are small (below WIDTH_THRESHOLD)
+ * and will be discarded at the end of analyze.
+ */
+ if ((!isnull) &&
+ (TupleDescAttr(tdesc, attnums[j] - 1)->attlen == -1))
+ {
+ if (toast_raw_datum_size(value) > WIDTH_THRESHOLD)
+ {
+ toowide = true;
+ break;
+ }
+
+ value = PointerGetDatum(PG_DETOAST_DATUM(value));
+ }
+
+ items[idx].values[j] = value;
+ items[idx].isnull[j] = isnull;
+ }
+
+ if (toowide)
+ continue;
+
+ idx++;
+ }
+
+ /* store the actual number of items (ignoring the too-wide ones) */
+ *nitems = idx;
+
+ /* all items were too wide */
+ if (idx == 0)
+ {
+ /* everything is allocated as a single chunk */
+ pfree(items);
+ return NULL;
+ }
+
+ /* do the sort, using the multi-sort */
+ qsort_arg((void *) items, idx, sizeof(SortItem),
+ multi_sort_compare, mss);
+
+ return items;
+}
+
+/*
+ * has_stats_of_kind
+ * Check whether the list contains statistic of a given kind
+ */
+bool
+has_stats_of_kind(List *stats, char requiredkind)
+{
+ ListCell *l;
+
+ foreach(l, stats)
+ {
+ StatisticExtInfo *stat = (StatisticExtInfo *) lfirst(l);
+
+ if (stat->kind == requiredkind)
+ return true;
+ }
+
+ return false;
+}
+
+/*
+ * choose_best_statistics
+ * Look for and return statistics with the specified 'requiredkind' which
+ * have keys that match at least two of the given attnums. Return NULL if
+ * there's no match.
+ *
+ * The current selection criteria is very simple - we choose the statistics
+ * object referencing the most attributes in covered (and still unestimated
+ * clauses), breaking ties in favor of objects with fewer keys overall.
+ *
+ * The clause_attnums is an array of bitmaps, storing attnums for individual
+ * clauses. A NULL element means the clause is either incompatible or already
+ * estimated.
+ *
+ * XXX If multiple statistics objects tie on both criteria, then which object
+ * is chosen depends on the order that they appear in the stats list. Perhaps
+ * further tiebreakers are needed.
+ */
+StatisticExtInfo *
+choose_best_statistics(List *stats, char requiredkind,
+ Bitmapset **clause_attnums, int nclauses)
+{
+ ListCell *lc;
+ StatisticExtInfo *best_match = NULL;
+ int best_num_matched = 2; /* goal #1: maximize */
+ int best_match_keys = (STATS_MAX_DIMENSIONS + 1); /* goal #2: minimize */
+
+ foreach(lc, stats)
+ {
+ int i;
+ StatisticExtInfo *info = (StatisticExtInfo *) lfirst(lc);
+ Bitmapset *matched = NULL;
+ int num_matched;
+ int numkeys;
+
+ /* skip statistics that are not of the correct type */
+ if (info->kind != requiredkind)
+ continue;
+
+ /*
+ * Collect attributes in remaining (unestimated) clauses fully covered
+ * by this statistic object.
+ */
+ for (i = 0; i < nclauses; i++)
+ {
+ /* ignore incompatible/estimated clauses */
+ if (!clause_attnums[i])
+ continue;
+
+ /* ignore clauses that are not covered by this object */
+ if (!bms_is_subset(clause_attnums[i], info->keys))
+ continue;
+
+ matched = bms_add_members(matched, clause_attnums[i]);
+ }
+
+ num_matched = bms_num_members(matched);
+ bms_free(matched);
+
+ /*
+ * save the actual number of keys in the stats so that we can choose
+ * the narrowest stats with the most matching keys.
+ */
+ numkeys = bms_num_members(info->keys);
+
+ /*
+ * Use this object when it increases the number of matched clauses or
+ * when it matches the same number of attributes but these stats have
+ * fewer keys than any previous match.
+ */
+ if (num_matched > best_num_matched ||
+ (num_matched == best_num_matched && numkeys < best_match_keys))
+ {
+ best_match = info;
+ best_num_matched = num_matched;
+ best_match_keys = numkeys;
+ }
+ }
+
+ return best_match;
+}
+
+/*
+ * statext_is_compatible_clause_internal
+ * Determines if the clause is compatible with MCV lists.
+ *
+ * Does the heavy lifting of actually inspecting the clauses for
+ * statext_is_compatible_clause. It needs to be split like this because
+ * of recursion. The attnums bitmap is an input/output parameter collecting
+ * attribute numbers from all compatible clauses (recursively).
+ */
+static bool
+statext_is_compatible_clause_internal(PlannerInfo *root, Node *clause,
+ Index relid, Bitmapset **attnums)
+{
+ /* Look inside any binary-compatible relabeling (as in examine_variable) */
+ if (IsA(clause, RelabelType))
+ clause = (Node *) ((RelabelType *) clause)->arg;
+
+ /* plain Var references (boolean Vars or recursive checks) */
+ if (IsA(clause, Var))
+ {
+ Var *var = (Var *) clause;
+
+ /* Ensure var is from the correct relation */
+ if (var->varno != relid)
+ return false;
+
+ /* we also better ensure the Var is from the current level */
+ if (var->varlevelsup > 0)
+ return false;
+
+ /* Also skip system attributes (we don't allow stats on those). */
+ if (!AttrNumberIsForUserDefinedAttr(var->varattno))
+ return false;
+
+ *attnums = bms_add_member(*attnums, var->varattno);
+
+ return true;
+ }
+
+ /* (Var op Const) or (Const op Var) */
+ if (is_opclause(clause))
+ {
+ RangeTblEntry *rte = root->simple_rte_array[relid];
+ OpExpr *expr = (OpExpr *) clause;
+ Var *var;
+
+ /* Only expressions with two arguments are considered compatible. */
+ if (list_length(expr->args) != 2)
+ return false;
+
+ /* Check if the expression has the right shape (one Var, one Const) */
+ if (!examine_clause_args(expr->args, &var, NULL, NULL))
+ return false;
+
+ /*
+ * If it's not one of the supported operators ("=", "<", ">", etc.),
+ * just ignore the clause, as it's not compatible with MCV lists.
+ *
+ * This uses the function for estimating selectivity, not the operator
+ * directly (a bit awkward, but well ...).
+ */
+ switch (get_oprrest(expr->opno))
+ {
+ case F_EQSEL:
+ case F_NEQSEL:
+ case F_SCALARLTSEL:
+ case F_SCALARLESEL:
+ case F_SCALARGTSEL:
+ case F_SCALARGESEL:
+ /* supported, will continue with inspection of the Var */
+ break;
+
+ default:
+ /* other estimators are considered unknown/unsupported */
+ return false;
+ }
+
+ /*
+ * If there are any securityQuals on the RTE from security barrier
+ * views or RLS policies, then the user may not have access to all the
+ * table's data, and we must check that the operator is leak-proof.
+ *
+ * If the operator is leaky, then we must ignore this clause for the
+ * purposes of estimating with MCV lists, otherwise the operator might
+ * reveal values from the MCV list that the user doesn't have
+ * permission to see.
+ */
+ if (rte->securityQuals != NIL &&
+ !get_func_leakproof(get_opcode(expr->opno)))
+ return false;
+
+ return statext_is_compatible_clause_internal(root, (Node *) var,
+ relid, attnums);
+ }
+
+ /* Var IN Array */
+ if (IsA(clause, ScalarArrayOpExpr))
+ {
+ RangeTblEntry *rte = root->simple_rte_array[relid];
+ ScalarArrayOpExpr *expr = (ScalarArrayOpExpr *) clause;
+ Var *var;
+
+ /* Only expressions with two arguments are considered compatible. */
+ if (list_length(expr->args) != 2)
+ return false;
+
+ /* Check if the expression has the right shape (one Var, one Const) */
+ if (!examine_clause_args(expr->args, &var, NULL, NULL))
+ return false;
+
+ /*
+ * If it's not one of the supported operators ("=", "<", ">", etc.),
+ * just ignore the clause, as it's not compatible with MCV lists.
+ *
+ * This uses the function for estimating selectivity, not the operator
+ * directly (a bit awkward, but well ...).
+ */
+ switch (get_oprrest(expr->opno))
+ {
+ case F_EQSEL:
+ case F_NEQSEL:
+ case F_SCALARLTSEL:
+ case F_SCALARLESEL:
+ case F_SCALARGTSEL:
+ case F_SCALARGESEL:
+ /* supported, will continue with inspection of the Var */
+ break;
+
+ default:
+ /* other estimators are considered unknown/unsupported */
+ return false;
+ }
+
+ /*
+ * If there are any securityQuals on the RTE from security barrier
+ * views or RLS policies, then the user may not have access to all the
+ * table's data, and we must check that the operator is leak-proof.
+ *
+ * If the operator is leaky, then we must ignore this clause for the
+ * purposes of estimating with MCV lists, otherwise the operator might
+ * reveal values from the MCV list that the user doesn't have
+ * permission to see.
+ */
+ if (rte->securityQuals != NIL &&
+ !get_func_leakproof(get_opcode(expr->opno)))
+ return false;
+
+ return statext_is_compatible_clause_internal(root, (Node *) var,
+ relid, attnums);
+ }
+
+ /* AND/OR/NOT clause */
+ if (is_andclause(clause) ||
+ is_orclause(clause) ||
+ is_notclause(clause))
+ {
+ /*
+ * AND/OR/NOT-clauses are supported if all sub-clauses are supported
+ *
+ * Perhaps we could improve this by handling mixed cases, when some of
+ * the clauses are supported and some are not. Selectivity for the
+ * supported subclauses would be computed using extended statistics,
+ * and the remaining clauses would be estimated using the traditional
+ * algorithm (product of selectivities).
+ *
+ * It however seems overly complex, and in a way we already do that
+ * because if we reject the whole clause as unsupported here, it will
+ * be eventually passed to clauselist_selectivity() which does exactly
+ * this (split into supported/unsupported clauses etc).
+ */
+ BoolExpr *expr = (BoolExpr *) clause;
+ ListCell *lc;
+
+ foreach(lc, expr->args)
+ {
+ /*
+ * Had we found incompatible clause in the arguments, treat the
+ * whole clause as incompatible.
+ */
+ if (!statext_is_compatible_clause_internal(root,
+ (Node *) lfirst(lc),
+ relid, attnums))
+ return false;
+ }
+
+ return true;
+ }
+
+ /* Var IS NULL */
+ if (IsA(clause, NullTest))
+ {
+ NullTest *nt = (NullTest *) clause;
+
+ /*
+ * Only simple (Var IS NULL) expressions supported for now. Maybe we
+ * could use examine_variable to fix this?
+ */
+ if (!IsA(nt->arg, Var))
+ return false;
+
+ return statext_is_compatible_clause_internal(root, (Node *) (nt->arg),
+ relid, attnums);
+ }
+
+ return false;
+}
+
+/*
+ * statext_is_compatible_clause
+ * Determines if the clause is compatible with MCV lists.
+ *
+ * Currently, we only support three types of clauses:
+ *
+ * (a) OpExprs of the form (Var op Const), or (Const op Var), where the op
+ * is one of ("=", "<", ">", ">=", "<=")
+ *
+ * (b) (Var IS [NOT] NULL)
+ *
+ * (c) combinations using AND/OR/NOT
+ *
+ * In the future, the range of supported clauses may be expanded to more
+ * complex cases, for example (Var op Var).
+ */
+static bool
+statext_is_compatible_clause(PlannerInfo *root, Node *clause, Index relid,
+ Bitmapset **attnums)
+{
+ RangeTblEntry *rte = root->simple_rte_array[relid];
+ RestrictInfo *rinfo = (RestrictInfo *) clause;
+ Oid userid;
+
+ if (!IsA(rinfo, RestrictInfo))
+ return false;
+
+ /* Pseudoconstants are not really interesting here. */
+ if (rinfo->pseudoconstant)
+ return false;
+
+ /* clauses referencing multiple varnos are incompatible */
+ if (bms_membership(rinfo->clause_relids) != BMS_SINGLETON)
+ return false;
+
+ /* Check the clause and determine what attributes it references. */
+ if (!statext_is_compatible_clause_internal(root, (Node *) rinfo->clause,
+ relid, attnums))
+ return false;
+
+ /*
+ * Check that the user has permission to read all these attributes. Use
+ * checkAsUser if it's set, in case we're accessing the table via a view.
+ */
+ userid = rte->checkAsUser ? rte->checkAsUser : GetUserId();
+
+ if (pg_class_aclcheck(rte->relid, userid, ACL_SELECT) != ACLCHECK_OK)
+ {
+ /* Don't have table privilege, must check individual columns */
+ if (bms_is_member(InvalidAttrNumber, *attnums))
+ {
+ /* Have a whole-row reference, must have access to all columns */
+ if (pg_attribute_aclcheck_all(rte->relid, userid, ACL_SELECT,
+ ACLMASK_ALL) != ACLCHECK_OK)
+ return false;
+ }
+ else
+ {
+ /* Check the columns referenced by the clause */
+ int attnum = -1;
+
+ while ((attnum = bms_next_member(*attnums, attnum)) >= 0)
+ {
+ if (pg_attribute_aclcheck(rte->relid, attnum, userid,
+ ACL_SELECT) != ACLCHECK_OK)
+ return false;
+ }
+ }
+ }
+
+ /* If we reach here, the clause is OK */
+ return true;
+}
+
+/*
+ * statext_mcv_clauselist_selectivity
+ * Estimate clauses using the best multi-column statistics.
+ *
+ * Applies available extended (multi-column) statistics on a table. There may
+ * be multiple applicable statistics (with respect to the clauses), in which
+ * case we use greedy approach. In each round we select the best statistic on
+ * a table (measured by the number of attributes extracted from the clauses
+ * and covered by it), and compute the selectivity for the supplied clauses.
+ * We repeat this process with the remaining clauses (if any), until none of
+ * the available statistics can be used.
+ *
+ * One of the main challenges with using MCV lists is how to extrapolate the
+ * estimate to the data not covered by the MCV list. To do that, we compute
+ * not only the "MCV selectivity" (selectivities for MCV items matching the
+ * supplied clauses), but also a couple of derived selectivities:
+ *
+ * - simple selectivity: Computed without extended statistic, i.e. as if the
+ * columns/clauses were independent
+ *
+ * - base selectivity: Similar to simple selectivity, but is computed using
+ * the extended statistic by adding up the base frequencies (that we compute
+ * and store for each MCV item) of matching MCV items.
+ *
+ * - total selectivity: Selectivity covered by the whole MCV list.
+ *
+ * - other selectivity: A selectivity estimate for data not covered by the MCV
+ * list (i.e. satisfying the clauses, but not common enough to make it into
+ * the MCV list)
+ *
+ * Note: While simple and base selectivities are defined in a quite similar
+ * way, the values are computed differently and are not therefore equal. The
+ * simple selectivity is computed as a product of per-clause estimates, while
+ * the base selectivity is computed by adding up base frequencies of matching
+ * items of the multi-column MCV list. So the values may differ for two main
+ * reasons - (a) the MCV list may not cover 100% of the data and (b) some of
+ * the MCV items did not match the estimated clauses.
+ *
+ * As both (a) and (b) reduce the base selectivity value, it generally holds
+ * that (simple_selectivity >= base_selectivity). If the MCV list covers all
+ * the data, the values may be equal.
+ *
+ * So, (simple_selectivity - base_selectivity) is an estimate for the part
+ * not covered by the MCV list, and (mcv_selectivity - base_selectivity) may
+ * be seen as a correction for the part covered by the MCV list. Those two
+ * statements are actually equivalent.
+ *
+ * Note: Due to rounding errors and minor differences in how the estimates
+ * are computed, the inequality may not always hold. Which is why we clamp
+ * the selectivities to prevent strange estimate (negative etc.).
+ *
+ * 'estimatedclauses' is an input/output parameter. We set bits for the
+ * 0-based 'clauses' indexes we estimate for and also skip clause items that
+ * already have a bit set.
+ */
+static Selectivity
+statext_mcv_clauselist_selectivity(PlannerInfo *root, List *clauses, int varRelid,
+ JoinType jointype, SpecialJoinInfo *sjinfo,
+ RelOptInfo *rel, Bitmapset **estimatedclauses)
+{
+ ListCell *l;
+ Bitmapset **list_attnums;
+ int listidx;
+ Selectivity sel = 1.0;
+
+ /* check if there's any stats that might be useful for us. */
+ if (!has_stats_of_kind(rel->statlist, STATS_EXT_MCV))
+ return 1.0;
+
+ list_attnums = (Bitmapset **) palloc(sizeof(Bitmapset *) *
+ list_length(clauses));
+
+ /*
+ * Pre-process the clauses list to extract the attnums seen in each item.
+ * We need to determine if there's any clauses which will be useful for
+ * selectivity estimations with extended stats. Along the way we'll record
+ * all of the attnums for each clause in a list which we'll reference
+ * later so we don't need to repeat the same work again. We'll also keep
+ * track of all attnums seen.
+ *
+ * We also skip clauses that we already estimated using different types of
+ * statistics (we treat them as incompatible).
+ */
+ listidx = 0;
+ foreach(l, clauses)
+ {
+ Node *clause = (Node *) lfirst(l);
+ Bitmapset *attnums = NULL;
+
+ if (!bms_is_member(listidx, *estimatedclauses) &&
+ statext_is_compatible_clause(root, clause, rel->relid, &attnums))
+ list_attnums[listidx] = attnums;
+ else
+ list_attnums[listidx] = NULL;
+
+ listidx++;
+ }
+
+ /* apply as many extended statistics as possible */
+ while (true)
+ {
+ StatisticExtInfo *stat;
+ List *stat_clauses;
+ Selectivity simple_sel,
+ mcv_sel,
+ mcv_basesel,
+ mcv_totalsel,
+ other_sel,
+ stat_sel;
+
+ /* find the best suited statistics object for these attnums */
+ stat = choose_best_statistics(rel->statlist, STATS_EXT_MCV,
+ list_attnums, list_length(clauses));
+
+ /*
+ * if no (additional) matching stats could be found then we've nothing
+ * to do
+ */
+ if (!stat)
+ break;
+
+ /* Ensure choose_best_statistics produced an expected stats type. */
+ Assert(stat->kind == STATS_EXT_MCV);
+
+ /* now filter the clauses to be estimated using the selected MCV */
+ stat_clauses = NIL;
+
+ listidx = 0;
+ foreach(l, clauses)
+ {
+ /*
+ * If the clause is compatible with the selected statistics, mark
+ * it as estimated and add it to the list to estimate.
+ */
+ if (list_attnums[listidx] != NULL &&
+ bms_is_subset(list_attnums[listidx], stat->keys))
+ {
+ stat_clauses = lappend(stat_clauses, (Node *) lfirst(l));
+ *estimatedclauses = bms_add_member(*estimatedclauses, listidx);
+
+ bms_free(list_attnums[listidx]);
+ list_attnums[listidx] = NULL;
+ }
+
+ listidx++;
+ }
+
+ /*
+ * First compute "simple" selectivity, i.e. without the extended
+ * statistics, and essentially assuming independence of the
+ * columns/clauses. We'll then use the various selectivities computed
+ * from MCV list to improve it.
+ */
+ simple_sel = clauselist_selectivity_simple(root, stat_clauses, varRelid,
+ jointype, sjinfo, NULL);
+
+ /*
+ * Now compute the multi-column estimate from the MCV list, along with
+ * the other selectivities (base & total selectivity).
+ */
+ mcv_sel = mcv_clauselist_selectivity(root, stat, stat_clauses, varRelid,
+ jointype, sjinfo, rel,
+ &mcv_basesel, &mcv_totalsel);
+
+ /* Estimated selectivity of values not covered by MCV matches */
+ other_sel = simple_sel - mcv_basesel;
+ CLAMP_PROBABILITY(other_sel);
+
+ /* The non-MCV selectivity can't exceed the 1 - mcv_totalsel. */
+ if (other_sel > 1.0 - mcv_totalsel)
+ other_sel = 1.0 - mcv_totalsel;
+
+ /*
+ * Overall selectivity is the combination of MCV and non-MCV
+ * estimates.
+ */
+ stat_sel = mcv_sel + other_sel;
+ CLAMP_PROBABILITY(stat_sel);
+
+ /* Factor the estimate from this MCV to the oveall estimate. */
+ sel *= stat_sel;
+ }
+
+ return sel;
+}
+
+/*
+ * statext_clauselist_selectivity
+ * Estimate clauses using the best multi-column statistics.
+ */
+Selectivity
+statext_clauselist_selectivity(PlannerInfo *root, List *clauses, int varRelid,
+ JoinType jointype, SpecialJoinInfo *sjinfo,
+ RelOptInfo *rel, Bitmapset **estimatedclauses)
+{
+ Selectivity sel;
+
+ /* First, try estimating clauses using a multivariate MCV list. */
+ sel = statext_mcv_clauselist_selectivity(root, clauses, varRelid, jointype,
+ sjinfo, rel, estimatedclauses);
+
+ /*
+ * Then, apply functional dependencies on the remaining clauses by calling
+ * dependencies_clauselist_selectivity. Pass 'estimatedclauses' so the
+ * function can properly skip clauses already estimated above.
+ *
+ * The reasoning for applying dependencies last is that the more complex
+ * stats can track more complex correlations between the attributes, and
+ * so may be considered more reliable.
+ *
+ * For example, MCV list can give us an exact selectivity for values in
+ * two columns, while functional dependencies can only provide information
+ * about the overall strength of the dependency.
+ */
+ sel *= dependencies_clauselist_selectivity(root, clauses, varRelid,
+ jointype, sjinfo, rel,
+ estimatedclauses);
+
+ return sel;
+}
+
+/*
+ * examine_opclause_expression
+ * Split expression into Var and Const parts.
+ *
+ * Attempts to match the arguments to either (Var op Const) or (Const op Var),
+ * possibly with a RelabelType on top. When the expression matches this form,
+ * returns true, otherwise returns false.
+ *
+ * Optionally returns pointers to the extracted Var/Const nodes, when passed
+ * non-null pointers (varp, cstp and varonleftp). The varonleftp flag specifies
+ * on which side of the operator we found the Var node.
+ */
+bool
+examine_clause_args(List *args, Var **varp, Const **cstp, bool *varonleftp)
+{
+ Var *var;
+ Const *cst;
+ bool varonleft;
+ Node *leftop,
+ *rightop;
+
+ /* enforced by statext_is_compatible_clause_internal */
+ Assert(list_length(args) == 2);
+
+ leftop = linitial(args);
+ rightop = lsecond(args);
+
+ /* strip RelabelType from either side of the expression */
+ if (IsA(leftop, RelabelType))
+ leftop = (Node *) ((RelabelType *) leftop)->arg;
+
+ if (IsA(rightop, RelabelType))
+ rightop = (Node *) ((RelabelType *) rightop)->arg;
+
+ if (IsA(leftop, Var) && IsA(rightop, Const))
+ {
+ var = (Var *) leftop;
+ cst = (Const *) rightop;
+ varonleft = true;
+ }
+ else if (IsA(leftop, Const) && IsA(rightop, Var))
+ {
+ var = (Var *) rightop;
+ cst = (Const *) leftop;
+ varonleft = false;
+ }
+ else
+ return false;
+
+ /* return pointers to the extracted parts if requested */
+ if (varp)
+ *varp = var;
+
+ if (cstp)
+ *cstp = cst;
+
+ if (varonleftp)
+ *varonleftp = varonleft;
+
+ return true;
+}