In the thread discussing ALL semantics and NULL [0], the question was
raised about adding a new regression test that checks selectivity
estimation. If the change gets committed, it would make sense to add
tests for this case as well.
Regarding the idea of optimizing the loop when all per-element
selectivities are the same: I ran some quick tests to see how much the
change in the v7-0002 patch affects planning time. Even without that
patch, iterating over an array with 50k elements takes about 30 ms.
```
CREATE TABLE t (val bytea PRIMARY KEY);
INSERT INTO t SELECT int4send(i) FROM generate_series(1,50000) AS i;
ANALYZE t;
SELECT n_distinct FROM pg_stats WHERE tablename = 't';
n_distinct
------------
-1
(1 row)
SELECT string_agg(format('int4send(%s)', i), ',') FROM
generate_series(1,50000) AS i \gset
EXPLAIN (SUMMARY) SELECT * FROM t WHERE val = ANY
(ARRAY[:string_agg]::bytea[]);
..........
Planning Time: 32.816 ms
(3 rows)
```
Given that, I don't see much benefit in adding additional logic here
just to avoid the loop. It would likely introduce extra code complexity
without a manful gain. If there is interest in optimization this case
further, I can revisit it and add the additional patch.
The patch v8 can still be reviewed as-is, and if the selectivity
regression test gets committed [0], I will add corresponding tests for
this change as well.
[0]:
https://www.postgresql.org/message-id/390a46f3-dbc4-4dc1-b49d-5cc61dd36026%40tantorlabs.com
--
Best regards,
Ilia Evdokimov,
Tantor Labs LLC,
https://tantorlabs.com/
From 22be37fc625921dbb1722a18dde6b6e9da00890a Mon Sep 17 00:00:00 2001
From: Ilia Evdokimov <[email protected]>
Date: Tue, 10 Mar 2026 17:11:16 +0300
Subject: [PATCH v8] Use hash-based MCV matching for ScalarArrayOpExpr
selectivity
When estimating selectivity for ScalarArrayOpExpr (IN / ANY / ALL) with
available MCV statistics, the planner currently matches IN-list elements
against the MCV array using nested loops. For large IN-lists and/or large
MCV lists this leads to O(N*M) planning-time behavior.
This patch adds a hash-based matching strategy, similar to the one used
in join selectivity estimation. When MCV statistics are available and the
operator supports hashing, the smaller of the two inputs (MCV list or
IN-list constant elements) is chosen as the hash table build side, and
the other side is scanned once, reducing complexity to O(N+M).
The hash-based path is restricted to equality and inequality operators
that use eqsel()/neqsel(), and is applied only when suitable hash
functions and MCV statistics are available.
---
src/backend/utils/adt/selfuncs.c | 518 ++++++++++++++++++++++++++++++-
1 file changed, 513 insertions(+), 5 deletions(-)
diff --git a/src/backend/utils/adt/selfuncs.c b/src/backend/utils/adt/selfuncs.c
index d4da0e8dea9..66c3e31eaa5 100644
--- a/src/backend/utils/adt/selfuncs.c
+++ b/src/backend/utils/adt/selfuncs.c
@@ -146,23 +146,27 @@
/*
* In production builds, switch to hash-based MCV matching when the lists are
* large enough to amortize hash setup cost. (This threshold is compared to
- * the sum of the lengths of the two MCV lists. This is simplistic but seems
+ * the sum of the lengths of the two lists. This is simplistic but seems
* to work well enough.) In debug builds, we use a smaller threshold so that
* the regression tests cover both paths well.
*/
#ifndef USE_ASSERT_CHECKING
-#define EQJOINSEL_MCV_HASH_THRESHOLD 200
+#define MCV_HASH_THRESHOLD 200
#else
-#define EQJOINSEL_MCV_HASH_THRESHOLD 20
+#define MCV_HASH_THRESHOLD 20
#endif
-/* Entries in the simplehash hash table used by eqjoinsel_find_matches */
+/*
+ * Entries in the simplehash hash table used by
+ * eqjoinsel_find_matches and scalararray_mcv_hash_match
+ */
typedef struct MCVHashEntry
{
Datum value; /* the value represented by this entry */
int index; /* its index in the relevant AttStatsSlot */
uint32 hash; /* hash code for the Datum */
char status; /* status code used by simplehash.h */
+ int count; /* number of occurrences of current value in */
} MCVHashEntry;
/* private_data for the simplehash hash table */
@@ -184,6 +188,16 @@ get_relation_stats_hook_type get_relation_stats_hook = NULL;
get_index_stats_hook_type get_index_stats_hook = NULL;
static double eqsel_internal(PG_FUNCTION_ARGS, bool negate);
+static double scalararray_mcv_hash_match(VariableStatData *vardata, Oid operator,
+ Oid collation, Selectivity s2,
+ Datum *elem_values, bool *elem_nulls,
+ int num_elems, bool *elem_const,
+ Oid nominal_element_type, bool useOr,
+ bool isEquality, bool isInequality);
+static void accum_scalararray_prob(double individual_s, int count,
+ bool useOr, bool isEquality,
+ bool isInequality, double nullfrac,
+ double *selec, double *s1disjoint);
static double eqjoinsel_inner(FmgrInfo *eqproc, Oid collation,
Oid hashLeft, Oid hashRight,
VariableStatData *vardata1, VariableStatData *vardata2,
@@ -1893,6 +1907,36 @@ strip_array_coercion(Node *node)
return node;
}
+/*
+ * Accumulate the selectivity contribution of a single array element
+ * into the running ScalarArrayOpExpr selectivity estimate.
+ */
+static void
+accum_scalararray_prob(double individual_s, int count, bool useOr, bool isEquality,
+ bool isInequality, double nullfrac, double *selec, double *s1disjoint)
+{
+ if (count <= 0)
+ return;
+
+ if (isInequality)
+ individual_s = 1.0 - individual_s - nullfrac;
+
+ CLAMP_PROBABILITY(individual_s);
+
+ if (useOr)
+ {
+ *selec = 1.0 - (1.0 - *selec) * pow(1.0 - individual_s, count);
+ if (isEquality)
+ *s1disjoint += individual_s * count;
+ }
+ else
+ {
+ *selec = (*selec) * pow(individual_s, count);
+ if (isInequality)
+ *s1disjoint += count * (individual_s - 1.0);
+ }
+}
+
/*
* scalararraysel - Selectivity of ScalarArrayOpExpr Node.
*/
@@ -2025,6 +2069,36 @@ scalararraysel(PlannerInfo *root,
elmlen, elmbyval, elmalign,
&elem_values, &elem_nulls, &num_elems);
+ /* Try to avoid O(N^2) selectivity calculation for ScalarArrayOpExpr */
+ if ((isEquality || isInequality) && !is_join_clause)
+ {
+ VariableStatData vardata;
+ Node *other_op = NULL;
+ bool var_on_left;
+ bool *elem_const = NULL;
+
+ /*
+ * If the clause is of the form "var OP something" or "something
+ * OP var", extract statistics for the variable. Otherwise, fall
+ * back to a default per-element estimate.
+ */
+ if (get_restriction_variable(root, clause->args, varRelid,
+ &vardata, &other_op, &var_on_left))
+ {
+ s1 = scalararray_mcv_hash_match(&vardata, operator,
+ clause->inputcollid, -1.0,
+ elem_values, elem_nulls,
+ num_elems, elem_const,
+ nominal_element_type, useOr,
+ isEquality, isInequality);
+
+ ReleaseVariableStats(vardata);
+
+ if (s1 >= 0.0)
+ return s1;
+ }
+ }
+
/*
* For generic operators, we assume the probability of success is
* independent for each array element. But for "= ANY" or "<> ALL",
@@ -2100,6 +2174,100 @@ scalararraysel(PlannerInfo *root,
get_typlenbyval(arrayexpr->element_typeid,
&elmlen, &elmbyval);
+ /* Try to avoid O(N^2) selectivity calculation for ScalarArrayOpExpr */
+ if ((isEquality || isInequality) && !is_join_clause)
+ {
+ VariableStatData vardata;
+ Node *other_op = NULL;
+ bool var_on_left;
+ int num_elems = list_length(arrayexpr->elements);
+
+ /*
+ * If expression is not variable = something or something =
+ * variable, then fall back to default code path to compute
+ * default selectivity.
+ */
+ if (get_restriction_variable(root, clause->args, varRelid,
+ &vardata, &other_op, &var_on_left))
+ {
+ Selectivity nonconst_sel;
+ Datum *elem_values;
+ bool *elem_nulls;
+ bool *elem_const;
+ ListCell *lc;
+
+ /*
+ * Build arrays describing ARRAY[] elements: - elem_values:
+ * Datum value for Const elements - elem_nulls: whether
+ * element is NULL - elem_const: whether element is a Const
+ * node
+ */
+ elem_values = palloc_array(Datum, num_elems);
+ elem_nulls = palloc0_array(bool, num_elems);
+ elem_const = palloc0_array(bool, num_elems);
+
+ foreach(lc, arrayexpr->elements)
+ {
+ Node *elem_value = (Node *) lfirst(lc);
+ int i = foreach_current_index(lc);
+
+ if (IsA(elem_value, Const))
+ {
+ elem_values[i] = ((Const *) elem_value)->constvalue;
+ elem_nulls[i] = ((Const *) elem_value)->constisnull;
+ elem_const[i] = true;
+ }
+ else
+ {
+ elem_nulls[i] = false;
+ elem_const[i] = false;
+ }
+
+ /*
+ * For ALL semantics, if the array contains NULL, assume
+ * operator is strict. The ScalarArrayOpExpr cannot
+ * evaluate to TRUE, so return zero.
+ */
+ if (!useOr && elem_nulls[i])
+ {
+ pfree(elem_values);
+ pfree(elem_nulls);
+ pfree(elem_const);
+
+ ReleaseVariableStats(vardata);
+
+ return (Selectivity) 0.0;
+ }
+ }
+
+ /*
+ * Compute per-element selectivity via eqsel()/neqsel
+ * semantics.
+ */
+ nonconst_sel = var_eq_non_const(&vardata, operator,
+ clause->inputcollid,
+ other_op, var_on_left,
+ isInequality);
+
+ s1 = scalararray_mcv_hash_match(&vardata, operator,
+ clause->inputcollid,
+ nonconst_sel, elem_values,
+ elem_nulls, num_elems,
+ elem_const,
+ nominal_element_type, useOr,
+ isEquality, isInequality);
+
+ pfree(elem_values);
+ pfree(elem_nulls);
+ pfree(elem_const);
+
+ ReleaseVariableStats(vardata);
+
+ if (s1 >= 0.0)
+ return s1;
+ }
+ }
+
/*
* We use the assumption of disjoint probabilities here too, although
* the odds of equal array elements are rather higher if the elements
@@ -2210,6 +2378,346 @@ scalararraysel(PlannerInfo *root,
return s1;
}
+/*
+ * Estimate selectivity of a ScalarArrayOpExpr (ANY/ALL) using MCV statistics
+ * with hash-based matching.
+ *
+ * This function follows the same probability model as the generic
+ * ScalarArrayOpExpr selectivity code (independent or disjoint probabilities
+ * for OR/AND combinations), but attempts to speed up matching between
+ * IN-list elements and the column's most-common-values (MCV) statistics by
+ * using hashing instead of nested loops.
+ *
+ * MCV statistics are used only to obtain per-value selectivities for
+ * constants that match MCV entries. All probabilities are combined using
+ * the standard ANY/ALL formulas, exactly as in the generic estimator.
+ *
+ * The function may return -1.0 to indicate that hash-based MCV estimation
+ * is not applicable (for example, missing statistics, unsupported operator,
+ * or unavailable hash functions), in which case the caller should fall back
+ * to the generic ScalarArrayOpExpr selectivity estimation.
+ *
+ * Inputs:
+ * vardata: statistics and metadata for the variable being estimated
+ * operator: equality or inequality operator to apply
+ * collation: OID of collation to use
+ * nonconst_sel: selectivity of non-const element
+ * elem_values: array of IN-list element values
+ * elem_nulls: array indicating which IN-list elements are NULL
+ * elem_const: array indicating which IN-list elements are Const nodes.
+ * array is NULL if all elemnets are const.
+ * num_elems: number of IN-list elements
+ * nominal_element_type: type of IN-list elements
+ * useOr: true if elements are combined using OR semantics, false for AND
+ * isEquality: true if the operator behaves like equality
+ * isInequality: true if the operator behaves like inequality
+ *
+ * Result:
+ * Selectivity estimate in the range [0.0, 1.0], or -1.0 if no estimate
+ * could be produced by this function.
+ *
+ * Note:
+ * This function assumes that the operator’s selectivity behavior matches
+ * eqsel()/neqsel semantics. It must not be used for operators with custom
+ * or non-standard selectivity behavior.
+ */
+static double
+scalararray_mcv_hash_match(VariableStatData *vardata, Oid operator,
+ Oid collation, Selectivity nonconst_sel,
+ Datum *elem_values, bool *elem_nulls, int num_elems,
+ bool *elem_const, Oid nominal_element_type,
+ bool useOr, bool isEquality, bool isInequality)
+{
+ Form_pg_statistic stats;
+ AttStatsSlot sslot;
+ FmgrInfo eqproc;
+ double selec = -1.0,
+ s1disjoint,
+ nullfrac = 0.0;
+ Oid hashLeft = InvalidOid,
+ hashRight = InvalidOid,
+ opfuncoid;
+ bool have_mcvs = false;
+
+ /*
+ * If the variable is known to be unique, MCV statistics do not represent
+ * a meaningful frequency distribution, so skip MCV-based estimation.
+ */
+ if (vardata->isunique && vardata->rel && vardata->rel->tuples >= 1.0)
+ return -1.0;
+
+ /*
+ * For inequality (<>, ALL), we compute probabilities using the negated
+ * equality operator and later transform them as
+ *
+ * p(x <> c) = 1 - p(x = c) - nullfrac
+ */
+ if (isInequality)
+ {
+ operator = get_negator(operator);
+ if (!OidIsValid(operator))
+ return -1.0;
+ }
+
+ opfuncoid = get_opcode(operator);
+ memset(&sslot, 0, sizeof(sslot));
+
+ if (HeapTupleIsValid(vardata->statsTuple))
+ {
+ if (statistic_proc_security_check(vardata, opfuncoid))
+ have_mcvs = get_attstatsslot(&sslot, vardata->statsTuple,
+ STATISTIC_KIND_MCV, InvalidOid,
+ ATTSTATSSLOT_VALUES | ATTSTATSSLOT_NUMBERS);
+ }
+
+ if (have_mcvs)
+ {
+ /*
+ * If the MCV list and IN-list are large enough, and the operator
+ * supports hashing, attempt to use hash functions so that MCV–IN
+ * matching can be done in O(N+M) instead of O(N×M).
+ */
+ if (sslot.nvalues + num_elems >= MCV_HASH_THRESHOLD)
+ {
+ fmgr_info(opfuncoid, &eqproc);
+ (void) get_op_hash_functions(operator, &hashLeft, &hashRight);
+ }
+ }
+
+ if (have_mcvs && OidIsValid(hashLeft) && OidIsValid(hashRight))
+ {
+ /* Use a hash table to speed up the matching */
+ LOCAL_FCINFO(fcinfo, 2);
+ LOCAL_FCINFO(hash_fcinfo, 1);
+ MCVHashTable_hash *hashTable;
+ FmgrInfo hash_proc;
+ MCVHashContext hashContext;
+ double sumallcommon = 0.0,
+ nonmcv_selec = 0.0;
+ bool isdefault;
+ bool hash_mcv;
+ double otherdistinct;
+ Datum *arrayHash;
+ Datum *arrayProbe;
+ int nvaluesHash;
+ int nvaluesProbe;
+ int nonmcv_cnt = num_elems;
+ int nonconst_cnt = 0;
+
+ /* Grab the nullfrac for use below. */
+ stats = (Form_pg_statistic) GETSTRUCT(vardata->statsTuple);
+ nullfrac = stats->stanullfrac;
+
+ selec = s1disjoint = (useOr ? 0.0 : 1.0);
+
+ InitFunctionCallInfoData(*fcinfo, &eqproc, 2, collation,
+ NULL, NULL);
+ fcinfo->args[0].isnull = false;
+ fcinfo->args[1].isnull = false;
+
+ for (int i = 0; i < sslot.nvalues; i++)
+ sumallcommon += sslot.numbers[i];
+
+ /*
+ * Compute the total probability mass of all non-MCV values. This is
+ * the part of the column distribution not covered by MCVs.
+ */
+ nonmcv_selec = 1.0 - sumallcommon - nullfrac;
+ CLAMP_PROBABILITY(nonmcv_selec);
+
+ /*
+ * Approximate the per-value probability of a non-MCV constant by
+ * dividing the remaining probability mass by the number of other
+ * distinct values.
+ */
+ otherdistinct = get_variable_numdistinct(vardata, &isdefault) - sslot.nnumbers;
+ if (otherdistinct > 1)
+ nonmcv_selec /= otherdistinct;
+
+ if (sslot.nnumbers > 0 &&
+ nonmcv_selec > sslot.numbers[sslot.nnumbers - 1])
+ {
+ nonmcv_selec = sslot.numbers[sslot.nnumbers - 1];
+ }
+
+ /* Make sure we build the hash table on the smaller array. */
+ if (sslot.nvalues <= num_elems)
+ {
+ hash_mcv = true;
+ nvaluesHash = sslot.nvalues;
+ nvaluesProbe = num_elems;
+ arrayHash = sslot.values;
+ arrayProbe = elem_values;
+ }
+ else
+ {
+ hash_mcv = false;
+ nvaluesHash = num_elems;
+ nvaluesProbe = sslot.nvalues;
+ arrayHash = elem_values;
+ arrayProbe = sslot.values;
+ }
+
+ fmgr_info(hash_mcv ? hashLeft : hashRight, &hash_proc);
+ InitFunctionCallInfoData(*hash_fcinfo, &hash_proc, 1, collation,
+ NULL, NULL);
+ hash_fcinfo->args[0].isnull = false;
+
+ hashContext.equal_fcinfo = fcinfo;
+ hashContext.hash_fcinfo = hash_fcinfo;
+ hashContext.op_is_reversed = hash_mcv;
+ hashContext.insert_mode = true;
+
+ get_typlenbyval(hash_mcv ? sslot.valuetype : nominal_element_type,
+ &hashContext.hash_typlen,
+ &hashContext.hash_typbyval);
+
+ hashTable = MCVHashTable_create(CurrentMemoryContext,
+ nvaluesHash,
+ &hashContext);
+
+ /* Build a hash table over the smaller input side. */
+ for (int i = 0; i < nvaluesHash; i++)
+ {
+ bool found = false;
+ MCVHashEntry *entry;
+
+ /*
+ * When hashing IN-list values (hash_mcv == false), we only insert
+ * constant, non-NULL elements. NULL and non-Const elements are
+ * counted separately, because they cannot participate in MCV
+ * matching and must be handled later using generic selectivity
+ * estimation.
+ */
+ if (!hash_mcv)
+ {
+ if (elem_nulls[i])
+ {
+ nonmcv_cnt--;
+ continue;
+ }
+
+ if (elem_const != NULL && !elem_const[i])
+ {
+ nonmcv_cnt--;
+ nonconst_cnt++;
+ continue;
+ }
+ }
+
+ entry = MCVHashTable_insert(hashTable, arrayHash[i], &found);
+
+ /*
+ * entry->count tracks how many times the same value appears, so
+ * that duplicate IN-list elements can be folded into the
+ * probability calculation.
+ */
+ if (likely(!found))
+ {
+ entry->index = i;
+ entry->count = 1;
+ }
+ else
+ entry->count++;
+ }
+
+ hashContext.insert_mode = false;
+ if (hashLeft != hashRight)
+ {
+ fmgr_info(hash_mcv ? hashRight : hashLeft, &hash_proc);
+ /* Resetting hash_fcinfo is probably unnecessary, but be safe */
+ InitFunctionCallInfoData(*hash_fcinfo, &hash_proc, 1, collation,
+ NULL, NULL);
+ hash_fcinfo->args[0].isnull = false;
+ }
+
+ for (int i = 0; i < nvaluesProbe; i++)
+ {
+ MCVHashEntry *entry;
+ Selectivity s1;
+ int nvaluesmcv;
+
+ /*
+ * When probing with IN-list elements, ignore NULLs and non-Const
+ * expressions: they cannot be matched against MCVs and will be
+ * accounted for later by generic estimation.
+ */
+ if (hash_mcv)
+ {
+ if (elem_nulls[i])
+ {
+ nonmcv_cnt--;
+ continue;
+ }
+
+ if (elem_const != NULL && !elem_const[i])
+ {
+ nonmcv_cnt--;
+ nonconst_cnt++;
+ continue;
+ }
+ }
+
+ entry = MCVHashTable_lookup(hashTable, arrayProbe[i]);
+
+ /*
+ * If found, obtain its MCV frequency and remember how many values
+ * on the hashed side map to this entry.
+ */
+ if (entry != NULL)
+ {
+ s1 = hash_mcv ? sslot.numbers[entry->index]
+ : sslot.numbers[i];
+
+ nvaluesmcv = entry->count;
+
+ accum_scalararray_prob(s1, nvaluesmcv, useOr, isEquality,
+ isInequality, nullfrac, &selec,
+ &s1disjoint);
+
+ /* Matched values are no longer considered non-MCV */
+ nonmcv_cnt -= nvaluesmcv;
+ }
+ }
+
+ /*
+ * Account for constant IN-list values that did not match any MCV.
+ *
+ * Each such value is assumed to have probability = nonmcv_selec,
+ * derived from the remaining (non-MCV) probability mass.
+ */
+ accum_scalararray_prob(nonmcv_selec, nonmcv_cnt, useOr, isEquality,
+ isInequality, nullfrac, &selec, &s1disjoint);
+
+ /*
+ * Account for non-Const IN-list elements.
+ *
+ * These values cannot be matched against MCVs, so we rely on the
+ * operator's generic selectivity estimator for each of them.
+ */
+ accum_scalararray_prob(nonconst_sel, nonconst_cnt, useOr, isEquality,
+ isInequality, nullfrac, &selec, &s1disjoint);
+
+ /*
+ * For = ANY or <> ALL, if the IN-list elements are assumed distinct,
+ * the events are disjoint and the total probability is the sum of
+ * individual probabilities. Use that estimate if it lies in [0,1].
+ */
+ if ((useOr ? isEquality : isInequality) &&
+ s1disjoint >= 0.0 && s1disjoint <= 1.0)
+ selec = s1disjoint;
+
+ CLAMP_PROBABILITY(selec);
+
+ MCVHashTable_destroy(hashTable);
+ }
+
+ if (have_mcvs)
+ free_attstatsslot(&sslot);
+
+ return selec;
+}
+
/*
* Estimate number of elements in the array yielded by an expression.
*
@@ -2446,7 +2954,7 @@ eqjoinsel(PG_FUNCTION_ARGS)
* If the MCV lists are long enough to justify hashing, try to look up
* hash functions for the join operator.
*/
- if ((sslot1.nvalues + sslot2.nvalues) >= EQJOINSEL_MCV_HASH_THRESHOLD)
+ if ((sslot1.nvalues + sslot2.nvalues) >= MCV_HASH_THRESHOLD)
(void) get_op_hash_functions(operator, &hashLeft, &hashRight);
}
else
--
2.34.1
