Fix BRIN cost estimation

The original code was overly optimistic about the cost of scanning a
BRIN index, leading to BRIN indexes being selected when they'd be a
worse choice than some other index.  This complete rewrite should be
more accurate.

Author: David Rowley, based on an earlier patch by Emre Hasegeli
Reviewed-by: Emre Hasegeli
Discussion: https://postgr.es/m/CAKJS1f9n-Wapop5Xz1dtGdpdqmzeGqQK4sV2MK-zZugfC14Xtw@mail.gmail.com

src/backend/access/brin/brin.c

@@ -1049,6 +1049,27 @@ brin_free_desc(BrinDesc *bdesc)
  MemoryContextDelete(bdesc->bd_context);
 }
 
+/*
+ * Fetch index's statistical data into *stats
+ */
+void
+brinGetStats(Relation index, BrinStatsData *stats)
+{
+ Buffer metabuffer;
+ Page metapage;
+ BrinMetaPageData *metadata;
+
+ metabuffer = ReadBuffer(index, BRIN_METAPAGE_BLKNO);
+ LockBuffer(metabuffer, BUFFER_LOCK_SHARE);
+ metapage = BufferGetPage(metabuffer);
+ metadata = (BrinMetaPageData *) PageGetContents(metapage);
+
+ stats->pagesPerRange = metadata->pagesPerRange;
+ stats->revmapNumPages = metadata->lastRevmapPage - 1;
+
+ UnlockReleaseBuffer(metabuffer);
+}
+
 /*
  * Initialize a BrinBuildState appropriate to create tuples on the given index.
  */

src/backend/utils/adt/selfuncs.c

@@ -101,6 +101,7 @@
 #include <float.h>
 #include <math.h>
 
+#include "access/brin.h"
 #include "access/gin.h"
 #include "access/htup_details.h"
 #include "access/sysattr.h"
@@ -7721,56 +7722,200 @@ brincostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 {
  IndexOptInfo *index = path->indexinfo;
  List *indexQuals = path->indexquals;
- List *indexOrderBys = path->indexorderbys;
  double numPages = index->pages;
- double numTuples = index->tuples;
+ RelOptInfo *baserel = index->rel;
+ RangeTblEntry *rte = planner_rt_fetch(baserel->relid, root);
  List *qinfos;
  Cost spc_seq_page_cost;
  Cost spc_random_page_cost;
- double qual_op_cost;
  double qual_arg_cost;
+ double qualSelectivity;
+ BrinStatsData statsData;
+ double indexRanges;
+ double minimalRanges;
+ double estimatedRanges;
+ double selec;
+ Relation indexRel;
+ ListCell *l;
+ VariableStatData vardata;
 
- /* Do preliminary analysis of indexquals */
- qinfos = deconstruct_indexquals(path);
+ Assert(rte->rtekind == RTE_RELATION);
 
- /* fetch estimated page cost for tablespace containing index */
+ /* fetch estimated page cost for the tablespace containing the index */
  get_tablespace_page_costs(index->reltablespace,
  &spc_random_page_cost,
  &spc_seq_page_cost);
 
  /*
- * BRIN indexes are always read in full; use that as startup cost.
+ * Obtain some data from the index itself.
+ */
+ indexRel = index_open(index->indexoid, AccessShareLock);
+ brinGetStats(indexRel, &statsData);
+ index_close(indexRel, AccessShareLock);
+
+ /*
+ * Compute index correlation
  *
- * XXX maybe only include revmap pages here?
+ * Because we can use all index quals equally when scanning, we can use
+ * the largest correlation (in absolute value) among columns used by the
+ * query. Start at zero, the worst possible case. If we cannot find
+ * any correlation statistics, we will keep it as 0.
+ */
+ *indexCorrelation = 0;
+
+ qinfos = deconstruct_indexquals(path);
+ foreach(l, qinfos)
+ {
+ IndexQualInfo *qinfo = (IndexQualInfo *) lfirst(l);
+ AttrNumber attnum = index->indexkeys[qinfo->indexcol];
+
+ /* attempt to lookup stats in relation for this index column */
+ if (attnum != 0)
+ {
+ /* Simple variable -- look to stats for the underlying table */
+ if (get_relation_stats_hook &&
+ (*get_relation_stats_hook) (root, rte, attnum, &vardata))
+ {
+ /*
+ * The hook took control of acquiring a stats tuple. If it
+ * did supply a tuple, it'd better have supplied a freefunc.
+ */
+ if (HeapTupleIsValid(vardata.statsTuple) && !vardata.freefunc)
+ elog(ERROR,
+ "no function provided to release variable stats with");
+ }
+ else
+ {
+ vardata.statsTuple =
+ SearchSysCache3(STATRELATTINH,
+ ObjectIdGetDatum(rte->relid),
+ Int16GetDatum(attnum),
+ BoolGetDatum(false));
+ vardata.freefunc = ReleaseSysCache;
+ }
+ }
+ else
+ {
+ /*
+ * Looks like we've found an expression column in the index. Let's
+ * see if there's any stats for it.
+ */
+
+ /* get the attnum from the 0-based index. */
+ attnum = qinfo->indexcol + 1;
+
+ if (get_index_stats_hook &&
+ (*get_index_stats_hook) (root, index->indexoid, attnum, &vardata))
+ {
+ /*
+ * The hook took control of acquiring a stats tuple. If it did
+ * supply a tuple, it'd better have supplied a freefunc.
+ */
+ if (HeapTupleIsValid(vardata.statsTuple) &&
+ !vardata.freefunc)
+ elog(ERROR, "no function provided to release variable stats with");
+ }
+ else
+ {
+ vardata.statsTuple = SearchSysCache3(STATRELATTINH,
+ ObjectIdGetDatum(index->indexoid),
+ Int16GetDatum(attnum),
+ BoolGetDatum(false));
+ vardata.freefunc = ReleaseSysCache;
+ }
+ }
+
+ if (HeapTupleIsValid(vardata.statsTuple))
+ {
+ float4 *numbers;
+ int nnumbers;
+
+ if (get_attstatsslot(vardata.statsTuple, InvalidOid, 0,
+ STATISTIC_KIND_CORRELATION,
+ InvalidOid,
+ NULL,
+ NULL, NULL,
+ &numbers, &nnumbers))
+ {
+ double varCorrelation = 0.0;
+
+ if (nnumbers > 0)
+ varCorrelation = Abs(numbers[0]);
+
+ if (varCorrelation > *indexCorrelation)
+ *indexCorrelation = varCorrelation;
+
+ free_attstatsslot(InvalidOid, NULL, 0, numbers, nnumbers);
+ }
+ }
+
+ ReleaseVariableStats(vardata);
+ }
+
+ qualSelectivity = clauselist_selectivity(root, indexQuals,
+ baserel->relid,
+ JOIN_INNER, NULL,
+ baserel);
+
+ /* work out the actual number of ranges in the index */
+ indexRanges = Max(ceil((double) baserel->pages / statsData.pagesPerRange),
+ 1.0);
+
+ /*
+ * Now calculate the minimum possible ranges we could match with if all of
+ * the rows were in the perfect order in the table's heap.
  */
- *indexStartupCost = spc_seq_page_cost * numPages * loop_count;
+ minimalRanges = ceil(indexRanges * qualSelectivity);
 
  /*
- * To read a BRIN index there might be a bit of back and forth over
- * regular pages, as revmap might point to them out of sequential order;
- * calculate this as reading the whole index in random order.
+ * Now estimate the number of ranges that we'll touch by using the
+ * indexCorrelation from the stats. Careful not to divide by zero
+ * (note we're using the absolute value of the correlation).
  */
- *indexTotalCost = spc_random_page_cost * numPages * loop_count;
+ if (*indexCorrelation < 1.0e-10)
+ estimatedRanges = indexRanges;
+ else
+ estimatedRanges = Min(minimalRanges / *indexCorrelation, indexRanges);
 
- *indexSelectivity =
-  clauselist_selectivity(root, indexQuals,
- path->indexinfo->rel->relid,
-  JOIN_INNER, NULL,
- path->indexinfo->rel);
- *indexCorrelation = 1;
+ /* we expect to visit this portion of the table */
+ selec = estimatedRanges / indexRanges;
+
+ CLAMP_PROBABILITY(selec);
+
+ *indexSelectivity = selec;
 
  /*
- * Add on index qual eval costs, much as in genericcostestimate.
+ * Compute the index qual costs, much as in genericcostestimate, to add
+ * to the index costs.
  */
  qual_arg_cost = other_operands_eval_cost(root, qinfos) +
  orderby_operands_eval_cost(root, path);
- qual_op_cost = cpu_operator_cost *
- (list_length(indexQuals) + list_length(indexOrderBys));
 
+ /*
+ * Compute the startup cost as the cost to read the whole revmap
+ * sequentially, including the cost to execute the index quals.
+ */
+ *indexStartupCost =
+ spc_seq_page_cost * statsData.revmapNumPages * loop_count;
  *indexStartupCost += qual_arg_cost;
- *indexTotalCost += qual_arg_cost;
- *indexTotalCost += (numTuples * *indexSelectivity) * (cpu_index_tuple_cost + qual_op_cost);
- *indexPages = index->pages;
 
- /* XXX what about pages_per_range? */
+ /*
+ * To read a BRIN index there might be a bit of back and forth over
+ * regular pages, as revmap might point to them out of sequential order;
+ * calculate the total cost as reading the whole index in random order.
+ */
+ *indexTotalCost = *indexStartupCost +
+ spc_random_page_cost * (numPages - statsData.revmapNumPages) * loop_count;
+
+ /*
+ * Charge a small amount per range tuple which we expect to match to. This
+ * is meant to reflect the costs of manipulating the bitmap. The BRIN scan
+ * will set a bit for each page in the range when we find a matching
+ * range, so we must multiply the charge by the number of pages in the
+ * range.
+ */
+ *indexTotalCost += 0.1 * cpu_operator_cost * estimatedRanges *
+ statsData.pagesPerRange;
+
+ *indexPages = index->pages;
 }

src/include/access/brin.h

@@ -25,6 +25,17 @@ typedef struct BrinOptions
  bool autosummarize;
 } BrinOptions;
 
+
+/*
+ * BrinStatsData represents stats data for planner use
+ */
+typedef struct BrinStatsData
+{
+ BlockNumber pagesPerRange;
+ BlockNumber revmapNumPages;
+} BrinStatsData;
+
+
 #define BRIN_DEFAULT_PAGES_PER_RANGE 128
 #define BrinGetPagesPerRange(relation) \
  ((relation)->rd_options ? \
@@ -35,4 +46,7 @@ typedef struct BrinOptions
  ((BrinOptions *) (relation)->rd_options)->autosummarize : \
  false)
 
+
+extern void brinGetStats(Relation index, BrinStatsData *stats);
+
 #endif /* BRIN_H */

src/test/regress/expected/brin.out

@@ -363,6 +363,8 @@ BEGIN
  END LOOP;
 END;
 $x$;
+RESET enable_seqscan;
+RESET enable_bitmapscan;
 INSERT INTO brintest SELECT
  repeat(stringu1, 42)::bytea,
  substr(stringu1, 1, 1)::"char",
@@ -481,3 +483,27 @@ SELECT brin_summarize_range('brin_summarize_idx', -1);
 ERROR: block number out of range: -1
 SELECT brin_summarize_range('brin_summarize_idx', 4294967296);
 ERROR: block number out of range: 4294967296
+-- test brin cost estimates behave sanely based on correlation of values
+CREATE TABLE brin_test (a INT, b INT);
+INSERT INTO brin_test SELECT x/100,x%100 FROM generate_series(1,10000) x(x);
+CREATE INDEX brin_test_a_idx ON brin_test USING brin (a) WITH (pages_per_range = 2);
+CREATE INDEX brin_test_b_idx ON brin_test USING brin (b) WITH (pages_per_range = 2);
+VACUUM ANALYZE brin_test;
+-- Ensure brin index is used when columns are perfectly correlated
+EXPLAIN (COSTS OFF) SELECT * FROM brin_test WHERE a = 1;
+ QUERY PLAN 
+--------------------------------------------
+ Bitmap Heap Scan on brin_test
+ Recheck Cond: (a = 1)
+ -> Bitmap Index Scan on brin_test_a_idx
+ Index Cond: (a = 1)
+(4 rows)
+
+-- Ensure brin index is not used when values are not correlated
+EXPLAIN (COSTS OFF) SELECT * FROM brin_test WHERE b = 1;
+ QUERY PLAN 
+-----------------------
+ Seq Scan on brin_test
+ Filter: (b = 1)
+(2 rows)
+

src/test/regress/sql/brin.sql

@@ -370,6 +370,9 @@ BEGIN
 END;
 $x$;
 
+RESET enable_seqscan;
+RESET enable_bitmapscan;
+
 INSERT INTO brintest SELECT
  repeat(stringu1, 42)::bytea,
  substr(stringu1, 1, 1)::"char",
@@ -444,3 +447,16 @@ SELECT brin_summarize_range('brin_summarize_idx', 4294967295);
 -- invalid block number values
 SELECT brin_summarize_range('brin_summarize_idx', -1);
 SELECT brin_summarize_range('brin_summarize_idx', 4294967296);
+
+
+-- test brin cost estimates behave sanely based on correlation of values
+CREATE TABLE brin_test (a INT, b INT);
+INSERT INTO brin_test SELECT x/100,x%100 FROM generate_series(1,10000) x(x);
+CREATE INDEX brin_test_a_idx ON brin_test USING brin (a) WITH (pages_per_range = 2);
+CREATE INDEX brin_test_b_idx ON brin_test USING brin (b) WITH (pages_per_range = 2);
+VACUUM ANALYZE brin_test;
+
+-- Ensure brin index is used when columns are perfectly correlated
+EXPLAIN (COSTS OFF) SELECT * FROM brin_test WHERE a = 1;
+-- Ensure brin index is not used when values are not correlated
+EXPLAIN (COSTS OFF) SELECT * FROM brin_test WHERE b = 1;