Adding upstream version 16.2.upstream/16.2

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 3292 insertions, 0 deletions

diff --git a/src/test/regress/expected/stats_ext.out b/src/test/regress/expected/stats_ext.out
new file mode 100644
index 0000000..a430153
--- /dev/null
+++ b/src/test/regress/expected/stats_ext.out
@@ -0,0 +1,3292 @@
+-- Generic extended statistics support
+--
+-- Note: tables for which we check estimated row counts should be created
+-- with autovacuum_enabled = off, so that we don't have unstable results
+-- from auto-analyze happening when we didn't expect it.
+--
+-- check the number of estimated/actual rows in the top node
+create function check_estimated_rows(text) returns table (estimated int, actual int)
+language plpgsql as
+$$
+declare
+    ln text;
+    tmp text[];
+    first_row bool := true;
+begin
+    for ln in
+        execute format('explain analyze %s', $1)
+    loop
+        if first_row then
+            first_row := false;
+            tmp := regexp_match(ln, 'rows=(\d*) .* rows=(\d*)');
+            return query select tmp[1]::int, tmp[2]::int;
+        end if;
+    end loop;
+end;
+$$;
+-- Verify failures
+CREATE TABLE ext_stats_test (x text, y int, z int);
+CREATE STATISTICS tst;
+ERROR:  syntax error at or near ";"
+LINE 1: CREATE STATISTICS tst;
+                             ^
+CREATE STATISTICS tst ON a, b;
+ERROR:  syntax error at or near ";"
+LINE 1: CREATE STATISTICS tst ON a, b;
+                                     ^
+CREATE STATISTICS tst FROM sometab;
+ERROR:  syntax error at or near "FROM"
+LINE 1: CREATE STATISTICS tst FROM sometab;
+                              ^
+CREATE STATISTICS tst ON a, b FROM nonexistent;
+ERROR:  relation "nonexistent" does not exist
+CREATE STATISTICS tst ON a, b FROM ext_stats_test;
+ERROR:  column "a" does not exist
+CREATE STATISTICS tst ON x, x, y FROM ext_stats_test;
+ERROR:  duplicate column name in statistics definition
+CREATE STATISTICS tst ON x, x, y, x, x, y, x, x, y FROM ext_stats_test;
+ERROR:  cannot have more than 8 columns in statistics
+CREATE STATISTICS tst ON x, x, y, x, x, (x || 'x'), (y + 1), (x || 'x'), (x || 'x'), (y + 1) FROM ext_stats_test;
+ERROR:  cannot have more than 8 columns in statistics
+CREATE STATISTICS tst ON (x || 'x'), (x || 'x'), (y + 1), (x || 'x'), (x || 'x'), (y + 1), (x || 'x'), (x || 'x'), (y + 1) FROM ext_stats_test;
+ERROR:  cannot have more than 8 columns in statistics
+CREATE STATISTICS tst ON (x || 'x'), (x || 'x'), y FROM ext_stats_test;
+ERROR:  duplicate expression in statistics definition
+CREATE STATISTICS tst (unrecognized) ON x, y FROM ext_stats_test;
+ERROR:  unrecognized statistics kind "unrecognized"
+-- incorrect expressions
+CREATE STATISTICS tst ON (y) FROM ext_stats_test; -- single column reference
+ERROR:  extended statistics require at least 2 columns
+CREATE STATISTICS tst ON y + z FROM ext_stats_test; -- missing parentheses
+ERROR:  syntax error at or near "+"
+LINE 1: CREATE STATISTICS tst ON y + z FROM ext_stats_test;
+                                   ^
+CREATE STATISTICS tst ON (x, y) FROM ext_stats_test; -- tuple expression
+ERROR:  syntax error at or near ","
+LINE 1: CREATE STATISTICS tst ON (x, y) FROM ext_stats_test;
+                                   ^
+DROP TABLE ext_stats_test;
+-- Ensure stats are dropped sanely, and test IF NOT EXISTS while at it
+CREATE TABLE ab1 (a INTEGER, b INTEGER, c INTEGER);
+CREATE STATISTICS IF NOT EXISTS ab1_a_b_stats ON a, b FROM ab1;
+COMMENT ON STATISTICS ab1_a_b_stats IS 'new comment';
+CREATE ROLE regress_stats_ext;
+SET SESSION AUTHORIZATION regress_stats_ext;
+COMMENT ON STATISTICS ab1_a_b_stats IS 'changed comment';
+ERROR:  must be owner of statistics object ab1_a_b_stats
+DROP STATISTICS ab1_a_b_stats;
+ERROR:  must be owner of statistics object ab1_a_b_stats
+ALTER STATISTICS ab1_a_b_stats RENAME TO ab1_a_b_stats_new;
+ERROR:  must be owner of statistics object ab1_a_b_stats
+RESET SESSION AUTHORIZATION;
+DROP ROLE regress_stats_ext;
+CREATE STATISTICS IF NOT EXISTS ab1_a_b_stats ON a, b FROM ab1;
+NOTICE:  statistics object "ab1_a_b_stats" already exists, skipping
+DROP STATISTICS ab1_a_b_stats;
+CREATE SCHEMA regress_schema_2;
+CREATE STATISTICS regress_schema_2.ab1_a_b_stats ON a, b FROM ab1;
+-- Let's also verify the pg_get_statisticsobjdef output looks sane.
+SELECT pg_get_statisticsobjdef(oid) FROM pg_statistic_ext WHERE stxname = 'ab1_a_b_stats';
+                      pg_get_statisticsobjdef                      
+-------------------------------------------------------------------
+ CREATE STATISTICS regress_schema_2.ab1_a_b_stats ON a, b FROM ab1
+(1 row)
+
+DROP STATISTICS regress_schema_2.ab1_a_b_stats;
+-- Ensure statistics are dropped when columns are
+CREATE STATISTICS ab1_b_c_stats ON b, c FROM ab1;
+CREATE STATISTICS ab1_a_b_c_stats ON a, b, c FROM ab1;
+CREATE STATISTICS ab1_b_a_stats ON b, a FROM ab1;
+ALTER TABLE ab1 DROP COLUMN a;
+\d ab1
+                Table "public.ab1"
+ Column |  Type   | Collation | Nullable | Default 
+--------+---------+-----------+----------+---------
+ b      | integer |           |          | 
+ c      | integer |           |          | 
+Statistics objects:
+    "public.ab1_b_c_stats" ON b, c FROM ab1
+
+-- Ensure statistics are dropped when table is
+SELECT stxname FROM pg_statistic_ext WHERE stxname LIKE 'ab1%';
+    stxname    
+---------------
+ ab1_b_c_stats
+(1 row)
+
+DROP TABLE ab1;
+SELECT stxname FROM pg_statistic_ext WHERE stxname LIKE 'ab1%';
+ stxname 
+---------
+(0 rows)
+
+-- Ensure things work sanely with SET STATISTICS 0
+CREATE TABLE ab1 (a INTEGER, b INTEGER);
+ALTER TABLE ab1 ALTER a SET STATISTICS 0;
+INSERT INTO ab1 SELECT a, a%23 FROM generate_series(1, 1000) a;
+CREATE STATISTICS ab1_a_b_stats ON a, b FROM ab1;
+ANALYZE ab1;
+WARNING:  statistics object "public.ab1_a_b_stats" could not be computed for relation "public.ab1"
+ALTER TABLE ab1 ALTER a SET STATISTICS -1;
+-- setting statistics target 0 skips the statistics, without printing any message, so check catalog
+ALTER STATISTICS ab1_a_b_stats SET STATISTICS 0;
+\d ab1
+                Table "public.ab1"
+ Column |  Type   | Collation | Nullable | Default 
+--------+---------+-----------+----------+---------
+ a      | integer |           |          | 
+ b      | integer |           |          | 
+Statistics objects:
+    "public.ab1_a_b_stats" ON a, b FROM ab1; STATISTICS 0
+
+ANALYZE ab1;
+SELECT stxname, stxdndistinct, stxddependencies, stxdmcv, stxdinherit
+  FROM pg_statistic_ext s LEFT JOIN pg_statistic_ext_data d ON (d.stxoid = s.oid)
+ WHERE s.stxname = 'ab1_a_b_stats';
+    stxname    | stxdndistinct | stxddependencies | stxdmcv | stxdinherit 
+---------------+---------------+------------------+---------+-------------
+ ab1_a_b_stats |               |                  |         | 
+(1 row)
+
+ALTER STATISTICS ab1_a_b_stats SET STATISTICS -1;
+\d+ ab1
+                                    Table "public.ab1"
+ Column |  Type   | Collation | Nullable | Default | Storage | Stats target | Description 
+--------+---------+-----------+----------+---------+---------+--------------+-------------
+ a      | integer |           |          |         | plain   |              | 
+ b      | integer |           |          |         | plain   |              | 
+Statistics objects:
+    "public.ab1_a_b_stats" ON a, b FROM ab1
+
+-- partial analyze doesn't build stats either
+ANALYZE ab1 (a);
+WARNING:  statistics object "public.ab1_a_b_stats" could not be computed for relation "public.ab1"
+ANALYZE ab1;
+DROP TABLE ab1;
+ALTER STATISTICS ab1_a_b_stats SET STATISTICS 0;
+ERROR:  statistics object "ab1_a_b_stats" does not exist
+ALTER STATISTICS IF EXISTS ab1_a_b_stats SET STATISTICS 0;
+NOTICE:  statistics object "ab1_a_b_stats" does not exist, skipping
+-- Ensure we can build statistics for tables with inheritance.
+CREATE TABLE ab1 (a INTEGER, b INTEGER);
+CREATE TABLE ab1c () INHERITS (ab1);
+INSERT INTO ab1 VALUES (1,1);
+CREATE STATISTICS ab1_a_b_stats ON a, b FROM ab1;
+ANALYZE ab1;
+DROP TABLE ab1 CASCADE;
+NOTICE:  drop cascades to table ab1c
+-- Tests for stats with inheritance
+CREATE TABLE stxdinh(a int, b int);
+CREATE TABLE stxdinh1() INHERITS(stxdinh);
+CREATE TABLE stxdinh2() INHERITS(stxdinh);
+INSERT INTO stxdinh SELECT mod(a,50), mod(a,100) FROM generate_series(0, 1999) a;
+INSERT INTO stxdinh1 SELECT mod(a,100), mod(a,100) FROM generate_series(0, 999) a;
+INSERT INTO stxdinh2 SELECT mod(a,100), mod(a,100) FROM generate_series(0, 999) a;
+VACUUM ANALYZE stxdinh, stxdinh1, stxdinh2;
+-- Ensure non-inherited stats are not applied to inherited query
+-- Without stats object, it looks like this
+SELECT * FROM check_estimated_rows('SELECT a, b FROM stxdinh* GROUP BY 1, 2');
+ estimated | actual 
+-----------+--------
+       400 |    150
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT a, b FROM stxdinh* WHERE a = 0 AND b = 0');
+ estimated | actual 
+-----------+--------
+         3 |     40
+(1 row)
+
+CREATE STATISTICS stxdinh ON a, b FROM stxdinh;
+VACUUM ANALYZE stxdinh, stxdinh1, stxdinh2;
+-- See if the extended stats affect the estimates
+SELECT * FROM check_estimated_rows('SELECT a, b FROM stxdinh* GROUP BY 1, 2');
+ estimated | actual 
+-----------+--------
+       150 |    150
+(1 row)
+
+-- Dependencies are applied at individual relations (within append), so
+-- this estimate changes a bit because we improve estimates for the parent
+SELECT * FROM check_estimated_rows('SELECT a, b FROM stxdinh* WHERE a = 0 AND b = 0');
+ estimated | actual 
+-----------+--------
+        22 |     40
+(1 row)
+
+-- Ensure correct (non-inherited) stats are applied to inherited query
+SELECT * FROM check_estimated_rows('SELECT a, b FROM ONLY stxdinh GROUP BY 1, 2');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT a, b FROM ONLY stxdinh WHERE a = 0 AND b = 0');
+ estimated | actual 
+-----------+--------
+        20 |     20
+(1 row)
+
+DROP TABLE stxdinh, stxdinh1, stxdinh2;
+-- Ensure inherited stats ARE applied to inherited query in partitioned table
+CREATE TABLE stxdinp(i int, a int, b int) PARTITION BY RANGE (i);
+CREATE TABLE stxdinp1 PARTITION OF stxdinp FOR VALUES FROM (1) TO (100);
+INSERT INTO stxdinp SELECT 1, a/100, a/100 FROM generate_series(1, 999) a;
+CREATE STATISTICS stxdinp ON (a + 1), a, b FROM stxdinp;
+VACUUM ANALYZE stxdinp; -- partitions are processed recursively
+SELECT 1 FROM pg_statistic_ext WHERE stxrelid = 'stxdinp'::regclass;
+ ?column? 
+----------
+        1
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT a, b FROM stxdinp GROUP BY 1, 2');
+ estimated | actual 
+-----------+--------
+        10 |     10
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT a + 1, b FROM ONLY stxdinp GROUP BY 1, 2');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+DROP TABLE stxdinp;
+-- basic test for statistics on expressions
+CREATE TABLE ab1 (a INTEGER, b INTEGER, c TIMESTAMP, d TIMESTAMPTZ);
+-- expression stats may be built on a single expression column
+CREATE STATISTICS ab1_exprstat_1 ON (a+b) FROM ab1;
+-- with a single expression, we only enable expression statistics
+CREATE STATISTICS ab1_exprstat_2 ON (a+b) FROM ab1;
+SELECT stxkind FROM pg_statistic_ext WHERE stxname = 'ab1_exprstat_2';
+ stxkind 
+---------
+ {e}
+(1 row)
+
+-- adding anything to the expression builds all statistics kinds
+CREATE STATISTICS ab1_exprstat_3 ON (a+b), a FROM ab1;
+SELECT stxkind FROM pg_statistic_ext WHERE stxname = 'ab1_exprstat_3';
+  stxkind  
+-----------
+ {d,f,m,e}
+(1 row)
+
+-- date_trunc on timestamptz is not immutable, but that should not matter
+CREATE STATISTICS ab1_exprstat_4 ON date_trunc('day', d) FROM ab1;
+-- date_trunc on timestamp is immutable
+CREATE STATISTICS ab1_exprstat_5 ON date_trunc('day', c) FROM ab1;
+-- check use of a boolean-returning expression
+CREATE STATISTICS ab1_exprstat_6 ON
+  (case a when 1 then true else false end), b FROM ab1;
+-- insert some data and run analyze, to test that these cases build properly
+INSERT INTO ab1
+SELECT x / 10, x / 3,
+    '2020-10-01'::timestamp + x * interval '1 day',
+    '2020-10-01'::timestamptz + x * interval '1 day'
+FROM generate_series(1, 100) x;
+ANALYZE ab1;
+-- apply some stats
+SELECT * FROM check_estimated_rows('SELECT * FROM ab1 WHERE (case a when 1 then true else false end) AND b=2');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+DROP TABLE ab1;
+-- Verify supported object types for extended statistics
+CREATE schema tststats;
+CREATE TABLE tststats.t (a int, b int, c text);
+CREATE INDEX ti ON tststats.t (a, b);
+CREATE SEQUENCE tststats.s;
+CREATE VIEW tststats.v AS SELECT * FROM tststats.t;
+CREATE MATERIALIZED VIEW tststats.mv AS SELECT * FROM tststats.t;
+CREATE TYPE tststats.ty AS (a int, b int, c text);
+CREATE FOREIGN DATA WRAPPER extstats_dummy_fdw;
+CREATE SERVER extstats_dummy_srv FOREIGN DATA WRAPPER extstats_dummy_fdw;
+CREATE FOREIGN TABLE tststats.f (a int, b int, c text) SERVER extstats_dummy_srv;
+CREATE TABLE tststats.pt (a int, b int, c text) PARTITION BY RANGE (a, b);
+CREATE TABLE tststats.pt1 PARTITION OF tststats.pt FOR VALUES FROM (-10, -10) TO (10, 10);
+CREATE STATISTICS tststats.s1 ON a, b FROM tststats.t;
+CREATE STATISTICS tststats.s2 ON a, b FROM tststats.ti;
+ERROR:  cannot define statistics for relation "ti"
+DETAIL:  This operation is not supported for indexes.
+CREATE STATISTICS tststats.s3 ON a, b FROM tststats.s;
+ERROR:  cannot define statistics for relation "s"
+DETAIL:  This operation is not supported for sequences.
+CREATE STATISTICS tststats.s4 ON a, b FROM tststats.v;
+ERROR:  cannot define statistics for relation "v"
+DETAIL:  This operation is not supported for views.
+CREATE STATISTICS tststats.s5 ON a, b FROM tststats.mv;
+CREATE STATISTICS tststats.s6 ON a, b FROM tststats.ty;
+ERROR:  cannot define statistics for relation "ty"
+DETAIL:  This operation is not supported for composite types.
+CREATE STATISTICS tststats.s7 ON a, b FROM tststats.f;
+CREATE STATISTICS tststats.s8 ON a, b FROM tststats.pt;
+CREATE STATISTICS tststats.s9 ON a, b FROM tststats.pt1;
+DO $$
+DECLARE
+	relname text := reltoastrelid::regclass FROM pg_class WHERE oid = 'tststats.t'::regclass;
+BEGIN
+	EXECUTE 'CREATE STATISTICS tststats.s10 ON a, b FROM ' || relname;
+EXCEPTION WHEN wrong_object_type THEN
+	RAISE NOTICE 'stats on toast table not created';
+END;
+$$;
+NOTICE:  stats on toast table not created
+DROP SCHEMA tststats CASCADE;
+NOTICE:  drop cascades to 7 other objects
+DETAIL:  drop cascades to table tststats.t
+drop cascades to sequence tststats.s
+drop cascades to view tststats.v
+drop cascades to materialized view tststats.mv
+drop cascades to type tststats.ty
+drop cascades to foreign table tststats.f
+drop cascades to table tststats.pt
+DROP FOREIGN DATA WRAPPER extstats_dummy_fdw CASCADE;
+NOTICE:  drop cascades to server extstats_dummy_srv
+-- n-distinct tests
+CREATE TABLE ndistinct (
+    filler1 TEXT,
+    filler2 NUMERIC,
+    a INT,
+    b INT,
+    filler3 DATE,
+    c INT,
+    d INT
+)
+WITH (autovacuum_enabled = off);
+-- over-estimates when using only per-column statistics
+INSERT INTO ndistinct (a, b, c, filler1)
+     SELECT i/100, i/100, i/100, cash_words((i/100)::money)
+       FROM generate_series(1,1000) s(i);
+ANALYZE ndistinct;
+-- Group Aggregate, due to over-estimate of the number of groups
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+       100 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY b, c');
+ estimated | actual 
+-----------+--------
+       100 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, c');
+ estimated | actual 
+-----------+--------
+       100 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, c, d');
+ estimated | actual 
+-----------+--------
+       200 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY b, c, d');
+ estimated | actual 
+-----------+--------
+       200 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (a+1)');
+ estimated | actual 
+-----------+--------
+       100 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       100 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100), (2*c)');
+ estimated | actual 
+-----------+--------
+       100 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       100 |     11
+(1 row)
+
+-- correct command
+CREATE STATISTICS s10 ON a, b, c FROM ndistinct;
+ANALYZE ndistinct;
+SELECT s.stxkind, d.stxdndistinct
+  FROM pg_statistic_ext s, pg_statistic_ext_data d
+ WHERE s.stxrelid = 'ndistinct'::regclass
+   AND d.stxoid = s.oid;
+ stxkind |                    stxdndistinct                    
+---------+-----------------------------------------------------
+ {d,f,m} | {"3, 4": 11, "3, 6": 11, "4, 6": 11, "3, 4, 6": 11}
+(1 row)
+
+-- minor improvement, make sure the ctid does not break the matching
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY ctid, a, b');
+ estimated | actual 
+-----------+--------
+      1000 |   1000
+(1 row)
+
+-- Hash Aggregate, thanks to estimates improved by the statistic
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+        11 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY b, c');
+ estimated | actual 
+-----------+--------
+        11 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, c');
+ estimated | actual 
+-----------+--------
+        11 |     11
+(1 row)
+
+-- partial improvement (match on attributes)
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (a+1)');
+ estimated | actual 
+-----------+--------
+        11 |     11
+(1 row)
+
+-- expressions - no improvement
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+        11 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100), (2*c)');
+ estimated | actual 
+-----------+--------
+        11 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+        11 |     11
+(1 row)
+
+-- last two plans keep using Group Aggregate, because 'd' is not covered
+-- by the statistic and while it's NULL-only we assume 200 values for it
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, c, d');
+ estimated | actual 
+-----------+--------
+       200 |     11
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY b, c, d');
+ estimated | actual 
+-----------+--------
+       200 |     11
+(1 row)
+
+TRUNCATE TABLE ndistinct;
+-- under-estimates when using only per-column statistics
+INSERT INTO ndistinct (a, b, c, filler1)
+     SELECT mod(i,13), mod(i,17), mod(i,19),
+            cash_words(mod(i,23)::int::money)
+       FROM generate_series(1,1000) s(i);
+ANALYZE ndistinct;
+SELECT s.stxkind, d.stxdndistinct
+  FROM pg_statistic_ext s, pg_statistic_ext_data d
+ WHERE s.stxrelid = 'ndistinct'::regclass
+   AND d.stxoid = s.oid;
+ stxkind |                      stxdndistinct                       
+---------+----------------------------------------------------------
+ {d,f,m} | {"3, 4": 221, "3, 6": 247, "4, 6": 323, "3, 4, 6": 1000}
+(1 row)
+
+-- correct estimates
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+       221 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, c');
+ estimated | actual 
+-----------+--------
+      1000 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, c, d');
+ estimated | actual 
+-----------+--------
+      1000 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY b, c, d');
+ estimated | actual 
+-----------+--------
+       323 |    323
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, d');
+ estimated | actual 
+-----------+--------
+       200 |     13
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (a+1)');
+ estimated | actual 
+-----------+--------
+       221 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       221 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100), (2*c)');
+ estimated | actual 
+-----------+--------
+      1000 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       221 |    221
+(1 row)
+
+DROP STATISTICS s10;
+SELECT s.stxkind, d.stxdndistinct
+  FROM pg_statistic_ext s, pg_statistic_ext_data d
+ WHERE s.stxrelid = 'ndistinct'::regclass
+   AND d.stxoid = s.oid;
+ stxkind | stxdndistinct 
+---------+---------------
+(0 rows)
+
+-- dropping the statistics results in under-estimates
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+       100 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, c');
+ estimated | actual 
+-----------+--------
+       100 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, c, d');
+ estimated | actual 
+-----------+--------
+       200 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY b, c, d');
+ estimated | actual 
+-----------+--------
+       200 |    323
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, d');
+ estimated | actual 
+-----------+--------
+       200 |     13
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (a+1)');
+ estimated | actual 
+-----------+--------
+       100 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       100 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100), (2*c)');
+ estimated | actual 
+-----------+--------
+       100 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       100 |    221
+(1 row)
+
+-- ndistinct estimates with statistics on expressions
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       100 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100), (2*c)');
+ estimated | actual 
+-----------+--------
+       100 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       100 |    221
+(1 row)
+
+CREATE STATISTICS s10 (ndistinct) ON (a+1), (b+100), (2*c) FROM ndistinct;
+ANALYZE ndistinct;
+SELECT s.stxkind, d.stxdndistinct
+  FROM pg_statistic_ext s, pg_statistic_ext_data d
+ WHERE s.stxrelid = 'ndistinct'::regclass
+   AND d.stxoid = s.oid;
+ stxkind |                           stxdndistinct                           
+---------+-------------------------------------------------------------------
+ {d,e}   | {"-1, -2": 221, "-1, -3": 247, "-2, -3": 323, "-1, -2, -3": 1000}
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       221 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a+1), (b+100), (2*c)');
+ estimated | actual 
+-----------+--------
+      1000 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (a+1), (b+100)');
+ estimated | actual 
+-----------+--------
+       221 |    221
+(1 row)
+
+DROP STATISTICS s10;
+-- a mix of attributes and expressions
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+       100 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (2*c)');
+ estimated | actual 
+-----------+--------
+       100 |    247
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (2*c)');
+ estimated | actual 
+-----------+--------
+       100 |   1000
+(1 row)
+
+CREATE STATISTICS s10 (ndistinct) ON a, b, (2*c) FROM ndistinct;
+ANALYZE ndistinct;
+SELECT s.stxkind, d.stxdndistinct
+  FROM pg_statistic_ext s, pg_statistic_ext_data d
+ WHERE s.stxrelid = 'ndistinct'::regclass
+   AND d.stxoid = s.oid;
+ stxkind |                        stxdndistinct                        
+---------+-------------------------------------------------------------
+ {d,e}   | {"3, 4": 221, "3, -1": 247, "4, -1": 323, "3, 4, -1": 1000}
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+       221 |    221
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (2*c)');
+ estimated | actual 
+-----------+--------
+       247 |    247
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (2*c)');
+ estimated | actual 
+-----------+--------
+      1000 |   1000
+(1 row)
+
+DROP STATISTICS s10;
+-- combination of multiple ndistinct statistics, with/without expressions
+TRUNCATE ndistinct;
+-- two mostly independent groups of columns
+INSERT INTO ndistinct (a, b, c, d)
+     SELECT mod(i,3), mod(i,9), mod(i,5), mod(i,20)
+       FROM generate_series(1,1000) s(i);
+ANALYZE ndistinct;
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+        27 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1)');
+ estimated | actual 
+-----------+--------
+        27 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), b');
+ estimated | actual 
+-----------+--------
+        27 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1)');
+ estimated | actual 
+-----------+--------
+        27 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1), c');
+ estimated | actual 
+-----------+--------
+       100 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (c*10)');
+ estimated | actual 
+-----------+--------
+       100 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1), c, (d - 1)');
+ estimated | actual 
+-----------+--------
+       100 |    180
+(1 row)
+
+-- basic statistics on both attributes (no expressions)
+CREATE STATISTICS s11 (ndistinct) ON a, b FROM ndistinct;
+CREATE STATISTICS s12 (ndistinct) ON c, d FROM ndistinct;
+ANALYZE ndistinct;
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1), c');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (c*10)');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1), c, (d - 1)');
+ estimated | actual 
+-----------+--------
+       100 |    180
+(1 row)
+
+-- replace the second statistics by statistics on expressions
+DROP STATISTICS s12;
+CREATE STATISTICS s12 (ndistinct) ON (c * 10), (d - 1) FROM ndistinct;
+ANALYZE ndistinct;
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1), c');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (c*10)');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1), c, (d - 1)');
+ estimated | actual 
+-----------+--------
+       100 |    180
+(1 row)
+
+-- replace the second statistics by statistics on both attributes and expressions
+DROP STATISTICS s12;
+CREATE STATISTICS s12 (ndistinct) ON c, d, (c * 10), (d - 1) FROM ndistinct;
+ANALYZE ndistinct;
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1), c');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (c*10)');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1), c, (d - 1)');
+ estimated | actual 
+-----------+--------
+       100 |    180
+(1 row)
+
+-- replace the other statistics by statistics on both attributes and expressions
+DROP STATISTICS s11;
+CREATE STATISTICS s11 (ndistinct) ON a, b, (a*5), (b+1) FROM ndistinct;
+ANALYZE ndistinct;
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1), c');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (c*10)');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1), c, (d - 1)');
+ estimated | actual 
+-----------+--------
+       100 |    180
+(1 row)
+
+-- replace statistics by somewhat overlapping ones (this expected to get worse estimate
+-- because the first statistics shall be applied to 3 columns, and the second one can't
+-- be really applied)
+DROP STATISTICS s11;
+DROP STATISTICS s12;
+CREATE STATISTICS s11 (ndistinct) ON a, b, (a*5), (b+1) FROM ndistinct;
+CREATE STATISTICS s12 (ndistinct) ON a, (b+1), (c * 10) FROM ndistinct;
+ANALYZE ndistinct;
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), b');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1)');
+ estimated | actual 
+-----------+--------
+         9 |      9
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY (a*5), (b+1), c');
+ estimated | actual 
+-----------+--------
+        45 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, b, (c*10)');
+ estimated | actual 
+-----------+--------
+       100 |     45
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT COUNT(*) FROM ndistinct GROUP BY a, (b+1), c, (d - 1)');
+ estimated | actual 
+-----------+--------
+       100 |    180
+(1 row)
+
+DROP STATISTICS s11;
+DROP STATISTICS s12;
+-- functional dependencies tests
+CREATE TABLE functional_dependencies (
+    filler1 TEXT,
+    filler2 NUMERIC,
+    a INT,
+    b TEXT,
+    filler3 DATE,
+    c INT,
+    d TEXT
+)
+WITH (autovacuum_enabled = off);
+CREATE INDEX fdeps_ab_idx ON functional_dependencies (a, b);
+CREATE INDEX fdeps_abc_idx ON functional_dependencies (a, b, c);
+-- random data (no functional dependencies)
+INSERT INTO functional_dependencies (a, b, c, filler1)
+     SELECT mod(i, 5), mod(i, 7), mod(i, 11), i FROM generate_series(1,1000) s(i);
+ANALYZE functional_dependencies;
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+        29 |     29
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+         3 |      3
+(1 row)
+
+-- create statistics
+CREATE STATISTICS func_deps_stat (dependencies) ON a, b, c FROM functional_dependencies;
+ANALYZE functional_dependencies;
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+        29 |     29
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+         3 |      3
+(1 row)
+
+-- a => b, a => c, b => c
+TRUNCATE functional_dependencies;
+DROP STATISTICS func_deps_stat;
+-- now do the same thing, but with expressions
+INSERT INTO functional_dependencies (a, b, c, filler1)
+     SELECT i, i, i, i FROM generate_series(1,5000) s(i);
+ANALYZE functional_dependencies;
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE mod(a, 11) = 1 AND mod(b::int, 13) = 1');
+ estimated | actual 
+-----------+--------
+         1 |     35
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE mod(a, 11) = 1 AND mod(b::int, 13) = 1 AND mod(c, 7) = 1');
+ estimated | actual 
+-----------+--------
+         1 |      5
+(1 row)
+
+-- create statistics
+CREATE STATISTICS func_deps_stat (dependencies) ON (mod(a,11)), (mod(b::int, 13)), (mod(c, 7)) FROM functional_dependencies;
+ANALYZE functional_dependencies;
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE mod(a, 11) = 1 AND mod(b::int, 13) = 1');
+ estimated | actual 
+-----------+--------
+        35 |     35
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE mod(a, 11) = 1 AND mod(b::int, 13) = 1 AND mod(c, 7) = 1');
+ estimated | actual 
+-----------+--------
+         5 |      5
+(1 row)
+
+-- a => b, a => c, b => c
+TRUNCATE functional_dependencies;
+DROP STATISTICS func_deps_stat;
+INSERT INTO functional_dependencies (a, b, c, filler1)
+     SELECT mod(i,100), mod(i,50), mod(i,25), i FROM generate_series(1,5000) s(i);
+ANALYZE functional_dependencies;
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+-- IN
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 51) AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         2 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 51) AND b IN (''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+         4 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 2, 51, 52) AND b IN (''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+         8 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 2, 51, 52) AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         4 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 26, 51, 76) AND b IN (''1'', ''26'') AND c = 1');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 26, 51, 76) AND b IN (''1'', ''26'') AND c IN (1)');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 2, 26, 27, 51, 52, 76, 77) AND b IN (''1'', ''2'', ''26'', ''27'') AND c IN (1, 2)');
+ estimated | actual 
+-----------+--------
+         3 |    400
+(1 row)
+
+-- OR clauses referencing the same attribute
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a = 1 OR a = 51) AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         2 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a = 1 OR a = 51) AND (b = ''1'' OR b = ''2'')');
+ estimated | actual 
+-----------+--------
+         4 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a = 1 OR a = 2 OR a = 51 OR a = 52) AND (b = ''1'' OR b = ''2'')');
+ estimated | actual 
+-----------+--------
+         8 |    200
+(1 row)
+
+-- OR clauses referencing different attributes
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a = 1 OR b = ''1'') AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         3 |    100
+(1 row)
+
+-- ANY
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 51]) AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         2 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 51]) AND b = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         4 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 2, 51, 52]) AND b = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         8 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 26, 51, 76]) AND b = ANY (ARRAY[''1'', ''26'']) AND c = 1');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 26, 51, 76]) AND b = ANY (ARRAY[''1'', ''26'']) AND c = ANY (ARRAY[1])');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 2, 26, 27, 51, 52, 76, 77]) AND b = ANY (ARRAY[''1'', ''2'', ''26'', ''27'']) AND c = ANY (ARRAY[1, 2])');
+ estimated | actual 
+-----------+--------
+         3 |    400
+(1 row)
+
+-- ANY with inequalities should not benefit from functional dependencies
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a < ANY (ARRAY[1, 51]) AND b > ''1''');
+ estimated | actual 
+-----------+--------
+      2472 |   2400
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a >= ANY (ARRAY[1, 51]) AND b <= ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+      1441 |   1250
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a <= ANY (ARRAY[1, 2, 51, 52]) AND b >= ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+      3909 |   2550
+(1 row)
+
+-- ALL (should not benefit from functional dependencies)
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 51) AND b = ALL (ARRAY[''1''])');
+ estimated | actual 
+-----------+--------
+         2 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 51) AND b = ALL (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 2, 51, 52) AND b = ALL (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+-- create statistics
+CREATE STATISTICS func_deps_stat (dependencies) ON a, b, c FROM functional_dependencies;
+ANALYZE functional_dependencies;
+-- print the detected dependencies
+SELECT dependencies FROM pg_stats_ext WHERE statistics_name = 'func_deps_stat';
+                                                dependencies                                                
+------------------------------------------------------------------------------------------------------------
+ {"3 => 4": 1.000000, "3 => 6": 1.000000, "4 => 6": 1.000000, "3, 4 => 6": 1.000000, "3, 6 => 4": 1.000000}
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+-- IN
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 51) AND b = ''1''');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 51) AND b IN (''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 2, 51, 52) AND b IN (''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 2, 51, 52) AND b = ''1''');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 26, 51, 76) AND b IN (''1'', ''26'') AND c = 1');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 26, 51, 76) AND b IN (''1'', ''26'') AND c IN (1)');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 2, 26, 27, 51, 52, 76, 77) AND b IN (''1'', ''2'', ''26'', ''27'') AND c IN (1, 2)');
+ estimated | actual 
+-----------+--------
+       400 |    400
+(1 row)
+
+-- OR clauses referencing the same attribute
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a = 1 OR a = 51) AND b = ''1''');
+ estimated | actual 
+-----------+--------
+        99 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a = 1 OR a = 51) AND (b = ''1'' OR b = ''2'')');
+ estimated | actual 
+-----------+--------
+        99 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a = 1 OR a = 2 OR a = 51 OR a = 52) AND (b = ''1'' OR b = ''2'')');
+ estimated | actual 
+-----------+--------
+       197 |    200
+(1 row)
+
+-- OR clauses referencing different attributes are incompatible
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a = 1 OR b = ''1'') AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         3 |    100
+(1 row)
+
+-- ANY
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 51]) AND b = ''1''');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 51]) AND b = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 2, 51, 52]) AND b = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 26, 51, 76]) AND b = ANY (ARRAY[''1'', ''26'']) AND c = 1');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 26, 51, 76]) AND b = ANY (ARRAY[''1'', ''26'']) AND c = ANY (ARRAY[1])');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = ANY (ARRAY[1, 2, 26, 27, 51, 52, 76, 77]) AND b = ANY (ARRAY[''1'', ''2'', ''26'', ''27'']) AND c = ANY (ARRAY[1, 2])');
+ estimated | actual 
+-----------+--------
+       400 |    400
+(1 row)
+
+-- ANY with inequalities should not benefit from functional dependencies
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a < ANY (ARRAY[1, 51]) AND b > ''1''');
+ estimated | actual 
+-----------+--------
+      2472 |   2400
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a >= ANY (ARRAY[1, 51]) AND b <= ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+      1441 |   1250
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a <= ANY (ARRAY[1, 2, 51, 52]) AND b >= ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+      3909 |   2550
+(1 row)
+
+-- ALL (should not benefit from functional dependencies)
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 51) AND b = ALL (ARRAY[''1''])');
+ estimated | actual 
+-----------+--------
+         2 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 51) AND b = ALL (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a IN (1, 2, 51, 52) AND b = ALL (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+-- changing the type of column c causes all its stats to be dropped, reverting
+-- to default estimates without any statistics, i.e. 0.5% selectivity for each
+-- condition
+ALTER TABLE functional_dependencies ALTER COLUMN c TYPE numeric;
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+ANALYZE functional_dependencies;
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+DROP STATISTICS func_deps_stat;
+-- now try functional dependencies with expressions
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = 2 AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = 2 AND upper(b) = ''1'' AND (c + 1) = 2');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+-- IN
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 102) AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 102) AND upper(b) IN (''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 4, 102, 104) AND upper(b) IN (''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 4, 102, 104) AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 52, 102, 152) AND upper(b) IN (''1'', ''26'') AND (c + 1) = 2');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 52, 102, 152) AND upper(b) IN (''1'', ''26'') AND (c + 1) IN (2)');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 4, 52, 54, 102, 104, 152, 154) AND upper(b) IN (''1'', ''2'', ''26'', ''27'') AND (c + 1) IN (2, 3)');
+ estimated | actual 
+-----------+--------
+         1 |    400
+(1 row)
+
+-- OR clauses referencing the same attribute
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE ((a * 2) = 2 OR (a * 2) = 102) AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE ((a * 2) = 2 OR (a * 2) = 102) AND (upper(b) = ''1'' OR upper(b) = ''2'')');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE ((a * 2) = 2 OR (a * 2) = 4 OR (a * 2) = 102 OR (a * 2) = 104) AND (upper(b) = ''1'' OR upper(b) = ''2'')');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+-- OR clauses referencing different attributes
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE ((a * 2) = 2 OR upper(b) = ''1'') AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+-- ANY
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 102]) AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 102]) AND upper(b) = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 4, 102, 104]) AND upper(b) = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 52, 102, 152]) AND upper(b) = ANY (ARRAY[''1'', ''26'']) AND (c + 1) = 2');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 52, 102, 152]) AND upper(b) = ANY (ARRAY[''1'', ''26'']) AND (c + 1) = ANY (ARRAY[2])');
+ estimated | actual 
+-----------+--------
+         1 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 4, 52, 54, 102, 104, 152, 154]) AND upper(b) = ANY (ARRAY[''1'', ''2'', ''26'', ''27'']) AND (c + 1) = ANY (ARRAY[2, 3])');
+ estimated | actual 
+-----------+--------
+         1 |    400
+(1 row)
+
+-- ANY with inequalities should not benefit from functional dependencies
+-- the estimates however improve thanks to having expression statistics
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) < ANY (ARRAY[2, 102]) AND upper(b) > ''1''');
+ estimated | actual 
+-----------+--------
+       926 |   2400
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) >= ANY (ARRAY[2, 102]) AND upper(b) <= ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+      1543 |   1250
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) <= ANY (ARRAY[2, 4, 102, 104]) AND upper(b) >= ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+      2229 |   2550
+(1 row)
+
+-- ALL (should not benefit from functional dependencies)
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 102) AND upper(b) = ALL (ARRAY[''1''])');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 102) AND upper(b) = ALL (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 4, 102, 104) AND upper(b) = ALL (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+-- create statistics on expressions
+CREATE STATISTICS func_deps_stat (dependencies) ON (a * 2), upper(b), (c + 1) FROM functional_dependencies;
+ANALYZE functional_dependencies;
+-- print the detected dependencies
+SELECT dependencies FROM pg_stats_ext WHERE statistics_name = 'func_deps_stat';
+                                                      dependencies                                                      
+------------------------------------------------------------------------------------------------------------------------
+ {"-1 => -2": 1.000000, "-1 => -3": 1.000000, "-2 => -3": 1.000000, "-1, -2 => -3": 1.000000, "-1, -3 => -2": 1.000000}
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = 2 AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = 2 AND upper(b) = ''1'' AND (c + 1) = 2');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+-- IN
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 102) AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 102) AND upper(b) IN (''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 4, 102, 104) AND upper(b) IN (''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 4, 102, 104) AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 52, 102, 152) AND upper(b) IN (''1'', ''26'') AND (c + 1) = 2');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 52, 102, 152) AND upper(b) IN (''1'', ''26'') AND (c + 1) IN (2)');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 4, 52, 54, 102, 104, 152, 154) AND upper(b) IN (''1'', ''2'', ''26'', ''27'') AND (c + 1) IN (2, 3)');
+ estimated | actual 
+-----------+--------
+       400 |    400
+(1 row)
+
+-- OR clauses referencing the same attribute
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE ((a * 2) = 2 OR (a * 2) = 102) AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+        99 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE ((a * 2) = 2 OR (a * 2) = 102) AND (upper(b) = ''1'' OR upper(b) = ''2'')');
+ estimated | actual 
+-----------+--------
+        99 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE ((a * 2) = 2 OR (a * 2) = 4 OR (a * 2) = 102 OR (a * 2) = 104) AND (upper(b) = ''1'' OR upper(b) = ''2'')');
+ estimated | actual 
+-----------+--------
+       197 |    200
+(1 row)
+
+-- OR clauses referencing different attributes
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE ((a * 2) = 2 OR upper(b) = ''1'') AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+         3 |    100
+(1 row)
+
+-- ANY
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 102]) AND upper(b) = ''1''');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 102]) AND upper(b) = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 4, 102, 104]) AND upper(b) = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 52, 102, 152]) AND upper(b) = ANY (ARRAY[''1'', ''26'']) AND (c + 1) = 2');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 52, 102, 152]) AND upper(b) = ANY (ARRAY[''1'', ''26'']) AND (c + 1) = ANY (ARRAY[2])');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) = ANY (ARRAY[2, 4, 52, 54, 102, 104, 152, 154]) AND upper(b) = ANY (ARRAY[''1'', ''2'', ''26'', ''27'']) AND (c + 1) = ANY (ARRAY[2, 3])');
+ estimated | actual 
+-----------+--------
+       400 |    400
+(1 row)
+
+-- ANY with inequalities should not benefit from functional dependencies
+-- the estimates however improve thanks to having expression statistics
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) < ANY (ARRAY[2, 102]) AND upper(b) > ''1''');
+ estimated | actual 
+-----------+--------
+      2472 |   2400
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) >= ANY (ARRAY[2, 102]) AND upper(b) <= ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+      1441 |   1250
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) <= ANY (ARRAY[2, 4, 102, 104]) AND upper(b) >= ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+      3909 |   2550
+(1 row)
+
+-- ALL (should not benefit from functional dependencies)
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 102) AND upper(b) = ALL (ARRAY[''1''])');
+ estimated | actual 
+-----------+--------
+         2 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 102) AND upper(b) = ALL (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies WHERE (a * 2) IN (2, 4, 102, 104) AND upper(b) = ALL (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+-- check the ability to use multiple functional dependencies
+CREATE TABLE functional_dependencies_multi (
+	a INTEGER,
+	b INTEGER,
+	c INTEGER,
+	d INTEGER
+)
+WITH (autovacuum_enabled = off);
+INSERT INTO functional_dependencies_multi (a, b, c, d)
+    SELECT
+         mod(i,7),
+         mod(i,7),
+         mod(i,11),
+         mod(i,11)
+    FROM generate_series(1,5000) s(i);
+ANALYZE functional_dependencies_multi;
+-- estimates without any functional dependencies
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE a = 0 AND b = 0');
+ estimated | actual 
+-----------+--------
+       102 |    714
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE 0 = a AND 0 = b');
+ estimated | actual 
+-----------+--------
+       102 |    714
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE c = 0 AND d = 0');
+ estimated | actual 
+-----------+--------
+        41 |    454
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE a = 0 AND b = 0 AND c = 0 AND d = 0');
+ estimated | actual 
+-----------+--------
+         1 |     64
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE 0 = a AND b = 0 AND 0 = c AND d = 0');
+ estimated | actual 
+-----------+--------
+         1 |     64
+(1 row)
+
+-- create separate functional dependencies
+CREATE STATISTICS functional_dependencies_multi_1 (dependencies) ON a, b FROM functional_dependencies_multi;
+CREATE STATISTICS functional_dependencies_multi_2 (dependencies) ON c, d FROM functional_dependencies_multi;
+ANALYZE functional_dependencies_multi;
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE a = 0 AND b = 0');
+ estimated | actual 
+-----------+--------
+       714 |    714
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE 0 = a AND 0 = b');
+ estimated | actual 
+-----------+--------
+       714 |    714
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE c = 0 AND d = 0');
+ estimated | actual 
+-----------+--------
+       454 |    454
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE a = 0 AND b = 0 AND c = 0 AND d = 0');
+ estimated | actual 
+-----------+--------
+        65 |     64
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM functional_dependencies_multi WHERE 0 = a AND b = 0 AND 0 = c AND d = 0');
+ estimated | actual 
+-----------+--------
+        65 |     64
+(1 row)
+
+DROP TABLE functional_dependencies_multi;
+-- MCV lists
+CREATE TABLE mcv_lists (
+    filler1 TEXT,
+    filler2 NUMERIC,
+    a INT,
+    b VARCHAR,
+    filler3 DATE,
+    c INT,
+    d TEXT,
+    ia INT[]
+)
+WITH (autovacuum_enabled = off);
+-- random data (no MCV list)
+INSERT INTO mcv_lists (a, b, c, filler1)
+     SELECT mod(i,37), mod(i,41), mod(i,43), mod(i,47) FROM generate_series(1,5000) s(i);
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         3 |      4
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+         1 |      1
+(1 row)
+
+-- create statistics
+CREATE STATISTICS mcv_lists_stats (mcv) ON a, b, c FROM mcv_lists;
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         3 |      4
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+         1 |      1
+(1 row)
+
+TRUNCATE mcv_lists;
+DROP STATISTICS mcv_lists_stats;
+-- random data (no MCV list), but with expression
+INSERT INTO mcv_lists (a, b, c, filler1)
+     SELECT i, i, i, i FROM generate_series(1,1000) s(i);
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,7) = 1 AND mod(b::int,11) = 1');
+ estimated | actual 
+-----------+--------
+         1 |     13
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,7) = 1 AND mod(b::int,11) = 1 AND mod(c,13) = 1');
+ estimated | actual 
+-----------+--------
+         1 |      1
+(1 row)
+
+-- create statistics
+CREATE STATISTICS mcv_lists_stats (mcv) ON (mod(a,7)), (mod(b::int,11)), (mod(c,13)) FROM mcv_lists;
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,7) = 1 AND mod(b::int,11) = 1');
+ estimated | actual 
+-----------+--------
+        13 |     13
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,7) = 1 AND mod(b::int,11) = 1 AND mod(c,13) = 1');
+ estimated | actual 
+-----------+--------
+         1 |      1
+(1 row)
+
+-- 100 distinct combinations, all in the MCV list
+TRUNCATE mcv_lists;
+DROP STATISTICS mcv_lists_stats;
+INSERT INTO mcv_lists (a, b, c, ia, filler1)
+     SELECT mod(i,100), mod(i,50), mod(i,25), array[mod(i,25)], i
+       FROM generate_series(1,5000) s(i);
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 = a AND ''1'' = b');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < 1 AND b < ''1''');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 > a AND ''1'' > b');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a <= 0 AND b <= ''0''');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 0 >= a AND ''0'' >= b');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < 5 AND b < ''1'' AND c < 5');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < 5 AND ''1'' > b AND 5 > c');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a <= 4 AND b <= ''0'' AND c <= 4');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 4 >= a AND ''0'' >= b AND 4 >= c');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 OR b = ''1'' OR c = 1');
+ estimated | actual 
+-----------+--------
+       343 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 OR b = ''1'' OR c = 1 OR d IS NOT NULL');
+ estimated | actual 
+-----------+--------
+       343 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IN (1, 2, 51, 52) AND b IN ( ''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+         8 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IN (1, 2, 51, 52, NULL) AND b IN ( ''1'', ''2'', NULL)');
+ estimated | actual 
+-----------+--------
+         8 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = ANY (ARRAY[1, 2, 51, 52]) AND b = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+         8 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = ANY (ARRAY[NULL, 1, 2, 51, 52]) AND b = ANY (ARRAY[''1'', ''2'', NULL])');
+ estimated | actual 
+-----------+--------
+         8 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a <= ANY (ARRAY[1, 2, 3]) AND b IN (''1'', ''2'', ''3'')');
+ estimated | actual 
+-----------+--------
+        26 |    150
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a <= ANY (ARRAY[1, NULL, 2, 3]) AND b IN (''1'', ''2'', NULL, ''3'')');
+ estimated | actual 
+-----------+--------
+        26 |    150
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < ALL (ARRAY[4, 5]) AND c > ANY (ARRAY[1, 2, 3])');
+ estimated | actual 
+-----------+--------
+        10 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < ALL (ARRAY[4, 5]) AND c > ANY (ARRAY[1, 2, 3, NULL])');
+ estimated | actual 
+-----------+--------
+        10 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < ALL (ARRAY[4, 5]) AND b IN (''1'', ''2'', ''3'') AND c > ANY (ARRAY[1, 2, 3])');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < ALL (ARRAY[4, 5]) AND b IN (''1'', ''2'', NULL, ''3'') AND c > ANY (ARRAY[1, 2, NULL, 3])');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = ANY (ARRAY[4,5]) AND 4 = ANY(ia)');
+ estimated | actual 
+-----------+--------
+         4 |     50
+(1 row)
+
+-- create statistics
+CREATE STATISTICS mcv_lists_stats (mcv) ON a, b, c, ia FROM mcv_lists;
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 = a AND ''1'' = b');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < 1 AND b < ''1''');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 > a AND ''1'' > b');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a <= 0 AND b <= ''0''');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 0 >= a AND ''0'' >= b');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1'' AND c = 1');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < 5 AND b < ''1'' AND c < 5');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < 5 AND ''1'' > b AND 5 > c');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a <= 4 AND b <= ''0'' AND c <= 4');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 4 >= a AND ''0'' >= b AND 4 >= c');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 OR b = ''1'' OR c = 1');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 OR b = ''1'' OR c = 1 OR d IS NOT NULL');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 OR b = ''1'' OR c = 1 OR d IS NOT NULL');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IN (1, 2, 51, 52) AND b IN ( ''1'', ''2'')');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IN (1, 2, 51, 52, NULL) AND b IN ( ''1'', ''2'', NULL)');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = ANY (ARRAY[1, 2, 51, 52]) AND b = ANY (ARRAY[''1'', ''2''])');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = ANY (ARRAY[NULL, 1, 2, 51, 52]) AND b = ANY (ARRAY[''1'', ''2'', NULL])');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a <= ANY (ARRAY[1, 2, 3]) AND b IN (''1'', ''2'', ''3'')');
+ estimated | actual 
+-----------+--------
+       150 |    150
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a <= ANY (ARRAY[1, NULL, 2, 3]) AND b IN (''1'', ''2'', NULL, ''3'')');
+ estimated | actual 
+-----------+--------
+       150 |    150
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < ALL (ARRAY[4, 5]) AND c > ANY (ARRAY[1, 2, 3])');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < ALL (ARRAY[4, 5]) AND c > ANY (ARRAY[1, 2, 3, NULL])');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < ALL (ARRAY[4, 5]) AND b IN (''1'', ''2'', ''3'') AND c > ANY (ARRAY[1, 2, 3])');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a < ALL (ARRAY[4, 5]) AND b IN (''1'', ''2'', NULL, ''3'') AND c > ANY (ARRAY[1, 2, NULL, 3])');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = ANY (ARRAY[4,5]) AND 4 = ANY(ia)');
+ estimated | actual 
+-----------+--------
+         4 |     50
+(1 row)
+
+-- check change of unrelated column type does not reset the MCV statistics
+ALTER TABLE mcv_lists ALTER COLUMN d TYPE VARCHAR(64);
+SELECT d.stxdmcv IS NOT NULL
+  FROM pg_statistic_ext s, pg_statistic_ext_data d
+ WHERE s.stxname = 'mcv_lists_stats'
+   AND d.stxoid = s.oid;
+ ?column? 
+----------
+ t
+(1 row)
+
+-- check change of column type resets the MCV statistics
+ALTER TABLE mcv_lists ALTER COLUMN c TYPE numeric;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 AND b = ''1''');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+-- 100 distinct combinations, all in the MCV list, but with expressions
+TRUNCATE mcv_lists;
+DROP STATISTICS mcv_lists_stats;
+INSERT INTO mcv_lists (a, b, c, filler1)
+     SELECT i, i, i, i FROM generate_series(1,1000) s(i);
+ANALYZE mcv_lists;
+-- without any stats on the expressions, we have to use default selectivities, which
+-- is why the estimates here are different from the pre-computed case above
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 AND mod(b::int,10) = 1');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 = mod(a,20) AND 1 = mod(b::int,10)');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) < 1 AND mod(b::int,10) < 1');
+ estimated | actual 
+-----------+--------
+       111 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 > mod(a,20) AND 1 > mod(b::int,10)');
+ estimated | actual 
+-----------+--------
+       111 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 AND mod(b::int,10) = 1 AND mod(c,5) = 1');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 OR mod(b::int,10) = 1 OR mod(c,25) = 1 OR d IS NOT NULL');
+ estimated | actual 
+-----------+--------
+        15 |    120
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) IN (1, 2, 51, 52, NULL) AND mod(b::int,10) IN ( 1, 2, NULL)');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = ANY (ARRAY[1, 2, 51, 52]) AND mod(b::int,10) = ANY (ARRAY[1, 2])');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) <= ANY (ARRAY[1, NULL, 2, 3]) AND mod(b::int,10) IN (1, 2, NULL, 3)');
+ estimated | actual 
+-----------+--------
+        11 |    150
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) < ALL (ARRAY[4, 5]) AND mod(b::int,10) IN (1, 2, 3) AND mod(c,5) > ANY (ARRAY[1, 2, 3])');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+-- create statistics with expressions only (we create three separate stats, in order not to build more complex extended stats)
+CREATE STATISTICS mcv_lists_stats_1 ON (mod(a,20)) FROM mcv_lists;
+CREATE STATISTICS mcv_lists_stats_2 ON (mod(b::int,10)) FROM mcv_lists;
+CREATE STATISTICS mcv_lists_stats_3 ON (mod(c,5)) FROM mcv_lists;
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 AND mod(b::int,10) = 1');
+ estimated | actual 
+-----------+--------
+         5 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 = mod(a,20) AND 1 = mod(b::int,10)');
+ estimated | actual 
+-----------+--------
+         5 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) < 1 AND mod(b::int,10) < 1');
+ estimated | actual 
+-----------+--------
+         5 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 > mod(a,20) AND 1 > mod(b::int,10)');
+ estimated | actual 
+-----------+--------
+         5 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 AND mod(b::int,10) = 1 AND mod(c,5) = 1');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 OR mod(b::int,10) = 1 OR mod(c,25) = 1 OR d IS NOT NULL');
+ estimated | actual 
+-----------+--------
+       149 |    120
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) IN (1, 2, 51, 52, NULL) AND mod(b::int,10) IN ( 1, 2, NULL)');
+ estimated | actual 
+-----------+--------
+        20 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = ANY (ARRAY[1, 2, 51, 52]) AND mod(b::int,10) = ANY (ARRAY[1, 2])');
+ estimated | actual 
+-----------+--------
+        20 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) <= ANY (ARRAY[1, NULL, 2, 3]) AND mod(b::int,10) IN (1, 2, NULL, 3)');
+ estimated | actual 
+-----------+--------
+       116 |    150
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) < ALL (ARRAY[4, 5]) AND mod(b::int,10) IN (1, 2, 3) AND mod(c,5) > ANY (ARRAY[1, 2, 3])');
+ estimated | actual 
+-----------+--------
+        12 |    100
+(1 row)
+
+DROP STATISTICS mcv_lists_stats_1;
+DROP STATISTICS mcv_lists_stats_2;
+DROP STATISTICS mcv_lists_stats_3;
+-- create statistics with both MCV and expressions
+CREATE STATISTICS mcv_lists_stats (mcv) ON (mod(a,20)), (mod(b::int,10)), (mod(c,5)) FROM mcv_lists;
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 AND mod(b::int,10) = 1');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 = mod(a,20) AND 1 = mod(b::int,10)');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) < 1 AND mod(b::int,10) < 1');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE 1 > mod(a,20) AND 1 > mod(b::int,10)');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 AND mod(b::int,10) = 1 AND mod(c,5) = 1');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 OR mod(b::int,10) = 1 OR mod(c,25) = 1 OR d IS NOT NULL');
+ estimated | actual 
+-----------+--------
+       105 |    120
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) IN (1, 2, 51, 52, NULL) AND mod(b::int,10) IN ( 1, 2, NULL)');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = ANY (ARRAY[1, 2, 51, 52]) AND mod(b::int,10) = ANY (ARRAY[1, 2])');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) <= ANY (ARRAY[1, NULL, 2, 3]) AND mod(b::int,10) IN (1, 2, NULL, 3)');
+ estimated | actual 
+-----------+--------
+       150 |    150
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) < ALL (ARRAY[4, 5]) AND mod(b::int,10) IN (1, 2, 3) AND mod(c,5) > ANY (ARRAY[1, 2, 3])');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+-- we can't use the statistic for OR clauses that are not fully covered (missing 'd' attribute)
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE mod(a,20) = 1 OR mod(b::int,10) = 1 OR mod(c,5) = 1 OR d IS NOT NULL');
+ estimated | actual 
+-----------+--------
+       200 |    200
+(1 row)
+
+-- 100 distinct combinations with NULL values, all in the MCV list
+TRUNCATE mcv_lists;
+DROP STATISTICS mcv_lists_stats;
+INSERT INTO mcv_lists (a, b, c, filler1)
+     SELECT
+         (CASE WHEN mod(i,100) = 1 THEN NULL ELSE mod(i,100) END),
+         (CASE WHEN mod(i,50) = 1  THEN NULL ELSE mod(i,50) END),
+         (CASE WHEN mod(i,25) = 1  THEN NULL ELSE mod(i,25) END),
+         i
+     FROM generate_series(1,5000) s(i);
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NULL AND b IS NULL');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NULL AND b IS NULL AND c IS NULL');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NULL AND b IS NOT NULL');
+ estimated | actual 
+-----------+--------
+        49 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NOT NULL AND b IS NULL AND c IS NOT NULL');
+ estimated | actual 
+-----------+--------
+        95 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IN (0, 1) AND b IN (''0'', ''1'')');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+-- create statistics
+CREATE STATISTICS mcv_lists_stats (mcv) ON a, b, c FROM mcv_lists;
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NULL AND b IS NULL');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NULL AND b IS NULL AND c IS NULL');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NULL AND b IS NOT NULL');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NOT NULL AND b IS NULL AND c IS NOT NULL');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IN (0, 1) AND b IN (''0'', ''1'')');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+-- test pg_mcv_list_items with a very simple (single item) MCV list
+TRUNCATE mcv_lists;
+INSERT INTO mcv_lists (a, b, c) SELECT 1, 2, 3 FROM generate_series(1,1000) s(i);
+ANALYZE mcv_lists;
+SELECT m.*
+  FROM pg_statistic_ext s, pg_statistic_ext_data d,
+       pg_mcv_list_items(d.stxdmcv) m
+ WHERE s.stxname = 'mcv_lists_stats'
+   AND d.stxoid = s.oid;
+ index | values  |  nulls  | frequency | base_frequency 
+-------+---------+---------+-----------+----------------
+     0 | {1,2,3} | {f,f,f} |         1 |              1
+(1 row)
+
+-- 2 distinct combinations with NULL values, all in the MCV list
+TRUNCATE mcv_lists;
+DROP STATISTICS mcv_lists_stats;
+INSERT INTO mcv_lists (a, b, c, d)
+     SELECT
+         NULL, -- always NULL
+         (CASE WHEN mod(i,2) = 0 THEN NULL ELSE 'x' END),
+         (CASE WHEN mod(i,2) = 0 THEN NULL ELSE 0 END),
+         (CASE WHEN mod(i,2) = 0 THEN NULL ELSE 'x' END)
+     FROM generate_series(1,5000) s(i);
+ANALYZE mcv_lists;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE b = ''x'' OR d = ''x''');
+ estimated | actual 
+-----------+--------
+      3750 |   2500
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 OR b = ''x'' OR d = ''x''');
+ estimated | actual 
+-----------+--------
+      3750 |   2500
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NULL AND (b = ''x'' OR d = ''x'')');
+ estimated | actual 
+-----------+--------
+      3750 |   2500
+(1 row)
+
+-- create statistics
+CREATE STATISTICS mcv_lists_stats (mcv) ON a, b, d FROM mcv_lists;
+ANALYZE mcv_lists;
+-- test pg_mcv_list_items with MCV list containing variable-length data and NULLs
+SELECT m.*
+  FROM pg_statistic_ext s, pg_statistic_ext_data d,
+       pg_mcv_list_items(d.stxdmcv) m
+ WHERE s.stxname = 'mcv_lists_stats'
+   AND d.stxoid = s.oid;
+ index |      values      |  nulls  | frequency | base_frequency 
+-------+------------------+---------+-----------+----------------
+     0 | {NULL,x,x}       | {t,f,f} |       0.5 |           0.25
+     1 | {NULL,NULL,NULL} | {t,t,t} |       0.5 |           0.25
+(2 rows)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE b = ''x'' OR d = ''x''');
+ estimated | actual 
+-----------+--------
+      2500 |   2500
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a = 1 OR b = ''x'' OR d = ''x''');
+ estimated | actual 
+-----------+--------
+      2500 |   2500
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists WHERE a IS NULL AND (b = ''x'' OR d = ''x'')');
+ estimated | actual 
+-----------+--------
+      2500 |   2500
+(1 row)
+
+-- mcv with pass-by-ref fixlen types, e.g. uuid
+CREATE TABLE mcv_lists_uuid (
+    a UUID,
+    b UUID,
+    c UUID
+)
+WITH (autovacuum_enabled = off);
+INSERT INTO mcv_lists_uuid (a, b, c)
+     SELECT
+         fipshash(mod(i,100)::text)::uuid,
+         fipshash(mod(i,50)::text)::uuid,
+         fipshash(mod(i,25)::text)::uuid
+     FROM generate_series(1,5000) s(i);
+ANALYZE mcv_lists_uuid;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_uuid WHERE a = ''e7f6c011-776e-8db7-cd33-0b54174fd76f'' AND b = ''e7f6c011-776e-8db7-cd33-0b54174fd76f''');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_uuid WHERE a = ''e7f6c011-776e-8db7-cd33-0b54174fd76f'' AND b = ''e7f6c011-776e-8db7-cd33-0b54174fd76f'' AND c = ''e7f6c011-776e-8db7-cd33-0b54174fd76f''');
+ estimated | actual 
+-----------+--------
+         1 |     50
+(1 row)
+
+CREATE STATISTICS mcv_lists_uuid_stats (mcv) ON a, b, c
+  FROM mcv_lists_uuid;
+ANALYZE mcv_lists_uuid;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_uuid WHERE a = ''e7f6c011-776e-8db7-cd33-0b54174fd76f'' AND b = ''e7f6c011-776e-8db7-cd33-0b54174fd76f''');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_uuid WHERE a = ''e7f6c011-776e-8db7-cd33-0b54174fd76f'' AND b = ''e7f6c011-776e-8db7-cd33-0b54174fd76f'' AND c = ''e7f6c011-776e-8db7-cd33-0b54174fd76f''');
+ estimated | actual 
+-----------+--------
+        50 |     50
+(1 row)
+
+DROP TABLE mcv_lists_uuid;
+-- mcv with arrays
+CREATE TABLE mcv_lists_arrays (
+    a TEXT[],
+    b NUMERIC[],
+    c INT[]
+)
+WITH (autovacuum_enabled = off);
+INSERT INTO mcv_lists_arrays (a, b, c)
+     SELECT
+         ARRAY[fipshash((i/100)::text), fipshash((i/100-1)::text), fipshash((i/100+1)::text)],
+         ARRAY[(i/100-1)::numeric/1000, (i/100)::numeric/1000, (i/100+1)::numeric/1000],
+         ARRAY[(i/100-1), i/100, (i/100+1)]
+     FROM generate_series(1,5000) s(i);
+CREATE STATISTICS mcv_lists_arrays_stats (mcv) ON a, b, c
+  FROM mcv_lists_arrays;
+ANALYZE mcv_lists_arrays;
+-- mcv with bool
+CREATE TABLE mcv_lists_bool (
+    a BOOL,
+    b BOOL,
+    c BOOL
+)
+WITH (autovacuum_enabled = off);
+INSERT INTO mcv_lists_bool (a, b, c)
+     SELECT
+         (mod(i,2) = 0), (mod(i,4) = 0), (mod(i,8) = 0)
+     FROM generate_series(1,10000) s(i);
+ANALYZE mcv_lists_bool;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_bool WHERE a AND b AND c');
+ estimated | actual 
+-----------+--------
+       156 |   1250
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_bool WHERE NOT a AND b AND c');
+ estimated | actual 
+-----------+--------
+       156 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_bool WHERE NOT a AND NOT b AND c');
+ estimated | actual 
+-----------+--------
+       469 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_bool WHERE NOT a AND b AND NOT c');
+ estimated | actual 
+-----------+--------
+      1094 |      0
+(1 row)
+
+CREATE STATISTICS mcv_lists_bool_stats (mcv) ON a, b, c
+  FROM mcv_lists_bool;
+ANALYZE mcv_lists_bool;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_bool WHERE a AND b AND c');
+ estimated | actual 
+-----------+--------
+      1250 |   1250
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_bool WHERE NOT a AND b AND c');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_bool WHERE NOT a AND NOT b AND c');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_bool WHERE NOT a AND b AND NOT c');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+-- mcv covering just a small fraction of data
+CREATE TABLE mcv_lists_partial (
+    a INT,
+    b INT,
+    c INT
+);
+-- 10 frequent groups, each with 100 elements
+INSERT INTO mcv_lists_partial (a, b, c)
+     SELECT
+         mod(i,10),
+         mod(i,10),
+         mod(i,10)
+     FROM generate_series(0,999) s(i);
+-- 100 groups that will make it to the MCV list (includes the 10 frequent ones)
+INSERT INTO mcv_lists_partial (a, b, c)
+     SELECT
+         i,
+         i,
+         i
+     FROM generate_series(0,99) s(i);
+-- 4000 groups in total, most of which won't make it (just a single item)
+INSERT INTO mcv_lists_partial (a, b, c)
+     SELECT
+         i,
+         i,
+         i
+     FROM generate_series(0,3999) s(i);
+ANALYZE mcv_lists_partial;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 0 AND b = 0 AND c = 0');
+ estimated | actual 
+-----------+--------
+         1 |    102
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 0 OR b = 0 OR c = 0');
+ estimated | actual 
+-----------+--------
+       300 |    102
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 10 AND b = 10 AND c = 10');
+ estimated | actual 
+-----------+--------
+         1 |      2
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 10 OR b = 10 OR c = 10');
+ estimated | actual 
+-----------+--------
+         6 |      2
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 0 AND b = 0 AND c = 10');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 0 OR b = 0 OR c = 10');
+ estimated | actual 
+-----------+--------
+       204 |    104
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE (a = 0 AND b = 0 AND c = 0) OR (a = 1 AND b = 1 AND c = 1) OR (a = 2 AND b = 2 AND c = 2)');
+ estimated | actual 
+-----------+--------
+         1 |    306
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE (a = 0 AND b = 0) OR (a = 0 AND c = 0) OR (b = 0 AND c = 0)');
+ estimated | actual 
+-----------+--------
+         6 |    102
+(1 row)
+
+CREATE STATISTICS mcv_lists_partial_stats (mcv) ON a, b, c
+  FROM mcv_lists_partial;
+ANALYZE mcv_lists_partial;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 0 AND b = 0 AND c = 0');
+ estimated | actual 
+-----------+--------
+       102 |    102
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 0 OR b = 0 OR c = 0');
+ estimated | actual 
+-----------+--------
+        96 |    102
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 10 AND b = 10 AND c = 10');
+ estimated | actual 
+-----------+--------
+         2 |      2
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 10 OR b = 10 OR c = 10');
+ estimated | actual 
+-----------+--------
+         2 |      2
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 0 AND b = 0 AND c = 10');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE a = 0 OR b = 0 OR c = 10');
+ estimated | actual 
+-----------+--------
+       102 |    104
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE (a = 0 AND b = 0 AND c = 0) OR (a = 1 AND b = 1 AND c = 1) OR (a = 2 AND b = 2 AND c = 2)');
+ estimated | actual 
+-----------+--------
+       306 |    306
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_partial WHERE (a = 0 AND b = 0) OR (a = 0 AND c = 0) OR (b = 0 AND c = 0)');
+ estimated | actual 
+-----------+--------
+       108 |    102
+(1 row)
+
+DROP TABLE mcv_lists_partial;
+-- check the ability to use multiple MCV lists
+CREATE TABLE mcv_lists_multi (
+	a INTEGER,
+	b INTEGER,
+	c INTEGER,
+	d INTEGER
+)
+WITH (autovacuum_enabled = off);
+INSERT INTO mcv_lists_multi (a, b, c, d)
+    SELECT
+         mod(i,5),
+         mod(i,5),
+         mod(i,7),
+         mod(i,7)
+    FROM generate_series(1,5000) s(i);
+ANALYZE mcv_lists_multi;
+-- estimates without any mcv statistics
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE a = 0 AND b = 0');
+ estimated | actual 
+-----------+--------
+       200 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE c = 0 AND d = 0');
+ estimated | actual 
+-----------+--------
+       102 |    714
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE b = 0 AND c = 0');
+ estimated | actual 
+-----------+--------
+       143 |    142
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE b = 0 OR c = 0');
+ estimated | actual 
+-----------+--------
+      1571 |   1572
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE a = 0 AND b = 0 AND c = 0 AND d = 0');
+ estimated | actual 
+-----------+--------
+         4 |    142
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE (a = 0 AND b = 0) OR (c = 0 AND d = 0)');
+ estimated | actual 
+-----------+--------
+       298 |   1572
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE a = 0 OR b = 0 OR c = 0 OR d = 0');
+ estimated | actual 
+-----------+--------
+      2649 |   1572
+(1 row)
+
+-- create separate MCV statistics
+CREATE STATISTICS mcv_lists_multi_1 (mcv) ON a, b FROM mcv_lists_multi;
+CREATE STATISTICS mcv_lists_multi_2 (mcv) ON c, d FROM mcv_lists_multi;
+ANALYZE mcv_lists_multi;
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE a = 0 AND b = 0');
+ estimated | actual 
+-----------+--------
+      1000 |   1000
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE c = 0 AND d = 0');
+ estimated | actual 
+-----------+--------
+       714 |    714
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE b = 0 AND c = 0');
+ estimated | actual 
+-----------+--------
+       143 |    142
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE b = 0 OR c = 0');
+ estimated | actual 
+-----------+--------
+      1571 |   1572
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE a = 0 AND b = 0 AND c = 0 AND d = 0');
+ estimated | actual 
+-----------+--------
+       143 |    142
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE (a = 0 AND b = 0) OR (c = 0 AND d = 0)');
+ estimated | actual 
+-----------+--------
+      1571 |   1572
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM mcv_lists_multi WHERE a = 0 OR b = 0 OR c = 0 OR d = 0');
+ estimated | actual 
+-----------+--------
+      1571 |   1572
+(1 row)
+
+DROP TABLE mcv_lists_multi;
+-- statistics on integer expressions
+CREATE TABLE expr_stats (a int, b int, c int);
+INSERT INTO expr_stats SELECT mod(i,10), mod(i,10), mod(i,10) FROM generate_series(1,1000) s(i);
+ANALYZE expr_stats;
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE (2*a) = 0 AND (3*b) = 0');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE (a+b) = 0 AND (a-b) = 0');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+CREATE STATISTICS expr_stats_1 (mcv) ON (a+b), (a-b), (2*a), (3*b) FROM expr_stats;
+ANALYZE expr_stats;
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE (2*a) = 0 AND (3*b) = 0');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE (a+b) = 0 AND (a-b) = 0');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+DROP STATISTICS expr_stats_1;
+DROP TABLE expr_stats;
+-- statistics on a mix columns and expressions
+CREATE TABLE expr_stats (a int, b int, c int);
+INSERT INTO expr_stats SELECT mod(i,10), mod(i,10), mod(i,10) FROM generate_series(1,1000) s(i);
+ANALYZE expr_stats;
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE a = 0 AND (2*a) = 0 AND (3*b) = 0');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE a = 3 AND b = 3 AND (a-b) = 0');
+ estimated | actual 
+-----------+--------
+         1 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE a = 0 AND b = 1 AND (a-b) = 0');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+CREATE STATISTICS expr_stats_1 (mcv) ON a, b, (2*a), (3*b), (a+b), (a-b) FROM expr_stats;
+ANALYZE expr_stats;
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE a = 0 AND (2*a) = 0 AND (3*b) = 0');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE a = 3 AND b = 3 AND (a-b) = 0');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE a = 0 AND b = 1 AND (a-b) = 0');
+ estimated | actual 
+-----------+--------
+         1 |      0
+(1 row)
+
+DROP TABLE expr_stats;
+-- statistics on expressions with different data types
+CREATE TABLE expr_stats (a int, b name, c text);
+INSERT INTO expr_stats SELECT mod(i,10), fipshash(mod(i,10)::text), fipshash(mod(i,10)::text) FROM generate_series(1,1000) s(i);
+ANALYZE expr_stats;
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE a = 0 AND (b || c) <= ''z'' AND (c || b) >= ''0''');
+ estimated | actual 
+-----------+--------
+        11 |    100
+(1 row)
+
+CREATE STATISTICS expr_stats_1 (mcv) ON a, b, (b || c), (c || b) FROM expr_stats;
+ANALYZE expr_stats;
+SELECT * FROM check_estimated_rows('SELECT * FROM expr_stats WHERE a = 0 AND (b || c) <= ''z'' AND (c || b) >= ''0''');
+ estimated | actual 
+-----------+--------
+       100 |    100
+(1 row)
+
+DROP TABLE expr_stats;
+-- test handling of a mix of compatible and incompatible expressions
+CREATE TABLE expr_stats_incompatible_test (
+    c0 double precision,
+    c1 boolean NOT NULL
+);
+CREATE STATISTICS expr_stat_comp_1 ON c0, c1 FROM expr_stats_incompatible_test;
+INSERT INTO expr_stats_incompatible_test VALUES (1234,false), (5678,true);
+ANALYZE expr_stats_incompatible_test;
+SELECT c0 FROM ONLY expr_stats_incompatible_test WHERE
+(
+  upper('x') LIKE ('x'||('[0,1]'::int4range))
+  AND
+  (c0 IN (0, 1) OR c1)
+);
+ c0 
+----
+(0 rows)
+
+DROP TABLE expr_stats_incompatible_test;
+-- Permission tests. Users should not be able to see specific data values in
+-- the extended statistics, if they lack permission to see those values in
+-- the underlying table.
+--
+-- Currently this is only relevant for MCV stats.
+CREATE SCHEMA tststats;
+CREATE TABLE tststats.priv_test_tbl (
+    a int,
+    b int
+);
+INSERT INTO tststats.priv_test_tbl
+     SELECT mod(i,5), mod(i,10) FROM generate_series(1,100) s(i);
+CREATE STATISTICS tststats.priv_test_stats (mcv) ON a, b
+  FROM tststats.priv_test_tbl;
+ANALYZE tststats.priv_test_tbl;
+-- Check printing info about extended statistics by \dX
+create table stts_t1 (a int, b int);
+create statistics (ndistinct) on a, b from stts_t1;
+create statistics (ndistinct, dependencies) on a, b from stts_t1;
+create statistics (ndistinct, dependencies, mcv) on a, b from stts_t1;
+create table stts_t2 (a int, b int, c int);
+create statistics on b, c from stts_t2;
+create table stts_t3 (col1 int, col2 int, col3 int);
+create statistics stts_hoge on col1, col2, col3 from stts_t3;
+create schema stts_s1;
+create schema stts_s2;
+create statistics stts_s1.stts_foo on col1, col2 from stts_t3;
+create statistics stts_s2.stts_yama (dependencies, mcv) on col1, col3 from stts_t3;
+insert into stts_t1 select i,i from generate_series(1,100) i;
+analyze stts_t1;
+set search_path to public, stts_s1, stts_s2, tststats;
+\dX
+                                                        List of extended statistics
+  Schema  |          Name          |                            Definition                            | Ndistinct | Dependencies |   MCV   
+----------+------------------------+------------------------------------------------------------------+-----------+--------------+---------
+ public   | func_deps_stat         | (a * 2), upper(b), (c + 1::numeric) FROM functional_dependencies |           | defined      | 
+ public   | mcv_lists_arrays_stats | a, b, c FROM mcv_lists_arrays                                    |           |              | defined
+ public   | mcv_lists_bool_stats   | a, b, c FROM mcv_lists_bool                                      |           |              | defined
+ public   | mcv_lists_stats        | a, b, d FROM mcv_lists                                           |           |              | defined
+ public   | stts_hoge              | col1, col2, col3 FROM stts_t3                                    | defined   | defined      | defined
+ public   | stts_t1_a_b_stat       | a, b FROM stts_t1                                                | defined   |              | 
+ public   | stts_t1_a_b_stat1      | a, b FROM stts_t1                                                | defined   | defined      | 
+ public   | stts_t1_a_b_stat2      | a, b FROM stts_t1                                                | defined   | defined      | defined
+ public   | stts_t2_b_c_stat       | b, c FROM stts_t2                                                | defined   | defined      | defined
+ stts_s1  | stts_foo               | col1, col2 FROM stts_t3                                          | defined   | defined      | defined
+ stts_s2  | stts_yama              | col1, col3 FROM stts_t3                                          |           | defined      | defined
+ tststats | priv_test_stats        | a, b FROM priv_test_tbl                                          |           |              | defined
+(12 rows)
+
+\dX stts_t*
+                             List of extended statistics
+ Schema |       Name        |    Definition     | Ndistinct | Dependencies |   MCV   
+--------+-------------------+-------------------+-----------+--------------+---------
+ public | stts_t1_a_b_stat  | a, b FROM stts_t1 | defined   |              | 
+ public | stts_t1_a_b_stat1 | a, b FROM stts_t1 | defined   | defined      | 
+ public | stts_t1_a_b_stat2 | a, b FROM stts_t1 | defined   | defined      | defined
+ public | stts_t2_b_c_stat  | b, c FROM stts_t2 | defined   | defined      | defined
+(4 rows)
+
+\dX *stts_hoge
+                               List of extended statistics
+ Schema |   Name    |          Definition           | Ndistinct | Dependencies |   MCV   
+--------+-----------+-------------------------------+-----------+--------------+---------
+ public | stts_hoge | col1, col2, col3 FROM stts_t3 | defined   | defined      | defined
+(1 row)
+
+\dX+
+                                                        List of extended statistics
+  Schema  |          Name          |                            Definition                            | Ndistinct | Dependencies |   MCV   
+----------+------------------------+------------------------------------------------------------------+-----------+--------------+---------
+ public   | func_deps_stat         | (a * 2), upper(b), (c + 1::numeric) FROM functional_dependencies |           | defined      | 
+ public   | mcv_lists_arrays_stats | a, b, c FROM mcv_lists_arrays                                    |           |              | defined
+ public   | mcv_lists_bool_stats   | a, b, c FROM mcv_lists_bool                                      |           |              | defined
+ public   | mcv_lists_stats        | a, b, d FROM mcv_lists                                           |           |              | defined
+ public   | stts_hoge              | col1, col2, col3 FROM stts_t3                                    | defined   | defined      | defined
+ public   | stts_t1_a_b_stat       | a, b FROM stts_t1                                                | defined   |              | 
+ public   | stts_t1_a_b_stat1      | a, b FROM stts_t1                                                | defined   | defined      | 
+ public   | stts_t1_a_b_stat2      | a, b FROM stts_t1                                                | defined   | defined      | defined
+ public   | stts_t2_b_c_stat       | b, c FROM stts_t2                                                | defined   | defined      | defined
+ stts_s1  | stts_foo               | col1, col2 FROM stts_t3                                          | defined   | defined      | defined
+ stts_s2  | stts_yama              | col1, col3 FROM stts_t3                                          |           | defined      | defined
+ tststats | priv_test_stats        | a, b FROM priv_test_tbl                                          |           |              | defined
+(12 rows)
+
+\dX+ stts_t*
+                             List of extended statistics
+ Schema |       Name        |    Definition     | Ndistinct | Dependencies |   MCV   
+--------+-------------------+-------------------+-----------+--------------+---------
+ public | stts_t1_a_b_stat  | a, b FROM stts_t1 | defined   |              | 
+ public | stts_t1_a_b_stat1 | a, b FROM stts_t1 | defined   | defined      | 
+ public | stts_t1_a_b_stat2 | a, b FROM stts_t1 | defined   | defined      | defined
+ public | stts_t2_b_c_stat  | b, c FROM stts_t2 | defined   | defined      | defined
+(4 rows)
+
+\dX+ *stts_hoge
+                               List of extended statistics
+ Schema |   Name    |          Definition           | Ndistinct | Dependencies |   MCV   
+--------+-----------+-------------------------------+-----------+--------------+---------
+ public | stts_hoge | col1, col2, col3 FROM stts_t3 | defined   | defined      | defined
+(1 row)
+
+\dX+ stts_s2.stts_yama
+                            List of extended statistics
+ Schema  |   Name    |       Definition        | Ndistinct | Dependencies |   MCV   
+---------+-----------+-------------------------+-----------+--------------+---------
+ stts_s2 | stts_yama | col1, col3 FROM stts_t3 |           | defined      | defined
+(1 row)
+
+create statistics (mcv) ON a, b, (a+b), (a-b) FROM stts_t1;
+create statistics (mcv) ON a, b, (a+b), (a-b) FROM stts_t1;
+create statistics (mcv) ON (a+b), (a-b) FROM stts_t1;
+\dX stts_t*expr*
+                                           List of extended statistics
+ Schema |            Name             |             Definition              | Ndistinct | Dependencies |   MCV   
+--------+-----------------------------+-------------------------------------+-----------+--------------+---------
+ public | stts_t1_a_b_expr_expr_stat  | a, b, (a + b), (a - b) FROM stts_t1 |           |              | defined
+ public | stts_t1_a_b_expr_expr_stat1 | a, b, (a + b), (a - b) FROM stts_t1 |           |              | defined
+ public | stts_t1_expr_expr_stat      | (a + b), (a - b) FROM stts_t1       |           |              | defined
+(3 rows)
+
+drop statistics stts_t1_a_b_expr_expr_stat;
+drop statistics stts_t1_a_b_expr_expr_stat1;
+drop statistics stts_t1_expr_expr_stat;
+set search_path to public, stts_s1;
+\dX
+                                                       List of extended statistics
+ Schema  |          Name          |                            Definition                            | Ndistinct | Dependencies |   MCV   
+---------+------------------------+------------------------------------------------------------------+-----------+--------------+---------
+ public  | func_deps_stat         | (a * 2), upper(b), (c + 1::numeric) FROM functional_dependencies |           | defined      | 
+ public  | mcv_lists_arrays_stats | a, b, c FROM mcv_lists_arrays                                    |           |              | defined
+ public  | mcv_lists_bool_stats   | a, b, c FROM mcv_lists_bool                                      |           |              | defined
+ public  | mcv_lists_stats        | a, b, d FROM mcv_lists                                           |           |              | defined
+ public  | stts_hoge              | col1, col2, col3 FROM stts_t3                                    | defined   | defined      | defined
+ public  | stts_t1_a_b_stat       | a, b FROM stts_t1                                                | defined   |              | 
+ public  | stts_t1_a_b_stat1      | a, b FROM stts_t1                                                | defined   | defined      | 
+ public  | stts_t1_a_b_stat2      | a, b FROM stts_t1                                                | defined   | defined      | defined
+ public  | stts_t2_b_c_stat       | b, c FROM stts_t2                                                | defined   | defined      | defined
+ stts_s1 | stts_foo               | col1, col2 FROM stts_t3                                          | defined   | defined      | defined
+(10 rows)
+
+create role regress_stats_ext nosuperuser;
+set role regress_stats_ext;
+\dX
+                                                       List of extended statistics
+ Schema |          Name          |                            Definition                            | Ndistinct | Dependencies |   MCV   
+--------+------------------------+------------------------------------------------------------------+-----------+--------------+---------
+ public | func_deps_stat         | (a * 2), upper(b), (c + 1::numeric) FROM functional_dependencies |           | defined      | 
+ public | mcv_lists_arrays_stats | a, b, c FROM mcv_lists_arrays                                    |           |              | defined
+ public | mcv_lists_bool_stats   | a, b, c FROM mcv_lists_bool                                      |           |              | defined
+ public | mcv_lists_stats        | a, b, d FROM mcv_lists                                           |           |              | defined
+ public | stts_hoge              | col1, col2, col3 FROM stts_t3                                    | defined   | defined      | defined
+ public | stts_t1_a_b_stat       | a, b FROM stts_t1                                                | defined   |              | 
+ public | stts_t1_a_b_stat1      | a, b FROM stts_t1                                                | defined   | defined      | 
+ public | stts_t1_a_b_stat2      | a, b FROM stts_t1                                                | defined   | defined      | defined
+ public | stts_t2_b_c_stat       | b, c FROM stts_t2                                                | defined   | defined      | defined
+(9 rows)
+
+reset role;
+drop table stts_t1, stts_t2, stts_t3;
+drop schema stts_s1, stts_s2 cascade;
+drop user regress_stats_ext;
+reset search_path;
+-- User with no access
+CREATE USER regress_stats_user1;
+GRANT USAGE ON SCHEMA tststats TO regress_stats_user1;
+SET SESSION AUTHORIZATION regress_stats_user1;
+SELECT * FROM tststats.priv_test_tbl; -- Permission denied
+ERROR:  permission denied for table priv_test_tbl
+-- Check individual columns if we don't have table privilege
+SELECT * FROM tststats.priv_test_tbl
+  WHERE a = 1 and tststats.priv_test_tbl.* > (1, 1) is not null;
+ERROR:  permission denied for table priv_test_tbl
+-- Attempt to gain access using a leaky operator
+CREATE FUNCTION op_leak(int, int) RETURNS bool
+    AS 'BEGIN RAISE NOTICE ''op_leak => %, %'', $1, $2; RETURN $1 < $2; END'
+    LANGUAGE plpgsql;
+CREATE OPERATOR <<< (procedure = op_leak, leftarg = int, rightarg = int,
+                     restrict = scalarltsel);
+SELECT * FROM tststats.priv_test_tbl WHERE a <<< 0 AND b <<< 0; -- Permission denied
+ERROR:  permission denied for table priv_test_tbl
+DELETE FROM tststats.priv_test_tbl WHERE a <<< 0 AND b <<< 0; -- Permission denied
+ERROR:  permission denied for table priv_test_tbl
+-- Grant access via a security barrier view, but hide all data
+RESET SESSION AUTHORIZATION;
+CREATE VIEW tststats.priv_test_view WITH (security_barrier=true)
+    AS SELECT * FROM tststats.priv_test_tbl WHERE false;
+GRANT SELECT, DELETE ON tststats.priv_test_view TO regress_stats_user1;
+-- Should now have access via the view, but see nothing and leak nothing
+SET SESSION AUTHORIZATION regress_stats_user1;
+SELECT * FROM tststats.priv_test_view WHERE a <<< 0 AND b <<< 0; -- Should not leak
+ a | b 
+---+---
+(0 rows)
+
+DELETE FROM tststats.priv_test_view WHERE a <<< 0 AND b <<< 0; -- Should not leak
+-- Grant table access, but hide all data with RLS
+RESET SESSION AUTHORIZATION;
+ALTER TABLE tststats.priv_test_tbl ENABLE ROW LEVEL SECURITY;
+GRANT SELECT, DELETE ON tststats.priv_test_tbl TO regress_stats_user1;
+-- Should now have direct table access, but see nothing and leak nothing
+SET SESSION AUTHORIZATION regress_stats_user1;
+SELECT * FROM tststats.priv_test_tbl WHERE a <<< 0 AND b <<< 0; -- Should not leak
+ a | b 
+---+---
+(0 rows)
+
+DELETE FROM tststats.priv_test_tbl WHERE a <<< 0 AND b <<< 0; -- Should not leak
+-- Tidy up
+DROP OPERATOR <<< (int, int);
+DROP FUNCTION op_leak(int, int);
+RESET SESSION AUTHORIZATION;
+DROP SCHEMA tststats CASCADE;
+NOTICE:  drop cascades to 2 other objects
+DETAIL:  drop cascades to table tststats.priv_test_tbl
+drop cascades to view tststats.priv_test_view
+DROP USER regress_stats_user1;