Hi,

I faced a correlation problem on a query today and tried the usual trick
consisting of using an functional index and rewriting the query to use it.

However, after writing the function, indexing it and rewriting the query, I
faced an optimizer behavior I was not expecting. I wrote a short scenario to
reproduce it on current HEAD:

  CREATE TABLE correl AS SELECT (i-1)%2 AS i, i%2 AS j 
  FROM generate_series(1,100000) AS i;

  ANALYZE correl ;

  EXPLAIN ANALYZE SELECT * FROM correl WHERE i = 1 AND j = 1;

  -- Seq Scan on correl (rows=25000) (rows=0)
  --    Filter: ((i = 1) AND (j = 1))
  --    Rows Removed by Filter: 100000
  -- Planning time: 0.356 ms
  -- Execution time: 21.937 ms

  CREATE FUNCTION fix_correl(int, int) RETURNS bool AS
    'BEGIN RETURN $1 = 1 AND $2 = 1; END '
    IMMUTABLE
    CALLED ON NULL INPUT
    LANGUAGE plpgsql;

  CREATE INDEX ON correl ( fix_correl(i, j) );

  ANALYZE correl ;

  EXPLAIN ANALYZE SELECT * FROM correl WHERE fix_correl(i, j);

  -- Index Scan using correl_fix_correl_idx on correl  (rows=33333) (rows=0)
  --    Index Cond: (fix_correl(i, j) = true)
  --    Filter: fix_correl(i, j)
  -- Planning time: 0.421 ms
  -- Execution time: 0.102 ms


Using a function returning integer work as expected:

  CREATE FUNCTION fix_correl_add(int, int) RETURNS int AS
    'BEGIN RETURN $1 + $2 ; END '
    IMMUTABLE
    CALLED ON NULL INPUT
    LANGUAGE plpgsql;

  CREATE INDEX ON correl ( fix_correl_add( i, j ) );

  ANALYZE correl ;

  EXPLAIN ANALYZE SELECT * FROM correl WHERE fix_correl_add( i, j ) = 2;
  -- Index Scan using correl_fix_correl_add_idx on correl  (rows=1) (rows=0)
  --    Index Cond: (fix_correl_add(i, j) = 2) 
  -- Planning time: 0.462 ms
  -- Execution time: 0.102 ms


It works works as expected with a simple index on (i + j) with no function, but
I wanted to have the same conditions in both tests.

Why does the optimizer behave differently in both cases? Why do it add a Filter
when index scan-ing on correl_fix_correl_idx indexing booleans?

Please, find the complete scenario in attachment.

Regards,
-- 
Jehan-Guillaume de Rorthais
Dalibo
http://www.dalibo.com
ioguix@erg:~$ dropdb correl 
ioguix@erg:~$ createdb correl
ioguix@erg:~$ psql -qtX correl 
correl=# CREATE TABLE correl AS SELECT (i-1)%2 AS i, i%2 AS j FROM 
generate_series(1,100000) AS i;

correl=# ANALYZE correl ;

correl=# EXPLAIN ANALYZE SELECT * FROM correl WHERE i = 1 AND j = 1;
 Seq Scan on correl  (cost=0.00..1943.00 rows=25000 width=8) (actual 
time=21.898..21.898 rows=0 loops=1)
   Filter: ((i = 1) AND (j = 1))
   Rows Removed by Filter: 100000
 Planning time: 0.356 ms
 Execution time: 21.937 ms

correl=# CREATE FUNCTION fix_correl(int, int) RETURNS bool AS '
BEGIN RETURN $1 = 1 AND $2 = 1; END '
IMMUTABLE
CALLED ON NULL INPUT
LANGUAGE plpgsql;

correl=# CREATE INDEX ON correl ( fix_correl(i, j) );

correl=# ANALYZE correl ;

correl=# EXPLAIN ANALYZE SELECT * FROM correl WHERE fix_correl(i, j);
 Index Scan using correl_fix_correl_idx on correl  (cost=0.29..4.56 rows=33333 
width=8) (actual time=0.053..0.053 rows=0 loops=1)
   Index Cond: (fix_correl(i, j) = true)
   Filter: fix_correl(i, j)
 Planning time: 0.421 ms
 Execution time: 0.102 ms

correl=# SELECT * FROM pg_stats WHERE tablename ~ '^correl_';
schemaname             | public
tablename              | correl_fix_correl_idx
attname                | fix_correl
inherited              | f
null_frac              | 0
avg_width              | 1
n_distinct             | 1
most_common_vals       | {f}
most_common_freqs      | {1}
histogram_bounds       | 
correlation            | 1
most_common_elems      | 
most_common_elem_freqs | 
elem_count_histogram   | 


correl=# CREATE INDEX ON correl ( (i + j) );

correl=# ANALYZE correl ;

correl=# EXPLAIN ANALYZE SELECT * FROM correl WHERE ( i + j ) = 2;
 Index Scan using correl_expr_idx on correl  (cost=0.29..4.31 rows=1 width=8) 
(actual time=0.027..0.027 rows=0 loops=1)
   Index Cond: ((i + j) = 2)
 Planning time: 0.175 ms
 Execution time: 0.076 ms

correl=# CREATE FUNCTION fix_correl_add(int, int) RETURNS int AS '
BEGIN RETURN $1 + $2 ; END '
IMMUTABLE
CALLED ON NULL INPUT
LANGUAGE plpgsql;

correl=# CREATE INDEX ON correl ( fix_correl_add( i, j ) );

correl=# ANALYZE correl ;

correl=# EXPLAIN ANALYZE SELECT * FROM correl WHERE fix_correl_add( i, j ) = 2;
 Index Scan using correl_fix_correl_add_idx on correl  (cost=0.29..4.31 rows=1 
width=8) (actual time=0.052..0.052 rows=0 loops=1)
   Index Cond: (fix_correl_add(i, j) = 2)
 Planning time: 0.462 ms
 Execution time: 0.102 ms

correl=# SELECT * FROM pg_stats WHERE tablename ~ '^correl_';
schemaname             | public
tablename              | correl_fix_correl_idx
attname                | fix_correl
inherited              | f
null_frac              | 0
avg_width              | 1
n_distinct             | 1
most_common_vals       | {f}
most_common_freqs      | {1}
histogram_bounds       | 
correlation            | 1
most_common_elems      | 
most_common_elem_freqs | 
elem_count_histogram   | 
-----------------------+--------------------------
schemaname             | public
tablename              | correl_expr_idx
attname                | expr
inherited              | f
null_frac              | 0
avg_width              | 4
n_distinct             | 1
most_common_vals       | {1}
most_common_freqs      | {1}
histogram_bounds       | 
correlation            | 1
most_common_elems      | 
most_common_elem_freqs | 
elem_count_histogram   | 
-----------------------+--------------------------
schemaname             | public
tablename              | correl_fix_correl_add_idx
attname                | fix_correl_add
inherited              | f
null_frac              | 0
avg_width              | 4
n_distinct             | 1
most_common_vals       | {1}
most_common_freqs      | {1}
histogram_bounds       | 
correlation            | 1
most_common_elems      | 
most_common_elem_freqs | 
elem_count_histogram   | 

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