-- date check
CREATE TABLE datetmp (a date);
\copy datetmp from 'data/date.data'
SET enable_seqscan=on;
SELECT count(*) FROM datetmp WHERE a <  '2001-02-13';
 count 
-------
   230
(1 row)

SELECT count(*) FROM datetmp WHERE a <= '2001-02-13';
 count 
-------
   231
(1 row)

SELECT count(*) FROM datetmp WHERE a  = '2001-02-13';
 count 
-------
     1
(1 row)

SELECT count(*) FROM datetmp WHERE a >= '2001-02-13';
 count 
-------
   314
(1 row)

SELECT count(*) FROM datetmp WHERE a >  '2001-02-13';
 count 
-------
   313
(1 row)

SELECT a, a <-> '2001-02-13' FROM datetmp ORDER BY a <-> '2001-02-13' LIMIT 3;
     a      | ?column? 
------------+----------
 02-13-2001 |        0
 02-11-2001 |        2
 03-24-2001 |       39
(3 rows)

CREATE INDEX dateidx ON datetmp USING gist ( a );
SET enable_seqscan=off;
SELECT count(*) FROM datetmp WHERE a <  '2001-02-13'::date;
 count 
-------
   230
(1 row)

SELECT count(*) FROM datetmp WHERE a <= '2001-02-13'::date;
 count 
-------
   231
(1 row)

SELECT count(*) FROM datetmp WHERE a  = '2001-02-13'::date;
 count 
-------
     1
(1 row)

SELECT count(*) FROM datetmp WHERE a >= '2001-02-13'::date;
 count 
-------
   314
(1 row)

SELECT count(*) FROM datetmp WHERE a >  '2001-02-13'::date;
 count 
-------
   313
(1 row)

EXPLAIN (COSTS OFF)
SELECT a, a <-> '2001-02-13' FROM datetmp ORDER BY a <-> '2001-02-13' LIMIT 3;
                   QUERY PLAN                   
------------------------------------------------
 Limit
   ->  Index Only Scan using dateidx on datetmp
         Order By: (a <-> '02-13-2001'::date)
(3 rows)

SELECT a, a <-> '2001-02-13' FROM datetmp ORDER BY a <-> '2001-02-13' LIMIT 3;
     a      | ?column? 
------------+----------
 02-13-2001 |        0
 02-11-2001 |        2
 03-24-2001 |       39
(3 rows)