SET enable_seqscan = off;
-- vector
CREATE TABLE t (val vector(3));
INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
CREATE INDEX ON t (val);
SELECT * FROM t WHERE val = '[1,2,3]';
   val   
---------
 [1,2,3]
(1 row)

SELECT * FROM t ORDER BY val;
   val   
---------
 [0,0,0]
 [1,1,1]
 [1,2,3]
 
(4 rows)

DROP TABLE t;
-- halfvec
CREATE TABLE t (val halfvec(3));
INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
CREATE INDEX ON t (val);
SELECT * FROM t WHERE val = '[1,2,3]';
   val   
---------
 [1,2,3]
(1 row)

SELECT * FROM t ORDER BY val;
   val   
---------
 [0,0,0]
 [1,1,1]
 [1,2,3]
 
(4 rows)

DROP TABLE t;
-- sparsevec
CREATE TABLE t (val sparsevec(3));
INSERT INTO t (val) VALUES ('{}/3'), ('{1:1,2:2,3:3}/3'), ('{1:1,2:1,3:1}/3'), (NULL);
CREATE INDEX ON t (val);
SELECT * FROM t WHERE val = '{1:1,2:2,3:3}/3';
       val       
-----------------
 {1:1,2:2,3:3}/3
(1 row)

SELECT * FROM t ORDER BY val;
       val       
-----------------
 {}/3
 {1:1,2:1,3:1}/3
 {1:1,2:2,3:3}/3
 
(4 rows)

DROP TABLE t;