SELECT l2_distance('{}'::sparsevec, '{0:3,1:4}');
 l2_distance 
-------------
           5
(1 row)

SELECT l2_distance('{}'::sparsevec, '{1:1}');
 l2_distance 
-------------
           1
(1 row)

SELECT '{}'::sparsevec <-> '{0:3,1:4}';
 ?column? 
----------
        5
(1 row)

SELECT inner_product('{0:1,1:2}'::sparsevec, '{0:2,1:4}');
 inner_product 
---------------
            10
(1 row)

SELECT sparsevec_negative_inner_product('{0:1,1:2}', '{0:2,1:4}');
 sparsevec_negative_inner_product 
----------------------------------
                              -10
(1 row)

SELECT cosine_distance('{0:1,1:2}'::sparsevec, '{0:2,1:4}');
 cosine_distance 
-----------------
               0
(1 row)

SELECT cosine_distance('{0:1,1:2}'::sparsevec, '{}');
 cosine_distance 
-----------------
             NaN
(1 row)

SELECT cosine_distance('{0:1,1:1}'::sparsevec, '{0:-1,1:-1}');
 cosine_distance 
-----------------
               2
(1 row)

SELECT cosine_distance('{0:1}'::sparsevec, '{1:2}');
 cosine_distance 
-----------------
               1
(1 row)

SELECT cosine_distance('{}'::sparsevec, '{}');
 cosine_distance 
-----------------
             NaN
(1 row)