text: --
  --  Test cube datatype
  --
  
  CREATE EXTENSION cube;
  
  -- Check whether any of our opclasses fail amvalidate
  SELECT amname, opcname
  FROM pg_opclass opc LEFT JOIN pg_am am ON am.oid = opcmethod
  WHERE opc.oid >= 16384 AND NOT amvalidate(opc.oid);
  
  --
  -- testing the input and output functions
  --
  
  -- Any number (a one-dimensional point)
  SELECT '1'::cube AS cube;
  SELECT '-1'::cube AS cube;
  SELECT '1.'::cube AS cube;
  SELECT '-1.'::cube AS cube;
  SELECT '.1'::cube AS cube;
  SELECT '-.1'::cube AS cube;
  SELECT '1.0'::cube AS cube;
  SELECT '-1.0'::cube AS cube;
  SELECT 'infinity'::cube AS cube;
  SELECT '-infinity'::cube AS cube;
  SELECT 'NaN'::cube AS cube;
  SELECT '.1234567890123456'::cube AS cube;
  SELECT '+.1234567890123456'::cube AS cube;
  SELECT '-.1234567890123456'::cube AS cube;
  
  -- simple lists (points)
  SELECT '()'::cube AS cube;
  SELECT '1,2'::cube AS cube;
  SELECT '(1,2)'::cube AS cube;
  SELECT '1,2,3,4,5'::cube AS cube;
  SELECT '(1,2,3,4,5)'::cube AS cube;
  
  -- double lists (cubes)
  SELECT '(),()'::cube AS cube;
  SELECT '(0),(0)'::cube AS cube;
  SELECT '(0),(1)'::cube AS cube;
  SELECT '[(0),(0)]'::cube AS cube;
  SELECT '[(0),(1)]'::cube AS cube;
  SELECT '(0,0,0,0),(0,0,0,0)'::cube AS cube;
  SELECT '(0,0,0,0),(1,0,0,0)'::cube AS cube;
  SELECT '[(0,0,0,0),(0,0,0,0)]'::cube AS cube;
  SELECT '[(0,0,0,0),(1,0,0,0)]'::cube AS cube;
  
  -- invalid input: parse errors
  SELECT ''::cube AS cube;
  SELECT 'ABC'::cube AS cube;
  SELECT '[]'::cube AS cube;
  SELECT '[()]'::cube AS cube;
  SELECT '[(1)]'::cube AS cube;
  SELECT '[(1),]'::cube AS cube;
  SELECT '[(1),2]'::cube AS cube;
  SELECT '[(1),(2),(3)]'::cube AS cube;
  SELECT '1,'::cube AS cube;
  SELECT '1,2,'::cube AS cube;
  SELECT '1,,2'::cube AS cube;
  SELECT '(1,)'::cube AS cube;
  SELECT '(1,2,)'::cube AS cube;
  SELECT '(1,,2)'::cube AS cube;
  
  -- invalid input: semantic errors and trailing garbage
  SELECT '[(1),(2)],'::cube AS cube; -- 0
  SELECT '[(1,2,3),(2,3)]'::cube AS cube; -- 1
  SELECT '[(1,2),(1,2,3)]'::cube AS cube; -- 1
  SELECT '(1),(2),'::cube AS cube; -- 2
  SELECT '(1,2,3),(2,3)'::cube AS cube; -- 3
  SELECT '(1,2),(1,2,3)'::cube AS cube; -- 3
  SELECT '(1,2,3)ab'::cube AS cube; -- 4
  SELECT '(1,2,3)a'::cube AS cube; -- 5
  SELECT '(1,2)('::cube AS cube; -- 5
  SELECT '1,2ab'::cube AS cube; -- 6
  SELECT '1 e7'::cube AS cube; -- 6
  SELECT '1,2a'::cube AS cube; -- 7
  SELECT '1..2'::cube AS cube; -- 7
  SELECT '-1e-700'::cube AS cube; -- out of range
  
  --
  -- Testing building cubes from float8 values
  --
  
  SELECT cube(0::float8);
  SELECT cube(1::float8);
  SELECT cube(1,2);
  SELECT cube(cube(1,2),3);
  SELECT cube(cube(1,2),3,4);
  SELECT cube(cube(cube(1,2),3,4),5);
  SELECT cube(cube(cube(1,2),3,4),5,6);
  
  --
  -- Test that the text -> cube cast was installed.
  --
  
  SELECT '(0)'::text::cube;
  
  --
  -- Test the float[] -> cube cast
  --
  SELECT cube('{0,1,2}'::float[], '{3,4,5}'::float[]);
  SELECT cube('{0,1,2}'::float[], '{3}'::float[]);
  SELECT cube(NULL::float[], '{3}'::float[]);
  SELECT cube('{0,1,2}'::float[]);
  SELECT cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[3,2,1,1]);
  SELECT cube_subset(cube('(1,3,5),(1,3,5)'), ARRAY[3,2,1,1]);
  SELECT cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[4,0]);
  SELECT cube_subset(cube('(6,7,8),(6,7,8)'), ARRAY[4,0]);
  -- test for limits: this should pass
  SELECT cube_subset(cube('(6,7,8),(6,7,8)'), array(SELECT 1 as a FROM generate_series(1,100)));
  -- and this should fail
  SELECT cube_subset(cube('(6,7,8),(6,7,8)'), array(SELECT 1 as a FROM generate_series(1,101)));
  
  
  
  --
  -- Test point processing
  --
  SELECT cube('(1,2),(1,2)'); -- cube_in
  SELECT cube('{0,1,2}'::float[], '{0,1,2}'::float[]); -- cube_a_f8_f8
  SELECT cube('{5,6,7,8}'::float[]); -- cube_a_f8
  SELECT cube(1.37); -- cube_f8
  SELECT cube(1.37, 1.37); -- cube_f8_f8
  SELECT cube(cube(1,1), 42); -- cube_c_f8
  SELECT cube(cube(1,2), 42); -- cube_c_f8
  SELECT cube(cube(1,1), 42, 42); -- cube_c_f8_f8
  SELECT cube(cube(1,1), 42, 24); -- cube_c_f8_f8
  SELECT cube(cube(1,2), 42, 42); -- cube_c_f8_f8
  SELECT cube(cube(1,2), 42, 24); -- cube_c_f8_f8
  
  --
  -- Testing limit of CUBE_MAX_DIM dimensions check in cube_in.
  --
  -- create too big cube from literal
  select '(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)'::cube;
  select '(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0),(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0)'::cube;
  -- from an array
  select cube(array(SELECT 0 as a FROM generate_series(1,101)));
  select cube(array(SELECT 0 as a FROM generate_series(1,101)),array(SELECT 0 as a FROM generate_series(1,101)));
  
  -- extend cube beyond limit
  -- this should work
  select cube(array(SELECT 0 as a FROM generate_series(1,100)));
  select cube(array(SELECT 0 as a FROM generate_series(1,100)),array(SELECT 0 as a FROM generate_series(1,100)));
  -- this should fail
  select cube(cube(array(SELECT 0 as a FROM generate_series(1,100))), 0);
  select cube(cube(array(SELECT 0 as a FROM generate_series(1,100)),array(SELECT 0 as a FROM generate_series(1,100))), 0, 0);
  
  
  --
  -- testing the  operators
  --
  
  -- equality/inequality:
  --
  SELECT '24, 33.20'::cube    =  '24, 33.20'::cube AS bool;
  SELECT '24, 33.20'::cube    != '24, 33.20'::cube AS bool;
  SELECT '24, 33.20'::cube    =  '24, 33.21'::cube AS bool;
  SELECT '24, 33.20'::cube    != '24, 33.21'::cube AS bool;
  SELECT '(2,0),(3,1)'::cube  =  '(2,0,0,0,0),(3,1,0,0,0)'::cube AS bool;
  SELECT '(2,0),(3,1)'::cube  =  '(2,0,0,0,0),(3,1,0,0,1)'::cube AS bool;
  
  -- "lower than" / "greater than"
  -- (these operators are not useful for anything but ordering)
  --
  SELECT '1'::cube   > '2'::cube AS bool;
  SELECT '1'::cube   < '2'::cube AS bool;
  SELECT '1,1'::cube > '1,2'::cube AS bool;
  SELECT '1,1'::cube < '1,2'::cube AS bool;
  
  SELECT '(2,0),(3,1)'::cube             > '(2,0,0,0,0),(3,1,0,0,1)'::cube AS bool;
  SELECT '(2,0),(3,1)'::cube             < '(2,0,0,0,0),(3,1,0,0,1)'::cube AS bool;
  SELECT '(2,0),(3,1)'::cube             > '(2,0,0,0,1),(3,1,0,0,0)'::cube AS bool;
  SELECT '(2,0),(3,1)'::cube             < '(2,0,0,0,1),(3,1,0,0,0)'::cube AS bool;
  SELECT '(2,0),(3,1)'::cube             > '(2,0,0,0,0),(3,1,0,0,0)'::cube AS bool;
  SELECT '(2,0),(3,1)'::cube             < '(2,0,0,0,0),(3,1,0,0,0)'::cube AS bool;
  SELECT '(2,0,0,0,0),(3,1,0,0,1)'::cube > '(2,0),(3,1)'::cube AS bool;
  SELECT '(2,0,0,0,0),(3,1,0,0,1)'::cube < '(2,0),(3,1)'::cube AS bool;
  SELECT '(2,0,0,0,1),(3,1,0,0,0)'::cube > '(2,0),(3,1)'::cube AS bool;
  SELECT '(2,0,0,0,1),(3,1,0,0,0)'::cube < '(2,0),(3,1)'::cube AS bool;
  SELECT '(2,0,0,0,0),(3,1,0,0,0)'::cube > '(2,0),(3,1)'::cube AS bool;
  SELECT '(2,0,0,0,0),(3,1,0,0,0)'::cube < '(2,0),(3,1)'::cube AS bool;
  
  
  -- "overlap"
  --
  SELECT '1'::cube && '1'::cube AS bool;
  SELECT '1'::cube && '2'::cube AS bool;
  
  SELECT '[(-1,-1,-1),(1,1,1)]'::cube && '0'::cube AS bool;
  SELECT '[(-1,-1,-1),(1,1,1)]'::cube && '1'::cube AS bool;
  SELECT '[(-1,-1,-1),(1,1,1)]'::cube && '1,1,1'::cube AS bool;
  SELECT '[(-1,-1,-1),(1,1,1)]'::cube && '[(1,1,1),(2,2,2)]'::cube AS bool;
  SELECT '[(-1,-1,-1),(1,1,1)]'::cube && '[(1,1),(2,2)]'::cube AS bool;
  SELECT '[(-1,-1,-1),(1,1,1)]'::cube && '[(2,1,1),(2,2,2)]'::cube AS bool;
  
  
  -- "contained in" (the left operand is the cube entirely enclosed by
  -- the right operand):
  --
  SELECT '0'::cube                 <@ '0'::cube                        AS bool;
  SELECT '0,0,0'::cube             <@ '0,0,0'::cube                    AS bool;
  SELECT '0,0'::cube               <@ '0,0,1'::cube                    AS bool;
  SELECT '0,0,0'::cube             <@ '0,0,1'::cube                    AS bool;
  SELECT '1,0,0'::cube             <@ '0,0,1'::cube                    AS bool;
  SELECT '(1,0,0),(0,0,1)'::cube   <@ '(1,0,0),(0,0,1)'::cube          AS bool;
  SELECT '(1,0,0),(0,0,1)'::cube   <@ '(-1,-1,-1),(1,1,1)'::cube       AS bool;
  SELECT '(1,0,0),(0,0,1)'::cube   <@ '(-1,-1,-1,-1),(1,1,1,1)'::cube  AS bool;
  SELECT '0'::cube                 <@ '(-1),(1)'::cube                 AS bool;
  SELECT '1'::cube                 <@ '(-1),(1)'::cube                 AS bool;
  SELECT '-1'::cube                <@ '(-1),(1)'::cube                 AS bool;
  SELECT '(-1),(1)'::cube          <@ '(-1),(1)'::cube                 AS bool;
  SELECT '(-1),(1)'::cube          <@ '(-1,-1),(1,1)'::cube            AS bool;
  SELECT '(-2),(1)'::cube          <@ '(-1),(1)'::cube                 AS bool;
  SELECT '(-2),(1)'::cube          <@ '(-1,-1),(1,1)'::cube            AS bool;
  
  
  -- "contains" (the left operand is the cube that entirely encloses the
  -- right operand)
  --
  SELECT '0'::cube                        @> '0'::cube                 AS bool;
  SELECT '0,0,0'::cube                    @> '0,0,0'::cube             AS bool;
  SELECT '0,0,1'::cube                    @> '0,0'::cube               AS bool;
  SELECT '0,0,1'::cube                    @> '0,0,0'::cube             AS bool;
  SELECT '0,0,1'::cube                    @> '1,0,0'::cube             AS bool;
  SELECT '(1,0,0),(0,0,1)'::cube          @> '(1,0,0),(0,0,1)'::cube   AS bool;
  SELECT '(-1,-1,-1),(1,1,1)'::cube       @> '(1,0,0),(0,0,1)'::cube   AS bool;
  SELECT '(-1,-1,-1,-1),(1,1,1,1)'::cube  @> '(1,0,0),(0,0,1)'::cube   AS bool;
  SELECT '(-1),(1)'::cube                 @> '0'::cube                 AS bool;
  SELECT '(-1),(1)'::cube                 @> '1'::cube                 AS bool;
  SELECT '(-1),(1)'::cube                 @> '-1'::cube                AS bool;
  SELECT '(-1),(1)'::cube                 @> '(-1),(1)'::cube          AS bool;
  SELECT '(-1,-1),(1,1)'::cube            @> '(-1),(1)'::cube          AS bool;
  SELECT '(-1),(1)'::cube                 @> '(-2),(1)'::cube          AS bool;
  SELECT '(-1,-1),(1,1)'::cube            @> '(-2),(1)'::cube          AS bool;
  
  -- Test of distance function
  --
  SELECT cube_distance('(0)'::cube,'(2,2,2,2)'::cube);
  SELECT cube_distance('(0)'::cube,'(.3,.4)'::cube);
  SELECT cube_distance('(2,3,4)'::cube,'(2,3,4)'::cube);
  SELECT cube_distance('(42,42,42,42)'::cube,'(137,137,137,137)'::cube);
  SELECT cube_distance('(42,42,42)'::cube,'(137,137)'::cube);
  
  -- Test of cube function (text to cube)
  --
  SELECT cube('(1,1.2)'::text);
  SELECT cube(NULL);
  
  -- Test of cube_dim function (dimensions stored in cube)
  --
  SELECT cube_dim('(0)'::cube);
  SELECT cube_dim('(0,0)'::cube);
  SELECT cube_dim('(0,0,0)'::cube);
  SELECT cube_dim('(42,42,42),(42,42,42)'::cube);
  SELECT cube_dim('(4,8,15,16,23),(4,8,15,16,23)'::cube);
  
  -- Test of cube_ll_coord function (retrieves LL coordinate values)
  --
  SELECT cube_ll_coord('(-1,1),(2,-2)'::cube, 1);
  SELECT cube_ll_coord('(-1,1),(2,-2)'::cube, 2);
  SELECT cube_ll_coord('(-1,1),(2,-2)'::cube, 3);
  SELECT cube_ll_coord('(1,2),(1,2)'::cube, 1);
  SELECT cube_ll_coord('(1,2),(1,2)'::cube, 2);
  SELECT cube_ll_coord('(1,2),(1,2)'::cube, 3);
  SELECT cube_ll_coord('(42,137)'::cube, 1);
  SELECT cube_ll_coord('(42,137)'::cube, 2);
  SELECT cube_ll_coord('(42,137)'::cube, 3);
  
  -- Test of cube_ur_coord function (retrieves UR coordinate values)
  --
  SELECT cube_ur_coord('(-1,1),(2,-2)'::cube, 1);
  SELECT cube_ur_coord('(-1,1),(2,-2)'::cube, 2);
  SELECT cube_ur_coord('(-1,1),(2,-2)'::cube, 3);
  SELECT cube_ur_coord('(1,2),(1,2)'::cube, 1);
  SELECT cube_ur_coord('(1,2),(1,2)'::cube, 2);
  SELECT cube_ur_coord('(1,2),(1,2)'::cube, 3);
  SELECT cube_ur_coord('(42,137)'::cube, 1);
  SELECT cube_ur_coord('(42,137)'::cube, 2);
  SELECT cube_ur_coord('(42,137)'::cube, 3);
  
  -- Test of cube_is_point
  --
  SELECT cube_is_point('(0)'::cube);
  SELECT cube_is_point('(0,1,2)'::cube);
  SELECT cube_is_point('(0,1,2),(0,1,2)'::cube);
  SELECT cube_is_point('(0,1,2),(-1,1,2)'::cube);
  SELECT cube_is_point('(0,1,2),(0,-1,2)'::cube);
  SELECT cube_is_point('(0,1,2),(0,1,-2)'::cube);
  
  -- Test of cube_enlarge (enlarging and shrinking cubes)
  --
  SELECT cube_enlarge('(0)'::cube, 0, 0);
  SELECT cube_enlarge('(0)'::cube, 0, 1);
  SELECT cube_enlarge('(0)'::cube, 0, 2);
  SELECT cube_enlarge('(2),(-2)'::cube, 0, 4);
  SELECT cube_enlarge('(0)'::cube, 1, 0);
  SELECT cube_enlarge('(0)'::cube, 1, 1);
  SELECT cube_enlarge('(0)'::cube, 1, 2);
  SELECT cube_enlarge('(2),(-2)'::cube, 1, 4);
  SELECT cube_enlarge('(0)'::cube, -1, 0);
  SELECT cube_enlarge('(0)'::cube, -1, 1);
  SELECT cube_enlarge('(0)'::cube, -1, 2);
  SELECT cube_enlarge('(2),(-2)'::cube, -1, 4);
  SELECT cube_enlarge('(0,0,0)'::cube, 1, 0);
  SELECT cube_enlarge('(0,0,0)'::cube, 1, 2);
  SELECT cube_enlarge('(2,-2),(-3,7)'::cube, 1, 2);
  SELECT cube_enlarge('(2,-2),(-3,7)'::cube, 3, 2);
  SELECT cube_enlarge('(2,-2),(-3,7)'::cube, -1, 2);
  SELECT cube_enlarge('(2,-2),(-3,7)'::cube, -3, 2);
  SELECT cube_enlarge('(42,-23,-23),(42,23,23)'::cube, -23, 5);
  SELECT cube_enlarge('(42,-23,-23),(42,23,23)'::cube, -24, 5);
  
  -- Test of cube_union (MBR for two cubes)
  --
  SELECT cube_union('(1,2),(3,4)'::cube, '(5,6,7),(8,9,10)'::cube);
  SELECT cube_union('(1,2)'::cube, '(4,2,0,0)'::cube);
  SELECT cube_union('(1,2),(1,2)'::cube, '(4,2),(4,2)'::cube);
  SELECT cube_union('(1,2),(1,2)'::cube, '(1,2),(1,2)'::cube);
  SELECT cube_union('(1,2),(1,2)'::cube, '(1,2,0),(1,2,0)'::cube);
  
  -- Test of cube_inter
  --
  SELECT cube_inter('(1,2),(10,11)'::cube, '(3,4), (16,15)'::cube); -- intersects
  SELECT cube_inter('(1,2),(10,11)'::cube, '(3,4), (6,5)'::cube); -- includes
  SELECT cube_inter('(1,2),(10,11)'::cube, '(13,14), (16,15)'::cube); -- no intersection
  SELECT cube_inter('(1,2),(10,11)'::cube, '(3,14), (16,15)'::cube); -- no intersection, but one dimension intersects
  SELECT cube_inter('(1,2),(10,11)'::cube, '(10,11), (16,15)'::cube); -- point intersection
  SELECT cube_inter('(1,2,3)'::cube, '(1,2,3)'::cube); -- point args
  SELECT cube_inter('(1,2,3)'::cube, '(5,6,3)'::cube); -- point args
  
  -- Test of cube_size
  --
  SELECT cube_size('(4,8),(15,16)'::cube);
  SELECT cube_size('(42,137)'::cube);
  
  -- Test of distances
  --
  SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
  SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
  SELECT distance_chebyshev('(1,1)'::cube, '(4,5)'::cube);
  SELECT '(1,1)'::cube <=> '(4,5)'::cube as d_c;
  SELECT distance_taxicab('(1,1)'::cube, '(4,5)'::cube);
  SELECT '(1,1)'::cube <#> '(4,5)'::cube as d_t;
  -- zero for overlapping
  SELECT cube_distance('(2,2),(10,10)'::cube, '(0,0),(5,5)'::cube);
  SELECT distance_chebyshev('(2,2),(10,10)'::cube, '(0,0),(5,5)'::cube);
  SELECT distance_taxicab('(2,2),(10,10)'::cube, '(0,0),(5,5)'::cube);
  -- coordinate access
  SELECT cube(array[10,20,30], array[40,50,60])->1;
  SELECT cube(array[40,50,60], array[10,20,30])->1;
  SELECT cube(array[10,20,30], array[40,50,60])->6;
  SELECT cube(array[10,20,30], array[40,50,60])->0;
  SELECT cube(array[10,20,30], array[40,50,60])->7;
  SELECT cube(array[10,20,30], array[40,50,60])->-1;
  SELECT cube(array[10,20,30], array[40,50,60])->-6;
  SELECT cube(array[10,20,30])->3;
  SELECT cube(array[10,20,30])->6;
  SELECT cube(array[10,20,30])->-6;
  -- "normalized" coordinate access
  SELECT cube(array[10,20,30], array[40,50,60])~>1;
  SELECT cube(array[40,50,60], array[10,20,30])~>1;
  SELECT cube(array[10,20,30], array[40,50,60])~>2;
  SELECT cube(array[40,50,60], array[10,20,30])~>2;
  SELECT cube(array[10,20,30], array[40,50,60])~>3;
  SELECT cube(array[40,50,60], array[10,20,30])~>3;
  
  SELECT cube(array[40,50,60], array[10,20,30])~>0;
  SELECT cube(array[40,50,60], array[10,20,30])~>4;
  SELECT cube(array[40,50,60], array[10,20,30])~>(-1);
  
  -- Load some example data and build the index
  --
  CREATE TABLE test_cube (c cube);
  
  \copy test_cube from 'data/test_cube.data'
  
  CREATE INDEX test_cube_ix ON test_cube USING gist (c);
  SELECT * FROM test_cube WHERE c && '(3000,1000),(0,0)' ORDER BY c;
  
  -- Test sorting
  SELECT * FROM test_cube WHERE c && '(3000,1000),(0,0)' GROUP BY c ORDER BY c;
  
  -- Test index-only scans
  SET enable_bitmapscan = false;
  EXPLAIN (COSTS OFF)
  SELECT c FROM test_cube WHERE c <@ '(3000,1000),(0,0)' ORDER BY c;
  SELECT c FROM test_cube WHERE c <@ '(3000,1000),(0,0)' ORDER BY c;
  RESET enable_bitmapscan;
  
  -- Test kNN
  INSERT INTO test_cube VALUES ('(1,1)'), ('(100000)'), ('(0, 100000)'); -- Some corner cases
  SET enable_seqscan = false;
  
  -- Test different metrics
  SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
  SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
  SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
  
  -- Test sorting by coordinates
  SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound
  SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound
  SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound
  SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound
  SELECT c~>(-1), c FROM test_cube ORDER BY c~>(-1) LIMIT 15; -- descending by left bound
  SELECT c~>(-2), c FROM test_cube ORDER BY c~>(-2) LIMIT 15; -- descending by right bound
  SELECT c~>(-3), c FROM test_cube ORDER BY c~>(-3) LIMIT 15; -- descending by lower bound
  SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upper bound
  
  -- Same queries with sequential scan (should give the same results as above)
  RESET enable_seqscan;
  SET enable_indexscan = OFF;
  SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
  SELECT *, c <=> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <=> '(100, 100),(500, 500)'::cube LIMIT 5;
  SELECT *, c <#> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <#> '(100, 100),(500, 500)'::cube LIMIT 5;
  SELECT c~>1, c FROM test_cube ORDER BY c~>1 LIMIT 15; -- ascending by left bound
  SELECT c~>2, c FROM test_cube ORDER BY c~>2 LIMIT 15; -- ascending by right bound
  SELECT c~>3, c FROM test_cube ORDER BY c~>3 LIMIT 15; -- ascending by lower bound
  SELECT c~>4, c FROM test_cube ORDER BY c~>4 LIMIT 15; -- ascending by upper bound
  SELECT c~>(-1), c FROM test_cube ORDER BY c~>(-1) LIMIT 15; -- descending by left bound
  SELECT c~>(-2), c FROM test_cube ORDER BY c~>(-2) LIMIT 15; -- descending by right bound
  SELECT c~>(-3), c FROM test_cube ORDER BY c~>(-3) LIMIT 15; -- descending by lower bound
  SELECT c~>(-4), c FROM test_cube ORDER BY c~>(-4) LIMIT 15; -- descending by upper bound
  RESET enable_indexscan;
  