cube — a multi-dimensional cube data type

This module implements a data type cube for representing multidimensional cubes.

This module is considered “trusted”, that is, it can be installed by non-superusers who have CREATE privilege on the current database.

---

Syntax

Table 1 shows the valid external representations for the cube type. x, y, etc. denote floating-point numbers.

Table 1. Cube External Representations

External Syntax	Meaning
x	A one-dimensional point (or, zero-length one-dimensional interval)
(x)	Same as above
x1,x2,...,xn	A point in n-dimensional space, represented internally as a zero-volume cube
(x1,x2,...,xn)	Same as above
(x),(y)	A one-dimensional interval starting at x and ending at y or vice versa; the order does not matter
[(x),(y)]	Same as above
(x1,...,xn),(y1,...,yn)	An n-dimensional cube represented by a pair of its diagonally opposite corners
[(x1,...,xn),(y1,...,yn)]	Same as above

It does not matter which order the opposite corners of a cube are entered in. The cube functions automatically swap values if needed to create a uniform “lower left — upper right” internal representation. When the corners coincide, cube stores only one corner along with an “is point” flag to avoid wasting space.

White space is ignored on input, so [(x),(y)] is the same as [ ( x ), ( y ) ].

---

Precision

Values are stored internally as 64-bit floating point numbers. This means that numbers with more than about 16 significant digits will be truncated.

---

Usage

The specialized operators provided for type cube are shown below.

cube && cube → boolean

Do the cubes overlap?

cube @> cube → boolean

Does the first cube contain the second?

cube <@ cube → boolean

Is the first cube contained in the second?

cube -> integer → float8

Extracts the n-th coordinate of the cube (counting from 1).

cube ~> integer → float8

Extracts the n-th coordinate of the cube, counting in the following way: n = 2 * k - 1 means lower bound of k-th dimension, n = 2 * k means upper bound of k-th dimension. Negative n denotes the inverse value of the corresponding positive coordinate. This operator is designed for KNN-GiST support.

cube <-> cube → float8

Computes the Euclidean distance between the two cubes.

cube <#> cube → float8

Computes the taxicab (L-1 metric) distance between the two cubes.

cube <=> cube → float8

Computes the Chebyshev (L-inf metric) distance between the two cubes.

In addition to the above operators, the usual comparison operators shown in Section Comparison Operators are available for type cube. These operators first compare the first coordinates, and if those are equal, compare the second coordinates, etc. They exist mainly to support the b-tree index operator class for cube, which can be useful for example if you would like a UNIQUE constraint on a cube column. Otherwise, this ordering is not of much practical use.

The cube module also provides a GiST index operator class for cube values. A cube GiST index can be used to search for values using the =, &&, @>, and <@ operators in WHERE clauses.

In addition, a cube GiST index can be used to find nearest neighbors using the metric operators <->, <#>, and <=> in ORDER BY clauses. For example, the nearest neighbor of the 3-D point (0.5, 0.5, 0.5) could be found efficiently with:

SELECT c FROM test ORDER BY c <-> cube(array[0.5,0.5,0.5]) LIMIT 1;

The ~> operator can also be used in this way to efficiently retrieve the first few values sorted by a selected coordinate. For example, to get the first few cubes ordered by the first coordinate (lower left corner) ascending one could use the following query:

SELECT c FROM test ORDER BY c ~> 1 LIMIT 5;

And to get 2-D cubes ordered by the first coordinate of the upper right corner descending:

SELECT c FROM test ORDER BY c ~> 3 DESC LIMIT 5;

The available cube functions are shown below.

cube ( float8 ) → cube

Makes a one dimensional cube with both coordinates the same.

Example:

cube(1) → (1)

cube ( float8, float8 ) → cube

Makes a one dimensional cube.

Example:

cube(1, 2) → (1),(2)

cube ( float8[] ) → cube

Makes a zero-volume cube using the coordinates defined by the array.

Example:

cube(ARRAY[1,2,3]) → (1, 2, 3)

cube ( float8[], float8[] ) → cube

Makes a cube with upper right and lower left coordinates as defined by the two arrays, which must be of the same length.

Example:

cube(ARRAY[1,2], ARRAY[3,4]) → (1, 2),(3, 4)

cube ( cube, float8 ) → cube

Makes a new cube by adding a dimension on to an existing cube, with the same values for both endpoints of the new coordinate. This is useful for building cubes piece by piece from calculated values.

Example:

cube('(1,2),(3,4)'::cube, 5) → (1, 2, 5),(3, 4, 5)

cube ( cube, float8, float8 ) → cube

Makes a new cube by adding a dimension on to an existing cube. This is useful for building cubes piece by piece from calculated values.

Example:

cube('(1,2),(3,4)'::cube, 5, 6) → (1, 2, 5),(3, 4, 6)

cube_dim ( cube ) → integer

Returns the number of dimensions of the cube.

Example:

cube_dim('(1,2),(3,4)') → 2

cube_ll_coord ( cube, integer ) → float8

Returns the n-th coordinate value for the lower left corner of the cube.

Example:

cube_ll_coord('(1,2),(3,4)', 2) → 2

cube_ur_coord ( cube, integer ) → float8

Returns the n-th coordinate value for the upper right corner of the cube.

Example:

cube_ur_coord('(1,2),(3,4)', 2) → 4

cube_is_point ( cube ) → boolean

Returns true if the cube is a point, that is, the two defining corners are the same.

Example:

cube_is_point(cube(1,1)) → t

cube_distance ( cube, cube ) → float8

Returns the distance between two cubes. If both cubes are points, this is the normal distance function.

Example:

cube_distance('(1,2)', '(3,4)') → 2.8284271247461903

cube_subset ( cube, integer[] ) → cube

Makes a new cube from an existing cube, using a list of dimension indexes from an array. Can be used to extract the endpoints of a single dimension, or to drop dimensions, or to reorder them as desired.

Examples:

cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[2]) → (3),(7)

cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[3,2,1,1]) → (5, 3, 1, 1),(8, 7, 6, 6)

cube_union ( cube, cube ) → cube

Produces the union of two cubes.

Example:

cube_union('(1,2)', '(3,4)') → (1, 2),(3, 4)

cube_inter ( cube, cube ) → cube

Produces the intersection of two cubes.

Example:

cube_inter('(1,2)', '(3,4)') → (3, 4),(1, 2)

cube_enlarge ( c cube, r double, n integer ) → cube

Increases the size of the cube by the specified radius r in at least n dimensions. If the radius is negative the cube is shrunk instead. All defined dimensions are changed by the radius r. Lower-left coordinates are decreased by r and upper-right coordinates are increased by r. If a lower-left coordinate is increased to more than the corresponding upper-right coordinate (this can only happen when r < 0) than both coordinates are set to their average. If n is greater than the number of defined dimensions and the cube is being enlarged (r > 0), then extra dimensions are added to make n altogether; 0 is used as the initial value for the extra coordinates. This function is useful for creating bounding boxes around a point for searching for nearby points.

Example:

cube_enlarge('(1,2),(3,4)', 0.5, 3) → (0.5, 1.5, -0.5),(3.5, 4.5, 0.5)

---

Defaults

This union:

select cube_union('(0,5,2),(2,3,1)', '0');
cube_union
-------------------
(0, 0, 0),(2, 5, 2)
(1 row)

does not contradict common sense, neither does the intersection:

select cube_inter('(0,-1),(1,1)', '(-2),(2)');
cube_inter
-------------
(0, 0),(1, 0)
(1 row)

In all binary operations on differently-dimensioned cubes, the lower-dimensional one is assumed to be a Cartesian projection, i. e., having zeroes in place of coordinates omitted in the string representation. The above examples are equivalent to:

cube_union('(0,5,2),(2,3,1)','(0,0,0),(0,0,0)');
cube_inter('(0,-1),(1,1)','(-2,0),(2,0)');

The following containment predicate uses the point syntax, while in fact the second argument is internally represented by a box. This syntax makes it unnecessary to define a separate point type and functions for (box,point) predicates.

select cube_contains('(0,0),(1,1)', '0.5,0.5');
cube_contains
--------------
t
(1 row)

---

Notes

To make it harder for people to break things, there is a limit of 100 on the number of dimensions of cubes. This is set in cubedata.h if you need something bigger.

---

cube Datatype Regression Test

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

-- Also try it with non-error-throwing API
SELECT pg_input_is_valid('(1,2)', 'cube');
SELECT pg_input_is_valid('[(1),]', 'cube');
SELECT pg_input_is_valid('-1e-700', 'cube');
SELECT * FROM pg_input_error_info('-1e-700', 'cube');

--
-- 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 (euclidean distance may not be bit-exact)
--
SET extra_float_digits = 0;
SELECT cube_distance('(1,1)'::cube, '(4,5)'::cube);
SELECT '(1,1)'::cube <-> '(4,5)'::cube as d_e;
RESET extra_float_digits;
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
SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
RESET extra_float_digits;
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;
SET extra_float_digits = 0;
SELECT *, c <-> '(100, 100),(500, 500)'::cube as dist FROM test_cube ORDER BY c <-> '(100, 100),(500, 500)'::cube LIMIT 5;
RESET extra_float_digits;
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;

---

Credits

Gene Selkov, Jr. selkovjr@mcs.anl.gov, Mathematics and Computer Science Division, Argonne National Laboratory.

My thanks are primarily to Prof. Joe Hellerstein (https://dsf.berkeley.edu/jmh/) for elucidating the gist of the GiST (http://gist.cs.berkeley.edu/), and to his former student Andy Dong for his example written for Illustra. I am also grateful to all Postgres developers, present and past, for enabling myself to create my own world and live undisturbed in it. And I would like to acknowledge my gratitude to Argonne Lab and to the U.S. Department of Energy for the years of faithful support of my database research.

Minor updates to this package were made by Bruno Wolff III (bruno@wolff.to) in August/September of 2002. These include changing the precision from single precision to double precision and adding some new functions.

Additional updates were made by Joshua Reich (josh@root.net) in July 2006. These include cube(float8[], float8[]) and cleaning up the code to use the V1 call protocol instead of the deprecated V0 protocol.