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postgresql/contrib/cube/sql/cube.sql
Andrew Gierth 02ddd49932 Change floating-point output format for improved performance. 
Previously, floating-point output was done by rounding to a specific
decimal precision; by default, to 6 or 15 decimal digits (losing
information) or as requested using extra_float_digits. Drivers that
wanted exact float values, and applications like pg_dump that must
preserve values exactly, set extra_float_digits=3 (or sometimes 2 for
historical reasons, though this isn't enough for float4).

Unfortunately, decimal rounded output is slow enough to become a
noticable bottleneck when dealing with large result sets or COPY of
large tables when many floating-point values are involved.

Floating-point output can be done much faster when the output is not
rounded to a specific decimal length, but rather is chosen as the
shortest decimal representation that is closer to the original float
value than to any other value representable in the same precision. The
recently published Ryu algorithm by Ulf Adams is both relatively
simple and remarkably fast.

Accordingly, change float4out/float8out to output shortest decimal
representations if extra_float_digits is greater than 0, and make that
the new default. Applications that need rounded output can set
extra_float_digits back to 0 or below, and take the resulting
performance hit.

We make one concession to portability for systems with buggy
floating-point input: we do not output decimal values that fall
exactly halfway between adjacent representable binary values (which
would rely on the reader doing round-to-nearest-even correctly). This
is known to be a problem at least for VS2013 on Windows.

Our version of the Ryu code originates from
https://github.com/ulfjack/ryu/ at commit c9c3fb1979, but with the
following (significant) modifications:

 - Output format is changed to use fixed-point notation for small
   exponents, as printf would, and also to use lowercase 'e', a
   minimum of 2 exponent digits, and a mandatory sign on the exponent,
   to keep the formatting as close as possible to previous output.

 - The output of exact midpoint values is disabled as noted above.

 - The integer fast-path code is changed somewhat (since we have
   fixed-point output and the upstream did not).

 - Our project style has been largely applied to the code with the
   exception of C99 declaration-after-statement, which has been
   retained as an exception to our present policy.

 - Most of upstream's debugging and conditionals are removed, and we
   use our own configure tests to determine things like uint128
   availability.

Changing the float output format obviously affects a number of
regression tests. This patch uses an explicit setting of
extra_float_digits=0 for test output that is not expected to be
exactly reproducible (e.g. due to numerical instability or differing
algorithms for transcendental functions).

Conversions from floats to numeric are unchanged by this patch. These
may appear in index expressions and it is not yet clear whether any
change should be made, so that can be left for another day.

This patch assumes that the only supported floating point format is
now IEEE format, and the documentation is updated to reflect that.

Code by me, adapting the work of Ulf Adams and other contributors.

References:
https://dl.acm.org/citation.cfm?id=3192369

Reviewed-by: Tom Lane, Andres Freund, Donald Dong
Discussion: https://postgr.es/m/87r2el1bx6.fsf@news-spur.riddles.org.uk
2019-02-13 15:20:33 +00:00

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--
-- 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 (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;
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