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Code and docs review for cube kNN support. 

Commit 33bd250f6c could have done with
some more review:

Adjust coding so that compilers unfamiliar with elog/ereport don't complain
about uninitialized values.

Fix misuse of PG_GETARG_INT16 to retrieve arguments declared as "integer"
at the SQL level.  (This was evidently copied from cube_ll_coord and
cube_ur_coord, but those were wrong too.)

Fix non-style-guide-conforming error messages.

Fix underparenthesized if statements, which pgindent would have made a
hash of, and remove some unnecessary parens elsewhere.

Run pgindent over new code.

Revise documentation: repeated accretion of more operators without any
rethinking of the text already there had left things in a bit of a mess.
Merge all the cube operators into one table and adjust surrounding text
appropriately.

David Rowley and Tom Lane
This commit is contained in:
Tom Lane 2015-12-28 14:39:09 -05:00
parent ac443d1034
commit 81ee726d87
6 changed files with 190 additions and 201 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

128
contrib/cube/cube.c
View File

@ -1275,6 +1275,7 @@ distance_taxicab(PG_FUNCTION_ARGS)
if (DIM(a) < DIM(b))
{
NDBOX *tmp = b;
b = a;
a = tmp;
swapped = true;
@ -1283,11 +1284,13 @@ distance_taxicab(PG_FUNCTION_ARGS)
distance = 0.0;
/* compute within the dimensions of (b) */
for (i = 0; i < DIM(b); i++)
distance += fabs(distance_1D(LL_COORD(a,i), UR_COORD(a,i), LL_COORD(b,i), UR_COORD(b,i)));
distance += fabs(distance_1D(LL_COORD(a, i), UR_COORD(a, i),
LL_COORD(b, i), UR_COORD(b, i)));
/* compute distance to zero for those dimensions in (a) absent in (b) */
for (i = DIM(b); i < DIM(a); i++)
distance += fabs(distance_1D(LL_COORD(a,i), UR_COORD(a,i), 0.0, 0.0));
distance += fabs(distance_1D(LL_COORD(a, i), UR_COORD(a, i),
0.0, 0.0));
if (swapped)
{
@ -1309,13 +1312,15 @@ distance_chebyshev(PG_FUNCTION_ARGS)
NDBOX *a = PG_GETARG_NDBOX(0),
*b = PG_GETARG_NDBOX(1);
bool swapped = false;
double d, distance;
double d,
distance;
int i;
/* swap the box pointers if needed */
if (DIM(a) < DIM(b))
{
NDBOX *tmp = b;
b = a;
a = tmp;
swapped = true;
@ -1325,7 +1330,8 @@ distance_chebyshev(PG_FUNCTION_ARGS)
/* compute within the dimensions of (b) */
for (i = 0; i < DIM(b); i++)
{
d = fabs(distance_1D(LL_COORD(a,i), UR_COORD(a,i), LL_COORD(b,i), UR_COORD(b,i)));
d = fabs(distance_1D(LL_COORD(a, i), UR_COORD(a, i),
LL_COORD(b, i), UR_COORD(b, i)));
if (d > distance)
distance = d;
}
@ -1333,7 +1339,7 @@ distance_chebyshev(PG_FUNCTION_ARGS)
/* compute distance to zero for those dimensions in (a) absent in (b) */
for (i = DIM(b); i < DIM(a); i++)
{
d = fabs(distance_1D(LL_COORD(a,i), UR_COORD(a,i), 0.0, 0.0));
d = fabs(distance_1D(LL_COORD(a, i), UR_COORD(a, i), 0.0, 0.0));
if (d > distance)
distance = d;
}
@ -1357,44 +1363,41 @@ g_cube_distance(PG_FUNCTION_ARGS)
{
GISTENTRY *entry = (GISTENTRY *) PG_GETARG_POINTER(0);
StrategyNumber strategy = (StrategyNumber) PG_GETARG_UINT16(2);
NDBOX *cube = DatumGetNDBOX(entry->key);
double retval;
NDBOX *cube = DatumGetNDBOX(entry->key);
double retval;
if (strategy == CubeKNNDistanceCoord)
{
int coord = PG_GETARG_INT32(1);
int coord = PG_GETARG_INT32(1);
if IS_POINT(cube)
{
retval = (cube)->x[(coord-1)%DIM(cube)];
}
if (IS_POINT(cube))
retval = cube->x[(coord - 1) % DIM(cube)];
else
{
retval = Min(
(cube)->x[(coord-1)%DIM(cube)],
(cube)->x[(coord-1)%DIM(cube) + DIM(cube)]
);
}
retval = Min(cube->x[(coord - 1) % DIM(cube)],
cube->x[(coord - 1) % DIM(cube) + DIM(cube)]);
}
else
{
NDBOX *query = PG_GETARG_NDBOX(1);
switch(strategy)
NDBOX *query = PG_GETARG_NDBOX(1);
switch (strategy)
{
case CubeKNNDistanceTaxicab:
retval = DatumGetFloat8(DirectFunctionCall2(distance_taxicab,
PointerGetDatum(cube), PointerGetDatum(query)));
break;
case CubeKNNDistanceEuclid:
retval = DatumGetFloat8(DirectFunctionCall2(cube_distance,
PointerGetDatum(cube), PointerGetDatum(query)));
break;
case CubeKNNDistanceChebyshev:
retval = DatumGetFloat8(DirectFunctionCall2(distance_chebyshev,
PointerGetDatum(cube), PointerGetDatum(query)));
break;
default:
elog(ERROR, "Cube: unknown strategy number.");
case CubeKNNDistanceTaxicab:
retval = DatumGetFloat8(DirectFunctionCall2(distance_taxicab,
PointerGetDatum(cube), PointerGetDatum(query)));
break;
case CubeKNNDistanceEuclid:
retval = DatumGetFloat8(DirectFunctionCall2(cube_distance,
PointerGetDatum(cube), PointerGetDatum(query)));
break;
case CubeKNNDistanceChebyshev:
retval = DatumGetFloat8(DirectFunctionCall2(distance_chebyshev,
PointerGetDatum(cube), PointerGetDatum(query)));
break;
default:
elog(ERROR, "unrecognized cube strategy number: %d", strategy);
retval = 0; /* keep compiler quiet */
break;
}
}
PG_RETURN_FLOAT8(retval);
@ -1466,7 +1469,7 @@ Datum
cube_ll_coord(PG_FUNCTION_ARGS)
{
NDBOX *c = PG_GETARG_NDBOX(0);
int n = PG_GETARG_INT16(1);
int n = PG_GETARG_INT32(1);
double result;
if (DIM(c) >= n && n > 0)
@ -1483,7 +1486,7 @@ Datum
cube_ur_coord(PG_FUNCTION_ARGS)
{
NDBOX *c = PG_GETARG_NDBOX(0);
int n = PG_GETARG_INT16(1);
int n = PG_GETARG_INT32(1);
double result;
if (DIM(c) >= n && n > 0)
@ -1504,21 +1507,17 @@ Datum
cube_coord(PG_FUNCTION_ARGS)
{
NDBOX *cube = PG_GETARG_NDBOX(0);
int coord = PG_GETARG_INT16(1);
int coord = PG_GETARG_INT32(1);
if ((coord > 0) && (coord <= 2*DIM(cube)))
{
if IS_POINT(cube)
PG_RETURN_FLOAT8( (cube)->x[(coord-1)%DIM(cube)] );
else
PG_RETURN_FLOAT8( (cube)->x[coord-1] );
}
else
{
if (coord <= 0 || coord > 2 * DIM(cube))
ereport(ERROR,
(errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
errmsg("Cube index out of bounds")));
}
(errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
errmsg("cube index %d is out of bounds", coord)));
if (IS_POINT(cube))
PG_RETURN_FLOAT8(cube->x[(coord - 1) % DIM(cube)]);
else
PG_RETURN_FLOAT8(cube->x[coord - 1]);
}
@ -1536,27 +1535,28 @@ Datum
cube_coord_llur(PG_FUNCTION_ARGS)
{
NDBOX *cube = PG_GETARG_NDBOX(0);
int coord = PG_GETARG_INT16(1);
int coord = PG_GETARG_INT32(1);
if ((coord > 0) && (coord <= DIM(cube)))
if (coord <= 0 || coord > 2 * DIM(cube))
ereport(ERROR,
(errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
errmsg("cube index %d is out of bounds", coord)));
if (coord <= DIM(cube))
{
if IS_POINT(cube)
PG_RETURN_FLOAT8( (cube)->x[coord-1] );
if (IS_POINT(cube))
PG_RETURN_FLOAT8(cube->x[coord - 1]);
else
PG_RETURN_FLOAT8( Min((cube)->x[coord-1], (cube)->x[coord-1+DIM(cube)]) );
}
else if ((coord > DIM(cube)) && (coord <= 2*DIM(cube)))
{
if IS_POINT(cube)
PG_RETURN_FLOAT8( (cube)->x[(coord-1)%DIM(cube)] );
else
PG_RETURN_FLOAT8( Max((cube)->x[coord-1], (cube)->x[coord-1-DIM(cube)]) );
PG_RETURN_FLOAT8(Min(cube->x[coord - 1],
cube->x[coord - 1 + DIM(cube)]));
}
else
{
ereport(ERROR,
(errcode(ERRCODE_ARRAY_ELEMENT_ERROR),
errmsg("Cube index out of bounds")));
if (IS_POINT(cube))
PG_RETURN_FLOAT8(cube->x[(coord - 1) % DIM(cube)]);
else
PG_RETURN_FLOAT8(Max(cube->x[coord - 1],
cube->x[coord - 1 - DIM(cube)]));
}
}

14
contrib/cube/expected/cube.out
View File

@ -1458,13 +1458,13 @@ SELECT cube(array[10,20,30], array[40,50,60])->6;
(1 row)
SELECT cube(array[10,20,30], array[40,50,60])->0;
ERROR: Cube index out of bounds
ERROR: cube index 0 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->7;
ERROR: Cube index out of bounds
ERROR: cube index 7 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->-1;
ERROR: Cube index out of bounds
ERROR: cube index -1 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->-6;
ERROR: Cube index out of bounds
ERROR: cube index -6 is out of bounds
SELECT cube(array[10,20,30])->3;
?column?
----------
@ -1478,7 +1478,7 @@ SELECT cube(array[10,20,30])->6;
(1 row)
SELECT cube(array[10,20,30])->-6;
ERROR: Cube index out of bounds
ERROR: cube index -6 is out of bounds
-- "normalized" coordinate access
SELECT cube(array[10,20,30], array[40,50,60])~>1;
?column?
@ -1517,7 +1517,7 @@ SELECT cube(array[40,50,60], array[10,20,30])~>3;
(1 row)
SELECT cube(array[40,50,60], array[10,20,30])~>0;
ERROR: Cube index out of bounds
ERROR: cube index 0 is out of bounds
SELECT cube(array[40,50,60], array[10,20,30])~>4;
?column?
----------
@ -1525,7 +1525,7 @@ SELECT cube(array[40,50,60], array[10,20,30])~>4;
(1 row)
SELECT cube(array[40,50,60], array[10,20,30])~>(-1);
ERROR: Cube index out of bounds
ERROR: cube index -1 is out of bounds
-- Load some example data and build the index
--
CREATE TABLE test_cube (c cube);

14
contrib/cube/expected/cube_1.out
View File

@ -1458,13 +1458,13 @@ SELECT cube(array[10,20,30], array[40,50,60])->6;
(1 row)
SELECT cube(array[10,20,30], array[40,50,60])->0;
ERROR: Cube index out of bounds
ERROR: cube index 0 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->7;
ERROR: Cube index out of bounds
ERROR: cube index 7 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->-1;
ERROR: Cube index out of bounds
ERROR: cube index -1 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->-6;
ERROR: Cube index out of bounds
ERROR: cube index -6 is out of bounds
SELECT cube(array[10,20,30])->3;
?column?
----------
@ -1478,7 +1478,7 @@ SELECT cube(array[10,20,30])->6;
(1 row)
SELECT cube(array[10,20,30])->-6;
ERROR: Cube index out of bounds
ERROR: cube index -6 is out of bounds
-- "normalized" coordinate access
SELECT cube(array[10,20,30], array[40,50,60])~>1;
?column?
@ -1517,7 +1517,7 @@ SELECT cube(array[40,50,60], array[10,20,30])~>3;
(1 row)
SELECT cube(array[40,50,60], array[10,20,30])~>0;
ERROR: Cube index out of bounds
ERROR: cube index 0 is out of bounds
SELECT cube(array[40,50,60], array[10,20,30])~>4;
?column?
----------
@ -1525,7 +1525,7 @@ SELECT cube(array[40,50,60], array[10,20,30])~>4;
(1 row)
SELECT cube(array[40,50,60], array[10,20,30])~>(-1);
ERROR: Cube index out of bounds
ERROR: cube index -1 is out of bounds
-- Load some example data and build the index
--
CREATE TABLE test_cube (c cube);

14
contrib/cube/expected/cube_2.out
View File

@ -1458,13 +1458,13 @@ SELECT cube(array[10,20,30], array[40,50,60])->6;
(1 row)
SELECT cube(array[10,20,30], array[40,50,60])->0;
ERROR: Cube index out of bounds
ERROR: cube index 0 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->7;
ERROR: Cube index out of bounds
ERROR: cube index 7 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->-1;
ERROR: Cube index out of bounds
ERROR: cube index -1 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->-6;
ERROR: Cube index out of bounds
ERROR: cube index -6 is out of bounds
SELECT cube(array[10,20,30])->3;
?column?
----------
@ -1478,7 +1478,7 @@ SELECT cube(array[10,20,30])->6;
(1 row)
SELECT cube(array[10,20,30])->-6;
ERROR: Cube index out of bounds
ERROR: cube index -6 is out of bounds
-- "normalized" coordinate access
SELECT cube(array[10,20,30], array[40,50,60])~>1;
?column?
@ -1517,7 +1517,7 @@ SELECT cube(array[40,50,60], array[10,20,30])~>3;
(1 row)
SELECT cube(array[40,50,60], array[10,20,30])~>0;
ERROR: Cube index out of bounds
ERROR: cube index 0 is out of bounds
SELECT cube(array[40,50,60], array[10,20,30])~>4;
?column?
----------
@ -1525,7 +1525,7 @@ SELECT cube(array[40,50,60], array[10,20,30])~>4;
(1 row)
SELECT cube(array[40,50,60], array[10,20,30])~>(-1);
ERROR: Cube index out of bounds
ERROR: cube index -1 is out of bounds
-- Load some example data and build the index
--
CREATE TABLE test_cube (c cube);

14
contrib/cube/expected/cube_3.out
View File

@ -1458,13 +1458,13 @@ SELECT cube(array[10,20,30], array[40,50,60])->6;
(1 row)
SELECT cube(array[10,20,30], array[40,50,60])->0;
ERROR: Cube index out of bounds
ERROR: cube index 0 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->7;
ERROR: Cube index out of bounds
ERROR: cube index 7 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->-1;
ERROR: Cube index out of bounds
ERROR: cube index -1 is out of bounds
SELECT cube(array[10,20,30], array[40,50,60])->-6;
ERROR: Cube index out of bounds
ERROR: cube index -6 is out of bounds
SELECT cube(array[10,20,30])->3;
?column?
----------
@ -1478,7 +1478,7 @@ SELECT cube(array[10,20,30])->6;
(1 row)
SELECT cube(array[10,20,30])->-6;
ERROR: Cube index out of bounds
ERROR: cube index -6 is out of bounds
-- "normalized" coordinate access
SELECT cube(array[10,20,30], array[40,50,60])~>1;
?column?
@ -1517,7 +1517,7 @@ SELECT cube(array[40,50,60], array[10,20,30])~>3;
(1 row)
SELECT cube(array[40,50,60], array[10,20,30])~>0;
ERROR: Cube index out of bounds
ERROR: cube index 0 is out of bounds
SELECT cube(array[40,50,60], array[10,20,30])~>4;
?column?
----------
@ -1525,7 +1525,7 @@ SELECT cube(array[40,50,60], array[10,20,30])~>4;
(1 row)
SELECT cube(array[40,50,60], array[10,20,30])~>(-1);
ERROR: Cube index out of bounds
ERROR: cube index -1 is out of bounds
-- Load some example data and build the index
--
CREATE TABLE test_cube (c cube);

207
doc/src/sgml/cube.sgml
View File

@ -75,8 +75,8 @@
entered in. The <type>cube</> functions
automatically swap values if needed to create a uniform
<quote>lower left &mdash; upper right</> internal representation.
When corners coincide cube stores only one corner along with a
special flag in order to reduce size wasted.
When the corners coincide, <type>cube</> stores only one corner
along with an <quote>is point</> flag to avoid wasting space.
</para>
<para>
@ -98,17 +98,17 @@
<title>Usage</title>
<para>
The <filename>cube</> module includes a GiST index operator class for
<type>cube</> values.
The operators supported by the GiST operator class are shown in <xref linkend="cube-gist-operators">.
<xref linkend="cube-operators"> shows the operators provided for type
<type>cube</>.
</para>
<table id="cube-gist-operators">
<title>Cube GiST Operators</title>
<tgroup cols="2">
<table id="cube-operators">
<title>Cube Operators</title>
<tgroup cols="3">
<thead>
<row>
<entry>Operator</entry>
<entry>Result</entry>
<entry>Description</entry>
</row>
</thead>
@ -116,36 +116,93 @@
<tbody>
<row>
<entry><literal>a = b</></entry>
<entry><type>boolean</></entry>
<entry>The cubes a and b are identical.</entry>
</row>
<row>
<entry><literal>a &amp;&amp; b</></entry>
<entry><type>boolean</></entry>
<entry>The cubes a and b overlap.</entry>
</row>
<row>
<entry><literal>a @&gt; b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a contains the cube b.</entry>
</row>
<row>
<entry><literal>a &lt;@ b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is contained in the cube b.</entry>
</row>
<row>
<entry><literal>a &lt; b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is less than the cube b.</entry>
</row>
<row>
<entry><literal>a &lt;= b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is less than or equal to the cube b.</entry>
</row>
<row>
<entry><literal>a &gt; b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is greater than the cube b.</entry>
</row>
<row>
<entry><literal>a &gt;= b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is greater than or equal to the cube b.</entry>
</row>
<row>
<entry><literal>a &lt;&gt; b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is not equal to the cube b.</entry>
</row>
<row>
<entry><literal>a -&gt; n</></entry>
<entry>Get n-th coordinate of cube.</entry>
<entry><type>float8</></entry>
<entry>Get <replaceable>n</>-th coordinate of cube (counting from 1).</entry>
</row>
<row>
<entry><literal>a ~&gt; n</></entry>
<entry><type>float8</></entry>
<entry>
Get n-th coordinate in 'normalized' cube representation. Noramlization
means coordinate rearrangement to form (lower left, upper right).
Get <replaceable>n</>-th coordinate in <quote>normalized</> cube
representation, in which the coordinates have been rearranged into
the form <quote>lower left &mdash; upper right</>; that is, the
smaller endpoint along each dimension appears first.
</entry>
</row>
<row>
<entry><literal>a &lt;-&gt; b</></entry>
<entry><type>float8</></entry>
<entry>Euclidean distance between a and b.</entry>
</row>
<row>
<entry><literal>a &lt;#&gt; b</></entry>
<entry><type>float8</></entry>
<entry>Taxicab (L-1 metric) distance between a and b.</entry>
</row>
<row>
<entry><literal>a &lt;=&gt; b</></entry>
<entry><type>float8</></entry>
<entry>Chebyshev (L-inf metric) distance between a and b.</entry>
</row>
</tbody>
</tgroup>
</table>
@ -159,117 +216,49 @@
</para>
<para>
GiST index can be used to retrieve nearest neighbours via several metric
operators. As always any of them can be used as ordinary function.
The scalar ordering operators (<literal>&lt;</>, <literal>&gt;=</>, etc)
do not make a lot of sense for any practical purpose but sorting. 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 <type>cube</>, which can be useful for
example if you would like a UNIQUE constraint on a <type>cube</> column.
</para>
<table id="cube-gistknn-operators">
<title>Cube GiST-kNN Operators</title>
<tgroup cols="2">
<thead>
<row>
<entry>Operator</entry>
<entry>Description</entry>
</row>
</thead>
<tbody>
<row>
<entry><literal>a &lt;-&gt; b</></entry>
<entry>Euclidean distance between a and b</entry>
</row>
<row>
<entry><literal>a &lt;#&gt; b</></entry>
<entry>Taxicab (L-1 metric) distance between a and b</entry>
</row>
<row>
<entry><literal>a &lt;=&gt; b</></entry>
<entry>Chebyshev (L-inf metric) distance between a and b</entry>
</row>
</tbody>
</tgroup>
</table>
<para>
Selection of nearing neigbours can be done in the following way:
The <filename>cube</> module also provides a GiST index operator class for
<type>cube</> values.
A <type>cube</> GiST index can be used to search for values using the
<literal>=</>, <literal>&amp;&amp;</>, <literal>@&gt;</>, and
<literal>&lt;@</> operators in <literal>WHERE</> clauses.
</para>
<para>
In addition, a <type>cube</> GiST index can be used to find nearest
neighbors using the metric operators
<literal>&lt;-&gt;</>, <literal>&lt;#&gt;</>, and
<literal>&lt;=&gt;</> in <literal>ORDER BY</> clauses.
For example, the nearest neighbor of the 3-D point (0.5, 0.5, 0.5)
could be found efficiently with:
<programlisting>
SELECT c FROM test
ORDER BY cube(array[0.5,0.5,0.5])<->c
SELECT c FROM test
ORDER BY cube(array[0.5,0.5,0.5]) <-> c
LIMIT 1;
</programlisting>
</para>
<para>
Also kNN framework allows us to cheat with metrics in order to get results
sorted by selected coodinate directly from the index without extra sorting
step. That technique significantly faster on small values of LIMIT, however
with bigger values of LIMIT planner will switch automatically to standart
index scan and sort.
That behavior can be achieved using coordinate operator
(cube c)~&gt;(int offset).
</para>
The <literal>~&gt;</> 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:
<programlisting>
=> select cube(array[0.41,0.42,0.43])~>2 as coord;
coord
-------
0.42
(1 row)
SELECT c FROM test ORDER BY c ~> 1 LIMIT 5;
</programlisting>
<para>
So using that operator as kNN metric we can obtain cubes sorted by it's
coordinate.
</para>
<para>
To get cubes ordered by first coordinate of lower left corner ascending
one can use the following query:
</para>
And to get 2-D cubes ordered by the first coordinate of the upper right
corner descending:
<programlisting>
SELECT c FROM test ORDER BY c~>1 LIMIT 5;
SELECT c FROM test ORDER BY c ~> 3 DESC LIMIT 5;
</programlisting>
<para>
And to get cubes descending by first coordinate of upper right corner
of 2d-cube:
</para>
<programlisting>
SELECT c FROM test ORDER BY c~>3 DESC LIMIT 5;
</programlisting>
<para>
The standard B-tree operators are also provided, for example
<informaltable>
<tgroup cols="2">
<thead>
<row>
<entry>Operator</entry>
<entry>Description</entry>
</row>
</thead>
<tbody>
<row>
<entry><literal>[a, b] &lt; [c, d]</literal></entry>
<entry>Less than</entry>
</row>
<row>
<entry><literal>[a, b] &gt; [c, d]</literal></entry>
<entry>Greater than</entry>
</row>
</tbody>
</tgroup>
</informaltable>
These operators do not make a lot of sense for any practical
purpose but sorting. These operators first compare (a) to (c),
and if these are equal, compare (b) to (d). That results in
reasonably good sorting in most cases, which is useful if
you want to use ORDER BY with this type.
</para>
<para>