The procedures described thus far let you define new types, new functions, and new operators. However, we cannot yet define an index on a column of a new data type. To do this, we must define an operator class for the new data type. Later in this section, we will illustrate this concept in an example: a new operator class for the B-tree index method that stores and sorts complex numbers in ascending absolute value order.
Operator classes can be grouped into operator families to show the relationships between semantically compatible classes. When only a single data type is involved, an operator class is sufficient, so we'll focus on that case first and then return to operator families.
The pg_am
table contains one
row for every index method (internally known as access method).
Support for regular access to tables is built into PostgreSQL, but all index methods are
described in pg_am
. It is
possible to add a new index access method by writing the
necessary code and then creating an entry in pg_am
— but that is beyond the scope of this
chapter (see
Chapter 61).
The routines for an index method do not directly know
anything about the data types that the index method will
operate on. Instead, an operator
class
identifies the set of operations that the index method needs to
use to work with a particular data type. Operator classes are
so called because one thing they specify is the set of
WHERE
-clause operators that can be
used with an index (i.e., can be converted into an index-scan
qualification). An operator class can also specify some
support function that are needed by
the internal operations of the index method, but do not
directly correspond to any WHERE
-clause operator that can be used with
the index.
It is possible to define multiple operator classes for the same data type and index method. By doing this, multiple sets of indexing semantics can be defined for a single data type. For example, a B-tree index requires a sort ordering to be defined for each data type it works on. It might be useful for a complex-number data type to have one B-tree operator class that sorts the data by complex absolute value, another that sorts by real part, and so on. Typically, one of the operator classes will be deemed most commonly useful and will be marked as the default operator class for that data type and index method.
The same operator class name can be used for several
different index methods (for example, both B-tree and hash
index methods have operator classes named int4_ops
), but each such class is an
independent entity and must be defined separately.
The operators associated with an operator class are
identified by “strategy
numbers”, which serve to identify the semantics
of each operator within the context of its operator class. For
example, B-trees impose a strict ordering on keys, lesser to
greater, and so operators like “less than” and
“greater than or equal
to” are interesting with respect to a B-tree.
Because PostgreSQL allows the
user to define operators, PostgreSQL cannot look at the name of an
operator (e.g., <
or
>=
) and tell what kind of
comparison it is. Instead, the index method defines a set of
“strategies”, which can be thought of as
generalized operators. Each operator class specifies which
actual operator corresponds to each strategy for a particular
data type and interpretation of the index semantics.
The B-tree index method defines five strategies, shown in Table 38.2.
Table 38.2. B-tree Strategies
Operation | Strategy Number |
---|---|
less than | 1 |
less than or equal | 2 |
equal | 3 |
greater than or equal | 4 |
greater than | 5 |
Hash indexes support only equality comparisons, and so they use only one strategy, shown in Table 38.3.
Table 38.3. Hash Strategies
Operation | Strategy Number |
---|---|
equal | 1 |
GiST indexes are more flexible: they do not have a fixed set of strategies at all. Instead, the “consistency” support routine of each particular GiST operator class interprets the strategy numbers however it likes. As an example, several of the built-in GiST index operator classes index two-dimensional geometric objects, providing the “R-tree” strategies shown in Table 38.4. Four of these are true two-dimensional tests (overlaps, same, contains, contained by); four of them consider only the X direction; and the other four provide the same tests in the Y direction.
Table 38.4. GiST Two-Dimensional “R-tree” Strategies
Operation | Strategy Number |
---|---|
strictly left of | 1 |
does not extend to right of | 2 |
overlaps | 3 |
does not extend to left of | 4 |
strictly right of | 5 |
same | 6 |
contains | 7 |
contained by | 8 |
does not extend above | 9 |
strictly below | 10 |
strictly above | 11 |
does not extend below | 12 |
SP-GiST indexes are similar to GiST indexes in flexibility: they don't have a fixed set of strategies. Instead the support routines of each operator class interpret the strategy numbers according to the operator class's definition. As an example, the strategy numbers used by the built-in operator classes for points are shown in Table 38.5.
Table 38.5. SP-GiST Point Strategies
Operation | Strategy Number |
---|---|
strictly left of | 1 |
strictly right of | 5 |
same | 6 |
contained by | 8 |
strictly below | 10 |
strictly above | 11 |
GIN indexes are similar to GiST and SP-GiST indexes, in that they don't have a fixed set of strategies either. Instead the support routines of each operator class interpret the strategy numbers according to the operator class's definition. As an example, the strategy numbers used by the built-in operator class for arrays are shown in Table 38.6.
Table 38.6. GIN Array Strategies
Operation | Strategy Number |
---|---|
overlap | 1 |
contains | 2 |
is contained by | 3 |
equal | 4 |
BRIN indexes are similar to GiST, SP-GiST and GIN indexes in
that they don't have a fixed set of strategies either. Instead
the support routines of each operator class interpret the
strategy numbers according to the operator class's definition.
As an example, the strategy numbers used by the built-in
Minmax
operator classes are shown
in Table 38.7.
Table 38.7. BRIN Minmax Strategies
Operation | Strategy Number |
---|---|
less than | 1 |
less than or equal | 2 |
equal | 3 |
greater than or equal | 4 |
greater than | 5 |
Notice that all the operators listed above return Boolean
values. In practice, all operators defined as index method
search operators must return type boolean
, since they must appear at the top level
of a WHERE
clause to be used with
an index. (Some index access methods also support ordering operators, which typically don't
return Boolean values; that feature is discussed in Section 38.15.7.)
Strategies aren't usually enough information for the system to figure out how to use an index. In practice, the index methods require additional support routines in order to work. For example, the B-tree index method must be able to compare two keys and determine whether one is greater than, equal to, or less than the other. Similarly, the hash index method must be able to compute hash codes for key values. These operations do not correspond to operators used in qualifications in SQL commands; they are administrative routines used by the index methods, internally.
Just as with strategies, the operator class identifies which specific functions should play each of these roles for a given data type and semantic interpretation. The index method defines the set of functions it needs, and the operator class identifies the correct functions to use by assigning them to the “support function numbers” specified by the index method.
B-trees require a comparison support function, and allow two additional support functions to be supplied at the operator class author's option, as shown in Table 38.8. The requirements for these support functions are explained further in Section 63.3.
Table 38.8. B-tree Support Functions
Function | Support Number |
---|---|
Compare two keys and return an integer less than zero, zero, or greater than zero, indicating whether the first key is less than, equal to, or greater than the second | 1 |
Return the addresses of C-callable sort support function(s) (optional) | 2 |
Compare a test value to a base value plus/minus an offset, and return true or false according to the comparison result (optional) | 3 |
Hash indexes require one support function, and allow a second one to be supplied at the operator class author's option, as shown in Table 38.9.
Table 38.9. Hash Support Functions
Function | Support Number |
---|---|
Compute the 32-bit hash value for a key | 1 |
Compute the 64-bit hash value for a key given a 64-bit salt; if the salt is 0, the low 32 bits of the result must match the value that would have been computed by function 1 (optional) | 2 |
GiST indexes have nine support functions, two of which are optional, as shown in Table 38.10. (For more information see Chapter 64.)
Table 38.10. GiST Support Functions
Function | Description | Support Number |
---|---|---|
consistent |
determine whether key satisfies the query qualifier | 1 |
union |
compute union of a set of keys | 2 |
compress |
compute a compressed representation of a key or value to be indexed | 3 |
decompress |
compute a decompressed representation of a compressed key | 4 |
penalty |
compute penalty for inserting new key into subtree with given subtree's key | 5 |
picksplit |
determine which entries of a page are to be moved to the new page and compute the union keys for resulting pages | 6 |
equal |
compare two keys and return true if they are equal | 7 |
distance |
determine distance from key to query value (optional) | 8 |
fetch |
compute original representation of a compressed key for index-only scans (optional) | 9 |
SP-GiST indexes require five support functions, as shown in Table 38.11. (For more information see Chapter 65.)
Table 38.11. SP-GiST Support Functions
Function | Description | Support Number |
---|---|---|
config |
provide basic information about the operator class | 1 |
choose |
determine how to insert a new value into an inner tuple | 2 |
picksplit |
determine how to partition a set of values | 3 |
inner_consistent |
determine which sub-partitions need to be searched for a query | 4 |
leaf_consistent |
determine whether key satisfies the query qualifier | 5 |
GIN indexes have six support functions, three of which are optional, as shown in Table 38.12. (For more information see Chapter 66.)
Table 38.12. GIN Support Functions
Function | Description | Support Number |
---|---|---|
compare |
compare two keys and return an integer less than zero, zero, or greater than zero, indicating whether the first key is less than, equal to, or greater than the second | 1 |
extractValue |
extract keys from a value to be indexed | 2 |
extractQuery |
extract keys from a query condition | 3 |
consistent |
determine whether value matches query condition (Boolean variant) (optional if support function 6 is present) | 4 |
comparePartial |
compare partial key from query and key from index, and return an integer less than zero, zero, or greater than zero, indicating whether GIN should ignore this index entry, treat the entry as a match, or stop the index scan (optional) | 5 |
triConsistent |
determine whether value matches query condition (ternary variant) (optional if support function 4 is present) | 6 |
BRIN indexes have four basic support functions, as shown in Table 38.13; those basic functions may require additional support functions to be provided. (For more information see Section 67.3.)
Table 38.13. BRIN Support Functions
Function | Description | Support Number |
---|---|---|
opcInfo |
return internal information describing the indexed columns' summary data | 1 |
add_value |
add a new value to an existing summary index tuple | 2 |
consistent |
determine whether value matches query condition | 3 |
union |
compute union of two summary tuples | 4 |
Unlike search operators, support functions return whichever data type the particular index method expects; for example in the case of the comparison function for B-trees, a signed integer. The number and types of the arguments to each support function are likewise dependent on the index method. For B-tree and hash the comparison and hashing support functions take the same input data types as do the operators included in the operator class, but this is not the case for most GiST, SP-GiST, GIN, and BRIN support functions.
Now that we have seen the ideas, here is the promised
example of creating a new operator class. (You can find a
working copy of this example in src/tutorial/complex.c
and src/tutorial/complex.sql
in the source
distribution.) The operator class encapsulates operators that
sort complex numbers in absolute value order, so we choose the
name complex_abs_ops
. First, we
need a set of operators. The procedure for defining operators
was discussed in Section 38.13.
For an operator class on B-trees, the operators we require
are:
The least error-prone way to define a related set of comparison operators is to write the B-tree comparison support function first, and then write the other functions as one-line wrappers around the support function. This reduces the odds of getting inconsistent results for corner cases. Following this approach, we first write:
#define Mag(c) ((c)->x*(c)->x + (c)->y*(c)->y) static int complex_abs_cmp_internal(Complex *a, Complex *b) { double amag = Mag(a), bmag = Mag(b); if (amag < bmag) return -1; if (amag > bmag) return 1; return 0; }
Now the less-than function looks like:
PG_FUNCTION_INFO_V1(complex_abs_lt); Datum complex_abs_lt(PG_FUNCTION_ARGS) { Complex *a = (Complex *) PG_GETARG_POINTER(0); Complex *b = (Complex *) PG_GETARG_POINTER(1); PG_RETURN_BOOL(complex_abs_cmp_internal(a, b) < 0); }
The other four functions differ only in how they compare the internal function's result to zero.
Next we declare the functions and the operators based on the functions to SQL:
CREATE FUNCTION complex_abs_lt(complex, complex) RETURNS bool
AS 'filename
', 'complex_abs_lt'
LANGUAGE C IMMUTABLE STRICT;
CREATE OPERATOR < (
leftarg = complex, rightarg = complex, procedure = complex_abs_lt,
commutator = > , negator = >= ,
restrict = scalarltsel, join = scalarltjoinsel
);
It is important to specify the correct commutator and negator operators, as well as suitable restriction and join selectivity functions, otherwise the optimizer will be unable to make effective use of the index.
Other things worth noting are happening here:
There can only be one operator named, say,
=
and taking type
complex
for both operands. In
this case we don't have any other operator =
for complex
,
but if we were building a practical data type we'd
probably want =
to be the
ordinary equality operation for complex numbers (and not
the equality of the absolute values). In that case, we'd
need to use some other operator name for complex_abs_eq
.
Although PostgreSQL
can cope with functions having the same SQL name as long
as they have different argument data types, C can only
cope with one global function having a given name. So we
shouldn't name the C function something simple like
abs_eq
. Usually it's a good
practice to include the data type name in the C function
name, so as not to conflict with functions for other data
types.
We could have made the SQL name of the function
abs_eq
, relying on
PostgreSQL to
distinguish it by argument data types from any other SQL
function of the same name. To keep the example simple, we
make the function have the same names at the C level and
SQL level.
The next step is the registration of the support routine required by B-trees. The example C code that implements this is in the same file that contains the operator functions. This is how we declare the function:
CREATE FUNCTION complex_abs_cmp(complex, complex)
RETURNS integer
AS 'filename
'
LANGUAGE C IMMUTABLE STRICT;
Now that we have the required operators and support routine, we can finally create the operator class:
CREATE OPERATOR CLASS complex_abs_ops DEFAULT FOR TYPE complex USING btree AS OPERATOR 1 < , OPERATOR 2 <= , OPERATOR 3 = , OPERATOR 4 >= , OPERATOR 5 > , FUNCTION 1 complex_abs_cmp(complex, complex);
And we're done! It should now be possible to create and use
B-tree indexes on complex
columns.
We could have written the operator entries more verbosely, as in:
OPERATOR 1 < (complex, complex) ,
but there is no need to do so when the operators take the same data type we are defining the operator class for.
The above example assumes that you want to make this new
operator class the default B-tree operator class for the
complex
data type. If you don't, just
leave out the word DEFAULT
.
So far we have implicitly assumed that an operator class deals with only one data type. While there certainly can be only one data type in a particular index column, it is often useful to index operations that compare an indexed column to a value of a different data type. Also, if there is use for a cross-data-type operator in connection with an operator class, it is often the case that the other data type has a related operator class of its own. It is helpful to make the connections between related classes explicit, because this can aid the planner in optimizing SQL queries (particularly for B-tree operator classes, since the planner contains a great deal of knowledge about how to work with them).
To handle these needs, PostgreSQL uses the concept of an operator family. An operator family contains one or more operator classes, and can also contain indexable operators and corresponding support functions that belong to the family as a whole but not to any single class within the family. We say that such operators and functions are “loose” within the family, as opposed to being bound into a specific class. Typically each operator class contains single-data-type operators while cross-data-type operators are loose in the family.
All the operators and functions in an operator family must have compatible semantics, where the compatibility requirements are set by the index method. You might therefore wonder why bother to single out particular subsets of the family as operator classes; and indeed for many purposes the class divisions are irrelevant and the family is the only interesting grouping. The reason for defining operator classes is that they specify how much of the family is needed to support any particular index. If there is an index using an operator class, then that operator class cannot be dropped without dropping the index — but other parts of the operator family, namely other operator classes and loose operators, could be dropped. Thus, an operator class should be specified to contain the minimum set of operators and functions that are reasonably needed to work with an index on a specific data type, and then related but non-essential operators can be added as loose members of the operator family.
As an example, PostgreSQL
has a built-in B-tree operator family integer_ops
, which includes operator classes
int8_ops
, int4_ops
, and int2_ops
for indexes on bigint
(int8
),
integer
(int4
), and smallint
(int2
) columns respectively. The
family also contains cross-data-type comparison operators
allowing any two of these types to be compared, so that an
index on one of these types can be searched using a comparison
value of another type. The family could be duplicated by these
definitions:
CREATE OPERATOR FAMILY integer_ops USING btree; CREATE OPERATOR CLASS int8_ops DEFAULT FOR TYPE int8 USING btree FAMILY integer_ops AS -- standard int8 comparisons OPERATOR 1 < , OPERATOR 2 <= , OPERATOR 3 = , OPERATOR 4 >= , OPERATOR 5 > , FUNCTION 1 btint8cmp(int8, int8) , FUNCTION 2 btint8sortsupport(internal) , FUNCTION 3 in_range(int8, int8, int8, boolean, boolean) ; CREATE OPERATOR CLASS int4_ops DEFAULT FOR TYPE int4 USING btree FAMILY integer_ops AS -- standard int4 comparisons OPERATOR 1 < , OPERATOR 2 <= , OPERATOR 3 = , OPERATOR 4 >= , OPERATOR 5 > , FUNCTION 1 btint4cmp(int4, int4) , FUNCTION 2 btint4sortsupport(internal) , FUNCTION 3 in_range(int4, int4, int4, boolean, boolean) ; CREATE OPERATOR CLASS int2_ops DEFAULT FOR TYPE int2 USING btree FAMILY integer_ops AS -- standard int2 comparisons OPERATOR 1 < , OPERATOR 2 <= , OPERATOR 3 = , OPERATOR 4 >= , OPERATOR 5 > , FUNCTION 1 btint2cmp(int2, int2) , FUNCTION 2 btint2sortsupport(internal) , FUNCTION 3 in_range(int2, int2, int2, boolean, boolean) ; ALTER OPERATOR FAMILY integer_ops USING btree ADD -- cross-type comparisons int8 vs int2 OPERATOR 1 < (int8, int2) , OPERATOR 2 <= (int8, int2) , OPERATOR 3 = (int8, int2) , OPERATOR 4 >= (int8, int2) , OPERATOR 5 > (int8, int2) , FUNCTION 1 btint82cmp(int8, int2) , -- cross-type comparisons int8 vs int4 OPERATOR 1 < (int8, int4) , OPERATOR 2 <= (int8, int4) , OPERATOR 3 = (int8, int4) , OPERATOR 4 >= (int8, int4) , OPERATOR 5 > (int8, int4) , FUNCTION 1 btint84cmp(int8, int4) , -- cross-type comparisons int4 vs int2 OPERATOR 1 < (int4, int2) , OPERATOR 2 <= (int4, int2) , OPERATOR 3 = (int4, int2) , OPERATOR 4 >= (int4, int2) , OPERATOR 5 > (int4, int2) , FUNCTION 1 btint42cmp(int4, int2) , -- cross-type comparisons int4 vs int8 OPERATOR 1 < (int4, int8) , OPERATOR 2 <= (int4, int8) , OPERATOR 3 = (int4, int8) , OPERATOR 4 >= (int4, int8) , OPERATOR 5 > (int4, int8) , FUNCTION 1 btint48cmp(int4, int8) , -- cross-type comparisons int2 vs int8 OPERATOR 1 < (int2, int8) , OPERATOR 2 <= (int2, int8) , OPERATOR 3 = (int2, int8) , OPERATOR 4 >= (int2, int8) , OPERATOR 5 > (int2, int8) , FUNCTION 1 btint28cmp(int2, int8) , -- cross-type comparisons int2 vs int4 OPERATOR 1 < (int2, int4) , OPERATOR 2 <= (int2, int4) , OPERATOR 3 = (int2, int4) , OPERATOR 4 >= (int2, int4) , OPERATOR 5 > (int2, int4) , FUNCTION 1 btint24cmp(int2, int4) , -- cross-type in_range functions FUNCTION 3 in_range(int4, int4, int8, boolean, boolean) , FUNCTION 3 in_range(int4, int4, int2, boolean, boolean) , FUNCTION 3 in_range(int2, int2, int8, boolean, boolean) , FUNCTION 3 in_range(int2, int2, int4, boolean, boolean) ;
Notice that this definition “overloads” the operator strategy and support function numbers: each number occurs multiple times within the family. This is allowed so long as each instance of a particular number has distinct input data types. The instances that have both input types equal to an operator class's input type are the primary operators and support functions for that operator class, and in most cases should be declared as part of the operator class rather than as loose members of the family.
In a B-tree operator family, all the operators in the family must sort compatibly, as is specified in detail in Section 63.2. For each operator in the family there must be a support function having the same two input data types as the operator. It is recommended that a family be complete, i.e., for each combination of data types, all operators are included. Each operator class should include just the non-cross-type operators and support function for its data type.
To build a multiple-data-type hash operator family, compatible hash support functions must be created for each data type supported by the family. Here compatibility means that the functions are guaranteed to return the same hash code for any two values that are considered equal by the family's equality operators, even when the values are of different types. This is usually difficult to accomplish when the types have different physical representations, but it can be done in some cases. Furthermore, casting a value from one data type represented in the operator family to another data type also represented in the operator family via an implicit or binary coercion cast must not change the computed hash value. Notice that there is only one support function per data type, not one per equality operator. It is recommended that a family be complete, i.e., provide an equality operator for each combination of data types. Each operator class should include just the non-cross-type equality operator and the support function for its data type.
GiST, SP-GiST, and GIN indexes do not have any explicit notion of cross-data-type operations. The set of operators supported is just whatever the primary support functions for a given operator class can handle.
In BRIN, the requirements depends on the framework that
provides the operator classes. For operator classes based on
minmax
, the behavior required is
the same as for B-tree operator families: all the operators in
the family must sort compatibly, and casts must not change the
associated sort ordering.
Prior to PostgreSQL 8.3, there was no concept of operator families, and so any cross-data-type operators intended to be used with an index had to be bound directly into the index's operator class. While this approach still works, it is deprecated because it makes an index's dependencies too broad, and because the planner can handle cross-data-type comparisons more effectively when both data types have operators in the same operator family.
PostgreSQL uses operator classes to infer the properties of operators in more ways than just whether they can be used with indexes. Therefore, you might want to create operator classes even if you have no intention of indexing any columns of your data type.
In particular, there are SQL features such as ORDER BY
and DISTINCT
that require comparison and sorting
of values. To implement these features on a user-defined data
type, PostgreSQL looks for the
default B-tree operator class for the data type. The
“equals”
member of this operator class defines the system's notion of
equality of values for GROUP BY
and DISTINCT
, and the sort
ordering imposed by the operator class defines the default
ORDER BY
ordering.
If there is no default B-tree operator class for a data type, the system will look for a default hash operator class. But since that kind of operator class only provides equality, it is only able to support grouping not sorting.
When there is no default operator class for a data type, you will get errors like “could not identify an ordering operator” if you try to use these SQL features with the data type.
In PostgreSQL versions
before 7.4, sorting and grouping operations would implicitly
use operators named =
,
<
, and >
. The new behavior of relying on default
operator classes avoids having to make any assumption about
the behavior of operators with particular names.
Sorting by a non-default B-tree operator class is possible
by specifying the class's less-than operator in a USING
option, for example
SELECT * FROM mytable ORDER BY somecol USING ~<~;
Alternatively, specifying the class's greater-than operator
in USING
selects a
descending-order sort.
Comparison of arrays of a user-defined type also relies on the semantics defined by the type's default B-tree operator class. If there is no default B-tree operator class, but there is a default hash operator class, then array equality is supported, but not ordering comparisons.
Another SQL feature that requires even more
data-type-specific knowledge is the RANGE
offset
PRECEDING
/FOLLOWING
framing option for window functions
(see Section 4.2.8).
For a query such as
SELECT sum(x) OVER (ORDER BY x RANGE BETWEEN 5 PRECEDING AND 10 FOLLOWING) FROM mytable;
it is not sufficient to know how to order by x
; the database must also understand how to
“subtract
5” or “add 10” to the current row's value of
x
to identify the bounds of the
current window frame. Comparing the resulting bounds to other
rows' values of x
is possible
using the comparison operators provided by the B-tree operator
class that defines the ORDER BY
ordering — but addition and subtraction operators are not part
of the operator class, so which ones should be used?
Hard-wiring that choice would be undesirable, because different
sort orders (different B-tree operator classes) might need
different behavior. Therefore, a B-tree operator class can
specify an in_range support function
that encapsulates the addition and subtraction behaviors that
make sense for its sort order. It can even provide more than
one in_range support function, in case there is more than one
data type that makes sense to use as the offset in RANGE
clauses. If the B-tree operator class
associated with the window's ORDER
BY
clause does not have a matching in_range support
function, the RANGE
offset
PRECEDING
/FOLLOWING
option is not supported.
Another important point is that an equality operator that appears in a hash operator family is a candidate for hash joins, hash aggregation, and related optimizations. The hash operator family is essential here since it identifies the hash function(s) to use.
Some index access methods (currently, only GiST) support the
concept of ordering operators. What
we have been discussing so far are search
operators. A search operator is one for which the index
can be searched to find all rows satisfying WHERE
indexed_column
operator
constant
. Note that nothing is
promised about the order in which the matching rows will be
returned. In contrast, an ordering operator does not restrict
the set of rows that can be returned, but instead determines
their order. An ordering operator is one for which the index
can be scanned to return rows in the order represented by
ORDER BY
indexed_column
operator
constant
. The reason for
defining ordering operators that way is that it supports
nearest-neighbor searches, if the operator is one that measures
distance. For example, a query like
SELECT * FROM places ORDER BY location <-> point '(101,456)' LIMIT 10;
finds the ten places closest to a given target point. A GiST
index on the location column can do this efficiently because
<->
is an ordering
operator.
While search operators have to return Boolean results,
ordering operators usually return some other type, such as
float or numeric for distances. This type is normally not the
same as the data type being indexed. To avoid hard-wiring
assumptions about the behavior of different data types, the
definition of an ordering operator is required to name a B-tree
operator family that specifies the sort ordering of the result
data type. As was stated in the previous section, B-tree
operator families define PostgreSQL's notion of ordering, so this
is a natural representation. Since the point <->
operator returns float8
, it could be specified in an operator
class creation command like this:
OPERATOR 15 <-> (point, point) FOR ORDER BY float_ops
where float_ops
is the built-in
operator family that includes operations on float8
. This declaration states that the index is
able to return rows in order of increasing values of the
<->
operator.
There are two special features of operator classes that we have not discussed yet, mainly because they are not useful with the most commonly used index methods.
Normally, declaring an operator as a member of an operator
class (or family) means that the index method can retrieve
exactly the set of rows that satisfy a WHERE
condition using the operator. For
example:
SELECT * FROM table WHERE integer_column < 4;
can be satisfied exactly by a B-tree index on the integer
column. But there are cases where an index is useful as an
inexact guide to the matching rows. For example, if a GiST
index stores only bounding boxes for geometric objects, then it
cannot exactly satisfy a WHERE
condition that tests overlap between nonrectangular objects
such as polygons. Yet we could use the index to find objects
whose bounding box overlaps the bounding box of the target
object, and then do the exact overlap test only on the objects
found by the index. If this scenario applies, the index is said
to be “lossy” for the operator. Lossy index
searches are implemented by having the index method return a
recheck flag when a row might or
might not really satisfy the query condition. The core system
will then test the original query condition on the retrieved
row to see whether it should be returned as a valid match. This
approach works if the index is guaranteed to return all the
required rows, plus perhaps some additional rows, which can be
eliminated by performing the original operator invocation. The
index methods that support lossy searches (currently, GiST,
SP-GiST and GIN) allow the support functions of individual
operator classes to set the recheck flag, and so this is
essentially an operator-class feature.
Consider again the situation where we are storing in the
index only the bounding box of a complex object such as a
polygon. In this case there's not much value in storing the
whole polygon in the index entry — we might as well store just
a simpler object of type box
. This
situation is expressed by the STORAGE
option in CREATE
OPERATOR CLASS
: we'd write something like:
CREATE OPERATOR CLASS polygon_ops DEFAULT FOR TYPE polygon USING gist AS ... STORAGE box;
At present, only the GiST, GIN and BRIN index methods
support a STORAGE
type that's
different from the column data type. The GiST compress
and decompress
support routines must deal with
data-type conversion when STORAGE
is used. In GIN, the STORAGE
type
identifies the type of the “key” values, which normally is different
from the type of the indexed column — for example, an operator
class for integer-array columns might have keys that are just
integers. The GIN extractValue
and extractQuery
support routines
are responsible for extracting keys from indexed values. BRIN
is similar to GIN: the STORAGE
type identifies the type of the stored summary values, and
operator classes' support procedures are responsible for
interpreting the summary values correctly.