PostgreSQL 7.4.7 Documentation | ||||
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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.

Note:Prior to PostgreSQL release 7.3, it was necessary to make manual additions to the system catalogs`pg_amop`

,`pg_amproc`

, and`pg_opclass`

in order to create a user-defined operator class. That approach is now deprecated in favor of usingCREATE OPERATOR CLASS, which is a much simpler and less error-prone way of creating the necessary catalog entries.

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 method by defining the required interface routines and
then creating a row in `pg_am`

--- but that is
far beyond the scope of this chapter.

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 may also specify some *support
procedures* 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
`oid_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 33-2.

**Table 33-2. 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 express only bitwise equality, and so they use only one strategy, shown in Table 33-3.

R-tree indexes express rectangle-containment relationships. They use eight strategies, shown in Table 33-4.

**Table 33-4. R-tree Strategies**

Operation | Strategy Number |
---|---|

left of | 1 |

left of or overlapping | 2 |

overlapping | 3 |

right of or overlapping | 4 |

right of | 5 |

same | 6 |

contains | 7 |

contained by | 8 |

GiST indexes are even 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.

Note that all strategy operators return Boolean values. In
practice, all operators defined as index method strategies must
return type `boolean`, since they must appear at the top
level of a `WHERE` clause to be used with an index.

By the way, the `amorderstrategy` column
in `pg_am`

tells whether
the index method supports ordered scans. Zero means it doesn't; if it
does, `amorderstrategy` is the strategy
number that corresponds to the ordering operator. For example, B-tree
has `amorderstrategy` = 1, which is its
"less than" strategy number.

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 R-tree index method must be able to compute intersections, unions, and sizes of rectangles. 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".

B-trees require a single support function, shown in Table 33-5.

**Table 33-5. 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 |

Hash indexes likewise require one support function, shown in Table 33-6.

R-tree indexes require three support functions, shown in Table 33-7.

GiST indexes require seven support functions, shown in Table 33-8.

**Table 33-8. GiST Support Functions**

Function | Support Number |
---|---|

consistent | 1 |

union | 2 |

compress | 3 |

decompress | 4 |

penalty | 5 |

picksplit | 6 |

equal | 7 |

Unlike strategy 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.

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 33.11. For an operator class on
B-trees, the operators we require are:

- absolute-value less-than (strategy 1)
- absolute-value less-than-or-equal (strategy 2)
- absolute-value equal (strategy 3)
- absolute-value greater-than-or-equal (strategy 4)
- absolute-value greater-than (strategy 5)

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 '', 'complex_abs_lt' LANGUAGE C IMMUTABLE STRICT; CREATE OPERATOR < ( leftarg = complex, rightarg = complex, procedure = complex_abs_lt, commutator = > , negator = >= , restrict = scalarltsel, join = scalarltjoinsel );filename

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. Note that the less-than, equal, and greater-than cases should use different selectivity functions.

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 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 PostgreSQL name of the function

`abs_eq`, relying on PostgreSQL to distinguish it by argument data types from any other PostgreSQL function of the same name. To keep the example simple, we make the function have the same names at the C level and PostgreSQL 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 '' LANGUAGE C IMMUTABLE STRICT;filename

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`.

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.

Comparison of arrays of user-defined types also relies on the semantics defined by the default B-tree operator class.

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, in practice it is only enough to support array equality.

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.

Note: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.

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 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 an R-tree index stores only
bounding boxes for 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, and we add `RECHECK` to the `OPERATOR` clause
in the `CREATE OPERATOR CLASS` command.
`RECHECK` is valid 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.

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 may 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 index method supports 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.