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# 11. INTERFACING EXTENSIONS TO INDICES

The procedures described thus far let you define a new type, new functions and new operators. However, we cannot yet define a secondary index (such as a B-tree, R-tree or hash access method) over a new type or its operators.

Look back at Figure 3. The right half shows the catalogs that we must modify in order to tell POSTGRES how to use a user-defined type and/or user-defined operators with an index (i.e., `pg_am, pg_amop, pg_amproc` and `pg_opclass`). Unfortunately, there is no simple command to do this. We will demonstrate how to modify these catalogs through a running example: a new operator class for the B-tree access method that sorts integers in ascending absolute value order.

The `pg_am` class contains one instance for every user defined access method. Support for the heap access method is built into POSTGRES, but every other access method is described here. The schema is

amname | name of the access method
| amowner | object id of the owner's instance in pg_user
amkind | not used at present, but set to 'o' as a place holder
amstrategies | number of strategies for this access method (see below)
amsupport | number of support routines for this access method (see below)
amgettuple aminsert ... | procedure identifiers for interface routines to the access method. For example, regproc ids for opening, closing, and getting instances from the access method appear here.

The object ID of the instance in `pg_am` is used as a foreign key in lots of other classes. You don't need to add a new instance to this class; all you're interested in is the object ID of the access method instance you want to extend:

             SELECT oid FROM pg_am WHERE amname = 'btree'

             +----+
             |oid |
             +----+
             |403 |
             +----+

The `amstrategies` attribute exists to standardize comparisons across data types. For example, B-trees impose a strict ordering on keys, lesser to greater. Since POSTGRES allows the user to define operators, POSTGRES cannot look at the name of an operator (eg, > or <) and tell what kind of comparison it is. In fact, some access methods don't impose any ordering at all. For example, R-trees express a rectangle-containment relationship, whereas a hashed data structure expresses only bitwise similarity based on the value of a hash function. POSTGRES needs some consistent way of taking a qualification in your query, looking at the operator and then deciding if a usable index exists. This implies that POSTGRES needs to know, for example, that the <= and > operators partition a B-tree. POSTGRES uses strategies to express these relationships between operators and the way they can be used to scan indices.

Defining a new set of strategies is beyond the scope of this discussion, but we'll explain how B-tree strategies work because you'll need to know that to add a new operator class. In the `pg_am` class, the amstrategies attribute is the number of strategies defined for this access method. For B-trees, this number is 5. These strategies correspond to

less than | 1
less than or equal | 2
equal | 3
greater than or equal | 4
greater than | 5

The idea is that you'll need to add procedures corresponding to the comparisons above to the `pg_amop` relation (see below). The access method code can use these strategy numbers, regardless of data type, to figure out how to partition the B-tree, compute selectivity, and so on. Don't worry about the details of adding procedures yet; just understand that there must be a set of these procedures for `int2, int4, oid,` and every other data type on which a B-tree can operate.

Sometimes, strategies aren't enough information for the system to figure out how to use an index. Some access methods require other support routines in order to work. For example, the B-tree access 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 access method must be able to compute intersections, unions, and sizes of rectangles. These operations do not correspond to user qualifications in SQL queries; they are administrative routines used by the access methods, internally.

In order to manage diverse support routines consistently across all POSTGRES access methods, `pg_am` includes an attribute called `amsupport`. This attribute records the number of support routines used by an access method. For B-trees, this number is one -- the routine to take two keys and return -1, 0, or +1, depending on whether the first key is less than, equal to, or greater than the second.[8]

The `amstrategies` entry in pg_am is just the number of strategies defined for the access method in question. The procedures for less than, less equal, and so on don't appear in `pg_am`. Similarly, `amsupport` is just the number of support routines required by the access method. The actual routines are listed elsewhere.

The next class of interest is pg_opclass. This class exists only to associate a name with an oid. In pg_amop, every B-tree operator class has a set of procedures, one through five, above. Some existing opclasses are `int2_ops, int4_ops, and oid_ops`. You need to add an instance with your opclass name (for example, `complex_abs_ops`) to `pg_opclass`. The `oid` of this instance is a foreign key in other classes.

             INSERT INTO pg_opclass (opcname) VALUES ('complex_abs_ops');

             SELECT oid, opcname
               FROM pg_opclass
               WHERE opcname = 'complex_abs_ops';

             +------+--------------+
             |oid   | opcname      |
             +------+--------------+
             |17314 | int4_abs_ops |
             +------+--------------+

Note that the oid for your `pg_opclass` instance will be different! You should substitute your value for 17314 wherever it appears in this discussion.

So now we have an access method and an operator class. We still need a set of operators; the procedure for defining operators was discussed earlier in this manual. For the complex_abs_ops operator class on Btrees, the operators we require are:

             absolute value less-than
             absolute value less-than-or-equal
             absolute value equal
             absolute value greater-than-or-equal
             absolute value greater-than

Suppose the code that implements the functions defined is stored in the file

             /usr/local/postgres95/src/tutorial/complex.c

Part of the code look like this: (note that we will only show the equality operator for the rest of the examples. The other four operators are very similar. Refer to `complex.c` or `complex.sql` for the details.)

             #define Mag(c) ((c)->x*(c)->x + (c)->y*(c)->y)

             bool
             complex_abs_eq(Complex *a, Complex *b)
             {
                 double amag = Mag(a), bmag = Mag(b);
                 return (amag==bmag);
             }

There are a couple of important things that are happening below.

First, note that operators for less-than, less-than-or equal, equal, greater-than-or-equal, and greater-than for `int4` are being defined. All of these operators are already defined for `int4` under the names <, <=, =, >=, and >. The new operators behave differently, of course. In order to guarantee that POSTGRES uses these new operators rather than the old ones, they need to be named differently from the old ones. This is a key point: you can overload operators in POSTGRES, but only if the operator isn't already defined for the argument types. That is, if you have < defined for (int4, int4), you can't define it again. POSTGRES does not check this when you define your operator, so be careful. To avoid this problem, odd names will be used for the operators. If you get this wrong, the access methods are likely to crash when you try to do scans.

The other important point is that all the operator functions return Boolean values. The access methods rely on this fact. (On the other hand, the support function returns whatever the particular access method expects -- in this case, a signed integer.) The final routine in the file is the "support routine" mentioned when we discussed the amsupport attribute of the `pg_am` class. We will use this later on. For now, ignore it.

             CREATE FUNCTION complex_abs_eq(complex, complex)
                  RETURNS bool
                  AS '/usr/local/postgres95/tutorial/obj/complex.so'
                  LANGUAGE 'c';

Now define the operators that use them. As noted, the operator names must be unique among all operators that take two `int4` operands. In order to see if the operator names listed below are taken, we can do a query on `pg_operator`:

             /*
              * this query uses the regular expression operator (~)
              * to find three-character operator names that end in
              * the character &
              */
             SELECT *
             FROM pg_operator
             WHERE oprname ~ '^..&$'::text;

to see if your name is taken for the types you want. The important things here are the procedure (which are the C functions defined above) and the restriction and join selectivity functions. You should just use the ones used below--note that there are different such functions for the less-than, equal, and greater-than cases. These must be supplied, or the access method will crash when it tries to use the operator. You should copy the names for restrict and join, but use the procedure names you defined in the last step.

             CREATE OPERATOR = (
                leftarg = complex, rightarg = complex, procedure = complex_abs_eq,
                restrict = eqsel, join = eqjoinsel
             )

Notice that five operators corresponding to less, less equal, equal, greater, and greater equal are defined.

We're just about finished. the last thing we need to do is to update the `pg_amop` relation. To do this, we need the following attributes:

amopid | the `oid` of the `pg_am` instance for B-tree (== 403, see above)
amopclaid | the `oid` of the `pg_opclass` instance for `int4_abs_ops` (== whatever you got instead of `17314`, see above)
amopopr | the `oid`s of the operators for the opclass (which we'll get in just a minute)
amopselect, amopnpages | cost functions.

The cost functions are used by the query optimizer to decide whether or not to use a given index in a scan. Fortunately, these already exist. The two functions we'll use are `btreesel`, which estimates the selectivity of the B-tree, and `btreenpage`, which estimates the number of pages a search will touch in the tree.

So we need the `oid`s of the operators we just defined. We'll look up the names of all the operators that take two `int4`s, and pick ours out:

             SELECT o.oid AS opoid, o.oprname
             INTO TABLE complex_ops_tmp
             FROM pg_operator o, pg_type t
             WHERE o.oprleft = t.oid and o.oprright = t.oid
                  and t.typname = 'complex';

         which returns:

             +------+---------+
             |oid   | oprname |
             +------+---------+
             |17321 | <       |
             +------+---------+
             |17322 | <=      |
             +------+---------+
             |17323 |  =      |
             +------+---------+
             |17324 | >=      |
             +------+---------+
             |17325 | >       |
             +------+---------+

(Again, some of your `oid` numbers will almost certainly be different.) The operators we are interested in are those with `oid`s 17321 through 17325. The values you get will probably be different, and you should substitute them for the values below. We can look at the operator names and pick out the ones we just added.

Now we're ready to update `pg_amop` with our new operator class. The most important thing in this entire discussion is that the operators are ordered, from less equal through greater equal, in `pg_amop`. We add the instances we need:

              INSERT INTO pg_amop (amopid, amopclaid, amopopr, amopstrategy,
                                  amopselect, amopnpages)
                  SELECT am.oid, opcl.oid, c.opoid, 3,
                     'btreesel'::regproc, 'btreenpage'::regproc
                  FROM pg_am am, pg_opclass opcl, complex_ops_tmp c
                  WHERE amname = 'btree' and opcname = 'complex_abs_ops'
                     and c.oprname = '=';

Note the order: "less than" is 1, "less than or equal" is 2, "equal" is 3, "greater than or equal" is 4, and "greater than" is 5.

The last step (finally!) is registration of the "support routine" previously described in our discussion of `pg_am`. The `oid` of this support routine is stored in the `pg_amproc` class, keyed by the access method `oid` and the operator class `oid`. First, we need to register the function in POSTGRES (recall that we put the C code that implements this routine in the bottom of the file in which we implemented the operator routines):

             CREATE FUNCTION int4_abs_cmp(int4, int4)
                   RETURNS int4
                   AS '/usr/local/postgres95/tutorial/obj/complex.so'
                   LANGUAGE 'c';

             SELECT oid, proname FROM pg_proc WHERE prname = 'int4_abs_cmp';

             +------+--------------+
             |oid   | proname      |
             +------+--------------+
             |17328 | int4_abs_cmp |
             +------+--------------+

(Again, your `oid` number will probably be different and you should substitute the value you see for the value below.) Recalling that the B-tree instance's oid is 403 and that of `int4_abs_ops` is 17314, we can add the new instance as follows:

             INSERT INTO pg_amproc (amid, amopclaid, amproc, amprocnum)
                  VALUES ('403'::oid,        -- btree oid
                          '17314'::oid,      --  pg_opclass tuple
                          '17328'::oid,      -- new pg_proc oid
                          '1'::int2);

[8] Strictly speaking, this routine can return a negative number (< 0), 0, or a non-zero positive number (> 0).

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