postgresql/doc/src/sgml/xindex.sgml

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Postgres documentation
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 <chapter id="xindex">
  <title>Interfacing Extensions To Indices</title>

  <para>
   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 <acronym>B-tree</acronym>, <acronym>R-tree</acronym> or
   hash access method) over a new type or its operators.
  </para>

  <para>
   Look back at
   <xref endterm="EXTEND-CATALOGS" linkend="EXTEND-CATALOGS">.
   The right half shows the  catalogs  that we must modify in order to tell
   <productname>Postgres</productname> how to use a user-defined type and/or
   user-defined  operators with an index (i.e., <filename>pg_am, pg_amop,
    pg_amproc, pg_operator</filename> and <filename>pg_opclass</filename>).
   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 <acronym>B-tree</acronym> access method that stores and
   sorts complex numbers in ascending absolute value order.
  </para>

  <para>
   The <filename>pg_am</filename> class contains one instance for every user
   defined access method.  Support for the heap access method is built into
   <productname>Postgres</productname>, but every other access method is
   described here.  The schema is

   <table tocentry="1">
    <title>Index Schema</title>
    <titleabbrev>Indices</titleabbrev>
    <tgroup cols="2">
     <thead>
      <row>
       <entry>Attribute</entry>
       <entry>Description</entry>
      </row>
     </thead>
     <tbody>
      <row>
       <entry>amname</entry>
       <entry>name of the access method</entry>
      </row>
      <row>
       <entry>amowner</entry>
       <entry>object id of the owner's instance in pg_user</entry>
      </row>
      <row>
       <entry>amstrategies</entry>
       <entry>number of strategies for this access method (see below)</entry>
      </row>
      <row>
       <entry>amsupport</entry>
       <entry>number of support routines for this access method (see below)</entry>
      </row>
      <row>
       <entry>amorderstrategy</entry>
       <entry>zero if the index offers no sort order, otherwise the strategy
        number of the strategy operator that describes the sort order</entry>
      </row>
      <row>
       <entry>amgettuple</entry>
      </row>
      <row>
       <entry>aminsert</entry>
      </row>
      <row>
       <entry>...</entry>
       <entry>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.</entry>
      </row>
     </tbody>
    </tgroup>
   </table>
  </para>

  <para>
   The <acronym>object ID</acronym> of the instance in
   <filename>pg_am</filename> 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 <acronym>object ID</acronym> of the access
   method instance you want to extend:

   <programlisting>
SELECT oid FROM pg_am WHERE amname = 'btree';

 oid
-----
 403
(1 row)
   </programlisting>

   We will use that <command>SELECT</command> in a <command>WHERE</command>
   clause later.
  </para>

  <para>
   The <filename>amstrategies</filename> attribute exists to standardize
   comparisons across data types.  For example, <acronym>B-tree</acronym>s
   impose a strict ordering on keys, lesser to greater.  Since
   <productname>Postgres</productname> allows the user to define operators,
   <productname>Postgres</productname> 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,
   <acronym>R-tree</acronym>s express a rectangle-containment relationship,
   whereas a hashed data structure expresses only bitwise similarity based
   on the value of a hash function.  <productname>Postgres</productname>
   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 <productname>Postgres</productname> needs to know, for
   example, that the  "<="  and  ">" operators partition a
   <acronym>B-tree</acronym>.  <productname>Postgres</productname>
   uses strategies to express these relationships  between
   operators and the way they can be used to scan indices.
  </para>

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

   <table tocentry="1">
    <title>B-tree Strategies</title>
    <titleabbrev>B-tree</titleabbrev>
    <tgroup cols="2">
     <thead>
      <row>
       <entry>Operation</entry>
       <entry>Index</entry>
      </row>
     </thead>
     <tbody>
      <row>
       <entry>less than</entry>
       <entry>1</entry>
      </row>
      <row>
       <entry>less than or equal</entry>
       <entry>2</entry>
      </row>
      <row>
       <entry>equal</entry>
       <entry>3</entry>
      </row>
      <row>
       <entry>greater than or equal</entry>
       <entry>4</entry>
      </row>
      <row>
       <entry>greater than</entry>
       <entry>5</entry>
      </row>
     </tbody>
    </tgroup>
   </table>
  </para>

  <para>
   The idea is that you'll need to add procedures corresponding to the
   comparisons above to the <filename>pg_amop</filename> relation (see below).
   The access method code can use these strategy numbers, regardless of data
   type, to figure out how to partition the <acronym>B-tree</acronym>,
   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 <filename>int2, int4, oid,</filename> and every other
   data type on which a <acronym>B-tree</acronym> can operate.
  </para>

  <para>
   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 <acronym>B-tree</acronym>
   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
   <acronym>R-tree</acronym> 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.
  </para>

  <para>
   In order to manage diverse support routines consistently across all
   <productname>Postgres</productname> access methods,
   <filename>pg_am</filename> includes an attribute called
   <filename>amsupport</filename>.  This attribute records the number of
   support routines used by an access method.  For <acronym>B-tree</acronym>s,
   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.

   <note>
    <para>
     Strictly  speaking, this routine can return a negative
     number (< 0), 0, or a non-zero positive number (> 0).
    </para>
   </note>
  </para>

  <para>
   The <filename>amstrategies</filename> entry in <filename>pg_am</filename>
   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
   <filename>pg_am</filename>.  Similarly, <filename>amsupport</filename>
   is just the number of support routines required by  the  access
   method.  The actual routines are listed elsewhere.
  </para>

  <para>
   By the way, the <filename>amorderstrategy</filename> entry tells whether
   the access method supports ordered scan.  Zero means it doesn't; if it
   does, <filename>amorderstrategy</filename> is the number of the strategy
   routine that corresponds to the ordering operator.  For example, btree
   has <filename>amorderstrategy</filename> = 1 which is its
   "less than" strategy number.
  </para>

  <para>
   The next class of interest is <filename>pg_opclass</filename>.  This class
   exists only to associate an operator class name and perhaps a default type
   with an operator class oid. Some existing opclasses are <filename>int2_ops,
   int4_ops,</filename> and <filename>oid_ops</filename>.  You need to add an
   instance with your opclass name (for example,
   <filename>complex_abs_ops</filename>) to
   <filename>pg_opclass</filename>.  The <filename>oid</filename> of
   this instance will be a foreign key in other classes, notably
   <filename>pg_amop</filename>.

   <programlisting>
INSERT INTO pg_opclass (opcname, opcdeftype)
    SELECT 'complex_abs_ops', oid FROM pg_type WHERE typname = 'complex';

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

  oid   |     opcname     | opcdeftype
--------+-----------------+------------
 277975 | complex_abs_ops |     277946
(1 row)
   </programlisting>

   Note that the oid for your <filename>pg_opclass</filename> instance will
   be different!  Don't worry about this though.  We'll get this number
   from the system later just like we got the oid of the type here.
  </para>

  <para>
   The above example assumes that you want to make this new opclass the
   default index opclass for the <filename>complex</filename> datatype.
   If you don't, just insert zero into <filename>opcdeftype</filename>,
   rather than inserting the datatype's oid:

   <programlisting>
INSERT INTO pg_opclass (opcname, opcdeftype) VALUES ('complex_abs_ops', 0);
   </programlisting>

  </para>

  <para>
   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  <filename>complex_abs_ops</filename>  operator  class on Btrees,
   the operators we require are:

   <programlisting>
        absolute value less-than
        absolute value less-than-or-equal
        absolute value equal
        absolute value greater-than-or-equal
        absolute value greater-than
   </programlisting>
  </para>

  <para>
   Suppose the code that implements the functions  defined
   is stored in the file
   <filename>PGROOT/src/tutorial/complex.c</filename>
  </para>

  <para>
   Part of the C code looks 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 <filename>complex.c</filename>
   or <filename>complex.source</filename> for the details.)

   <programlisting>
#define Mag(c) ((c)-&gt;x*(c)-&gt;x + (c)-&gt;y*(c)-&gt;y)

         bool
         complex_abs_eq(Complex *a, Complex *b)
         {
             double amag = Mag(a), bmag = Mag(b);
             return (amag==bmag);
         }
   </programlisting>
  </para>

  <para>
   We make the function known to Postgres like this:
   <programlisting>
CREATE FUNCTION complex_abs_eq(complex, complex)
              RETURNS bool
              AS 'PGROOT/tutorial/obj/complex.so'
              LANGUAGE 'c';
   </programlisting>
  </para>

  <para>
   There are some important things that are happening here.
  </para>

  <para>
   First, note that operators for less-than, less-than-or-equal, equal,
   greater-than-or-equal, and greater-than for <filename>complex</filename>
   are being defined.  We can only have one operator named, say, = and
   taking type <filename>complex</filename> for both operands.  In this case
   we don't have any other operator = for <filename>complex</filename>,
   but if we were building a practical datatype we'd probably want = to
   be the ordinary equality operation for complex numbers.  In that case,
   we'd need to use some other operator name for complex_abs_eq.
  </para>

  <para>
   Second, although Postgres can cope with operators having
   the same name as long as they have different input datatypes, C can only
   cope with one global routine having a given name, period.  So we shouldn't
   name the C function something simple like <filename>abs_eq</filename>.
   Usually it's a good practice to include the datatype name in the C
   function name, so as not to conflict with functions for other datatypes.
  </para>

  <para>
   Third, we could have made the Postgres name of the function
   <filename>abs_eq</filename>, relying on Postgres to distinguish it
   by input datatypes from any other Postgres function of the same name.
   To keep the example simple, we make the function have the same names
   at the C level and Postgres level.
  </para>

  <para>
   Finally, note that these 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 <filename>pg_am</filename> class.  We will use this
   later on.  For now, ignore it.
  </para>

  <para>
   Now we are ready to define the operators:

   <programlisting>
CREATE OPERATOR = (
     leftarg = complex, rightarg = complex,
     procedure = complex_abs_eq,
     restrict = eqsel, join = eqjoinsel
         )
   </programlisting>

   The important
   things here are the procedure names (which are the <acronym>C</acronym>
   functions defined above) and the restriction and join selectivity
   functions.  You should just use the selectivity functions used in
   the example (see <filename>complex.source</filename>).
   Note that there
   are different such functions for the less-than, equal, and greater-than
   cases.  These must be supplied, or the optimizer will be unable to
   make effective use of the index.
  </para>

  <para>
   The next step is to add entries for these operators to
   the <filename>pg_amop</filename> relation.  To do this,
   we'll need the <filename>oid</filename>s of the operators we just
   defined.  We'll look up the names of all the operators that take
   two <filename>complex</filename>es, and pick ours out:
   
   <programlisting>
    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';

 opoid  | oprname
--------+---------
 277963 | +
 277970 | &lt;
 277971 | &lt;=
 277972 | =
 277973 | &gt;=
 277974 | &gt;
(6 rows)
   </programlisting>

   (Again, some of your <filename>oid</filename> numbers will almost
   certainly be different.)  The operators we are interested in are those
   with <filename>oid</filename>s 277970 through 277974.  The values you
   get will probably be different, and you should substitute them for the
   values below.  We will do this with a select statement.
  </para>

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

   <programlisting>
    INSERT INTO pg_amop (amopid, amopclaid, amopopr, amopstrategy)
        SELECT am.oid, opcl.oid, c.opoid, 1
        FROM pg_am am, pg_opclass opcl, complex_ops_tmp c
        WHERE amname = 'btree' AND
            opcname = 'complex_abs_ops' AND
            c.oprname = '<';
   </programlisting>

   Now do this for the other operators substituting for the "1" in the
   third line above and the "<" in the last line.  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.
  </para>

  <para>
   The next step is registration of the "support routine" previously
   described in our discussion of <filename>pg_am</filename>.  The
   <filename>oid</filename> of this support routine is stored in the
   <filename>pg_amproc</filename> class, keyed by the access method
   <filename>oid</filename> and the operator class <filename>oid</filename>.
   First, we need to register the function in
   <productname>Postgres</productname> (recall that we put the
   <acronym>C</acronym> code that implements this routine in the bottom of
   the file in which we implemented the operator routines):

   <programlisting>
    CREATE FUNCTION complex_abs_cmp(complex, complex)
     RETURNS int4
     AS 'PGROOT/tutorial/obj/complex.so'
     LANGUAGE 'c';

    SELECT oid, proname FROM pg_proc
     WHERE proname = 'complex_abs_cmp';

  oid   |     proname
--------+-----------------
 277997 | complex_abs_cmp
(1 row)
   </programlisting>

   (Again, your <filename>oid</filename> number will probably be different.)
   We can add the new instance as follows:

   <programlisting>
    INSERT INTO pg_amproc (amid, amopclaid, amproc, amprocnum)
        SELECT a.oid, b.oid, c.oid, 1
            FROM pg_am a, pg_opclass b, pg_proc c
            WHERE a.amname = 'btree' AND
                b.opcname = 'complex_abs_ops' AND
                c.proname = 'complex_abs_cmp';
   </programlisting>
  </para>

  <para>
   And we're done!  (Whew.)  It should now be possible to create
   and use btree indexes on <filename>complex</filename> columns.
  </para>

 </chapter>

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