<!-- doc/src/sgml/indices.sgml -->

<chapter id="indexes">
 <title>Indexes</title>

 <indexterm zone="indexes">
  <primary>index</primary>
 </indexterm>

 <para>
  Indexes are a common way to enhance database performance.  An index
  allows the database server to find and retrieve specific rows much
  faster than it could do without an index.  But indexes also add
  overhead to the database system as a whole, so they should be used
  sensibly.
 </para>


 <sect1 id="indexes-intro">
  <title>Introduction</title>

  <para>
   Suppose we have a table similar to this:
<programlisting>
CREATE TABLE test1 (
    id integer,
    content varchar
);
</programlisting>
   and the application issues many queries of the form:
<programlisting>
SELECT content FROM test1 WHERE id = <replaceable>constant</replaceable>;
</programlisting>
   With no advance preparation, the system would have to scan the entire
   <structname>test1</structname> table, row by row, to find all
   matching entries.  If there are many rows in
   <structname>test1</structname> and only a few rows (perhaps zero
   or one) that would be returned by such a query, this is clearly an
   inefficient method.  But if the system has been instructed to maintain an
   index on the <structfield>id</structfield> column, it can use a more
   efficient method for locating matching rows.  For instance, it
   might only have to walk a few levels deep into a search tree.
  </para>

  <para>
   A similar approach is used in most non-fiction books:  terms and
   concepts that are frequently looked up by readers are collected in
   an alphabetic index at the end of the book.  The interested reader
   can scan the index relatively quickly and flip to the appropriate
   page(s), rather than having to read the entire book to find the
   material of interest.  Just as it is the task of the author to
   anticipate the items that readers are likely to look up,
   it is the task of the database programmer to foresee which indexes
   will be useful.
  </para>

  <para>
   The following command can be used to create an index on the
   <structfield>id</structfield> column, as discussed:
<programlisting>
CREATE INDEX test1_id_index ON test1 (id);
</programlisting>
   The name <structname>test1_id_index</structname> can be chosen
   freely, but you should pick something that enables you to remember
   later what the index was for.
  </para>

  <para>
   To remove an index, use the <command>DROP INDEX</command> command.
   Indexes can be added to and removed from tables at any time.
  </para>

  <para>
   Once an index is created, no further intervention is required: the
   system will update the index when the table is modified, and it will
   use the index in queries when it thinks doing so would be more efficient
   than a sequential table scan.  But you might have to run the
   <command>ANALYZE</command> command regularly to update
   statistics to allow the query planner to make educated decisions.
   See <xref linkend="performance-tips"> for information about
   how to find out whether an index is used and when and why the
   planner might choose <emphasis>not</emphasis> to use an index.
  </para>

  <para>
   Indexes can also benefit <command>UPDATE</command> and
   <command>DELETE</command> commands with search conditions.
   Indexes can moreover be used in join searches.  Thus,
   an index defined on a column that is part of a join condition can
   also significantly speed up queries with joins.
  </para>

  <para>
   Creating an index on a large table can take a long time.  By default,
   <productname>PostgreSQL</productname> allows reads (<command>SELECT</command> statements) to occur
   on the table in parallel with index creation, but writes (<command>INSERT</command>,
   <command>UPDATE</command>, <command>DELETE</command>) are blocked until the index build is finished.
   In production environments this is often unacceptable.
   It is possible to allow writes to occur in parallel with index
   creation, but there are several caveats to be aware of &mdash;
   for more information see <xref linkend="SQL-CREATEINDEX-CONCURRENTLY"
   endterm="SQL-CREATEINDEX-CONCURRENTLY-title">.
  </para>

  <para>
   After an index is created, the system has to keep it synchronized with the
   table.  This adds overhead to data manipulation operations.
   Therefore indexes that are seldom or never used in queries
   should be removed.
  </para>
 </sect1>


 <sect1 id="indexes-types">
  <title>Index Types</title>

  <para>
   <productname>PostgreSQL</productname> provides several index types:
   B-tree, Hash, GiST, SP-GiST, GIN and BRIN.
   Each index type uses a different
   algorithm that is best suited to different types of queries.
   By default, the <command>CREATE INDEX</command> command creates
   B-tree indexes, which fit the most common situations.
  </para>

  <para>
   <indexterm>
    <primary>index</primary>
    <secondary>B-tree</secondary>
   </indexterm>
   <indexterm>
    <primary>B-tree</primary>
    <see>index</see>
   </indexterm>
   B-trees can handle equality and range queries on data that can be sorted
   into some ordering.
   In particular, the <productname>PostgreSQL</productname> query planner
   will consider using a B-tree index whenever an indexed column is
   involved in a comparison using one of these operators:

   <simplelist>
    <member><literal>&lt;</literal></member>
    <member><literal>&lt;=</literal></member>
    <member><literal>=</literal></member>
    <member><literal>&gt;=</literal></member>
    <member><literal>&gt;</literal></member>
   </simplelist>

   Constructs equivalent to combinations of these operators, such as
   <literal>BETWEEN</> and <literal>IN</>, can also be implemented with
   a B-tree index search.  Also, an <literal>IS NULL</> or <literal>IS NOT
   NULL</> condition on an index column can be used with a B-tree index.
  </para>

  <para>
   The optimizer can also use a B-tree index for queries involving the
   pattern matching operators <literal>LIKE</> and <literal>~</literal>
   <emphasis>if</emphasis> the pattern is a constant and is anchored to
   the beginning of the string &mdash; for example, <literal>col LIKE
   'foo%'</literal> or <literal>col ~ '^foo'</literal>, but not
   <literal>col LIKE '%bar'</literal>. However, if your database does not
   use the C locale you will need to create the index with a special
   operator class to support indexing of pattern-matching queries; see
   <xref linkend="indexes-opclass"> below. It is also possible to use
   B-tree indexes for <literal>ILIKE</literal> and
   <literal>~*</literal>, but only if the pattern starts with
   non-alphabetic characters, i.e., characters that are not affected by
   upper/lower case conversion.
  </para>

  <para>
   B-tree indexes can also be used to retrieve data in sorted order.
   This is not always faster than a simple scan and sort, but it is
   often helpful.
  </para>

  <para>
   <indexterm>
    <primary>index</primary>
    <secondary>hash</secondary>
   </indexterm>
   <indexterm>
    <primary>hash</primary>
    <see>index</see>
   </indexterm>
   Hash indexes can only handle simple equality comparisons.
   The query planner will consider using a hash index whenever an
   indexed column is involved in a comparison using the
   <literal>=</literal> operator.
   The following command is used to create a hash index:
<synopsis>
CREATE INDEX <replaceable>name</replaceable> ON <replaceable>table</replaceable> USING HASH (<replaceable>column</replaceable>);
</synopsis>
  </para>

  <caution>
   <para>
    Hash index operations are not presently WAL-logged,
    so hash indexes might need to be rebuilt with <command>REINDEX</>
    after a database crash if there were unwritten changes.
    Also, changes to hash indexes are not replicated over streaming or
    file-based replication after the initial base backup, so they
    give wrong answers to queries that subsequently use them.
    For these reasons, hash index use is presently discouraged.
   </para>
  </caution>

  <para>
   <indexterm>
    <primary>index</primary>
    <secondary>GiST</secondary>
   </indexterm>
   <indexterm>
    <primary>GiST</primary>
    <see>index</see>
   </indexterm>
   GiST indexes are not a single kind of index, but rather an infrastructure
   within which many different indexing strategies can be implemented.
   Accordingly, the particular operators with which a GiST index can be
   used vary depending on the indexing strategy (the <firstterm>operator
   class</>).  As an example, the standard distribution of
   <productname>PostgreSQL</productname> includes GiST operator classes
   for several two-dimensional geometric data types, which support indexed
   queries using these operators:

   <simplelist>
    <member><literal>&lt;&lt;</literal></member>
    <member><literal>&amp;&lt;</literal></member>
    <member><literal>&amp;&gt;</literal></member>
    <member><literal>&gt;&gt;</literal></member>
    <member><literal>&lt;&lt;|</literal></member>
    <member><literal>&amp;&lt;|</literal></member>
    <member><literal>|&amp;&gt;</literal></member>
    <member><literal>|&gt;&gt;</literal></member>
    <member><literal>@&gt;</literal></member>
    <member><literal>&lt;@</literal></member>
    <member><literal>~=</literal></member>
    <member><literal>&amp;&amp;</literal></member>
   </simplelist>

   (See <xref linkend="functions-geometry"> for the meaning of
   these operators.)
   The GiST operator classes included in the standard distribution are
   documented in <xref linkend="gist-builtin-opclasses-table">.
   Many other GiST operator
   classes are available in the <literal>contrib</> collection or as separate
   projects.  For more information see <xref linkend="GiST">.
  </para>

  <para>
   GiST indexes are also capable of optimizing <quote>nearest-neighbor</>
   searches, such as
<programlisting><![CDATA[
SELECT * FROM places ORDER BY location <-> point '(101,456)' LIMIT 10;
]]>
</programlisting>
   which finds the ten places closest to a given target point.  The ability
   to do this is again dependent on the particular operator class being used.
   In <xref linkend="gist-builtin-opclasses-table">, operators that can be
   used in this way are listed in the column <quote>Ordering Operators</>.
  </para>

  <para>
   <indexterm>
    <primary>index</primary>
    <secondary>SP-GiST</secondary>
   </indexterm>
   <indexterm>
    <primary>SP-GiST</primary>
    <see>index</see>
   </indexterm>
   SP-GiST indexes, like GiST indexes, offer an infrastructure that supports
   various kinds of searches.  SP-GiST permits implementation of a wide range
   of different non-balanced disk-based data structures, such as quadtrees,
   k-d trees, and radix trees (tries).  As an example, the standard distribution of
   <productname>PostgreSQL</productname> includes SP-GiST operator classes
   for two-dimensional points, which support indexed
   queries using these operators:

   <simplelist>
    <member><literal>&lt;&lt;</literal></member>
    <member><literal>&gt;&gt;</literal></member>
    <member><literal>~=</literal></member>
    <member><literal>&lt;@</literal></member>
    <member><literal>&lt;^</literal></member>
    <member><literal>&gt;^</literal></member>
   </simplelist>

   (See <xref linkend="functions-geometry"> for the meaning of
   these operators.)
   The SP-GiST operator classes included in the standard distribution are
   documented in <xref linkend="spgist-builtin-opclasses-table">.
   For more information see <xref linkend="SPGiST">.
  </para>

  <para>
   <indexterm>
    <primary>index</primary>
    <secondary>GIN</secondary>
   </indexterm>
   <indexterm>
    <primary>GIN</primary>
    <see>index</see>
   </indexterm>
   GIN indexes are inverted indexes which can handle values that contain more
   than one key, arrays for example. Like GiST and SP-GiST, GIN can support
   many different user-defined indexing strategies and the particular
   operators with which a GIN index can be used vary depending on the
   indexing strategy.
   As an example, the standard distribution of
   <productname>PostgreSQL</productname> includes GIN operator classes
   for one-dimensional arrays, which support indexed
   queries using these operators:

   <simplelist>
    <member><literal>&lt;@</literal></member>
    <member><literal>@&gt;</literal></member>
    <member><literal>=</literal></member>
    <member><literal>&amp;&amp;</literal></member>
   </simplelist>

   (See <xref linkend="functions-array"> for the meaning of
   these operators.)
   The GIN operator classes included in the standard distribution are
   documented in <xref linkend="gin-builtin-opclasses-table">.
   Many other GIN operator
   classes are available in the <literal>contrib</> collection or as separate
   projects.  For more information see <xref linkend="GIN">.
  </para>

  <para>
   <indexterm>
    <primary>index</primary>
    <secondary>BRIN</secondary>
   </indexterm>
   <indexterm>
    <primary>BRIN</primary>
    <see>index</see>
   </indexterm>
   BRIN indexes (a shorthand for Block Range indexes)
   store summaries about the values stored in consecutive table physical block ranges.
   Like GiST, SP-GiST and GIN,
   BRIN can support many different indexing strategies,
   and the particular operators with which a BRIN index can be used
   vary depending on the indexing strategy.
   For data types that have a linear sort order, the indexed data
   corresponds to the minimum and maximum values of the
   values in the column for each block range,
   which support indexed queries using these operators:

   <simplelist>
    <member><literal>&lt;</literal></member>
    <member><literal>&lt;=</literal></member>
    <member><literal>=</literal></member>
    <member><literal>&gt;=</literal></member>
    <member><literal>&gt;</literal></member>
   </simplelist>

   The BRIN operator classes included in the standard distribution are
   documented in <xref linkend="brin-builtin-opclasses-table">.
   For more information see <xref linkend="BRIN">.
  </para>
 </sect1>


 <sect1 id="indexes-multicolumn">
  <title>Multicolumn Indexes</title>

  <indexterm zone="indexes-multicolumn">
   <primary>index</primary>
   <secondary>multicolumn</secondary>
  </indexterm>

  <para>
   An index can be defined on more than one column of a table.  For example, if
   you have a table of this form:
<programlisting>
CREATE TABLE test2 (
  major int,
  minor int,
  name varchar
);
</programlisting>
   (say, you keep your <filename class="directory">/dev</filename>
   directory in a database...) and you frequently issue queries like:
<programlisting>
SELECT name FROM test2 WHERE major = <replaceable>constant</replaceable> AND minor = <replaceable>constant</replaceable>;
</programlisting>
   then it might be appropriate to define an index on the columns
   <structfield>major</structfield> and
   <structfield>minor</structfield> together, e.g.:
<programlisting>
CREATE INDEX test2_mm_idx ON test2 (major, minor);
</programlisting>
  </para>

  <para>
   Currently, only the B-tree, GiST, GIN, and BRIN
   index types support multicolumn
   indexes.  Up to 32 columns can be specified.  (This limit can be
   altered when building <productname>PostgreSQL</productname>; see the
   file <filename>pg_config_manual.h</filename>.)
  </para>

  <para>
   A multicolumn B-tree index can be used with query conditions that
   involve any subset of the index's columns, but the index is most
   efficient when there are constraints on the leading (leftmost) columns.
   The exact rule is that equality constraints on leading columns, plus
   any inequality constraints on the first column that does not have an
   equality constraint, will be used to limit the portion of the index
   that is scanned.  Constraints on columns to the right of these columns
   are checked in the index, so they save visits to the table proper, but
   they do not reduce the portion of the index that has to be scanned.
   For example, given an index on <literal>(a, b, c)</literal> and a
   query condition <literal>WHERE a = 5 AND b &gt;= 42 AND c &lt; 77</>,
   the index would have to be scanned from the first entry with
   <literal>a</> = 5 and <literal>b</> = 42 up through the last entry with
   <literal>a</> = 5.  Index entries with <literal>c</> &gt;= 77 would be
   skipped, but they'd still have to be scanned through.
   This index could in principle be used for queries that have constraints
   on <literal>b</> and/or <literal>c</> with no constraint on <literal>a</>
   &mdash; but the entire index would have to be scanned, so in most cases
   the planner would prefer a sequential table scan over using the index.
  </para>

  <para>
   A multicolumn GiST index can be used with query conditions that
   involve any subset of the index's columns. Conditions on additional
   columns restrict the entries returned by the index, but the condition on
   the first column is the most important one for determining how much of
   the index needs to be scanned.  A GiST index will be relatively
   ineffective if its first column has only a few distinct values, even if
   there are many distinct values in additional columns.
  </para>

  <para>
   A multicolumn GIN index can be used with query conditions that
   involve any subset of the index's columns. Unlike B-tree or GiST,
   index search effectiveness is the same regardless of which index column(s)
   the query conditions use.
  </para>

  <para>
   A multicolumn BRIN index can be used with query conditions that
   involve any subset of the index's columns. Like GIN and unlike B-tree or
   GiST, index search effectiveness is the same regardless of which index
   column(s) the query conditions use. The only reason to have multiple BRIN
   indexes instead of one multicolumn BRIN index on a single table is to have
   a different <literal>pages_per_range</literal> storage parameter.
  </para>

  <para>
   Of course, each column must be used with operators appropriate to the index
   type; clauses that involve other operators will not be considered.
  </para>

  <para>
   Multicolumn indexes should be used sparingly.  In most situations,
   an index on a single column is sufficient and saves space and time.
   Indexes with more than three columns are unlikely to be helpful
   unless the usage of the table is extremely stylized.  See also
   <xref linkend="indexes-bitmap-scans"> for some discussion of the
   merits of different index configurations.
  </para>
 </sect1>


 <sect1 id="indexes-ordering">
  <title>Indexes and <literal>ORDER BY</></title>

  <indexterm zone="indexes-ordering">
   <primary>index</primary>
   <secondary>and <literal>ORDER BY</></secondary>
  </indexterm>

  <para>
   In addition to simply finding the rows to be returned by a query,
   an index may be able to deliver them in a specific sorted order.
   This allows a query's <literal>ORDER BY</> specification to be honored
   without a separate sorting step.  Of the index types currently
   supported by <productname>PostgreSQL</productname>, only B-tree
   can produce sorted output &mdash; the other index types return
   matching rows in an unspecified, implementation-dependent order.
  </para>

  <para>
   The planner will consider satisfying an <literal>ORDER BY</> specification
   either by scanning an available index that matches the specification,
   or by scanning the table in physical order and doing an explicit
   sort.  For a query that requires scanning a large fraction of the
   table, an explicit sort is likely to be faster than using an index
   because it requires
   less disk I/O due to following a sequential access pattern.  Indexes are
   more useful when only a few rows need be fetched.  An important
   special case is <literal>ORDER BY</> in combination with
   <literal>LIMIT</> <replaceable>n</>: an explicit sort will have to process
   all the data to identify the first <replaceable>n</> rows, but if there is
   an index matching the <literal>ORDER BY</>, the first <replaceable>n</>
   rows can be retrieved directly, without scanning the remainder at all.
  </para>

  <para>
   By default, B-tree indexes store their entries in ascending order
   with nulls last.  This means that a forward scan of an index on
   column <literal>x</> produces output satisfying <literal>ORDER BY x</>
   (or more verbosely, <literal>ORDER BY x ASC NULLS LAST</>).  The
   index can also be scanned backward, producing output satisfying
   <literal>ORDER BY x DESC</>
   (or more verbosely, <literal>ORDER BY x DESC NULLS FIRST</>, since
   <literal>NULLS FIRST</> is the default for <literal>ORDER BY DESC</>).
  </para>

  <para>
   You can adjust the ordering of a B-tree index by including the
   options <literal>ASC</>, <literal>DESC</>, <literal>NULLS FIRST</>,
   and/or <literal>NULLS LAST</> when creating the index; for example:
<programlisting>
CREATE INDEX test2_info_nulls_low ON test2 (info NULLS FIRST);
CREATE INDEX test3_desc_index ON test3 (id DESC NULLS LAST);
</programlisting>
   An index stored in ascending order with nulls first can satisfy
   either <literal>ORDER BY x ASC NULLS FIRST</> or
   <literal>ORDER BY x DESC NULLS LAST</> depending on which direction
   it is scanned in.
  </para>

  <para>
   You might wonder why bother providing all four options, when two
   options together with the possibility of backward scan would cover
   all the variants of <literal>ORDER BY</>.  In single-column indexes
   the options are indeed redundant, but in multicolumn indexes they can be
   useful.  Consider a two-column index on <literal>(x, y)</>: this can
   satisfy <literal>ORDER BY x, y</> if we scan forward, or
   <literal>ORDER BY x DESC, y DESC</> if we scan backward.
   But it might be that the application frequently needs to use
   <literal>ORDER BY x ASC, y DESC</>.  There is no way to get that
   ordering from a plain index, but it is possible if the index is defined
   as <literal>(x ASC, y DESC)</> or <literal>(x DESC, y ASC)</>.
  </para>

  <para>
   Obviously, indexes with non-default sort orderings are a fairly
   specialized feature, but sometimes they can produce tremendous
   speedups for certain queries.  Whether it's worth maintaining such an
   index depends on how often you use queries that require a special
   sort ordering.
  </para>
 </sect1>


 <sect1 id="indexes-bitmap-scans">
  <title>Combining Multiple Indexes</title>

  <indexterm zone="indexes-bitmap-scans">
   <primary>index</primary>
   <secondary>combining multiple indexes</secondary>
  </indexterm>

  <indexterm zone="indexes-bitmap-scans">
   <primary>bitmap scan</primary>
  </indexterm>

  <para>
   A single index scan can only use query clauses that use the index's
   columns with operators of its operator class and are joined with
   <literal>AND</>.  For example, given an index on <literal>(a, b)</literal>
   a query condition like <literal>WHERE a = 5 AND b = 6</> could
   use the index, but a query like <literal>WHERE a = 5 OR b = 6</> could not
   directly use the index.
  </para>

  <para>
   Fortunately,
   <productname>PostgreSQL</> has the ability to combine multiple indexes
   (including multiple uses of the same index) to handle cases that cannot
   be implemented by single index scans.  The system can form <literal>AND</>
   and <literal>OR</> conditions across several index scans.  For example,
   a query like <literal>WHERE x = 42 OR x = 47 OR x = 53 OR x = 99</>
   could be broken down into four separate scans of an index on <literal>x</>,
   each scan using one of the query clauses.  The results of these scans are
   then ORed together to produce the result.  Another example is that if we
   have separate indexes on <literal>x</> and <literal>y</>, one possible
   implementation of a query like <literal>WHERE x = 5 AND y = 6</> is to
   use each index with the appropriate query clause and then AND together
   the index results to identify the result rows.
  </para>

  <para>
   To combine multiple indexes, the system scans each needed index and
   prepares a <firstterm>bitmap</> in memory giving the locations of
   table rows that are reported as matching that index's conditions.
   The bitmaps are then ANDed and ORed together as needed by the query.
   Finally, the actual table rows are visited and returned.  The table rows
   are visited in physical order, because that is how the bitmap is laid
   out; this means that any ordering of the original indexes is lost, and
   so a separate sort step will be needed if the query has an <literal>ORDER
   BY</> clause.  For this reason, and because each additional index scan
   adds extra time, the planner will sometimes choose to use a simple index
   scan even though additional indexes are available that could have been
   used as well.
  </para>

  <para>
   In all but the simplest applications, there are various combinations of
   indexes that might be useful, and the database developer must make
   trade-offs to decide which indexes to provide.  Sometimes multicolumn
   indexes are best, but sometimes it's better to create separate indexes
   and rely on the index-combination feature.  For example, if your
   workload includes a mix of queries that sometimes involve only column
   <literal>x</>, sometimes only column <literal>y</>, and sometimes both
   columns, you might choose to create two separate indexes on
   <literal>x</> and <literal>y</>, relying on index combination to
   process the queries that use both columns.  You could also create a
   multicolumn index on <literal>(x, y)</>.  This index would typically be
   more efficient than index combination for queries involving both
   columns, but as discussed in <xref linkend="indexes-multicolumn">, it
   would be almost useless for queries involving only <literal>y</>, so it
   should not be the only index.  A combination of the multicolumn index
   and a separate index on <literal>y</> would serve reasonably well.  For
   queries involving only <literal>x</>, the multicolumn index could be
   used, though it would be larger and hence slower than an index on
   <literal>x</> alone.  The last alternative is to create all three
   indexes, but this is probably only reasonable if the table is searched
   much more often than it is updated and all three types of query are
   common.  If one of the types of query is much less common than the
   others, you'd probably settle for creating just the two indexes that
   best match the common types.
  </para>

 </sect1>


 <sect1 id="indexes-unique">
  <title>Unique Indexes</title>

  <indexterm zone="indexes-unique">
   <primary>index</primary>
   <secondary>unique</secondary>
  </indexterm>

  <para>
   Indexes can also be used to enforce uniqueness of a column's value,
   or the uniqueness of the combined values of more than one column.
<synopsis>
CREATE UNIQUE INDEX <replaceable>name</replaceable> ON <replaceable>table</replaceable> (<replaceable>column</replaceable> <optional>, ...</optional>);
</synopsis>
   Currently, only B-tree indexes can be declared unique.
  </para>

  <para>
   When an index is declared unique, multiple table rows with equal
   indexed values are not allowed.  Null values are not considered
   equal.  A multicolumn unique index will only reject cases where all
   indexed columns are equal in multiple rows.
  </para>

  <para>
   <productname>PostgreSQL</productname> automatically creates a unique
   index when a unique constraint or primary key is defined for a table.
   The index covers the columns that make up the primary key or unique
   constraint (a multicolumn index, if appropriate), and is the mechanism
   that enforces the constraint.
  </para>

  <note>
   <para>
    There's no need to manually
    create indexes on unique columns; doing so would just duplicate
    the automatically-created index.
   </para>
  </note>
 </sect1>


 <sect1 id="indexes-expressional">
  <title>Indexes on Expressions</title>

  <indexterm zone="indexes-expressional">
   <primary>index</primary>
   <secondary sortas="expressions">on expressions</secondary>
  </indexterm>

  <para>
   An index column need not be just a column of the underlying table,
   but can be a function or scalar expression computed from one or
   more columns of the table.  This feature is useful to obtain fast
   access to tables based on the results of computations.
  </para>

  <para>
   For example, a common way to do case-insensitive comparisons is to
   use the <function>lower</function> function:
<programlisting>
SELECT * FROM test1 WHERE lower(col1) = 'value';
</programlisting>
   This query can use an index if one has been
   defined on the result of the <literal>lower(col1)</literal>
   function:
<programlisting>
CREATE INDEX test1_lower_col1_idx ON test1 (lower(col1));
</programlisting>
  </para>

  <para>
   If we were to declare this index <literal>UNIQUE</>, it would prevent
   creation of rows whose <literal>col1</> values differ only in case,
   as well as rows whose <literal>col1</> values are actually identical.
   Thus, indexes on expressions can be used to enforce constraints that
   are not definable as simple unique constraints.
  </para>

  <para>
   As another example, if one often does queries like:
<programlisting>
SELECT * FROM people WHERE (first_name || ' ' || last_name) = 'John Smith';
</programlisting>
   then it might be worth creating an index like this:
<programlisting>
CREATE INDEX people_names ON people ((first_name || ' ' || last_name));
</programlisting>
  </para>

  <para>
   The syntax of the <command>CREATE INDEX</> command normally requires
   writing parentheses around index expressions, as shown in the second
   example.  The parentheses can be omitted when the expression is just
   a function call, as in the first example.
  </para>

  <para>
   Index expressions are relatively expensive to maintain, because the
   derived expression(s) must be computed for each row upon insertion
   and whenever it is updated.  However, the index expressions are
   <emphasis>not</> recomputed during an indexed search, since they are
   already stored in the index.  In both examples above, the system
   sees the query as just <literal>WHERE indexedcolumn = 'constant'</>
   and so the speed of the search is equivalent to any other simple index
   query.  Thus, indexes on expressions are useful when retrieval speed
   is more important than insertion and update speed.
  </para>
 </sect1>


 <sect1 id="indexes-partial">
  <title>Partial Indexes</title>

  <indexterm zone="indexes-partial">
   <primary>index</primary>
   <secondary>partial</secondary>
  </indexterm>

  <para>
   A <firstterm>partial index</firstterm> is an index built over a
   subset of a table; the subset is defined by a conditional
   expression (called the <firstterm>predicate</firstterm> of the
   partial index).  The index contains entries only for those table
   rows that satisfy the predicate.  Partial indexes are a specialized
   feature, but there are several situations in which they are useful.
  </para>

  <para>
   One major reason for using a partial index is to avoid indexing common
   values.  Since a query searching for a common value (one that
   accounts for more than a few percent of all the table rows) will not
   use the index anyway, there is no point in keeping those rows in the
   index at all.  This reduces the size of the index, which will speed
   up those queries that do use the index.  It will also speed up many table
   update operations because the index does not need to be
   updated in all cases.  <xref linkend="indexes-partial-ex1"> shows a
   possible application of this idea.
  </para>

  <example id="indexes-partial-ex1">
   <title>Setting up a Partial Index to Exclude Common Values</title>

   <para>
    Suppose you are storing web server access logs in a database.
    Most accesses originate from the IP address range of your organization but
    some are from elsewhere (say, employees on dial-up connections).
    If your searches by IP are primarily for outside accesses,
    you probably do not need to index the IP range that corresponds to your
    organization's subnet.
   </para>

   <para>
    Assume a table like this:
<programlisting>
CREATE TABLE access_log (
    url varchar,
    client_ip inet,
    ...
);
</programlisting>
   </para>

   <para>
    To create a partial index that suits our example, use a command
    such as this:
<programlisting>
CREATE INDEX access_log_client_ip_ix ON access_log (client_ip)
WHERE NOT (client_ip &gt; inet '192.168.100.0' AND
           client_ip &lt; inet '192.168.100.255');
</programlisting>
   </para>

   <para>
    A typical query that can use this index would be:
<programlisting>
SELECT *
FROM access_log
WHERE url = '/index.html' AND client_ip = inet '212.78.10.32';
</programlisting>
    A query that cannot use this index is:
<programlisting>
SELECT *
FROM access_log
WHERE client_ip = inet '192.168.100.23';
</programlisting>
   </para>

   <para>
    Observe that this kind of partial index requires that the common
    values be predetermined, so such partial indexes are best used for
    data distributions that do not change.  The indexes can be recreated
    occasionally to adjust for new data distributions, but this adds
    maintenance effort.
   </para>
  </example>

  <para>
   Another possible use for a partial index is to exclude values from the
   index that the
   typical query workload is not interested in; this is shown in <xref
   linkend="indexes-partial-ex2">.  This results in the same
   advantages as listed above, but it prevents the
   <quote>uninteresting</quote> values from being accessed via that
   index, even if an index scan might be profitable in that
   case.  Obviously, setting up partial indexes for this kind of
   scenario will require a lot of care and experimentation.
  </para>

  <example id="indexes-partial-ex2">
   <title>Setting up a Partial Index to Exclude Uninteresting Values</title>

   <para>
    If you have a table that contains both billed and unbilled orders,
    where the unbilled orders take up a small fraction of the total
    table and yet those are the most-accessed rows, you can improve
    performance by creating an index on just the unbilled rows.  The
    command to create the index would look like this:
<programlisting>
CREATE INDEX orders_unbilled_index ON orders (order_nr)
    WHERE billed is not true;
</programlisting>
   </para>

   <para>
    A possible query to use this index would be:
<programlisting>
SELECT * FROM orders WHERE billed is not true AND order_nr &lt; 10000;
</programlisting>
    However, the index can also be used in queries that do not involve
    <structfield>order_nr</> at all, e.g.:
<programlisting>
SELECT * FROM orders WHERE billed is not true AND amount &gt; 5000.00;
</programlisting>
    This is not as efficient as a partial index on the
    <structfield>amount</> column would be, since the system has to
    scan the entire index.  Yet, if there are relatively few unbilled
    orders, using this partial index just to find the unbilled orders
    could be a win.
   </para>

   <para>
    Note that this query cannot use this index:
<programlisting>
SELECT * FROM orders WHERE order_nr = 3501;
</programlisting>
    The order 3501 might be among the billed or unbilled
    orders.
   </para>
  </example>

  <para>
   <xref linkend="indexes-partial-ex2"> also illustrates that the
   indexed column and the column used in the predicate do not need to
   match.  <productname>PostgreSQL</productname> supports partial
   indexes with arbitrary predicates, so long as only columns of the
   table being indexed are involved.  However, keep in mind that the
   predicate must match the conditions used in the queries that
   are supposed to benefit from the index.  To be precise, a partial
   index can be used in a query only if the system can recognize that
   the <literal>WHERE</> condition of the query mathematically implies
   the predicate of the index.
   <productname>PostgreSQL</productname> does not have a sophisticated
   theorem prover that can recognize mathematically equivalent
   expressions that are written in different forms.  (Not
   only is such a general theorem prover extremely difficult to
   create, it would probably be too slow to be of any real use.)
   The system can recognize simple inequality implications, for example
   <quote>x &lt; 1</quote> implies <quote>x &lt; 2</quote>; otherwise
   the predicate condition must exactly match part of the query's
   <literal>WHERE</> condition
   or the index will not be recognized as usable. Matching takes
   place at query planning time, not at run time. As a result,
   parameterized query clauses do not work with a partial index. For
   example a prepared query with a parameter might specify
   <quote>x &lt; ?</quote> which will never imply
   <quote>x &lt; 2</quote> for all possible values of the parameter.
  </para>

  <para>
   A third possible use for partial indexes does not require the
   index to be used in queries at all.  The idea here is to create
   a unique index over a subset of a table, as in <xref
   linkend="indexes-partial-ex3">.  This enforces uniqueness
   among the rows that satisfy the index predicate, without constraining
   those that do not.
  </para>

  <example id="indexes-partial-ex3">
   <title>Setting up a Partial Unique Index</title>

   <para>
    Suppose that we have a table describing test outcomes.  We wish
    to ensure that there is only one <quote>successful</> entry for
    a given subject and target combination, but there might be any number of
    <quote>unsuccessful</> entries.  Here is one way to do it:
<programlisting>
CREATE TABLE tests (
    subject text,
    target text,
    success boolean,
    ...
);

CREATE UNIQUE INDEX tests_success_constraint ON tests (subject, target)
    WHERE success;
</programlisting>
    This is a particularly efficient approach when there are few
    successful tests and many unsuccessful ones.
   </para>
  </example>

  <para>
   Finally, a partial index can also be used to override the system's
   query plan choices.  Also, data sets with peculiar
   distributions might cause the system to use an index when it really
   should not.  In that case the index can be set up so that it is not
   available for the offending query.  Normally,
   <productname>PostgreSQL</> makes reasonable choices about index
   usage (e.g., it avoids them when retrieving common values, so the
   earlier example really only saves index size, it is not required to
   avoid index usage), and grossly incorrect plan choices are cause
   for a bug report.
  </para>

  <para>
   Keep in mind that setting up a partial index indicates that you
   know at least as much as the query planner knows, in particular you
   know when an index might be profitable.  Forming this knowledge
   requires experience and understanding of how indexes in
   <productname>PostgreSQL</> work.  In most cases, the advantage of a
   partial index over a regular index will be minimal.
  </para>

  <para>
   More information about partial indexes can be found in <xref
   linkend="STON89b">, <xref linkend="OLSON93">, and <xref
   linkend="SESHADRI95">.
  </para>
 </sect1>


 <sect1 id="indexes-opclass">
  <title>Operator Classes and Operator Families</title>

  <indexterm zone="indexes-opclass">
   <primary>operator class</primary>
  </indexterm>

  <indexterm zone="indexes-opclass">
   <primary>operator family</primary>
  </indexterm>

  <para>
   An index definition can specify an <firstterm>operator
   class</firstterm> for each column of an index.
<synopsis>
CREATE INDEX <replaceable>name</replaceable> ON <replaceable>table</replaceable> (<replaceable>column</replaceable> <replaceable>opclass</replaceable> <optional><replaceable>sort options</replaceable></optional> <optional>, ...</optional>);
</synopsis>
   The operator class identifies the operators to be used by the index
   for that column.  For example, a B-tree index on the type <type>int4</type>
   would use the <literal>int4_ops</literal> class; this operator
   class includes comparison functions for values of type <type>int4</type>.
   In practice the default operator class for the column's data type is
   usually sufficient.  The main reason for having operator classes is
   that for some data types, there could be more than one meaningful
   index behavior.  For example, we might want to sort a complex-number data
   type either by absolute value or by real part.  We could do this by
   defining two operator classes for the data type and then selecting
   the proper class when making an index.  The operator class determines
   the basic sort ordering (which can then be modified by adding sort options
   <literal>COLLATE</literal>,
   <literal>ASC</>/<literal>DESC</> and/or
   <literal>NULLS FIRST</>/<literal>NULLS LAST</>).
  </para>

  <para>
   There are also some built-in operator classes besides the default ones:

   <itemizedlist>
    <listitem>
     <para>
      The operator classes <literal>text_pattern_ops</literal>,
      <literal>varchar_pattern_ops</literal>, and
      <literal>bpchar_pattern_ops</literal> support B-tree indexes on
      the types <type>text</type>, <type>varchar</type>, and
      <type>char</type> respectively.  The
      difference from the default operator classes is that the values
      are compared strictly character by character rather than
      according to the locale-specific collation rules.  This makes
      these operator classes suitable for use by queries involving
      pattern matching expressions (<literal>LIKE</literal> or POSIX
      regular expressions) when the database does not use the standard
      <quote>C</quote> locale.  As an example, you might index a
      <type>varchar</type> column like this:
<programlisting>
CREATE INDEX test_index ON test_table (col varchar_pattern_ops);
</programlisting>
      Note that you should also create an index with the default operator
      class if you want queries involving ordinary <literal>&lt;</>,
      <literal>&lt;=</>, <literal>&gt;</>, or <literal>&gt;=</> comparisons
      to use an index.  Such queries cannot use the
      <literal><replaceable>xxx</replaceable>_pattern_ops</literal>
      operator classes.  (Ordinary equality comparisons can use these
      operator classes, however.)  It is possible to create multiple
      indexes on the same column with different operator classes.
      If you do use the C locale, you do not need the
      <literal><replaceable>xxx</replaceable>_pattern_ops</literal>
      operator classes, because an index with the default operator class
      is usable for pattern-matching queries in the C locale.
     </para>
    </listitem>
   </itemizedlist>
  </para>

  <para>
    The following query shows all defined operator classes:

<programlisting>
SELECT am.amname AS index_method,
       opc.opcname AS opclass_name,
       opc.opcintype::regtype AS indexed_type,
       opc.opcdefault AS is_default
    FROM pg_am am, pg_opclass opc
    WHERE opc.opcmethod = am.oid
    ORDER BY index_method, opclass_name;
</programlisting>
  </para>

  <para>
   An operator class is actually just a subset of a larger structure called an
   <firstterm>operator family</>.  In cases where several data types have
   similar behaviors, it is frequently useful to define cross-data-type
   operators and allow these to work with indexes.  To do this, the operator
   classes for each of the types must be grouped into the same operator
   family.  The cross-type operators are members of the family, but are not
   associated with any single class within the family.
  </para>

  <para>
    This expanded version of the previous query shows the operator family
    each operator class belongs to:
<programlisting>
SELECT am.amname AS index_method,
       opc.opcname AS opclass_name,
       opf.opfname AS opfamily_name,
       opc.opcintype::regtype AS indexed_type,
       opc.opcdefault AS is_default
    FROM pg_am am, pg_opclass opc, pg_opfamily opf
    WHERE opc.opcmethod = am.oid AND
          opc.opcfamily = opf.oid
    ORDER BY index_method, opclass_name;
</programlisting>
  </para>

  <para>
    This query shows all defined operator families and all
    the operators included in each family:
<programlisting>
SELECT am.amname AS index_method,
       opf.opfname AS opfamily_name,
       amop.amopopr::regoperator AS opfamily_operator
    FROM pg_am am, pg_opfamily opf, pg_amop amop
    WHERE opf.opfmethod = am.oid AND
          amop.amopfamily = opf.oid
    ORDER BY index_method, opfamily_name, opfamily_operator;
</programlisting>
  </para>
 </sect1>


 <sect1 id="indexes-collations">
  <title>Indexes and Collations</title>

  <para>
   An index can support only one collation per index column.
   If multiple collations are of interest, multiple indexes may be needed.
  </para>

  <para>
   Consider these statements:
<programlisting>
CREATE TABLE test1c (
    id integer,
    content varchar COLLATE "x"
);

CREATE INDEX test1c_content_index ON test1c (content);
</programlisting>
   The index automatically uses the collation of the
   underlying column.  So a query of the form
<programlisting>
SELECT * FROM test1c WHERE content &gt; <replaceable>constant</replaceable>;
</programlisting>
   could use the index, because the comparison will by default use the
   collation of the column.  However, this index cannot accelerate queries
   that involve some other collation.  So if queries of the form, say,
<programlisting>
SELECT * FROM test1c WHERE content &gt; <replaceable>constant</replaceable> COLLATE "y";
</programlisting>
   are also of interest, an additional index could be created that supports
   the <literal>"y"</literal> collation, like this:
<programlisting>
CREATE INDEX test1c_content_y_index ON test1c (content COLLATE "y");
</programlisting>
  </para>
 </sect1>


 <sect1 id="indexes-examine">
  <title>Examining Index Usage</title>

  <indexterm zone="indexes-examine">
   <primary>index</primary>
   <secondary>examining usage</secondary>
  </indexterm>

  <para>
   Although indexes in <productname>PostgreSQL</> do not need
   maintenance or tuning, it is still important to check
   which indexes are actually used by the real-life query workload.
   Examining index usage for an individual query is done with the
   <xref linkend="sql-explain">
   command; its application for this purpose is
   illustrated in <xref linkend="using-explain">.
   It is also possible to gather overall statistics about index usage
   in a running server, as described in <xref linkend="monitoring-stats">.
  </para>

  <para>
   It is difficult to formulate a general procedure for determining
   which indexes to create.  There are a number of typical cases that
   have been shown in the examples throughout the previous sections.
   A good deal of experimentation is often necessary.
   The rest of this section gives some tips for that:
  </para>

  <itemizedlist>
   <listitem>
    <para>
     Always run <xref linkend="sql-analyze">
     first.  This command
     collects statistics about the distribution of the values in the
     table.  This information is required to estimate the number of rows
     returned by a query, which is needed by the planner to assign
     realistic costs to each possible query plan.  In absence of any
     real statistics, some default values are assumed, which are
     almost certain to be inaccurate.  Examining an application's
     index usage without having run <command>ANALYZE</command> is
     therefore a lost cause.
     See <xref linkend="vacuum-for-statistics">
     and <xref linkend="autovacuum"> for more information.
    </para>
   </listitem>

   <listitem>
    <para>
     Use real data for experimentation.  Using test data for setting
     up indexes will tell you what indexes you need for the test data,
     but that is all.
    </para>

    <para>
     It is especially fatal to use very small test data sets.
     While selecting 1000 out of 100000 rows could be a candidate for
     an index, selecting 1 out of 100 rows will hardly be, because the
     100 rows probably fit within a single disk page, and there
     is no plan that can beat sequentially fetching 1 disk page.
    </para>

    <para>
     Also be careful when making up test data, which is often
     unavoidable when the application is not yet in production.
     Values that are very similar, completely random, or inserted in
     sorted order will skew the statistics away from the distribution
     that real data would have.
    </para>
   </listitem>

   <listitem>
    <para>
     When indexes are not used, it can be useful for testing to force
     their use.  There are run-time parameters that can turn off
     various plan types (see <xref linkend="runtime-config-query-enable">).
     For instance, turning off sequential scans
     (<varname>enable_seqscan</>) and nested-loop joins
     (<varname>enable_nestloop</>), which are the most basic plans,
     will force the system to use a different plan.  If the system
     still chooses a sequential scan or nested-loop join then there is
     probably a more fundamental reason why the index is not being
     used; for example, the query condition does not match the index.
     (What kind of query can use what kind of index is explained in
     the previous sections.)
    </para>
   </listitem>

   <listitem>
    <para>
     If forcing index usage does use the index, then there are two
     possibilities: Either the system is right and using the index is
     indeed not appropriate, or the cost estimates of the query plans
     are not reflecting reality.  So you should time your query with
     and without indexes.  The <command>EXPLAIN ANALYZE</command>
     command can be useful here.
    </para>
   </listitem>

   <listitem>
    <para>
     If it turns out that the cost estimates are wrong, there are,
     again, two possibilities.  The total cost is computed from the
     per-row costs of each plan node times the selectivity estimate of
     the plan node.  The costs estimated for the plan nodes can be adjusted
     via run-time parameters (described in <xref
     linkend="runtime-config-query-constants">).
     An inaccurate selectivity estimate is due to
     insufficient statistics.  It might be possible to improve this by
     tuning the statistics-gathering parameters (see
     <xref linkend="sql-altertable">).
    </para>

    <para>
     If you do not succeed in adjusting the costs to be more
     appropriate, then you might have to resort to forcing index usage
     explicitly.  You might also want to contact the
     <productname>PostgreSQL</> developers to examine the issue.
    </para>
   </listitem>
  </itemizedlist>
 </sect1>
</chapter>
