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

<chapter id="brin">
<title>BRIN Indexes</title>

   <indexterm>
    <primary>index</primary>
    <secondary>BRIN</secondary>
   </indexterm>

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

 <para>
  <acronym>BRIN</acronym> stands for Block Range Index.
  <acronym>BRIN</acronym> is designed for handling very large tables
  in which certain columns have some natural correlation with their
  physical location within the table.
  A <firstterm>block range</firstterm> is a group of pages that are physically
  adjacent in the table; for each block range, some summary info is stored
  by the index.
  For example, a table storing a store's sale orders might have
  a date column on which each order was placed, and most of the time
  the entries for earlier orders will appear earlier in the table as well;
  a table storing a ZIP code column might have all codes for a city
  grouped together naturally.
 </para>

 <para>
  <acronym>BRIN</acronym> indexes can satisfy queries via regular bitmap
  index scans, and will return all tuples in all pages within each range if
  the summary info stored by the index is <firstterm>consistent</firstterm> with the
  query conditions.
  The query executor is in charge of rechecking these tuples and discarding
  those that do not match the query conditions &mdash; in other words, these
  indexes are lossy.
  Because a <acronym>BRIN</acronym> index is very small, scanning the index
  adds little overhead compared to a sequential scan, but may avoid scanning
  large parts of the table that are known not to contain matching tuples.
 </para>

 <para>
  The specific data that a <acronym>BRIN</acronym> index will store,
  as well as the specific queries that the index will be able to satisfy,
  depend on the operator class selected for each column of the index.
  Data types having a linear sort order can have operator classes that
  store the minimum and maximum value within each block range, for instance;
  geometrical types might store the bounding box for all the objects
  in the block range.
 </para>

 <para>
  The size of the block range is determined at index creation time by
  the <literal>pages_per_range</literal> storage parameter.  The number of index
  entries will be equal to the size of the relation in pages divided by
  the selected value for <literal>pages_per_range</literal>.  Therefore, the smaller
  the number, the larger the index becomes (because of the need to
  store more index entries), but at the same time the summary data stored can
  be more precise and more data blocks can be skipped during an index scan.
 </para>

 <sect2 id="brin-operation">
  <title>Index Maintenance</title>

  <para>
   At the time of creation, all existing heap pages are scanned and a
   summary index tuple is created for each range, including the
   possibly-incomplete range at the end.
   As new pages are filled with data, page ranges that are already
   summarized will cause the summary information to be updated with data
   from the new tuples.
   When a new page is created that does not fall within the last
   summarized range, that range does not automatically acquire a summary
   tuple; those tuples remain unsummarized until a summarization run is
   invoked later, creating initial summaries.
   This process can be invoked manually using the
   <function>brin_summarize_range(regclass, bigint)</function> or
   <function>brin_summarize_new_values(regclass)</function> functions;
   automatically when <command>VACUUM</command> processes the table;
   or by automatic summarization executed by autovacuum, as insertions
   occur.  (This last trigger is disabled by default and can be enabled
   with the <literal>autosummarize</literal> parameter.)
   Conversely, a range can be de-summarized using the
   <function>brin_desummarize_range(regclass, bigint)</function> function,
   which is useful when the index tuple is no longer a very good
   representation because the existing values have changed.
  </para>

  <para>
   When autosummarization is enabled, each time a page range is filled a
   request is sent to autovacuum for it to execute a targeted summarization
   for that range, to be fulfilled at the end of the next worker run on the
   same database.  If the request queue is full, the request is not recorded
   and a message is sent to the server log:
<screen>
LOG:  request for BRIN range summarization for index "brin_wi_idx" page 128 was not recorded
</screen>
   When this happens, the range will be summarized normally during the next
   regular vacuum of the table.
  </para>
 </sect2>
</sect1>

<sect1 id="brin-builtin-opclasses">
 <title>Built-in Operator Classes</title>

 <para>
  The core <productname>PostgreSQL</productname> distribution
  includes the <acronym>BRIN</acronym> operator classes shown in
  <xref linkend="brin-builtin-opclasses-table"/>.
 </para>

 <para>
  The <firstterm>minmax</firstterm>
  operator classes store the minimum and the maximum values appearing
  in the indexed column within the range.  The <firstterm>inclusion</firstterm>
  operator classes store a value which includes the values in the indexed
  column within the range.
 </para>

 <table id="brin-builtin-opclasses-table">
  <title>Built-in <acronym>BRIN</acronym> Operator Classes</title>
  <tgroup cols="2">
   <thead>
    <row>
     <entry>Name</entry>
     <entry>Indexable Operators</entry>
    </row>
   </thead>
   <tbody>
    <row>
     <entry valign="middle" morerows="4"><literal>bit_minmax_ops</literal></entry>
     <entry><literal>= (bit,bit)</literal></entry>
    </row>
    <row><entry><literal>&lt; (bit,bit)</literal></entry></row>
    <row><entry><literal>&gt; (bit,bit)</literal></entry></row>
    <row><entry><literal>&lt;= (bit,bit)</literal></entry></row>
    <row><entry><literal>&gt;= (bit,bit)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="12"><literal>box_inclusion_ops</literal></entry>
     <entry><literal>@&gt; (box,point)</literal></entry>
    </row>
    <row><entry><literal>&lt;&lt; (box,box)</literal></entry></row>
    <row><entry><literal>&amp;&lt; (box,box)</literal></entry></row>
    <row><entry><literal>&amp;&gt; (box,box)</literal></entry></row>
    <row><entry><literal>&gt;&gt; (box,box)</literal></entry></row>
    <row><entry><literal>&lt;@ (box,box)</literal></entry></row>
    <row><entry><literal>@&gt; (box,box)</literal></entry></row>
    <row><entry><literal>~= (box,box)</literal></entry></row>
    <row><entry><literal>&amp;&amp; (box,box)</literal></entry></row>
    <row><entry><literal>&lt;&lt;| (box,box)</literal></entry></row>
    <row><entry><literal>&amp;&lt;| (box,box)</literal></entry></row>
    <row><entry><literal>|&amp;&gt; (box,box)</literal></entry></row>
    <row><entry><literal>|&gt;&gt; (box,box)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>bpchar_minmax_ops</literal></entry>
     <entry><literal>= (character,character)</literal></entry>
    </row>
    <row><entry><literal>&lt; (character,character)</literal></entry></row>
    <row><entry><literal>&lt;= (character,character)</literal></entry></row>
    <row><entry><literal>&gt; (character,character)</literal></entry></row>
    <row><entry><literal>&gt;= (character,character)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>bytea_minmax_ops</literal></entry>
     <entry><literal>= (bytea,bytea)</literal></entry>
    </row>
    <row><entry><literal>&lt; (bytea,bytea)</literal></entry></row>
    <row><entry><literal>&lt;= (bytea,bytea)</literal></entry></row>
    <row><entry><literal>&gt; (bytea,bytea)</literal></entry></row>
    <row><entry><literal>&gt;= (bytea,bytea)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>char_minmax_ops</literal></entry>
     <entry><literal>= ("char","char")</literal></entry>
    </row>
    <row><entry><literal>&lt; ("char","char")</literal></entry></row>
    <row><entry><literal>&lt;= ("char","char")</literal></entry></row>
    <row><entry><literal>&gt; ("char","char")</literal></entry></row>
    <row><entry><literal>&gt;= ("char","char")</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>date_minmax_ops</literal></entry>
     <entry><literal>= (date,date)</literal></entry>
    </row>
    <row><entry><literal>&lt; (date,date)</literal></entry></row>
    <row><entry><literal>&lt;= (date,date)</literal></entry></row>
    <row><entry><literal>&gt; (date,date)</literal></entry></row>
    <row><entry><literal>&gt;= (date,date)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>float4_minmax_ops</literal></entry>
     <entry><literal>= (float4,float4)</literal></entry>
    </row>
    <row><entry><literal>&lt; (float4,float4)</literal></entry></row>
    <row><entry><literal>&gt; (float4,float4)</literal></entry></row>
    <row><entry><literal>&lt;= (float4,float4)</literal></entry></row>
    <row><entry><literal>&gt;= (float4,float4)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>float8_minmax_ops</literal></entry>
     <entry><literal>= (float8,float8)</literal></entry>
    </row>
    <row><entry><literal>&lt; (float8,float8)</literal></entry></row>
    <row><entry><literal>&lt;= (float8,float8)</literal></entry></row>
    <row><entry><literal>&gt; (float8,float8)</literal></entry></row>
    <row><entry><literal>&gt;= (float8,float8)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="5"><literal>inet_inclusion_ops</literal></entry>
     <entry><literal>&lt;&lt; (inet,inet)</literal></entry>
    </row>
    <row><entry><literal>&lt;&lt;= (inet,inet)</literal></entry></row>
    <row><entry><literal>&gt;&gt; (inet,inet)</literal></entry></row>
    <row><entry><literal>&gt;&gt;= (inet,inet)</literal></entry></row>
    <row><entry><literal>= (inet,inet)</literal></entry></row>
    <row><entry><literal>&amp;&amp; (inet,inet)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>inet_minmax_ops</literal></entry>
     <entry><literal>= (inet,inet)</literal></entry>
    </row>
    <row><entry><literal>&lt; (inet,inet)</literal></entry></row>
    <row><entry><literal>&lt;= (inet,inet)</literal></entry></row>
    <row><entry><literal>&gt; (inet,inet)</literal></entry></row>
    <row><entry><literal>&gt;= (inet,inet)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>int2_minmax_ops</literal></entry>
     <entry><literal>= (int2,int2)</literal></entry>
    </row>
    <row><entry><literal>&lt; (int2,int2)</literal></entry></row>
    <row><entry><literal>&gt; (int2,int2)</literal></entry></row>
    <row><entry><literal>&lt;= (int2,int2)</literal></entry></row>
    <row><entry><literal>&gt;= (int2,int2)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>int4_minmax_ops</literal></entry>
     <entry><literal>= (int4,int4)</literal></entry>
    </row>
    <row><entry><literal>&lt; (int4,int4)</literal></entry></row>
    <row><entry><literal>&gt; (int4,int4)</literal></entry></row>
    <row><entry><literal>&lt;= (int4,int4)</literal></entry></row>
    <row><entry><literal>&gt;= (int4,int4)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>int8_minmax_ops</literal></entry>
     <entry><literal>= (bigint,bigint)</literal></entry>
    </row>
    <row><entry><literal>&lt; (bigint,bigint)</literal></entry></row>
    <row><entry><literal>&gt; (bigint,bigint)</literal></entry></row>
    <row><entry><literal>&lt;= (bigint,bigint)</literal></entry></row>
    <row><entry><literal>&gt;= (bigint,bigint)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>interval_minmax_ops</literal></entry>
     <entry><literal>= (interval,interval)</literal></entry>
    </row>
    <row><entry><literal>&lt; (interval,interval)</literal></entry></row>
    <row><entry><literal>&lt;= (interval,interval)</literal></entry></row>
    <row><entry><literal>&gt; (interval,interval)</literal></entry></row>
    <row><entry><literal>&gt;= (interval,interval)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>macaddr_minmax_ops</literal></entry>
     <entry><literal>= (macaddr,macaddr)</literal></entry>
    </row>
    <row><entry><literal>&lt; (macaddr,macaddr)</literal></entry></row>
    <row><entry><literal>&lt;= (macaddr,macaddr)</literal></entry></row>
    <row><entry><literal>&gt; (macaddr,macaddr)</literal></entry></row>
    <row><entry><literal>&gt;= (macaddr,macaddr)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>macaddr8_minmax_ops</literal></entry>
     <entry><literal>= (macaddr8,macaddr8)</literal></entry>
    </row>
    <row><entry><literal>&lt; (macaddr8,macaddr8)</literal></entry></row>
    <row><entry><literal>&lt;= (macaddr8,macaddr8)</literal></entry></row>
    <row><entry><literal>&gt; (macaddr8,macaddr8)</literal></entry></row>
    <row><entry><literal>&gt;= (macaddr8,macaddr8)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>name_minmax_ops</literal></entry>
     <entry><literal>= (name,name)</literal></entry>
    </row>
    <row><entry><literal>&lt; (name,name)</literal></entry></row>
    <row><entry><literal>&lt;= (name,name)</literal></entry></row>
    <row><entry><literal>&gt; (name,name)</literal></entry></row>
    <row><entry><literal>&gt;= (name,name)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>numeric_minmax_ops</literal></entry>
     <entry><literal>= (numeric,numeric)</literal></entry>
    </row>
    <row><entry><literal>&lt; (numeric,numeric)</literal></entry></row>
    <row><entry><literal>&lt;= (numeric,numeric)</literal></entry></row>
    <row><entry><literal>&gt; (numeric,numeric)</literal></entry></row>
    <row><entry><literal>&gt;= (numeric,numeric)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>oid_minmax_ops</literal></entry>
     <entry><literal>= (oid,oid)</literal></entry>
    </row>
    <row><entry><literal>&lt; (oid,oid)</literal></entry></row>
    <row><entry><literal>&gt; (oid,oid)</literal></entry></row>
    <row><entry><literal>&lt;= (oid,oid)</literal></entry></row>
    <row><entry><literal>&gt;= (oid,oid)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>pg_lsn_minmax_ops</literal></entry>
     <entry><literal>= (pg_lsn,pg_lsn)</literal></entry>
    </row>
    <row><entry><literal>&lt; (pg_lsn,pg_lsn)</literal></entry></row>
    <row><entry><literal>&gt; (pg_lsn,pg_lsn)</literal></entry></row>
    <row><entry><literal>&lt;= (pg_lsn,pg_lsn)</literal></entry></row>
    <row><entry><literal>&gt;= (pg_lsn,pg_lsn)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="13"><literal>range_inclusion_ops</literal></entry>
     <entry><literal>= (anyrange,anyrange)</literal></entry>
    </row>
    <row><entry><literal>&lt; (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&lt;= (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&gt;= (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&gt; (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&amp;&amp; (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>@&gt; (anyrange,anyelement)</literal></entry></row>
    <row><entry><literal>@&gt; (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&lt;@ (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&lt;&lt; (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&gt;&gt; (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&amp;&lt; (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>&amp;&gt; (anyrange,anyrange)</literal></entry></row>
    <row><entry><literal>-|- (anyrange,anyrange)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>text_minmax_ops</literal></entry>
     <entry><literal>= (text,text)</literal></entry>
    </row>
    <row><entry><literal>&lt; (text,text)</literal></entry></row>
    <row><entry><literal>&lt;= (text,text)</literal></entry></row>
    <row><entry><literal>&gt; (text,text)</literal></entry></row>
    <row><entry><literal>&gt;= (text,text)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>tid_minmax_ops</literal></entry>
     <entry><literal>= (tid,tid)</literal></entry>
    </row>
    <row><entry><literal>&lt; (tid,tid)</literal></entry></row>
    <row><entry><literal>&gt; (tid,tid)</literal></entry></row>
    <row><entry><literal>&lt;= (tid,tid)</literal></entry></row>
    <row><entry><literal>&gt;= (tid,tid)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>timestamp_minmax_ops</literal></entry>
     <entry><literal>= (timestamp,timestamp)</literal></entry>
    </row>
    <row><entry><literal>&lt; (timestamp,timestamp)</literal></entry></row>
    <row><entry><literal>&lt;= (timestamp,timestamp)</literal></entry></row>
    <row><entry><literal>&gt; (timestamp,timestamp)</literal></entry></row>
    <row><entry><literal>&gt;= (timestamp,timestamp)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>timestamptz_minmax_ops</literal></entry>
     <entry><literal>= (timestamptz,timestamptz)</literal></entry>
    </row>
    <row><entry><literal>&lt; (timestamptz,timestamptz)</literal></entry></row>
    <row><entry><literal>&lt;= (timestamptz,timestamptz)</literal></entry></row>
    <row><entry><literal>&gt; (timestamptz,timestamptz)</literal></entry></row>
    <row><entry><literal>&gt;= (timestamptz,timestamptz)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>time_minmax_ops</literal></entry>
     <entry><literal>= (time,time)</literal></entry>
    </row>
    <row><entry><literal>&lt; (time,time)</literal></entry></row>
    <row><entry><literal>&lt;= (time,time)</literal></entry></row>
    <row><entry><literal>&gt; (time,time)</literal></entry></row>
    <row><entry><literal>&gt;= (time,time)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>timetz_minmax_ops</literal></entry>
     <entry><literal>= (timetz,timetz)</literal></entry>
    </row>
    <row><entry><literal>&lt; (timetz,timetz)</literal></entry></row>
    <row><entry><literal>&lt;= (timetz,timetz)</literal></entry></row>
    <row><entry><literal>&gt; (timetz,timetz)</literal></entry></row>
    <row><entry><literal>&gt;= (timetz,timetz)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>uuid_minmax_ops</literal></entry>
     <entry><literal>= (uuid,uuid)</literal></entry>
    </row>
    <row><entry><literal>&lt; (uuid,uuid)</literal></entry></row>
    <row><entry><literal>&gt; (uuid,uuid)</literal></entry></row>
    <row><entry><literal>&lt;= (uuid,uuid)</literal></entry></row>
    <row><entry><literal>&gt;= (uuid,uuid)</literal></entry></row>

    <row>
     <entry valign="middle" morerows="4"><literal>varbit_minmax_ops</literal></entry>
     <entry><literal>= (varbit,varbit)</literal></entry>
    </row>
    <row><entry><literal>&lt; (varbit,varbit)</literal></entry></row>
    <row><entry><literal>&gt; (varbit,varbit)</literal></entry></row>
    <row><entry><literal>&lt;= (varbit,varbit)</literal></entry></row>
    <row><entry><literal>&gt;= (varbit,varbit)</literal></entry></row>
   </tbody>
  </tgroup>
 </table>
</sect1>

<sect1 id="brin-extensibility">
 <title>Extensibility</title>

 <para>
  The <acronym>BRIN</acronym> interface has a high level of abstraction,
  requiring the access method implementer only to implement the semantics
  of the data type being accessed.  The <acronym>BRIN</acronym> layer
  itself takes care of concurrency, logging and searching the index structure.
 </para>

 <para>
  All it takes to get a <acronym>BRIN</acronym> access method working is to
  implement a few user-defined methods, which define the behavior of
  summary values stored in the index and the way they interact with
  scan keys.
  In short, <acronym>BRIN</acronym> combines
  extensibility with generality, code reuse, and a clean interface.
 </para>

 <para>
  There are four methods that an operator class for <acronym>BRIN</acronym>
  must provide:

  <variablelist>
   <varlistentry>
    <term><function>BrinOpcInfo *opcInfo(Oid type_oid)</function></term>
    <listitem>
     <para>
      Returns internal information about the indexed columns' summary data.
      The return value must point to a palloc'd <structname>BrinOpcInfo</structname>,
      which has this definition:
<programlisting>
typedef struct BrinOpcInfo
{
    /* Number of columns stored in an index column of this opclass */
    uint16      oi_nstored;

    /* Opaque pointer for the opclass' private use */
    void       *oi_opaque;

    /* Type cache entries of the stored columns */
    TypeCacheEntry *oi_typcache[FLEXIBLE_ARRAY_MEMBER];
} BrinOpcInfo;
</programlisting>
      <structname>BrinOpcInfo</structname>.<structfield>oi_opaque</structfield> can be used by the
      operator class routines to pass information between support functions
      during an index scan.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><function>bool consistent(BrinDesc *bdesc, BrinValues *column,
       ScanKey key)</function></term>
    <listitem>
     <para>
      Returns whether the ScanKey is consistent with the given indexed
      values for a range.
      The attribute number to use is passed as part of the scan key.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><function>bool addValue(BrinDesc *bdesc, BrinValues *column,
       Datum newval, bool isnull)</function></term>
    <listitem>
     <para>
      Given an index tuple and an indexed value, modifies the indicated
      attribute of the tuple so that it additionally represents the new value.
      If any modification was done to the tuple, <literal>true</literal> is
      returned.
     </para>
    </listitem>
   </varlistentry>

   <varlistentry>
    <term><function>bool unionTuples(BrinDesc *bdesc, BrinValues *a,
       BrinValues *b)</function></term>
    <listitem>
     <para>
      Consolidates two index tuples. Given two index tuples, modifies the
      indicated attribute of the first of them so that it represents both tuples.
      The second tuple is not modified.
     </para>
    </listitem>
   </varlistentry>
  </variablelist>

  An operator class for <acronym>BRIN</acronym> can optionally specify the
  following method:

  <variablelist>
    <varlistentry>
     <term><function>void options(local_relopts *relopts)</function></term>
     <listitem>
      <para>
       Defines a set of user-visible parameters that control operator class
       behavior.
      </para>

      <para>
       The <function>options</function> function is passed a pointer to a
       <structname>local_relopts</structname> struct, which needs to be
       filled with a set of operator class specific options.  The options
       can be accessed from other support functions using the
       <literal>PG_HAS_OPCLASS_OPTIONS()</literal> and
       <literal>PG_GET_OPCLASS_OPTIONS()</literal> macros.
      </para>

      <para>
       Since both key extraction of indexed values and representation of the
       key in <acronym>BRIN</acronym> are flexible, they may depend on
       user-specified parameters.
      </para>
     </listitem>
    </varlistentry>
  </variablelist>

  The core distribution includes support for two types of operator classes:
  minmax and inclusion.  Operator class definitions using them are shipped for
  in-core data types as appropriate.  Additional operator classes can be
  defined by the user for other data types using equivalent definitions,
  without having to write any source code; appropriate catalog entries being
  declared is enough.  Note that assumptions about the semantics of operator
  strategies are embedded in the support functions' source code.
 </para>

 <para>
  Operator classes that implement completely different semantics are also
  possible, provided implementations of the four main support functions
  described above are written.  Note that backwards compatibility across major
  releases is not guaranteed: for example, additional support functions might
  be required in later releases.
 </para>

 <para>
  To write an operator class for a data type that implements a totally
  ordered set, it is possible to use the minmax support functions
  alongside the corresponding operators, as shown in
  <xref linkend="brin-extensibility-minmax-table"/>.
  All operator class members (functions and operators) are mandatory.
 </para>

 <table id="brin-extensibility-minmax-table">
  <title>Function and Support Numbers for Minmax Operator Classes</title>
  <tgroup cols="2">
   <colspec colname="col1" colwidth="1*"/>
   <colspec colname="col2" colwidth="2*"/>
   <thead>
    <row>
     <entry>Operator class member</entry>
     <entry>Object</entry>
    </row>
   </thead>
   <tbody>
    <row>
     <entry>Support Function 1</entry>
     <entry>internal function <function>brin_minmax_opcinfo()</function></entry>
    </row>
    <row>
     <entry>Support Function 2</entry>
     <entry>internal function <function>brin_minmax_add_value()</function></entry>
    </row>
    <row>
     <entry>Support Function 3</entry>
     <entry>internal function <function>brin_minmax_consistent()</function></entry>
    </row>
    <row>
     <entry>Support Function 4</entry>
     <entry>internal function <function>brin_minmax_union()</function></entry>
    </row>
    <row>
     <entry>Operator Strategy 1</entry>
     <entry>operator less-than</entry>
    </row>
    <row>
     <entry>Operator Strategy 2</entry>
     <entry>operator less-than-or-equal-to</entry>
    </row>
    <row>
     <entry>Operator Strategy 3</entry>
     <entry>operator equal-to</entry>
    </row>
    <row>
     <entry>Operator Strategy 4</entry>
     <entry>operator greater-than-or-equal-to</entry>
    </row>
    <row>
     <entry>Operator Strategy 5</entry>
     <entry>operator greater-than</entry>
    </row>
   </tbody>
  </tgroup>
 </table>

 <para>
  To write an operator class for a complex data type which has values
  included within another type, it's possible to use the inclusion support
  functions alongside the corresponding operators, as shown
  in <xref linkend="brin-extensibility-inclusion-table"/>.  It requires
  only a single additional function, which can be written in any language.
  More functions can be defined for additional functionality.  All operators
  are optional.  Some operators require other operators, as shown as
  dependencies on the table.
 </para>

 <table id="brin-extensibility-inclusion-table">
  <title>Function and Support Numbers for Inclusion Operator Classes</title>
  <tgroup cols="3">
   <colspec colname="col1" colwidth="1*"/>
   <colspec colname="col2" colwidth="2*"/>
   <colspec colname="col3" colwidth="1*"/>
   <thead>
    <row>
     <entry>Operator class member</entry>
     <entry>Object</entry>
     <entry>Dependency</entry>
    </row>
   </thead>
   <tbody>
    <row>
     <entry>Support Function 1</entry>
     <entry>internal function <function>brin_inclusion_opcinfo()</function></entry>
     <entry></entry>
    </row>
    <row>
     <entry>Support Function 2</entry>
     <entry>internal function <function>brin_inclusion_add_value()</function></entry>
     <entry></entry>
    </row>
    <row>
     <entry>Support Function 3</entry>
     <entry>internal function <function>brin_inclusion_consistent()</function></entry>
     <entry></entry>
    </row>
    <row>
     <entry>Support Function 4</entry>
     <entry>internal function <function>brin_inclusion_union()</function></entry>
     <entry></entry>
    </row>
    <row>
     <entry>Support Function 11</entry>
     <entry>function to merge two elements</entry>
     <entry></entry>
    </row>
    <row>
     <entry>Support Function 12</entry>
     <entry>optional function to check whether two elements are mergeable</entry>
     <entry></entry>
    </row>
    <row>
     <entry>Support Function 13</entry>
     <entry>optional function to check if an element is contained within another</entry>
     <entry></entry>
    </row>
    <row>
     <entry>Support Function 14</entry>
     <entry>optional function to check whether an element is empty</entry>
     <entry></entry>
    </row>
    <row>
     <entry>Operator Strategy 1</entry>
     <entry>operator left-of</entry>
     <entry>Operator Strategy 4</entry>
    </row>
    <row>
     <entry>Operator Strategy 2</entry>
     <entry>operator does-not-extend-to-the-right-of</entry>
     <entry>Operator Strategy 5</entry>
    </row>
    <row>
     <entry>Operator Strategy 3</entry>
     <entry>operator overlaps</entry>
     <entry></entry>
    </row>
    <row>
     <entry>Operator Strategy 4</entry>
     <entry>operator does-not-extend-to-the-left-of</entry>
     <entry>Operator Strategy 1</entry>
    </row>
    <row>
     <entry>Operator Strategy 5</entry>
     <entry>operator right-of</entry>
     <entry>Operator Strategy 2</entry>
    </row>
    <row>
     <entry>Operator Strategy 6, 18</entry>
     <entry>operator same-as-or-equal-to</entry>
     <entry>Operator Strategy 7</entry>
    </row>
    <row>
     <entry>Operator Strategy 7, 13, 16, 24, 25</entry>
     <entry>operator contains-or-equal-to</entry>
     <entry></entry>
    </row>
    <row>
     <entry>Operator Strategy 8, 14, 26, 27</entry>
     <entry>operator is-contained-by-or-equal-to</entry>
     <entry>Operator Strategy 3</entry>
    </row>
    <row>
     <entry>Operator Strategy 9</entry>
     <entry>operator does-not-extend-above</entry>
     <entry>Operator Strategy 11</entry>
    </row>
    <row>
     <entry>Operator Strategy 10</entry>
     <entry>operator is-below</entry>
     <entry>Operator Strategy 12</entry>
    </row>
    <row>
     <entry>Operator Strategy 11</entry>
     <entry>operator is-above</entry>
     <entry>Operator Strategy 9</entry>
    </row>
    <row>
     <entry>Operator Strategy 12</entry>
     <entry>operator does-not-extend-below</entry>
     <entry>Operator Strategy 10</entry>
    </row>
    <row>
     <entry>Operator Strategy 20</entry>
     <entry>operator less-than</entry>
     <entry>Operator Strategy 5</entry>
    </row>
    <row>
     <entry>Operator Strategy 21</entry>
     <entry>operator less-than-or-equal-to</entry>
     <entry>Operator Strategy 5</entry>
    </row>
    <row>
     <entry>Operator Strategy 22</entry>
     <entry>operator greater-than</entry>
     <entry>Operator Strategy 1</entry>
    </row>
    <row>
     <entry>Operator Strategy 23</entry>
     <entry>operator greater-than-or-equal-to</entry>
     <entry>Operator Strategy 1</entry>
    </row>
   </tbody>
  </tgroup>
 </table>

 <para>
    Support function numbers 1 through 10 are reserved for the BRIN internal
    functions, so the SQL level functions start with number 11.  Support
    function number 11 is the main function required to build the index.
    It should accept two arguments with the same data type as the operator class,
    and return the union of them.  The inclusion operator class can store union
    values with different data types if it is defined with the
    <literal>STORAGE</literal> parameter.  The return value of the union
    function should match the <literal>STORAGE</literal> data type.
 </para>

 <para>
    Support function numbers 12 and 14 are provided to support
    irregularities of built-in data types.  Function number 12
    is used to support network addresses from different families which
    are not mergeable.  Function number 14 is used to support
    empty ranges.  Function number 13 is an optional but
    recommended one, which allows the new value to be checked before
    it is passed to the union function.  As the BRIN framework can shortcut
    some operations when the union is not changed, using this
    function can improve index performance.
 </para>

 <para>
    Both minmax and inclusion operator classes support cross-data-type
    operators, though with these the dependencies become more complicated.
    The minmax operator class requires a full set of operators to be
    defined with both arguments having the same data type.  It allows
    additional data types to be supported by defining extra sets
    of operators.  Inclusion operator class operator strategies are dependent
    on another operator strategy as shown in
    <xref linkend="brin-extensibility-inclusion-table"/>, or the same
    operator strategy as themselves.  They require the dependency
    operator to be defined with the <literal>STORAGE</literal> data type as the
    left-hand-side argument and the other supported data type to be the
    right-hand-side argument of the supported operator.  See
    <literal>float4_minmax_ops</literal> as an example of minmax, and
    <literal>box_inclusion_ops</literal> as an example of inclusion.
 </para>
</sect1>
</chapter>
