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

<chapter id="spgist">
<title>SP-GiST Indexes</title>

   <indexterm>
    <primary>index</primary>
    <secondary>SP-GiST</secondary>
   </indexterm>

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

 <para>
  <acronym>SP-GiST</acronym> is an abbreviation for space-partitioned
  <acronym>GiST</acronym>.  <acronym>SP-GiST</acronym> supports partitioned
  search trees, which facilitate development of a wide range of different
  non-balanced data structures, such as quad-trees, k-d trees, and radix
  trees (tries).  The common feature of these structures is that they
  repeatedly divide the search space into partitions that need not be
  of equal size.  Searches that are well matched to the partitioning rule
  can be very fast.
 </para>

 <para>
  These popular data structures were originally developed for in-memory
  usage.  In main memory, they are usually designed as a set of dynamically
  allocated nodes linked by pointers.  This is not suitable for direct
  storing on disk, since these chains of pointers can be rather long which
  would require too many disk accesses.  In contrast, disk-based data
  structures should have a high fanout to minimize I/O.  The challenge
  addressed by <acronym>SP-GiST</acronym> is to map search tree nodes to
  disk pages in such a way that a search need access only a few disk pages,
  even if it traverses many nodes.
 </para>

 <para>
  Like <acronym>GiST</acronym>, <acronym>SP-GiST</acronym> is meant to allow
  the development of custom data types with the appropriate access methods,
  by an expert in the domain of the data type, rather than a database expert.
 </para>

 <para>
  Some of the information here is derived from Purdue University's
  SP-GiST Indexing Project
  <ulink url="https://www.cs.purdue.edu/spgist/">web site</ulink>.
  The <acronym>SP-GiST</acronym> implementation in
  <productname>PostgreSQL</productname> is primarily maintained by Teodor
  Sigaev and Oleg Bartunov, and there is more information on their
  <!-- URL will be changed -->
  <ulink url="http://www.sai.msu.su/~megera/wiki/spgist_dev">web site</ulink>.
 </para>

</sect1>

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

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

  <table id="spgist-builtin-opclasses-table">
   <title>Built-in <acronym>SP-GiST</acronym> Operator Classes</title>
   <tgroup cols="3">
    <thead>
     <row>
      <entry>Name</entry>
      <entry>Indexable Operators</entry>
      <entry>Ordering Operators</entry>
     </row>
    </thead>
    <tbody>
     <row>
      <entry valign="middle" morerows="11"><literal>box_ops</literal></entry>
      <entry><literal>&lt;&lt; (box,box)</literal></entry>
      <entry valign="middle" morerows="11"><literal>&lt;-&gt; (box,point)</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="5"><literal>kd_point_ops</literal></entry>
      <entry><literal>|&gt;&gt; (point,point)</literal></entry>
      <entry valign="middle" morerows="5"><literal>&lt;-&gt; (point,point)</literal></entry>
     </row>
     <row><entry><literal>&lt;&lt; (point,point)</literal></entry></row>
     <row><entry><literal>&gt;&gt; (point,point)</literal></entry></row>
     <row><entry><literal>&lt;&lt;| (point,point)</literal></entry></row>
     <row><entry><literal>~= (point,point)</literal></entry></row>
     <row><entry><literal>&lt;@ (point,box)</literal></entry></row>

     <row>
      <entry valign="middle" morerows="10"><literal>network_ops</literal></entry>
      <entry><literal>&lt;&lt; (inet,inet)</literal></entry>
      <entry valign="middle" morerows="10"></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>&lt;&gt; (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><literal>&amp;&amp; (inet,inet)</literal></entry></row>

     <row>
      <entry valign="middle" morerows="11"><literal>poly_ops</literal></entry>
      <entry><literal>&lt;&lt; (polygon,polygon)</literal></entry>
      <entry valign="middle" morerows="11"><literal>&lt;-&gt; (polygon,point)</literal></entry>
     </row>
     <row><entry><literal>&amp;&lt; (polygon,polygon)</literal></entry></row>
     <row><entry><literal>&amp;&gt; (polygon,polygon)</literal></entry></row>
     <row><entry><literal>&gt;&gt; (polygon,polygon)</literal></entry></row>
     <row><entry><literal>&lt;@ (polygon,polygon)</literal></entry></row>
     <row><entry><literal>@&gt; (polygon,polygon)</literal></entry></row>
     <row><entry><literal>~= (polygon,polygon)</literal></entry></row>
     <row><entry><literal>&amp;&amp; (polygon,polygon)</literal></entry></row>
     <row><entry><literal>&lt;&lt;| (polygon,polygon)</literal></entry></row>
     <row><entry><literal>&amp;&lt;| (polygon,polygon)</literal></entry></row>
     <row><entry><literal>|&gt;&gt; (polygon,polygon)</literal></entry></row>
     <row><entry><literal>|&amp;&gt; (polygon,polygon)</literal></entry></row>

     <row>
      <entry valign="middle" morerows="5"><literal>quad_point_ops</literal></entry>
      <entry><literal>|&gt;&gt; (point,point)</literal></entry>
      <entry valign="middle" morerows="5"><literal>&lt;-&gt; (point,point)</literal></entry>
     </row>
     <row><entry><literal>&lt;&lt; (point,point)</literal></entry></row>
     <row><entry><literal>&gt;&gt; (point,point)</literal></entry></row>
     <row><entry><literal>&lt;&lt;| (point,point)</literal></entry></row>
     <row><entry><literal>~= (point,point)</literal></entry></row>
     <row><entry><literal>&lt;@ (point,box)</literal></entry></row>

     <row>
      <entry valign="middle" morerows="9"><literal>range_ops</literal></entry>
      <entry><literal>= (anyrange,anyrange)</literal></entry>
      <entry valign="middle" morerows="9"></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="9"><literal>text_ops</literal></entry>
      <entry><literal>= (text,text)</literal></entry>
      <entry valign="middle" morerows="9"></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><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><literal>^@ (text,text)</literal></entry></row>
    </tbody>
   </tgroup>
  </table>

 <para>
  Of the two operator classes for type <type>point</type>,
  <literal>quad_point_ops</literal> is the default.  <literal>kd_point_ops</literal>
  supports the same operators but uses a different index data structure that
  may offer better performance in some applications.
 </para>
 <para>
  The <literal>quad_point_ops</literal>, <literal>kd_point_ops</literal> and
  <literal>poly_ops</literal> operator classes support the <literal>&lt;-&gt;</literal>
  ordering operator, which enables the k-nearest neighbor (<literal>k-NN</literal>)
  search over indexed point or polygon data sets.
 </para>

</sect1>

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

 <para>
  <acronym>SP-GiST</acronym> offers an interface with a high level of
  abstraction, requiring the access method developer to implement only
  methods specific to a given data type. The <acronym>SP-GiST</acronym> core
  is responsible for efficient disk mapping and searching the tree structure.
  It also takes care of concurrency and logging considerations.
 </para>

 <para>
  Leaf tuples of an <acronym>SP-GiST</acronym> tree usually contain values
  of the same data type as the indexed column, although it is also possible
  for them to contain lossy representations of the indexed column.
  Leaf tuples stored at the root level will directly represent
  the original indexed data value, but leaf tuples at lower
  levels might contain only a partial value, such as a suffix.
  In that case the operator class support functions must be able to
  reconstruct the original value using information accumulated from the
  inner tuples that are passed through to reach the leaf level.
 </para>

 <para>
  When an <acronym>SP-GiST</acronym> index is created with
  <literal>INCLUDE</literal> columns, the values of those columns are also
  stored in leaf tuples.  The <literal>INCLUDE</literal> columns are of no
  concern to the <acronym>SP-GiST</acronym> operator class, so they are
  not discussed further here.
 </para>

 <para>
  Inner tuples are more complex, since they are branching points in the
  search tree.  Each inner tuple contains a set of one or more
  <firstterm>nodes</firstterm>, which represent groups of similar leaf values.
  A node contains a downlink that leads either to another, lower-level inner
  tuple, or to a short list of leaf tuples that all lie on the same index page.
  Each node normally has a <firstterm>label</firstterm> that describes it; for example,
  in a radix tree the node label could be the next character of the string
  value.  (Alternatively, an operator class can omit the node labels, if it
  works with a fixed set of nodes for all inner tuples;
  see <xref linkend="spgist-null-labels"/>.)
  Optionally, an inner tuple can have a <firstterm>prefix</firstterm> value
  that describes all its members.  In a radix tree this could be the common
  prefix of the represented strings.  The prefix value is not necessarily
  really a prefix, but can be any data needed by the operator class;
  for example, in a quad-tree it can store the central point that the four
  quadrants are measured with respect to.  A quad-tree inner tuple would
  then also contain four nodes corresponding to the quadrants around this
  central point.
 </para>

 <para>
  Some tree algorithms require knowledge of level (or depth) of the current
  tuple, so the <acronym>SP-GiST</acronym> core provides the possibility for
  operator classes to manage level counting while descending the tree.
  There is also support for incrementally reconstructing the represented
  value when that is needed, and for passing down additional data (called
  <firstterm>traverse values</firstterm>) during a tree descent.
 </para>

 <note>
  <para>
   The <acronym>SP-GiST</acronym> core code takes care of null entries.
   Although <acronym>SP-GiST</acronym> indexes do store entries for nulls
   in indexed columns, this is hidden from the index operator class code:
   no null index entries or search conditions will ever be passed to the
   operator class methods.  (It is assumed that <acronym>SP-GiST</acronym>
   operators are strict and so cannot succeed for null values.)  Null values
   are therefore not discussed further here.
  </para>
 </note>

 <para>
  There are five user-defined methods that an index operator class for
  <acronym>SP-GiST</acronym> must provide, and two are optional.  All five
  mandatory methods follow the convention of accepting two <type>internal</type>
  arguments, the first of which is a pointer to a C struct containing input
  values for the support method, while the second argument is a pointer to a
  C struct where output values must be placed.  Four of the mandatory methods just
  return <type>void</type>, since all their results appear in the output struct; but
  <function>leaf_consistent</function> returns a <type>boolean</type> result.
  The methods must not modify any fields of their input structs.  In all
  cases, the output struct is initialized to zeroes before calling the
  user-defined method.  The optional sixth method <function>compress</function>
  accepts a <type>datum</type> to be indexed as the only argument and returns a value suitable
  for physical storage in a leaf tuple.  The optional seventh method
  <function>options</function> accepts an <type>internal</type> pointer to a C struct, where
  opclass-specific parameters should be placed, and returns <type>void</type>.
 </para>

 <para>
  The five mandatory user-defined methods are:
 </para>

 <variablelist>
    <varlistentry>
     <term><function>config</function></term>
     <listitem>
      <para>
       Returns static information about the index implementation, including
       the data type OIDs of the prefix and node label data types.
      </para>
     <para>
      The <acronym>SQL</acronym> declaration of the function must look like this:
<programlisting>
CREATE FUNCTION my_config(internal, internal) RETURNS void ...
</programlisting>
      The first argument is a pointer to a <structname>spgConfigIn</structname>
      C struct, containing input data for the function.
      The second argument is a pointer to a <structname>spgConfigOut</structname>
      C struct, which the function must fill with result data.
<programlisting>
typedef struct spgConfigIn
{
    Oid         attType;        /* Data type to be indexed */
} spgConfigIn;

typedef struct spgConfigOut
{
    Oid         prefixType;     /* Data type of inner-tuple prefixes */
    Oid         labelType;      /* Data type of inner-tuple node labels */
    Oid         leafType;       /* Data type of leaf-tuple values */
    bool        canReturnData;  /* Opclass can reconstruct original data */
    bool        longValuesOK;   /* Opclass can cope with values &gt; 1 page */
} spgConfigOut;
</programlisting>

      <structfield>attType</structfield> is passed in order to support polymorphic
      index operator classes; for ordinary fixed-data-type operator classes, it
      will always have the same value and so can be ignored.
     </para>

     <para>
      For operator classes that do not use prefixes,
      <structfield>prefixType</structfield> can be set to <literal>VOIDOID</literal>.
      Likewise, for operator classes that do not use node labels,
      <structfield>labelType</structfield> can be set to <literal>VOIDOID</literal>.
      <structfield>canReturnData</structfield> should be set true if the operator class
      is capable of reconstructing the originally-supplied index value.
      <structfield>longValuesOK</structfield> should be set true only when the
      <structfield>attType</structfield> is of variable length and the operator
      class is capable of segmenting long values by repeated suffixing
      (see <xref linkend="spgist-limits"/>).
     </para>

     <para>
      <structfield>leafType</structfield> should match the index storage type
      defined by the operator class's <structfield>opckeytype</structfield>
      catalog entry.
      (Note that <structfield>opckeytype</structfield> can be zero,
      implying the storage type is the same as the operator class's input
      type, which is the most common situation.)
      For reasons of backward compatibility, the <function>config</function>
      method can set <structfield>leafType</structfield> to some other value,
      and that value will be used; but this is deprecated since the index
      contents are then incorrectly identified in the catalogs.
      Also, it's permissible to
      leave <structfield>leafType</structfield> uninitialized (zero);
      that is interpreted as meaning the index storage type derived from
      <structfield>opckeytype</structfield>.
     </para>

     <para>
      When <structfield>attType</structfield>
      and <structfield>leafType</structfield> are different, the optional
      method <function>compress</function> must be provided.
      Method <function>compress</function> is responsible
      for transformation of datums to be indexed from <structfield>attType</structfield>
      to <structfield>leafType</structfield>.
     </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><function>choose</function></term>
     <listitem>
      <para>
        Chooses a method for inserting a new value into an inner tuple.
      </para>

     <para>
      The <acronym>SQL</acronym> declaration of the function must look like this:
<programlisting>
CREATE FUNCTION my_choose(internal, internal) RETURNS void ...
</programlisting>
      The first argument is a pointer to a <structname>spgChooseIn</structname>
      C struct, containing input data for the function.
      The second argument is a pointer to a <structname>spgChooseOut</structname>
      C struct, which the function must fill with result data.
<programlisting>
typedef struct spgChooseIn
{
    Datum       datum;          /* original datum to be indexed */
    Datum       leafDatum;      /* current datum to be stored at leaf */
    int         level;          /* current level (counting from zero) */

    /* Data from current inner tuple */
    bool        allTheSame;     /* tuple is marked all-the-same? */
    bool        hasPrefix;      /* tuple has a prefix? */
    Datum       prefixDatum;    /* if so, the prefix value */
    int         nNodes;         /* number of nodes in the inner tuple */
    Datum      *nodeLabels;     /* node label values (NULL if none) */
} spgChooseIn;

typedef enum spgChooseResultType
{
    spgMatchNode = 1,           /* descend into existing node */
    spgAddNode,                 /* add a node to the inner tuple */
    spgSplitTuple               /* split inner tuple (change its prefix) */
} spgChooseResultType;

typedef struct spgChooseOut
{
    spgChooseResultType resultType;     /* action code, see above */
    union
    {
        struct                  /* results for spgMatchNode */
        {
            int         nodeN;      /* descend to this node (index from 0) */
            int         levelAdd;   /* increment level by this much */
            Datum       restDatum;  /* new leaf datum */
        }           matchNode;
        struct                  /* results for spgAddNode */
        {
            Datum       nodeLabel;  /* new node's label */
            int         nodeN;      /* where to insert it (index from 0) */
        }           addNode;
        struct                  /* results for spgSplitTuple */
        {
            /* Info to form new upper-level inner tuple with one child tuple */
            bool        prefixHasPrefix;    /* tuple should have a prefix? */
            Datum       prefixPrefixDatum;  /* if so, its value */
            int         prefixNNodes;       /* number of nodes */
            Datum      *prefixNodeLabels;   /* their labels (or NULL for
                                             * no labels) */
            int         childNodeN;         /* which node gets child tuple */

            /* Info to form new lower-level inner tuple with all old nodes */
            bool        postfixHasPrefix;   /* tuple should have a prefix? */
            Datum       postfixPrefixDatum; /* if so, its value */
        }           splitTuple;
    }           result;
} spgChooseOut;
</programlisting>

       <structfield>datum</structfield> is the original datum of
       <structname>spgConfigIn</structname>.<structfield>attType</structfield>
       type that was to be inserted into the index.
       <structfield>leafDatum</structfield> is a value of
       <structname>spgConfigOut</structname>.<structfield>leafType</structfield>
       type, which is initially a result of method
       <function>compress</function> applied to <structfield>datum</structfield>
       when method <function>compress</function> is provided, or the same value as
       <structfield>datum</structfield> otherwise.
       <structfield>leafDatum</structfield> can change at lower levels of the tree
       if the <function>choose</function> or <function>picksplit</function>
       methods change it.  When the insertion search reaches a leaf page,
       the current value of <structfield>leafDatum</structfield> is what will be stored
       in the newly created leaf tuple.
       <structfield>level</structfield> is the current inner tuple's level, starting at
       zero for the root level.
       <structfield>allTheSame</structfield> is true if the current inner tuple is
       marked as containing multiple equivalent nodes
       (see <xref linkend="spgist-all-the-same"/>).
       <structfield>hasPrefix</structfield> is true if the current inner tuple contains
       a prefix; if so,
       <structfield>prefixDatum</structfield> is its value.
       <structfield>nNodes</structfield> is the number of child nodes contained in the
       inner tuple, and
       <structfield>nodeLabels</structfield> is an array of their label values, or
       NULL if there are no labels.
      </para>

      <para>
       The <function>choose</function> function can determine either that
       the new value matches one of the existing child nodes, or that a new
       child node must be added, or that the new value is inconsistent with
       the tuple prefix and so the inner tuple must be split to create a
       less restrictive prefix.
      </para>

      <para>
       If the new value matches one of the existing child nodes,
       set <structfield>resultType</structfield> to <literal>spgMatchNode</literal>.
       Set <structfield>nodeN</structfield> to the index (from zero) of that node in
       the node array.
       Set <structfield>levelAdd</structfield> to the increment in
       <structfield>level</structfield> caused by descending through that node,
       or leave it as zero if the operator class does not use levels.
       Set <structfield>restDatum</structfield> to equal <structfield>leafDatum</structfield>
       if the operator class does not modify datums from one level to the
       next, or otherwise set it to the modified value to be used as
       <structfield>leafDatum</structfield> at the next level.
      </para>

      <para>
       If a new child node must be added,
       set <structfield>resultType</structfield> to <literal>spgAddNode</literal>.
       Set <structfield>nodeLabel</structfield> to the label to be used for the new
       node, and set <structfield>nodeN</structfield> to the index (from zero) at which
       to insert the node in the node array.
       After the node has been added, the <function>choose</function>
       function will be called again with the modified inner tuple;
       that call should result in an <literal>spgMatchNode</literal> result.
      </para>

      <para>
       If the new value is inconsistent with the tuple prefix,
       set <structfield>resultType</structfield> to <literal>spgSplitTuple</literal>.
       This action moves all the existing nodes into a new lower-level
       inner tuple, and replaces the existing inner tuple with a tuple
       having a single downlink pointing to the new lower-level inner tuple.
       Set <structfield>prefixHasPrefix</structfield> to indicate whether the new
       upper tuple should have a prefix, and if so set
       <structfield>prefixPrefixDatum</structfield> to the prefix value.  This new
       prefix value must be sufficiently less restrictive than the original
       to accept the new value to be indexed.
       Set <structfield>prefixNNodes</structfield> to the number of nodes needed in the
       new tuple, and set <structfield>prefixNodeLabels</structfield> to a palloc'd array
       holding their labels, or to NULL if node labels are not required.
       Note that the total size of the new upper tuple must be no more
       than the total size of the tuple it is replacing; this constrains
       the lengths of the new prefix and new labels.
       Set <structfield>childNodeN</structfield> to the index (from zero) of the node
       that will downlink to the new lower-level inner tuple.
       Set <structfield>postfixHasPrefix</structfield> to indicate whether the new
       lower-level inner tuple should have a prefix, and if so set
       <structfield>postfixPrefixDatum</structfield> to the prefix value.  The
       combination of these two prefixes and the downlink node's label
       (if any) must have the same meaning as the original prefix, because
       there is no opportunity to alter the node labels that are moved to
       the new lower-level tuple, nor to change any child index entries.
       After the node has been split, the <function>choose</function>
       function will be called again with the replacement inner tuple.
       That call may return an <literal>spgAddNode</literal> result, if no suitable
       node was created by the <literal>spgSplitTuple</literal> action.  Eventually
       <function>choose</function> must return <literal>spgMatchNode</literal> to
       allow the insertion to descend to the next level.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><function>picksplit</function></term>
     <listitem>
      <para>
       Decides how to create a new inner tuple over a set of leaf tuples.
      </para>

      <para>
        The <acronym>SQL</acronym> declaration of the function must look like this:
<programlisting>
CREATE FUNCTION my_picksplit(internal, internal) RETURNS void ...
</programlisting>
      The first argument is a pointer to a <structname>spgPickSplitIn</structname>
      C struct, containing input data for the function.
      The second argument is a pointer to a <structname>spgPickSplitOut</structname>
      C struct, which the function must fill with result data.
<programlisting>
typedef struct spgPickSplitIn
{
    int         nTuples;        /* number of leaf tuples */
    Datum      *datums;         /* their datums (array of length nTuples) */
    int         level;          /* current level (counting from zero) */
} spgPickSplitIn;

typedef struct spgPickSplitOut
{
    bool        hasPrefix;      /* new inner tuple should have a prefix? */
    Datum       prefixDatum;    /* if so, its value */

    int         nNodes;         /* number of nodes for new inner tuple */
    Datum      *nodeLabels;     /* their labels (or NULL for no labels) */

    int        *mapTuplesToNodes;   /* node index for each leaf tuple */
    Datum      *leafTupleDatums;    /* datum to store in each new leaf tuple */
} spgPickSplitOut;
</programlisting>

       <structfield>nTuples</structfield> is the number of leaf tuples provided.
       <structfield>datums</structfield> is an array of their datum values of
       <structname>spgConfigOut</structname>.<structfield>leafType</structfield>
       type.
       <structfield>level</structfield> is the current level that all the leaf tuples
       share, which will become the level of the new inner tuple.
      </para>

      <para>
       Set <structfield>hasPrefix</structfield> to indicate whether the new inner
       tuple should have a prefix, and if so set
       <structfield>prefixDatum</structfield> to the prefix value.
       Set <structfield>nNodes</structfield> to indicate the number of nodes that
       the new inner tuple will contain, and
       set <structfield>nodeLabels</structfield> to an array of their label values,
       or to NULL if node labels are not required.
       Set <structfield>mapTuplesToNodes</structfield> to an array that gives the index
       (from zero) of the node that each leaf tuple should be assigned to.
       Set <structfield>leafTupleDatums</structfield> to an array of the values to
       be stored in the new leaf tuples (these will be the same as the
       input <structfield>datums</structfield> if the operator class does not modify
       datums from one level to the next).
       Note that the <function>picksplit</function> function is
       responsible for palloc'ing the
       <structfield>nodeLabels</structfield>, <structfield>mapTuplesToNodes</structfield> and
       <structfield>leafTupleDatums</structfield> arrays.
      </para>

      <para>
       If more than one leaf tuple is supplied, it is expected that the
       <function>picksplit</function> function will classify them into more than
       one node; otherwise it is not possible to split the leaf tuples
       across multiple pages, which is the ultimate purpose of this
       operation.  Therefore, if the <function>picksplit</function> function
       ends up placing all the leaf tuples in the same node, the core
       SP-GiST code will override that decision and generate an inner
       tuple in which the leaf tuples are assigned at random to several
       identically-labeled nodes.  Such a tuple is marked
       <literal>allTheSame</literal> to signify that this has happened.  The
       <function>choose</function> and <function>inner_consistent</function> functions
       must take suitable care with such inner tuples.
       See <xref linkend="spgist-all-the-same"/> for more information.
      </para>

      <para>
       <function>picksplit</function> can be applied to a single leaf tuple only
       in the case that the <function>config</function> function set
       <structfield>longValuesOK</structfield> to true and a larger-than-a-page input
       value has been supplied.  In this case the point of the operation is
       to strip off a prefix and produce a new, shorter leaf datum value.
       The call will be repeated until a leaf datum short enough to fit on
       a page has been produced.  See <xref linkend="spgist-limits"/> for
       more information.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><function>inner_consistent</function></term>
     <listitem>
      <para>
       Returns set of nodes (branches) to follow during tree search.
      </para>

      <para>
       The <acronym>SQL</acronym> declaration of the function must look like this:
<programlisting>
CREATE FUNCTION my_inner_consistent(internal, internal) RETURNS void ...
</programlisting>
      The first argument is a pointer to a <structname>spgInnerConsistentIn</structname>
      C struct, containing input data for the function.
      The second argument is a pointer to a <structname>spgInnerConsistentOut</structname>
      C struct, which the function must fill with result data.

<programlisting>
typedef struct spgInnerConsistentIn
{
    ScanKey     scankeys;       /* array of operators and comparison values */
    ScanKey     orderbys;       /* array of ordering operators and comparison
                                 * values */
    int         nkeys;          /* length of scankeys array */
    int         norderbys;      /* length of orderbys array */

    Datum       reconstructedValue;     /* value reconstructed at parent */
    void       *traversalValue; /* opclass-specific traverse value */
    MemoryContext traversalMemoryContext;   /* put new traverse values here */
    int         level;          /* current level (counting from zero) */
    bool        returnData;     /* original data must be returned? */

    /* Data from current inner tuple */
    bool        allTheSame;     /* tuple is marked all-the-same? */
    bool        hasPrefix;      /* tuple has a prefix? */
    Datum       prefixDatum;    /* if so, the prefix value */
    int         nNodes;         /* number of nodes in the inner tuple */
    Datum      *nodeLabels;     /* node label values (NULL if none) */
} spgInnerConsistentIn;

typedef struct spgInnerConsistentOut
{
    int         nNodes;         /* number of child nodes to be visited */
    int        *nodeNumbers;    /* their indexes in the node array */
    int        *levelAdds;      /* increment level by this much for each */
    Datum      *reconstructedValues;    /* associated reconstructed values */
    void      **traversalValues;        /* opclass-specific traverse values */
    double    **distances;              /* associated distances */
} spgInnerConsistentOut;
</programlisting>

       The array <structfield>scankeys</structfield>, of length <structfield>nkeys</structfield>,
       describes the index search condition(s).  These conditions are
       combined with AND &mdash; only index entries that satisfy all of
       them are interesting.  (Note that <structfield>nkeys</structfield> = 0 implies
       that all index entries satisfy the query.)  Usually the consistent
       function only cares about the <structfield>sk_strategy</structfield> and
       <structfield>sk_argument</structfield> fields of each array entry, which
       respectively give the indexable operator and comparison value.
       In particular it is not necessary to check <structfield>sk_flags</structfield> to
       see if the comparison value is NULL, because the SP-GiST core code
       will filter out such conditions.
       The array <structfield>orderbys</structfield>, of length <structfield>norderbys</structfield>,
       describes ordering operators (if any) in the same manner.
       <structfield>reconstructedValue</structfield> is the value reconstructed for the
       parent tuple; it is <literal>(Datum) 0</literal> at the root level or if the
       <function>inner_consistent</function> function did not provide a value at the
       parent level.
       <structfield>traversalValue</structfield> is a pointer to any traverse data
       passed down from the previous call of <function>inner_consistent</function>
       on the parent index tuple, or NULL at the root level.
       <structfield>traversalMemoryContext</structfield> is the memory context in which
       to store output traverse values (see below).
       <structfield>level</structfield> is the current inner tuple's level, starting at
       zero for the root level.
       <structfield>returnData</structfield> is <literal>true</literal> if reconstructed data is
       required for this query; this will only be so if the
       <function>config</function> function asserted <structfield>canReturnData</structfield>.
       <structfield>allTheSame</structfield> is true if the current inner tuple is
       marked <quote>all-the-same</quote>; in this case all the nodes have the
       same label (if any) and so either all or none of them match the query
       (see <xref linkend="spgist-all-the-same"/>).
       <structfield>hasPrefix</structfield> is true if the current inner tuple contains
       a prefix; if so,
       <structfield>prefixDatum</structfield> is its value.
       <structfield>nNodes</structfield> is the number of child nodes contained in the
       inner tuple, and
       <structfield>nodeLabels</structfield> is an array of their label values, or
       NULL if the nodes do not have labels.
      </para>

      <para>
       <structfield>nNodes</structfield> must be set to the number of child nodes that
       need to be visited by the search, and
       <structfield>nodeNumbers</structfield> must be set to an array of their indexes.
       If the operator class keeps track of levels, set
       <structfield>levelAdds</structfield> to an array of the level increments
       required when descending to each node to be visited.  (Often these
       increments will be the same for all the nodes, but that's not
       necessarily so, so an array is used.)
       If value reconstruction is needed, set
       <structfield>reconstructedValues</structfield> to an array of the values
       reconstructed for each child node to be visited; otherwise, leave
       <structfield>reconstructedValues</structfield> as NULL.
       The reconstructed values are assumed to be of type
       <structname>spgConfigOut</structname>.<structfield>leafType</structfield>.
       (However, since the core system will do nothing with them except
       possibly copy them, it is sufficient for them to have the
       same <literal>typlen</literal> and <literal>typbyval</literal>
       properties as <structfield>leafType</structfield>.)
       If ordered search is performed, set <structfield>distances</structfield>
       to an array of distance values according to <structfield>orderbys</structfield>
       array (nodes with lowest distances will be processed first).  Leave it
       NULL otherwise.
       If it is desired to pass down additional out-of-band information
       (<quote>traverse values</quote>) to lower levels of the tree search,
       set <structfield>traversalValues</structfield> to an array of the appropriate
       traverse values, one for each child node to be visited; otherwise,
       leave <structfield>traversalValues</structfield> as NULL.
       Note that the <function>inner_consistent</function> function is
       responsible for palloc'ing the
       <structfield>nodeNumbers</structfield>, <structfield>levelAdds</structfield>,
       <structfield>distances</structfield>,
       <structfield>reconstructedValues</structfield>, and
       <structfield>traversalValues</structfield> arrays in the current memory context.
       However, any output traverse values pointed to by
       the <structfield>traversalValues</structfield> array should be allocated
       in <structfield>traversalMemoryContext</structfield>.
       Each traverse value must be a single palloc'd chunk.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><function>leaf_consistent</function></term>
     <listitem>
      <para>
       Returns true if a leaf tuple satisfies a query.
      </para>

      <para>
       The <acronym>SQL</acronym> declaration of the function must look like this:
<programlisting>
CREATE FUNCTION my_leaf_consistent(internal, internal) RETURNS bool ...
</programlisting>
      The first argument is a pointer to a <structname>spgLeafConsistentIn</structname>
      C struct, containing input data for the function.
      The second argument is a pointer to a <structname>spgLeafConsistentOut</structname>
      C struct, which the function must fill with result data.
<programlisting>
typedef struct spgLeafConsistentIn
{
    ScanKey     scankeys;       /* array of operators and comparison values */
    ScanKey     orderbys;       /* array of ordering operators and comparison
                                 * values */
    int         nkeys;          /* length of scankeys array */
    int         norderbys;      /* length of orderbys array */

    Datum       reconstructedValue;     /* value reconstructed at parent */
    void       *traversalValue; /* opclass-specific traverse value */
    int         level;          /* current level (counting from zero) */
    bool        returnData;     /* original data must be returned? */

    Datum       leafDatum;      /* datum in leaf tuple */
} spgLeafConsistentIn;

typedef struct spgLeafConsistentOut
{
    Datum       leafValue;        /* reconstructed original data, if any */
    bool        recheck;          /* set true if operator must be rechecked */
    bool        recheckDistances; /* set true if distances must be rechecked */
    double     *distances;        /* associated distances */
} spgLeafConsistentOut;
</programlisting>

       The array <structfield>scankeys</structfield>, of length <structfield>nkeys</structfield>,
       describes the index search condition(s).  These conditions are
       combined with AND &mdash; only index entries that satisfy all of
       them satisfy the query.  (Note that <structfield>nkeys</structfield> = 0 implies
       that all index entries satisfy the query.)  Usually the consistent
       function only cares about the <structfield>sk_strategy</structfield> and
       <structfield>sk_argument</structfield> fields of each array entry, which
       respectively give the indexable operator and comparison value.
       In particular it is not necessary to check <structfield>sk_flags</structfield> to
       see if the comparison value is NULL, because the SP-GiST core code
       will filter out such conditions.
       The array <structfield>orderbys</structfield>, of length <structfield>norderbys</structfield>,
       describes the ordering operators in the same manner.
       <structfield>reconstructedValue</structfield> is the value reconstructed for the
       parent tuple; it is <literal>(Datum) 0</literal> at the root level or if the
       <function>inner_consistent</function> function did not provide a value at the
       parent level.
       <structfield>traversalValue</structfield> is a pointer to any traverse data
       passed down from the previous call of <function>inner_consistent</function>
       on the parent index tuple, or NULL at the root level.
       <structfield>level</structfield> is the current leaf tuple's level, starting at
       zero for the root level.
       <structfield>returnData</structfield> is <literal>true</literal> if reconstructed data is
       required for this query; this will only be so if the
       <function>config</function> function asserted <structfield>canReturnData</structfield>.
       <structfield>leafDatum</structfield> is the key value of
       <structname>spgConfigOut</structname>.<structfield>leafType</structfield>
       stored in the current leaf tuple.
      </para>

      <para>
       The function must return <literal>true</literal> if the leaf tuple matches the
       query, or <literal>false</literal> if not.  In the <literal>true</literal> case,
       if <structfield>returnData</structfield> is <literal>true</literal> then
       <structfield>leafValue</structfield> must be set to the value (of type
       <structname>spgConfigIn</structname>.<structfield>attType</structfield>)
       originally supplied to be indexed for this leaf tuple.  Also,
       <structfield>recheck</structfield> may be set to <literal>true</literal> if the match
       is uncertain and so the operator(s) must be re-applied to the actual
       heap tuple to verify the match.
       If ordered search is performed, set <structfield>distances</structfield>
       to an array of distance values according to <structfield>orderbys</structfield>
       array.  Leave it NULL otherwise.  If at least one of returned distances
       is not exact, set <structfield>recheckDistances</structfield> to true.
       In this case, the executor will calculate the exact distances after
       fetching the tuple from the heap, and will reorder the tuples if needed.
      </para>
     </listitem>
    </varlistentry>
   </variablelist>

 <para>
  The optional user-defined methods are:
 </para>

 <variablelist>
    <varlistentry>
     <term><function>Datum compress(Datum in)</function></term>
     <listitem>
      <para>
       Converts a data item into a format suitable for physical storage in
       a leaf tuple of the index.  It accepts a value of type
       <structname>spgConfigIn</structname>.<structfield>attType</structfield>
       and returns a value of type
       <structname>spgConfigOut</structname>.<structfield>leafType</structfield>.
       The output value must not contain an out-of-line TOAST pointer.
      </para>

      <para>
       Note: the <function>compress</function> method is only applied to
       values to be stored.  The consistent methods receive query scankeys
       unchanged, without transformation using <function>compress</function>.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><function>options</function></term>
     <listitem>
      <para>
       Defines a set of user-visible parameters that control operator class
       behavior.
      </para>

      <para>
        The <acronym>SQL</acronym> declaration of the function must look like this:

<programlisting>
CREATE OR REPLACE FUNCTION my_options(internal)
RETURNS void
AS 'MODULE_PATHNAME'
LANGUAGE C STRICT;
</programlisting>
      </para>

      <para>
       The 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 the representation of the key in <acronym>SP-GiST</acronym> is
       flexible, it may depend on user-specified parameters.
      </para>
     </listitem>
    </varlistentry>
  </variablelist>

  <para>
   All the SP-GiST support methods are normally called in a short-lived
   memory context; that is, <varname>CurrentMemoryContext</varname> will be reset
   after processing of each tuple.  It is therefore not very important to
   worry about pfree'ing everything you palloc.  (The <function>config</function>
   method is an exception: it should try to avoid leaking memory.  But
   usually the <function>config</function> method need do nothing but assign
   constants into the passed parameter struct.)
  </para>

  <para>
   If the indexed column is of a collatable data type, the index collation
   will be passed to all the support methods, using the standard
   <function>PG_GET_COLLATION()</function> mechanism.
  </para>

</sect1>

<sect1 id="spgist-implementation">
 <title>Implementation</title>

  <para>
   This section covers implementation details and other tricks that are
   useful for implementers of <acronym>SP-GiST</acronym> operator classes to
   know.
  </para>

 <sect2 id="spgist-limits">
  <title>SP-GiST Limits</title>

  <para>
   Individual leaf tuples and inner tuples must fit on a single index page
   (8kB by default).  Therefore, when indexing values of variable-length
   data types, long values can only be supported by methods such as radix
   trees, in which each level of the tree includes a prefix that is short
   enough to fit on a page, and the final leaf level includes a suffix also
   short enough to fit on a page.  The operator class should set
   <structfield>longValuesOK</structfield> to true only if it is prepared to arrange for
   this to happen.  Otherwise, the <acronym>SP-GiST</acronym> core will
   reject any request to index a value that is too large to fit
   on an index page.
  </para>

  <para>
   Likewise, it is the operator class's responsibility that inner tuples
   do not grow too large to fit on an index page; this limits the number
   of child nodes that can be used in one inner tuple, as well as the
   maximum size of a prefix value.
  </para>

  <para>
   Another limitation is that when an inner tuple's node points to a set
   of leaf tuples, those tuples must all be in the same index page.
   (This is a design decision to reduce seeking and save space in the
   links that chain such tuples together.)  If the set of leaf tuples
   grows too large for a page, a split is performed and an intermediate
   inner tuple is inserted.  For this to fix the problem, the new inner
   tuple <emphasis>must</emphasis> divide the set of leaf values into more than one
   node group.  If the operator class's <function>picksplit</function> function
   fails to do that, the <acronym>SP-GiST</acronym> core resorts to
   extraordinary measures described in <xref linkend="spgist-all-the-same"/>.
  </para>

  <para>
   When <structfield>longValuesOK</structfield> is true, it is expected
   that successive levels of the <acronym>SP-GiST</acronym> tree will
   absorb more and more information into the prefixes and node labels of
   the inner tuples, making the required leaf datum smaller and smaller,
   so that eventually it will fit on a page.
   To prevent bugs in operator classes from causing infinite insertion
   loops, the <acronym>SP-GiST</acronym> core will raise an error if the
   leaf datum does not become any smaller within ten cycles
   of <function>choose</function> method calls.
  </para>
 </sect2>

 <sect2 id="spgist-null-labels">
  <title>SP-GiST Without Node Labels</title>

  <para>
   Some tree algorithms use a fixed set of nodes for each inner tuple;
   for example, in a quad-tree there are always exactly four nodes
   corresponding to the four quadrants around the inner tuple's centroid
   point.  In such a case the code typically works with the nodes by
   number, and there is no need for explicit node labels.  To suppress
   node labels (and thereby save some space), the <function>picksplit</function>
   function can return NULL for the <structfield>nodeLabels</structfield> array,
   and likewise the <function>choose</function> function can return NULL for
   the <structfield>prefixNodeLabels</structfield> array during
   a <literal>spgSplitTuple</literal> action.
   This will in turn result in <structfield>nodeLabels</structfield> being NULL during
   subsequent calls to <function>choose</function> and <function>inner_consistent</function>.
   In principle, node labels could be used for some inner tuples and omitted
   for others in the same index.
  </para>

  <para>
   When working with an inner tuple having unlabeled nodes, it is an error
   for <function>choose</function> to return <literal>spgAddNode</literal>, since the set
   of nodes is supposed to be fixed in such cases.
  </para>
 </sect2>

 <sect2 id="spgist-all-the-same">
  <title><quote>All-the-Same</quote> Inner Tuples</title>

  <para>
   The <acronym>SP-GiST</acronym> core can override the results of the
   operator class's <function>picksplit</function> function when
   <function>picksplit</function> fails to divide the supplied leaf values into
   at least two node categories.  When this happens, the new inner tuple
   is created with multiple nodes that each have the same label (if any)
   that <function>picksplit</function> gave to the one node it did use, and the
   leaf values are divided at random among these equivalent nodes.
   The <literal>allTheSame</literal> flag is set on the inner tuple to warn the
   <function>choose</function> and <function>inner_consistent</function> functions that the
   tuple does not have the node set that they might otherwise expect.
  </para>

  <para>
   When dealing with an <literal>allTheSame</literal> tuple, a <function>choose</function>
   result of <literal>spgMatchNode</literal> is interpreted to mean that the new
   value can be assigned to any of the equivalent nodes; the core code will
   ignore the supplied  <structfield>nodeN</structfield> value and descend into one
   of the nodes at random (so as to keep the tree balanced).  It is an
   error for <function>choose</function> to return <literal>spgAddNode</literal>, since
   that would make the nodes not all equivalent; the
   <literal>spgSplitTuple</literal> action must be used if the value to be inserted
   doesn't match the existing nodes.
  </para>

  <para>
   When dealing with an <literal>allTheSame</literal> tuple, the
   <function>inner_consistent</function> function should return either all or none
   of the nodes as targets for continuing the index search, since they are
   all equivalent.  This may or may not require any special-case code,
   depending on how much the <function>inner_consistent</function> function normally
   assumes about the meaning of the nodes.
  </para>
 </sect2>

</sect1>

<sect1 id="spgist-examples">
 <title>Examples</title>

 <para>
  The <productname>PostgreSQL</productname> source distribution includes
  several examples of index operator classes for <acronym>SP-GiST</acronym>,
  as described in <xref linkend="spgist-builtin-opclasses-table"/>.  Look
  into <filename>src/backend/access/spgist/</filename>
  and <filename>src/backend/utils/adt/</filename> to see the code.
 </para>

</sect1>

</chapter>
