Extend index AM API for parallel index scans.

[postgresql] / doc / src / sgml / indexam.sgml

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

<chapter id="indexam">
 <title>Index Access Method Interface Definition</title>

  <para>
   This chapter defines the interface between the core
   <productname>PostgreSQL</productname> system and <firstterm>index access
   methods</>, which manage individual index types.  The core system
   knows nothing about indexes beyond what is specified here, so it is
   possible to develop entirely new index types by writing add-on code.
  </para>

  <para>
   All indexes in <productname>PostgreSQL</productname> are what are known
   technically as <firstterm>secondary indexes</>; that is, the index is
   physically separate from the table file that it describes.  Each index
   is stored as its own physical <firstterm>relation</> and so is described
   by an entry in the <structname>pg_class</> catalog.  The contents of an
   index are entirely under the control of its index access method.  In
   practice, all index access methods divide indexes into standard-size
   pages so that they can use the regular storage manager and buffer manager
   to access the index contents.  (All the existing index access methods
   furthermore use the standard page layout described in <xref
   linkend="storage-page-layout">, and most use the same format for index
   tuple headers; but these decisions are not forced on an access method.)
  </para>

  <para>
   An index is effectively a mapping from some data key values to
   <firstterm>tuple identifiers</>, or <acronym>TIDs</>, of row versions
   (tuples) in the index's parent table.  A TID consists of a
   block number and an item number within that block (see <xref
   linkend="storage-page-layout">).  This is sufficient
   information to fetch a particular row version from the table.
   Indexes are not directly aware that under MVCC, there might be multiple
   extant versions of the same logical row; to an index, each tuple is
   an independent object that needs its own index entry.  Thus, an
   update of a row always creates all-new index entries for the row, even if
   the key values did not change.  (HOT tuples are an exception to this
   statement; but indexes do not deal with those, either.)  Index entries for
   dead tuples are reclaimed (by vacuuming) when the dead tuples themselves
   are reclaimed.
  </para>

 <sect1 id="index-api">
  <title>Basic API Structure for Indexes</title>

  <para>
   Each index access method is described by a row in the
   <link linkend="catalog-pg-am"><structname>pg_am</structname></link>
   system catalog.  The <structname>pg_am</structname> entry
   specifies a name and a <firstterm>handler function</> for the access
   method.  These entries can be created and deleted using the
   <xref linkend="sql-create-access-method"> and
   <xref linkend="sql-drop-access-method"> SQL commands.
  </para>

  <para>
   An index access method handler function must be declared to accept a
   single argument of type <type>internal</> and to return the
   pseudo-type <type>index_am_handler</>.  The argument is a dummy value that
   simply serves to prevent handler functions from being called directly from
   SQL commands.  The result of the function must be a palloc'd struct of
   type <structname>IndexAmRoutine</structname>, which contains everything
   that the core code needs to know to make use of the index access method.
   The <structname>IndexAmRoutine</structname> struct, also called the access
   method's <firstterm>API struct</>, includes fields specifying assorted
   fixed properties of the access method, such as whether it can support
   multicolumn indexes.  More importantly, it contains pointers to support
   functions for the access method, which do all of the real work to access
   indexes.  These support functions are plain C functions and are not
   visible or callable at the SQL level.  The support functions are described
   in <xref linkend="index-functions">.
  </para>

  <para>
   The structure <structname>IndexAmRoutine</structname> is defined thus:
<programlisting>
typedef struct IndexAmRoutine
{
    NodeTag     type;

    /*
     * Total number of strategies (operators) by which we can traverse/search
     * this AM.  Zero if AM does not have a fixed set of strategy assignments.
     */
    uint16      amstrategies;
    /* total number of support functions that this AM uses */
    uint16      amsupport;
    /* does AM support ORDER BY indexed column's value? */
    bool        amcanorder;
    /* does AM support ORDER BY result of an operator on indexed column? */
    bool        amcanorderbyop;
    /* does AM support backward scanning? */
    bool        amcanbackward;
    /* does AM support UNIQUE indexes? */
    bool        amcanunique;
    /* does AM support multi-column indexes? */
    bool        amcanmulticol;
    /* does AM require scans to have a constraint on the first index column? */
    bool        amoptionalkey;
    /* does AM handle ScalarArrayOpExpr quals? */
    bool        amsearcharray;
    /* does AM handle IS NULL/IS NOT NULL quals? */
    bool        amsearchnulls;
    /* can index storage data type differ from column data type? */
    bool        amstorage;
    /* can an index of this type be clustered on? */
    bool        amclusterable;
    /* does AM handle predicate locks? */
    bool        ampredlocks;
    /* type of data stored in index, or InvalidOid if variable */
    Oid         amkeytype;

    /* interface functions */
    ambuild_function ambuild;
    ambuildempty_function ambuildempty;
    aminsert_function aminsert;
    ambulkdelete_function ambulkdelete;
    amvacuumcleanup_function amvacuumcleanup;
    amcanreturn_function amcanreturn;   /* can be NULL */
    amcostestimate_function amcostestimate;
    amoptions_function amoptions;
    amproperty_function amproperty;     /* can be NULL */
    amvalidate_function amvalidate;
    ambeginscan_function ambeginscan;
    amrescan_function amrescan;
    amgettuple_function amgettuple;     /* can be NULL */
    amgetbitmap_function amgetbitmap;   /* can be NULL */
    amendscan_function amendscan;
    ammarkpos_function ammarkpos;       /* can be NULL */
    amrestrpos_function amrestrpos;     /* can be NULL */

    /* interface functions to support parallel index scans */
    amestimateparallelscan_function amestimateparallelscan;    /* can be NULL */
    aminitparallelscan_function aminitparallelscan;    /* can be NULL */
    amparallelrescan_function amparallelrescan;    /* can be NULL */
} IndexAmRoutine;
</programlisting>
  </para>

  <para>
   To be useful, an index access method must also have one or more
   <firstterm>operator families</> and
   <firstterm>operator classes</> defined in
   <link linkend="catalog-pg-opfamily"><structname>pg_opfamily</structname></link>,
   <link linkend="catalog-pg-opclass"><structname>pg_opclass</structname></link>,
   <link linkend="catalog-pg-amop"><structname>pg_amop</structname></link>, and
   <link linkend="catalog-pg-amproc"><structname>pg_amproc</structname></link>.
   These entries allow the planner
   to determine what kinds of query qualifications can be used with
   indexes of this access method.  Operator families and classes are described
   in <xref linkend="xindex">, which is prerequisite material for reading
   this chapter.
  </para>

  <para>
   An individual index is defined by a
   <link linkend="catalog-pg-class"><structname>pg_class</structname></link>
   entry that describes it as a physical relation, plus a
   <link linkend="catalog-pg-index"><structname>pg_index</structname></link>
   entry that shows the logical content of the index &mdash; that is, the set
   of index columns it has and the semantics of those columns, as captured by
   the associated operator classes.  The index columns (key values) can be
   either simple columns of the underlying table or expressions over the table
   rows.  The index access method normally has no interest in where the index
   key values come from (it is always handed precomputed key values) but it
   will be very interested in the operator class information in
   <structname>pg_index</structname>.  Both of these catalog entries can be
   accessed as part of the <structname>Relation</> data structure that is
   passed to all operations on the index.
  </para>

  <para>
   Some of the flag fields of <structname>IndexAmRoutine</> have nonobvious
   implications.  The requirements of <structfield>amcanunique</structfield>
   are discussed in <xref linkend="index-unique-checks">.
   The <structfield>amcanmulticol</structfield> flag asserts that the
   access method supports multicolumn indexes, while
   <structfield>amoptionalkey</structfield> asserts that it allows scans
   where no indexable restriction clause is given for the first index column.
   When <structfield>amcanmulticol</structfield> is false,
   <structfield>amoptionalkey</structfield> essentially says whether the
   access method supports full-index scans without any restriction clause.
   Access methods that support multiple index columns <emphasis>must</>
   support scans that omit restrictions on any or all of the columns after
   the first; however they are permitted to require some restriction to
   appear for the first index column, and this is signaled by setting
   <structfield>amoptionalkey</structfield> false.
   One reason that an index AM might set
   <structfield>amoptionalkey</structfield> false is if it doesn't index
   null values.  Since most indexable operators are
   strict and hence cannot return true for null inputs,
   it is at first sight attractive to not store index entries for null values:
   they could never be returned by an index scan anyway.  However, this
   argument fails when an index scan has no restriction clause for a given
   index column.  In practice this means that
   indexes that have <structfield>amoptionalkey</structfield> true must
   index nulls, since the planner might decide to use such an index
   with no scan keys at all.  A related restriction is that an index
   access method that supports multiple index columns <emphasis>must</>
   support indexing null values in columns after the first, because the planner
   will assume the index can be used for queries that do not restrict
   these columns.  For example, consider an index on (a,b) and a query with
   <literal>WHERE a = 4</literal>.  The system will assume the index can be
   used to scan for rows with <literal>a = 4</literal>, which is wrong if the
   index omits rows where <literal>b</> is null.
   It is, however, OK to omit rows where the first indexed column is null.
   An index access method that does index nulls may also set
   <structfield>amsearchnulls</structfield>, indicating that it supports
   <literal>IS NULL</> and <literal>IS NOT NULL</> clauses as search
   conditions.
  </para>

 </sect1>

 <sect1 id="index-functions">
  <title>Index Access Method Functions</title>

  <para>
   The index construction and maintenance functions that an index access
   method must provide in <structname>IndexAmRoutine</structname> are:
  </para>

  <para>
<programlisting>
IndexBuildResult *
ambuild (Relation heapRelation,
         Relation indexRelation,
         IndexInfo *indexInfo);
</programlisting>
   Build a new index.  The index relation has been physically created,
   but is empty.  It must be filled in with whatever fixed data the
   access method requires, plus entries for all tuples already existing
   in the table.  Ordinarily the <function>ambuild</> function will call
   <function>IndexBuildHeapScan()</> to scan the table for existing tuples
   and compute the keys that need to be inserted into the index.
   The function must return a palloc'd struct containing statistics about
   the new index.
  </para>

  <para>
<programlisting>
void
ambuildempty (Relation indexRelation);
</programlisting>
   Build an empty index, and write it to the initialization fork (<symbol>INIT_FORKNUM</symbol>)
   of the given relation.  This method is called only for unlogged indexes; the
   empty index written to the initialization fork will be copied over the main
   relation fork on each server restart.
  </para>

  <para>
<programlisting>
bool
aminsert (Relation indexRelation,
          Datum *values,
          bool *isnull,
          ItemPointer heap_tid,
          Relation heapRelation,
          IndexUniqueCheck checkUnique);
</programlisting>
   Insert a new tuple into an existing index.  The <literal>values</> and
   <literal>isnull</> arrays give the key values to be indexed, and
   <literal>heap_tid</> is the TID to be indexed.
   If the access method supports unique indexes (its
   <structfield>amcanunique</> flag is true) then
   <literal>checkUnique</> indicates the type of uniqueness check to
   perform.  This varies depending on whether the unique constraint is
   deferrable; see <xref linkend="index-unique-checks"> for details.
   Normally the access method only needs the <literal>heapRelation</>
   parameter when performing uniqueness checking (since then it will have to
   look into the heap to verify tuple liveness).
  </para>

  <para>
   The function's Boolean result value is significant only when
   <literal>checkUnique</> is <literal>UNIQUE_CHECK_PARTIAL</>.
   In this case a TRUE result means the new entry is known unique, whereas
   FALSE means it might be non-unique (and a deferred uniqueness check must
   be scheduled).  For other cases a constant FALSE result is recommended.
  </para>

  <para>
   Some indexes might not index all tuples.  If the tuple is not to be
   indexed, <function>aminsert</> should just return without doing anything.
  </para>

  <para>
<programlisting>
IndexBulkDeleteResult *
ambulkdelete (IndexVacuumInfo *info,
              IndexBulkDeleteResult *stats,
              IndexBulkDeleteCallback callback,
              void *callback_state);
</programlisting>
   Delete tuple(s) from the index.  This is a <quote>bulk delete</> operation
   that is intended to be implemented by scanning the whole index and checking
   each entry to see if it should be deleted.
   The passed-in <literal>callback</> function must be called, in the style
   <literal>callback(<replaceable>TID</>, callback_state) returns bool</literal>,
   to determine whether any particular index entry, as identified by its
   referenced TID, is to be deleted.  Must return either NULL or a palloc'd
   struct containing statistics about the effects of the deletion operation.
   It is OK to return NULL if no information needs to be passed on to
   <function>amvacuumcleanup</>.
  </para>

  <para>
   Because of limited <varname>maintenance_work_mem</>,
   <function>ambulkdelete</> might need to be called more than once when many
   tuples are to be deleted.  The <literal>stats</> argument is the result
   of the previous call for this index (it is NULL for the first call within a
   <command>VACUUM</> operation).  This allows the AM to accumulate statistics
   across the whole operation.  Typically, <function>ambulkdelete</> will
   modify and return the same struct if the passed <literal>stats</> is not
   null.
  </para>

  <para>
<programlisting>
IndexBulkDeleteResult *
amvacuumcleanup (IndexVacuumInfo *info,
                 IndexBulkDeleteResult *stats);
</programlisting>
   Clean up after a <command>VACUUM</command> operation (zero or more
   <function>ambulkdelete</> calls).  This does not have to do anything
   beyond returning index statistics, but it might perform bulk cleanup
   such as reclaiming empty index pages.  <literal>stats</> is whatever the
   last <function>ambulkdelete</> call returned, or NULL if
   <function>ambulkdelete</> was not called because no tuples needed to be
   deleted.  If the result is not NULL it must be a palloc'd struct.
   The statistics it contains will be used to update <structname>pg_class</>,
   and will be reported by <command>VACUUM</> if <literal>VERBOSE</> is given.
   It is OK to return NULL if the index was not changed at all during the
   <command>VACUUM</command> operation, but otherwise correct stats should
   be returned.
  </para>

  <para>
   As of <productname>PostgreSQL</productname> 8.4,
   <function>amvacuumcleanup</> will also be called at completion of an
   <command>ANALYZE</> operation.  In this case <literal>stats</> is always
   NULL and any return value will be ignored.  This case can be distinguished
   by checking <literal>info-&gt;analyze_only</literal>.  It is recommended
   that the access method do nothing except post-insert cleanup in such a
   call, and that only in an autovacuum worker process.
  </para>

  <para>
<programlisting>
bool
amcanreturn (Relation indexRelation, int attno);
</programlisting>
   Check whether the index can support <link
   linkend="indexes-index-only-scans"><firstterm>index-only scans</></link> on
   the given column, by returning the indexed column values for an index entry
   in the form of an <structname>IndexTuple</structname>.  The attribute number
   is 1-based, i.e. the first column's attno is 1. Returns TRUE if supported,
   else FALSE.  If the access method does not support index-only scans at all,
   the <structfield>amcanreturn</> field in its <structname>IndexAmRoutine</>
   struct can be set to NULL.
  </para>

  <para>
<programlisting>
void
amcostestimate (PlannerInfo *root,
                IndexPath *path,
                double loop_count,
                Cost *indexStartupCost,
                Cost *indexTotalCost,
                Selectivity *indexSelectivity,
                double *indexCorrelation);
</programlisting>
   Estimate the costs of an index scan.  This function is described fully
   in <xref linkend="index-cost-estimation">, below.
  </para>

  <para>
<programlisting>
bytea *
amoptions (ArrayType *reloptions,
           bool validate);
</programlisting>
   Parse and validate the reloptions array for an index.  This is called only
   when a non-null reloptions array exists for the index.
   <parameter>reloptions</> is a <type>text</> array containing entries of the
   form <replaceable>name</><literal>=</><replaceable>value</>.
   The function should construct a <type>bytea</> value, which will be copied
   into the <structfield>rd_options</> field of the index's relcache entry.
   The data contents of the <type>bytea</> value are open for the access
   method to define; most of the standard access methods use struct
   <structname>StdRdOptions</>.
   When <parameter>validate</> is true, the function should report a suitable
   error message if any of the options are unrecognized or have invalid
   values; when <parameter>validate</> is false, invalid entries should be
   silently ignored.  (<parameter>validate</> is false when loading options
   already stored in <structname>pg_catalog</>; an invalid entry could only
   be found if the access method has changed its rules for options, and in
   that case ignoring obsolete entries is appropriate.)
   It is OK to return NULL if default behavior is wanted.
  </para>

  <para>
<programlisting>
bool
amproperty (Oid index_oid, int attno,
            IndexAMProperty prop, const char *propname,
            bool *res, bool *isnull);
</programlisting>
   The <function>amproperty</> method allows index access methods to override
   the default behavior of <function>pg_index_column_has_property</function>
   and related functions.
   If the access method does not have any special behavior for index property
   inquiries, the <structfield>amproperty</> field in
   its <structname>IndexAmRoutine</> struct can be set to NULL.
   Otherwise, the <function>amproperty</> method will be called with
   <parameter>index_oid</> and <parameter>attno</> both zero for
   <function>pg_indexam_has_property</function> calls,
   or with <parameter>index_oid</> valid and <parameter>attno</> zero for
   <function>pg_index_has_property</function> calls,
   or with <parameter>index_oid</> valid and <parameter>attno</> greater than
   zero for <function>pg_index_column_has_property</function> calls.
   <parameter>prop</> is an enum value identifying the property being tested,
   while <parameter>propname</> is the original property name string.
   If the core code does not recognize the property name
   then <parameter>prop</> is <literal>AMPROP_UNKNOWN</>.
   Access methods can define custom property names by
   checking <parameter>propname</> for a match (use <function>pg_strcasecmp</>
   to match, for consistency with the core code); for names known to the core
   code, it's better to inspect <parameter>prop</>.
   If the <structfield>amproperty</> method returns <literal>true</> then
   it has determined the property test result: it must set <literal>*res</>
   to the boolean value to return, or set <literal>*isnull</>
   to <literal>true</> to return a NULL.  (Both of the referenced variables
   are initialized to <literal>false</> before the call.)
   If the <structfield>amproperty</> method returns <literal>false</> then
   the core code will proceed with its normal logic for determining the
   property test result.
  </para>

  <para>
   Access methods that support ordering operators should
   implement <literal>AMPROP_DISTANCE_ORDERABLE</> property testing, as the
   core code does not know how to do that and will return NULL.  It may
   also be advantageous to implement <literal>AMPROP_RETURNABLE</> testing,
   if that can be done more cheaply than by opening the index and calling
   <structfield>amcanreturn</>, which is the core code's default behavior.
   The default behavior should be satisfactory for all other standard
   properties.
  </para>

  <para>
<programlisting>
bool
amvalidate (Oid opclassoid);
</programlisting>
   Validate the catalog entries for the specified operator class, so far as
   the access method can reasonably do that.  For example, this might include
   testing that all required support functions are provided.
   The <function>amvalidate</> function must return false if the opclass is
   invalid.  Problems should be reported with <function>ereport</> messages.
  </para>


  <para>
   The purpose of an index, of course, is to support scans for tuples matching
   an indexable <literal>WHERE</> condition, often called a
   <firstterm>qualifier</> or <firstterm>scan key</>.  The semantics of
   index scanning are described more fully in <xref linkend="index-scanning">,
   below.  An index access method can support <quote>plain</> index scans,
   <quote>bitmap</> index scans, or both.  The scan-related functions that an
   index access method must or may provide are:
  </para>

  <para>
<programlisting>
IndexScanDesc
ambeginscan (Relation indexRelation,
             int nkeys,
             int norderbys);
</programlisting>
   Prepare for an index scan.  The <literal>nkeys</> and <literal>norderbys</>
   parameters indicate the number of quals and ordering operators that will be
   used in the scan; these may be useful for space allocation purposes.
   Note that the actual values of the scan keys aren't provided yet.
   The result must be a palloc'd struct.
   For implementation reasons the index access method
   <emphasis>must</> create this struct by calling
   <function>RelationGetIndexScan()</>.  In most cases
   <function>ambeginscan</> does little beyond making that call and perhaps
   acquiring locks;
   the interesting parts of index-scan startup are in <function>amrescan</>.
  </para>

  <para>
<programlisting>
void
amrescan (IndexScanDesc scan,
          ScanKey keys,
          int nkeys,
          ScanKey orderbys,
          int norderbys);
</programlisting>
   Start or restart an index scan, possibly with new scan keys.  (To restart
   using previously-passed keys, NULL is passed for <literal>keys</> and/or
   <literal>orderbys</>.)  Note that it is not allowed for
   the number of keys or order-by operators to be larger than
   what was passed to <function>ambeginscan</>.  In practice the restart
   feature is used when a new outer tuple is selected by a nested-loop join
   and so a new key comparison value is needed, but the scan key structure
   remains the same.
  </para>

  <para>
<programlisting>
boolean
amgettuple (IndexScanDesc scan,
            ScanDirection direction);
</programlisting>
   Fetch the next tuple in the given scan, moving in the given
   direction (forward or backward in the index).  Returns TRUE if a tuple was
   obtained, FALSE if no matching tuples remain.  In the TRUE case the tuple
   TID is stored into the <literal>scan</> structure.  Note that
   <quote>success</> means only that the index contains an entry that matches
   the scan keys, not that the tuple necessarily still exists in the heap or
   will pass the caller's snapshot test.  On success, <function>amgettuple</>
   must also set <literal>scan-&gt;xs_recheck</> to TRUE or FALSE.
   FALSE means it is certain that the index entry matches the scan keys.
   TRUE means this is not certain, and the conditions represented by the
   scan keys must be rechecked against the heap tuple after fetching it.
   This provision supports <quote>lossy</> index operators.
   Note that rechecking will extend only to the scan conditions; a partial
   index predicate (if any) is never rechecked by <function>amgettuple</>
   callers.
  </para>

  <para>
   If the index supports <link linkend="indexes-index-only-scans">index-only
   scans</link> (i.e., <function>amcanreturn</function> returns TRUE for it),
   then on success the AM must also check
   <literal>scan-&gt;xs_want_itup</>, and if that is true it must return
   the original indexed data for the index entry, in the form of an
   <structname>IndexTuple</> pointer stored at <literal>scan-&gt;xs_itup</>,
   with tuple descriptor <literal>scan-&gt;xs_itupdesc</>.
   (Management of the data referenced by the pointer is the access method's
   responsibility.  The data must remain good at least until the next
   <function>amgettuple</>, <function>amrescan</>, or <function>amendscan</>
   call for the scan.)
  </para>

  <para>
   The <function>amgettuple</> function need only be provided if the access
   method supports <quote>plain</> index scans.  If it doesn't, the
   <structfield>amgettuple</> field in its <structname>IndexAmRoutine</>
   struct must be set to NULL.
  </para>

  <para>
<programlisting>
int64
amgetbitmap (IndexScanDesc scan,
             TIDBitmap *tbm);
</programlisting>
   Fetch all tuples in the given scan and add them to the caller-supplied
   <type>TIDBitmap</type> (that is, OR the set of tuple IDs into whatever set is already
   in the bitmap).  The number of tuples fetched is returned (this might be
   just an approximate count, for instance some AMs do not detect duplicates).
   While inserting tuple IDs into the bitmap, <function>amgetbitmap</> can
   indicate that rechecking of the scan conditions is required for specific
   tuple IDs.  This is analogous to the <literal>xs_recheck</> output parameter
   of <function>amgettuple</>.  Note: in the current implementation, support
   for this feature is conflated with support for lossy storage of the bitmap
   itself, and therefore callers recheck both the scan conditions and the
   partial index predicate (if any) for recheckable tuples.  That might not
   always be true, however.
   <function>amgetbitmap</> and
   <function>amgettuple</> cannot be used in the same index scan; there
   are other restrictions too when using <function>amgetbitmap</>, as explained
   in <xref linkend="index-scanning">.
  </para>

  <para>
   The <function>amgetbitmap</> function need only be provided if the access
   method supports <quote>bitmap</> index scans.  If it doesn't, the
   <structfield>amgetbitmap</> field in its <structname>IndexAmRoutine</>
   struct must be set to NULL.
  </para>

  <para>
<programlisting>
void
amendscan (IndexScanDesc scan);
</programlisting>
   End a scan and release resources.  The <literal>scan</> struct itself
   should not be freed, but any locks or pins taken internally by the
   access method must be released.
  </para>

  <para>
<programlisting>
void
ammarkpos (IndexScanDesc scan);
</programlisting>
   Mark current scan position.  The access method need only support one
   remembered scan position per scan.
  </para>

  <para>
   The <function>ammarkpos</> function need only be provided if the access
   method supports ordered scans.  If it doesn't,
   the <structfield>ammarkpos</> field in its <structname>IndexAmRoutine</>
   struct may be set to NULL.
  </para>

  <para>
<programlisting>
void
amrestrpos (IndexScanDesc scan);
</programlisting>
   Restore the scan to the most recently marked position.
  </para>

  <para>
   The <function>amrestrpos</> function need only be provided if the access
   method supports ordered scans.  If it doesn't,
   the <structfield>amrestrpos</> field in its <structname>IndexAmRoutine</>
   struct may be set to NULL.
  </para>

  <para>
   In addition to supporting ordinary index scans, some types of index
   may wish to support <firstterm>parallel index scans</>, which allow
   multiple backends to cooperate in performing an index scan.  The
   index access method should arrange things so that each cooperating
   process returns a subset of the tuples that would be performed by
   an ordinary, non-parallel index scan, but in such a way that the
   union of those subsets is equal to the set of tuples that would be
   returned by an ordinary, non-parallel index scan.  Furthermore, while
   there need not be any global ordering of tuples returned by a parallel
   scan, the ordering of that subset of tuples returned within each
   cooperating backend must match the requested ordering.  The following
   functions may be implemented to support parallel index scans:
  </para>

  <para>
<programlisting>
Size
amestimateparallelscan (void);
</programlisting>
   Estimate and return the number of bytes of dynamic shared memory which
   the access method will be needed to perform a parallel scan.  (This number
   is in addition to, not in lieu of, the amount of space needed for
   AM-independent data in <structname>ParallelIndexScanDescData</>.)
  </para>

  <para>
   It is not necessary to implement this function for access methods which
   do not support parallel scans or for which the number of additional bytes
   of storage required is zero.
  </para>

  <para>
<programlisting>
void
aminitparallelscan (void *target);
</programlisting>
   This function will be called to initialize dynamic shared memory at the
   beginning of a parallel scan.  <parameter>target</> will point to at least
   the number of bytes previously returned by
   <function>amestimateparallelscan</>, and this function may use that
   amount of space to store whatever data it wishes.
  </para>

  <para>
   It is not necessary to implement this function for access methods which
   do not support parallel scans or in cases where the shared memory space
   required needs no initialization.
  </para>

  <para>
<programlisting>
void
amparallelrescan (IndexScanDesc scan);
</programlisting>
   This function, if implemented, will be called when a parallel index scan
   must be restarted.  It should reset any shared state set up by
   <function>aminitparallelscan</> such that the scan will be restarted from
   the beginning.
  </para>

 </sect1>

 <sect1 id="index-scanning">
  <title>Index Scanning</title>

  <para>
   In an index scan, the index access method is responsible for regurgitating
   the TIDs of all the tuples it has been told about that match the
   <firstterm>scan keys</>.  The access method is <emphasis>not</> involved in
   actually fetching those tuples from the index's parent table, nor in
   determining whether they pass the scan's time qualification test or other
   conditions.
  </para>

  <para>
   A scan key is the internal representation of a <literal>WHERE</> clause of
   the form <replaceable>index_key</> <replaceable>operator</>
   <replaceable>constant</>, where the index key is one of the columns of the
   index and the operator is one of the members of the operator family
   associated with that index column.  An index scan has zero or more scan
   keys, which are implicitly ANDed &mdash; the returned tuples are expected
   to satisfy all the indicated conditions.
  </para>

  <para>
   The access method can report that the index is <firstterm>lossy</>, or
   requires rechecks, for a particular query.  This implies that the index
   scan will return all the entries that pass the scan key, plus possibly
   additional entries that do not.  The core system's index-scan machinery
   will then apply the index conditions again to the heap tuple to verify
   whether or not it really should be selected.  If the recheck option is not
   specified, the index scan must return exactly the set of matching entries.
  </para>

  <para>
   Note that it is entirely up to the access method to ensure that it
   correctly finds all and only the entries passing all the given scan keys.
   Also, the core system will simply hand off all the <literal>WHERE</>
   clauses that match the index keys and operator families, without any
   semantic analysis to determine whether they are redundant or
   contradictory.  As an example, given
   <literal>WHERE x &gt; 4 AND x &gt; 14</> where <literal>x</> is a b-tree
   indexed column, it is left to the b-tree <function>amrescan</> function
   to realize that the first scan key is redundant and can be discarded.
   The extent of preprocessing needed during <function>amrescan</> will
   depend on the extent to which the index access method needs to reduce
   the scan keys to a <quote>normalized</> form.
  </para>

  <para>
   Some access methods return index entries in a well-defined order, others
   do not.  There are actually two different ways that an access method can
   support sorted output:

    <itemizedlist>
     <listitem>
      <para>
       Access methods that always return entries in the natural ordering
       of their data (such as btree) should set
       <structfield>amcanorder</> to true.
       Currently, such access methods must use btree-compatible strategy
       numbers for their equality and ordering operators.
      </para>
     </listitem>
     <listitem>
      <para>
       Access methods that support ordering operators should set
       <structfield>amcanorderbyop</> to true.
       This indicates that the index is capable of returning entries in
       an order satisfying <literal>ORDER BY</> <replaceable>index_key</>
       <replaceable>operator</> <replaceable>constant</>.  Scan modifiers
       of that form can be passed to <function>amrescan</> as described
       previously.
      </para>
     </listitem>
    </itemizedlist>
  </para>

  <para>
   The <function>amgettuple</> function has a <literal>direction</> argument,
   which can be either <literal>ForwardScanDirection</> (the normal case)
   or  <literal>BackwardScanDirection</>.  If the first call after
   <function>amrescan</> specifies <literal>BackwardScanDirection</>, then the
   set of matching index entries is to be scanned back-to-front rather than in
   the normal front-to-back direction, so <function>amgettuple</> must return
   the last matching tuple in the index, rather than the first one as it
   normally would.  (This will only occur for access
   methods that set <structfield>amcanorder</> to true.)  After the
   first call, <function>amgettuple</> must be prepared to advance the scan in
   either direction from the most recently returned entry.  (But if
   <structfield>amcanbackward</> is false, all subsequent
   calls will have the same direction as the first one.)
  </para>

  <para>
   Access methods that support ordered scans must support <quote>marking</> a
   position in a scan and later returning to the marked position.  The same
   position might be restored multiple times.  However, only one position need
   be remembered per scan; a new <function>ammarkpos</> call overrides the
   previously marked position.  An access method that does not support ordered
   scans need not provide <function>ammarkpos</> and <function>amrestrpos</>
   functions in <structname>IndexAmRoutine</>; set those pointers to NULL
   instead.
  </para>

  <para>
   Both the scan position and the mark position (if any) must be maintained
   consistently in the face of concurrent insertions or deletions in the
   index.  It is OK if a freshly-inserted entry is not returned by a scan that
   would have found the entry if it had existed when the scan started, or for
   the scan to return such an entry upon rescanning or backing
   up even though it had not been returned the first time through.  Similarly,
   a concurrent delete might or might not be reflected in the results of a scan.
   What is important is that insertions or deletions not cause the scan to
   miss or multiply return entries that were not themselves being inserted or
   deleted.
  </para>

  <para>
   If the index stores the original indexed data values (and not some lossy
   representation of them), it is useful to
   support <link linkend="indexes-index-only-scans">index-only scans</link>, in
   which the index returns the actual data not just the TID of the heap tuple.
   This will only avoid I/O if the visibility map shows that the TID is on an
   all-visible page; else the heap tuple must be visited anyway to check
   MVCC visibility.  But that is no concern of the access method's.
  </para>

  <para>
   Instead of using <function>amgettuple</>, an index scan can be done with
   <function>amgetbitmap</> to fetch all tuples in one call.  This can be
   noticeably more efficient than <function>amgettuple</> because it allows
   avoiding lock/unlock cycles within the access method.  In principle
   <function>amgetbitmap</> should have the same effects as repeated
   <function>amgettuple</> calls, but we impose several restrictions to
   simplify matters.  First of all, <function>amgetbitmap</> returns all
   tuples at once and marking or restoring scan positions isn't
   supported. Secondly, the tuples are returned in a bitmap which doesn't
   have any specific ordering, which is why <function>amgetbitmap</> doesn't
   take a <literal>direction</> argument.  (Ordering operators will never be
   supplied for such a scan, either.)
   Also, there is no provision for index-only scans with
   <function>amgetbitmap</>, since there is no way to return the contents of
   index tuples.
   Finally, <function>amgetbitmap</>
   does not guarantee any locking of the returned tuples, with implications
   spelled out in <xref linkend="index-locking">.
  </para>

  <para>
   Note that it is permitted for an access method to implement only
   <function>amgetbitmap</> and not <function>amgettuple</>, or vice versa,
   if its internal implementation is unsuited to one API or the other.
  </para>

 </sect1>

 <sect1 id="index-locking">
  <title>Index Locking Considerations</title>

  <para>
   Index access methods must handle concurrent updates
   of the index by multiple processes.
   The core <productname>PostgreSQL</productname> system obtains
   <literal>AccessShareLock</> on the index during an index scan, and
   <literal>RowExclusiveLock</> when updating the index (including plain
   <command>VACUUM</>).  Since these lock types do not conflict, the access
   method is responsible for handling any fine-grained locking it might need.
   An exclusive lock on the index as a whole will be taken only during index
   creation, destruction, or <command>REINDEX</>.
  </para>

  <para>
   Building an index type that supports concurrent updates usually requires
   extensive and subtle analysis of the required behavior.  For the b-tree
   and hash index types, you can read about the design decisions involved in
   <filename>src/backend/access/nbtree/README</> and
   <filename>src/backend/access/hash/README</>.
  </para>

  <para>
   Aside from the index's own internal consistency requirements, concurrent
   updates create issues about consistency between the parent table (the
   <firstterm>heap</>) and the index.  Because
   <productname>PostgreSQL</productname> separates accesses
   and updates of the heap from those of the index, there are windows in
   which the index might be inconsistent with the heap.  We handle this problem
   with the following rules:

    <itemizedlist>
     <listitem>
      <para>
       A new heap entry is made before making its index entries.  (Therefore
       a concurrent index scan is likely to fail to see the heap entry.
       This is okay because the index reader would be uninterested in an
       uncommitted row anyway.  But see <xref linkend="index-unique-checks">.)
      </para>
     </listitem>
     <listitem>
      <para>
       When a heap entry is to be deleted (by <command>VACUUM</>), all its
       index entries must be removed first.
      </para>
     </listitem>
     <listitem>
      <para>
       An index scan must maintain a pin
       on the index page holding the item last returned by
       <function>amgettuple</>, and <function>ambulkdelete</> cannot delete
       entries from pages that are pinned by other backends.  The need
       for this rule is explained below.
      </para>
     </listitem>
    </itemizedlist>

   Without the third rule, it is possible for an index reader to
   see an index entry just before it is removed by <command>VACUUM</>, and
   then to arrive at the corresponding heap entry after that was removed by
   <command>VACUUM</>.
   This creates no serious problems if that item
   number is still unused when the reader reaches it, since an empty
   item slot will be ignored by <function>heap_fetch()</>.  But what if a
   third backend has already re-used the item slot for something else?
   When using an MVCC-compliant snapshot, there is no problem because
   the new occupant of the slot is certain to be too new to pass the
   snapshot test.  However, with a non-MVCC-compliant snapshot (such as
   <literal>SnapshotAny</>), it would be possible to accept and return
   a row that does not in fact match the scan keys.  We could defend
   against this scenario by requiring the scan keys to be rechecked
   against the heap row in all cases, but that is too expensive.  Instead,
   we use a pin on an index page as a proxy to indicate that the reader
   might still be <quote>in flight</> from the index entry to the matching
   heap entry.  Making <function>ambulkdelete</> block on such a pin ensures
   that <command>VACUUM</> cannot delete the heap entry before the reader
   is done with it.  This solution costs little in run time, and adds blocking
   overhead only in the rare cases where there actually is a conflict.
  </para>

  <para>
   This solution requires that index scans be <quote>synchronous</>: we have
   to fetch each heap tuple immediately after scanning the corresponding index
   entry.  This is expensive for a number of reasons.  An
   <quote>asynchronous</> scan in which we collect many TIDs from the index,
   and only visit the heap tuples sometime later, requires much less index
   locking overhead and can allow a more efficient heap access pattern.
   Per the above analysis, we must use the synchronous approach for
   non-MVCC-compliant snapshots, but an asynchronous scan is workable
   for a query using an MVCC snapshot.
  </para>

  <para>
   In an <function>amgetbitmap</> index scan, the access method does not
   keep an index pin on any of the returned tuples.  Therefore
   it is only safe to use such scans with MVCC-compliant snapshots.
  </para>

  <para>
   When the <structfield>ampredlocks</> flag is not set, any scan using that
   index access method within a serializable transaction will acquire a
   nonblocking predicate lock on the full index.  This will generate a
   read-write conflict with the insert of any tuple into that index by a
   concurrent serializable transaction.  If certain patterns of read-write
   conflicts are detected among a set of concurrent serializable
   transactions, one of those transactions may be canceled to protect data
   integrity.  When the flag is set, it indicates that the index access
   method implements finer-grained predicate locking, which will tend to
   reduce the frequency of such transaction cancellations.
  </para>

 </sect1>

 <sect1 id="index-unique-checks">
  <title>Index Uniqueness Checks</title>

  <para>
   <productname>PostgreSQL</productname> enforces SQL uniqueness constraints
   using <firstterm>unique indexes</>, which are indexes that disallow
   multiple entries with identical keys.  An access method that supports this
   feature sets <structfield>amcanunique</> true.
   (At present, only b-tree supports it.)
  </para>

  <para>
   Because of MVCC, it is always necessary to allow duplicate entries to
   exist physically in an index: the entries might refer to successive
   versions of a single logical row.  The behavior we actually want to
   enforce is that no MVCC snapshot could include two rows with equal
   index keys.  This breaks down into the following cases that must be
   checked when inserting a new row into a unique index:

    <itemizedlist>
     <listitem>
      <para>
       If a conflicting valid row has been deleted by the current transaction,
       it's okay.  (In particular, since an UPDATE always deletes the old row
       version before inserting the new version, this will allow an UPDATE on
       a row without changing the key.)
      </para>
     </listitem>
     <listitem>
      <para>
       If a conflicting row has been inserted by an as-yet-uncommitted
       transaction, the would-be inserter must wait to see if that transaction
       commits.  If it rolls back then there is no conflict.  If it commits
       without deleting the conflicting row again, there is a uniqueness
       violation.  (In practice we just wait for the other transaction to
       end and then redo the visibility check in toto.)
      </para>
     </listitem>
     <listitem>
      <para>
       Similarly, if a conflicting valid row has been deleted by an
       as-yet-uncommitted transaction, the would-be inserter must wait
       for that transaction to commit or abort, and then repeat the test.
      </para>
     </listitem>
    </itemizedlist>
  </para>

  <para>
   Furthermore, immediately before reporting a uniqueness violation
   according to the above rules, the access method must recheck the
   liveness of the row being inserted.  If it is committed dead then
   no violation should be reported.  (This case cannot occur during the
   ordinary scenario of inserting a row that's just been created by
   the current transaction.  It can happen during
   <command>CREATE UNIQUE INDEX CONCURRENTLY</>, however.)
  </para>

  <para>
   We require the index access method to apply these tests itself, which
   means that it must reach into the heap to check the commit status of
   any row that is shown to have a duplicate key according to the index
   contents.  This is without a doubt ugly and non-modular, but it saves
   redundant work: if we did a separate probe then the index lookup for
   a conflicting row would be essentially repeated while finding the place to
   insert the new row's index entry.  What's more, there is no obvious way
   to avoid race conditions unless the conflict check is an integral part
   of insertion of the new index entry.
  </para>

  <para>
   If the unique constraint is deferrable, there is additional complexity:
   we need to be able to insert an index entry for a new row, but defer any
   uniqueness-violation error until end of statement or even later.  To
   avoid unnecessary repeat searches of the index, the index access method
   should do a preliminary uniqueness check during the initial insertion.
   If this shows that there is definitely no conflicting live tuple, we
   are done.  Otherwise, we schedule a recheck to occur when it is time to
   enforce the constraint.  If, at the time of the recheck, both the inserted
   tuple and some other tuple with the same key are live, then the error
   must be reported.  (Note that for this purpose, <quote>live</> actually
   means <quote>any tuple in the index entry's HOT chain is live</>.)
   To implement this, the <function>aminsert</> function is passed a
   <literal>checkUnique</> parameter having one of the following values:

    <itemizedlist>
     <listitem>
      <para>
       <literal>UNIQUE_CHECK_NO</> indicates that no uniqueness checking
       should be done (this is not a unique index).
      </para>
     </listitem>
     <listitem>
      <para>
       <literal>UNIQUE_CHECK_YES</> indicates that this is a non-deferrable
       unique index, and the uniqueness check must be done immediately, as
       described above.
      </para>
     </listitem>
     <listitem>
      <para>
       <literal>UNIQUE_CHECK_PARTIAL</> indicates that the unique
       constraint is deferrable. <productname>PostgreSQL</productname>
       will use this mode to insert each row's index entry.  The access
       method must allow duplicate entries into the index, and report any
       potential duplicates by returning FALSE from <function>aminsert</>.
       For each row for which FALSE is returned, a deferred recheck will
       be scheduled.
      </para>

      <para>
       The access method must identify any rows which might violate the
       unique constraint, but it is not an error for it to report false
       positives. This allows the check to be done without waiting for other
       transactions to finish; conflicts reported here are not treated as
       errors and will be rechecked later, by which time they may no longer
       be conflicts.
      </para>
     </listitem>
     <listitem>
      <para>
       <literal>UNIQUE_CHECK_EXISTING</> indicates that this is a deferred
       recheck of a row that was reported as a potential uniqueness violation.
       Although this is implemented by calling <function>aminsert</>, the
       access method must <emphasis>not</> insert a new index entry in this
       case.  The index entry is already present.  Rather, the access method
       must check to see if there is another live index entry.  If so, and
       if the target row is also still live, report error.
      </para>

      <para>
       It is recommended that in a <literal>UNIQUE_CHECK_EXISTING</> call,
       the access method further verify that the target row actually does
       have an existing entry in the index, and report error if not.  This
       is a good idea because the index tuple values passed to
       <function>aminsert</> will have been recomputed.  If the index
       definition involves functions that are not really immutable, we
       might be checking the wrong area of the index.  Checking that the
       target row is found in the recheck verifies that we are scanning
       for the same tuple values as were used in the original insertion.
      </para>
     </listitem>
    </itemizedlist>
  </para>

 </sect1>

 <sect1 id="index-cost-estimation">
  <title>Index Cost Estimation Functions</title>

  <para>
   The <function>amcostestimate</> function is given information describing
   a possible index scan, including lists of WHERE and ORDER BY clauses that
   have been determined to be usable with the index.  It must return estimates
   of the cost of accessing the index and the selectivity of the WHERE
   clauses (that is, the fraction of parent-table rows that will be
   retrieved during the index scan).  For simple cases, nearly all the
   work of the cost estimator can be done by calling standard routines
   in the optimizer; the point of having an <function>amcostestimate</> function is
   to allow index access methods to provide index-type-specific knowledge,
   in case it is possible to improve on the standard estimates.
  </para>

  <para>
   Each <function>amcostestimate</> function must have the signature:

<programlisting>
void
amcostestimate (PlannerInfo *root,
                IndexPath *path,
                double loop_count,
                Cost *indexStartupCost,
                Cost *indexTotalCost,
                Selectivity *indexSelectivity,
                double *indexCorrelation);
</programlisting>

   The first three parameters are inputs:

   <variablelist>
    <varlistentry>
     <term><parameter>root</></term>
     <listitem>
      <para>
       The planner's information about the query being processed.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><parameter>path</></term>
     <listitem>
      <para>
       The index access path being considered.  All fields except cost and
       selectivity values are valid.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><parameter>loop_count</></term>
     <listitem>
      <para>
       The number of repetitions of the index scan that should be factored
       into the cost estimates.  This will typically be greater than one when
       considering a parameterized scan for use in the inside of a nestloop
       join.  Note that the cost estimates should still be for just one scan;
       a larger <parameter>loop_count</> means that it may be appropriate
       to allow for some caching effects across multiple scans.
      </para>
     </listitem>
    </varlistentry>
   </variablelist>
  </para>

  <para>
   The last four parameters are pass-by-reference outputs:

   <variablelist>
    <varlistentry>
     <term><parameter>*indexStartupCost</></term>
     <listitem>
      <para>
       Set to cost of index start-up processing
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><parameter>*indexTotalCost</></term>
     <listitem>
      <para>
       Set to total cost of index processing
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><parameter>*indexSelectivity</></term>
     <listitem>
      <para>
       Set to index selectivity
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term><parameter>*indexCorrelation</></term>
     <listitem>
      <para>
       Set to correlation coefficient between index scan order and
       underlying table's order
      </para>
     </listitem>
    </varlistentry>
   </variablelist>
  </para>

  <para>
   Note that cost estimate functions must be written in C, not in SQL or
   any available procedural language, because they must access internal
   data structures of the planner/optimizer.
  </para>

  <para>
   The index access costs should be computed using the parameters used by
   <filename>src/backend/optimizer/path/costsize.c</filename>: a sequential
   disk block fetch has cost <varname>seq_page_cost</>, a nonsequential fetch
   has cost <varname>random_page_cost</>, and the cost of processing one index
   row should usually be taken as <varname>cpu_index_tuple_cost</>.  In
   addition, an appropriate multiple of <varname>cpu_operator_cost</> should
   be charged for any comparison operators invoked during index processing
   (especially evaluation of the indexquals themselves).
  </para>

  <para>
   The access costs should include all disk and CPU costs associated with
   scanning the index itself, but <emphasis>not</> the costs of retrieving or
   processing the parent-table rows that are identified by the index.
  </para>

  <para>
   The <quote>start-up cost</quote> is the part of the total scan cost that
   must be expended before we can begin to fetch the first row.  For most
   indexes this can be taken as zero, but an index type with a high start-up
   cost might want to set it nonzero.
  </para>

  <para>
   The <parameter>indexSelectivity</> should be set to the estimated fraction of the parent
   table rows that will be retrieved during the index scan.  In the case
   of a lossy query, this will typically be higher than the fraction of
   rows that actually pass the given qual conditions.
  </para>

  <para>
   The <parameter>indexCorrelation</> should be set to the correlation (ranging between
   -1.0 and 1.0) between the index order and the table order.  This is used
   to adjust the estimate for the cost of fetching rows from the parent
   table.
  </para>

  <para>
   When <parameter>loop_count</> is greater than one, the returned numbers
   should be averages expected for any one scan of the index.
  </para>

  <procedure>
   <title>Cost Estimation</title>
   <para>
    A typical cost estimator will proceed as follows:
   </para>

   <step>
    <para>
     Estimate and return the fraction of parent-table rows that will be visited
     based on the given qual conditions.  In the absence of any index-type-specific
     knowledge, use the standard optimizer function <function>clauselist_selectivity()</function>:

<programlisting>
*indexSelectivity = clauselist_selectivity(root, path-&gt;indexquals,
                                           path-&gt;indexinfo-&gt;rel-&gt;relid,
                                           JOIN_INNER, NULL);
</programlisting>
    </para>
   </step>

   <step>
    <para>
     Estimate the number of index rows that will be visited during the
     scan.  For many index types this is the same as <parameter>indexSelectivity</> times
     the number of rows in the index, but it might be more.  (Note that the
     index's size in pages and rows is available from the
     <literal>path-&gt;indexinfo</> struct.)
    </para>
   </step>

   <step>
    <para>
     Estimate the number of index pages that will be retrieved during the scan.
     This might be just <parameter>indexSelectivity</> times the index's size in pages.
    </para>
   </step>

   <step>
    <para>
     Compute the index access cost.  A generic estimator might do this:

<programlisting>
/*
 * Our generic assumption is that the index pages will be read
 * sequentially, so they cost seq_page_cost each, not random_page_cost.
 * Also, we charge for evaluation of the indexquals at each index row.
 * All the costs are assumed to be paid incrementally during the scan.
 */
cost_qual_eval(&amp;index_qual_cost, path-&gt;indexquals, root);
*indexStartupCost = index_qual_cost.startup;
*indexTotalCost = seq_page_cost * numIndexPages +
    (cpu_index_tuple_cost + index_qual_cost.per_tuple) * numIndexTuples;
</programlisting>

     However, the above does not account for amortization of index reads
     across repeated index scans.
    </para>
   </step>

   <step>
    <para>
     Estimate the index correlation.  For a simple ordered index on a single
     field, this can be retrieved from pg_statistic.  If the correlation
     is not known, the conservative estimate is zero (no correlation).
    </para>
   </step>
  </procedure>

  <para>
   Examples of cost estimator functions can be found in
   <filename>src/backend/utils/adt/selfuncs.c</filename>.
  </para>
 </sect1>
</chapter>