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 <chapter id="indexcost">
  <title>Index Cost Estimation Functions</title>

  <note>
   <title>Author</title>

   <para>
    Written by Tom Lane (<email>tgl@sss.pgh.pa.us</email>) on 2000-01-24
   </para>
  </note>

   <note>
    <para>
     This must eventually become part of a much larger chapter about
     writing new index access methods.
    </para>
   </note>

  <para>
   Every index access method must provide a cost estimation function for
   use by the planner/optimizer.  The procedure OID of this function is
   given in the <literal>amcostestimate</literal> field of the access
   method's <literal>pg_am</literal> entry.

   <note>
    <para>
     Prior to <productname>PostgreSQL</productname> 7.0, a different
     scheme was used for registering 
     index-specific cost estimation functions.
    </para>
   </note>
  </para>

  <para>
   The amcostestimate function is given a list of WHERE 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 main-table tuples 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 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 amcostestimate function must have the signature:

   <programlisting>
void
amcostestimate (Query *root,
                RelOptInfo *rel,
                IndexOptInfo *index,
                List *indexQuals,
                Cost *indexStartupCost,
                Cost *indexTotalCost,
                Selectivity *indexSelectivity,
                double *indexCorrelation);
   </programlisting>

   The first four parameters are inputs:

   <variablelist>
    <varlistentry>
     <term>root</term>
     <listitem>
      <para>
       The query being processed.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term>rel</term>
     <listitem>
      <para>
       The relation the index is on.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term>index</term>
     <listitem>
      <para>
       The index itself.
      </para>
     </listitem>
    </varlistentry>

    <varlistentry>
     <term>indexQuals</term>
     <listitem>
      <para>
       List of index qual clauses (implicitly ANDed);
       a NIL list indicates no qualifiers are available.
      </para>
     </listitem>
    </varlistentry>
   </variablelist>
  </para>

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

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

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

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

    <varlistentry>
     <term>*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 in the units used by
   <filename>src/backend/optimizer/path/costsize.c</filename>: a sequential disk block fetch
   has cost 1.0, a nonsequential fetch has cost random_page_cost, and
   the cost of processing one index tuple should usually be taken as
   cpu_index_tuple_cost (which is a user-adjustable optimizer parameter).
   In addition, an appropriate multiple of 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 NOT the costs of retrieving or processing
   the main-table tuples 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 tuple.  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 indexSelectivity should be set to the estimated fraction of the main
   table tuples that will be retrieved during the index scan.  In the case
   of a lossy index, this will typically be higher than the fraction of
   tuples that actually pass the given qual conditions.
  </para>

  <para>
   The 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 tuples from the main
   table.
  </para>

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

   <step>
    <para>
     Estimate and return the fraction of main-table tuples 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, indexQuals,
                                           lfirsti(rel->relids));
     </programlisting>
    </para>
   </step>

   <step>
    <para>
     Estimate the number of index tuples that will be visited during the
     scan.  For many index types this is the same as indexSelectivity times
     the number of tuples in the index, but it might be more.  (Note that the
     index's size in pages and tuples is available from the IndexOptInfo struct.)
    </para>
   </step>

   <step>
    <para>
     Estimate the number of index pages that will be retrieved during the scan.
     This might be just 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 have cost 1.0 each, not random_page_cost.
     * Also, we charge for evaluation of the indexquals at each index tuple.
     * All the costs are assumed to be paid incrementally during the scan.
     */
    *indexStartupCost = 0;
    *indexTotalCost = numIndexPages +
        (cpu_index_tuple_cost + cost_qual_eval(indexQuals)) * numIndexTuples;
     </programlisting>
    </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>

  <para>
   By convention, the <literal>pg_proc</literal> entry for an
   <literal>amcostestimate</literal> function should show
   eight arguments all declared as <type>internal</> (since none of them have
   types that are known to SQL), and the return type is <type>void</>.
  </para>
 </chapter>

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