--- /dev/null
+<!--
+$PostgreSQL: pgsql/doc/src/sgml/planstats.sgml,v 1.1 2005/02/27 00:49:28 momjian Exp $
+-->
+
+<chapter id="planner-stats">
+ <title>How the Planner Uses Statistics</title>
+
+ <para>
+ This chapter builds on the material covered in <xref linkend="using-explain">
+ and <xref linkend="planner-stats">, and shows how the planner uses the
+ system statistics to estimate the number of rows each stage in a query might
+ return. This is a significant part of the planning / optimizing process,
+ providing much of the raw material for cost calculation.
+ </para>
+
+ <para>
+ The intent of this chapter is not to document the code —
+ better done in the code itself, but to present an overview of how it works.
+ This will perhaps ease the learning curve for someone who subsequently
+ wishes to read the code. As a consequence, the approach chosen is to analyze
+ a series of incrementally more complex examples.
+ </para>
+
+ <para>
+ The outputs and algorithms shown below are taken from version 8.0.
+ The behaviour of earlier (or later) versions may vary.
+ </para>
+
+ <sect1 id="row-estimation-examples">
+ <title>Row Estimation Examples</title>
+
+ <indexterm zone="row-estimation-examples">
+ <primary>row estimation</primary>
+ <secondary>planner</secondary>
+ </indexterm>
+
+ <para>
+ Using examples drawn from the regression test database, let's start with a
+ very simple query:
+<programlisting>
+EXPLAIN SELECT * FROM tenk1;
+
+ QUERY PLAN
+-------------------------------------------------------------
+ Seq Scan on tenk1 (cost=0.00..445.00 rows=10000 width=244)
+</programlisting>
+
+ How the planner determines the cardinality of <classname>tenk1</classname>
+ is covered in <xref linkend="using-explain">, but is repeated here for
+ completeness. The number of rows is looked up from
+ <classname>pg_class</classname>:
+
+<programlisting>
+SELECT reltuples, relpages FROM pg_class WHERE relname = 'tenk1';
+
+ relpages | reltuples
+----------+-----------
+ 345 | 10000
+</programlisting>
+ The planner will check the <structfield>relpages<structfield> estimate
+ (this is a cheap operation) and if incorrect may scale
+ <structfield>reltuples<structfield> to obtain a row estimate. In this case it
+ does not, thus:
+
+<programlisting>
+rows = 10000
+</programlisting>
+
+ </para>
+
+ <para>
+ let's move on to an example with a range condition in its
+ <literal>WHERE</literal> clause:
+
+<programlisting>
+EXPLAIN SELECT * FROM tenk1 WHERE unique1 < 1000;
+
+ QUERY PLAN
+------------------------------------------------------------
+ Seq Scan on tenk1 (cost=0.00..470.00 rows=1031 width=244)
+ Filter: (unique1 < 1000)
+</programlisting>
+
+ The planner examines the <literal>WHERE</literal> clause condition:
+
+<programlisting>
+unique1 < 1000
+</programlisting>
+
+ and looks up the restriction function for the operator
+ <literal><</literal> in <classname>pg_operator</classname>.
+ This is held in the column <structfield>oprrest</structfield>,
+ and the result in this case is <function>scalarltsel</function>.
+ The <function>scalarltsel</function> function retrieves the histogram for
+ <structfield>unique1</structfield> from <classname>pg_statistics</classname>
+ - we can follow this by using the simpler <classname>pg_stats</classname>
+ view:
+
+<programlisting>
+SELECT histogram_bounds FROM pg_stats
+WHERE tablename='tenk1' AND attname='unique1';
+
+ histogram_bounds
+------------------------------------------------------
+ {1,970,1943,2958,3971,5069,6028,7007,7919,8982,9995}
+</programlisting>
+
+ Next the fraction of the histogram occupied by <quote>< 1000</quote>
+ is worked out. This is the selectivity. The histogram divides the range
+ into equal frequency buckets, so all we have to do is locate the bucket
+ that our value is in and count <emphasis>part</emphasis> of it and
+ <emphasis>all</emphasis> of the ones before. The value 1000 is clearly in
+ the second (970 - 1943) bucket, so by assuming a linear distribution of
+ values inside each bucket we can calculate the selectivity as:
+
+<programlisting>
+selectivity = (1 + (1000 - bckt[2].min)/(bckt[2].max - bckt[2].min))/num_bckts
+ = (1 + (1000 - 970)/(1943 - 970))/10
+ = 0.1031
+</programlisting>
+
+ that is, one whole bucket plus a linear fraction of the second, divided by
+ the number of buckets. The estimated number of rows can now be calculated as
+ the product of the selectivity and the cardinality of
+ <classname>tenk1</classname>:
+
+<programlisting>
+rows = rel_cardinality * selectivity
+ = 10000 * 0.1031
+ = 1031
+</programlisting>
+
+ </para>
+
+ <para>
+ Next let's consider an example with equality condition in its
+ <literal>WHERE</literal> clause:
+
+<programlisting>
+EXPLAIN SELECT * FROM tenk1 WHERE stringu1 = 'ATAAAA';
+
+ QUERY PLAN
+----------------------------------------------------------
+ Seq Scan on tenk1 (cost=0.00..470.00 rows=31 width=244)
+ Filter: (stringu1 = 'ATAAAA'::name)
+</programlisting>
+
+ Again the planner examines the <literal>WHERE</literal> clause condition:
+
+<programlisting>
+stringu1 = 'ATAAAA'
+</programlisting>
+
+ and looks up the restriction function for <literal>=</literal>, which is
+ <function>eqsel</function>. This case is a bit different, as the most
+ common values — <acronym>MCV</acronym>s, are used to determine the
+ selectivity. Let's have a look at these, with some extra columns that will
+ be useful later:
+
+<programlisting>
+SELECT null_frac, n_distinct, most_common_vals, most_common_freqs FROM pg_stats
+WHERE tablename='tenk1' AND attname='stringu1';
+
+null_frac | 0
+n_distinct | 672
+most_common_vals | {FDAAAA,NHAAAA,ATAAAA,BGAAAA,EBAAAA,MOAAAA,NDAAAA,OWAAAA,BHAAAA,BJAAAA}
+most_common_freqs | {0.00333333,0.00333333,0.003,0.003,0.003,0.003,0.003,0.003,0.00266667,0.00266667}
+</programlisting>
+
+ The selectivity is merely the most common frequency (<acronym>MCF</acronym>)
+ corresponding to the third <acronym>MCV</acronym> — 'ATAAAA':
+
+<programlisting>
+selectivity = mcf[3]
+ = 0.003
+</programlisting>
+
+ The estimated number of rows is just the product of this with the
+ cardinality of <classname>tenk1</classname> as before:
+
+<programlisting>
+rows = 10000 * 0.003
+ = 30
+</programlisting>
+
+ The number displayed by <command>EXPLAIN</command> is one more than this,
+ due to some post estimation checks.
+ </para>
+
+ <para>
+ Now consider the same query, but with a constant that is not in the
+ <acronym>MCV</acronym> list:
+
+<programlisting>
+EXPLAIN SELECT * FROM tenk1 WHERE stringu1 = 'xxx';
+
+ QUERY PLAN
+----------------------------------------------------------
+ Seq Scan on tenk1 (cost=0.00..470.00 rows=15 width=244)
+ Filter: (stringu1 = 'xxx'::name)
+</programlisting>
+
+ This is quite a different problem, how to estimate the selectivity when the
+ value is <emphasis>not</emphasis> in the <acronym>MCV</acronym> list.
+ The approach is to use the fact that the value is not in the list,
+ combined with the knowledge of the frequencies for all of the
+ <acronym>MCV</acronym>s:
+
+<programlisting>
+selectivity = (1 - sum(mvf))/(num_distinct - num_mcv)
+ = (1 - (0.00333333 + 0.00333333 + 0.003 + 0.003 + 0.003
+ + 0.003 + 0.003 + 0.003 + 0.00266667 + 0.00266667))/(672 - 10)
+ = 0.001465
+</programlisting>
+
+ That is, add up all the frequencies for the <acronym>MCV</acronym>s and
+ subtract them from one — because it is <emphasis>not</emphasis> one
+ of these, and divide by the <emphasis>remaining</emphasis> distinct values.
+ Notice that there are no null values so we don't have to worry about those.
+ The estimated number of rows is calculated as usual:
+
+<programlisting>
+rows = 10000 * 0.001465
+ = 15
+</programlisting>
+
+ </para>
+
+ <para>
+ Let's increase the complexity to consider a case with more than one
+ condition in the <literal>WHERE</literal> clause:
+
+<programlisting>
+EXPLAIN SELECT * FROM tenk1 WHERE unique1 < 1000 AND stringu1 = 'xxx';
+
+ QUERY PLAN
+-----------------------------------------------------------
+ Seq Scan on tenk1 (cost=0.00..495.00 rows=2 width=244)
+ Filter: ((unique1 < 1000) AND (stringu1 = 'xxx'::name))
+</programlisting>
+
+ An assumption of independence is made and the selectivities of the
+ individual restrictions are multiplied together:
+
+<programlisting>
+selectivity = selectivity(unique1 < 1000) * selectivity(stringu1 = 'xxx')
+ = 0.1031 * 0.001465
+ = 0.00015104
+</programlisting>
+
+ The row estimates are calculated as before:
+
+<programlisting>
+rows = 10000 * 0.00015104
+ = 2
+</programlisting>
+ </para>
+
+ <para>
+ Finally we will examine a query that includes a <literal>JOIN</literal>
+ together with a <literal>WHERE</literal> clause:
+
+<programlisting>
+EXPLAIN SELECT * FROM tenk1 t1, tenk2 t2
+WHERE t1.unique1 < 50 AND t1.unique2 = t2.unique2;
+
+ QUERY PLAN
+-----------------------------------------------------------------------------------------
+ Nested Loop (cost=0.00..346.90 rows=51 width=488)
+ -> Index Scan using tenk1_unique1 on tenk1 t1 (cost=0.00..192.57 rows=51 width=244)
+ Index Cond: (unique1 < 50)
+ -> Index Scan using tenk2_unique2 on tenk2 t2 (cost=0.00..3.01 rows=1 width=244)
+ Index Cond: ("outer".unique2 = t2.unique2)
+</programlisting>
+
+ The restriction on <classname>tenk1</classname>
+ <quote>unique1 < 50</quote> is evaluated before the nested-loop join.
+ This is handled analogously to the previous range example. The restriction
+ operator for <literal><</literal> is <function>scalarlteqsel</function>
+ as before, but this time the value 50 is in the first bucket of the
+ <structfield>unique1</structfield> histogram:
+
+<programlisting>
+selectivity = (0 + (50 - bckt[1].min)/(bckt[1].max - bckt[1].min))/num_bckts
+ = (0 + (50 - 1)/(970 - 1))/10
+ = 0.005057
+
+rows = 10000 * 0.005057
+ = 51
+</programlisting>
+
+ The restriction for the join is:
+
+<programlisting>
+t2.unique2 = t1.unique2
+</programlisting>
+
+ This is due to the join method being nested-loop, with
+ <classname>tenk1</classname> being in the outer loop. The operator is just
+ our familiar <literal>=<literal>, however the restriction function is
+ obtained from the <structfield>oprjoin</structfield> column of
+ <classname>pg_operator</classname> - and is <function>eqjoinsel</function>.
+ Additionally we use the statistical information for both
+ <classname>tenk2</classname> and <classname>tenk1</classname>:
+
+<programlisting>
+SELECT tablename, null_frac,n_distinct, most_common_vals FROM pg_stats
+WHERE tablename IN ('tenk1', 'tenk2') AND attname='unique2';
+
+tablename | null_frac | n_distinct | most_common_vals
+-----------+-----------+------------+------------------
+ tenk1 | 0 | -1 |
+ tenk2 | 0 | -1 |
+</programlisting>
+
+ In this case there is no <acronym>MCV</acronym> information for
+ <structfield>unique2</structfield> because all the values appear to be
+ unique, so we can use an algorithm that relies only on the number of
+ distinct values for both relations together with their null fractions:
+
+<programlisting>
+selectivity = (1 - null_frac1) * (1 - null_frac2) * min(1/num_distinct1, 1/num_distinct2)
+ = (1 - 0) * (1 - 0) * min(1/10000, 1/1000)
+ = 0.0001
+</programlisting>
+
+ This is, subtract the null fraction from one for each of the relations,
+ and divide by the maximum of the two distinct values. The number of rows
+ that the join is likely to emit is calculated as the cardinality of
+ cartesian product of the two nodes in the nested-loop, multiplied by the
+ selectivity:
+
+<programlisting>
+rows = (outer_cardinality * inner_cardinality) * selectivity
+ = (51 * 10000) * 0.0001
+ = 51
+</programlisting>
+ </para>
+
+ <para>
+ For those interested in further details, estimation of the number of rows in
+ a relation is covered in
+ <filename>src/backend/optimizer/util/plancat.c</filename>. The calculation
+ logic for clause selectivities is in
+ <filename>src/backend/optimizer/path/clausesel.c</filename>. The actual
+ implementations of the operator and join restriction functions can be found
+ in <filename>src/backend/utils/adt/selfuncs.c</filename>.
+ </para>
+
+ </sect1>
+
+
+</chapter>
+
+<!-- Keep this comment at the end of the file
+Local variables:
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+sgml-local-catalogs:("/usr/lib/sgml/catalog")
+sgml-local-ecat-files:nil
+End:
+-->
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